Finite Group Databasebeta

← #13284003

Subgroups — #13284003

Order 1792.

1542 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×C7×#387C211yesmaximal, characteristic, complemented
2C2×#89764C211yesmaximal, characteristic
3C2×#89440C211yesmaximal, characteristic
4#11729324C211yesmaximal, characteristic
5#11729320C211yesmaximal, characteristic, complemented
6#11729317C211yesmaximal, characteristic, complemented
7#11729291C211yesmaximal, characteristic
8#11729290C211yesmaximal, characteristic, complemented
9(C2×D7)⋊#95C211yesmaximal, characteristic
10(C2×D7)⋊#95C211yesmaximal, characteristic
11#11727169C211yesmaximal, characteristic, complemented
12#11727163C211yesmaximal, characteristic, complemented
13#11727163C211yesmaximal, characteristic, complemented
14#11727162C211yesmaximal, characteristic
15#11727155C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C7×#387—24no—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7⋊#95C2211yescharacteristic
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
52#89764C418yescomplemented
53#89440—24no—
54#14584—71nomaximal, Sylow
55C24×D7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×Dic7C2311yescharacteristic
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C22×C4×D7—22no—
71C22×C4×D7—22no—
72C22×C4×D7—22no—
73C22×C4×D7—41no—
74C22×C4×D7—41no—
75C22×C4×D7—41no—
76C22×C4×D7—41no—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—41no—
81C2×C7×C4⋊C4—41no—
82C2×C7×C4⋊C4C2×C414yescomplemented
83C2×C42×C7—22no—
84C2×C42×C7—41no—
85C2×C42×C7—41no—
86C2×(C2×D7)⋊C4—22no—
87C2×(C2×D7)⋊C4—22no—
88C2×(C2×D7)⋊C4—22no—
89C2×(C2×D7)⋊C4—22no—
90C2×(C2×D7)⋊C4—22no—
91C2×(C2×D7)⋊C4—22no—
92C2×(C2×D7)⋊C4—41no—
93C2×(C2×D7)⋊C4—41no—
94C2×(C2×D7)⋊C4—41no—
95C2×(C2×D7)⋊C4—41no—
96C2×(C2×D7)⋊C4—41no—
97C2×(C2×D7)⋊C4—41no—
98C2×(C2×D7)⋊C4—41no—
99C2×(C2×D7)⋊C4—41no—
100C2×(C2×D7)⋊C4C2×C414yes—
101C2×(C2×D7)⋊C4C2×C414yes—
102C2×(C2×D7)⋊C4C2×C414yes—
103C2×(C2×D7)⋊C4Q814yes—
104C2×C4⋊Dic7—22no—
105C2×C4⋊Dic7—22no—
106C2×C4⋊Dic7—41no—
107C2×Dic7⋊C4—22no—
108C2×Dic7⋊C4—41no—
109C2×Dic7⋊C4—41no—
110C2×Dic7⋊C4—41no—
111C2×Dic7⋊C4—41no—
112C2×Dic7⋊C4—41no—
113C2×Dic7⋊C4—41no—
114C2×Dic7⋊C4C2×C414yescomplemented
115C2×Dic7⋊C4C2×C414yescomplemented
116C2×C4×Dic7—22no—
117C2×C4×Dic7—22no—
118C2×C4×Dic7—41no—
119C7×#95—22no—
120C7×#95—22no—
121C7×#95—22no—
122C7×#95D414yes—
123C7⋊#95—22no—
124C7⋊#95—22no—
125C7⋊#95—22no—
126C7⋊#95—41no—
127C7⋊#95—41no—
128C7⋊#95—41no—
129C7⋊#95—41no—
130C7⋊#95—41no—
131C7⋊#95—41no—
132C7⋊#95—41no—
133C7⋊#95—41no—
134C7⋊#95—41no—
135C7⋊#95—41no—
136C7⋊#95—41no—
137C7⋊#95—41no—
138C7⋊#95C2×C414yescomplemented
139C2×#399—71no—
140C2×#387D711yescharacteristic, complemented
141C2×#385—71no—
142#1442—71no—
143#1441—71no—
144#1441—71no—
145#1441—71no—
146#1439—71no—
147#1437—71no—
148#1437—71no—
149#1436—71no—
150C4⋊#95—71no—
151#1434—71no—
152C22⋊#95—71no—
153C22⋊#95—71no—
154C24×C7C2411yescharacteristic
155C23×D7—21no—
