Finite Group Databasebeta

← C2×#11740209 #13521276

Subgroups — C2×#11740209 #13521276

Order 1792.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×#6509C211yesmaximal, characteristic, complemented
3C23×Dic7⋊C4C211yesmaximal, characteristic, complemented
4C22×(C22⋊D7)⋊C4C211yesmaximal, characteristic
5C2×#90001C211yesmaximal, characteristic, complemented
6C2×#89985C211yesmaximal, characteristic
7#11740209C2116yesmaximal, direct product factor
8C2×#89764C211yesmaximal, characteristic, complemented
9C2×#89766C211yesmaximal, characteristic, complemented
10C2×#89761C211yesmaximal, characteristic, complemented
11C2×#89756C211yesmaximal, characteristic, complemented
12C2×#89745C211yesmaximal, characteristic, complemented
13C2×#89750C211yesmaximal, characteristic, complemented
14C2×#89730C211yesmaximal, characteristic
15C2×#89722C211yesmaximal, characteristic, complemented
16C2×#89718C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C23×C4×D7C2211yescharacteristic
23C2×C7×C22⋊Q8—28no—
24C2×C7×C22⋊Q8C2218yescomplemented
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C4⋊C4C2211yescharacteristic
27C22×C7×C4⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C2×#6509—28no—
32C2×#6509C2218yescomplemented
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×Dic7⋊C4—28no—
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×Dic7⋊C4C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C22×Dic7⋊C4C2211yescharacteristic
47C22×Dic7⋊C4C2211yescharacteristic
48C22×Dic7⋊C4C2218yescomplemented
49C22×C4×Dic7C2211yescharacteristic
50C2×(C22⋊D7)⋊C4—28no—
51C2×(C22⋊D7)⋊C4C2218yes—
52#90001C2218yescomplemented
53#89985C2218yes—
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61C2×C7⋊#95C2211yescharacteristic
62#89766C2218yescomplemented
63#89764C2218yescomplemented
64#89761C2218yescomplemented
65#89756C2218yescomplemented
66#89750C2218yescomplemented
67#89745C2218yescomplemented
68#89730C2218yes—
69#89722C2218yescomplemented
70#89718C2218yescomplemented
71C2×#2449—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C24×D7C2311yescharacteristic
74C22×C7×Q8—24no—
75C22×C7×Q8—24no—
76C22×C7×Q8—42no—
77C22×C7×Q8C2314yes—
78C23×C4×C7—24no—
79C23×C4×C7—24no—
80C23×C4×C7—42no—
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2314yes—
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C22×C22⋊D7—24no—
89C22×C22⋊D7—24no—
90C22×C22⋊D7Q818yescomplemented
91C22×C22⋊D7C2314yes—
92C23×Dic7—24no—
93C23×Dic7—24no—
94C23×Dic7—24no—
95C23×Dic7—24no—
96C23×Dic7—24no—
97C23×Dic7—42no—
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2314yes—
102C23×Dic7C2314yes—
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2311yescharacteristic
105C23×Dic7C2311yescharacteristic
106C23×Dic7C2311yescharacteristic
107C22×C4×D7—24no—
108C22×C4×D7—24no—
109C22×C4×D7—42no—
