Finite Group Databasebeta

← #13281768

Subgroups — #13281768

Order 1792.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C211yesmaximal, characteristic
2C2×#89757C211yesmaximal, characteristic, complemented
3C2×#89723C211yesmaximal, characteristic
4C2×#89722C211yesmaximal, characteristic
5C2×#89722C211yesmaximal, characteristic
6C2×#89722C211yesmaximal, characteristic
7C2×#89707C211yesmaximal, characteristic, complemented
8#11729319C211yesmaximal, characteristic, complemented
9#11729300C211yesmaximal, characteristic
10#11729300C211yesmaximal, characteristic
11#11729288C211yesmaximal, characteristic, complemented
12#11727173C211yesmaximal, characteristic, complemented
13#11727173C211yesmaximal, characteristic, complemented
14#11727166C211yesmaximal, characteristic, complemented
15#11727161C211yesmaximal, characteristic, complemented
16C24×Dic7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×C4⋊Dic7C2211yescharacteristic
32C22×C4⋊Dic7C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C7×#388C418yescomplemented
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#89757—24no—
53#89723—24no—
54#89722—24no—
55#89722—24no—
56#89722—24no—
57#89707—24no—
58#14405—71nomaximal, Sylow
59C25×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×Dic7—22no—
67C23×Dic7—22no—
68C23×Dic7—22no—
69C23×Dic7—41no—
70C23×Dic7—41no—
71C23×Dic7—41no—
72C23×Dic7—41no—
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4C2×C414yescomplemented
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4C2×C414yes—
89C2×C7×C22⋊C4C2×C414yes—
90C2×C7×C22⋊C4C2×C414yes—
91C2×C7×C22⋊C4D414yes—
92C2×C7×C22⋊C4Q814yes—
93C2×C42×C7—22no—
94C2×C42×C7—22no—
95C2×C42×C7C2×C414yescomplemented
96C2×C22⋊Dic7—22no—
97C2×C22⋊Dic7—22no—
98C2×C22⋊Dic7—22no—
99C2×C22⋊Dic7—22no—
100C2×C22⋊Dic7—22no—
101C2×C22⋊Dic7—41no—
102C2×C22⋊Dic7—41no—
103C2×C22⋊Dic7—41no—
104C2×C22⋊Dic7—41no—
105C2×C4⋊Dic7—22no—
106C2×C4⋊Dic7—22no—
107C2×C4⋊Dic7—22no—
108C2×C4⋊Dic7—22no—
109C2×C4⋊Dic7—22no—
110C2×C4⋊Dic7—22no—
111C2×C4⋊Dic7—22no—
112C2×C4⋊Dic7—22no—
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×C4⋊Dic7—41no—
123C2×C4⋊Dic7—41no—
124C2×C4⋊Dic7—41no—
125C2×C4⋊Dic7—41no—
126C2×C4⋊Dic7—41no—
127C2×C4⋊Dic7—41no—
128C2×C4⋊Dic7—41no—
129C2×C4⋊Dic7—41no—
130C2×C4⋊Dic7—41no—
131C2×C4⋊Dic7D414yes—
132C2×C4×Dic7—22no—
133C2×C4×Dic7—22no—
134C2×C4×Dic7—41no—
135C7×#95C2×C414yescomplemented
136C7×#95C2×C414yescomplemented
137C7⋊#95—22no—
138C7⋊#95—22no—
139C7⋊#95—22no—
140C7⋊#95—22no—
141C7⋊#95—22no—
142C7⋊#95—22no—
143C7⋊#95—22no—
144C7⋊#95—22no—
145C7⋊#95—22no—
146C7⋊#95—22no—
147C7⋊#95—41no—
148C7⋊#95—41no—
149C7⋊#95—41no—
150C7⋊#95D414yes—
151C2×#389—71no—
152C2×#388—71no—
153C2×#388D711yescharacteristic
154C2×#385—71no—
155C2×#385—71no—
156C2×#385—71no—
157C2×#384—71no—
158#1444—71no—
159#1444—71no—
160#1442—71no—
161#1441—71no—
162#1439—71no—
163#1439—71no—
164#1436—71no—
165#1434—71no—
166C24×C7—21no—
167C24×C7—21no—
168C24×C7—21no—
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7—21no—
173C24×C7—21no—
174C24×C7—21no—
175C24×C7—21no—
176C24×C7—21no—
177C24×C7—21no—
178C24×C7C22×C412yes—
179C24×C7C2×D412yes—
180C24×C7C2×Q812yes—