156C23×D7—21no—
157C23×D7—21no—
158C23×D7—21no—
159C23×D7—21no—
160C23×D7—21no—
161C23×D7—21no—
162C23×D7—21no—
163C23×D7—21no—
164C23×D7—21no—
165C23×D7—21no—
166C23×D7—21no—
167C23×D7C22×C412yes—
168C23×D7C2×Q812yes—
169C23×D7#4112yes—
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—21no—
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—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7C22×C412yes—
212C22×C4×C7C22×C412yes—
213C22×C4×C7C22×C412yes—
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2×D412yes—
216C22×C4×C7C2×D412yes—
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×Dic7C22×C412yes—
263C22×Dic7C22×C412yes—
264C22×Dic7C22×C412yes—
265C22×Dic7C2×Q812yes—
266C22×Dic7#4112yes—
267C22×Dic7#4112yes—
268C2×C4×D7—44no—
269C2×C4×D7—44no—
270C2×C4×D7—44no—
271C2×C4×D7—44no—
272C2×C4×D7—44no—
273C2×C4×D7—44no—
274C2×C4×D7—44no—
275C7×C4⋊C4—28no—
276C7×C4⋊C4—44no—
277C42×C7—44no—
278(C2×D7)⋊C4—28no—
279(C2×D7)⋊C4—44no—
280(C2×D7)⋊C4—44no—
281(C2×D7)⋊C4—44no—
282(C2×D7)⋊C4—44no—
283(C2×D7)⋊C4—44no—
284C4⋊Dic7—44no—
285Dic7⋊C4—44no—
286Dic7⋊C4—44no—
287Dic7⋊C4—44no—
288C4×Dic7—44no—
289C24×C4—71no—
290C22×C4⋊C4—71no—
291C22×C4⋊C4—71no—
292C22×C4⋊C4—71no—
293C22×C4⋊C4—71no—
294C22×C4⋊C4C2×D711yescharacteristic
295C22×C4⋊C4C2×D711yescharacteristic
296C22×C22⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4—71no—
299C22×C22⋊C4—71no—
300C22×C22⋊C4—71no—
301C22×C22⋊C4—71no—
302C22×C42—71no—
303C22×C42C2×D711yescharacteristic
304#399—78no—
305#387—24no—
306#385—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×C7C23×C411yescharacteristic
328C23×C7C22×D411yescharacteristic
329C23×C7C22×Q811yescharacteristic
330C23×C7C2×#4111yescharacteristic
331C23×C7C2×#4111yescharacteristic
332C23×C7C2×#4111yescharacteristic
333C23×C7C2×#4111yescharacteristic
334C23×C7H(5,𝔽2)11yescharacteristic
335C23×C7H(5,𝔽2)11yescharacteristic
336C23×C7H(5,𝔽2)11yescharacteristic
337C23×C7H(5,𝔽2)11yescharacteristic
338C23×C7H(5,𝔽2)11yescharacteristic
339C23×C7H(5,𝔽2)11yescharacteristic
340C23×C72−1+411yescharacteristic
341C23×C72−1+411yescharacteristic
342C22×D7—22no—
343C22×D7—22no—
344C22×D7—22no—
345C22×D7—22no—
346C22×D7—22no—
347C22×D7—22no—
348C22×D7—22no—
349C22×D7—22no—
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—41no—
361C22×D7—41no—
362C22×D7—41no—
363C22×D7—41no—
364C22×D7—41no—
365C22×D7—41no—
366C22×D7—41no—
367C22×D7—41no—
368C22×D7—41no—
369C22×D7—41no—
370C22×D7—41no—
371C22×D7—41no—
372C22×D7—41no—
373C22×D7—41no—
374C22×D7—41no—
375C22×D7—41no—
376C22×D7C4×Q814yes—
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—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
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×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7C4×D414yes—
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—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
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—