110C22×C4×D7C2314yes—
111C7×C22⋊Q8—232no—
112C2×C7×C4⋊C4—24no—
113C2×C7×C4⋊C4—24no—
114C2×C7×C4⋊C4—24no—
115C2×C7×C4⋊C4C2314yes—
116C2×C7×C4⋊C4C2314yes—
117C2×C7×C4⋊C4C2314yes—
118C2×C7×C22⋊C4—24no—
119C2×C7×C22⋊C4D418yes—
120C2×C7×C22⋊C4C2314yes—
121C2×C7×C22⋊C4C2314yes—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7C2314yes—
124#6509—232no—
125C2×(C2×D7)⋊C4—24no—
126C2×(C2×D7)⋊C4—24no—
127C2×(C2×D7)⋊C4—24no—
128C2×(C2×D7)⋊C4—24no—
129C2×(C2×D7)⋊C4—42no—
130C2×(C2×D7)⋊C4C2314yes—
131C2×(C2×D7)⋊C4C2314yes—
132C2×(C2×D7)⋊C4C2314yes—
133C2×(C2×D7)⋊C4C2314yes—
134C2×(C2×D7)⋊C4C2314yes—
135C2×C4⋊Dic7—24no—
136C2×C4⋊Dic7—24no—
137C2×C4⋊Dic7C2314yes—
138C2×C4⋊Dic7C2314yes—
139C2×Dic7⋊C4—24no—
140C2×Dic7⋊C4—24no—
141C2×Dic7⋊C4—24no—
142C2×Dic7⋊C4—24no—
143C2×Dic7⋊C4—24no—
144C2×Dic7⋊C4—232no—
145C2×Dic7⋊C4—42no—
146C2×Dic7⋊C4D418yescomplemented
147C2×Dic7⋊C4C2314yes—
148C2×Dic7⋊C4C2314yes—
149C2×Dic7⋊C4C2314yes—
150C2×Dic7⋊C4C2314yes—
151C2×Dic7⋊C4C2314yes—
152C2×Dic7⋊C4C2314yes—
153C2×Dic7⋊C4C2314yes—
154C2×C4×Dic7—24no—
155C2×C4×Dic7C2314yes—
156(C22⋊D7)⋊C4—232no—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C7⋊#95C2314yes—
160C7⋊#95C2314yes—
161C7⋊#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C22×C22⋊Q8—71no—
166C22×C22⋊Q8D711yescharacteristic, complemented
167C22×C4×D4—71no—
168C23×C4⋊C4—71no—
169#2449—716no—
170C2×#399—71no—
171C2×#398—71no—
172C2×#396—71no—
173C2×#395—71no—
174C2×#389—71no—
175C2×#387—71no—
176C2×#386—71no—
177C2×#386—71no—
178C2×#385—71no—
179C2×#385—71no—
180C2×#385—71no—
181C24×C7—22no—
182C24×C7—22no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7C2×D414yes—
186C24×C7C2×Q814yes—
187C24×C7#4114yes—
188C24×C7C2412yes—
189C24×C7C2411yescharacteristic
190C23×D7—22no—
191C23×D7—22no—
192C23×D7—22no—
193C23×D7—22no—
194C23×D7—22no—
195C23×D7—22no—
196C23×D7C2×Q814yes—
197C23×D7C2412yes—
198C2×C7×Q8—28no—
199C2×C7×Q8—28no—
200C2×C7×Q8—44no—
201C2×C7×Q8—416no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—28no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—28no—
219C22×C4×C7—44no—
220C22×C4×C7—416no—
221C22×C4×C7C2×D414yes—
222C22×C4×C7C2×D414yes—
223C22×C4×C7C2×D414yes—
224C22×C4×C7C2412yes—
225C22×C4×C7C2412yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2412yes—
230C2×C22⋊D7—232no—
231C2×C22⋊D7—28no—
232C2×C22⋊D7—28no—
233C2×C22⋊D7C2×Q8116yescomplemented
234C22×Dic7—232no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—28no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—28no—
245C22×Dic7—28no—
246C22×Dic7—28no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—28no—
257C22×Dic7—44no—
258C22×Dic7—416no—
259C22×Dic7C2×D414yes—
260C22×Dic7C2×D414yes—
261C22×Dic7C2×Q814yes—
262C22×Dic7#4114yes—
263C22×Dic7C2412yes—
264C22×Dic7C2412yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C22×Dic7C2412yes—
