Finite Group Databasebeta

← #13281180

Subgroups — #13281180

Order 1792.

1866 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
1C22×#6441C211yesmaximal, characteristic
2C2×C7×#388C211yesmaximal, characteristic
3C2×#89723C211yesmaximal, characteristic
4C2×#89715C211yesmaximal, characteristic
5C2×#89701C211yesmaximal, characteristic, complemented
6#11729320C211yesmaximal, characteristic, complemented
7#11729317C211yesmaximal, characteristic, complemented
8#11729303C211yesmaximal, characteristic
9#11729303C211yesmaximal, characteristic
10#11729298C211yesmaximal, characteristic
11#11729290C211yesmaximal, characteristic, complemented
12#11727178C211yesmaximal, characteristic, complemented
13#11727176C211yesmaximal, characteristic, complemented
14#11727164C211yesmaximal, characteristic, complemented
15#11727159C211yesmaximal, characteristic, complemented
16C24×Dic7C2211yescharacteristic
17C23×Dic14C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C42×C7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C2×#6441—24no—
32C2×#6441—24no—
33C2×#6441C418yescomplemented
34C7×#388—24no—
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
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55#89723—24no—
56#89715—24no—
57#89701—24no—
58#14364—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—22no—
70C23×Dic7—41no—
71C23×Dic7—41no—
72C23×Dic7C2×C414yes—
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C22×Dic14—22no—
82C22×Dic14—22no—
83C22×Dic14—22no—
84C22×Dic14—22no—
85C22×Dic14—41no—
86C22×Dic14—41no—
87C22×Dic14C2×C414yes—
88C2×C7×C4⋊C4—22no—
89C2×C7×C4⋊C4—22no—
90C2×C7×C4⋊C4—41no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—22no—
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—22no—
95C2×C7×C22⋊C4—41no—
96C2×C7×C22⋊C4—41no—
97C2×C7×C22⋊C4C2×C414yes—
98C2×C7×C22⋊C4D414yes—
99C2×C7×C22⋊C4D414yes—
100C2×C42×C7—22no—
101C2×C42×C7—22no—
102C2×C42×C7—41no—
103C2×C22⋊Dic7—22no—
104C2×C22⋊Dic7—22no—
105C2×C22⋊Dic7—22no—
106C2×C22⋊Dic7—22no—
107C2×C22⋊Dic7—22no—
108C2×C22⋊Dic7—22no—
109C2×C22⋊Dic7—41no—
110C2×C22⋊Dic7—41no—
111C2×C22⋊Dic7C2×C414yes—
112C2×C4⋊Dic7—22no—
113C2×C4⋊Dic7—22no—
114C2×C4⋊Dic7—22no—
115C2×C4⋊Dic7—22no—
116C2×C4⋊Dic7—41no—
117C2×C4⋊Dic7C2×C414yes—
118C2×Dic7⋊C4—22no—
119C2×Dic7⋊C4—22no—
120C2×Dic7⋊C4—22no—
121C2×Dic7⋊C4—22no—
122C2×Dic7⋊C4C2×C414yes—
123C2×Dic7⋊C4C2×C414yes—
124C2×C4×Dic7—22no—
125C2×C4×Dic7—22no—
126C2×C4×Dic7—41no—
127#6441—232no—
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—22no—
138C7⋊#95—22no—
139C7⋊#95—22no—
140C7⋊#95—22no—
141C7⋊#95—41no—
142C7⋊#95—41no—
143C7⋊#95—41no—
144C7⋊#95—41no—
145C7⋊#95—41no—
146C7⋊#95—41no—
147C7⋊#95D414yes—
148C22×C22⋊Q8—71no—
149C2×#391—71no—
150C2×#388—71no—
151C2×#388D711yescharacteristic
152C2×#381—71no—
153#1446—71no—
154#1445—71no—
155#1441—71no—
156#1441—71no—
157#1440—71no—
158#1440—71no—
159#1436—71no—
160#1436—71no—
161C4⋊#95—71no—
162C22⋊#95—71no—
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×C7—21no—
174C24×C7—21no—
175C24×C7C22×C412yes—
176C24×C7C2×D412yes—
177C24×C7C2×D412yes—
178C24×C7C2411yescharacteristic
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×C7C22×C412yes—
214C22×C4×C7C22×C412yes—
215C22×C4×C7C2×D412yes—
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2×D412yes—
219C22×C4×C7C2×D412yes—
220C22×C4×C7#4112yes—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—28no—
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—28no—
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—44no—
272C22×Dic7—44no—
273C22×Dic7—44no—
274C22×Dic7—44no—
