Finite Group Databasebeta

← #13277292

Subgroups — #13277292

Order 1792.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89761C211yesmaximal, characteristic
2C2×#89759C211yesmaximal, characteristic
3C2×D7×#95C211yesmaximal, characteristic
4C2×#89425C211yesmaximal, characteristic, complemented
5C2×#89438C211yesmaximal, characteristic
6C7×#1441C211yesmaximal, characteristic, complemented
7#11729318C211yesmaximal, characteristic, complemented
8#11729318C211yesmaximal, characteristic, complemented
9(C2×D7)⋊#95C211yesmaximal, characteristic
10(C2×D7)⋊#95C211yesmaximal, characteristic
11(C2×D7)⋊#95C211yesmaximal, characteristic
12#11727177C211yesmaximal, characteristic, complemented
13#11727171C211yesmaximal, characteristic, complemented
14#11727168C211yesmaximal, characteristic, complemented
15#11727155C211yesmaximal, 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×Dic7⋊C4C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2211yescharacteristic
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#89759C418yescomplemented
53#89438—24no—
54D7×#95—24no—
55#89425—24no—
56#14028—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—22no—
84C22×C4×D7—22no—
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×D7Q814yes—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4—41no—
96C2×C7×C4⋊C4—41no—
97C2×C7×C4⋊C4—41no—
98C2×C7×C4⋊C4C2×C414yescomplemented
99C2×(C2×D7)⋊C4—22no—
100C2×(C2×D7)⋊C4—22no—
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×C4⋊Dic7—22no—
112C2×C4⋊Dic7—22no—
113C2×C4⋊Dic7C2×C414yescomplemented
114C2×Dic7⋊C4—22no—
115C2×Dic7⋊C4—22no—
116C2×Dic7⋊C4—41no—
117C2×C4×Dic7—22no—
118C2×C4×Dic7—22no—
119C2×C4×Dic7—22no—
120C2×C4×Dic7—22no—
121C2×C4×Dic7—41no—
122C2×C4×Dic7—41no—
123C7×#95—22no—
124C7×#95—22no—
125C7×#95—22no—
126C7×#95—22no—
127C7×#95—41no—
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⋊#95C2×C414yescomplemented
143C7⋊#95C2×C414yescomplemented
144C7⋊#95D414yes—
145C2×#387—71no—
146C2×#385—71no—
147C2×#380—71no—
148C2×C4×C22⋊C4—71no—
149C22×#95—71no—
150#1445—71no—
151#1443—71no—
152#1442—71no—
153#1441D711yescharacteristic, complemented
154#1436—71no—
155#1436—71no—
156#1434—71no—
157C22⋊#95—71no—
158C22⋊#95—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×D7C22×C412yes—
170C23×D7C2×D412yes—
171C23×D7C2×Q812yes—
172C23×D7#4112yes—
173C23×D7#4112yes—
174C23×D7#4112yes—
175C23×D7#4112yes—
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×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×C7C22×C412yes—
218C22×C4×C7C22×C412yes—
219C22×C4×C7C22×C412yes—
220C22×C4×C7C2×D412yes—
221C22×C4×C7C2×D412yes—
222C22×C4×C7C2×Q812yes—
223C22×C4×C7#4112yes—
224C22×C4×C7#4112yes—
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×Dic7C22×C412yes—
267C22×Dic7C22×C412yes—
268C22×Dic7C22×C412yes—
269C22×Dic7C2×D412yes—
270C22×Dic7C2×D412yes—
271C22×Dic7C2×D412yes—
272C22×Dic7C2×Q812yes—
273C22×Dic7#4112yes—
274C2×C4×D7—28no—
275C2×C4×D7—28no—
276C2×C4×D7—28no—
277C2×C4×D7—28no—
278C2×C4×D7—28no—
279C2×C4×D7—44no—
280C2×C4×D7—44no—
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—
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—
295C7×C4⋊C4—44no—
296C7×C4⋊C4—44no—
297(C2×D7)⋊C4—28no—
298(C2×D7)⋊C4—28no—
299(C2×D7)⋊C4—28no—
300(C2×D7)⋊C4—44no—
301C4⋊Dic7—28no—
302Dic7⋊C4—44no—
303C4×Dic7—44no—
304C4×Dic7—44no—
305C24×C4—71no—
306C24×C4—71no—
307C24×C4—71no—
308C22×C4⋊C4—71no—
309C22×C4⋊C4—71no—
310C22×C4⋊C4C2×D711yescharacteristic
311C22×C4⋊C4C2×D711yescharacteristic
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C42—71no—
317C22×C42—71no—
318#387—144no—
