Finite Group Databasebeta

← #13277504

Subgroups — #13277504

Order 1792.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89761C211yesmaximal, characteristic
2C2×#89440C211yesmaximal, characteristic
3C2×#89440C211yesmaximal, characteristic
4C2×D7×#95C211yesmaximal, characteristic
5C2×#89438C211yesmaximal, characteristic
6C7×#1442C211yesmaximal, characteristic, complemented
7#11729317C211yesmaximal, characteristic, complemented
8(C2×D7)⋊#95C211yesmaximal, characteristic
9(C2×D7)⋊#95C211yesmaximal, characteristic
10#11727167C211yesmaximal, characteristic, complemented
11#11727165C211yesmaximal, characteristic, complemented
12#11727163C211yesmaximal, characteristic, complemented
13#11727161C211yesmaximal, characteristic, complemented
14#11727161C211yesmaximal, characteristic, complemented
15Dic7⋊#95C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
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
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
51#89761—24no—
52#89440—24no—
53#89440C418yescomplemented
54#89438—24no—
55D7×#95—24no—
56#14044—71nomaximal, Sylow
57C24×D7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C22×C4×D7—22no—
73C22×C4×D7—22no—
74C22×C4×D7—22no—
75C22×C4×D7—22no—
76C22×C4×D7—22no—
77C22×C4×D7—22no—
78C22×C4×D7—22no—
79C22×C4×D7—22no—
80C22×C4×D7—22no—
81C22×C4×D7—22no—
82C22×C4×D7—22no—
83C22×C4×D7—41no—
84C22×C4×D7—41no—
85C22×C4×D7—41no—
86C22×C4×D7—41no—
87C22×C4×D7—41no—
88C22×C4×D7—41no—
89C22×C4×D7—41no—
90C22×C4×D7—41no—
91C22×C4×D7C2×C414yes—
92C22×C4×D7D414yes—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4—41no—
96C2×(C2×D7)⋊C4—22no—
97C2×(C2×D7)⋊C4—22no—
98C2×(C2×D7)⋊C4—22no—
99C2×(C2×D7)⋊C4—22no—
100C2×(C2×D7)⋊C4—22no—
101C2×(C2×D7)⋊C4—22no—
102C2×(C2×D7)⋊C4—22no—
103C2×(C2×D7)⋊C4C2×C414yes—
104C2×(C2×D7)⋊C4C2×C414yes—
105C2×(C2×D7)⋊C4D414yes—
106C2×(C2×D7)⋊C4Q814yes—
107C2×(C2×D7)⋊C4Q814yes—
108C2×C4⋊Dic7—22no—
109C2×C4⋊Dic7—22no—
110C2×C4⋊Dic7—22no—
111C2×C4⋊Dic7—41no—
112C2×C4⋊Dic7—41no—
113C2×C4⋊Dic7C2×C414yescomplemented
114C2×Dic7⋊C4—22no—
115C2×Dic7⋊C4—22no—
116C2×Dic7⋊C4—22no—
117C2×Dic7⋊C4—41no—
118C2×Dic7⋊C4—41no—
119C2×Dic7⋊C4—41no—
120C2×Dic7⋊C4—41no—
121C2×Dic7⋊C4—41no—
122C2×Dic7⋊C4C2×C414yescomplemented
123C2×C4×Dic7—22no—
124C2×C4×Dic7—22no—
125C2×C4×Dic7—22no—
126C2×C4×Dic7—22no—
127C2×C4×Dic7—41no—
128C2×C4×Dic7—41no—
129C7×#95—22no—
130C7×#95—22no—
131C7×#95—22no—
132C7×#95—22no—
133C7×#95—41no—
134C7×#95C2×C414yescomplemented
135C7⋊#95—22no—
136C7⋊#95—22no—
137C7⋊#95—22no—
138C7⋊#95—22no—
139C7⋊#95—22no—
140C7⋊#95—22no—
141C7⋊#95—22no—
142C7⋊#95—22no—
143C7⋊#95—41no—
144C7⋊#95—41no—
145C7⋊#95—41no—
146C7⋊#95—41no—
147C7⋊#95—41no—
148C7⋊#95C2×C414yescomplemented
149C2×#385—71no—
150C2×#385—71no—
151C2×#385—71no—
152C2×C4×C22⋊C4—71no—
153C22×#95—71no—
154#1442—71no—
155#1442D711yescharacteristic, complemented
156#1441—71no—
157#1441—71no—
158#1436—71no—
159#1436—71no—
