Finite Group Databasebeta

← #13281960

Subgroups — #13281960

Order 1792.

1670 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6507C211yesmaximal, characteristic
2C2×#90002C211yesmaximal, characteristic
3C2×#89418C211yesmaximal, characteristic
4C2×#89427C211yesmaximal, characteristic
5C2×#89424C211yesmaximal, characteristic
6C7×#1446C211yesmaximal, characteristic
7#11727178C211yesmaximal, characteristic
8#11727175C211yesmaximal, characteristic
9#11727175C211yesmaximal, characteristic
10#11727164C211yesmaximal, characteristic
11#11727163C211yesmaximal, characteristic
12#11727160C211yesmaximal, characteristic
13#11727159C211yesmaximal, characteristic
14#11727157C211yesmaximal, characteristic
15#11727155C211yesmaximal, characteristic
16C23×C7×Q8C2211yescharacteristic
17C23×Dic14C2211yescharacteristic
18C2×#6507—24no—
19C2×#6507—24no—
20C2×#6507C418yescomplemented
21C22×C4⋊Dic7C2211yescharacteristic
22C22×Dic7⋊C4C2211yescharacteristic
23C22×Dic7⋊C4C2211yescharacteristic
24C22×Dic7⋊C4C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36#90002—24no—
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#89427—24no—
56#89424—24no—
57#89418—24no—
58#14420—71nomaximal, Sylow
59C22×C7×Q8—22no—
60C22×C7×Q8—22no—
61C22×C7×Q8—22no—
62C22×C7×Q8—22no—
63C22×C7×Q8—41no—
64C22×C7×Q8—41no—
65C22×C7×Q8C2×C414yes—
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
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—
88#6507—232no—
89C2×C4⋊Dic7—22no—
90C2×C4⋊Dic7—22no—
91C2×C4⋊Dic7—41no—
92C2×Dic7⋊C4—22no—
93C2×Dic7⋊C4—22no—
94C2×Dic7⋊C4—22no—
95C2×Dic7⋊C4—22no—
96C2×Dic7⋊C4—22no—
97C2×Dic7⋊C4—22no—
98C2×Dic7⋊C4—22no—
99C2×Dic7⋊C4—22no—
100C2×Dic7⋊C4—41no—
101C2×Dic7⋊C4C2×C414yes—
102C2×Dic7⋊C4C2×C414yes—
103C2×Dic7⋊C4C2×C414yes—
104C2×Dic7⋊C4C2×C414yes—
105C2×Dic7⋊C4D414yes—
106C2×Dic7⋊C4D414yes—
107C2×C4×Dic7—22no—
108C2×C4×Dic7—22no—
109C2×C4×Dic7—22no—
110C2×C4×Dic7—22no—
111C2×C4×Dic7—22no—
112C2×C4×Dic7—22no—
113C2×C4×Dic7—41no—
114C2×C4×Dic7—41no—
115C2×C4×Dic7C2×C414yes—
116C7×#95—22no—
117C7×#95—22no—
118C7×#95—22no—
119C7×#95—22no—
120C7×#95—41no—
121C7×#95—41no—
122C7⋊#95—22no—
123C7⋊#95—22no—
124C7⋊#95—22no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—22no—
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—41no—
137C7⋊#95—41no—
138C7⋊#95D414yes—
139C7⋊#95Q814yescomplemented
140C22×C4⋊Q8—71no—
141C2×#391—71no—
142C2×#391—71no—
143C2×#387—71no—
144C2×#387—71no—
145#1446—71no—
146#1446D711yescharacteristic
147#1445—71no—
148#1445—71no—
149#1441—71no—
150#1441—71no—
151#1436—71no—
152#1436—71no—
153#1434—71no—
154#1434—71no—
155C24×C7C2411yescharacteristic
156C2×C7×Q8—28no—
157C2×C7×Q8—28no—
158C2×C7×Q8—44no—
159C2×C7×Q8—44no—
160C2×C7×Q8—44no—
161C2×C7×Q8—44no—
162C2×C7×Q8—44no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
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×C7C22×C412yes—
205C22×C4×C7C22×C412yes—
206C22×C4×C7C22×C412yes—
207C22×C4×C7C2×D412yes—
208C22×C4×C7C2×D412yes—
209C22×C4×C7C2×D412yes—
210C22×C4×C7C2×Q812yes—
211C22×C4×C7#4112yes—
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