319#385—144no—
320#380—78no—
321C4×C22⋊C4—144no—
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×#95—71no—
338C2×#95—71no—
339C2×#95—144no—
340C2×#95C2×D711yescharacteristic
341C2×#95C2×D711yescharacteristic
342C2×#95C2×D711yescharacteristic
343C2×#95C2×D711yescharacteristic
344C2×#95C2×D711yescharacteristic
345C23×C7C23×C411yescharacteristic
346C23×C7C22×D411yescharacteristic
347C23×C7C22×D411yescharacteristic
348C23×C7C22×Q811yescharacteristic
349C23×C7C2×#4111yescharacteristic
350C23×C7C2×#4111yescharacteristic
351C23×C7C2×#4111yescharacteristic
352C23×C7C2×#4111yescharacteristic
353C23×C7C2×#4111yescharacteristic
354C23×C7C2×#4111yescharacteristic
355C23×C7C2×#4111yescharacteristic
356C23×C7H(5,𝔽2)11yescharacteristic
357C23×C7H(5,𝔽2)11yescharacteristic
358C23×C7H(5,𝔽2)11yescharacteristic
359C23×C72−1+411yescharacteristic
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—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#11714yes—
389C22×D7C4×D414yes—
390C22×D7C4×Q814yes—
391C22×D7C22⋊Q814yes—
392C22×D7#12314yes—
393C22×D7#12514yes—
394C22×D7#12614yes—
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×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7C4×D414yes—
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—22no—
460C2×Dic7—22no—
461C2×Dic7—22no—
462C2×Dic7—22no—
463C2×Dic7—22no—
464C2×Dic7—22no—
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×Dic7C22⋊Q814yes—
493C4×D7—416no—
494C4×D7—416no—
495C4×D7—416no—
496C25—71no—
497C23×C4—71no—
498C23×C4—71no—
499C23×C4—71no—
500C23×C4—71no—
501C23×C4—71no—
502C23×C4—71no—
503C23×C4—74no—
504C23×C4—74no—
505C23×C4—71no—
506C23×C4—142no—
507C23×C4—142no—
508C23×C4—142no—
509C23×C4—142no—
510C23×C4—142no—
511C23×C4—142no—
512C23×C4—142no—
513C23×C4—142no—
514C23×C4—142no—
515C23×C4—142no—
516C23×C4—142no—
517C23×C4—142no—
518C23×C4—142no—
519C23×C4—281no—
520C23×C4—281no—
521C23×C4—281no—
522C23×C4—281no—
523C23×C4—281no—
524C23×C4—281no—
525C23×C4C22×D711yescharacteristic
526C23×C4C22×D711yescharacteristic
527C23×C4C22×D711yescharacteristic
528C23×C4C22×D711yescharacteristic
529C23×C4C22×D711yescharacteristic
530C23×C4C22×D711yescharacteristic
531C23×C4C22×D711yescharacteristic
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4—41no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—74no—
538C2×C4⋊C4—142no—
539C2×C4⋊C4—142no—
540C2×C4⋊C4—142no—
541C2×C4⋊C4—142no—
542C2×C4⋊C4—281no—
543C2×C4⋊C4C4×D714yescomplemented
544C2×C22⋊C4—74no—
545C2×C22⋊C4—74no—
546C2×C22⋊C4—74no—
547C2×C22⋊C4—142no—
548C2×C22⋊C4—142no—
549C2×C22⋊C4—142no—
550C2×C22⋊C4—142no—
551C2×C22⋊C4—142no—
552C2×C22⋊C4—142no—
553C2×C22⋊C4—142no—
554C2×C22⋊C4—142no—
555C2×C22⋊C4—142no—
556C2×C42—142no—
557C2×C42—142no—
558C2×C42—142no—
559C2×C42—142no—
560C2×C42—281no—
561C2×C42—281no—
562#95—22no—
563#95—22no—
564#95—22no—
565#95—22no—
566#95—41no—
567#95—74no—
568#95—74no—
569#95—74no—
570#95—142no—
571#95—142no—
572#95—142no—
573#95—142no—
574#95—142no—
575#95—142no—
576#95—142no—
577#95—142no—
578#95—142no—
579#95—281no—
580#95—281no—
581#95—281no—
582#95—281no—
583#95—281no—
584C22×C7C2×#11711yescharacteristic
585C22×C7C2×C4×D411yescharacteristic
586C22×C7C2×C4×D411yescharacteristic
587C22×C7C2×C4×Q811yescharacteristic
588C22×C7C4×#4111yescharacteristic
589C22×C7#51811yescharacteristic
590C22×C7#52011yescharacteristic
591C22×C7C2×C22⋊Q811yescharacteristic
592C22×C7C2×C22⋊Q811yescharacteristic
593C22×C7C2×#12311yescharacteristic
594C22×C7#52511yescharacteristic
595C22×C7C2×#12511yescharacteristic
596C22×C7C2×#12611yescharacteristic
597C22×C7#52911yescharacteristic
