Finite Group Databasebeta

← #13283546

Subgroups — #13283546

Order 1792.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#396C211yesmaximal, characteristic
2C2×#89757C211yesmaximal, characteristic, complemented
3C2×#89753C211yesmaximal, characteristic, complemented
4C2×#89722C211yesmaximal, characteristic
5C2×#89722C211yesmaximal, characteristic
6#11729319C211yesmaximal, characteristic, complemented
7#11729319C211yesmaximal, characteristic, complemented
8#11729318C211yesmaximal, characteristic, complemented
9#11729317C211yesmaximal, characteristic, complemented
10#11729300C211yesmaximal, characteristic
11#11729299C211yesmaximal, characteristic
12#11729299C211yesmaximal, characteristic
13#11729298C211yesmaximal, characteristic
14#11727173C211yesmaximal, characteristic, complemented
15#11727170C211yesmaximal, characteristic, complemented
16C24×Dic7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C7×#396C418yescomplemented
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#89757—24no—
53#89753—24no—
54#89722—24no—
55#89722—24no—
56#14549—71nomaximal, Sylow
57C25×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×Dic7—22no—
65C23×Dic7—22no—
66C23×Dic7—22no—
67C23×Dic7—41no—
68C23×Dic7—41no—
69C23×Dic7—41no—
70C23×Dic7—41no—
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—41no—
84C2×C7×C4⋊C4—41no—
85C2×C7×C4⋊C4C2×C414yescomplemented
86C2×C7×C4⋊C4C2×C414yescomplemented
87C2×C7×C4⋊C4C2×C414yescomplemented
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—22no—
90C2×C7×C22⋊C4—22no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—41no—
93C2×C7×C22⋊C4—41no—
94C2×C7×C22⋊C4C2×C414yes—
95C2×C7×C22⋊C4C2×C414yes—
96C2×C7×C22⋊C4C2×C414yes—
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×C22⋊Dic7Q814yes—
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—41no—
113C2×C4⋊Dic7—41no—
114C2×C4⋊Dic7—41no—
115C2×C4⋊Dic7—41no—
116C2×C4⋊Dic7—41no—
117C2×C4⋊Dic7—41no—
118C2×C4⋊Dic7—41no—
119C2×C4⋊Dic7—41no—
120C2×C4⋊Dic7D414yes—
121C2×C4×Dic7—22no—
122C2×C4×Dic7—22no—
123C2×C4×Dic7—22no—
124C2×C4×Dic7—41no—
125C2×C4×Dic7—41no—
126C2×C4×Dic7—41no—
127C7×#95C2×C414yescomplemented
128C7⋊#95—22no—
129C7⋊#95—22no—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—22no—
136C7⋊#95—22no—
137C7⋊#95—41no—
138C7⋊#95—41no—
139C7⋊#95—41no—
140C7⋊#95—41no—
141C7⋊#95—41no—
142C7⋊#95—41no—
143C7⋊#95—41no—
144C7⋊#95D414yes—
145C2×#396D711yescharacteristic
146C2×#389—71no—
147C2×#387—71no—
148C2×#385—71no—
149C2×#385—71no—
150#1444—71no—
151#1443—71no—
152#1441—71no—
153#1441—71no—
154#1439—71no—
155#1437—71no—
156#1437—71no—
157#1436—71no—
158C4⋊#95—71no—
159C22⋊#95—71no—
160C24×C7—21no—
161C24×C7—21no—
162C24×C7—21no—
163C24×C7—21no—
164C24×C7—21no—
165C24×C7—21no—
166C24×C7—21no—
167C24×C7—21no—
168C24×C7—21no—
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7C22×C412yes—
173C24×C7C2×Q812yes—
174C24×C7#4112yes—
175C24×C7C2411yescharacteristic
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×C7C22×C412yes—
209C22×C4×C7C22×C412yes—
210C22×C4×C7C22×C412yes—
211C22×C4×C7C22×C412yes—
212C22×C4×C7C22×C412yes—
213C22×C4×C7C22×C412yes—
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2×D412yes—
216C22×C4×C7#4112yes—
217C22×C4×C7#4112yes—
218C22×Dic7—21no—
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×Dic7—21no—
268C22×Dic7—44no—
269C22×Dic7—44no—
270C22×Dic7—44no—
271C22×Dic7—44no—
272C22×Dic7—44no—
273C22×Dic7—44no—
274C22×Dic7—44no—
275C22×Dic7C2×D412yes—
276C22×Dic7C2×D412yes—
277C22×Dic7C2×D412yes—
278C22×Dic7C2×D412yes—
279C22×Dic7C2×Q812yes—
280C22×Dic7C2×Q812yes—
281C7×C4⋊C4—28no—
282C7×C4⋊C4—28no—
283C7×C4⋊C4—44no—
284C7×C22⋊C4—28no—
285C7×C22⋊C4—28no—