181C24×C7C2411yescharacteristic
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×C7C22×C412yes—
211C22×C4×C7C22×C412yes—
212C22×C4×C7C22×C412yes—
213C22×C4×C7C22×C412yes—
214C22×C4×C7C22×C412yes—
215C22×C4×C7C22×C412yes—
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2×D412yes—
219C22×C4×C7C2×D412yes—
220C22×C4×C7C2×Q812yes—
221C22×C4×C7C2×Q812yes—
222C22×C4×C7#4112yes—
223C22×C4×C7#4112yes—
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×Dic7—21no—
268C22×Dic7—21no—
269C22×Dic7—21no—
270C22×Dic7—21no—
271C22×Dic7—21no—
272C22×Dic7—21no—
273C22×Dic7—21no—
274C22×Dic7—21no—
275C22×Dic7—21no—
276C22×Dic7—44no—
277C22×Dic7—44no—
278C22×Dic7—44no—
279C22×Dic7—44no—
280C22×Dic7—44no—
281C22×Dic7—44no—
282C22×Dic7—44no—
283C22×Dic7C2×D412yes—
284C22×Dic7C2×D412yes—
285C22×Dic7C2×D412yes—
286C22×Dic7C2×D412yes—
287C7×C4⋊C4—28no—
288C7×C22⋊C4—28no—
289C7×C22⋊C4—28no—
290C7×C22⋊C4C4⋊C4116yescomplemented
291C42×C7—28no—
292C22⋊Dic7—44no—
293C22⋊Dic7—44no—
294C22⋊Dic7—44no—
295C4⋊Dic7—44no—
296C4⋊Dic7—44no—
297C4⋊Dic7—44no—
298C4⋊Dic7—44no—
299C4⋊Dic7—44no—
300C4⋊Dic7—44no—
301C4⋊Dic7—44no—
302C4⋊Dic7—44no—
303C4⋊Dic7—44no—
304C4×Dic7—44no—
305C24×C4—71no—
306C22×C4⋊C4—71no—
307C22×C4⋊C4—71no—
308C22×C4⋊C4—71no—
309C22×C4⋊C4—71no—
310C22×C4⋊C4—71no—
311C22×C4⋊C4—71no—
312C22×C4⋊C4—71no—
313C22×C4⋊C4—71no—
314C22×C4⋊C4—71no—
315C22×C4⋊C4C2×D711yescharacteristic
316C22×C22⋊C4—71no—
317C22×C22⋊C4—71no—
318C22×C22⋊C4—71no—
319C22×C22⋊C4C2×D711yescharacteristic
320C22×C22⋊C4C2×D711yescharacteristic
321C22×C22⋊C4C2×D711yescharacteristic
322C22×C42—71no—
323C22×C42C2×D711yescharacteristic
324#389—144no—
325#388—144no—
326#388Dic718yescomplemented
327#385—144no—
328#385—144no—
329#385—144no—
330#384—144no—
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—71no—
345C2×#95C2×D711yescharacteristic
346C2×#95C2×D711yescharacteristic
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—41no—
366C23×C7—41no—
367C23×C7—41no—
368C23×C7—41no—
369C23×C7—41no—
370C23×C7—41no—
371C23×C7—41no—
372C23×C7—41no—
373C23×C7—41no—
374C23×C7—41no—
375C23×C7—41no—
376C23×C7—41no—
377C23×C7—41no—
378C23×C7—41no—
379C23×C7—41no—
380C23×C7—41no—
381C23×C7C2×C4⋊C414yes—
382C23×C7C23×C411yescharacteristic
383C23×C7C22×D411yescharacteristic
384C23×C7C22×D411yescharacteristic
385C23×C7C22×D411yescharacteristic
386C23×C7C22×Q811yescharacteristic
387C23×C7C2×#4111yescharacteristic
388C23×C7C2×#4111yescharacteristic
389C23×C7H(5,𝔽2)11yescharacteristic
390C23×C7H(5,𝔽2)11yescharacteristic
391C23×C7H(5,𝔽2)11yescharacteristic
392C23×C7H(5,𝔽2)11yescharacteristic
393C23×C72−1+411yescharacteristic
394C23×C72−1+411yescharacteristic
395C23×C72−1+411yescharacteristic
396C23×C72−1+411yescharacteristic
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
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—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
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×C7C2×C4⋊C414yes—
436C2×C4×C7C2×C4⋊C414yes—
437C2×C4×C7C4×D414yes—
438C2×C4×C7C4×D414yes—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—416no—
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—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—