275C22×Dic7—44no—
276C22×Dic7C22×C412yes—
277C22×Dic7C22×C412yes—
278C22×Dic7C22×C412yes—
279C22×Dic7C22×C412yes—
280C22×Dic7C2×D412yes—
281C22×Dic7C2×D412yes—
282C22×Dic7#4112yes—
283C22×Dic7#4112yes—
284C2×Dic14—28no—
285C2×Dic14—28no—
286C2×Dic14—44no—
287C2×Dic14—44no—
288C2×Dic14—44no—
289C2×Dic14—44no—
290C2×Dic14—44no—
291C7×C4⋊C4—44no—
292C7×C22⋊C4—44no—
293C7×C22⋊C4—44no—
294C7×C22⋊C4C22⋊C4116yes—
295C42×C7—44no—
296C22⋊Dic7—28no—
297C22⋊Dic7—44no—
298C22⋊Dic7—44no—
299C4⋊Dic7—28no—
300C4⋊Dic7—44no—
301Dic7⋊C4—28no—
302Dic7⋊C4—28no—
303C4×Dic7—44no—
304C23×Q8—71no—
305C24×C4—71no—
306C2×C22⋊Q8—78no—
307C2×C22⋊Q8—144no—
308C2×C22⋊Q8—144no—
309C22×C4⋊C4—71no—
310C22×C4⋊C4—71no—
311C22×C4⋊C4—71no—
312C22×C4⋊C4—71no—
313C22×C4⋊C4C2×D711yescharacteristic
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C22⋊C4—71no—
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C22⋊C4C2×D711yescharacteristic
319C22×C22⋊C4C2×D711yescharacteristic
320C22×C42—71no—
321C22×C42C2×D711yescharacteristic
322#391—144no—
323#388—24no—
324#388—144no—
325#381—144no—
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—71no—
340C2×#95—71no—
341C2×#95—71no—
342C2×#95—71no—
343C2×#95—71no—
344C2×#95C2×D711yescharacteristic
345C2×#95C2×D711yescharacteristic
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—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
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—41no—
374C23×C7—41no—
375C23×C7—41no—
376C23×C7—41no—
377C23×C7—41no—
378C23×C7—41no—
379C23×C7—41no—
380C23×C7C2×C22⋊C414yes—
381C23×C7C23×C411yescharacteristic
382C23×C7C22×D411yescharacteristic
383C23×C7C22×D411yescharacteristic
384C23×C7C22×D411yescharacteristic
385C23×C7C2×#4111yescharacteristic
386C23×C7C2×#4111yescharacteristic
387C23×C7C2×#4111yescharacteristic
388C23×C7H(5,𝔽2)11yescharacteristic
389C23×C7H(5,𝔽2)11yescharacteristic
390C23×C7H(5,𝔽2)11yescharacteristic
391C23×C72−1+411yescharacteristic
392C23×C72−1+411yescharacteristic
393C23×C72−1+411yescharacteristic
394C23×C72−1+411yescharacteristic
395C23×C72−1+411yescharacteristic
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—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—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7C2×C22⋊C414yes—
437C2×C4×C7C2×C22⋊C414yes—
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—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—416no—
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×Dic7C4×D414yes—
495Dic14—416no—
496C25C22×D711yescharacteristic
497C22×Q8—74no—
498C22×Q8—142no—
499C22×Q8—142no—
500C22×Q8—142no—
501C22×Q8—142no—
502C22×Q8—281no—
503C22×Q8—281no—
504C23×C4—71no—
505C23×C4—71no—
506C23×C4—71no—
507C23×C4—71no—
508C23×C4—71no—
509C23×C4—71no—
510C23×C4—74no—
511C23×C4—71no—
512C23×C4—71no—
513C23×C4—142no—
514C23×C4—142no—
515C23×C4—142no—
516C23×C4—142no—
517C23×C4—281no—
518C23×C4—281no—
519C23×C4C22×D711yescharacteristic
520C23×C4C22×D711yescharacteristic
521C23×C4C22×D711yescharacteristic
522C23×C4C22×D711yescharacteristic
523C23×C4C22×D711yescharacteristic
524C23×C4C22×D711yescharacteristic
525C22⋊Q8—1432no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4—74no—
530C2×C4⋊C4—74no—
531C2×C4⋊C4—74no—
532C2×C4⋊C4—142no—
533C2×C4⋊C4—142no—
534C2×C4⋊C4—142no—
535C2×C4⋊C4—142no—
536C2×C4⋊C4—142no—
537C2×C4⋊C4—142no—
538C2×C4⋊C4—142no—
539C2×C4⋊C4—142no—
540C2×C4⋊C4—281no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4—41no—
547C2×C22⋊C4—74no—
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—281no—
555C2×C22⋊C4—281no—
556C2×C22⋊C4C4×D714yes—
