Finite Group Databasebeta

← #13283886

Subgroups — #13283886

Order 1792.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#391C211yesmaximal, characteristic, complemented
2C2×#90003C211yesmaximal, characteristic
3C2×#90002C211yesmaximal, characteristic, complemented
4C2×#89761C211yesmaximal, characteristic
5C2×#89440C211yesmaximal, characteristic
6#11729322C211yesmaximal, characteristic, complemented
7#11729291C211yesmaximal, characteristic
8#11729288C211yesmaximal, characteristic, complemented
9#11727182C211yesmaximal, characteristic
10(C2×D7)⋊#95C211yesmaximal, characteristic
11#11727174C211yesmaximal, characteristic, complemented
12#11727168C211yesmaximal, characteristic, complemented
13#11727167C211yesmaximal, characteristic, complemented
14#11727162C211yesmaximal, characteristic
15#11727155C211yesmaximal, characteristic, complemented
16C23×C7×Q8C2211yescharacteristic
17C23×C4×D7C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C7×#391—24no—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36#90003C418yescomplemented
37#90002—24no—
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
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54#89761—24no—
55#89440—24no—
56#14575—71nomaximal, Sylow
57C24×D7C2311yescharacteristic
58C22×C7×Q8—22no—
59C22×C7×Q8—22no—
60C22×C7×Q8—22no—
61C22×C7×Q8—22no—
62C22×C7×Q8—41no—
63C22×C7×Q8—41no—
64C22×C7×Q8C2×C414yescomplemented
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C22×C4×D7—22no—
80C22×C4×D7—22no—
81C22×C4×D7—22no—
82C22×C4×D7—41no—
83C22×C4×D7—41no—
84C22×C4×D7—41no—
85C22×C4×D7—41no—
86C2×C7×C4⋊C4—22no—
87C2×C7×C4⋊C4—22no—
88C2×C7×C4⋊C4—41no—
89C2×C42×C7—22no—
90C2×C42×C7—22no—
91C2×C42×C7—41no—
92C2×(C2×D7)⋊C4—22no—
93C2×(C2×D7)⋊C4—22no—
94C2×(C2×D7)⋊C4—22no—
95C2×(C2×D7)⋊C4—22no—
96C2×(C2×D7)⋊C4—22no—
97C2×(C2×D7)⋊C4—22no—
98C2×(C2×D7)⋊C4—22no—
99C2×(C2×D7)⋊C4—22no—
100C2×(C2×D7)⋊C4—41no—
101C2×(C2×D7)⋊C4—41no—
102C2×(C2×D7)⋊C4—41no—
103C2×(C2×D7)⋊C4—41no—
104C2×(C2×D7)⋊C4—41no—
105C2×(C2×D7)⋊C4—41no—
106C2×(C2×D7)⋊C4C2×C414yes—
107C2×(C2×D7)⋊C4C2×C414yes—
108C2×(C2×D7)⋊C4C2×C414yes—
109C2×(C2×D7)⋊C4Q814yescomplemented
110C2×C4⋊Dic7—22no—
111C2×C4⋊Dic7—22no—
112C2×C4⋊Dic7—41no—
113C2×Dic7⋊C4—22no—
114C2×Dic7⋊C4—22no—
115C2×Dic7⋊C4—41no—
116C2×Dic7⋊C4—41no—
117C2×Dic7⋊C4—41no—
118C2×Dic7⋊C4—41no—
119C2×Dic7⋊C4—41no—
120C2×Dic7⋊C4—41no—
121C2×Dic7⋊C4—41no—
122C2×C4×Dic7—22no—
123C2×C4×Dic7—22no—
124C2×C4×Dic7—41no—
125C7×#95—22no—
126C7×#95—22no—
127C7×#95—22no—
128C7×#95D414yes—
129C7⋊#95—22no—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—41no—
135C7⋊#95—41no—
136C7⋊#95—41no—
137C7⋊#95—41no—
138C7⋊#95—41no—
139C7⋊#95—41no—
140C7⋊#95—41no—
141C7⋊#95C2×C414yescomplemented
142C7⋊#95C2×C414yescomplemented
143C7⋊#95C2×C414yescomplemented
144C7⋊#95D414yes—
145C2×#393—71no—
146C2×#391—71no—
147C2×#391D711yescharacteristic, complemented
148C2×#385—71no—
149C2×#385—71no—
150#1444—71no—
151#1444—71no—
152#1442—71no—
153#1442—71no—
154#1439—71no—
155#1437—71no—
156#1437—71no—
157#1434—71no—
158#1434—71no—
159C22⋊#95—71no—
160C24×C7C2411yescharacteristic
161C23×D7—21no—
162C23×D7—21no—
163C23×D7—21no—
