Finite Group Databasebeta

← #13277004

Subgroups — #13277004

Order 1792.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89761C211yesmaximal, characteristic
2C2×#89759C211yesmaximal, characteristic
3C2×#89757C211yesmaximal, characteristic, complemented
4C2×#89440C211yesmaximal, characteristic
5C2×#89440C211yesmaximal, characteristic
6C2×D7×#95C211yesmaximal, characteristic
7C2×#89438C211yesmaximal, characteristic
8C7×#1441C211yesmaximal, characteristic, complemented
9#11729318C211yesmaximal, characteristic, complemented
10(C2×D7)⋊#95C211yesmaximal, characteristic
11#11727174C211yesmaximal, characteristic, complemented
12#11727169C211yesmaximal, characteristic, complemented
13#11727164C211yesmaximal, characteristic, complemented
14#11727160C211yesmaximal, characteristic, complemented
15Dic7⋊#95C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
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#89761C418yescomplemented
52#89759—24no—
53#89757—24no—
54#89440—24no—
55#89440—24no—
56#89438—24no—
57D7×#95—24no—
58#14004—71nomaximal, Sylow
59C24×D7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
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—22no—
84C22×C4×D7—22no—
85C22×C4×D7—22no—
86C22×C4×D7—22no—
87C22×C4×D7—41no—
88C22×C4×D7—41no—
89C22×C4×D7—41no—
90C22×C4×D7—41no—
91C22×C4×D7—41no—
92C22×C4×D7—41no—
93C22×C4×D7C2×C414yes—
94C22×C4×D7Q814yes—
95C2×C7×C4⋊C4—22no—
96C2×C7×C4⋊C4—22no—
97C2×C7×C4⋊C4—22no—
98C2×C7×C4⋊C4—22no—
99C2×C7×C4⋊C4—41no—
100C2×C7×C4⋊C4C2×C414yescomplemented
101C2×(C2×D7)⋊C4—22no—
102C2×(C2×D7)⋊C4—22no—
103C2×(C2×D7)⋊C4—22no—
104C2×(C2×D7)⋊C4—22no—
105C2×(C2×D7)⋊C4—22no—
106C2×(C2×D7)⋊C4—22no—
107C2×(C2×D7)⋊C4—22no—
108C2×(C2×D7)⋊C4C2×C414yes—
109C2×(C2×D7)⋊C4C2×C414yes—
110C2×(C2×D7)⋊C4D414yes—
111C2×(C2×D7)⋊C4D414yes—
112C2×(C2×D7)⋊C4Q814yes—
113C2×C4⋊Dic7—22no—
114C2×C4⋊Dic7—22no—
115C2×C4⋊Dic7—22no—
116C2×C4⋊Dic7—22no—
117C2×C4⋊Dic7—22no—
118C2×C4⋊Dic7—22no—
119C2×C4⋊Dic7—41no—
120C2×C4⋊Dic7—41no—
121C2×C4⋊Dic7—41no—
122C2×Dic7⋊C4—22no—
123C2×Dic7⋊C4—22no—
124C2×Dic7⋊C4—22no—
125C2×Dic7⋊C4—22no—
126C2×Dic7⋊C4—41no—
127C2×Dic7⋊C4—41no—
128C2×Dic7⋊C4—41no—
129C2×Dic7⋊C4—41no—
130C2×Dic7⋊C4C2×C414yescomplemented
131C2×C4×Dic7—22no—
132C2×C4×Dic7—22no—
133C2×C4×Dic7—22no—
134C2×C4×Dic7—22no—
135C2×C4×Dic7—41no—
136C2×C4×Dic7—41no—
137C7×#95—22no—
138C7×#95—22no—
139C7×#95—22no—
140C7×#95—22no—
141C7×#95—41no—
142C7⋊#95—22no—
143C7⋊#95—22no—
144C7⋊#95—22no—
145C7⋊#95—22no—
146C7⋊#95—22no—
147C7⋊#95—22no—
148C7⋊#95—22no—
149C7⋊#95—22no—
150C7⋊#95—22no—
151C7⋊#95—41no—
152C7⋊#95C2×C414yescomplemented
153C7⋊#95C2×C414yescomplemented
154C7⋊#95D414yes—
155C2×#389—71no—
156C2×#385—71no—
157C2×#385—71no—
158C2×#385—71no—
159C2×#380—71no—
160C2×C4×C22⋊C4—71no—
161C22×#95—71no—
162#1444—71no—
163#1442—71no—
164#1441—71no—
165#1441D711yescharacteristic, complemented
166#1436—71no—
167#1436—71no—
168C4⋊#95—71no—
169C22⋊#95—71no—