598C22×C7#53311yescharacteristic
599C22×C7#53811yescharacteristic
600C22×C7#53911yescharacteristic
601C22×C7#54311yescharacteristic
602C22×C7#54411yescharacteristic
603C22×C7D4211yescharacteristic
604C22×C7#54611yescharacteristic
605C22×C7#54611yescharacteristic
606C22×C7#54611yescharacteristic
607C22×C7#54611yescharacteristic
608C22×C7#54711yescharacteristic
609C22×C7#54811yescharacteristic
610C22×C7#55111yescharacteristic
611C22×C7#55111yescharacteristic
612C22×C7#55111yescharacteristic
613C22×C7#55111yescharacteristic
614C22×C7#55211yescharacteristic
615C22×C7#55211yescharacteristic
616C22×C7#55311yescharacteristic
617C22×C7#55311yescharacteristic
618C22×C7#55311yescharacteristic
619C2×D7—24no—
620C2×D7—24no—
621C2×D7—24no—
622C2×D7—24no—
623C2×D7—24no—
624C2×D7—24no—
625C2×D7—24no—
626C2×D7—24no—
627C2×D7—24no—
628C2×D7—24no—
629C2×D7—24no—
630C2×D7—24no—
631C2×D7—24no—
632C2×D7—24no—
633C2×D7#38718yescomplemented
634C4×C7—24no—
635C4×C7—42no—
636C4×C7—42no—
637C4×C7—42no—
638C4×C7—42no—
639C4×C7—42no—
640C4×C7—81no—
641Dic7—24no—
642Dic7—42no—
643Dic7—42no—
644Dic7—42no—
645Dic7—42no—
646Dic7—42no—
647Dic7—81no—
648C24—72no—
649C24—72no—
650C24—72no—
651C24—72no—
652C24—72no—
653C24—72no—
654C24—72no—
655C24—141no—
656C24—141no—
657C24—141no—
658C24—141no—
659C24—141no—
660C24—141no—
661C24—141no—
662C24—141no—
663C24C23×D711yescharacteristic
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—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—72no—
712C22×C4—72no—
713C22×C4—148no—
714C22×C4—148no—
715C22×C4—148no—
716C22×C4—148no—
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—148no—
752C22×C4—141no—
753C22×C4—141no—
754C22×C4—141no—
755C22×C4—141no—
756C22×C4—141no—
757C22×C4—141no—
758C22×C4—141no—
759C22×C4—284no—
760C22×C4—284no—
761C22×C4—284no—
762C22×C4—284no—
763C22×C4—284no—
764C22×C4—284no—
765C22×C4—284no—
766C22×C4—284no—
767C22×C4—284no—
768C22×C4—284no—
769C22×C4—284no—
770C22×C4—284no—
771C22×C4—284no—
772C22×C4—284no—
773C22×C4—284no—
774C22×C4—284no—
775C22×C4C2×C4×D712yes—
776C22×C4C2×C4×D712yes—
777C22×C4C2×C4×D712yes—
778C22×C4D4×D712yes—
779C22×C4D4×D712yes—
780C22×C4#115912yes—
781C22×C4Q8×D712yes—
782C22×C4#116112yes—
783C4⋊C4—44no—
784C4⋊C4—44no—
785C4⋊C4—148no—
786C4⋊C4—284no—
787C22⋊C4—148no—
788C22⋊C4—148no—
789C22⋊C4—148no—
790C22⋊C4—284no—
791C42—284no—
792C42—284no—
793C2×C7C2×#38711yescharacteristic
794C2×C7C4×C22⋊Q811yescharacteristic
795C2×C7#232911yescharacteristic
796C2×C7#234211yescharacteristic
797C2×C7#234311yescharacteristic
798C2×C7#236111yescharacteristic
799C2×C7#236411yescharacteristic
800C2×C7#241811yescharacteristic
801C2×C7#241911yescharacteristic
802C2×C7#243711yescharacteristic
803C2×C7#243811yescharacteristic
804C2×C7#244211yescharacteristic
805C2×C7#248111yescharacteristic
806C2×C7#251011yescharacteristic
807C2×C7#256911yescharacteristic
808D7—28no—
809C23—74no—
810C23—74no—
811C23—74no—
812C23—74no—
813C23—74no—
814C23—74no—
815C23—74no—
816C23—142no—
817C23—142no—
818C23—142no—
819C23—142no—
820C23—142no—
821C23—142no—
822C23—142no—
823C23—142no—
824C23—142no—
825C23—142no—
826C23—142no—
827C23—142no—
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—
844C23C22×C4×D711yescharacteristic
845C23C2×D4×D711yescharacteristic
846C23C2×D4×D711yescharacteristic
847C23C2×#115911yescharacteristic
848C23#654811yescharacteristic
849C23#654811yescharacteristic
850C23C2×Q8×D711yescharacteristic
851C23C2×#116111yescharacteristic
852C23#655111yescharacteristic
853C23D7×#4111yescharacteristic
854C23D7×#4111yescharacteristic
855C23D7×#4111yescharacteristic