164C23×D7—21no—
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×Q812yes—
175C23×D7#4112yes—
176C2×C7×Q8—28no—
177C2×C7×Q8—28no—
178C2×C7×Q8—44no—
179C2×C7×Q8—44no—
180C2×C7×Q8—44no—
181C2×C7×Q8—44no—
182C2×C7×Q8—44no—
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×C7—21no—
222C22×C4×C7C22×C412yes—
223C22×C4×C7C22×C412yes—
224C22×C4×C7C22×C412yes—
225C22×C4×C7C2×D412yes—
226C22×C4×C7C2×D412yes—
227C22×C4×C7C2×D412yes—
228C22×C4×C7C2×D412yes—
229C22×C4×C7C2×Q812yes—
230C22×C4×C7#4112yes—
231C22×C4×C7#4112yes—
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×Dic7C22×C412yes—
276C22×Dic7C22×C412yes—
277C22×Dic7C22×C412yes—
278C22×Dic7C2×D412yes—
279C22×Dic7C2×D412yes—
280C22×Dic7C2×Q812yes—
281C2×C4×D7—44no—
282C2×C4×D7—44no—
283C2×C4×D7—44no—
284C2×C4×D7—44no—
285C2×C4×D7—44no—
286C2×C4×D7—44no—
287C2×C4×D7—44no—
288C7×C4⋊C4—44no—
289C42×C7—44no—
290(C2×D7)⋊C4—28no—
291(C2×D7)⋊C4—28no—
292(C2×D7)⋊C4—44no—
293(C2×D7)⋊C4—44no—
294(C2×D7)⋊C4—44no—
295(C2×D7)⋊C4—44no—
296C4⋊Dic7—44no—
297Dic7⋊C4—44no—
298Dic7⋊C4—44no—
299Dic7⋊C4—44no—
300C4×Dic7—44no—
301C23×Q8C2×D711yescharacteristic
302C24×C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4—71no—
305C22×C4⋊C4—71no—
306C22×C4⋊C4—71no—
307C22×C4⋊C4C2×D711yescharacteristic
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C42—71no—
315C22×C42C2×D711yescharacteristic
316#393—78no—
317#391—24no—
318#391—144no—
319#385—144no—
320#385—144no—
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×#95—71no—
337C2×#95C2×D711yescharacteristic
338C2×#95C2×D711yescharacteristic
339C2×#95C2×D711yescharacteristic
340C2×#95C2×D711yescharacteristic
341C23×C7C23×C411yescharacteristic
342C23×C7C22×D411yescharacteristic
343C23×C7C22×D411yescharacteristic
344C23×C7C22×Q811yescharacteristic
345C23×C7C2×#4111yescharacteristic
346C23×C7C2×#4111yescharacteristic
347C23×C7C2×#4111yescharacteristic
348C23×C7H(5,𝔽2)11yescharacteristic
349C23×C7H(5,𝔽2)11yescharacteristic
350C23×C7H(5,𝔽2)11yescharacteristic
351C23×C7H(5,𝔽2)11yescharacteristic
352C23×C7H(5,𝔽2)11yescharacteristic
353C23×C72−1+411yescharacteristic
354C23×C72−1+411yescharacteristic
355C23×C72−1+411yescharacteristic
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
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—41no—
375C22×D7—41no—
376C22×D7—41no—
377C22×D7—41no—
378C22×D7—41no—
379C22×D7—41no—
380C22×D7—41no—
381C22×D7—41no—
382C22×D7—41no—
383C22×D7—41no—
384C22×D7—41no—
385C22×D7—41no—
386C22×D7—41no—
387C22×D7—41no—
388C22×D7—41no—
389C22×D7—41no—
390C22×D7C4×Q814yes—
391C7×Q8—416no—
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—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
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×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×C7C4×D414yes—
440C2×C4×C7C4×D414yes—
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—22no—
452C2×Dic7—22no—
453C2×Dic7—22no—
454C2×Dic7—22no—
455C2×Dic7—22no—
456C2×Dic7—22no—
457C2×Dic7—22no—
458C2×Dic7—22no—
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—
490C4×D7—416no—
491C25—71no—
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—22no—