475C4×D7—416no—
476C25—71no—
477C23×C4—71no—
478C23×C4—71no—
479C23×C4—71no—
480C23×C4—71no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4—142no—
485C23×C4—142no—
486C23×C4—142no—
487C23×C4—281no—
488C23×C4—281no—
489C23×C4—281no—
490C23×C4—281no—
491C23×C4C22×D711yescharacteristic
492C23×C4C22×D711yescharacteristic
493C23×C4C22×D711yescharacteristic
494C23×C4C22×D711yescharacteristic
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4—41no—
503C2×C4⋊C4—74no—
504C2×C4⋊C4—74no—
505C2×C4⋊C4—142no—
506C2×C4⋊C4—142no—
507C2×C4⋊C4—142no—
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⋊C4C4×D714yescomplemented
516C2×C22⋊C4—74no—
517C2×C22⋊C4—74no—
518C2×C22⋊C4—74no—
519C2×C22⋊C4—74no—
520C2×C22⋊C4—142no—
521C2×C22⋊C4—142no—
522C2×C22⋊C4—142no—
523C2×C22⋊C4—142no—
524C2×C22⋊C4—142no—
525C2×C22⋊C4—142no—
526C2×C22⋊C4—281no—
527C2×C22⋊C4—281no—
528C2×C22⋊C4—281no—
529C2×C22⋊C4—281no—
530C2×C22⋊C4—281no—
531C2×C22⋊C4—281no—
532C2×C22⋊C4—281no—
533C2×C22⋊C4—281no—
534C2×C42—22no—
535C2×C42—41no—
536C2×C42—41no—
537C2×C42—142no—
538C2×C42—142no—
539C2×C42—281no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—74no—
544#95—142no—
545#95—142no—
546#95—142no—
547#95—281no—
548#95—281no—
549#95—281no—
550#95—281no—
551#95—281no—
552#95—281no—
553#95—281no—
554#95—281no—
555#95—281no—
556#95—281no—
557#95—281no—
558#95—281no—
559#95C22⋊D714yes—
560C22×C7C2×C4×D411yescharacteristic
561C22×C7C2×C4×Q811yescharacteristic
562C22×C7C4×#4111yescharacteristic
563C22×C7#51811yescharacteristic
564C22×C7#51811yescharacteristic
565C22×C7#52011yescharacteristic
566C22×C7#52011yescharacteristic
567C22×C7#53511yescharacteristic
568C22×C7#53511yescharacteristic
569C22×C7#53811yescharacteristic
570C22×C7#53811yescharacteristic
571C22×C7#53911yescharacteristic
572C22×C7#53911yescharacteristic
573C22×C7#54011yescharacteristic
574C22×C7#54011yescharacteristic
575C22×C7#54011yescharacteristic
576C22×C7#54211yescharacteristic
577C22×C7#54311yescharacteristic
578C22×C7#54411yescharacteristic
579C22×C7#54611yescharacteristic
580C22×C7#54611yescharacteristic
581C22×C7#54711yescharacteristic
582C22×C7D4×Q811yescharacteristic
583C22×C7#55111yescharacteristic
584C22×C7#55111yescharacteristic
585C22×C7#55111yescharacteristic
586C22×C7#55211yescharacteristic
587C22×C7#55211yescharacteristic
588C22×C7#55411yescharacteristic
589C22×C7#55411yescharacteristic
590C22×C7#55411yescharacteristic
591C22×C7#56011yescharacteristic
592C22×C7#56211yescharacteristic
593C22×C7#56211yescharacteristic
594C22×C7#56311yescharacteristic
595C2×D7—24no—
596C2×D7—24no—
597C2×D7—24no—
598C2×D7—42no—
599C2×D7—42no—
600C2×D7—42no—
601C2×D7—42no—
602C2×D7—42no—
603C2×D7—42no—
604C2×D7—42no—
605C2×D7—42no—
606C2×D7—42no—
607C2×D7—42no—
608C2×D7—42no—
609C2×D7—42no—
610C4×C7—24no—
611C4×C7—42no—
612C4×C7—42no—
613C4×C7—42no—
614C4×C7—42no—
615C4×C7—42no—
616C4×C7—81no—
617Dic7—42no—
618Dic7—42no—
619Dic7—42no—
620Dic7—42no—
621Dic7—42no—