269C22×Dic7C2412yes—
270C2×C4×D7—28no—
271C2×C4×D7—28no—
272C2×C4×D7—44no—
273C2×C4×D7—416no—
274C7×C4⋊C4—28no—
275C7×C4⋊C4—28no—
276C7×C4⋊C4—28no—
277C7×C22⋊C4—28no—
278C7×C22⋊C4C2×D4116yes—
279C22⋊Dic7—28no—
280(C2×D7)⋊C4—28no—
281(C2×D7)⋊C4—28no—
282(C2×D7)⋊C4—28no—
283(C2×D7)⋊C4—28no—
284(C2×D7)⋊C4—44no—
285C4⋊Dic7—28no—
286C4⋊Dic7—28no—
287Dic7⋊C4—28no—
288Dic7⋊C4—28no—
289Dic7⋊C4—28no—
290Dic7⋊C4—28no—
291Dic7⋊C4—28no—
292Dic7⋊C4—44no—
293Dic7⋊C4C2×D4116yescomplemented
294C4×Dic7—28no—
295C23×Q8C2×D711yescharacteristic
296C23×D4—71no—
297C24×C4—71no—
298C24×C4—71no—
299C24×C4—71no—
300C24×C4C2×D711yescharacteristic
301C2×C22⋊Q8—28no—
302C2×C22⋊Q8—78no—
303C2×C22⋊Q8—148no—
304C2×C22⋊Q8C2×D718yescomplemented
305C2×C4×D4—78no—
306C2×C4×D4—148no—
307C22×C4⋊C4—71no—
308C22×C4⋊C4—71no—
309C22×C4⋊C4—71no—
310C22×C4⋊C4—71no—
311C22×C4⋊C4—71no—
312C22×C4⋊C4—71no—
313C22×C4⋊C4—71no—
314C22×C4⋊C4—78no—
315C22×C4⋊C4—71no—
316C22×C4⋊C4—71no—
317C22×C4⋊C4—148no—
318C22×C4⋊C4C2×D711yescharacteristic
319C22×C4⋊C4C2×D711yescharacteristic
320C22×C4⋊C4C2×D711yescharacteristic
321C22×C22⋊C4—71no—
322C22×C22⋊C4—71no—
323C22×C22⋊C4—71no—
324C22×C22⋊C4—71no—
325C22×C22⋊C4—71no—
326C22×C22⋊C4—71no—
327C22×C22⋊C4C2×D711yescharacteristic
328C22×C22⋊C4C2×D711yescharacteristic
329C22×C42—71no—
330#399—78no—
331#398—78no—
332#396—78no—
333#395—78no—
334#389—78no—
335#387—78no—
336#386—78no—
337#386—78no—
338#385—78no—
339#385—78no—
340#385—78no—
341C2×#95—71no—
342C2×#95—71no—
343C2×#95—71no—
344C2×#95—71no—
345C2×#95—71no—
346C2×#95—71no—
347C2×#95—71no—
348C2×#95—71no—
349C23×C7—28no—
350C23×C7—28no—
351C23×C7—28no—
352C23×C7—28no—
353C23×C7—28no—
354C23×C7—28no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7C22⋊Q8116yescomplemented
360C23×C7C22×D412yes—
361C23×C7C22×D414yes—
362C23×C7C22×D412yes—
363C23×C7C22×Q814yes—
364C23×C7C22×Q812yes—
365C23×C7C2×#4114yes—
366C23×C7C2×#4112yes—
367C23×C7C2×#4112yes—
368C23×C7H(5,𝔽2)12yes—
369C23×C72−1+412yes—
370C23×C7C2511yescharacteristic
371C22×D7—28no—
372C22×D7—28no—
373C22×D7—28no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—44no—
381C22×D7—44no—
382C22×D7—44no—
383C22×D7—44no—
384C22×D7C22×Q814yes—
385C7×Q8—416no—
386C2×C4×C7—28no—
387C2×C4×C7—28no—
388C2×C4×C7—28no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—416no—
405C2×C4×C7—44no—
406C2×C4×C7—44no—
407C2×C4×C7—44no—
408C2×C4×C7C22×D414yes—
409C2×C4×C7C22×D414yes—
410C2×C4×C7C22×D414yes—
411C22⋊D7—232no—
412C2×Dic7—232no—
413C2×Dic7—28no—
414C2×Dic7—28no—
415C2×Dic7—28no—
416C2×Dic7—28no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—416no—
435C2×Dic7—44no—
436C2×Dic7—44no—
437C2×Dic7—44no—
438C2×Dic7C22×D414yes—
439C2×Dic7C22×D414yes—
440C2×Dic7C22×Q814yes—
441C2×Dic7C2×#4114yes—
442C4×D7—416no—
443C25—71no—