170C24×C7C2411yescharacteristic
171C23×D7—21no—
172C23×D7—21no—
173C23×D7—21no—
174C23×D7—21no—
175C23×D7—21no—
176C23×D7—21no—
177C23×D7—21no—
178C23×D7—21no—
179C23×D7C22×C412yes—
180C23×D7C2×D412yes—
181C23×D7C2×D412yes—
182C23×D7C2×Q812yes—
183C23×D7C2×Q812yes—
184C23×D7#4112yes—
185C23×D7#4112yes—
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×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7C22×C412yes—
226C22×C4×C7C22×C412yes—
227C22×C4×C7C22×C412yes—
228C22×C4×C7C2×D412yes—
229C22×C4×C7C2×D412yes—
230C22×C4×C7C2×D412yes—
231C22×C4×C7C2×Q812yes—
232C22×C4×C7C2×Q812yes—
233C22×C4×C7#4112yes—
234C22×C4×C7#4112yes—
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×Dic7—21no—
269C22×Dic7—21no—
270C22×Dic7—21no—
271C22×Dic7—21no—
272C22×Dic7—21no—
273C22×Dic7—21no—
274C22×Dic7C22×C412yes—
275C22×Dic7C22×C412yes—
276C22×Dic7C22×C412yes—
277C22×Dic7C2×D412yes—
278C22×Dic7C2×D412yes—
279C22×Dic7C2×D412yes—
280C22×Dic7C2×D412yes—
281C22×Dic7C2×Q812yes—
282C22×Dic7C2×Q812yes—
283C22×Dic7#4112yes—
284C2×C4×D7—28no—
285C2×C4×D7—28no—
286C2×C4×D7—28no—
287C2×C4×D7—28no—
288C2×C4×D7—28no—
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—
299C2×C4×D7—44no—
300C2×C4×D7—44no—
301C2×C4×D7—44no—
302C2×C4×D7—44no—
303C2×C4×D7—44no—
304C2×C4×D7—44no—
305C7×C4⋊C4—28no—
306C7×C4⋊C4—44no—
307(C2×D7)⋊C4—28no—
308(C2×D7)⋊C4—28no—
309(C2×D7)⋊C4—44no—
310(C2×D7)⋊C4C4⋊C4116yescomplemented
311C4⋊Dic7—44no—
312C4⋊Dic7—44no—
313C4⋊Dic7—44no—
314Dic7⋊C4—44no—
315Dic7⋊C4—44no—
316Dic7⋊C4—44no—
317C4×Dic7—44no—
318C4×Dic7—44no—
319C24×C4—71no—
320C24×C4—71no—
321C24×C4—71no—
322C22×C4⋊C4—71no—
323C22×C4⋊C4—71no—
324C22×C4⋊C4—71no—
325C22×C4⋊C4—71no—
326C22×C4⋊C4—71no—
327C22×C4⋊C4—71no—
328C22×C4⋊C4C2×D711yescharacteristic
329C22×C4⋊C4C2×D711yescharacteristic
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4—71no—
333C22×C22⋊C4—71no—
334C22×C42—71no—
335C22×C42—71no—
336#389—144no—
337#385—78no—
338#385—144no—
339#385—144no—
340#380—144no—
341C4×C22⋊C4—144no—
342C2×#95—71no—
343C2×#95—71no—
344C2×#95—71no—
345C2×#95—71no—
346C2×#95—71no—
347C2×#95—71no—
348C2×#95—71no—
349C2×#95—71no—
350C2×#95—71no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—71no—
355C2×#95—144no—
356C2×#95C2×D711yescharacteristic
357C2×#95C2×D711yescharacteristic
358C2×#95C2×D711yescharacteristic
359C2×#95C2×D711yescharacteristic
360C2×#95C2×D711yescharacteristic
361C23×C7C23×C411yescharacteristic
362C23×C7C22×D411yescharacteristic
363C23×C7C22×D411yescharacteristic
364C23×C7C22×D411yescharacteristic
365C23×C7C22×Q811yescharacteristic
366C23×C7C22×Q811yescharacteristic
367C23×C7C2×#4111yescharacteristic
368C23×C7C2×#4111yescharacteristic
369C23×C7C2×#4111yescharacteristic
370C23×C7C2×#4111yescharacteristic
371C23×C7C2×#4111yescharacteristic
372C23×C7H(5,𝔽2)11yescharacteristic
373C23×C7H(5,𝔽2)11yescharacteristic
374C23×C7H(5,𝔽2)11yescharacteristic
375C23×C72−1+411yescharacteristic