622Dic7—42no—
623Dic7—81no—
624C24—72no—
625C24—72no—
626C24—72no—
627C24—141no—
628C24—141no—
629C24—141no—
630C24—141no—
631C24—141no—
632C24—141no—
633C24—141no—
634C24—141no—
635C24—141no—
636C24—141no—
637C24—141no—
638C24—141no—
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—21no—
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—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—72no—
682C22×C4—72no—
683C22×C4—72no—
684C22×C4—72no—
685C22×C4—72no—
686C22×C4—72no—
687C22×C4—141no—
688C22×C4—141no—
689C22×C4—141no—
690C22×C4—141no—
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—284no—
731C22×C4—284no—
732C22×C4—284no—
733C22×C4—284no—
734C22×C4—284no—
735C22×C4—284no—
736C22×C4—284no—
737C22×C4C2×C4×D712yes—
738C22×C4C2×C4×D712yes—
739C22×C4C2×C4×D712yes—
740C22×C4#115712yes—
741C22×C4Q8×D712yes—
742C22×C4C2×C22⋊D712yes—
743C22×C4C2×C22⋊D712yes—
744C22×C4C2×C22⋊D712yes—
745C4⋊C4—28no—
746C4⋊C4—44no—
747C4⋊C4—284no—
748C4⋊C4—284no—
749C4⋊C4—284no—
750C4⋊C4—284no—
751C22⋊C4—148no—
752C22⋊C4—284no—
753C22⋊C4—284no—
754C22⋊C4—284no—
755C22⋊C4—284no—
756C22⋊C4—284no—
757C42—44no—
758C42—284no—
759C2×C7#232811yescharacteristic
760C2×C7#232911yescharacteristic
761C2×C7#233511yescharacteristic
762C2×C7#235911yescharacteristic
763C2×C7#236011yescharacteristic
764C2×C7#236811yescharacteristic
765C2×C7#237611yescharacteristic
766C2×C7#268511yescharacteristic
767C2×C7#269211yescharacteristic
768C2×C7#270611yescharacteristic
769C2×C7#272011yescharacteristic
770C2×C7#273811yescharacteristic
771C2×C7#274311yescharacteristic
772C2×C7#274811yescharacteristic
773C2×C7#276811yescharacteristic
774D7—44no—
775C23—74no—
776C23—142no—
777C23—142no—
778C23—142no—
779C23—142no—
780C23—142no—
781C23—142no—
782C23—142no—
783C23—142no—
784C23—142no—
785C23—142no—
786C23—142no—
787C23—142no—
788C23—142no—
789C23—142no—
790C23—142no—
791C23—142no—
792C23—142no—
793C23—142no—
794C23—281no—
795C23—281no—
796C23—281no—
797C23—281no—
798C23—281no—
799C23—281no—
800C23—281no—
801C23—281no—
802C23—281no—
803C23—281no—
804C23—281no—
805C23—281no—
806C23—281no—
807C23—281no—
808C23—281no—
809C23—281no—
810C23C22×C4×D711yescharacteristic
811C23C2×#115711yescharacteristic
812C23#654811yescharacteristic
813C23#654811yescharacteristic
814C23C2×Q8×D711yescharacteristic
815C23#655111yescharacteristic
816C23D7×#4111yescharacteristic
817C23D7×#4111yescharacteristic
818C23D7×#4111yescharacteristic
819C23#655311yescharacteristic
820C23#655311yescharacteristic
821C23#655311yescharacteristic
822C23#655311yescharacteristic
823C23#655411yescharacteristic
824C23C22×C22⋊D711yescharacteristic
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—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
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—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
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—142no—
890C2×C4—142no—
891C2×C4—2816no—