286C7×C22⋊C4—44no—
287C22⋊Dic7—44no—
288C22⋊Dic7—44no—
289C22⋊Dic7—44no—
290C4⋊Dic7—44no—
291C4⋊Dic7—44no—
292C4⋊Dic7—44no—
293C4⋊Dic7—44no—
294C4⋊Dic7—44no—
295C4×Dic7—44no—
296C4×Dic7—44no—
297C24×C4—71no—
298C22×C4⋊C4—71no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4C2×D711yescharacteristic
304C22×C4⋊C4C2×D711yescharacteristic
305C22×C4⋊C4C2×D711yescharacteristic
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4C2×D711yescharacteristic
310C22×C22⋊C4C2×D711yescharacteristic
311C22×C22⋊C4C2×D711yescharacteristic
312C22×C42—71no—
313C22×C42—71no—
314#396Dic718yescomplemented
315#389—144no—
316#387—144no—
317#385—144no—
318#385—144no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95—71no—
326C2×#95—71no—
327C2×#95—71no—
328C2×#95—71no—
329C2×#95—71no—
330C2×#95—71no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95C2×D711yescharacteristic
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—22no—
346C23×C7—22no—
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—41no—
356C23×C7—41no—
357C23×C7—41no—
358C23×C7—41no—
359C23×C7—41no—
360C23×C7—41no—
361C23×C7—41no—
362C23×C7—41no—
363C23×C7—41no—
364C23×C7—41no—
365C23×C7—41no—
366C23×C7—41no—
367C23×C7—41no—
368C23×C7—41no—
369C23×C7—41no—
370C23×C7—41no—
371C23×C7C4×Q814yes—
372C23×C7C23×C411yescharacteristic
373C23×C7C22×D411yescharacteristic
374C23×C7C22×D411yescharacteristic
375C23×C7C22×Q811yescharacteristic
376C23×C7C2×#4111yescharacteristic
377C23×C7C2×#4111yescharacteristic
378C23×C7C2×#4111yescharacteristic
379C23×C7H(5,𝔽2)11yescharacteristic
380C23×C7H(5,𝔽2)11yescharacteristic
381C23×C7H(5,𝔽2)11yescharacteristic
382C23×C7H(5,𝔽2)11yescharacteristic
383C23×C7H(5,𝔽2)11yescharacteristic
384C23×C72−1+411yescharacteristic
385C23×C72−1+411yescharacteristic
386C23×C72−1+411yescharacteristic
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—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—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×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7C4×D414yes—
428C2×C4×C7C4×D414yes—
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—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—416no—
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—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—
486C25C22×D711yescharacteristic
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—71no—
491C23×C4—71no—
492C23×C4—71no—
493C23×C4—71no—
494C23×C4—71no—
495C23×C4—142no—
496C23×C4—142no—
497C23×C4—142no—
498C23×C4—281no—
499C23×C4—281no—
500C23×C4—281no—
501C23×C4—281no—
502C23×C4C22×D711yescharacteristic
503C23×C4C22×D711yescharacteristic
504C23×C4C22×D711yescharacteristic
505C23×C4C22×D711yescharacteristic
506C23×C4C22×D711yescharacteristic
507C23×C4C22×D711yescharacteristic
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4—41no—
514C2×C4⋊C4—74no—
515C2×C4⋊C4—142no—
516C2×C4⋊C4—142no—
517C2×C4⋊C4—142no—
518C2×C4⋊C4—142no—
519C2×C4⋊C4—142no—
520C2×C4⋊C4—142no—
521C2×C4⋊C4—281no—
522C2×C4⋊C4—281no—
523C2×C4⋊C4—281no—
524C2×C4⋊C4—281no—
525C2×C4⋊C4—281no—
526C2×C4⋊C4—281no—
527C2×C4⋊C4—281no—
528C2×C4⋊C4—281no—
529C2×C4⋊C4C2×Dic714yescomplemented
530C2×C4⋊C4C2×Dic714yescomplemented
531C2×C4⋊C4C2×Dic714yescomplemented
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—41no—
537C2×C22⋊C4—41no—
538C2×C22⋊C4—74no—
539C2×C22⋊C4—142no—
540C2×C22⋊C4—142no—
541C2×C22⋊C4—142no—
542C2×C22⋊C4—142no—
543C2×C22⋊C4—281no—
544C2×C22⋊C4—281no—
545C2×C22⋊C4—281no—
546C2×C22⋊C4—281no—
547C2×C22⋊C4C2×Dic714yes—
548C2×C22⋊C4C2×Dic714yes—
549C2×C22⋊C4C2×Dic714yes—
550C2×C42—142no—
551C2×C42—142no—
552C2×C42—142no—
553C2×C42—281no—
554C2×C42—281no—
