Finite Group Databasebeta

← #13524865

Subgroups — #13524865

Order 1792.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C7×C22⋊Q8C211yesmaximal, characteristic
2#11740227C211yesmaximal, characteristic
3#11740213C211yesmaximal, characteristic
4#11739912C211yesmaximal, characteristic, complemented
5#11739896C211yesmaximal, characteristic, complemented
6C4×#6487C211yesmaximal, characteristic
7C4×#6489C211yesmaximal, characteristic
8#11733995C211yesmaximal, characteristic, complemented
9#11733972C211yesmaximal, characteristic, complemented
10#11733527C211yesmaximal, characteristic, complemented
11#11733462C211yesmaximal, characteristic, complemented
12#11732543C211yesmaximal, characteristic, complemented
13#11732540C211yesmaximal, characteristic, complemented
14#11732485C211yesmaximal, characteristic, complemented
15#11732440C211yesmaximal, characteristic, complemented
16#11731925C211yesmaximal, characteristic
17#11731919C211yesmaximal, characteristic
18#11731913C211yesmaximal, characteristic
19#11731878C211yesmaximal, characteristic
20#11731391C211yesmaximal, characteristic
21#11731375C211yesmaximal, characteristic
22#11731114C211yesmaximal, characteristic, complemented
23C4×#6452C211yesmaximal, characteristic, complemented
24C4×#6452C211yesmaximal, characteristic, complemented
25#11731064C211yesmaximal, characteristic, complemented
26#11731064C211yesmaximal, characteristic, complemented
27C4×#6450C211yesmaximal, characteristic, complemented
28#11730925C211yesmaximal, characteristic
29#11730925C211yesmaximal, characteristic
30#11730885C211yesmaximal, characteristic
31#11730885C211yesmaximal, characteristic
32C2×C7×C22⋊Q8C2211yescharacteristic
33C2×C4×C7×Q8C2211yescharacteristic
34C22×C42×C7C2211yescharacteristic
35C2×#6489C2211yescharacteristic
36C2×#6489C2211yescharacteristic
37C2×#6487C2211yescharacteristic
38C2×#6452C2211yescharacteristic
39C2×#6452C2211yescharacteristic
40C2×#6450C2211yescharacteristic
41C2×#6450C2211yescharacteristic
42C2×C4×Dic14C2211yescharacteristic
43C2×C4×Dic14C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C7×#391C2211yescharacteristic
46C7×#389C2211yescharacteristic
47C7×#387C2211yescharacteristic
48C7×#387C2211yescharacteristic
49C7×#385C2211yescharacteristic
50C7×#385C2211yescharacteristic
51C7×#380C2211yescharacteristic
52C4×C7×C4⋊C4C2211yescharacteristic
53C4×C7×C4⋊C4C2211yescharacteristic
54C4×C7×C4⋊C4C2211yescharacteristic
55C4×C7×C22⋊C4C2211yescharacteristic
56C4×C7×C22⋊C4C2211yescharacteristic
57#90002C2211yescharacteristic
58#90002C2211yescharacteristic
59#90001C2211yescharacteristic
60#90001C2211yescharacteristic
61#89984C2211yescharacteristic
62#89982C2211yescharacteristic
63#89982C2211yescharacteristic
64C4×C22⋊Dic7C2211yescharacteristic
65C4×C22⋊Dic7C2211yescharacteristic
66C4×C22⋊Dic7C2211yescharacteristic
67C4×C22⋊Dic7C2211yescharacteristic
68C4×C22⋊Dic7C2211yescharacteristic
69C4×C22⋊Dic7C2211yescharacteristic
70#89757C2211yescharacteristic
71#89757C2211yescharacteristic
72#89756C2211yescharacteristic
73#89756C2211yescharacteristic
74#89755C2211yescharacteristic
75#89755C2211yescharacteristic
76#89753C2211yescharacteristic
77#89753C2211yescharacteristic
78#89753C2211yescharacteristic
79#89753C2211yescharacteristic
80#89753C2211yescharacteristic
81#89753C2211yescharacteristic
82#89752C2211yescharacteristic
83#89752C2211yescharacteristic
84#89751C2211yescharacteristic
85#89751C2211yescharacteristic
86#89751C2211yescharacteristic
87#89751C2211yescharacteristic
88#89750C2211yescharacteristic
89#89750C2211yescharacteristic
90#89750C2211yescharacteristic
91#89750C2211yescharacteristic
92#89750C2211yescharacteristic
93#89750C2211yescharacteristic
94C4⋊C4×Dic7C2211yescharacteristic
95C4⋊C4×Dic7C2211yescharacteristic
96#89744C2211yescharacteristic
97#89744C2211yescharacteristic
98#89744C2211yescharacteristic
99#89744C2211yescharacteristic