495C22×Q8—22no—
496C22×Q8—41no—
497C22×Q8—41no—
498C22×Q8C4×D714yescomplemented
499C23×C4—71no—
500C23×C4—71no—
501C23×C4—71no—
502C23×C4—71no—
503C23×C4—71no—
504C23×C4—71no—
505C23×C4—71no—
506C23×C4—142no—
507C23×C4—142no—
508C23×C4—142no—
509C23×C4—281no—
510C23×C4—281no—
511C23×C4—281no—
512C23×C4—281no—
513C23×C4C22×D711yescharacteristic
514C23×C4C22×D711yescharacteristic
515C23×C4C22×D711yescharacteristic
516C23×C4C22×D711yescharacteristic
517C23×C4C22×D711yescharacteristic
518C23×C4C22×D711yescharacteristic
519C23×C4C22×D711yescharacteristic
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—142no—
524C2×C4⋊C4—142no—
525C2×C4⋊C4—142no—
526C2×C4⋊C4—142no—
527C2×C4⋊C4—281no—
528C2×C4⋊C4—281no—
529C2×C4⋊C4—281no—
530C2×C4⋊C4—281no—
531C2×C4⋊C4—281no—
532C2×C4⋊C4—281no—
533C2×C4⋊C4—281no—
534C2×C4⋊C4—281no—
535C2×C22⋊C4—74no—
536C2×C22⋊C4—74no—
537C2×C22⋊C4—74no—
538C2×C22⋊C4—74no—
539C2×C22⋊C4—142no—
540C2×C22⋊C4—142no—
541C2×C22⋊C4—142no—
542C2×C22⋊C4—142no—
543C2×C22⋊C4—142no—
544C2×C22⋊C4—142no—
545C2×C22⋊C4—142no—
546C2×C22⋊C4—142no—
547C2×C22⋊C4—281no—
548C2×C22⋊C4—281no—
549C2×C22⋊C4—281no—
550C2×C22⋊C4—281no—
551C2×C22⋊C4—281no—
552C2×C22⋊C4—281no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—41no—
556C2×C42—142no—
557C2×C42—142no—
558C2×C42—281no—
559#95—22no—
560#95—22no—
561#95—22no—
562#95—74no—
563#95—74no—
564#95—74no—
565#95—74no—
566#95—142no—
567#95—142no—
568#95—142no—
569#95—142no—
570#95—142no—
571#95—281no—
572#95—281no—
573#95—281no—
574#95—281no—
575#95—281no—
576#95—281no—
577#95—281no—
578#95C22⋊D714yes—
579C22×C7C2×C4×D411yescharacteristic
580C22×C7C2×C4×D411yescharacteristic
581C22×C7C2×C4×Q811yescharacteristic
582C22×C7#51811yescharacteristic
583C22×C7#52011yescharacteristic
584C22×C7#52011yescharacteristic
585C22×C7#52011yescharacteristic
586C22×C7#53511yescharacteristic
587C22×C7#53511yescharacteristic
588C22×C7#53611yescharacteristic
589C22×C7#53611yescharacteristic
590C22×C7#53811yescharacteristic
591C22×C7#53911yescharacteristic
592C22×C7#54211yescharacteristic
593C22×C7#54211yescharacteristic
594C22×C7#54211yescharacteristic
595C22×C7#54211yescharacteristic
596C22×C7#54311yescharacteristic
597C22×C7#54411yescharacteristic
598C22×C7D4211yescharacteristic
599C22×C7#54611yescharacteristic
600C22×C7#54611yescharacteristic
601C22×C7#54611yescharacteristic
602C22×C7#54611yescharacteristic
603C22×C7D4×Q811yescharacteristic
604C22×C7D4×Q811yescharacteristic
605C22×C7#55111yescharacteristic
606C22×C7#55211yescharacteristic
607C22×C7#55211yescharacteristic
608C22×C7#55411yescharacteristic
609C22×C7#55411yescharacteristic
610C22×C7H(3,𝔽4)11yescharacteristic
611C22×C7#56211yescharacteristic
612C22×C7#56211yescharacteristic
613C22×C7#56311yescharacteristic
614C2×D7—24no—
615C2×D7—24no—
616C2×D7—24no—
617C2×D7—42no—
618C2×D7—42no—
619C2×D7—42no—
620C2×D7—42no—
621C2×D7—42no—
622C2×D7—42no—
623C2×D7—42no—
624C2×D7—42no—
625C2×D7—42no—
626C2×D7—42no—
627C2×D7—42no—
628C2×D7—42no—
629C4×C7—24no—
630C4×C7—24no—
631C4×C7—42no—
632C4×C7—42no—
633C4×C7—42no—
634C4×C7—42no—
635C4×C7—81no—
636Dic7—42no—
637Dic7—42no—
638Dic7—42no—