160C4⋊#95—71no—
161C4⋊#95—71no—
162C22⋊#95—71no—
163C22⋊#95—71no—
164C24×C7C2411yescharacteristic
165C23×D7—21no—
166C23×D7—21no—
167C23×D7—21no—
168C23×D7—21no—
169C23×D7—21no—
170C23×D7—21no—
171C23×D7—21no—
172C23×D7—21no—
173C23×D7C22×C412yes—
174C23×D7C2×D412yes—
175C23×D7C2×D412yes—
176C23×D7C2×Q812yes—
177C23×D7C2×Q812yes—
178C23×D7#4112yes—
179C23×D7#4112yes—
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×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7C22×C412yes—
222C22×C4×C7C22×C412yes—
223C22×C4×C7C22×C412yes—
224C22×C4×C7C2×D412yes—
225C22×C4×C7C2×D412yes—
226C22×C4×C7C2×Q812yes—
227C22×C4×C7C2×Q812yes—
228C22×C4×C7#4112yes—
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×Dic7—21no—
268C22×Dic7C22×C412yes—
269C22×Dic7C22×C412yes—
270C22×Dic7C22×C412yes—
271C22×Dic7C2×D412yes—
272C22×Dic7C2×D412yes—
273C22×Dic7C2×Q812yes—
274C22×Dic7C2×Q812yes—
275C22×Dic7#4112yes—
276C22×Dic7#4112yes—
277C22×Dic7#4112yes—
278C2×C4×D7—28no—
279C2×C4×D7—28no—
280C2×C4×D7—28no—
281C2×C4×D7—28no—
282C2×C4×D7—44no—
283C2×C4×D7—44no—
284C2×C4×D7—44no—
285C2×C4×D7—44no—
286C2×C4×D7—44no—
287C2×C4×D7—44no—
288C2×C4×D7—44no—
289C2×C4×D7—44no—
290C2×C4×D7—44no—
291C2×C4×D7—44no—
292C2×C4×D7—44no—
293C2×C4×D7—44no—
294C2×C4×D7—44no—
295C2×C4×D7—44no—
296C2×C4×D7—44no—
297C2×C4×D7—44no—
298C2×C4×D7—44no—
299C7×C4⋊C4—44no—
300(C2×D7)⋊C4—28no—
301(C2×D7)⋊C4—28no—
302(C2×D7)⋊C4—44no—
303(C2×D7)⋊C4C4⋊C4116yescomplemented
304C4⋊Dic7—44no—
305C4⋊Dic7—44no—
306Dic7⋊C4—44no—
307Dic7⋊C4—44no—
308Dic7⋊C4—44no—
309C4×Dic7—44no—
310C4×Dic7—44no—
311C24×C4—71no—
312C24×C4—71no—
313C24×C4—71no—
314C22×C4⋊C4—71no—
315C22×C4⋊C4—71no—
316C22×C4⋊C4—71no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4C2×D711yescharacteristic
320C22×C22⋊C4—71no—
321C22×C22⋊C4—71no—
322C22×C22⋊C4—71no—
323C22×C22⋊C4—71no—
324C22×C42—71no—
325C22×C42—71no—
326#385—78no—
327#385—144no—
328#385—144no—
329C4×C22⋊C4—144no—
330C2×#95—71no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C2×#95—71no—
343C2×#95—71no—
344C2×#95—144no—
345C2×#95C2×D711yescharacteristic
346C2×#95C2×D711yescharacteristic
347C2×#95C2×D711yescharacteristic
348C2×#95C2×D711yescharacteristic
349C2×#95C2×D711yescharacteristic
350C2×#95C2×D711yescharacteristic
351C23×C7C23×C411yescharacteristic
352C23×C7C22×D411yescharacteristic
353C23×C7C22×D411yescharacteristic
354C23×C7C22×Q811yescharacteristic
355C23×C7C22×Q811yescharacteristic
356C23×C7C2×#4111yescharacteristic
357C23×C7C2×#4111yescharacteristic
358C23×C7C2×#4111yescharacteristic
359C23×C7C2×#4111yescharacteristic
360C23×C7C2×#4111yescharacteristic
361C23×C7C2×#4111yescharacteristic
362C23×C7H(5,𝔽2)11yescharacteristic
363C23×C7H(5,𝔽2)11yescharacteristic
364C23×C7H(5,𝔽2)11yescharacteristic
365C23×C7H(5,𝔽2)11yescharacteristic
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—22no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—22no—
386C22×D7—22no—