555C2×C42—281no—
556#95—74no—
557#95—142no—
558#95—142no—
559#95—142no—
560#95—142no—
561#95—142no—
562#95—142no—
563#95—142no—
564#95—142no—
565#95—142no—
566#95—281no—
567#95—281no—
568#95—281no—
569#95—281no—
570#95—281no—
571#95—281no—
572#95—281no—
573#95C2×Dic714yescomplemented
574C22×C7—24no—
575C22×C7—24no—
576C22×C7—24no—
577C22×C7—42no—
578C22×C7—42no—
579C22×C7—42no—
580C22×C7—42no—
581C22×C7—42no—
582C22×C7—42no—
583C22×C7—42no—
584C22×C7—42no—
585C22×C7—42no—
586C22×C7—42no—
587C22×C7—42no—
588C22×C7—42no—
589C22×C7C2×C4×D411yescharacteristic
590C22×C7C2×C4×D411yescharacteristic
591C22×C7C2×C4×Q811yescharacteristic
592C22×C7#51811yescharacteristic
593C22×C7#52011yescharacteristic
594C22×C7#52011yescharacteristic
595C22×C7#52011yescharacteristic
596C22×C7#53411yescharacteristic
597C22×C7#53511yescharacteristic
598C22×C7#53711yescharacteristic
599C22×C7#53711yescharacteristic
600C22×C7#53811yescharacteristic
601C22×C7#53811yescharacteristic
602C22×C7#53911yescharacteristic
603C22×C7#53911yescharacteristic
604C22×C7#54011yescharacteristic
605C22×C7#54211yescharacteristic
606C22×C7#54311yescharacteristic
607C22×C7#54411yescharacteristic
608C22×C7D4211yescharacteristic
609C22×C7#54611yescharacteristic
610C22×C7#54611yescharacteristic
611C22×C7#54711yescharacteristic
612C22×C7#54811yescharacteristic
613C22×C7D4×Q811yescharacteristic
614C22×C7D4×Q811yescharacteristic
615C22×C7#55211yescharacteristic
616C22×C7#55211yescharacteristic
617C22×C7#55311yescharacteristic
618C22×C7#55411yescharacteristic
619C22×C7#55411yescharacteristic
620C22×C7#56011yescharacteristic
621C22×C7#56311yescharacteristic
622C22×C7#56311yescharacteristic
623C22×C7#56311yescharacteristic
624C4×C7—24no—
625C4×C7—24no—
626C4×C7—42no—
627C4×C7—42no—
628C4×C7—42no—
629C4×C7—42no—
630Dic7—42no—
631Dic7—42no—
632Dic7—42no—
633Dic7—42no—
634Dic7—42no—
635Dic7—42no—
636Dic7—81no—
637Dic7—81no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24Q8×D712yes—
651C24#116112yes—
652C24C22×Dic712yes—
653C24C23×D711yescharacteristic
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—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—72no—
687C22×C4—72no—
688C22×C4—72no—
689C22×C4—72no—
690C22×C4—72no—
691C22×C4—72no—
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×C4—141no—
740C22×C4—141no—
741C22×C4—141no—
742C22×C4—284no—
743C22×C4—284no—
744C22×C4—284no—
745C22×C4—284no—
746C22×C4—284no—
747C22×C4—284no—
748C22×C4—284no—
749C22×C4D4×D712yes—
750C22×C4D4×D712yes—
751C22×C4#115912yes—
752C22×C4#115912yes—
753C22×C4C22×Dic712yes—
754C22×C4C22×Dic712yes—
755C22×C4C22×Dic712yes—
756C22×C4C22×Dic712yes—
757C22×C4C22×Dic712yes—
758C22×C4C22×Dic712yes—
759C4⋊C4—28no—
760C4⋊C4—28no—
761C4⋊C4—44no—
762C4⋊C4—284no—
763C4⋊C4—284no—
764C4⋊C4—284no—
765C4⋊C4—284no—
766C4⋊C4—284no—
767C22⋊C4—28no—
768C22⋊C4—28no—
769C22⋊C4—44no—
770C22⋊C4—284no—
771C22⋊C4—284no—
772C22⋊C4—284no—
773C42—284no—
774C42—284no—
775C2×C7—44no—
776C2×C7#232411yescharacteristic
777C2×C7#232511yescharacteristic
778C2×C7#232911yescharacteristic
779C2×C7#236011yescharacteristic
780C2×C7#236011yescharacteristic
781C2×C7#236111yescharacteristic
782C2×C7#238311yescharacteristic
783C2×C7#267811yescharacteristic
784C2×C7#268311yescharacteristic
785C2×C7#269511yescharacteristic
786C2×C7#270711yescharacteristic
787C2×C7#272011yescharacteristic
788C2×C7#272911yescharacteristic
789C2×C7#276511yescharacteristic
790C2×C7#278011yescharacteristic
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23Q8×Dic714yes—
826C23C2×D4×D711yescharacteristic
827C23C2×D4×D711yescharacteristic
828C23C2×#115911yescharacteristic
829C23C2×#115911yescharacteristic