444C25C22×D711yescharacteristic
445C22×Q8—24no—
446C22×Q8—24no—
447C22×Q8—42no—
448C22×Q8C22×D714yes—
449C22×D4—78no—
450C22×D4—74no—
451C22×D4—144no—
452C22×D4—144no—
453C23×C4—24no—
454C23×C4—24no—
455C23×C4—42no—
456C23×C4—71no—
457C23×C4—71no—
458C23×C4—71no—
459C23×C4—71no—
460C23×C4—74no—
461C23×C4—71no—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4—74no—
465C23×C4—74no—
466C23×C4—144no—
467C23×C4—144no—
468C23×C4—144no—
469C23×C4—144no—
470C23×C4—144no—
471C23×C4—144no—
472C23×C4—144no—
473C23×C4—282no—
474C23×C4—282no—
475C23×C4C22×D711yescharacteristic
476C23×C4C22×D711yescharacteristic
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D714yes—
479C23×C4C22×D711yescharacteristic
480C23×C4C22×D711yescharacteristic
481C23×C4C22×D711yescharacteristic
482C22⋊Q8—232no—
483C22⋊Q8—1432no—
484C4×D4—1432no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—78no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—74no—
491C2×C4⋊C4—74no—
492C2×C4⋊C4—74no—
493C2×C4⋊C4—74no—
494C2×C4⋊C4—74no—
495C2×C4⋊C4—74no—
496C2×C4⋊C4—74no—
497C2×C4⋊C4—74no—
498C2×C4⋊C4—1432no—
499C2×C4⋊C4—144no—
500C2×C4⋊C4—144no—
501C2×C4⋊C4—144no—
502C2×C4⋊C4—144no—
503C2×C4⋊C4—144no—
504C2×C4⋊C4—144no—
505C2×C4⋊C4—144no—
506C2×C4⋊C4—282no—
507C2×C4⋊C4C22×D714yes—
508C2×C4⋊C4C22×D714yes—
509C2×C4⋊C4C22×D714yes—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—74no—
512C2×C22⋊C4—74no—
513C2×C22⋊C4—74no—
514C2×C22⋊C4—74no—
515C2×C22⋊C4—74no—
516C2×C22⋊C4—74no—
517C2×C22⋊C4—144no—
518C2×C22⋊C4—144no—
519C2×C22⋊C4—144no—
520C2×C22⋊C4—144no—
521C2×C22⋊C4—144no—
522C2×C22⋊C4—282no—
523C2×C22⋊C4C22⋊D718yes—
524C2×C22⋊C4C22×D714yes—
525C2×C22⋊C4C22×D714yes—
526C2×C42—74no—
527C2×C42—144no—
528#95—74no—
529#95—74no—
530#95—74no—
531#95—74no—
532#95—74no—
533#95—74no—
534#95—74no—
535#95—74no—
536C22×C7—24no—
537C22×C7—24no—
538C22×C7—24no—
539C22×C7—24no—
540C22×C7—24no—
541C22×C7—24no—
542C22×C7—232no—
543C22×C7C2×C22⋊Q814yes—
544C22×C7C2×C22⋊Q818yescomplemented
545C22×C7#52514yes—
546C22×C7#53914yes—
547C22×C7D4214yes—
548C22×C7#54714yes—
549C22×C7D4×Q814yes—
550C22×C7#55414yes—
551C22×C7C23×D411yescharacteristic
552C22×C7C23×D411yescharacteristic
553C22×C7C23×Q811yescharacteristic
554C22×C7C22×#4111yescharacteristic
555C22×C7C22×#4111yescharacteristic
556C22×C7C2×H(5,𝔽2)11yescharacteristic
557C22×C7C2×2−1+411yescharacteristic
558C2×D7—24no—
559C2×D7—24no—
560C2×D7—24no—
561C2×D7—42no—
562C2×D7—42no—
563C2×D7—42no—
564C2×D7—42no—
565C2×D7—416no—
566C4×C7—24no—
567C4×C7—24no—
568C4×C7—24no—
569C4×C7—42no—
570C4×C7—42no—
571C4×C7—42no—
572Dic7—24no—
573Dic7—24no—
574Dic7—24no—
575Dic7—24no—
576Dic7—42no—
577Dic7—42no—
578Dic7—42no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—74no—
584C24—72no—
585C24—142no—
586C24—142no—
587C24—142no—
588C24—142no—
589C24—142no—
590C24—142no—
