Finite Group Databasebeta

← C2×#11731932 #13525009

Subgroups — C2×#11731932 #13525009

Order 1792.

3222 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D7C211yesmaximal, characteristic
2C22×#6450C211yesmaximal, characteristic, complemented
3C2×C7×#385C211yesmaximal, characteristic, complemented
4C2×#89982C211yesmaximal, characteristic, complemented
5C2×#89764C211yesmaximal, characteristic, complemented
6C2×#89761C211yesmaximal, characteristic, complemented
7C2×#89744C211yesmaximal, characteristic, complemented
8C2×#89721C211yesmaximal, characteristic, complemented
9C2×#89719C211yesmaximal, characteristic, complemented
10C2×#89729C211yesmaximal, characteristic
11C2×#89729C211yesmaximal, characteristic
12#11731932C2116yesmaximal, direct product factor
13C2×#89445C211yesmaximal, characteristic, complemented
14C2×#89440C211yesmaximal, characteristic, complemented
15C2×#89419C211yesmaximal, characteristic, complemented
16C2×#89422C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C23×Dic14C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C2×C4×C22⋊D7—28no—
29C2×C4×C22⋊D7C2218yes—
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6450—28no—
47C2×#6450C2218yescomplemented
48C7×#385C2218yescomplemented
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51#89982C2218yescomplemented
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58#89764C2218yescomplemented
59#89761C2218yescomplemented
60#89744C2218yescomplemented
61#89729C2218yes—
62#89729C2218yes—
63#89721C2218yescomplemented
64#89719C2218yescomplemented
65#89445C2218yescomplemented
66#89440C2218yescomplemented
67#89422C2218yescomplemented
68#89419C2218yescomplemented
69C2×#2580—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C23×C4×C7—24no—
73C23×C4×C7—42no—
74C23×C4×C7—42no—
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2314yes—
82C22×C22⋊D7—24no—
83C22×C22⋊D7—24no—
84C22×C22⋊D7Q818yescomplemented
85C22×C22⋊D7C2314yes—
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C22×C4×D7—24no—
94C22×C4×D7—42no—
95C22×C4×D7—42no—
96C22×C4×D7C2314yes—
97C22×Dic14—24no—
98C22×Dic14—24no—
99C22×Dic14—24no—
100C22×Dic14C2314yes—
101C2×C7×C4⋊C4—24no—
102C2×C7×C4⋊C4—42no—
103C2×C7×C4⋊C4C2314yes—
104C2×C7×C4⋊C4C2314yes—
105C2×C7×C22⋊C4—24no—
106C2×C7×C22⋊C4—42no—
107C2×C7×C22⋊C4C2314yes—
108C2×C7×C22⋊C4C2314yes—
109C2×C22⋊Dic7—24no—
110C2×C22⋊Dic7—24no—
111C2×C22⋊Dic7—42no—
112C2×C22⋊Dic7C2314yes—
113C2×C22⋊Dic7C2314yes—
114C2×C22⋊Dic7C2314yes—
115C4×C22⋊D7—232no—
116C2×(C2×D7)⋊C4—24no—
117C2×(C2×D7)⋊C4—24no—
118C2×(C2×D7)⋊C4—24no—
119C2×(C2×D7)⋊C4—42no—
120C2×(C2×D7)⋊C4—42no—
121C2×(C2×D7)⋊C4C2314yes—
122C2×(C2×D7)⋊C4C2314yes—
123C2×(C2×D7)⋊C4C2314yes—
124C2×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×C4⋊Dic7—42no—
127C2×C4⋊Dic7C2314yes—
128C2×Dic7⋊C4—24no—
129C2×Dic7⋊C4—24no—
130C2×Dic7⋊C4—24no—
131C2×Dic7⋊C4—24no—
132C2×Dic7⋊C4—24no—
133C2×Dic7⋊C4—42no—
134C2×Dic7⋊C4—42no—
135C2×Dic7⋊C4C2314yes—
136C2×Dic7⋊C4C2314yes—
137C2×Dic7⋊C4C2314yes—