496C25C22×D711yescharacteristic
497C23×C4—71no—
498C23×C4—71no—
499C23×C4—71no—
500C23×C4—71no—
501C23×C4—71no—
502C23×C4—71no—
503C23×C4—71no—
504C23×C4—71no—
505C23×C4—142no—
506C23×C4—142no—
507C23×C4—142no—
508C23×C4—281no—
509C23×C4—281no—
510C23×C4—281no—
511C23×C4—281no—
512C23×C4C22×D711yescharacteristic
513C23×C4C22×D711yescharacteristic
514C23×C4C22×D711yescharacteristic
515C23×C4C22×D711yescharacteristic
516C23×C4C22×D711yescharacteristic
517C23×C4C22×D711yescharacteristic
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—74no—
521C2×C4⋊C4—142no—
522C2×C4⋊C4—142no—
523C2×C4⋊C4—142no—
524C2×C4⋊C4—142no—
525C2×C4⋊C4—142no—
526C2×C4⋊C4—142no—
527C2×C4⋊C4—142no—
528C2×C4⋊C4—142no—
529C2×C4⋊C4—142no—
530C2×C4⋊C4—142no—
531C2×C4⋊C4—142no—
532C2×C4⋊C4—142no—
533C2×C4⋊C4—142no—
534C2×C4⋊C4—142no—
535C2×C4⋊C4—281no—
536C2×C4⋊C4—281no—
537C2×C4⋊C4—281no—
538C2×C4⋊C4—281no—
539C2×C4⋊C4—281no—
540C2×C4⋊C4—281no—
541C2×C4⋊C4—281no—
542C2×C4⋊C4—281no—
543C2×C4⋊C4—281no—
544C2×C4⋊C4—281no—
545C2×C4⋊C4—281no—
546C2×C4⋊C4—281no—
547C2×C4⋊C4C2×Dic714yescomplemented
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—142no—
553C2×C22⋊C4—142no—
554C2×C22⋊C4—142no—
555C2×C22⋊C4—142no—
556C2×C22⋊C4—142no—
557C2×C22⋊C4—281no—
558C2×C22⋊C4—281no—
559C2×C22⋊C4—281no—
560C2×C22⋊C4—281no—
561C2×C22⋊C4Dic1414yes—
562C2×C22⋊C4D2814yes—
563C2×C22⋊C4C2×Dic714yes—
564C2×C22⋊C4C2×Dic714yes—
565C2×C22⋊C4C2×Dic714yes—
566C2×C42—22no—
567C2×C42—22no—
568C2×C42—142no—
569C2×C42—142no—
570C2×C42—281no—
571C2×C42C2×Dic714yescomplemented
572#95—74no—
573#95—142no—
574#95—142no—
575#95—142no—
576#95—142no—
577#95—142no—
578#95—142no—
579#95—142no—
580#95—142no—
581#95—142no—
582#95—142no—
583#95—281no—
584#95—281no—
585#95—281no—
586#95C2×Dic714yescomplemented
587#95C2×Dic714yescomplemented
588C22×C7—24no—
589C22×C7—24no—
590C22×C7—24no—
591C22×C7—42no—
592C22×C7—42no—
593C22×C7—42no—
594C22×C7—42no—
595C22×C7—42no—
596C22×C7—42no—
597C22×C7—42no—
598C22×C7—42no—
599C22×C7—42no—
600C22×C7—42no—
601C22×C7—42no—
602C22×C7—42no—
603C22×C7C22×C4⋊C411yescharacteristic
604C22×C7C2×C4×D411yescharacteristic
605C22×C7C2×C4×D411yescharacteristic
606C22×C7#52011yescharacteristic
607C22×C7#52011yescharacteristic
608C22×C7#52011yescharacteristic
609C22×C7#52011yescharacteristic
610C22×C7#53411yescharacteristic
611C22×C7#53511yescharacteristic
612C22×C7#53511yescharacteristic
613C22×C7#53611yescharacteristic
614C22×C7#53611yescharacteristic
615C22×C7#53611yescharacteristic
616C22×C7#53911yescharacteristic
617C22×C7#53911yescharacteristic
618C22×C7#54211yescharacteristic
619C22×C7#54211yescharacteristic
620C22×C7#54411yescharacteristic
621C22×C7#54411yescharacteristic
622C22×C7D4211yescharacteristic
623C22×C7D4211yescharacteristic
624C22×C7D4211yescharacteristic
625C22×C7#54711yescharacteristic
626C22×C7#54711yescharacteristic
627C22×C7#54711yescharacteristic
628C22×C7#54811yescharacteristic
629C22×C7D4×Q811yescharacteristic
630C22×C7D4×Q811yescharacteristic
631C22×C7#55311yescharacteristic
632C22×C7#55411yescharacteristic
633C22×C7#55411yescharacteristic
634C22×C7#56011yescharacteristic
