Finite Group Databasebeta

← #13281679

Subgroups — #13281679

Order 1792.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89982C211yesmaximal, characteristic
2C2×#89984C211yesmaximal, characteristic
3C2×#89427C211yesmaximal, characteristic, complemented
4C7×C22⋊#95C211yesmaximal, characteristic
5#11729301C211yesmaximal, characteristic
6#11729301C211yesmaximal, characteristic
7#11729299C211yesmaximal, characteristic
8#11729299C211yesmaximal, characteristic
9#11727174C211yesmaximal, characteristic, complemented
10#11727171C211yesmaximal, characteristic, complemented
11#11727168C211yesmaximal, characteristic, complemented
12#11727164C211yesmaximal, characteristic, complemented
13#11727161C211yesmaximal, characteristic, complemented
14#11727160C211yesmaximal, characteristic, complemented
15Dic7⋊#95C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic7C2211yescharacteristic
20C22×C22⋊Dic7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C4⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35#89984—24no—
36#89982C418yescomplemented
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2211yescharacteristic
39C2×C7⋊#95C2211yescharacteristic
40C2×C7⋊#95C2211yescharacteristic
41C2×C7⋊#95C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53#89427—24no—
54#14398—71nomaximal, Sylow
55C25×C7C2311yescharacteristic
56C23×C4×C7—22no—
57C23×C4×C7—22no—
58C23×C4×C7—41no—
59C23×C4×C7—41no—
60C23×C4×C7—41no—
61C23×C4×C7—41no—
62C23×C4×C7C2×C414yes—
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—41no—
79C2×C7×C22⋊C4—41no—
80C2×C7×C22⋊C4—41no—
81C2×C7×C22⋊C4—41no—
82C2×C7×C22⋊C4Q814yes—
83C2×C22⋊Dic7—22no—
84C2×C22⋊Dic7—22no—
85C2×C22⋊Dic7—22no—
86C2×C22⋊Dic7—22no—
87C2×C22⋊Dic7—22no—
88C2×C22⋊Dic7—22no—
89C2×C22⋊Dic7—41no—
90C2×C22⋊Dic7—41no—
91C2×C22⋊Dic7—41no—
92C2×C22⋊Dic7—41no—
93C2×C22⋊Dic7C2×C414yes—
94C2×C22⋊Dic7C2×C414yes—
95C2×C4⋊Dic7—22no—
96C2×C4⋊Dic7—41no—
97C2×C4⋊Dic7—41no—
98C2×C4⋊Dic7—41no—
99C2×C4⋊Dic7—41no—
100C2×C4⋊Dic7D414yes—
101C2×Dic7⋊C4—22no—
102C2×Dic7⋊C4—22no—
103C2×Dic7⋊C4—22no—
104C2×Dic7⋊C4—41no—
105C2×Dic7⋊C4—41no—
106C2×Dic7⋊C4—41no—
107C2×Dic7⋊C4—41no—
108C2×Dic7⋊C4—41no—
109C2×Dic7⋊C4—41no—
110C2×Dic7⋊C4—41no—
111C2×Dic7⋊C4C2×C414yes—
112C2×Dic7⋊C4C2×C414yes—
113C2×C4×Dic7—22no—
114C2×C4×Dic7—22no—
115C2×C4×Dic7—41no—
116C2×C4×Dic7—41no—
117C2×C4×Dic7—41no—
118C2×C4×Dic7—41no—
119C7×#95—22no—
120C7×#95—22no—
121C7×#95—41no—
122C7×#95—41no—
123C7⋊#95—22no—
124C7⋊#95—22no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—22no—
128C7⋊#95—22no—
129C7⋊#95—22no—
130C7⋊#95—41no—
131C7⋊#95—41no—
132C7⋊#95—41no—
133C7⋊#95—41no—
134C7⋊#95—41no—
135C7⋊#95—41no—
136C7⋊#95—41no—
137C7⋊#95C2×C414yes—
138C7⋊#95C2×C414yes—
139C2×#387—71no—
140C2×#385—71no—
141C2×#380—71no—
142#1444—71no—
143#1443—71no—
144#1442—71no—
145#1441—71no—
146#1439—71no—
147#1439—71no—
148#1437—71no—
149#1437—71no—
150#1436—71no—
151#1436—71no—
152C4⋊#95—71no—
153C22⋊#95D711yescharacteristic
154C24×C7—21no—
155C24×C7—21no—
156C24×C7—21no—
157C24×C7—21no—
158C24×C7—21no—
159C24×C7—21no—
160C24×C7—21no—
161C24×C7—21no—
162C24×C7—21no—
163C24×C7—21no—
164C24×C7—21no—
165C24×C7—21no—
166C24×C7C22×C412yes—
167C24×C7C2×Q812yes—
168C24×C7#4112yes—
