Finite Group Databasebeta

← #13285647

Subgroups — #13285647

Order 1792.

1678 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
2C2×#89982C211yesmaximal, characteristic
3C2×#89982C211yesmaximal, characteristic
4C2×#89700C211yesmaximal, characteristic, complemented
5C2×#89705C211yesmaximal, characteristic, complemented
6C2×#89429C211yesmaximal, characteristic, complemented
7#11729301C211yesmaximal, characteristic
8#11729301C211yesmaximal, characteristic
9#11729300C211yesmaximal, characteristic
10#11729300C211yesmaximal, characteristic
11#11729290C211yesmaximal, characteristic, complemented
12#11729290C211yesmaximal, characteristic, complemented
13#11727168C211yesmaximal, characteristic, complemented
14#11727166C211yesmaximal, characteristic, complemented
15#11727163C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C4×C7×C22⋊C4—24no—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36#89982—24no—
37#89982—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#89705—24no—
55#89700—24no—
56#89429—24no—
57#14753—71nomaximal, Sylow
58C25×C7C2311yescharacteristic
59C23×C4×C7—22no—
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7—41no—
65C23×C4×C7—41no—
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
79C23×Dic7C2311yescharacteristic
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4Q814yes—
86C2×C42×C7—22no—
87C2×C42×C7—22no—
88C2×C42×C7—22no—
89C2×C42×C7—22no—
90C2×C42×C7—41no—
91C2×C42×C7—41no—
92C2×C22⋊Dic7—22no—
93C2×C22⋊Dic7—22no—
94C2×C22⋊Dic7—22no—
95C2×C22⋊Dic7—22no—
96C2×C22⋊Dic7—22no—
97C2×C22⋊Dic7—22no—
98C2×C22⋊Dic7—22no—
99C2×C22⋊Dic7—22no—
100C2×C22⋊Dic7—22no—
101C2×C22⋊Dic7—22no—
102C2×C22⋊Dic7—41no—
103C2×C22⋊Dic7—41no—
104C2×C4⋊Dic7—22no—
105C2×C4⋊Dic7—22no—
106C2×C4⋊Dic7—22no—
107C2×C4⋊Dic7—22no—
108C2×C4⋊Dic7—22no—
109C2×C4⋊Dic7—41no—
110C2×Dic7⋊C4—22no—
111C2×Dic7⋊C4—22no—
112C2×Dic7⋊C4—22no—
113C2×Dic7⋊C4—22no—
114C2×Dic7⋊C4—22no—
115C2×Dic7⋊C4—22no—
116C2×Dic7⋊C4—22no—
117C2×Dic7⋊C4—22no—
118C2×Dic7⋊C4—22no—
119C2×Dic7⋊C4—22no—
120C2×Dic7⋊C4—22no—
121C2×Dic7⋊C4—22no—
122C2×Dic7⋊C4—22no—
123C2×Dic7⋊C4—41no—
124C2×Dic7⋊C4—41no—
125C2×Dic7⋊C4—41no—
126C2×Dic7⋊C4—41no—
127C2×Dic7⋊C4D414yes—
128C7×#95—22no—
129C7×#95D414yes—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—22no—
136C7⋊#95—22no—
137C7⋊#95—22no—
138C7⋊#95—22no—
139C7⋊#95—22no—
140C7⋊#95—22no—
141C7⋊#95—22no—
142C7⋊#95—22no—
143C7⋊#95—22no—
144C7⋊#95—41no—
145C7⋊#95D414yes—
146C2×#398—71no—
147C2×#389—71no—
148C2×#387—71no—
149C2×#385—71no—
150C2×#385—71no—
151C2×C4×C22⋊C4D711yescharacteristic
152#1442—71no—
153#1442—71no—
154#1441—71no—
155#1439—71no—
156#1439—71no—
157#1439—71no—
158#1439—71no—
159#1436—71no—
160#1436—71no—
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×C7—21no—
173C24×C7C2×Q812yes—
174C24×C7#4112yes—
175C24×C7#4112yes—
176C24×C7C2411yescharacteristic
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—28no—
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—44no—
211C22×C4×C7—44no—
212C22×C4×C7—44no—
213C22×C4×C7—44no—
214C22×C4×C7—44no—
215C22×C4×C7—44no—
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2×D412yes—
219C22×C4×C7C2×D412yes—
220C22×C4×C7C2×D412yes—
221C22×C4×C7C2×Q812yes—
222C22×C4×C7C2×Q812yes—
223C22×C4×C7#4112yes—
224C22×C4×C7#4112yes—
225C22×C4×C7#4112yes—
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×Dic7C2×D412yes—