639Dic7—42no—
640Dic7—42no—
641Dic7—42no—
642Dic7—81no—
643C24—72no—
644C24—72no—
645C24—72no—
646C24—141no—
647C24—141no—
648C24—141no—
649C24—141no—
650C24—141no—
651C24—141no—
652C24—141no—
653C24—141no—
654C24—141no—
655C24—141no—
656C24—141no—
657C24—141no—
658C24C23×D711yescharacteristic
659C2×Q8—28no—
660C2×Q8—28no—
661C2×Q8—44no—
662C2×Q8—44no—
663C2×Q8—44no—
664C2×Q8—44no—
665C2×Q8—44no—
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—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—72no—
706C22×C4—72no—
707C22×C4—72no—
708C22×C4—72no—
709C22×C4—72no—
710C22×C4—72no—
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—141no—
753C22×C4—141no—
754C22×C4—284no—
755C22×C4—284no—
756C22×C4—284no—
757C22×C4—284no—
758C22×C4—284no—
759C22×C4—284no—
760C22×C4—284no—
761C22×C4C2×C4×D712yes—
762C22×C4C2×C4×D712yes—
763C22×C4C2×C4×D712yes—
764C22×C4#115712yes—
765C22×C4D4×D712yes—
766C22×C4#115912yes—
767C22×C4Q8×D712yes—
768C22×C4C2×C22⋊D712yes—
769C22×C4C2×C22⋊D712yes—
770C22×C4C2×C22⋊D712yes—
771C4⋊C4—44no—
772C4⋊C4—284no—
773C4⋊C4—284no—
774C4⋊C4—284no—
775C4⋊C4—284no—
776C22⋊C4—148no—
777C22⋊C4—148no—
778C22⋊C4—284no—
779C22⋊C4—284no—
780C22⋊C4—284no—
781C22⋊C4—284no—
782C42—44no—
783C42—284no—
784C2×C7#232611yescharacteristic
785C2×C7#232611yescharacteristic
786C2×C7#232911yescharacteristic
787C2×C7#235811yescharacteristic
788C2×C7#236011yescharacteristic
789C2×C7#236011yescharacteristic
790C2×C7#237911yescharacteristic
791C2×C7#267011yescharacteristic
792C2×C7#267711yescharacteristic
793C2×C7#268711yescharacteristic
794C2×C7#268711yescharacteristic
795C2×C7#269211yescharacteristic
796C2×C7#269211yescharacteristic
797C2×C7#276311yescharacteristic
798C2×C7#276411yescharacteristic
799D7—44no—
800C23—74no—
801C23—142no—
802C23—142no—
803C23—142no—
804C23—142no—
805C23—142no—
806C23—142no—
807C23—142no—
808C23—142no—
809C23—142no—
810C23—142no—
811C23—142no—
812C23—142no—
813C23—142no—
814C23—142no—
815C23—142no—
816C23—142no—
817C23—142no—
818C23—142no—
819C23—281no—
820C23—281no—
821C23—281no—
822C23—281no—
823C23—281no—
824C23—281no—
825C23—281no—
826C23—281no—
827C23—281no—
828C23—281no—
829C23—281no—
830C23—281no—
831C23—281no—
832C23—281no—
833C23—281no—
834C23—281no—
835C23C22×C4×D711yescharacteristic
836C23C2×#115711yescharacteristic
837C23C2×D4×D711yescharacteristic
838C23C2×#115911yescharacteristic
839C23#654811yescharacteristic
840C23#654811yescharacteristic
841C23C2×Q8×D711yescharacteristic
842C23#655111yescharacteristic
843C23#655111yescharacteristic
844C23#655111yescharacteristic
845C23D7×#4111yescharacteristic
846C23#655311yescharacteristic
847C23#655311yescharacteristic
848C23#655311yescharacteristic
849C23C22×C22⋊D711yescharacteristic
850Q8—416no—
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—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—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
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—41no—
896C2×C4—41no—
897C2×C4—41no—
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—142no—
908C2×C4—142no—
909C2×C4—142no—
910C2×C4—142no—
911C2×C4—142no—
912C2×C4—142no—