387C22×D7—22no—
388C22×D7—22no—
389C22×D7—22no—
390C22×D7—22no—
391C22×D7—22no—
392C22×D7—22no—
393C22×D7—22no—
394C22×D7C2×C4⋊C414yes—
395C22×D7C4×D414yes—
396C22×D7C4×Q814yes—
397C22×D7#12114yes—
398C22×D7C22⋊Q814yes—
399C22×D7#12514yes—
400C22×D7C4⋊Q814yes—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7C2×C4⋊C414yes—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—22no—
454C2×Dic7—22no—
455C2×Dic7—22no—
456C2×Dic7—22no—
457C2×Dic7—22no—
458C2×Dic7—22no—
459C2×Dic7—22no—
460C2×Dic7—22no—
461C2×Dic7—22no—
462C2×Dic7—22no—
463C2×Dic7—22no—
464C2×Dic7—22no—
465C2×Dic7—22no—
466C2×Dic7—22no—
467C2×Dic7—22no—
468C2×Dic7—22no—
469C2×Dic7—22no—
470C2×Dic7—22no—
471C2×Dic7—22no—
472C2×Dic7—22no—
473C2×Dic7—22no—
474C2×Dic7—41no—
475C2×Dic7—41no—
476C2×Dic7—41no—
477C2×Dic7—41no—
478C2×Dic7—41no—
479C2×Dic7—41no—
480C2×Dic7—41no—
481C2×Dic7—41no—
482C2×Dic7—41no—
483C2×Dic7—41no—
484C2×Dic7—41no—
485C2×Dic7—41no—
486C2×Dic7—41no—
487C2×Dic7—41no—
488C2×Dic7—41no—
489C2×Dic7—41no—
490C2×Dic7—41no—
491C2×Dic7—41no—
492C2×Dic7—41no—
493C2×Dic7—41no—
494C2×Dic7—41no—
495C2×Dic7—41no—
496C2×Dic7—41no—
497C2×Dic7C2×C4⋊C414yes—
498C2×Dic7#12314yes—
499C4×D7—416no—
500C4×D7—416no—
501C4×D7—416no—
502C25—71no—
503C23×C4—71no—
504C23×C4—71no—
505C23×C4—71no—
506C23×C4—71no—
507C23×C4—71no—
508C23×C4—71no—
509C23×C4—74no—
510C23×C4—74no—
511C23×C4—71no—
512C23×C4—142no—
513C23×C4—142no—
514C23×C4—142no—
515C23×C4—142no—
516C23×C4—142no—
517C23×C4—142no—
518C23×C4—142no—
519C23×C4—142no—
520C23×C4—142no—
521C23×C4—142no—
522C23×C4—142no—
523C23×C4—281no—
524C23×C4—281no—
525C23×C4—281no—
526C23×C4—281no—
527C23×C4—281no—
528C23×C4—281no—
529C23×C4—281no—
530C23×C4—281no—
531C23×C4C22×D711yescharacteristic
532C23×C4C22×D711yescharacteristic
533C23×C4C22×D711yescharacteristic
534C23×C4C22×D711yescharacteristic
535C23×C4C22×D711yescharacteristic
536C23×C4C22×D711yescharacteristic
537C23×C4C22×D711yescharacteristic
538C2×C4⋊C4—22no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—41no—
541C2×C4⋊C4—74no—
542C2×C4⋊C4—74no—
543C2×C4⋊C4—142no—
544C2×C4⋊C4—142no—
545C2×C4⋊C4—142no—
546C2×C4⋊C4—142no—
547C2×C4⋊C4—142no—
548C2×C4⋊C4—142no—
549C2×C4⋊C4—281no—
550C2×C4⋊C4—281no—
551C2×C4⋊C4—281no—
552C2×C4⋊C4—281no—
553C2×C4⋊C4—281no—
554C2×C4⋊C4—281no—
555C2×C4⋊C4—281no—
556C2×C22⋊C4—74no—
557C2×C22⋊C4—74no—
558C2×C22⋊C4—74no—
559C2×C22⋊C4—74no—
560C2×C22⋊C4—74no—
561C2×C22⋊C4—142no—
562C2×C22⋊C4—142no—
563C2×C22⋊C4—142no—
564C2×C22⋊C4—142no—
565C2×C22⋊C4—142no—
566C2×C22⋊C4—142no—
567C2×C22⋊C4—142no—
568C2×C42—142no—
569C2×C42—142no—
570C2×C42—142no—
571C2×C42—142no—
572C2×C42—281no—
573C2×C42—281no—
574#95—22no—
575#95—22no—
576#95—22no—
577#95—22no—
578#95—41no—
579#95—74no—
580#95—142no—
581#95—142no—
582#95—142no—
583#95—142no—
584#95—142no—
585#95—142no—
586#95—142no—
587#95—142no—
588#95—281no—
589#95—281no—
590#95—281no—
591#95—281no—
592#95—281no—