277C22×Dic7C2×D412yes—
278C22×Dic7C2×D412yes—
279C22×Dic7C2×D412yes—
280C22×Dic7#4112yes—
281C22×Dic7#4112yes—
282C7×C22⋊C4—28no—
283C7×C22⋊C4—28no—
284C42×C7—44no—
285C42×C7—44no—
286C22⋊Dic7—28no—
287C22⋊Dic7—28no—
288C22⋊Dic7—44no—
289C22⋊Dic7—44no—
290C4⋊Dic7—28no—
291C4⋊Dic7—44no—
292Dic7⋊C4—28no—
293Dic7⋊C4—44no—
294Dic7⋊C4—44no—
295Dic7⋊C4—44no—
296Dic7⋊C4—44no—
297Dic7⋊C4—44no—
298C24×C4C2×D711yescharacteristic
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4—71no—
305C22×C4⋊C4—71no—
306C22×C4⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4C2×D711yescharacteristic
312C22×C22⋊C4C2×D711yescharacteristic
313C22×C42C2×D711yescharacteristic
314C22×C42C2×D711yescharacteristic
315#398—144no—
316#389—144no—
317#387—144no—
318#385—144no—
319#385—144no—
320C4×C22⋊C4—24no—
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
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—22no—
356C23×C7—22no—
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×C7—41no—
372C23×C7—41no—
373C23×C7#12514yes—
374C23×C7C22×D411yescharacteristic
375C23×C7C22×D411yescharacteristic
376C23×C7C22×D411yescharacteristic
377C23×C7C22×Q811yescharacteristic
378C23×C7C2×#4111yescharacteristic
379C23×C7C2×#4111yescharacteristic
380C23×C7C2×#4111yescharacteristic
381C23×C7C2×#4111yescharacteristic
382C23×C7C2×#4111yescharacteristic
383C23×C7C2×#4111yescharacteristic
384C23×C7C2×#4111yescharacteristic
385C23×C7H(5,𝔽2)11yescharacteristic
386C23×C7H(5,𝔽2)11yescharacteristic
387C23×C72−1+411yescharacteristic
388C23×C72−1+411yescharacteristic
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—22no—
412C2×C4×C7—22no—
413C2×C4×C7—416no—
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×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7#12114yes—
431C2×C4×C7C22⋊Q814yes—
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—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
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—
486C2×Dic7—41no—
487C2×Dic7—41no—
488C25C22×D711yescharacteristic
489C23×C4—22no—
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—22no—
493C23×C4—22no—
494C23×C4—41no—
495C23×C4—41no—
496C23×C4—71no—
497C23×C4—71no—
498C23×C4—71no—
499C23×C4—71no—
500C23×C4—71no—
501C23×C4—71no—
502C23×C4—71no—
503C23×C4—71no—
504C23×C4C22×D711yescharacteristic
505C23×C4C22×D711yescharacteristic
506C23×C4C22×D711yescharacteristic
507C23×C4C22×D711yescharacteristic
508C23×C4C22×D711yescharacteristic
509C23×C4C22×D711yescharacteristic
510C2×C4⋊C4—74no—
511C2×C4⋊C4—142no—
512C2×C4⋊C4—142no—
513C2×C4⋊C4—142no—
514C2×C4⋊C4—142no—
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—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—281no—
530C2×C4⋊C4—281no—
531C2×C4⋊C4—281no—
532C2×C4⋊C4—281no—
533C2×C4⋊C4—281no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
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—142no—
548C2×C22⋊C4—142no—
549C2×C22⋊C4—281no—
550C2×C22⋊C4—281no—
551C2×C22⋊C4Dic1414yes—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—41no—
557C2×C42—41no—
558#95—22no—
559#95—74no—
560#95—142no—
561#95—142no—
562#95—142no—
563#95—142no—
564#95—142no—
565#95—142no—
566#95—142no—
567#95—142no—
568#95—142no—
569#95—142no—
570#95—142no—
571#95—142no—
572#95—142no—
573#95—142no—
574#95—281no—