100#89744C2211yescharacteristic
101#89744C2211yescharacteristic
102#89721C2211yescharacteristic
103#89721C2211yescharacteristic
104#89720C2211yescharacteristic
105#89720C2211yescharacteristic
106#89720C2211yescharacteristic
107#89720C2211yescharacteristic
108#89719C2211yescharacteristic
109#89719C2211yescharacteristic
110#89717C2211yescharacteristic
111#89717C2211yescharacteristic
112#89717C2211yescharacteristic
113#89717C2211yescharacteristic
114#89716C2211yescharacteristic
115#89716C2211yescharacteristic
116#89716C2211yescharacteristic
117#89716C2211yescharacteristic
118C4×C4⋊Dic7C2211yescharacteristic
119C4×C4⋊Dic7C2211yescharacteristic
120C4×C4⋊Dic7C2211yescharacteristic
121C4×C4⋊Dic7C2211yescharacteristic
122C4×C4⋊Dic7C2211yescharacteristic
123C4×C4⋊Dic7C2211yescharacteristic
124C4×C4⋊Dic7C2211yescharacteristic
125#89705C2211yescharacteristic
126#89705C2211yescharacteristic
127#89704C2211yescharacteristic
128#89704C2211yescharacteristic
129#89704C2211yescharacteristic
130#89704C2211yescharacteristic
131C4×Dic7⋊C4C2211yescharacteristic
132C4×Dic7⋊C4C2211yescharacteristic
133C4×Dic7⋊C4C2211yescharacteristic
134C4×Dic7⋊C4C2211yescharacteristic
135C4×Dic7⋊C4C2211yescharacteristic
136C4×Dic7⋊C4C2211yescharacteristic
137C4×Dic7⋊C4C2211yescharacteristic
138C4×Dic7⋊C4C2211yescharacteristic
139C4×Dic7⋊C4C2211yescharacteristic
140C4×Dic7⋊C4C2211yescharacteristic
141C42×Dic7C2211yescharacteristic
142C42×Dic7C2211yescharacteristic
143C42×Dic7C2211yescharacteristic
144C42×Dic7C2211yescharacteristic
145#89701C2211yescharacteristic
146#89700C2211yescharacteristic
147#89433C2211yescharacteristic
148#89433C2211yescharacteristic
149#89432C2211yescharacteristic
150#89432C2211yescharacteristic
151#89429C2211yescharacteristic
152#89429C2211yescharacteristic
153#89429C2211yescharacteristic
154#89429C2211yescharacteristic
155#89428C2211yescharacteristic
156#89428C2211yescharacteristic
157#89428C2211yescharacteristic
158#89428C2211yescharacteristic
159#89426C2211yescharacteristic
160#89426C2211yescharacteristic
161#89426C2211yescharacteristic
162#89426C2211yescharacteristic
163#89425C2211yescharacteristic
164#89425C2211yescharacteristic
165#89425C2211yescharacteristic
166#89425C2211yescharacteristic
167#89425C2211yescharacteristic
168#89425C2211yescharacteristic
169#89425C2211yescharacteristic
170#89425C2211yescharacteristic
171#89425C2211yescharacteristic
172#89425C2211yescharacteristic
173#89424C2211yescharacteristic
174#89424C2211yescharacteristic
175#89422C2211yescharacteristic
176#89422C2211yescharacteristic
177#89421C2211yescharacteristic
178#89421C2211yescharacteristic
179#89421C2211yescharacteristic
180#89421C2211yescharacteristic
181#89419C2211yescharacteristic
182#89419C2211yescharacteristic
183#89418C2211yescharacteristic
184#89418C2211yescharacteristic
185#89418C2211yescharacteristic
186#89418C2211yescharacteristic
187#34882—71nomaximal, Sylow
188C22×C7×Q8C2311yescharacteristic
189C23×C4×C7C2311yescharacteristic
190C23×C4×C7C2311yescharacteristic
191C23×C4×C7C2311yescharacteristic
192C22×Dic14C2311yescharacteristic
193C22×Dic14C2311yescharacteristic
194C22×Dic14C2311yescharacteristic
195C7×C22⋊Q8—24no—
196C4×C7×Q8—24no—
197C2×C7×C4⋊C4C2311yescharacteristic
198C2×C7×C4⋊C4C2311yescharacteristic
199C2×C7×C4⋊C4C2311yescharacteristic
200C2×C7×C4⋊C4C2311yescharacteristic
201C2×C7×C4⋊C4C2311yescharacteristic
202C2×C7×C4⋊C4C2311yescharacteristic
203C2×C7×C4⋊C4C2311yescharacteristic
204C2×C7×C4⋊C4C2311yescharacteristic
205C2×C7×C4⋊C4C2311yescharacteristic
206C2×C7×C22⋊C4C2311yescharacteristic
207C2×C7×C22⋊C4C2311yescharacteristic
208C2×C7×C22⋊C4C2311yescharacteristic
209C2×C7×C22⋊C4C2311yescharacteristic
210C2×C42×C7—24no—
211C2×C42×C7C2311yescharacteristic
212C2×C42×C7C2311yescharacteristic
213C2×C42×C7C2311yescharacteristic
214C2×C42×C7C2311yescharacteristic
215C2×C42×C7C2311yescharacteristic