635C22×C7#56311yescharacteristic
636C22×C7#56311yescharacteristic
637C22×C7#56311yescharacteristic
638C4×C7—24no—
639C4×C7—24no—
640C4×C7—24no—
641C4×C7—24no—
642C4×C7—42no—
643C4×C7—42no—
644Dic7—42no—
645Dic7—42no—
646Dic7—42no—
647Dic7—42no—
648Dic7—81no—
649Dic7—81no—
650Dic7—81no—
651Dic7—81no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24C2×Dic1412yes—
665C24C2×D2812yes—
666C24C22×Dic712yes—
667C24C23×D711yescharacteristic
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—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—72no—
697C22×C4—72no—
698C22×C4—72no—
699C22×C4—72no—
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×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—284no—
753C22×C4—284no—
754C22×C4—284no—
755C22×C4—284no—
756C22×C4—284no—
757C22×C4—284no—
758C22×C4—284no—
759C22×C4C2×Dic1412yes—
760C22×C4C2×Dic1412yes—
761C22×C4C2×D2812yes—
762C22×C4C2×D2812yes—
763C22×C4D4×D712yes—
764C22×C4D4×D712yes—
765C22×C4#115912yes—
766C22×C4#115912yes—
767C22×C4C22×Dic712yes—
768C22×C4C22×Dic712yes—
769C22×C4C22×Dic712yes—
770C22×C4C22×Dic712yes—
771C22×C4C22×Dic712yes—
772C22×C4C22×Dic712yes—
773C4⋊C4—28no—
774C4⋊C4—284no—
775C4⋊C4—284no—
776C4⋊C4—284no—
777C4⋊C4—284no—
778C4⋊C4—284no—
779C4⋊C4—284no—
780C4⋊C4—284no—
781C4⋊C4—284no—
782C4⋊C4—284no—
783C22⋊C4—28no—
784C22⋊C4—28no—
785C22⋊C4—284no—
786C22⋊C4—284no—
787C22⋊C4—284no—
788C22⋊C4C4⋊Dic7116yescomplemented
789C42—28no—
790C42—284no—
791C2×C7—44no—
792C2×C7#231711yescharacteristic
793C2×C7#232211yescharacteristic
794C2×C7#232611yescharacteristic
795C2×C7D4×C4⋊C411yescharacteristic
796C2×C7D4×C4⋊C411yescharacteristic
797C2×C7#236111yescharacteristic
798C2×C7#238311yescharacteristic
799C2×C7#266911yescharacteristic
800C2×C7#267411yescharacteristic
801C2×C7#267711yescharacteristic
802C2×C7#268011yescharacteristic
803C2×C7#271811yescharacteristic
804C2×C7#272011yescharacteristic
805C2×C7#272911yescharacteristic
806C2×C7#279011yescharacteristic
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23C2×C4⋊Dic714yes—
842C23C22×Dic1411yescharacteristic
843C23C22×D2811yescharacteristic
844C23C2×D4×D711yescharacteristic
845C23C2×D4×D711yescharacteristic
846C23C2×#115911yescharacteristic
847C23C2×#115911yescharacteristic
848C23#655311yescharacteristic
849C23#655311yescharacteristic
850C23#655311yescharacteristic
851C23#655311yescharacteristic
852C23#655411yescharacteristic
853C23#655411yescharacteristic
854C23#655411yescharacteristic
855C23#655411yescharacteristic
856C23C23×Dic711yescharacteristic
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
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—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—142no—
896C2×C4—142no—
897C2×C4—142no—
898C2×C4—142no—
899C2×C4—142no—
900C2×C4—142no—
901C2×C4—142no—
902C2×C4—142no—
903C2×C4—142no—
904C2×C4—142no—
905C2×C4—142no—
906C2×C4—142no—
907C2×C4—2816no—
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—281no—
924C2×C4—281no—
925C2×C4—281no—
926C2×C4—281no—
927C2×C4—281no—
928C2×C4—281no—
929C2×C4—281no—
930C2×C4—281no—
931C2×C4—281no—
932C2×C4—281no—
933C2×C4—281no—
934C2×C4—281no—
935C2×C4—281no—
936C2×C4—281no—