557C2×C22⋊C4D2814yes—
558C2×C22⋊C4C22⋊D714yes—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—41no—
562C2×C42—142no—
563C2×C42—142no—
564C2×C42—281no—
565#95—22no—
566#95—22no—
567#95—74no—
568#95—142no—
569#95—142no—
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—
584#95—281no—
585C22×C7—24no—
586C22×C7—24no—
587C22×C7—24no—
588C22×C7—42no—
589C22×C7—42no—
590C22×C7—42no—
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×C7C22×C22⋊C411yescharacteristic
601C22×C7C2×C4×D411yescharacteristic
602C22×C7C4×#4111yescharacteristic
603C22×C7#51811yescharacteristic
604C22×C7#51911yescharacteristic
605C22×C7#51911yescharacteristic
606C22×C7#52011yescharacteristic
607C22×C7#53611yescharacteristic
608C22×C7#53611yescharacteristic
609C22×C7#53611yescharacteristic
610C22×C7#53611yescharacteristic
611C22×C7#53611yescharacteristic
612C22×C7#53711yescharacteristic
613C22×C7#53911yescharacteristic
614C22×C7#53911yescharacteristic
615C22×C7#54111yescharacteristic
616C22×C7#54211yescharacteristic
617C22×C7#54211yescharacteristic
618C22×C7#54211yescharacteristic
619C22×C7D4211yescharacteristic
620C22×C7D4211yescharacteristic
621C22×C7#54611yescharacteristic
622C22×C7#54611yescharacteristic
623C22×C7#54611yescharacteristic
624C22×C7#54611yescharacteristic
625C22×C7#54711yescharacteristic
626C22×C7#54711yescharacteristic
627C22×C7#54711yescharacteristic
628C22×C7#54811yescharacteristic
629C22×C7#55211yescharacteristic
630C22×C7#55611yescharacteristic
631C22×C7#56211yescharacteristic
632C22×C7#56211yescharacteristic
633C22×C7#56311yescharacteristic
634C22×C7#56311yescharacteristic
635C4×C7—24no—
636C4×C7—24no—
637C4×C7—42no—
638C4×C7—42no—
639C4×C7—81no—
640C4×C7—81no—
641Dic7—24no—
642Dic7—42no—
643Dic7—42no—
644Dic7—42no—
645Dic7—42no—
646Dic7—42no—
647Dic7—81no—
648Dic7—81no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24C2×C4×D712yes—
662C24C2×D2812yes—
663C24C2×C22⋊D712yes—
664C24C23×D711yescharacteristic
665C2×Q8—148no—
666C2×Q8—148no—
667C2×Q8—284no—
668C2×Q8—284no—
669C2×Q8—284no—
670C2×Q8—284no—
671C2×Q8—284no—
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—21no—
706C22×C4—72no—
707C22×C4—72no—
708C22×C4—72no—
709C22×C4—72no—
710C22×C4—72no—
711C22×C4—72no—
712C22×C4—72no—
713C22×C4—72no—
714C22×C4—148no—
715C22×C4—141no—
716C22×C4—141no—
717C22×C4—141no—
718C22×C4—141no—
719C22×C4—148no—
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—141no—
755C22×C4—141no—
756C22×C4—141no—
757C22×C4—141no—
758C22×C4—141no—
759C22×C4—141no—
760C22×C4—141no—
761C22×C4—141no—
762C22×C4—141no—
763C22×C4—141no—
764C22×C4—284no—
765C22×C4—284no—
766C22×C4—284no—
767C22×C4—284no—
768C22×C4—284no—
769C22×C4C2×C4×D712yes—
770C22×C4C2×C4×D712yes—
771C22×C4C2×D2812yes—
772C22×C4C2×D2812yes—
773C22×C4D4×D712yes—
774C22×C4#115912yes—
775C22×C4C2×C22⋊D712yes—
776C22×C4C2×C22⋊D712yes—
777C4⋊C4—44no—
778C4⋊C4—148no—
779C4⋊C4—148no—
780C4⋊C4—148no—
781C4⋊C4—284no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—148no—
785C22⋊C4—284no—
786C22⋊C4—284no—
787C22⋊C4(C2×D7)⋊C4116yes—
788C42—44no—
789C42—284no—
790C2×C7—44no—
791C2×C7#231011yescharacteristic
792C2×C7#232311yescharacteristic
793C2×C7#233211yescharacteristic
794C2×C7D4×C22⋊C411yescharacteristic
795C2×C7#233911yescharacteristic
796C2×C7#236211yescharacteristic
797C2×C7#237811yescharacteristic
798C2×C7#267211yescharacteristic
799C2×C7#267411yescharacteristic
800C2×C7#268011yescharacteristic
801C2×C7#268111yescharacteristic
802C2×C7#268711yescharacteristic
803C2×C7#268911yescharacteristic
804C2×C7#269811yescharacteristic
805C2×C7#270011yescharacteristic