216C2×C42×C7C2311yescharacteristic
217C2×C42×C7C2311yescharacteristic
218C2×C42×C7C2311yescharacteristic
219C2×C22⋊Dic7C2311yescharacteristic
220C2×C22⋊Dic7C2311yescharacteristic
221C2×C22⋊Dic7C2311yescharacteristic
222C2×C22⋊Dic7C2311yescharacteristic
223C2×C22⋊Dic7C2311yescharacteristic
224C2×C22⋊Dic7C2311yescharacteristic
225C2×C22⋊Dic7C2311yescharacteristic
226C2×C22⋊Dic7C2311yescharacteristic
227#6489—24no—
228#6489Q818yescomplemented
229C2×C4⋊Dic7C2311yescharacteristic
230C2×C4⋊Dic7C2311yescharacteristic
231C2×C4⋊Dic7C2311yescharacteristic
232C2×C4⋊Dic7C2311yescharacteristic
233C2×C4⋊Dic7C2311yescharacteristic
234C2×C4⋊Dic7C2311yescharacteristic
235C2×C4⋊Dic7C2311yescharacteristic
236C2×C4⋊Dic7C2311yescharacteristic
237C2×C4⋊Dic7C2311yescharacteristic
238C2×C4⋊Dic7C2311yescharacteristic
239C2×C4⋊Dic7C2311yescharacteristic
240C2×C4⋊Dic7C2311yescharacteristic
241C2×C4⋊Dic7C2311yescharacteristic
242#6487—24no—
243C2×Dic7⋊C4C2311yescharacteristic
244C2×Dic7⋊C4C2311yescharacteristic
245C2×Dic7⋊C4C2311yescharacteristic
246C2×Dic7⋊C4C2311yescharacteristic
247C2×Dic7⋊C4C2311yescharacteristic
248C2×Dic7⋊C4C2311yescharacteristic
249C2×Dic7⋊C4C2311yescharacteristic
250C2×Dic7⋊C4C2311yescharacteristic
251C2×Dic7⋊C4C2311yescharacteristic
252C2×Dic7⋊C4C2311yescharacteristic
253C2×Dic7⋊C4C2311yescharacteristic
254C2×Dic7⋊C4C2311yescharacteristic
255C2×Dic7⋊C4C2311yescharacteristic
256C2×Dic7⋊C4C2311yescharacteristic
257C2×Dic7⋊C4C2311yescharacteristic
258C2×Dic7⋊C4C2311yescharacteristic
259C2×Dic7⋊C4C2311yescharacteristic
260C2×Dic7⋊C4C2311yescharacteristic
261C2×Dic7⋊C4C2311yescharacteristic
262C2×Dic7⋊C4C2311yescharacteristic
263C2×Dic7⋊C4C2311yescharacteristic
264C2×Dic7⋊C4C2311yescharacteristic
265C2×Dic7⋊C4C2311yescharacteristic
266C2×Dic7⋊C4C2311yescharacteristic
267C2×Dic7⋊C4C2311yescharacteristic
268C2×Dic7⋊C4C2311yescharacteristic
269C2×C4×Dic7C2311yescharacteristic
270C2×C4×Dic7C2311yescharacteristic
271C2×C4×Dic7C2311yescharacteristic
272C2×C4×Dic7C2311yescharacteristic
273C2×C4×Dic7C2311yescharacteristic
274C2×C4×Dic7C2311yescharacteristic
275C2×C4×Dic7C2311yescharacteristic
276C2×C4×Dic7C2311yescharacteristic
277C2×C4×Dic7C2311yescharacteristic
278C2×C4×Dic7C2311yescharacteristic
279C2×C4×Dic7C2311yescharacteristic
280C2×C4×Dic7C2311yescharacteristic
281C2×C4×Dic7C2311yescharacteristic
282C2×C4×Dic7C2311yescharacteristic
283C2×C4×Dic7C2311yescharacteristic
284C2×C4×Dic7C2311yescharacteristic
285C2×C4×Dic7C2311yescharacteristic
286C2×C4×Dic7C2311yescharacteristic
287C2×C4×Dic7C2311yescharacteristic
288C2×C4×Dic7C2311yescharacteristic
289C2×C4×Dic7C2311yescharacteristic
290C2×C4×Dic7C2311yescharacteristic
291C2×C4×Dic7C2311yescharacteristic
292C2×C4×Dic7C2311yescharacteristic
293#6452—24no—
294#6452—24no—
295#6450—24no—
296#6450—24no—
297C4×Dic14—24no—
298C4×Dic14—24no—
299C4×Dic14—24no—
300C7×#95C2311yescharacteristic
301C7×#95C2311yescharacteristic
302C7×#95C2311yescharacteristic
303C7×#95C2311yescharacteristic
304C7×#95C2311yescharacteristic
305C7×#95C2311yescharacteristic
306C7×#95C2311yescharacteristic
307C7×#95C2311yescharacteristic
308C7×#95C2311yescharacteristic
309C7×#95C2311yescharacteristic
310C7⋊#95C2311yescharacteristic
311C7⋊#95C2311yescharacteristic
312C7⋊#95C2311yescharacteristic
313C7⋊#95C2311yescharacteristic
314C7⋊#95C2311yescharacteristic
315C7⋊#95C2311yescharacteristic
316C7⋊#95C2311yescharacteristic
317C7⋊#95C2311yescharacteristic
318C7⋊#95C2311yescharacteristic
319C7⋊#95C2311yescharacteristic
320C7⋊#95C2311yescharacteristic
321C7⋊#95C2311yescharacteristic
322C7⋊#95C2311yescharacteristic
323C7⋊#95C2311yescharacteristic
324C7⋊#95C2311yescharacteristic
325C7⋊#95C2311yescharacteristic
326C7⋊#95C2311yescharacteristic
327C7⋊#95C2311yescharacteristic
328C7⋊#95C2311yescharacteristic
329C7⋊#95C2311yescharacteristic
330C7⋊#95C2311yescharacteristic
331C7⋊#95C2311yescharacteristic