593#95C4×D714yescomplemented
594C22×C7C22×C4⋊C411yescharacteristic
595C22×C7C2×C4×D411yescharacteristic
596C22×C7C2×C4×Q811yescharacteristic
597C22×C7C4×#4111yescharacteristic
598C22×C7C4×#4111yescharacteristic
599C22×C7#51811yescharacteristic
600C22×C7#51811yescharacteristic
601C22×C7C2×#12111yescharacteristic
602C22×C7C2×C22⋊Q811yescharacteristic
603C22×C7C2×#12311yescharacteristic
604C22×C7#52511yescharacteristic
605C22×C7C2×#12511yescharacteristic
606C22×C7#52911yescharacteristic
607C22×C7#52911yescharacteristic
608C22×C7C2×C4⋊Q811yescharacteristic
609C22×C7#53411yescharacteristic
610C22×C7#53511yescharacteristic
611C22×C7#53811yescharacteristic
612C22×C7#53811yescharacteristic
613C22×C7#54611yescharacteristic
614C22×C7#54611yescharacteristic
615C22×C7#54611yescharacteristic
616C22×C7#54611yescharacteristic
617C22×C7#55111yescharacteristic
618C22×C7#55111yescharacteristic
619C22×C7#55111yescharacteristic
620C22×C7#55111yescharacteristic
621C22×C7#55411yescharacteristic
622C22×C7#55411yescharacteristic
623C22×C7#55411yescharacteristic
624C22×C7#55411yescharacteristic
625C22×C7#55411yescharacteristic
626C22×C7#55411yescharacteristic
627C22×C7#55411yescharacteristic
628C22×C7#55411yescharacteristic
629C2×D7—24no—
630C2×D7—24no—
631C2×D7—24no—
632C2×D7—24no—
633C2×D7—24no—
634C2×D7—24no—
635C2×D7—24no—
636C2×D7—24no—
637C2×D7—24no—
638C2×D7—24no—
639C2×D7—24no—
640C2×D7—24no—
641C2×D7—24no—
642C2×D7—24no—
643C2×D7#38918yes—
644C4×C7—24no—
645C4×C7—42no—
646C4×C7—42no—
647C4×C7—42no—
648C4×C7—42no—
649C4×C7—42no—
650C4×C7—81no—
651Dic7—24no—
652Dic7—24no—
653Dic7—42no—
654Dic7—42no—
655Dic7—42no—
656Dic7—42no—
657Dic7—81no—
658C24—72no—
659C24—72no—
660C24—72no—
661C24—72no—
662C24—72no—
663C24—72no—
664C24—72no—
665C24—141no—
666C24—141no—
667C24—141no—
668C24—141no—
669C24—141no—
670C24—141no—
671C24—141no—
672C24—141no—
673C24C23×D711yescharacteristic
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—72no—
716C22×C4—72no—
717C22×C4—72no—
718C22×C4—72no—
719C22×C4—72no—
720C22×C4—72no—
721C22×C4—72no—
722C22×C4—72no—
723C22×C4—72no—
724C22×C4—72no—
725C22×C4—148no—
726C22×C4—148no—
727C22×C4—148no—
728C22×C4—148no—
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×C4—141no—
740C22×C4—141no—
741C22×C4—141no—
742C22×C4—141no—
743C22×C4—141no—
744C22×C4—141no—
745C22×C4—141no—
746C22×C4—141no—
747C22×C4—141no—
748C22×C4—141no—
749C22×C4—141no—
750C22×C4—141no—
751C22×C4—141no—
752C22×C4—141no—
753C22×C4—141no—
754C22×C4—141no—
755C22×C4—141no—
756C22×C4—141no—
757C22×C4—141no—
758C22×C4—141no—
759C22×C4—141no—
760C22×C4—141no—
761C22×C4—141no—
762C22×C4—141no—
763C22×C4—141no—
764C22×C4—141no—
765C22×C4—141no—
766C22×C4—141no—
767C22×C4—141no—
768C22×C4—284no—
769C22×C4—284no—
770C22×C4—284no—
771C22×C4—284no—
772C22×C4—284no—
773C22×C4—284no—
774C22×C4—284no—
775C22×C4—284no—
776C22×C4—284no—
777C22×C4—284no—
778C22×C4—284no—
779C22×C4—284no—
780C22×C4—284no—