169C24×C7C2411yescharacteristic
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—28no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—44no—
208C22×C4×C7—44no—
209C22×C4×C7—44no—
210C22×C4×C7—44no—
211C22×C4×C7—44no—
212C22×C4×C7—44no—
213C22×C4×C7C22×C412yes—
214C22×C4×C7C22×C412yes—
215C22×C4×C7C2×D412yes—
216C22×C4×C7C2×Q812yes—
217C22×C4×C7C2×Q812yes—
218C22×C4×C7#4112yes—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7—21no—
248C22×Dic7—21no—
249C22×Dic7—21no—
250C22×Dic7—21no—
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7—21no—
260C22×Dic7—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—21no—
264C22×Dic7—21no—
265C22×Dic7—21no—
266C22×Dic7—21no—
267C22×Dic7C22×C412yes—
268C22×Dic7C22×C412yes—
269C22×Dic7C22×C412yes—
270C22×Dic7C22×C412yes—
271C22×Dic7C2×D412yes—
272C22×Dic7C2×D412yes—
273C22×Dic7#4112yes—
274C22×Dic7#4112yes—
275C7×C22⋊C4—44no—
276C7×C22⋊C4—44no—
277C22⋊Dic7—28no—
278C22⋊Dic7—44no—
279C22⋊Dic7—44no—
280C22⋊Dic7—44no—
281C4⋊Dic7—44no—
282C4⋊Dic7—44no—
283Dic7⋊C4—28no—
284Dic7⋊C4—44no—
285Dic7⋊C4—44no—
286Dic7⋊C4—44no—
287C4×Dic7—44no—
288C4×Dic7—44no—
289C24×C4C2×D711yescharacteristic
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×C22⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4—71no—
299C22×C22⋊C4—71no—
300C22×C22⋊C4C2×D711yescharacteristic
301C22×C22⋊C4C2×D711yescharacteristic
302C22×C42—71no—
303C22×C42—71no—
304#387—144no—
305#385—78no—
306#380—144no—
307C2×#95—71no—
308C2×#95—71no—
309C2×#95—71no—
310C2×#95—71no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95C2×D711yescharacteristic
324C2×#95C2×D711yescharacteristic
325C2×#95C2×D711yescharacteristic
326C2×#95C2×D711yescharacteristic
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—41no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—41no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7—41no—
352C23×C7—41no—
353C23×C7—41no—
354C23×C7—41no—
355C23×C7—41no—
356C23×C7—41no—
357C23×C7—41no—
358C23×C7—41no—
359C23×C7—41no—
360C23×C7—41no—
361C23×C7C4×Q814yes—
362C23×C7C23×C411yescharacteristic
363C23×C7C22×D411yescharacteristic
364C23×C7C22×Q811yescharacteristic
365C23×C7C2×#4111yescharacteristic
366C23×C7C2×#4111yescharacteristic
367C23×C7C2×#4111yescharacteristic
368C23×C7C2×#4111yescharacteristic
369C23×C7H(5,𝔽2)11yescharacteristic
370C23×C7H(5,𝔽2)11yescharacteristic
371C23×C7H(5,𝔽2)11yescharacteristic
372C23×C7H(5,𝔽2)11yescharacteristic
373C23×C7H(5,𝔽2)11yescharacteristic
374C23×C7H(5,𝔽2)11yescharacteristic
375C23×C72−1+411yescharacteristic
376C23×C72−1+411yescharacteristic
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—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—416no—
393C2×C4×C7—41no—
394C2×C4×C7—41no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7—41no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7C4×D414yes—
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—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—41no—
442C2×Dic7—41no—
443C2×Dic7—41no—
444C2×Dic7—41no—
445C2×Dic7—41no—
446C2×Dic7—41no—
447C2×Dic7—41no—
448C2×Dic7—41no—
449C2×Dic7—41no—
450C2×Dic7—41no—
451C2×Dic7—41no—
452C2×Dic7—41no—
453C2×Dic7—41no—
454C2×Dic7—41no—
455C2×Dic7—41no—
456C2×Dic7—41no—
457C2×Dic7—41no—