332C7⋊#95C2311yescharacteristic
333C7⋊#95C2311yescharacteristic
334C7⋊#95C2311yescharacteristic
335C7⋊#95C2311yescharacteristic
336C7⋊#95C2311yescharacteristic
337C7⋊#95C2311yescharacteristic
338C7⋊#95C2311yescharacteristic
339C7⋊#95C2311yescharacteristic
340C7⋊#95C2311yescharacteristic
341C7⋊#95C2311yescharacteristic
342C7⋊#95C2311yescharacteristic
343C7⋊#95C2311yescharacteristic
344C7⋊#95C2311yescharacteristic
345C7⋊#95C2311yescharacteristic
346C7⋊#95C2311yescharacteristic
347C7⋊#95C2311yescharacteristic
348C7⋊#95C2311yescharacteristic
349C7⋊#95C2311yescharacteristic
350C7⋊#95C2311yescharacteristic
351C7⋊#95C2311yescharacteristic
352C7⋊#95C2311yescharacteristic
353C7⋊#95C2311yescharacteristic
354C7⋊#95C2311yescharacteristic
355C7⋊#95C2311yescharacteristic
356#2586—71no—
357#2586—71no—
358#2585—71no—
359#2585—71no—
360#2574—71no—
361#2574—71no—
362#2556—71no—
363#2556—71no—
364#2522—71no—
365#2522—71no—
366#2520—71no—
367#2520—71no—
368#2465—71no—
369#2465—71no—
370#2462—71no—
371#2462—71no—
372#2399—71no—
373#2399—71no—
374#2396—71no—
375#2396—71no—
376C4×#125—71no—
377C4×#125—71no—
378C4×C22⋊Q8—71no—
379C4×C22⋊Q8D711yescharacteristic
380#2298—71no—
381#2298—71no—
382#2295—71no—
383#2295—71no—
384#2295—71no—
385C42×Q8—71no—
386C4×#117—71no—
387C24×C7C2411yescharacteristic
388C2×C7×Q8—22no—
389C2×C7×Q8—22no—
390C2×C7×Q8—41no—
391C22×C4×C7—22no—
392C22×C4×C7—22no—
393C22×C4×C7—22no—
394C22×C4×C7—22no—
395C22×C4×C7—22no—
396C22×C4×C7—22no—
397C22×C4×C7—41no—
398C22×C4×C7—41no—
399C22×C4×C7C2×Q814yes—
400C22×C4×C7C2411yescharacteristic
401C22×C4×C7C2411yescharacteristic
402C22×C4×C7C2411yescharacteristic
403C22×C4×C7C2411yescharacteristic
404C22×C4×C7C2411yescharacteristic
405C22×C4×C7C2411yescharacteristic
406C22×C4×C7C2411yescharacteristic
407C22×C4×C7C2411yescharacteristic
408C22×C4×C7C2411yescharacteristic
409C22×C4×C7C2411yescharacteristic
410C22×C4×C7C2411yescharacteristic
411C22×C4×C7C2411yescharacteristic
412C22×C4×C7C2411yescharacteristic
413C22×C4×C7C2411yescharacteristic
414C22×Dic7C2411yescharacteristic
415C22×Dic7C2411yescharacteristic
416C22×Dic7C2411yescharacteristic
417C22×Dic7C2411yescharacteristic
418C22×Dic7C2411yescharacteristic
419C22×Dic7C2411yescharacteristic
420C22×Dic7C2411yescharacteristic
421C22×Dic7C2411yescharacteristic
422C22×Dic7C2411yescharacteristic
423C22×Dic7C2411yescharacteristic
424C22×Dic7C2411yescharacteristic
425C22×Dic7C2411yescharacteristic
426C22×Dic7C2411yescharacteristic
427C22×Dic7C2411yescharacteristic
428C22×Dic7C2411yescharacteristic
429C22×Dic7C2411yescharacteristic
430C2×Dic14—22no—
431C2×Dic14—22no—
432C2×Dic14—22no—
433C2×Dic14—22no—
434C2×Dic14—22no—
435C2×Dic14—22no—
436C2×Dic14—41no—
437C2×Dic14—41no—
438C2×Dic14—41no—
439C7×C4⋊C4—22no—
440C7×C4⋊C4—22no—
441C7×C4⋊C4—22no—
442C7×C4⋊C4—22no—
443C7×C4⋊C4—22no—
444C7×C4⋊C4—22no—
445C7×C4⋊C4—22no—
446C7×C4⋊C4—41no—
447C7×C4⋊C4#4114yes—
448C7×C22⋊C4—22no—
449C7×C22⋊C4—22no—
450C7×C22⋊C4—41no—
451C7×C22⋊C4—41no—
452C42×C7—22no—
453C42×C7—22no—
454C42×C7—22no—
455C42×C7—22no—
456C42×C7—22no—
457C42×C7—22no—
458C42×C7—22no—
459C42×C7#4114yes—
460C22⋊Dic7—22no—
461C22⋊Dic7—22no—
462C22⋊Dic7—22no—
463C22⋊Dic7—22no—
464C22⋊Dic7—41no—
465C22⋊Dic7—41no—
466C22⋊Dic7C2×Q814yes—
467C22⋊Dic7C2×Q814yes—
468C4⋊Dic7—22no—
469C4⋊Dic7—22no—
470C4⋊Dic7—22no—
471C4⋊Dic7—22no—
472C4⋊Dic7—22no—
473C4⋊Dic7—22no—
474C4⋊Dic7—22no—
475C4⋊Dic7—22no—
476C4⋊Dic7—41no—
477C4⋊Dic7—41no—
478C4⋊Dic7—41no—
479C4⋊Dic7C2×Q814yes—
480C4⋊Dic7C2×Q814yes—
481Dic7⋊C4—22no—
482Dic7⋊C4—22no—
483Dic7⋊C4—22no—
484Dic7⋊C4—22no—
485Dic7⋊C4—22no—
486Dic7⋊C4—22no—
487Dic7⋊C4—22no—
488Dic7⋊C4—22no—
489Dic7⋊C4—22no—
490Dic7⋊C4—22no—
491Dic7⋊C4—22no—
492Dic7⋊C4—22no—
493Dic7⋊C4—22no—
494Dic7⋊C4—22no—
495Dic7⋊C4—22no—
496Dic7⋊C4—22no—
497Dic7⋊C4—22no—
498Dic7⋊C4—41no—
499Dic7⋊C4—41no—
500Dic7⋊C4—41no—
501Dic7⋊C4—41no—
502Dic7⋊C4—41no—
503Dic7⋊C4—41no—