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×D7—22no—
395C22×D7—22no—
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—22no—
400C22×D7—22no—
401C22×D7—22no—
402C22×D7—22no—
403C22×D7—22no—
404C22×D7C2×C4⋊C414yes—
405C22×D7C4×D414yes—
406C22×D7C4×Q814yes—
407C22×D7#12114yes—
408C22×D7C22⋊Q814yes—
409C22×D7#12514yes—
410C22×D7C4⋊Q814yes—
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—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
430C2×C4×C7—22no—
431C2×C4×C7—22no—
432C2×C4×C7—22no—
433C2×C4×C7—22no—
434C2×C4×C7—22no—
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×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7—41no—
454C2×C4×C7—41no—
455C2×C4×C7—41no—
456C2×C4×C7—41no—
457C2×C4×C7—41no—
458C2×C4×C7C2×C4⋊C414yes—
459C2×C4×C7C4×D414yes—
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—22no—
475C2×Dic7—22no—
476C2×Dic7—22no—
477C2×Dic7—22no—
478C2×Dic7—22no—
479C2×Dic7—22no—
480C2×Dic7—22no—
481C2×Dic7—22no—
482C2×Dic7—22no—
483C2×Dic7—22no—
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×Dic7—41no—
498C2×Dic7—41no—
499C2×Dic7—41no—
500C2×Dic7—41no—
501C2×Dic7—41no—
502C2×Dic7—41no—
503C2×Dic7—41no—
504C2×Dic7—41no—
505C2×Dic7—41no—
506C2×Dic7—41no—
507C2×Dic7C2×C4⋊C414yes—
508C2×Dic7C22⋊Q814yes—
509C4×D7—416no—
510C4×D7—416no—
511C4×D7—416no—
512C25—71no—
513C23×C4—71no—
514C23×C4—71no—
515C23×C4—71no—
516C23×C4—71no—
517C23×C4—71no—
518C23×C4—71no—
519C23×C4—74no—
520C23×C4—74no—
521C23×C4—71no—
522C23×C4—142no—
523C23×C4—142no—
524C23×C4—142no—
525C23×C4—142no—
526C23×C4—142no—
527C23×C4—142no—
528C23×C4—142no—
529C23×C4—142no—
530C23×C4—142no—
531C23×C4—142no—
532C23×C4—142no—
533C23×C4—142no—
534C23×C4—142no—
535C23×C4—281no—
536C23×C4—281no—
537C23×C4—281no—
538C23×C4—281no—
539C23×C4—281no—
540C23×C4—281no—
541C23×C4C22×D711yescharacteristic
542C23×C4C22×D711yescharacteristic
543C23×C4C22×D711yescharacteristic
544C23×C4C22×D711yescharacteristic
545C23×C4C22×D711yescharacteristic
546C23×C4C22×D711yescharacteristic
547C23×C4C22×D711yescharacteristic
548C2×C4⋊C4—22no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—22no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4—74no—
554C2×C4⋊C4—142no—
555C2×C4⋊C4—142no—
556C2×C4⋊C4—142no—
557C2×C4⋊C4—142no—
558C2×C4⋊C4—142no—
559C2×C4⋊C4—142no—
560C2×C4⋊C4—142no—
561C2×C4⋊C4—142no—
562C2×C4⋊C4—142no—
563C2×C4⋊C4—142no—
564C2×C4⋊C4—281no—
565C2×C4⋊C4—281no—
566C2×C4⋊C4—281no—
567C2×C4⋊C4—281no—
568C2×C4⋊C4—281no—
569C2×C4⋊C4—281no—
570C2×C4⋊C4—281no—
571C2×C4⋊C4C4×D714yescomplemented
572C2×C22⋊C4—74no—
573C2×C22⋊C4—74no—
574C2×C22⋊C4—74no—
575C2×C22⋊C4—74no—
576C2×C22⋊C4—74no—
577C2×C22⋊C4—142no—
578C2×C22⋊C4—142no—
579C2×C22⋊C4—142no—
580C2×C22⋊C4—142no—
581C2×C22⋊C4—142no—
582C2×C22⋊C4—142no—
583C2×C22⋊C4—142no—
584C2×C42—142no—
585C2×C42—142no—
586C2×C42—142no—
587C2×C42—142no—
588C2×C42—281no—
589C2×C42—281no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—41no—