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×C4C4×C22⋊D714yes—
924C7#1458411yescharacteristic, complemented, Sylow
925C22—144no—
926C22—144no—
927C22—144no—
928C22—282no—
929C22—282no—
930C22—282no—
931C22—282no—
932C22—282no—
933C22—282no—
934C22—282no—
935C22—282no—
936C22—282no—
937C22—282no—
938C22—282no—
939C22—282no—
940C22#9021311yescharacteristic
941C22#9021411yescharacteristic
942C22#9021811yescharacteristic
943C22#9022211yescharacteristic
944C22#9023611yescharacteristic
945C22#9023611yescharacteristic
946C22#9025311yescharacteristic
947C22#9025311yescharacteristic
948C22C4×Q8×D711yescharacteristic
949C22#9026511yescharacteristic
950C22#9027011yescharacteristic
951C22#9027211yescharacteristic
952C22#9032511yescharacteristic
953C22#9032711yescharacteristic
954C22#9033111yescharacteristic
955C22#9033811yescharacteristic
956C22#9035011yescharacteristic
957C22#9035111yescharacteristic
958C22#9035411yescharacteristic
959C22#9035811yescharacteristic
960C22#9038011yescharacteristic
961C22#9038111yescharacteristic
962C22#9038311yescharacteristic
963C22#9039011yescharacteristic
964C22#9039511yescharacteristic
965C22#9039511yescharacteristic
966C22#9039611yescharacteristic
967C22#9040211yescharacteristic
968C22C2×C4×C22⋊D711yescharacteristic
969C22#9049611yescharacteristic
970C22Q8×C22⋊D711yescharacteristic
971C22#9051511yescharacteristic
972C22#9052011yescharacteristic
973C22#9052011yescharacteristic
974C22#9052111yescharacteristic
975C4—24no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—81no—
982C4—282no—
983C4—282no—
984C4—282no—
985C4—282no—
986C4—282no—
987C4—282no—
988C4—561no—
989C2—284no—
990C2#1173265711yescharacteristic
991C2#1173274411yescharacteristic
992C2#1173274711yescharacteristic
993C2#1173275511yescharacteristic
994C2#1173275711yescharacteristic
995C2#1173284711yescharacteristic
996C2#1173285711yescharacteristic
997C2#1173286711yescharacteristic
998C2#1173968711yescharacteristic
999C2#1173977411yescharacteristic
1000C2#1173993511yescharacteristic
1001C2#1174027511yescharacteristic
1002C2#1174032711yescharacteristic
1003C2#1174049611yescharacteristic
1004C2#1174055911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#387C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#387D7
hypocenterC7#14584
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C2×C7×#387C2semidirect
5. #11729320C2semidirect
6. #11729317C2semidirect
8. #11729290C2semidirect
11. #11727169C2semidirect
12. #11727163C2semidirect
13. #11727163C2semidirect
15. #11727155C2semidirect
52. #89764C4semidirect
82. C2×C7×C4⋊C4C2×C4semidirect
114. C2×Dic7⋊C4C2×C4semidirect
115. C2×Dic7⋊C4C2×C4semidirect
138. C7⋊#95C2×C4semidirect
140. C2×#387D7semidirect
515. C2×C4⋊C4C4×D7semidirect
924. C7#14584semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3872
C2×#897642
C2×#894402
#117293242
#117293202
#117293172
#117292912
#117292902
(C2×D7)⋊#952
#117271692
#117271632
#117271622
#117271552
#145847