504Dic7⋊C4—41no—
505Dic7⋊C4—41no—
506Dic7⋊C4#4114yes—
507C4×Dic7—22no—
508C4×Dic7—22no—
509C4×Dic7—22no—
510C4×Dic7—22no—
511C4×Dic7—22no—
512C4×Dic7—22no—
513C4×Dic7—22no—
514C4×Dic7—22no—
515C4×Dic7—22no—
516C4×Dic7—22no—
517C4×Dic7—22no—
518C4×Dic7—22no—
519C4×Dic7—22no—
520C4×Dic7—41no—
521C4×Dic7—41no—
522C4×Dic7—41no—
523C4×Dic7—41no—
524C4×Dic7—41no—
525C4×Dic7—41no—
526C4×Dic7—41no—
527C4×Dic7—41no—
528C4×Dic7C2×Q814yes—
529C4×Dic7C2×Q814yes—
530C4×Dic7#4114yes—
531C2×#125—71no—
532C2×#125—71no—
533C2×C22⋊Q8—71no—
534C2×C22⋊Q8C2×D711yescharacteristic
535C2×C4×Q8—71no—
536C2×C4×Q8—71no—
537C2×C4×Q8—71no—
538C2×C4×Q8—71no—
539C2×C4×Q8—71no—
540C2×C4×Q8C2×D711yescharacteristic
541C2×#117—71no—
542C2×#117—71no—
543C22×C42C2×D711yescharacteristic
544#400—71no—
545#400—71no—
546#399—71no—
547#399—71no—
548#398—71no—
549#398—71no—
550#398—71no—
551#398—71no—
552#398—71no—
553#398—71no—
554#398—71no—
555#398—71no—
556#398—71no—
557#398—71no—
558#398—71no—
559#398—71no—
560#396—71no—
561#396—71no—
562#396—71no—
563#396—71no—
564#395—71no—
565#395—71no—
566#395—71no—
567#395—71no—
568#395—71no—
569#395—71no—
570#395—71no—
571#395—71no—
572#395—71no—
573#395—71no—
574#393—71no—
575#393—71no—
576#391—71no—
577#391—71no—
578#391—71no—
579#391—71no—
580#391—71no—
581#391—71no—
582#391—71no—
583#391C2×D711yescharacteristic
584#389—71no—
585#389—71no—
586#389—71no—
587#389—71no—
588#389—71no—
589#389—71no—
590#389—71no—
591#389—71no—
592#389—71no—
593#389—71no—
594#389—71no—
595#389C2×D711yescharacteristic
596#388—71no—
597#388—71no—
598#388—71no—
599#388—71no—
600#388—71no—
601#388—71no—
602#388—71no—
603#388—71no—
604#387—71no—
605#387—71no—
606#387—71no—
607#387—71no—
608#387—71no—
609#387—71no—
610#387—71no—
611#387—71no—
612#387—71no—
613#387—71no—
614#387—71no—
615#387—71no—
616#387—71no—
617#387—71no—
618#387—71no—
619#387—71no—
620#387—71no—
621#387—71no—
622#387—71no—
623#387—71no—
624#387—71no—
625#387—71no—
626#387—71no—
627#387—71no—
628#387—71no—
629#387—71no—
630#387—71no—
631#387—71no—
632#387—71no—
633#387—71no—
634#387C2×D711yescharacteristic
635#387C2×D711yescharacteristic
636#385—71no—
637#385—71no—
638#385C2×D711yescharacteristic
639#385C2×D711yescharacteristic
640#382—71no—
641#382—71no—
642#380—71no—
643#380C2×D711yescharacteristic
644C4×C4⋊C4—71no—
645C4×C4⋊C4—71no—
646C4×C4⋊C4—71no—
647C4×C4⋊C4—71no—
648C4×C4⋊C4—71no—
649C4×C4⋊C4—71no—
650C4×C4⋊C4—71no—
651C4×C4⋊C4—71no—
652C4×C4⋊C4—71no—
653C4×C4⋊C4—71no—
654C4×C4⋊C4—71no—
655C4×C4⋊C4—71no—
656C4×C4⋊C4—71no—
657C4×C4⋊C4—71no—
658C4×C4⋊C4—71no—
659C4×C4⋊C4—71no—
660C4×C4⋊C4—71no—
661C4×C4⋊C4—71no—
662C4×C4⋊C4—71no—
663C4×C4⋊C4—71no—
664C4×C4⋊C4—71no—
665C4×C4⋊C4—71no—
666C4×C4⋊C4—71no—
667C4×C4⋊C4C2×D711yescharacteristic
668C4×C4⋊C4C2×D711yescharacteristic
669C4×C4⋊C4C2×D711yescharacteristic
670C4×C22⋊C4—71no—
671C4×C22⋊C4—71no—
672C4×C22⋊C4—71no—
673C4×C22⋊C4—71no—
674C4×C22⋊C4—71no—
675C4×C22⋊C4—71no—
676C4×C22⋊C4C2×D711yescharacteristic
677C4×C22⋊C4C2×D711yescharacteristic
678#376—71no—
679#376—71no—
680#376—71no—
681#376—71no—
682C43—71no—
683C43—71no—
684C43—71no—
685C43—71no—
686C23×C7—21no—
687C23×C7—21no—
688C23×C7—21no—
689C23×C7—21no—
690C23×C7—21no—
691C23×C7—21no—
692C23×C7C22×Q812yes—
693C23×C7C2511yescharacteristic
694C7×Q8—44no—
695C2×C4×C7—21no—
696C2×C4×C7—21no—
697C2×C4×C7—21no—
698C2×C4×C7—21no—
699C2×C4×C7—21no—
700C2×C4×C7—21no—
701C2×C4×C7—21no—
702C2×C4×C7—21no—
703C2×C4×C7—21no—
704C2×C4×C7—21no—
705C2×C4×C7—21no—
706C2×C4×C7—21no—
707C2×C4×C7—21no—
708C2×C4×C7—21no—
709C2×C4×C7—28no—
710C2×C4×C7—21no—
711C2×C4×C7—21no—
712C2×C4×C7—21no—
713C2×C4×C7—21no—
714C2×C4×C7—21no—
715C2×C4×C7—21no—
716C2×C4×C7—21no—
717C2×C4×C7—21no—
718C2×C4×C7—21no—
719C2×C4×C7—21no—
720C2×C4×C7—21no—
721C2×C4×C7—21no—
722C2×C4×C7—21no—
723C2×C4×C7—21no—
724C2×C4×C7—21no—
725C2×C4×C7—21no—
726C2×C4×C7—21no—
727C2×C4×C7—21no—