591C24Q8×D714yes—
592C24#116114yes—
593C24C2×C22⋊D714yes—
594C24C23×D712yes—
595C24C23×D711yescharacteristic
596C2×Q8—28no—
597C2×Q8—28no—
598C2×Q8—44no—
599C2×Q8—416no—
600C2×D4—716no—
601C2×D4—1432no—
602C2×D4—148no—
603C2×D4—148no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—28no—
620C22×C4—28no—
621C22×C4—44no—
622C22×C4—416no—
623C22×C4—74no—
624C22×C4—74no—
625C22×C4—74no—
626C22×C4—74no—
627C22×C4—72no—
628C22×C4—72no—
629C22×C4—72no—
630C22×C4—72no—
631C22×C4—72no—
632C22×C4—72no—
633C22×C4—72no—
634C22×C4—148no—
635C22×C4—148no—
636C22×C4—148no—
637C22×C4—148no—
638C22×C4—1432no—
639C22×C4—142no—
640C22×C4—142no—
641C22×C4—148no—
642C22×C4—142no—
643C22×C4—142no—
644C22×C4—142no—
645C22×C4—142no—
646C22×C4—142no—
647C22×C4—142no—
648C22×C4—142no—
649C22×C4—142no—
650C22×C4—142no—
651C22×C4—142no—
652C22×C4—142no—
653C22×C4—142no—
654C22×C4—142no—
655C22×C4—142no—
656C22×C4—142no—
657C22×C4—148no—
658C22×C4—148no—
659C22×C4—284no—
660C22×C4—2816no—
661C22×C4—284no—
662C22×C4—2816no—
663C22×C4D4×D714yes—
664C22×C4C2×C22⋊D714yes—
665C22×C4C2×C22⋊D714yes—
666C22×C4C23×D712yes—
667C22×C4C23×D712yes—
668C22×C4C23×D712yes—
669C22×C4C23×D712yes—
670C22×C4C23×D712yes—
671C22×C4C23×D712yes—
672C4⋊C4—28no—
673C4⋊C4—28no—
674C4⋊C4—28no—
675C4⋊C4—716no—
676C4⋊C4—148no—
677C4⋊C4—148no—
678C4⋊C4—148no—
679C4⋊C4—148no—
680C4⋊C4—148no—
681C4⋊C4—148no—
682C4⋊C4—148no—
683C4⋊C4—284no—
684C22⋊C4—28no—
685C22⋊C4—148no—
686C22⋊C4—148no—
687C22⋊C4—148no—
688C22⋊C4—148no—
689C22⋊C4—148no—
690C22⋊C4—284no—
691C22⋊C4C2×C22⋊D7116yes—
692C42—148no—
693C2×C7—28no—
694C2×C7#244918yescomplemented
695C2×C7C22×C22⋊Q811yescharacteristic
696C2×C7C2×#52511yescharacteristic
697C2×C7C2×#53911yescharacteristic
698C2×C7C2×D4211yescharacteristic
699C2×C7C2×#54711yescharacteristic
700C2×C7C2×D4×Q811yescharacteristic
701C2×C7C2×#55411yescharacteristic
702D7—44no—
703C23—28no—
704C23—28no—
705C23—28no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—74no—
714C23—148no—
715C23—148no—
716C23—148no—
717C23—142no—
718C23—142no—
719C23—142no—
720C23—142no—
721C23—142no—
722C23—142no—
723C23—284no—
724C23—284no—
725C23—284no—
726C23—284no—
727C23#6509116yescomplemented
728C23C2×D4×D712yes—
729C23#654812yes—
730C23C2×Q8×D714yes—
731C23C2×Q8×D712yes—
732C23C2×#116114yes—
733C23C2×#116112yes—
734C23D7×#4112yes—
735C23#655412yes—
736C23C22×C22⋊D714yes—
737C23C22×C22⋊D712yes—
738C23C24×D711yescharacteristic
739Q8—416no—
740D4—1432no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—416no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—74no—
764C2×C4—74no—
765C2×C4—74no—
766C2×C4—74no—
767C2×C4—1432no—
768C2×C4—148no—
769C2×C4—148no—
770C2×C4—148no—
771C2×C4—148no—
772C2×C4—142no—
773C2×C4—142no—
774C2×C4—142no—
775C2×C4—142no—
776C2×C4—142no—
777C2×C4—142no—
778C2×C4—142no—