458C2×Dic7—41no—
459C2×Dic7—41no—
460C2×Dic7—41no—
461C2×Dic7—41no—
462C2×Dic7—41no—
463C2×Dic7—41no—
464C2×Dic7—41no—
465C2×Dic7—41no—
466C2×Dic7—41no—
467C2×Dic7—41no—
468C2×Dic7—41no—
469C2×Dic7—41no—
470C2×Dic7—41no—
471C2×Dic7—41no—
472C2×Dic7—41no—
473C2×Dic7—41no—
474C2×Dic7—41no—
475C2×Dic7#11714yes—
476C25C22×D711yescharacteristic
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—41no—
480C23×C4—41no—
481C23×C4—41no—
482C23×C4—41no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—71no—
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—71no—
491C23×C4C4×D714yes—
492C23×C4C22×D711yescharacteristic
493C23×C4C22×D711yescharacteristic
494C23×C4C22×D711yescharacteristic
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C2×C4⋊C4—74no—
499C2×C4⋊C4—74no—
500C2×C4⋊C4—74no—
501C2×C4⋊C4—142no—
502C2×C4⋊C4—142no—
503C2×C4⋊C4—142no—
504C2×C4⋊C4—142no—
505C2×C4⋊C4—281no—
506C2×C4⋊C4—281no—
507C2×C4⋊C4—281no—
508C2×C4⋊C4—281no—
509C2×C4⋊C4—281no—
510C2×C4⋊C4—281no—
511C2×C4⋊C4—281no—
512C2×C4⋊C4—281no—
513C2×C4⋊C4—281no—
514C2×C4⋊C4—281no—
515C2×C4⋊C4—281no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—41no—
518C2×C22⋊C4—41no—
519C2×C22⋊C4—41no—
520C2×C22⋊C4—41no—
521C2×C22⋊C4—74no—
522C2×C22⋊C4—74no—
523C2×C22⋊C4—142no—
524C2×C22⋊C4—142no—
525C2×C22⋊C4—142no—
526C2×C22⋊C4—142no—
527C2×C22⋊C4—142no—
528C2×C22⋊C4—142no—
529C2×C22⋊C4—281no—
530C2×C22⋊C4—281no—
531C2×C22⋊C4—281no—
532C2×C22⋊C4—281no—
533C2×C22⋊C4Dic1414yes—
534C2×C42—142no—
535C2×C42—142no—
536C2×C42—281no—
537C2×C42—281no—
538C2×C42—281no—
539C2×C42—281no—
540#95—22no—
541#95—22no—
542#95—41no—
543#95—41no—
544#95—74no—
545#95—74no—
546#95—142no—
547#95—142no—
548#95—142no—
549#95—142no—
550#95—142no—
551#95—142no—
552#95—142no—
553#95—281no—
554#95—281no—
555#95—281no—
556#95—281no—
557#95—281no—
558#95—281no—
559#95—281no—
560C22×C7—24no—
561C22×C7—24no—
562C22×C7—24no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—42no—
572C22×C7—42no—
573C22×C7—42no—
574C22×C7—42no—
575C22×C7C2×#11711yescharacteristic
576C22×C7C2×C4×D411yescharacteristic
577C22×C7C2×C4×Q811yescharacteristic
578C22×C7#51811yescharacteristic
579C22×C7#51811yescharacteristic
580C22×C7#52011yescharacteristic
581C22×C7#52011yescharacteristic
582C22×C7#53411yescharacteristic
583C22×C7#53511yescharacteristic
584C22×C7#53811yescharacteristic
585C22×C7#53811yescharacteristic
586C22×C7#53811yescharacteristic
587C22×C7#53811yescharacteristic
588C22×C7#53811yescharacteristic
589C22×C7#53911yescharacteristic
590C22×C7#53911yescharacteristic
591C22×C7#53911yescharacteristic
592C22×C7#54311yescharacteristic
593C22×C7#54411yescharacteristic
594C22×C7#54611yescharacteristic
595C22×C7#54711yescharacteristic
596C22×C7D4×Q811yescharacteristic
597C22×C7#55011yescharacteristic
598C22×C7#55211yescharacteristic
599C22×C7#55311yescharacteristic
600C22×C7#55311yescharacteristic
601C22×C7#55411yescharacteristic
602C22×C7#55411yescharacteristic
603C22×C7#55411yescharacteristic
604C22×C7#55511yescharacteristic
605C22×C7#55611yescharacteristic
606C22×C7#56011yescharacteristic
607C22×C7#56211yescharacteristic
608C22×C7#56211yescharacteristic
609C22×C7#56311yescharacteristic
610C4×C7—24no—
611C4×C7—42no—
612C4×C7—42no—