728C2×C4×C7—44no—
729C2×C4×C7—44no—
730C2×C4×C7C22×Q812yes—
731C2×C4×C7C22×Q812yes—
732C2×C4×C7C2×#4112yes—
733C2×C4×C7C2×#4112yes—
734C2×C4×C7C2×#4112yes—
735C2×C4×C7C2×#4112yes—
736C2×C4×C7C2×#4112yes—
737C2×C4×C7C2×#4112yes—
738C2×C4×C7C2×#4112yes—
739C2×C4×C7C2×#4112yes—
740C2×Dic7—21no—
741C2×Dic7—21no—
742C2×Dic7—21no—
743C2×Dic7—21no—
744C2×Dic7—21no—
745C2×Dic7—21no—
746C2×Dic7—21no—
747C2×Dic7—21no—
748C2×Dic7—21no—
749C2×Dic7—21no—
750C2×Dic7—21no—
751C2×Dic7—21no—
752C2×Dic7—21no—
753C2×Dic7—21no—
754C2×Dic7—21no—
755C2×Dic7—21no—
756C2×Dic7—21no—
757C2×Dic7—21no—
758C2×Dic7—21no—
759C2×Dic7—21no—
760C2×Dic7—21no—
761C2×Dic7—21no—
762C2×Dic7—21no—
763C2×Dic7—21no—
764C2×Dic7—21no—
765C2×Dic7—21no—
766C2×Dic7—21no—
767C2×Dic7—21no—
768C2×Dic7—21no—
769C2×Dic7—21no—
770C2×Dic7—21no—
771C2×Dic7—21no—
772C2×Dic7—21no—
773C2×Dic7—21no—
774C2×Dic7—21no—
775C2×Dic7—21no—
776C2×Dic7—21no—
777C2×Dic7—21no—
778C2×Dic7—21no—
779C2×Dic7—21no—
780C2×Dic7C22×Q812yes—
781C2×Dic7C22×Q812yes—
782C2×Dic7C22×Q812yes—
783C2×Dic7C22×Q812yes—
784C2×Dic7C2×#4112yes—
785C2×Dic7C2×#4112yes—
786C2×Dic7C2×#4112yes—
787C2×Dic7C2×#4112yes—
788Dic14—28no—
789Dic14—44no—
790Dic14—44no—
791C22×Q8—71no—
792C22×Q8—71no—
793C22×Q8—71no—
794C22×Q8C22×D711yescharacteristic
795C23×C4C22×D711yescharacteristic
796C23×C4C22×D711yescharacteristic
797C23×C4C22×D711yescharacteristic
798#125—144no—
799#125—144no—
800C22⋊Q8—24no—
801C22⋊Q8—144no—
802C4×Q8—24no—
803C4×Q8—144no—
804C4×Q8—144no—
805C4×Q8—144no—
806C4×Q8—144no—
807C4×Q8—144no—
808#117—78no—
809#117—144no—
810C2×C4⋊C4—71no—
811C2×C4⋊C4—71no—
812C2×C4⋊C4—71no—
813C2×C4⋊C4—71no—
814C2×C4⋊C4—71no—
815C2×C4⋊C4—71no—
816C2×C4⋊C4—71no—
817C2×C4⋊C4—71no—
818C2×C4⋊C4—71no—
819C2×C4⋊C4—71no—
820C2×C4⋊C4—71no—
821C2×C4⋊C4—71no—
822C2×C4⋊C4—71no—
823C2×C4⋊C4—71no—
824C2×C4⋊C4—71no—
825C2×C4⋊C4—71no—
826C2×C4⋊C4—71no—
827C2×C4⋊C4—71no—
828C2×C4⋊C4—71no—
829C2×C4⋊C4—71no—
830C2×C4⋊C4—71no—
831C2×C4⋊C4—71no—
832C2×C4⋊C4—71no—
833C2×C4⋊C4—71no—
834C2×C4⋊C4—71no—
835C2×C4⋊C4—71no—
836C2×C4⋊C4—71no—
837C2×C4⋊C4—71no—
838C2×C4⋊C4—71no—
839C2×C4⋊C4—71no—
840C2×C4⋊C4—71no—
841C2×C4⋊C4—71no—
842C2×C4⋊C4—71no—
843C2×C4⋊C4—71no—
844C2×C4⋊C4—71no—
845C2×C4⋊C4—71no—
846C2×C4⋊C4—71no—
847C2×C4⋊C4—71no—
848C2×C4⋊C4—71no—
849C2×C4⋊C4C22×D711yescharacteristic
850C2×C4⋊C4C22×D711yescharacteristic
851C2×C4⋊C4C22×D711yescharacteristic
852C2×C4⋊C4C22×D711yescharacteristic
853C2×C4⋊C4C22×D711yescharacteristic
854C2×C4⋊C4C22×D711yescharacteristic
855C2×C4⋊C4C22×D711yescharacteristic
856C2×C4⋊C4C22×D711yescharacteristic
857C2×C4⋊C4C22×D711yescharacteristic
858C2×C22⋊C4—71no—
859C2×C22⋊C4—71no—
860C2×C22⋊C4—71no—
861C2×C22⋊C4—71no—
862C2×C22⋊C4—71no—
863C2×C22⋊C4—71no—
864C2×C22⋊C4—71no—
865C2×C22⋊C4—71no—
866C2×C22⋊C4C22×D711yescharacteristic
867C2×C22⋊C4C22×D711yescharacteristic
868C2×C22⋊C4C22×D711yescharacteristic
869C2×C22⋊C4C22×D711yescharacteristic
870C2×C42—24no—
871C2×C42—71no—
872C2×C42—71no—
873C2×C42—71no—
874C2×C42—71no—
875C2×C42—71no—
876C2×C42—71no—
877C2×C42—71no—
878C2×C42—71no—
879C2×C42—71no—
880C2×C42—71no—
881C2×C42—71no—
882C2×C42—71no—
883C2×C42—71no—
884C2×C42—71no—
885C2×C42—71no—
886C2×C42—71no—
887C2×C42—71no—
888C2×C42—71no—
889C2×C42—71no—
890C2×C42—71no—
891C2×C42—71no—
892C2×C42—71no—
893C2×C42—71no—
894C2×C42—71no—
895C2×C42C22×D711yescharacteristic
896C2×C42C22×D711yescharacteristic
897C2×C42C22×D711yescharacteristic
898C2×C42C22×D711yescharacteristic
899C2×C42C22×D711yescharacteristic
900C2×C42C22×D711yescharacteristic
901C2×C42C22×D711yescharacteristic
902C2×C42C22×D711yescharacteristic
903#95—71no—
904#95—71no—
905#95—71no—
906#95—71no—
907#95—71no—
908#95—71no—
909#95—71no—
910#95—71no—
911#95—71no—
912#95—71no—
913#95—71no—
914#95—71no—
915#95—71no—
916#95—71no—
917#95—71no—
918#95—71no—
919#95—71no—
920#95—71no—
921#95—71no—
922#95—71no—
923#95—71no—