575#95C22⋊D714yes—
576C22×C7—24no—
577C22×C7—24no—
578C22×C7—24no—
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×C7—42no—
590C22×C7—42no—
591C22×C7C2×#12111yescharacteristic
592C22×C7C2×C22⋊Q811yescharacteristic
593C22×C7#52511yescharacteristic
594C22×C7#52511yescharacteristic
595C22×C7#52511yescharacteristic
596C22×C7#52511yescharacteristic
597C22×C7#52511yescharacteristic
598C22×C7C2×#12511yescharacteristic
599C22×C7#52911yescharacteristic
600C22×C7#52911yescharacteristic
601C22×C7#52911yescharacteristic
602C22×C7#53211yescharacteristic
603C22×C7#53311yescharacteristic
604C22×C7#53811yescharacteristic
605C22×C7#53911yescharacteristic
606C22×C7#53911yescharacteristic
607C22×C7#53911yescharacteristic
608C22×C7#54111yescharacteristic
609C22×C7#54211yescharacteristic
610C22×C7D4211yescharacteristic
611C22×C7D4211yescharacteristic
612C22×C7#54611yescharacteristic
613C22×C7#54611yescharacteristic
614C22×C7#54711yescharacteristic
615C22×C7#54711yescharacteristic
616C22×C7#54811yescharacteristic
617C22×C7#54811yescharacteristic
618C22×C7D4×Q811yescharacteristic
619C22×C7D4×Q811yescharacteristic
620C22×C7#55111yescharacteristic
621C22×C7#55211yescharacteristic
622C22×C7#55211yescharacteristic
623C22×C7#55411yescharacteristic
624C22×C7#55411yescharacteristic
625C22×C7#55911yescharacteristic
626C4×C7—24no—
627C4×C7—24no—
628C4×C7—42no—
629C4×C7—42no—
630C4×C7—42no—
631C4×C7—42no—
632Dic7—42no—
633Dic7—42no—
634Dic7—42no—
635Dic7—42no—
636Dic7—42no—
637Dic7—42no—
638Dic7—81no—
639Dic7—81no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24C2×Dic1412yes—
653C24#115712yes—
654C24#115712yes—
655C24C23×D711yescharacteristic
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—28no—
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—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—72no—
696C22×C4—72no—
697C22×C4—72no—
698C22×C4—72no—
699C22×C4—72no—
700C22×C4—72no—
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×C4C2×Dic1412yes—
752C22×C4C2×Dic1412yes—
753C22×C4#115712yes—
754C22×C4#115712yes—
755C22×C4#115712yes—
756C22×C4D4×D712yes—
757C22×C4D4×D712yes—
758C22×C4C2×C22⋊D712yes—
759C22×C4C2×C22⋊D712yes—
760C22×C4C2×C22⋊D712yes—
761C4⋊C4—148no—
762C4⋊C4—148no—
763C4⋊C4—284no—
764C4⋊C4—284no—
765C4⋊C4—284no—
766C4⋊C4—284no—
767C4⋊C4—284no—
768C4⋊C4—284no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—148no—
772C22⋊C4—148no—
773C22⋊C4—284no—
774C22⋊C4—284no—
775C42—44no—
776C42—44no—
777C2×C7—44no—
778C2×C7#239211yescharacteristic
779C2×C7#242411yescharacteristic
780C2×C7#242911yescharacteristic
781C2×C7#244911yescharacteristic
782C2×C7#245211yescharacteristic
783C2×C7#245511yescharacteristic
784C2×C7#245811yescharacteristic
785C2×C7#246311yescharacteristic
786C2×C7#247311yescharacteristic
787C2×C7#247311yescharacteristic
788C2×C7#247511yescharacteristic
789C2×C7#255311yescharacteristic
790C2×C7#258911yescharacteristic
791C2×C7#265211yescharacteristic
792C2×C7#285111yescharacteristic
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—22no—
810C23—22no—
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—
825C23—41no—
826C23—41no—
827C23#643314yes—
828C23C22×Dic1411yescharacteristic
829C23C2×#115711yescharacteristic
830C23C2×#115711yescharacteristic
831C23C2×#115711yescharacteristic
832C23C2×#115711yescharacteristic
833C23C2×#115711yescharacteristic