806C23—22no—
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—41no—
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—
840C23C2×(C2×D7)⋊C414yes—
841C23C22×C4×D711yescharacteristic
842C23C22×D2811yescharacteristic
843C23C2×D4×D711yescharacteristic
844C23C2×#115911yescharacteristic
845C23#654811yescharacteristic
846C23#654811yescharacteristic
847C23D7×#4111yescharacteristic
848C23D7×#4111yescharacteristic
849C23#655311yescharacteristic
850C23#655411yescharacteristic
851C23#655411yescharacteristic
852C23#655411yescharacteristic
853C23#655411yescharacteristic
854C23#655411yescharacteristic
855C23C22×C22⋊D711yescharacteristic
856Q8—2816no—
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—74no—
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—142no—
917C2×C4—142no—
918C2×C4—142no—
919C2×C4—2816no—
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×C4—281no—
953C2×C4—281no—
954C2×C4C2×(C2×D7)⋊C414yes—
955C2×C4C2×(C2×D7)⋊C414yes—
956C7#1436411yescharacteristic, 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#9020711yescharacteristic
973C22#9020711yescharacteristic
974C22#9021711yescharacteristic
975C22#9021711yescharacteristic
976C22C4×#115911yescharacteristic
977C22C4×D4×D711yescharacteristic
978C22#9023611yescharacteristic
979C22#9023711yescharacteristic
980C22D4×D2811yescharacteristic
981C22#9024511yescharacteristic
982C22#9024511yescharacteristic
983C22#9024611yescharacteristic
984C22#9028911yescharacteristic
985C22#9029311yescharacteristic
986C22#9029911yescharacteristic
987C22#9031211yescharacteristic
988C22#9033911yescharacteristic
989C22#9034211yescharacteristic
990C22#9034611yescharacteristic
991C22#9035111yescharacteristic
992C22#9036011yescharacteristic
993C22#9036211yescharacteristic
994C22#9037311yescharacteristic
995C22#9037511yescharacteristic
996C22#9039211yescharacteristic
997C22#9039911yescharacteristic
998C22#9040111yescharacteristic
999C22#9040311yescharacteristic
1000C22C22×(C2×D7)⋊C411yescharacteristic
1001C22D4×C22⋊D711yescharacteristic
1002C22#9049711yescharacteristic
1003C22#9051511yescharacteristic
1004C22#9051611yescharacteristic
1005C22#9051611yescharacteristic
1006C22#9052011yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—144no—
1014C4—282no—
1015C4—282no—
1016C4—282no—
1017C4—282no—
1018C4—282no—
1019C4—561no—
1020C4—561no—
1021C2—44no—
1022C2#1173290511yescharacteristic
1023C2#1173290811yescharacteristic
1024C2#1173292411yescharacteristic
1025C2#1173293711yescharacteristic
1026C2#1173311011yescharacteristic
1027C2#1173311111yescharacteristic
1028C2#1173311511yescharacteristic
1029C2#1173311611yescharacteristic
1030C2#1173967511yescharacteristic
1031C2#1173977511yescharacteristic
1032C2D4×(C2×D7)⋊C411yescharacteristic
1033C2#1174013011yescharacteristic
1034C2#1174031611yescharacteristic
1035C2#1174043011yescharacteristic
1036C2#1174053811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#388C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#388D7
hypocenterC7#14364
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
5. C2×#89701C2semidirect
6. #11729320C2semidirect
7. #11729317C2semidirect
11. #11729290C2semidirect
12. #11727178C2semidirect
13. #11727176C2semidirect
14. #11727164C2semidirect
15. #11727159C2semidirect
33. C2×#6441C4semidirect
956. C7#14364semidirect

Maximal subgroups

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

subgroupindex
C22×#64412
C2×C7×#3882
C2×#897232
C2×#897152
C2×#897012
#117293202
#117293172
#117293032
#117292982
#117292902
#117271782
#117271762
#117271642
#117271592
#143647