138C2×Dic7⋊C4C2314yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×C4×Dic7—24no—
143C2×C4×Dic7—24no—
144C2×C4×Dic7D418yes—
145C2×C4×Dic7C2314yes—
146C2×C4×Dic7C2314yes—
147C2×C4×Dic7C2314yes—
148#6450—232no—
149C7×#95C2314yes—
150C7×#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C22×C4×Q8—71no—
158C22×C4×D4—71no—
159#2580—716no—
160C2×#399—71no—
161C2×#399—71no—
162C2×#393—71no—
163C2×#393—71no—
164C2×#390—71no—
165C2×#390—71no—
166C2×#389—71no—
167C2×#389—71no—
168C2×#385—71no—
169C2×#385—71no—
170C2×#385—71no—
171C2×#385D711yescharacteristic, complemented
172C2×#382—71no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7C2×Q814yes—
180C24×C7C2412yes—
181C24×C7C2411yescharacteristic
182C23×D7—22no—
183C23×D7—22no—
184C23×D7—22no—
185C23×D7—22no—
186C23×D7—22no—
187C23×D7—22no—
188C23×D7C2×Q814yes—
189C23×D7C2412yes—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—28no—
207C22×C4×C7—44no—
208C22×C4×C7—44no—
209C22×C4×C7—416no—
210C22×C4×C7C2×D414yes—
211C22×C4×C7#4114yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2412yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2412yes—
218C2×C22⋊D7—232no—
219C2×C22⋊D7—28no—
220C2×C22⋊D7—28no—
221C2×C22⋊D7C2×Q8116yescomplemented
222C22×Dic7—22no—
223C22×Dic7—22no—
224C22×Dic7—22no—
225C22×Dic7—22no—
226C22×Dic7—22no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7C2×D414yes—
239C22×Dic7C2×D414yes—
240C22×Dic7C2×Q814yes—
241C22×Dic7#4114yes—
242C22×Dic7#4114yes—
243C22×Dic7C2412yes—
244C22×Dic7C2412yes—
245C22×Dic7C2412yes—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C2×C4×D7—28no—
251C2×C4×D7—44no—
252C2×C4×D7—44no—
253C2×C4×D7—416no—
254C2×Dic14—232no—
255C2×Dic14—28no—
256C2×Dic14—28no—
257C2×Dic14—28no—
258C7×C4⋊C4—28no—
259C7×C4⋊C4—44no—
260C7×C22⋊C4—28no—
261C7×C22⋊C4—44no—
262C22⋊Dic7—28no—
263C22⋊Dic7—28no—
264C22⋊Dic7—44no—
265(C2×D7)⋊C4—28no—
266(C2×D7)⋊C4—28no—
267(C2×D7)⋊C4—28no—
268(C2×D7)⋊C4—44no—
269(C2×D7)⋊C4—44no—
270C4⋊Dic7—44no—
271Dic7⋊C4—28no—
272Dic7⋊C4—28no—
273Dic7⋊C4—28no—
274Dic7⋊C4—28no—
275Dic7⋊C4—28no—
276Dic7⋊C4—44no—
277Dic7⋊C4—44no—
278C4×Dic7—28no—
279C4×Dic7—28no—
280C4×Dic7C2×D4116yes—
281C23×Q8—71no—
282C23×D4—71no—
283C24×C4—71no—
284C24×C4C2×D711yescharacteristic
285C2×C4×Q8—78no—
286C2×C4×Q8—148no—
287C2×C4×D4—78no—
288C2×C4×D4—148no—
289C22×C4⋊C4—71no—
290C22×C4⋊C4—71no—
291C22×C4⋊C4—71no—
292C22×C4⋊C4—71no—
293C22×C4⋊C4—71no—
294C22×C4⋊C4—71no—
295C22×C4⋊C4—71no—
296C22×C4⋊C4—71no—
297C22×C4⋊C4C2×D711yescharacteristic
298C22×C4⋊C4C2×D711yescharacteristic
299C22×C22⋊C4—71no—
300C22×C22⋊C4—71no—
301C22×C22⋊C4—71no—
302C22×C22⋊C4—71no—
303C22×C22⋊C4—71no—
304C22×C22⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4C2×D711yescharacteristic
308C22×C22⋊C4C2×D711yescharacteristic
309C22×C42—71no—
310C22×C42—71no—
311C22×C42—71no—
312#399—78no—
313#399—78no—
314#393—78no—
315#393—78no—
316#390—78no—
317#390—78no—
318#389—78no—
319#389—78no—
320#385—78no—
321#385—78no—
322#385—78no—
323#385C2×D718yescomplemented
324#382—78no—
325C2×#95—71no—
326C2×#95—71no—
327C2×#95—71no—