834C23C2×D4×D711yescharacteristic
835C23C2×D4×D711yescharacteristic
836C23#654811yescharacteristic
837C23#654811yescharacteristic
838C23D7×#4111yescharacteristic
839C23D7×#4111yescharacteristic
840C23#655411yescharacteristic
841C23#655411yescharacteristic
842C23C22×C22⋊D711yescharacteristic
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—22no—
866C2×C4—22no—
867C2×C4—416no—
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—41no—
882C2×C4—41no—
883C2×C4—41no—
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—142no—
900C2×C4—142no—
901C2×C4—142no—
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×C4—281no—
939C2×C4—281no—
940C2×C4#644714yes—
941C2×C4#648714yes—
942C7#1475311yescharacteristic, complemented, Sylow
943C22—24no—
944C22—24no—
945C22—24no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22C2×#643311yescharacteristic
959C22#9016111yescharacteristic
960C22#9017011yescharacteristic
961C22#9017011yescharacteristic
962C22C2×#644711yescharacteristic
963C22#9018111yescharacteristic
964C22#9018111yescharacteristic
965C22#9018511yescharacteristic
966C22#9020911yescharacteristic
967C22#9021911yescharacteristic
968C22#9022211yescharacteristic
969C22#9022211yescharacteristic
970C22D4×Dic1411yescharacteristic
971C22D4×Dic1411yescharacteristic
972C22#9023011yescharacteristic
973C22#9023011yescharacteristic
974C22#9023811yescharacteristic
975C22#9023811yescharacteristic
976C22#9023811yescharacteristic
977C22#9023911yescharacteristic
978C22#9024211yescharacteristic
979C22#9024311yescharacteristic
980C22#9024711yescharacteristic
981C22#9025011yescharacteristic
982C22#9025211yescharacteristic
983C22#9025511yescharacteristic
984C22#9025511yescharacteristic
985C22#9025511yescharacteristic
986C22C2×#648711yescharacteristic
987C22#9048211yescharacteristic
988C22#9048211yescharacteristic
989C22D4×C22⋊D711yescharacteristic
990C22D4×C22⋊D711yescharacteristic
991C22#9051511yescharacteristic
992C22#9052211yescharacteristic
993C4—24no—
994C4—24no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—282no—
1000C4—282no—
1001C4—282no—
1002C4—282no—
1003C4—282no—
1004C4—282no—
1005C4—561no—
1006C4—561no—
1007C2—44no—
1008C2#1173093311yescharacteristic
1009C2#1173094111yescharacteristic
1010C2#1173094611yescharacteristic
1011C2#1173094611yescharacteristic
1012C2#1173099411yescharacteristic
1013C2#1173100011yescharacteristic
1014C2#1173102611yescharacteristic
1015C2#1173104311yescharacteristic
1016C2#1173951911yescharacteristic
1017C2#1173955411yescharacteristic
1018C2#1173969611yescharacteristic
1019C2#1173980511yescharacteristic
1020C2#1173980711yescharacteristic
1021C2#1173981311yescharacteristic
1022C2#1173985511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutator, socle, cosocleC24×C7C24
FittingC2×C4×C7×C22⋊C4C2
prime radicalC25×C7C23
hypercenterC2×C4×C22⋊C4D7
hypocenterC7#14753
LCSG ▷ C24×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#89700C2semidirect
5. C2×#89705C2semidirect
6. C2×#89429C2semidirect
11. #11729290C2semidirect
12. #11729290C2semidirect
13. #11727168C2semidirect
14. #11727166C2semidirect
15. #11727163C2semidirect
942. C7#14753semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C22⋊C42
C2×#899822
C2×#897002
C2×#897052
C2×#894292
#117293012
#117293002
#117292902
#117271682
#117271662
#117271632
#147537