937C2×C4—281no—
938C2×C4—281no—
939C2×C4—281no—
940C2×C4—281no—
941C2×C4—281no—
942C2×C4—281no—
943C2×C4—281no—
944C2×C4—281no—
945C2×C4—281no—
946C2×C4—281no—
947C2×C4—281no—
948C2×C4—281no—
949C2×C4—281no—
950C2×C4—281no—
951C2×C4—281no—
952C2×C4C2×C4⋊Dic714yes—
953C2×C4C2×C4⋊Dic714yes—
954C2×C4D4×Dic714yes—
955C2×C4D4×Dic714yes—
956C7#1440511yescharacteristic, complemented, Sylow
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22#9021011yescharacteristic
973C22#9021011yescharacteristic
974C22#9021611yescharacteristic
975C22#9021711yescharacteristic
976C22D4×Dic1411yescharacteristic
977C22D4×Dic1411yescharacteristic
978C22#9023411yescharacteristic
979C22#9023411yescharacteristic
980C22D4×D2811yescharacteristic
981C22D4×D2811yescharacteristic
982C22#9024611yescharacteristic
983C22#9024611yescharacteristic
984C22#9028911yescharacteristic
985C22#9030011yescharacteristic
986C22#9030211yescharacteristic
987C22#9030911yescharacteristic
988C22#9033911yescharacteristic
989C22#9034411yescharacteristic
990C22#9035611yescharacteristic
991C22#9035611yescharacteristic
992C22#9036511yescharacteristic
993C22#9036611yescharacteristic
994C22#9037311yescharacteristic
995C22#9037311yescharacteristic
996C22#9040211yescharacteristic
997C22#9040311yescharacteristic
998C22#9040311yescharacteristic
999C22#9040311yescharacteristic
1000C22C22×C4⋊Dic711yescharacteristic
1001C22C2×D4×Dic711yescharacteristic
1002C22C2×D4×Dic711yescharacteristic
1003C22#9051811yescharacteristic
1004C22#9051811yescharacteristic
1005C22#9051811yescharacteristic
1006C22#9051811yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—282no—
1014C4—282no—
1015C4—282no—
1016C4—282no—
1017C4—561no—
1018C4—561no—
1019C4—561no—
1020C4—561no—
1021C2—44no—
1022C2#1173311111yescharacteristic
1023C2#1173311211yescharacteristic
1024C2#1173311311yescharacteristic
1025C2#1173314111yescharacteristic
1026C2#1173314311yescharacteristic
1027C2#1173315111yescharacteristic
1028C2#1173323211yescharacteristic
1029C2#1173335711yescharacteristic
1030C2#1173967811yescharacteristic
1031C2D4×C4⋊Dic711yescharacteristic
1032C2D4×C4⋊Dic711yescharacteristic
1033C2#1174008111yescharacteristic
1034C2#1174028111yescharacteristic
1035C2#1174039811yescharacteristic
1036C2#1174052111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#388C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#388D7
hypocenterC7#14405
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#89757C2semidirect
7. C2×#89707C2semidirect
8. #11729319C2semidirect
11. #11729288C2semidirect
12. #11727173C2semidirect
13. #11727173C2semidirect
14. #11727166C2semidirect
15. #11727161C2semidirect
35. C7×#388C4semidirect
83. C2×C7×C4⋊C4C2×C4semidirect
95. C2×C42×C7C2×C4semidirect
135. C7×#95C2×C4semidirect
136. C7×#95C2×C4semidirect
290. C7×C22⋊C4C4⋊C4semidirect
326. #388Dic7semidirect
547. C2×C4⋊C4C2×Dic7semidirect
571. C2×C42C2×Dic7semidirect
586. #95C2×Dic7semidirect
587. #95C2×Dic7semidirect
788. C22⋊C4C4⋊Dic7semidirect
956. C7#14405semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×#897572
C2×#897232
C2×#897222
C2×#897072
#117293192
#117293002
#117292882
#117271732
#117271662
#117271612
#144057