328C2×#95—71no—
329C2×#95—71no—
330C2×#95—71no—
331C2×#95C2×D711yescharacteristic
332C2×#95C2×D711yescharacteristic
333C23×C7—28no—
334C23×C7—28no—
335C23×C7—28no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—44no—
343C23×C7—44no—
344C23×C7—44no—
345C23×C7—44no—
346C23×C7C22×D412yes—
347C23×C7C22×Q814yes—
348C23×C7C22×Q812yes—
349C23×C7C2×#4112yes—
350C23×C7C2×#4112yes—
351C23×C7C2×#4112yes—
352C23×C7H(5,𝔽2)12yes—
353C23×C7H(5,𝔽2)12yes—
354C23×C7C2511yescharacteristic
355C22×D7—28no—
356C22×D7—28no—
357C22×D7—28no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—44no—
365C22×D7—44no—
366C22×D7—44no—
367C22×D7—44no—
368C22×D7C22×Q814yes—
369C2×C4×C7—28no—
370C2×C4×C7—28no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—416no—
388C2×C4×C7—44no—
389C2×C4×C7—44no—
390C2×C4×C7—44no—
391C2×C4×C7—44no—
392C2×C4×C7C22×D414yes—
393C2×C4×C7C2×#4114yes—
394C22⋊D7—232no—
395C2×Dic7—28no—
396C2×Dic7—28no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—44no—
414C2×Dic7—44no—
415C2×Dic7—44no—
416C2×Dic7—44no—
417C2×Dic7C22⋊Q8116yes—
418C2×Dic7C22×D414yes—
419C2×Dic7C22×D414yes—
420C2×Dic7C22×Q814yes—
421C2×Dic7C2×#4114yes—
422C2×Dic7C2×#4114yes—
423C4×D7—416no—
424Dic14—232no—
425C25—71no—
426C25C22×D711yescharacteristic
427C22×Q8—74no—
428C22×Q8—144no—
429C22×Q8—144no—
430C22×Q8—144no—
431C22×D4—78no—
432C22×D4—74no—
433C22×D4—144no—
434C22×D4—144no—
435C23×C4—24no—
436C23×C4—42no—
437C23×C4—42no—
438C23×C4—71no—
439C23×C4—71no—
440C23×C4—71no—
441C23×C4—71no—
442C23×C4—71no—
443C23×C4—71no—
444C23×C4—71no—
445C23×C4—74no—
446C23×C4—144no—
447C23×C4—282no—
448C23×C4—282no—
449C23×C4C22×D711yescharacteristic
450C23×C4C22×D711yescharacteristic
451C23×C4C22×D711yescharacteristic
452C23×C4C22×D711yescharacteristic
453C23×C4C22×D711yescharacteristic
454C23×C4C22×D711yescharacteristic
455C23×C4C22×D714yes—
456C4×Q8—1432no—
457C4×D4—1432no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—74no—
461C2×C4⋊C4—74no—
462C2×C4⋊C4—74no—
463C2×C4⋊C4—74no—
464C2×C4⋊C4—74no—
465C2×C4⋊C4—74no—
466C2×C4⋊C4—74no—
467C2×C4⋊C4—74no—
468C2×C4⋊C4—144no—
469C2×C4⋊C4—144no—
470C2×C4⋊C4—144no—
471C2×C4⋊C4—144no—
472C2×C4⋊C4—144no—
473C2×C4⋊C4—282no—
474C2×C4⋊C4—282no—
475C2×C4⋊C4—282no—
476C2×C4⋊C4C22×D714yes—
477C2×C4⋊C4C22×D714yes—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—74no—
481C2×C22⋊C4—74no—
482C2×C22⋊C4—74no—
483C2×C22⋊C4—74no—
484C2×C22⋊C4—74no—
485C2×C22⋊C4—74no—
486C2×C22⋊C4—74no—
487C2×C22⋊C4—74no—
488C2×C22⋊C4—144no—
489C2×C22⋊C4—144no—
490C2×C22⋊C4—144no—
491C2×C22⋊C4—144no—
492C2×C22⋊C4—144no—
493C2×C22⋊C4—282no—
494C2×C22⋊C4—282no—
495C2×C22⋊C4—282no—
496C2×C22⋊C4C22×D714yes—
497C2×C22⋊C4C22×D714yes—
498C2×C42—78no—
499C2×C42—74no—
500C2×C42—74no—
501C2×C42—74no—
502C2×C42—144no—
503C2×C42—144no—
504#95—74no—
505#95—74no—
506#95—74no—
507#95—74no—
508#95—74no—
509#95—74no—
510#95C22×D714yes—
511#95C22×D714yes—
512C22×C7—24no—
513C22×C7—24no—
514C22×C7—24no—
515C22×C7—416no—
516C22×C7—42no—
517C22×C7—42no—
518C22×C7—42no—
519C22×C7—42no—