830C23#654811yescharacteristic
831C23#654811yescharacteristic
832C23C2×Q8×D711yescharacteristic
833C23C2×#116111yescharacteristic
834C23#655311yescharacteristic
835C23#655311yescharacteristic
836C23#655311yescharacteristic
837C23#655411yescharacteristic
838C23#655411yescharacteristic
839C23#655411yescharacteristic
840C23C23×Dic711yescharacteristic
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
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—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
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—142no—
892C2×C4—142no—
893C2×C4—142no—
894C2×C4—142no—
895C2×C4—142no—
896C2×C4—142no—
897C2×C4—142no—
898C2×C4—142no—
899C2×C4—2816no—
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—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×C4D4×Dic714yes—
939C2×C4D4×Dic714yes—
940C7#1454911yescharacteristic, complemented, Sylow
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22#9028811yescharacteristic
957C22#9028911yescharacteristic
958C22#9029311yescharacteristic
959C22#9029411yescharacteristic
960C22#9029611yescharacteristic
961C22#9029811yescharacteristic
962C22#9029911yescharacteristic
963C22#9030011yescharacteristic
964C22#9030211yescharacteristic
965C22#9030811yescharacteristic
966C22#9030911yescharacteristic
967C22#9031011yescharacteristic
968C22#9031411yescharacteristic
969C22#9032111yescharacteristic
970C22#9032111yescharacteristic
971C22#9032311yescharacteristic
972C22#9032311yescharacteristic
973C22#9032511yescharacteristic
974C22#9032611yescharacteristic
975C22#9032611yescharacteristic
976C22#9033311yescharacteristic
977C22#9033311yescharacteristic
978C22#9033511yescharacteristic
979C22#9033611yescharacteristic
980C22#9040211yescharacteristic
981C22#9040311yescharacteristic
982C22#9040311yescharacteristic
983C22#9040311yescharacteristic
984C22C2×D4×Dic711yescharacteristic
985C22C2×D4×Dic711yescharacteristic
986C22#9048911yescharacteristic
987C22C2×Q8×Dic711yescharacteristic
988C22#9051811yescharacteristic
989C22#9051811yescharacteristic
990C22#9051811yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—282no—
998C4—282no—
999C4—282no—
1000C4—282no—
1001C4—282no—
1002C4—282no—
1003C4—561no—
1004C4—561no—
1005C2—44no—
1006C2#1173479511yescharacteristic
1007C2#1173480311yescharacteristic
1008C2#1173480811yescharacteristic
1009C2#1173481411yescharacteristic
1010C2#1173482711yescharacteristic
1011C2#1173487511yescharacteristic
1012C2#1173487811yescharacteristic
1013C2#1173489011yescharacteristic
1014C2#1174007811yescharacteristic
1015C2#1174007911yescharacteristic
1016C2#1174008111yescharacteristic
1017C2#1174019011yescharacteristic
1018C2#1174019211yescharacteristic
1019C2#1174019211yescharacteristic
1020C2#1174052111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#396C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#396D7
hypocenterC7#14549
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
2. C2×#89757C2semidirect
3. C2×#89753C2semidirect
6. #11729319C2semidirect
7. #11729319C2semidirect
8. #11729318C2semidirect
9. #11729317C2semidirect
14. #11727173C2semidirect
15. #11727170C2semidirect
33. C7×#396C4semidirect
85. C2×C7×C4⋊C4C2×C4semidirect
86. C2×C7×C4⋊C4C2×C4semidirect
87. C2×C7×C4⋊C4C2×C4semidirect
127. C7×#95C2×C4semidirect
314. #396Dic7semidirect
529. C2×C4⋊C4C2×Dic7semidirect
530. C2×C4⋊C4C2×Dic7semidirect
531. C2×C4⋊C4C2×Dic7semidirect
573. #95C2×Dic7semidirect
940. C7#14549semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3962
C2×#897572
C2×#897532
C2×#897222
#117293192
#117293182
#117293172
#117293002
#117292992
#117292982
#117271732
#117271702
#145497