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×Dic7C22×C412yes—
256C22×Dic7C22×C412yes—
257C22×Dic7C22×C412yes—
258C22×Dic7C22×C412yes—
259C22×Dic7C2×D412yes—
260C22×Dic7C2×D412yes—
261C22×Dic7C2×D412yes—
262C22×Dic7C2×D412yes—
263C22×Dic7C2×D412yes—
264C22×Dic7C2×D412yes—
265C22×Dic7C2×Q812yes—
266C22×Dic7C2×Q812yes—
267C22×Dic7#4112yes—
268C2×Dic14—28no—
269C2×Dic14—28no—
270C2×Dic14—44no—
271C2×Dic14—44no—
272C2×Dic14—44no—
273C2×Dic14—44no—
274C2×Dic14—44no—
275C4⋊Dic7—44no—
276Dic7⋊C4—28no—
277Dic7⋊C4—28no—
278Dic7⋊C4—28no—
279Dic7⋊C4—44no—
280Dic7⋊C4C22⋊C4116yes—
281C4×Dic7—28no—
282C4×Dic7—44no—
283C4×Dic7—44no—
284C23×Q8—71no—
285C23×Q8C2×D711yescharacteristic
286C2×C4⋊Q8—78no—
287C2×C4⋊Q8—144no—
288C2×C4⋊Q8—144no—
289C22×C4⋊C4—71no—
290C22×C4⋊C4—71no—
291C22×C4⋊C4—71no—
292C22×C4⋊C4—71no—
293C22×C4⋊C4—71no—
294C22×C4⋊C4—71no—
295C22×C42—71no—
296C22×C42—71no—
297C22×C42—71no—
298#391—144no—
299#391—144no—
300#387—144no—
301#387—144no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95—71no—
305C2×#95—71no—
306C2×#95—71no—
307C2×#95—71no—
308C2×#95—71no—
309C2×#95—71no—
310C2×#95—71no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95C2×D711yescharacteristic
321C2×#95C2×D711yescharacteristic
322C2×#95C2×D711yescharacteristic
323C2×#95C2×D711yescharacteristic
324C2×#95C2×D711yescharacteristic
325C2×#95C2×D711yescharacteristic
326C23×C7C23×C411yescharacteristic
327C23×C7C22×D411yescharacteristic
328C23×C7C22×D411yescharacteristic
329C23×C7C22×D411yescharacteristic
330C23×C7C22×Q811yescharacteristic
331C23×C7C2×#4111yescharacteristic
332C23×C7C2×#4111yescharacteristic
333C23×C7H(5,𝔽2)11yescharacteristic
334C23×C7H(5,𝔽2)11yescharacteristic
335C23×C72−1+411yescharacteristic
336C23×C72−1+411yescharacteristic
337C23×C72−1+411yescharacteristic
338C23×C72−1+411yescharacteristic
339C23×C72−1+411yescharacteristic
340C23×C72−1+411yescharacteristic
341C7×Q8—416no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—41no—
370C2×C4×C7—41no—
371C2×C4×C7—41no—
372C2×C4×C7—41no—
373C2×C4×C7—41no—
374C2×C4×C7—41no—
375C2×C4×C7—41no—
376C2×C4×C7—41no—
377C2×C4×C7—41no—
378C2×C4×C7—41no—
379C2×C4×C7—41no—
380C2×C4×C7—41no—
381C2×C4×C7—41no—
382C2×C4×C7—41no—
383C2×C4×C7—41no—
384C2×C4×C7—41no—
385C2×C4×C7—41no—
386C2×C4×C7—41no—
387C2×C4×C7—41no—
388C2×C4×C7—41no—
389C2×C4×C7C2×C22⋊C414yes—
390C2×C4×C7C4×D414yes—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—41no—
422C2×Dic7—41no—
423C2×Dic7—41no—
424C2×Dic7—41no—
425C2×Dic7—41no—
426C2×Dic7—41no—
427C2×Dic7—41no—
428C2×Dic7—41no—
429C2×Dic7—41no—
430C2×Dic7—41no—
431C2×Dic7—41no—
432C2×Dic7—41no—
433C2×Dic7—41no—
434C2×Dic7—41no—
435C2×Dic7—41no—
436C2×Dic7—41no—
437C2×Dic7—41no—
438C2×Dic7—41no—
439C2×Dic7—41no—
440C2×Dic7—41no—
441C2×Dic7—41no—
442C2×Dic7—41no—
443C2×Dic7—41no—
444C2×Dic7C2×C22⋊C414yes—
445C2×Dic7C2×C22⋊C414yes—
446C2×Dic7C4×Q814yes—
447Dic14—416no—
448C22×Q8—22no—
449C22×Q8—22no—
450C22×Q8—22no—
451C22×Q8—22no—
452C22×Q8—41no—
453C22×Q8—41no—
454C22×Q8—74no—
455C22×Q8—142no—
456C22×Q8—142no—
457C22×Q8—142no—