520C22×C7C2×C22⋊Q814yes—
521C22×C7#52514yes—
522C22×C7#53514yes—
523C22×C7#55414yes—
524C22×C7#55414yes—
525C22×C7#55914yes—
526C22×C7#55914yes—
527C22×C7C23×D411yescharacteristic
528C22×C7C23×Q811yescharacteristic
529C22×C7C22×#4111yescharacteristic
530C22×C7C22×#4111yescharacteristic
531C22×C7C22×#4111yescharacteristic
532C22×C7C2×H(5,𝔽2)11yescharacteristic
533C22×C7C2×H(5,𝔽2)11yescharacteristic
534C2×D7—24no—
535C2×D7—24no—
536C2×D7—24no—
537C2×D7—416no—
538C2×D7—42no—
539C2×D7—42no—
540C2×D7—42no—
541C2×D7—42no—
542C4×C7—24no—
543C4×C7—24no—
544C4×C7—42no—
545C4×C7—42no—
546C4×C7—42no—
547C4×C7—42no—
548Dic7—24no—
549Dic7—24no—
550Dic7—42no—
551Dic7—42no—
552Dic7—42no—
553Dic7—42no—
554Dic7C2×C22⋊Q818yes—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—74no—
562C24—72no—
563C24—142no—
564C24—142no—
565C24—142no—
566C24—142no—
567C24—142no—
568C24—142no—
569C24Q8×D714yes—
570C24C23×D712yes—
571C24C23×D711yescharacteristic
572C2×Q8—148no—
573C2×Q8—148no—
574C2×Q8—1432no—
575C2×Q8—148no—
576C2×D4—716no—
577C2×D4—148no—
578C2×D4—1432no—
579C2×D4—148no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—28no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—416no—
600C22×C4—74no—
601C22×C4—74no—
602C22×C4—74no—
603C22×C4—72no—
604C22×C4—74no—
605C22×C4—74no—
606C22×C4—72no—
607C22×C4—72no—
608C22×C4—72no—
609C22×C4—72no—
610C22×C4—72no—
611C22×C4—72no—
612C22×C4—142no—
613C22×C4—142no—
614C22×C4—142no—
615C22×C4—142no—
616C22×C4—142no—
617C22×C4—142no—
618C22×C4—142no—
619C22×C4—142no—
620C22×C4—142no—
621C22×C4—142no—
622C22×C4—142no—
623C22×C4—142no—
624C22×C4—142no—
625C22×C4—142no—
626C22×C4—142no—
627C22×C4—142no—
628C22×C4—148no—
629C22×C4—284no—
630C22×C4—284no—
631C22×C4—2816no—
632C22×C4#115714yes—
633C22×C4D4×D714yes—
634C22×C4C23×D712yes—
635C22×C4C23×D712yes—
636C22×C4C23×D712yes—
637C22×C4C23×D712yes—
638C22×C4C23×D712yes—
639C22×C4C23×D712yes—
640C4⋊C4—28no—
641C4⋊C4—44no—
642C4⋊C4—148no—
643C4⋊C4—148no—
644C4⋊C4—148no—
645C4⋊C4—148no—
646C4⋊C4—148no—
647C4⋊C4—284no—
648C4⋊C4—284no—
649C4⋊C4—284no—
650C22⋊C4—28no—
651C22⋊C4—44no—
652C22⋊C4—148no—
653C22⋊C4—148no—
654C22⋊C4—148no—
655C22⋊C4—148no—
656C22⋊C4—148no—
657C22⋊C4—284no—
658C22⋊C4—284no—
659C22⋊C4—284no—
660C42—716no—
661C42—148no—
662C42—148no—
663C2×C7—44no—
664C2×C7#258018yescomplemented
665C2×C7C22×C22⋊Q811yescharacteristic
666C2×C7C2×#52511yescharacteristic
667C2×C7C2×#53511yescharacteristic
668C2×C7C2×#55411yescharacteristic
669C2×C7C2×#55411yescharacteristic
670C2×C7C2×#55911yescharacteristic
671C2×C7C2×#55911yescharacteristic
672D7—44no—
673C23—28no—
674C23—28no—
675C23—28no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—74no—
687C23—148no—
688C23—148no—
689C23—148no—
690C23—142no—
691C23—142no—
692C23—142no—
693C23—142no—
694C23—142no—
695C23—142no—
696C23—284no—
697C23—284no—
698C23—284no—
699C23—284no—
700C23C2×#115712yes—
701C23C2×D4×D712yes—
702C23#654812yes—
703C23#654812yes—
704C23C2×Q8×D714yes—
705C23C2×Q8×D712yes—
706C23D7×#4112yes—
707C23D7×#4112yes—