913C2×C4—142no—
914C2×C4—142no—
915C2×C4—142no—
916C2×C4—2816no—
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(C22⋊D7)⋊C414yes—
949C2×C4C4×C22⋊D714yes—
950C7#1457511yescharacteristic, complemented, Sylow
951C22—144no—
952C22—144no—
953C22—144no—
954C22—282no—
955C22—282no—
956C22—282no—
957C22—282no—
958C22—282no—
959C22—282no—
960C22—282no—
961C22—282no—
962C22—282no—
963C22—282no—
964C22—282no—
965C22—282no—
966C22C2×(C22⋊D7)⋊C411yescharacteristic
967C22#9017711yescharacteristic
968C22#9018111yescharacteristic
969C22#9018611yescharacteristic
970C22C4×Q8×D711yescharacteristic
971C22#9026511yescharacteristic
972C22#9026511yescharacteristic
973C22#9026511yescharacteristic
974C22#9027011yescharacteristic
975C22#9027211yescharacteristic
976C22#9027311yescharacteristic
977C22#9027311yescharacteristic
978C22#9032511yescharacteristic
979C22#9032611yescharacteristic
980C22#9032911yescharacteristic
981C22#9033011yescharacteristic
982C22#9033411yescharacteristic
983C22#9033411yescharacteristic
984C22#9033811yescharacteristic
985C22#9033811yescharacteristic
986C22#9036511yescharacteristic
987C22#9036711yescharacteristic
988C22#9036911yescharacteristic
989C22#9037411yescharacteristic
990C22#9041511yescharacteristic
991C22#9041811yescharacteristic
992C22#9042011yescharacteristic
993C22#9042611yescharacteristic
994C22C2×C4×C22⋊D711yescharacteristic
995C22D4×C22⋊D711yescharacteristic
996C22#9049711yescharacteristic
997C22Q8×C22⋊D711yescharacteristic
998C22#9050711yescharacteristic
999C22#9052011yescharacteristic
1000C22#9052111yescharacteristic
1001C4—24no—
1002C4—24no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—81no—
1008C4—282no—
1009C4—282no—
1010C4—282no—
1011C4—282no—
1012C4—282no—
1013C4—282no—
1014C4—561no—
1015C2—284no—
1016C2#1173392911yescharacteristic
1017C2#1173394111yescharacteristic
1018C2#1173400911yescharacteristic
1019C2#1173403111yescharacteristic
1020C2#1173403211yescharacteristic
1021C2#1173405711yescharacteristic
1022C2#1173406011yescharacteristic
1023C2#1173409111yescharacteristic
1024C2#1173954411yescharacteristic
1025C2#1173990011yescharacteristic
1026C2#1173993511yescharacteristic
1027C2#1174023911yescharacteristic
1028C2#1174024211yescharacteristic
1029C2#1174044811yescharacteristic
1030C2#1174071111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#391C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#391D7
hypocenterC7#14575
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. C2×C7×#391C2semidirect
3. C2×#90002C2semidirect
6. #11729322C2semidirect
8. #11729288C2semidirect
11. #11727174C2semidirect
12. #11727168C2semidirect
13. #11727167C2semidirect
15. #11727155C2semidirect
36. #90003C4semidirect
64. C22×C7×Q8C2×C4semidirect
109. C2×(C2×D7)⋊C4Q8semidirect
141. C7⋊#95C2×C4semidirect
142. C7⋊#95C2×C4semidirect
143. C7⋊#95C2×C4semidirect
147. C2×#391D7semidirect
498. C22×Q8C4×D7semidirect
950. C7#14575semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3912
C2×#900032
C2×#900022
C2×#897612
C2×#894402
#117293222
#117292912
#117292882
#117271822
(C2×D7)⋊#952
#117271742
#117271682
#117271672
#117271622
#117271552
#145757