458C22×Q8—142no—
459C22×Q8—281no—
460C22×Q8—281no—
461C22×Q8C4×D714yes—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4C22×D711yescharacteristic
471C23×C4C22×D711yescharacteristic
472C23×C4C22×D711yescharacteristic
473C23×C4C22×D711yescharacteristic
474C23×C4C22×D711yescharacteristic
475C23×C4C22×D711yescharacteristic
476C23×C4C22×D711yescharacteristic
477C4⋊Q8—1432no—
478C2×C4⋊C4—74no—
479C2×C4⋊C4—74no—
480C2×C4⋊C4—74no—
481C2×C4⋊C4—74no—
482C2×C4⋊C4—74no—
483C2×C4⋊C4—74no—
484C2×C4⋊C4—142no—
485C2×C4⋊C4—142no—
486C2×C4⋊C4—142no—
487C2×C4⋊C4—142no—
488C2×C4⋊C4—142no—
489C2×C4⋊C4—142no—
490C2×C4⋊C4—142no—
491C2×C4⋊C4—142no—
492C2×C4⋊C4—142no—
493C2×C4⋊C4—142no—
494C2×C4⋊C4—281no—
495C2×C4⋊C4—281no—
496C2×C42—74no—
497C2×C42—142no—
498C2×C42—142no—
499C2×C42—142no—
500C2×C42—142no—
501C2×C42—142no—
502C2×C42—142no—
503C2×C42—281no—
504C2×C42—281no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—41no—
510#95—41no—
511#95—74no—
512#95—74no—
513#95—142no—
514#95—142no—
515#95—142no—
516#95—142no—
517#95—142no—
518#95—142no—
519#95—142no—
520#95—142no—
521#95—142no—
522#95—142no—
523#95—142no—
524#95—142no—
525#95—142no—
526#95—142no—
527#95—281no—
528#95—281no—
529C22×C7C22×C22⋊C411yescharacteristic
530C22×C7C2×C4×D411yescharacteristic
531C22×C7C2×C4×Q811yescharacteristic
532C22×C7#51811yescharacteristic
533C22×C7#51911yescharacteristic
534C22×C7#51911yescharacteristic
535C22×C7#51911yescharacteristic
536C22×C7#53611yescharacteristic
537C22×C7#53611yescharacteristic
538C22×C7#53611yescharacteristic
539C22×C7#53611yescharacteristic
540C22×C7#53611yescharacteristic
541C22×C7#53611yescharacteristic
542C22×C7#54111yescharacteristic
543C22×C7#54111yescharacteristic
544C22×C7#54211yescharacteristic
545C22×C7#54211yescharacteristic
546C22×C7#54411yescharacteristic
547C22×C7#54411yescharacteristic
548C22×C7D4211yescharacteristic
549C22×C7D4211yescharacteristic
550C22×C7#54611yescharacteristic
551C22×C7#54611yescharacteristic
552C22×C7#54711yescharacteristic
553C22×C7#54811yescharacteristic
554C22×C7#54811yescharacteristic
555C22×C7D4×Q811yescharacteristic
556C22×C7D4×Q811yescharacteristic
557C22×C7D4×Q811yescharacteristic
558C22×C7#55611yescharacteristic
559C22×C7#55711yescharacteristic
560C22×C7#56311yescharacteristic
561C22×C7#56311yescharacteristic
562C22×C7#56311yescharacteristic
563C22×C7#56311yescharacteristic
564C4×C7—24no—
565C4×C7—24no—
566C4×C7—42no—
567C4×C7—42no—
568C4×C7—81no—
569C4×C7—81no—
570C4×C7—81no—
571Dic7—24no—
572Dic7—24no—
573Dic7—24no—
574Dic7—42no—
575Dic7—42no—
576Dic7—42no—
577Dic7—42no—
578Dic7—81no—
579C24C23×D711yescharacteristic
580C2×Q8—28no—
581C2×Q8—28no—
582C2×Q8—44no—
583C2×Q8—44no—
584C2×Q8—44no—
585C2×Q8—44no—
586C2×Q8—44no—
587C2×Q8—148no—
588C2×Q8—148no—
589C2×Q8—284no—
590C2×Q8—284no—
591C2×Q8—284no—
592C2×Q8—284no—
593C2×Q8—284no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—72no—
636C22×C4—72no—
637C22×C4—72no—
638C22×C4—72no—
639C22×C4—72no—
640C22×C4—72no—
641C22×C4—72no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—72no—
645C22×C4—72no—
646C22×C4—72no—