595#95—74no—
596#95—74no—
597#95—74no—
598#95—142no—
599#95—142no—
600#95—142no—
601#95—142no—
602#95—142no—
603#95—142no—
604#95—142no—
605#95—142no—
606#95—142no—
607#95—281no—
608C22×C7C22×C4⋊C411yescharacteristic
609C22×C7C2×C4×D411yescharacteristic
610C22×C7C2×C4×D411yescharacteristic
611C22×C7C2×C4×Q811yescharacteristic
612C22×C7C4×#4111yescharacteristic
613C22×C7#51811yescharacteristic
614C22×C7#52011yescharacteristic
615C22×C7C2×#12111yescharacteristic
616C22×C7C2×C22⋊Q811yescharacteristic
617C22×C7C2×C22⋊Q811yescharacteristic
618C22×C7#52511yescharacteristic
619C22×C7C2×#12511yescharacteristic
620C22×C7#52911yescharacteristic
621C22×C7C2×C4⋊Q811yescharacteristic
622C22×C7#53311yescharacteristic
623C22×C7#53811yescharacteristic
624C22×C7#53911yescharacteristic
625C22×C7#54311yescharacteristic
626C22×C7#54411yescharacteristic
627C22×C7D4211yescharacteristic
628C22×C7D4211yescharacteristic
629C22×C7#54611yescharacteristic
630C22×C7#54611yescharacteristic
631C22×C7#54611yescharacteristic
632C22×C7#54611yescharacteristic
633C22×C7#54611yescharacteristic
634C22×C7#54711yescharacteristic
635C22×C7#54711yescharacteristic
636C22×C7D4×Q811yescharacteristic
637C22×C7#55111yescharacteristic
638C22×C7#55111yescharacteristic
639C22×C7#55211yescharacteristic
640C22×C7#55411yescharacteristic
641C22×C7#55411yescharacteristic
642C22×C7#55411yescharacteristic
643C2×D7—24no—
644C2×D7—24no—
645C2×D7—24no—
646C2×D7—24no—
647C2×D7—24no—
648C2×D7—24no—
649C2×D7—24no—
650C2×D7—24no—
651C2×D7—24no—
652C2×D7—24no—
653C2×D7—24no—
654C2×D7—24no—
655C2×D7—24no—
656C2×D7—24no—
657C2×D7#38918yescomplemented
658C4×C7—24no—
659C4×C7—24no—
660C4×C7—42no—
661C4×C7—42no—
662C4×C7—42no—
663C4×C7—42no—
664C4×C7—81no—
665Dic7—24no—
666Dic7—24no—
667Dic7—42no—
668Dic7—42no—
669Dic7—42no—
670Dic7—42no—
671Dic7—81no—
672C24—72no—
673C24—72no—
674C24—72no—
675C24—72no—
676C24—72no—
677C24—72no—
678C24—72no—
679C24—141no—
680C24—141no—
681C24—141no—
682C24—141no—
683C24—141no—
684C24—141no—
685C24—141no—
686C24—141no—
687C24C23×D711yescharacteristic
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—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—72no—
728C22×C4—72no—
729C22×C4—72no—
730C22×C4—72no—
731C22×C4—72no—
732C22×C4—72no—
733C22×C4—72no—
734C22×C4—72no—
735C22×C4—72no—
736C22×C4—72no—
737C22×C4—148no—
738C22×C4—148no—
739C22×C4—148no—
740C22×C4—148no—
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—141no—
769C22×C4—141no—
770C22×C4—141no—
771C22×C4—141no—
772C22×C4—141no—
773C22×C4—148no—
774C22×C4—141no—
775C22×C4—141no—
776C22×C4—141no—
777C22×C4—141no—
778C22×C4—141no—
779C22×C4—141no—
780C22×C4—141no—
781C22×C4—284no—
782C22×C4—284no—
783C22×C4—284no—
784C22×C4—284no—
785C22×C4—284no—
786C22×C4—284no—
787C22×C4—284no—
788C22×C4—284no—
789C22×C4—284no—
790C22×C4—284no—
791C22×C4—284no—
792C22×C4—284no—
793C22×C4—284no—
794C22×C4—284no—
795C22×C4—284no—