613C4×C7—42no—
614C4×C7—81no—
615C4×C7—81no—
616Dic7—24no—
617Dic7—42no—
618Dic7—42no—
619Dic7—42no—
620Dic7—42no—
621Dic7—42no—
622Dic7—81no—
623Dic7—81no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24C2×Dic1412yes—
637C24C2×C4×D712yes—
638C24#115712yes—
639C24C23×D711yescharacteristic
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—28no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—72no—
684C22×C4—72no—
685C22×C4—72no—
686C22×C4—72no—
687C22×C4—72no—
688C22×C4—72no—
689C22×C4—72no—
690C22×C4—72no—
691C22×C4—141no—
692C22×C4—141no—
693C22×C4—141no—
694C22×C4—141no—
695C22×C4—141no—
696C22×C4—141no—
697C22×C4—141no—
698C22×C4—141no—
699C22×C4—141no—
700C22×C4—141no—
701C22×C4—141no—
702C22×C4—141no—
703C22×C4—141no—
704C22×C4—141no—
705C22×C4—141no—
706C22×C4—141no—
707C22×C4—141no—
708C22×C4—141no—
709C22×C4—141no—
710C22×C4—141no—
711C22×C4—141no—
712C22×C4—141no—
713C22×C4—141no—
714C22×C4—141no—
715C22×C4—141no—
716C22×C4—141no—
717C22×C4—141no—
718C22×C4—141no—
719C22×C4—141no—
720C22×C4—141no—
721C22×C4—141no—
722C22×C4—141no—
723C22×C4—141no—
724C22×C4—141no—
725C22×C4—141no—
726C22×C4—141no—
727C22×C4—141no—
728C22×C4—141no—
729C22×C4—141no—
730C22×C4—141no—
731C22×C4—141no—
732C22×C4—141no—
733C22×C4—141no—
734C22×C4—141no—
735C22×C4—141no—
736C22×C4—141no—
737C22×C4—141no—
738C22×C4—141no—
739C22×C4C2×Dic1412yes—
740C22×C4C2×Dic1412yes—
741C22×C4C2×C4×D712yes—
742C22×C4C2×C4×D712yes—
743C22×C4D4×D712yes—
744C22×C4#115912yes—
745C4⋊C4—148no—
746C4⋊C4—284no—
747C4⋊C4—284no—
748C4⋊C4—284no—
749C4⋊C4—284no—
750C4⋊C4—284no—
751C22⋊C4—44no—
752C22⋊C4—44no—
753C22⋊C4—148no—
754C22⋊C4—284no—
755C22⋊C4—284no—
756C22⋊C4—284no—
757C42—284no—
758C42—284no—
759C2×C7—44no—
760C2×C7#231811yescharacteristic
761C2×C7#232111yescharacteristic
762C2×C7#232911yescharacteristic
763C2×C7#234511yescharacteristic
764C2×C7#235411yescharacteristic
765C2×C7#236011yescharacteristic
766C2×C7#237611yescharacteristic
767C2×C7#270811yescharacteristic
768C2×C7#271411yescharacteristic
769C2×C7#272011yescharacteristic
770C2×C7#273211yescharacteristic
771C2×C7#278111yescharacteristic
772C2×C7#278411yescharacteristic
773C2×C7#278711yescharacteristic
774C2×C7#278811yescharacteristic
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23C4×Dic1414yes—
810C23C22×Dic1411yescharacteristic
811C23C22×C4×D711yescharacteristic
812C23C2×#115711yescharacteristic
813C23C2×D4×D711yescharacteristic
814C23C2×#115911yescharacteristic
815C23#654811yescharacteristic
816C23#654811yescharacteristic
817C23#654811yescharacteristic
818C23#654811yescharacteristic
819C23#654811yescharacteristic
820C23#655111yescharacteristic
821C23D7×#4111yescharacteristic
822C23D7×#4111yescharacteristic
823C23#655311yescharacteristic
824C23#655411yescharacteristic
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—416no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—74no—
868C2×C4—142no—
869C2×C4—142no—
870C2×C4—142no—
871C2×C4—142no—
872C2×C4—142no—
873C2×C4—142no—
874C2×C4—142no—
875C2×C4—142no—
876C2×C4—142no—
877C2×C4—142no—
878C2×C4—142no—
879C2×C4—142no—
880C2×C4—142no—
881C2×C4—142no—
882C2×C4—142no—
883C2×C4—142no—
884C2×C4—142no—
885C2×C4—142no—
886C2×C4—142no—
887C2×C4—142no—