924#95—71no—
925#95—71no—
926#95—71no—
927#95—71no—
928#95—71no—
929#95—71no—
930#95—71no—
931#95—71no—
932#95—71no—
933#95—71no—
934#95—71no—
935#95—71no—
936#95—71no—
937#95—71no—
938#95—71no—
939#95—71no—
940#95—71no—
941#95—71no—
942#95—71no—
943#95—71no—
944#95—71no—
945#95—71no—
946#95—71no—
947#95—71no—
948#95—71no—
949#95C22×D711yescharacteristic
950#95C22×D711yescharacteristic
951#95C22×D711yescharacteristic
952#95C22×D711yescharacteristic
953#95C22×D711yescharacteristic
954#95C22×D711yescharacteristic
955#95C22×D711yescharacteristic
956#95C22×D711yescharacteristic
957#95C22×D711yescharacteristic
958#95C22×D711yescharacteristic
959C22×C7—22no—
960C22×C7—22no—
961C22×C7—22no—
962C22×C7—41no—
963C22×C7—41no—
964C22×C7—41no—
965C22×C7—41no—
966C22×C7C23×Q811yescharacteristic
967C22×C7C22×#4111yescharacteristic
968C22×C7C22×#4111yescharacteristic
969C22×C7C22×#4111yescharacteristic
970C22×C7C22×#4111yescharacteristic
971C22×C7#58511yescharacteristic
972C22×C7#58511yescharacteristic
973C4×C7—22no—
974C4×C7—22no—
975C4×C7—22no—
976C4×C7—22no—
977C4×C7—22no—
978C4×C7—22no—
979C4×C7—22no—
980C4×C7—41no—
981C4×C7—41no—
982C4×C7—41no—
983C4×C7—41no—
984C4×C7—41no—
985C4×C7—41no—
986C4×C7#53314yes—
987Dic7—22no—
988Dic7—22no—
989Dic7—22no—
990Dic7—22no—
991Dic7—22no—
992Dic7—22no—
993Dic7—22no—
994Dic7—22no—
995Dic7—41no—
996Dic7—41no—
997Dic7—41no—
998Dic7—41no—
999Dic7—41no—
1000Dic7—41no—
1001Dic7—41no—
1002Dic7—41no—
1003C24C23×D711yescharacteristic
1004C2×Q8—22no—
1005C2×Q8—22no—
1006C2×Q8—41no—
1007C2×Q8—142no—
1008C2×Q8—142no—
1009C2×Q8—142no—
1010C2×Q8—142no—
1011C2×Q8—142no—
1012C2×Q8—142no—
1013C2×Q8—281no—
1014C2×Q8—281no—
1015C2×Q8—281no—
1016C22×C4—22no—
1017C22×C4—22no—
1018C22×C4—22no—
1019C22×C4—22no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—41no—
1023C22×C4—41no—
1024C22×C4—71no—
1025C22×C4—71no—
1026C22×C4—71no—
1027C22×C4—71no—
1028C22×C4—71no—
1029C22×C4—71no—
1030C22×C4—71no—
1031C22×C4—71no—
1032C22×C4—71no—
1033C22×C4—71no—
1034C22×C4—71no—
1035C22×C4—71no—
1036C22×C4—71no—
1037C22×C4—71no—
1038C22×C4—71no—
1039C22×C4—71no—
1040C22×C4Q8×D714yes—
1041C22×C4C23×D711yescharacteristic
1042C22×C4C23×D711yescharacteristic
1043C22×C4C23×D711yescharacteristic
1044C22×C4C23×D711yescharacteristic
1045C22×C4C23×D711yescharacteristic
1046C22×C4C23×D711yescharacteristic
1047C22×C4C23×D711yescharacteristic
1048C22×C4C23×D711yescharacteristic
1049C22×C4C23×D711yescharacteristic
1050C22×C4C23×D711yescharacteristic
1051C22×C4C23×D711yescharacteristic
1052C22×C4C23×D711yescharacteristic
1053C22×C4C23×D711yescharacteristic
1054C22×C4C23×D711yescharacteristic
1055C4⋊C4—22no—
1056C4⋊C4—22no—
1057C4⋊C4—22no—
1058C4⋊C4—22no—
1059C4⋊C4—22no—
1060C4⋊C4—22no—
1061C4⋊C4—22no—
1062C4⋊C4—41no—
1063C4⋊C4—74no—
1064C4⋊C4—74no—
1065C4⋊C4—74no—
1066C4⋊C4—142no—
1067C4⋊C4—142no—
1068C4⋊C4—142no—
1069C4⋊C4—142no—
1070C4⋊C4—142no—
1071C4⋊C4—142no—
1072C4⋊C4—142no—
1073C4⋊C4—142no—
1074C4⋊C4—142no—
1075C4⋊C4—142no—
1076C4⋊C4—142no—
1077C4⋊C4—142no—
1078C4⋊C4—142no—
1079C4⋊C4—142no—
1080C4⋊C4—142no—
1081C4⋊C4—142no—
1082C4⋊C4—142no—
1083C4⋊C4—142no—
1084C4⋊C4—142no—
1085C4⋊C4—142no—
1086C4⋊C4—142no—
1087C4⋊C4—142no—
1088C4⋊C4—142no—
1089C4⋊C4—142no—
1090C4⋊C4—142no—
1091C4⋊C4—281no—
1092C4⋊C4—281no—
1093C4⋊C4—281no—
1094C4⋊C4—281no—
1095C4⋊C4—281no—
1096C4⋊C4—281no—
1097C4⋊C4—281no—
1098C4⋊C4—281no—
1099C4⋊C4—281no—
1100C4⋊C4—281no—
1101C4⋊C4—281no—
1102C4⋊C4#115714yes—
1103C22⋊C4—22no—
1104C22⋊C4—22no—
1105C22⋊C4—41no—
1106C22⋊C4—41no—
1107C22⋊C4—74no—
1108C22⋊C4—74no—
1109C22⋊C4—142no—
1110C22⋊C4—142no—
1111C22⋊C4—142no—
1112C22⋊C4—142no—
1113C22⋊C4—281no—
1114C22⋊C4—281no—
1115C42—22no—
1116C42—22no—
1117C42—22no—
1118C42—22no—
1119C42—22no—
1120C42—22no—
1121C42—22no—
1122C42—74no—
1123C42—74no—
1124C42—74no—
1125C42—142no—
1126C42—142no—
1127C42—142no—
1128C42—142no—
1129C42—142no—