796C22×C4—284no—
797C22×C4C2×C4×D712yes—
798C22×C4C2×C4×D712yes—
799C22×C4C2×C4×D712yes—
800C22×C4D4×D712yes—
801C22×C4D4×D712yes—
802C22×C4D4×D712yes—
803C22×C4#115912yes—
804C22×C4Q8×D712yes—
805C22×C4Q8×D712yes—
806C22×C4#116112yes—
807C4⋊C4—28no—
808C4⋊C4—44no—
809C4⋊C4—284no—
810C4⋊C4—284no—
811C4⋊C4—284no—
812C4⋊C4—284no—
813C4⋊C4—284no—
814C4⋊C4—284no—
815C22⋊C4—716no—
816C22⋊C4—148no—
817C22⋊C4—148no—
818C22⋊C4—284no—
819C42—284no—
820C42—284no—
821C2×C7C2×#38911yescharacteristic
822C2×C7C4×C22⋊Q811yescharacteristic
823C2×C7#232911yescharacteristic
824C2×C7D4×C4⋊C411yescharacteristic
825C2×C7#234911yescharacteristic
826C2×C7#235811yescharacteristic
827C2×C7#235911yescharacteristic
828C2×C7#242411yescharacteristic
829C2×C7#242511yescharacteristic
830C2×C7#243711yescharacteristic
831C2×C7#243811yescharacteristic
832C2×C7#244011yescharacteristic
833C2×C7#247311yescharacteristic
834C2×C7#250511yescharacteristic
835C2×C7#254911yescharacteristic
836D7—28no—
837C23—74no—
838C23—74no—
839C23—74no—
840C23—74no—
841C23—74no—
842C23—74no—
843C23—74no—
844C23—142no—
845C23—142no—
846C23—142no—
847C23—142no—
848C23—142no—
849C23—142no—
850C23—142no—
851C23—142no—
852C23—142no—
853C23—142no—
854C23—142no—
855C23—142no—
856C23—142no—
857C23—142no—
858C23—142no—
859C23—142no—
860C23—142no—
861C23—142no—
862C23—142no—
863C23—142no—
864C23—142no—
865C23—142no—
866C23—142no—
867C23—142no—
868C23—142no—
869C23—142no—
870C23—142no—
871C23—142no—
872C23C22×C4×D711yescharacteristic
873C23C2×D4×D711yescharacteristic
874C23C2×D4×D711yescharacteristic
875C23C2×D4×D711yescharacteristic
876C23C2×#115911yescharacteristic
877C23#654811yescharacteristic
878C23C2×Q8×D711yescharacteristic
879C23C2×Q8×D711yescharacteristic
880C23C2×#116111yescharacteristic
881C23D7×#4111yescharacteristic
882C23D7×#4111yescharacteristic
883C23D7×#4111yescharacteristic
884C23#655311yescharacteristic
885C23#655311yescharacteristic
886C23#655411yescharacteristic
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
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—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—74no—
935C2×C4—74no—
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—142no—
946C2×C4—142no—
947C2×C4—142no—
948C2×C4—142no—
949C2×C4—142no—
950C2×C4—142no—
951C2×C4—142no—
952C2×C4—142no—
953C2×C4—142no—
954C2×C4—142no—
955C2×C4—142no—
956C2×C4—142no—
957C2×C4—142no—
958C2×C4—142no—
959C2×C4—142no—
960C2×C4—2816no—
961C2×C4—2816no—
962C2×C4—2816no—
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×C4—281no—
972C2×C4—281no—
973C2×C4—281no—
974C2×C4—281no—
975C2×C4—281no—
976C2×C4—281no—
977C2×C4—281no—
978C2×C4—281no—
979C2×C4—281no—
980C2×C4—281no—
981C2×C4—281no—
982C2×C4—281no—
983C2×C4—281no—
984C2×C4—281no—
985C2×C4—281no—
986C2×C4(C22⋊D7)⋊C414yes—
987C2×C4D7×C4⋊C414yes—
988C7#1400411yescharacteristic, complemented, Sylow
989C22—78no—
990C22—144no—
991C22—144no—
992C22—144no—