888C2×C4—142no—
889C2×C4—281no—
890C2×C4—281no—
891C2×C4—281no—
892C2×C4—281no—
893C2×C4—281no—
894C2×C4—281no—
895C2×C4—281no—
896C2×C4—281no—
897C2×C4—281no—
898C2×C4—281no—
899C2×C4—281no—
900C2×C4—281no—
901C2×C4—281no—
902C2×C4—281no—
903C2×C4—281no—
904C2×C4—281no—
905C2×C4—281no—
906C2×C4—281no—
907C2×C4—281no—
908C2×C4—281no—
909C2×C4—281no—
910C2×C4—281no—
911C2×C4—281no—
912C2×C4—281no—
913C2×C4—281no—
914C2×C4—281no—
915C2×C4—281no—
916C2×C4—281no—
917C2×C4—281no—
918C2×C4—281no—
919C2×C4—281no—
920C2×C4—281no—
921C2×C4—281no—
922C2×C4—281no—
923C2×C4(C22⋊D7)⋊C414yes—
924C7#1439811yescharacteristic, complemented, Sylow
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C2×C4×Dic1411yescharacteristic
941C22#9017411yescharacteristic
942C22C2×(C22⋊D7)⋊C411yescharacteristic
943C22#9017711yescharacteristic
944C22#9017711yescharacteristic
945C22#9018511yescharacteristic
946C22#9019111yescharacteristic
947C22#9019511yescharacteristic
948C22#9020611yescharacteristic
949C22D7×#11711yescharacteristic
950C22#9021411yescharacteristic
951C22D4×Dic1411yescharacteristic
952C22#9023011yescharacteristic
953C22#9023011yescharacteristic
954C22#9023111yescharacteristic
955C22#9023111yescharacteristic
956C22#9023211yescharacteristic
957C22#9023411yescharacteristic
958C22#9024111yescharacteristic
959C22#9028011yescharacteristic
960C22#9028311yescharacteristic
961C22#9028411yescharacteristic
962C22#9028411yescharacteristic
963C22#9029011yescharacteristic
964C22#9030711yescharacteristic
965C22#9031111yescharacteristic
966C22#9031211yescharacteristic
967C22#9032211yescharacteristic
968C22#9033211yescharacteristic
969C22#9033711yescharacteristic
970C22#9033811yescharacteristic
971C22#9034811yescharacteristic
972C22#9034811yescharacteristic
973C22#9035111yescharacteristic
974C22#9035111yescharacteristic
975C4—24no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—81no—
980C4—81no—
981C4—144no—
982C4—282no—
983C4—282no—
984C4—282no—
985C4—282no—
986C4—282no—
987C4—561no—
988C4—561no—
989C2—44no—
990C2#1173077911yescharacteristic
991C2#1173090311yescharacteristic
992C2#1173091011yescharacteristic
993C2#1173126611yescharacteristic
994C2#1173133011yescharacteristic
995C2#1173145811yescharacteristic
996C2#1173156511yescharacteristic
997C2#1173197911yescharacteristic
998C2#1173201711yescharacteristic
999C2#1173201911yescharacteristic
1000C2#1173208411yescharacteristic
1001C2#1173226811yescharacteristic
1002C2#1173227511yescharacteristic
1003C2#1173230411yescharacteristic
1004C2#1173230611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C22⋊#95C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC22⋊#95D7
hypocenterC7#14398
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#89427C2semidirect
9. #11727174C2semidirect
10. #11727171C2semidirect
11. #11727168C2semidirect
12. #11727164C2semidirect
13. #11727161C2semidirect
14. #11727160C2semidirect
15. Dic7⋊#95C2semidirect
36. #89982C4semidirect
924. C7#14398semidirect

Maximal subgroups

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

subgroupindex
C2×#899822
C2×#899842
C2×#894272
C7×C22⋊#952
#117293012
#117292992
#117271742
#117271712
#117271682
#117271642
#117271612
#117271602
Dic7⋊#952
#143987