1130C42—142no—
1131C42—142no—
1132C42—142no—
1133C42—142no—
1134C42—142no—
1135C42—142no—
1136C42—142no—
1137C42—142no—
1138C42—281no—
1139C42—281no—
1140C42—281no—
1141C42—281no—
1142C42—281no—
1143C42—281no—
1144C42—281no—
1145C42—281no—
1146C42#115914yes—
1147C2×C7—42no—
1148C2×C7C2×#53311yescharacteristic
1149C2×C7#344411yescharacteristic
1150C2×C7#345511yescharacteristic
1151C2×C7#347511yescharacteristic
1152C2×C7#347511yescharacteristic
1153C2×C7Q8×#4111yescharacteristic
1154C2×C7Q8×#4111yescharacteristic
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23C2×Q8×D712yes—
1162C23C24×D711yescharacteristic
1163Q8—44no—
1164Q8—148no—
1165Q8—284no—
1166Q8—284no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—28no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—44no—
1201C2×C4—44no—
1202C2×C4—72no—
1203C2×C4—72no—
1204C2×C4—72no—
1205C2×C4—72no—
1206C2×C4—72no—
1207C2×C4—72no—
1208C2×C4—72no—
1209C2×C4—72no—
1210C2×C4—141no—
1211C2×C4—141no—
1212C2×C4—141no—
1213C2×C4—141no—
1214C2×C4—141no—
1215C2×C4—141no—
1216C2×C4—141no—
1217C2×C4—141no—
1218C2×C4—141no—
1219C2×C4—141no—
1220C2×C4—141no—
1221C2×C4—141no—
1222C2×C4—141no—
1223C2×C4—141no—
1224C2×C4—141no—
1225C2×C4—141no—
1226C2×C4—141no—
1227C2×C4—141no—
1228C2×C4—141no—
1229C2×C4—141no—
1230C2×C4—141no—
1231C2×C4—141no—
1232C2×C4—141no—
1233C2×C4—141no—
1234C2×C4—141no—
1235C2×C4—141no—
1236C2×C4—141no—
1237C2×C4—141no—
1238C2×C4—141no—
1239C2×C4—141no—
1240C2×C4—141no—
1241C2×C4—141no—
1242C2×C4—141no—
1243C2×C4—141no—
1244C2×C4—141no—
1245C2×C4—141no—
1246C2×C4—141no—
1247C2×C4—141no—
1248C2×C4—141no—
1249C2×C4—141no—
1250C2×C4C2×#115712yes—
1251C2×C4C2×#115712yes—
1252C2×C4C2×#115712yes—
1253C2×C4C2×#115912yes—
1254C2×C4C2×#115912yes—
1255C2×C4C2×#115912yes—
1256C2×C4C2×Q8×D712yes—
1257C2×C4C2×Q8×D712yes—
1258C2×C4D7×#4112yes—
1259C2×C4D7×#4112yes—
1260C7#3488211yescharacteristic, complemented, Sylow
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22C22×#115711yescharacteristic
1269C22C22×#115911yescharacteristic
1270C22C22×Q8×D711yescharacteristic
1271C22C2×D7×#4111yescharacteristic
1272C22C2×D7×#4111yescharacteristic
1273C22#9061611yescharacteristic
1274C22#9061611yescharacteristic
1275C4—22no—
1276C4—22no—
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—142no—
1289C4—142no—
1290C4—142no—
1291C4—142no—
1292C4—142no—
1293C4—142no—
1294C4—142no—
1295C4—142no—
1296C4—281no—
1297C4—281no—
1298C4—281no—
1299C4—281no—
1300C4—281no—
1301C4—281no—
1302C4—281no—
1303C4—281no—
1304C4#9031314yes—
1305C2—42no—
1306C2#1174283211yescharacteristic
1307C2Q8×#115711yescharacteristic
1308C2#1174290411yescharacteristic
1309C2C2×#9031311yescharacteristic
1310C2#1174308911yescharacteristic
1311C2#1174321411yescharacteristic
1312C2#1174334511yescharacteristic
subgroupG/H
centerC22×C4C23×D7
commutator, socle, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC4×C7×C22⋊Q8C2
prime radicalC24×C7C24
hypercenterC4×C22⋊Q8D7
hypocenterC7#34882
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C4×C22⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #11739912C2semidirect
5. #11739896C2semidirect
8. #11733995C2semidirect
9. #11733972C2semidirect
10. #11733527C2semidirect
11. #11733462C2semidirect
12. #11732543C2semidirect
13. #11732540C2semidirect
14. #11732485C2semidirect
15. #11732440C2semidirect
22. #11731114C2semidirect
23. C4×#6452C2semidirect
24. C4×#6452C2semidirect
25. #11731064C2semidirect
26. #11731064C2semidirect
27. C4×#6450C2semidirect
228. #6489Q8semidirect
1260. C7#34882semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×C7×C22⋊Q82
#117402272
#117402132
#117399122
#117398962
C4×#64872
C4×#64892
#117339952
#117339722
#117335272
#117334622
#117325432
#117325402
#117324852
#117324402
#117319252
#117319192
#117319132
#117318782
#117313912
#117313752
#117311142
C4×#64522
#117310642
C4×#64502
#117309252
#117308852
#348827