708C23C24×D711yescharacteristic
709Q8—1432no—
710D4—1432no—
711C2×C4—28no—
712C2×C4—28no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—416no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—716no—
735C2×C4—74no—
736C2×C4—74no—
737C2×C4—74no—
738C2×C4—74no—
739C2×C4—74no—
740C2×C4—148no—
741C2×C4—148no—
742C2×C4—142no—
743C2×C4—142no—
744C2×C4—142no—
745C2×C4—142no—
746C2×C4—142no—
747C2×C4—142no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—142no—
752C2×C4—142no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—142no—
756C2×C4—142no—
757C2×C4—142no—
758C2×C4—2816no—
759C2×C4—284no—
760C2×C4—284no—
761C2×C4—284no—
762C2×C4—284no—
763C2×C4C2×#115714yes—
764C2×C4C2×D4×D714yes—
765C7C2×#258011yescharacteristic, complemented, Sylow
766C22—24no—
767C22—24no—
768C22—24no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—416no—
774C22—144no—
775C22—144no—
776C22—144no—
777C22—282no—
778C22—282no—
779C22—282no—
780C22—282no—
781C22—2816no—
782C22#9020214yes—
783C22#9023814yes—
784C22#9025014yes—
785C22#9028314yes—
786C22D7×C22⋊Q814yes—
787C22#9032714yes—
788C22#9035514yes—
789C22C22×#115711yescharacteristic
790C22C22×D4×D711yescharacteristic
791C22C2×#654811yescharacteristic
792C22C2×#654811yescharacteristic
793C22C22×Q8×D711yescharacteristic
794C22C2×D7×#4111yescharacteristic
795C22C2×D7×#4111yescharacteristic
796C4—24no—
797C4—24no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—78no—
803C4—144no—
804C4—144no—
805C4—282no—
806C4—282no—
807C4—282no—
808C4—282no—
809C2—44no—
810C2—284no—
811C2#1173193218yesdirect product factor
812C2C2×#9020211yescharacteristic
813C2C2×#9025011yescharacteristic
814C2C2×#9023811yescharacteristic
815C2C2×#9028311yescharacteristic
816C2C2×#9032711yescharacteristic
817C2C2×D7×C22⋊Q811yescharacteristic
818C2C2×#9035511yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#385C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#385D7
hypocenterC7C2×#2580
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#6450C2semidirect
3. C2×C7×#385C2semidirect
4. C2×#89982C2semidirect
5. C2×#89764C2semidirect
6. C2×#89761C2semidirect
7. C2×#89744C2semidirect
8. C2×#89721C2semidirect
9. C2×#89719C2semidirect
12. #11731932C2direct (N × H)
13. C2×#89445C2semidirect
14. C2×#89440C2semidirect
15. C2×#89419C2semidirect
16. C2×#89422C2semidirect
47. C2×#6450C22semidirect
48. C7×#385C22semidirect
51. #89982C22semidirect
58. #89764C22semidirect
59. #89761C22semidirect
60. #89744C22semidirect
63. #89721C22semidirect
64. #89719C22semidirect
65. #89445C22semidirect
66. #89440C22semidirect
67. #89422C22semidirect
68. #89419C22semidirect
84. C22×C22⋊D7Q8semidirect
171. C2×#385D7semidirect
221. C2×C22⋊D7C2×Q8semidirect
323. #385C2×D7semidirect
664. C2×C7#2580semidirect
765. C7C2×#2580semidirect
811. C2#11731932direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D72
C22×#64502
C2×C7×#3852
C2×#899822
C2×#897642
C2×#897612
C2×#897442
C2×#897212
C2×#897192
C2×#897292
#117319322
C2×#894452
C2×#894402
C2×#894192
C2×#894222
C2×#25807