781C22×C4—284no—
782C22×C4—284no—
783C22×C4—284no—
784C22×C4—284no—
785C22×C4C2×C4×D712yes—
786C22×C4C2×C4×D712yes—
787C22×C4C2×C4×D712yes—
788C22×C4D4×D712yes—
789C22×C4D4×D712yes—
790C22×C4#115912yes—
791C22×C4Q8×D712yes—
792C22×C4Q8×D712yes—
793C4⋊C4—44no—
794C4⋊C4—284no—
795C4⋊C4—284no—
796C4⋊C4—284no—
797C4⋊C4—284no—
798C4⋊C4—284no—
799C22⋊C4—716no—
800C22⋊C4—148no—
801C22⋊C4—148no—
802C22⋊C4—284no—
803C42—284no—
804C42—284no—
805C2×C7C2×#38911yescharacteristic
806C2×C7C4×#12311yescharacteristic
807C2×C7#232111yescharacteristic
808C2×C7#234911yescharacteristic
809C2×C7#234911yescharacteristic
810C2×C7#236811yescharacteristic
811C2×C7#236811yescharacteristic
812C2×C7#241111yescharacteristic
813C2×C7#241211yescharacteristic
814C2×C7#245011yescharacteristic
815C2×C7#245011yescharacteristic
816C2×C7#250211yescharacteristic
817C2×C7#250511yescharacteristic
818C2×C7#250511yescharacteristic
819C2×C7#258311yescharacteristic
820D7—28no—
821C23—74no—
822C23—74no—
823C23—74no—
824C23—74no—
825C23—74no—
826C23—74no—
827C23—74no—
828C23—142no—
829C23—142no—
830C23—142no—
831C23—142no—
832C23—142no—
833C23—142no—
834C23—142no—
835C23—142no—
836C23—142no—
837C23—142no—
838C23—142no—
839C23—142no—
840C23—142no—
841C23—142no—
842C23—142no—
843C23—142no—
844C23—142no—
845C23—142no—
846C23—142no—
847C23—142no—
848C23—142no—
849C23—142no—
850C23—142no—
851C23—142no—
852C23—142no—
853C23—142no—
854C23—142no—
855C23—142no—
856C23C22×C4×D711yescharacteristic
857C23C2×D4×D711yescharacteristic
858C23C2×D4×D711yescharacteristic
859C23C2×#115911yescharacteristic
860C23#654811yescharacteristic
861C23C2×Q8×D711yescharacteristic
862C23C2×Q8×D711yescharacteristic
863C23D7×#4111yescharacteristic
864C23D7×#4111yescharacteristic
865C23D7×#4111yescharacteristic
866C23D7×#4111yescharacteristic
867C23D7×#4111yescharacteristic
868C23#655311yescharacteristic
869C23#655311yescharacteristic
870C23#655311yescharacteristic
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—74no—
920C2×C4—74no—
921C2×C4—142no—
922C2×C4—142no—
923C2×C4—142no—
924C2×C4—142no—
925C2×C4—142no—
926C2×C4—142no—
927C2×C4—142no—
928C2×C4—142no—
929C2×C4—142no—
930C2×C4—142no—
931C2×C4—142no—
932C2×C4—142no—
933C2×C4—142no—
934C2×C4—142no—
935C2×C4—142no—
936C2×C4—142no—
937C2×C4—142no—
938C2×C4—142no—
939C2×C4—142no—
940C2×C4—142no—
941C2×C4—142no—
942C2×C4—142no—
943C2×C4—142no—
944C2×C4—142no—
945C2×C4—2816no—
946C2×C4—2816no—
947C2×C4—2816no—
948C2×C4—281no—
949C2×C4—281no—
950C2×C4—281no—
951C2×C4—281no—
952C2×C4—281no—
953C2×C4—281no—
954C2×C4—281no—
955C2×C4—281no—
956C2×C4—281no—
957C2×C4—281no—
958C2×C4—281no—
959C2×C4—281no—
960C2×C4—281no—
961C2×C4—281no—
962C2×C4—281no—
963C2×C4—281no—
964C2×C4—281no—
965C2×C4—281no—
966C2×C4—281no—
967C2×C4—281no—
968C2×C4—281no—
969C2×C4—281no—
970C2×C4—281no—
971C2×C4D7×C4⋊C414yes—
972C7#1404411yescharacteristic, complemented, Sylow
973C22—78no—
974C22—144no—