856C23D7×#4111yescharacteristic
857C23D7×#4111yescharacteristic
858C23#655311yescharacteristic
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—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—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—74no—
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—142no—
917C2×C4—142no—
918C2×C4—142no—
919C2×C4—142no—
920C2×C4—142no—
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—2816no—
930C2×C4—2816no—
931C2×C4—2816no—
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×C4—281no—
953C2×C4—281no—
954C2×C4—281no—
955C2×C4—281no—
956C2×C4—281no—
957C2×C4—281no—
958C2×C4—281no—
959C2×C4#645614yes—
960C7#1402811yescharacteristic, complemented, Sylow
961C22—78no—
962C22—144no—
963C22—144no—
964C22—144no—
965C22—144no—
966C22—144no—
967C22—144no—
968C22—144no—
969C22—144no—
970C22—144no—
971C22—144no—
972C22—144no—
973C22—144no—
974C22—144no—
975C22—144no—
976C22#9017711yescharacteristic
977C22C2×#645611yescharacteristic
978C22D7×#11711yescharacteristic
979C22C4×#115911yescharacteristic
980C22C4×D4×D711yescharacteristic
981C22C4×Q8×D711yescharacteristic
982C22#9026511yescharacteristic
983C22#9028211yescharacteristic
984C22#9029711yescharacteristic
985C22#9030011yescharacteristic
986C22#9030111yescharacteristic
987C22#9030111yescharacteristic
988C22#9030311yescharacteristic
989C22#9030511yescharacteristic
990C22D7×C22⋊Q811yescharacteristic
991C22D7×C22⋊Q811yescharacteristic
992C22#9032411yescharacteristic
993C22#9032511yescharacteristic
994C22#9032811yescharacteristic
995C22#9032811yescharacteristic
996C22#9032911yescharacteristic
997C22#9033011yescharacteristic
998C22D7×#12311yescharacteristic
999C22#9034911yescharacteristic
1000C22#9035211yescharacteristic
1001C22#9036911yescharacteristic
1002C22D7×#12511yescharacteristic
1003C22#9038211yescharacteristic
1004C22#9038411yescharacteristic
1005C22#9038611yescharacteristic
1006C22D7×#12611yescharacteristic
1007C22#9039611yescharacteristic
1008C22#9041711yescharacteristic
1009C22#9041911yescharacteristic
1010C22#9042011yescharacteristic
1011C4—24no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—81no—
1018C4—144no—
1019C4—282no—
1020C4—282no—
1021C4—282no—
1022C4—282no—
1023C4—282no—
1024C4—561no—
1025C2—148no—
1026C2#1173145411yescharacteristic
1027C2#1173232611yescharacteristic
1028C2D7×#38711yescharacteristic
1029C2#1173274811yescharacteristic
1030C2#1173341011yescharacteristic
1031C2#1173365111yescharacteristic
1032C2#1173405711yescharacteristic
1033C2#1173455711yescharacteristic
1034C2#1173469611yescharacteristic
1035C2#1173474911yescharacteristic
1036C2#1173486311yescharacteristic
1037C2#1173519111yescharacteristic
1038C2#1173539211yescharacteristic
1039C2#1173540411yescharacteristic
1040C2#1173580011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1441C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1441D7
hypocenterC7#14028
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
4. C2×#89425C2semidirect
6. C7×#1441C2semidirect
7. #11729318C2semidirect
8. #11729318C2semidirect
12. #11727177C2semidirect
13. #11727171C2semidirect
14. #11727168C2semidirect
15. #11727155C2semidirect
52. #89759C4semidirect
98. C2×C7×C4⋊C4C2×C4semidirect
113. C2×C4⋊Dic7C2×C4semidirect
142. C7⋊#95C2×C4semidirect
143. C7⋊#95C2×C4semidirect
153. #1441D7semidirect
543. C2×C4⋊C4C4×D7semidirect
633. C2×D7#387semidirect
960. C7#14028semidirect

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×D7×#952
C2×#894252
C2×#894382
C7×#14412
#117293182
(C2×D7)⋊#952
#117271772
#117271712
#117271682
#117271552
#140287