993C22—144no—
994C22—144no—
995C22—144no—
996C22—144no—
997C22—144no—
998C22—144no—
999C22—144no—
1000C22—144no—
1001C22—144no—
1002C22—144no—
1003C22—144no—
1004C22C2×(C22⋊D7)⋊C411yescharacteristic
1005C22C2×D7×C4⋊C411yescharacteristic
1006C22#9021411yescharacteristic
1007C22C4×D4×D711yescharacteristic
1008C22#9023611yescharacteristic
1009C22C4×Q8×D711yescharacteristic
1010C22C4×#116111yescharacteristic
1011C22#9028211yescharacteristic
1012C22D7×#12111yescharacteristic
1013C22#9030011yescharacteristic
1014C22#9030011yescharacteristic
1015C22#9030111yescharacteristic
1016C22#9030211yescharacteristic
1017C22#9030311yescharacteristic
1018C22D7×C22⋊Q811yescharacteristic
1019C22D7×C22⋊Q811yescharacteristic
1020C22#9031811yescharacteristic
1021C22#9032111yescharacteristic
1022C22#9032111yescharacteristic
1023C22#9032311yescharacteristic
1024C22#9032511yescharacteristic
1025C22#9032611yescharacteristic
1026C22#9034611yescharacteristic
1027C22#9034911yescharacteristic
1028C22#9035111yescharacteristic
1029C22#9037111yescharacteristic
1030C22D7×#12511yescharacteristic
1031C22#9038011yescharacteristic
1032C22#9038111yescharacteristic
1033C22#9038511yescharacteristic
1034C22#9039511yescharacteristic
1035C22#9039611yescharacteristic
1036C22D7×C4⋊Q811yescharacteristic
1037C22#9041911yescharacteristic
1038C22#9042111yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—81no—
1046C4—144no—
1047C4—144no—
1048C4—282no—
1049C4—282no—
1050C4—282no—
1051C4—282no—
1052C4—561no—
1053C2—148no—
1054C2#1173145511yescharacteristic
1055C2#1173232411yescharacteristic
1056C2#1173274411yescharacteristic
1057C2#1173275311yescharacteristic
1058C2D7×#38911yescharacteristic
1059C2#1173364811yescharacteristic
1060C2#1173392411yescharacteristic
1061C2#1173456011yescharacteristic
1062C2#1173469811yescharacteristic
1063C2#1173486111yescharacteristic
1064C2#1173486311yescharacteristic
1065C2#1173519011yescharacteristic
1066C2#1173520311yescharacteristic
1067C2#1173539411yescharacteristic
1068C2#1173579711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1441C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1441D7
hypocenterC7#14004
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. C2×#89757C2semidirect
8. C7×#1441C2semidirect
9. #11729318C2semidirect
11. #11727174C2semidirect
12. #11727169C2semidirect
13. #11727164C2semidirect
14. #11727160C2semidirect
15. Dic7⋊#95C2semidirect
51. #89761C4semidirect
100. C2×C7×C4⋊C4C2×C4semidirect
130. C2×Dic7⋊C4C2×C4semidirect
152. C7⋊#95C2×C4semidirect
153. C7⋊#95C2×C4semidirect
165. #1441D7semidirect
310. (C2×D7)⋊C4C4⋊C4semidirect
571. C2×C4⋊C4C4×D7semidirect
657. C2×D7#389semidirect
988. C7#14004semidirect

Maximal subgroups

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

subgroupindex
C2×#897612
C2×#897592
C2×#897572
C2×#894402
C2×D7×#952
C2×#894382
C7×#14412
#117293182
(C2×D7)⋊#952
#117271742
#117271692
#117271642
#117271602
Dic7⋊#952
#140047