975C22—144no—
976C22—144no—
977C22—144no—
978C22—144no—
979C22—144no—
980C22—144no—
981C22—144no—
982C22—144no—
983C22—144no—
984C22—144no—
985C22—144no—
986C22—144no—
987C22—144no—
988C22C2×D7×C4⋊C411yescharacteristic
989C22#9021211yescharacteristic
990C22#9021311yescharacteristic
991C22C4×#115911yescharacteristic
992C22C4×D4×D711yescharacteristic
993C22#9023611yescharacteristic
994C22C4×Q8×D711yescharacteristic
995C22#9028211yescharacteristic
996C22D7×#12111yescharacteristic
997C22#9029711yescharacteristic
998C22#9029811yescharacteristic
999C22D7×C22⋊Q811yescharacteristic
1000C22#9032611yescharacteristic
1001C22#9032611yescharacteristic
1002C22#9032711yescharacteristic
1003C22#9032711yescharacteristic
1004C22D7×#12311yescharacteristic
1005C22#9034411yescharacteristic
1006C22#9034511yescharacteristic
1007C22#9034911yescharacteristic
1008C22#9035011yescharacteristic
1009C22#9036711yescharacteristic
1010C22#9036711yescharacteristic
1011C22#9036911yescharacteristic
1012C22#9037111yescharacteristic
1013C22D7×#12511yescharacteristic
1014C22#9038111yescharacteristic
1015C22#9038111yescharacteristic
1016C22#9038111yescharacteristic
1017C22#9038111yescharacteristic
1018C22#9039511yescharacteristic
1019C22#9039611yescharacteristic
1020C22#9039611yescharacteristic
1021C22#9039711yescharacteristic
1022C22D7×C4⋊Q811yescharacteristic
1023C4—24no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—81no—
1030C4—144no—
1031C4—144no—
1032C4—282no—
1033C4—282no—
1034C4—282no—
1035C4—282no—
1036C4—561no—
1037C2—148no—
1038C2#1173167311yescharacteristic
1039C2#1173183911yescharacteristic
1040C2#1173275511yescharacteristic
1041C2#1173275611yescharacteristic
1042C2#1173289811yescharacteristic
1043C2#1173327211yescharacteristic
1044C2D7×#38911yescharacteristic
1045C2#1173431111yescharacteristic
1046C2#1173455411yescharacteristic
1047C2#1173511311yescharacteristic
1048C2#1173521011yescharacteristic
1049C2#1173540611yescharacteristic
1050C2#1173578911yescharacteristic
1051C2#1173579711yescharacteristic
1052C2#1173579911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1442C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1442D7
hypocenterC7#14044
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
6. C7×#1442C2semidirect
7. #11729317C2semidirect
10. #11727167C2semidirect
11. #11727165C2semidirect
12. #11727163C2semidirect
13. #11727161C2semidirect
14. #11727161C2semidirect
15. Dic7⋊#95C2semidirect
53. #89440C4semidirect
113. C2×C4⋊Dic7C2×C4semidirect
122. C2×Dic7⋊C4C2×C4semidirect
134. C7×#95C2×C4semidirect
148. C7⋊#95C2×C4semidirect
155. #1442D7semidirect
303. (C2×D7)⋊C4C4⋊C4semidirect
593. #95C4×D7semidirect
972. C7#14044semidirect

Maximal subgroups

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

subgroupindex
C2×#897612
C2×#894402
C2×D7×#952
C2×#894382
C7×#14422
#117293172
(C2×D7)⋊#952
#117271672
#117271652
#117271632
#117271612
Dic7⋊#952
#140447