779C2×C4—142no—
780C2×C4—142no—
781C2×C4—142no—
782C2×C4—142no—
783C2×C4—142no—
784C2×C4—142no—
785C2×C4—142no—
786C2×C4—142no—
787C2×C4—142no—
788C2×C4—142no—
789C2×C4—2816no—
790C2×C4—2816no—
791C2×C4—284no—
792C2×C4—284no—
793C2×C4—284no—
794C2×C4C2×D4×D714yes—
795C2×C4C22×C22⋊D714yes—
796C2×C4C22×C22⋊D714yes—
797C7C2×#244911yescharacteristic, complemented, Sylow
798C22—232no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—144no—
806C22—144no—
807C22—144no—
808C22—2816no—
809C22—282no—
810C22—282no—
811C22—282no—
812C22—282no—
813C22#9031814yes—
814C22#9032314yes—
815C22#9032714yes—
816C22#9033614yes—
817C22D4×C22⋊D714yes—
818C22C2×#650914yes—
819C22C2×#650918yescomplemented
820C22#9051514yes—
821C22C22×D4×D711yescharacteristic
822C22C2×#654811yescharacteristic
823C22C22×Q8×D711yescharacteristic
824C22C22×#116111yescharacteristic
825C22C2×D7×#4111yescharacteristic
826C22C2×#655411yescharacteristic
827C22C23×C22⋊D711yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—144no—
835C4—144no—
836C4—144no—
837C4—144no—
838C4—282no—
839C4—282no—
840C4—282no—
841C2—28no—
842C2—284no—
843C2#1174020918yesdirect product factor
844C2C2×#9031811yescharacteristic
845C2C2×#9033611yescharacteristic
846C2C2×#9032311yescharacteristic
847C2C2×#9032711yescharacteristic
848C2C2×D4×C22⋊D711yescharacteristic
849C2C22×#650911yescharacteristic
850C2C2×#9051511yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C7×C22⋊Q8C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC22×C22⋊Q8D7
hypocenterC7C2×#2449
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C7×C22⋊Q8C2semidirect
2. C22×#6509C2semidirect
3. C23×Dic7⋊C4C2semidirect
5. C2×#90001C2semidirect
7. #11740209C2direct (N × H)
8. C2×#89764C2semidirect
9. C2×#89766C2semidirect
10. C2×#89761C2semidirect
11. C2×#89756C2semidirect
12. C2×#89745C2semidirect
13. C2×#89750C2semidirect
15. C2×#89722C2semidirect
16. C2×#89718C2semidirect
24. C2×C7×C22⋊Q8C22semidirect
32. C2×#6509C22semidirect
48. C22×Dic7⋊C4C22semidirect
52. #90001C22semidirect
62. #89766C22semidirect
63. #89764C22semidirect
64. #89761C22semidirect
65. #89756C22semidirect
66. #89750C22semidirect
67. #89745C22semidirect
69. #89722C22semidirect
70. #89718C22semidirect
90. C22×C22⋊D7Q8semidirect
146. C2×Dic7⋊C4D4semidirect
166. C22×C22⋊Q8D7semidirect
233. C2×C22⋊D7C2×Q8semidirect
293. Dic7⋊C4C2×D4semidirect
304. C2×C22⋊Q8C2×D7semidirect
359. C23×C7C22⋊Q8semidirect
544. C22×C7C2×C22⋊Q8semidirect
694. C2×C7#2449semidirect
727. C23#6509semidirect
797. C7C2×#2449semidirect
819. C22C2×#6509semidirect
843. C2#11740209direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×C22⋊Q82
C22×#65092
C23×Dic7⋊C42
C22×(C22⋊D7)⋊C42
C2×#900012
C2×#899852
#117402092
C2×#897642
C2×#897662
C2×#897612
C2×#897562
C2×#897452
C2×#897502
C2×#897302
C2×#897222
C2×#897182
C2×#24497