647C22×C4—72no—
648C22×C4—141no—
649C22×C4—141no—
650C22×C4—141no—
651C22×C4—141no—
652C22×C4—141no—
653C22×C4—141no—
654C22×C4—141no—
655C22×C4—141no—
656C22×C4—141no—
657C22×C4—141no—
658C22×C4—141no—
659C22×C4—141no—
660C22×C4—141no—
661C22×C4—141no—
662C22×C4—141no—
663C22×C4—141no—
664C22×C4—141no—
665C22×C4—141no—
666C22×C4—141no—
667C22×C4—141no—
668C22×C4—141no—
669C22×C4—141no—
670C22×C4—141no—
671C22×C4—141no—
672C22×C4—141no—
673C22×C4—141no—
674C22×C4—141no—
675C22×C4—141no—
676C22×C4—141no—
677C22×C4—141no—
678C22×C4—141no—
679C22×C4—141no—
680C22×C4—141no—
681C22×C4—141no—
682C22×C4—141no—
683C22×C4—141no—
684C22×C4—141no—
685C22×C4—141no—
686C22×C4—141no—
687C22×C4—141no—
688C22×C4—141no—
689C22×C4—141no—
690C22×C4—141no—
691C22×C4C2×C4×D712yes—
692C22×C4C2×C4×D712yes—
693C22×C4C2×C4×D712yes—
694C22×C4D4×D712yes—
695C22×C4D4×D712yes—
696C22×C4D4×D712yes—
697C22×C4#115912yes—
698C22×C4Q8×D712yes—
699C4⋊C4—716no—
700C4⋊C4—148no—
701C4⋊C4—148no—
702C4⋊C4—148no—
703C4⋊C4—284no—
704C4⋊C4—284no—
705C42—148no—
706C42—284no—
707C42—284no—
708C2×C7#231011yescharacteristic
709C2×C7#232711yescharacteristic
710C2×C7#233111yescharacteristic
711C2×C7D4×C22⋊C411yescharacteristic
712C2×C7Q8×C22⋊C411yescharacteristic
713C2×C7#236511yescharacteristic
714C2×C7#238111yescharacteristic
715C2×C7#267411yescharacteristic
716C2×C7#267411yescharacteristic
717C2×C7#267711yescharacteristic
718C2×C7#267711yescharacteristic
719C2×C7#271311yescharacteristic
720C2×C7#271311yescharacteristic
721C2×C7#271611yescharacteristic
722C2×C7#271611yescharacteristic
723C23C22×C4×D711yescharacteristic
724C23C2×D4×D711yescharacteristic
725C23C2×D4×D711yescharacteristic
726C23C2×D4×D711yescharacteristic
727C23C2×#115911yescharacteristic
728C23#654811yescharacteristic
729C23#654811yescharacteristic
730C23C2×Q8×D711yescharacteristic
731C23#655111yescharacteristic
732C23#655111yescharacteristic
733C23#655111yescharacteristic
734C23D7×#4111yescharacteristic
735C23#655411yescharacteristic
736C23#655411yescharacteristic
737C23#655411yescharacteristic
738Q8—416no—
739Q8—2816no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—74no—
788C2×C4—74no—
789C2×C4—74no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—142no—
795C2×C4—142no—
796C2×C4—142no—
797C2×C4—142no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—142no—
801C2×C4—142no—
802C2×C4—142no—
803C2×C4—142no—
804C2×C4—142no—
805C2×C4—142no—
806C2×C4—142no—
807C2×C4—142no—
808C2×C4—142no—
809C2×C4—142no—
810C2×C4—142no—
811C2×C4—142no—
812C2×C4—142no—
813C2×C4—142no—
814C2×C4—142no—
815C2×C4—142no—
816C2×C4—142no—
817C2×C4—142no—
818C2×C4—142no—
819C2×C4—142no—
820C2×C4—281no—
821C2×C4—281no—
822C2×C4—281no—
823C2×C4—281no—
824C2×C4—281no—
825C2×C4—281no—
826C2×C4—281no—
827C2×C4—281no—
828C2×C4—281no—
829C2×C4—281no—
830C2×C4—281no—
831C2×C4—281no—
832C2×C4—281no—
833C2×C4—281no—
834C2×C4—281no—
835C2×C4—281no—
836C2×C4—281no—
837C2×C4—281no—
838C2×C4—281no—
839C2×C4—281no—
840C2×C4—281no—
841C2×C4—281no—
842C2×C4—281no—
843C2×C4D7×C22⋊C414yes—
844C2×C4(C22⋊D7)⋊C414yes—
845C7#1442011yescharacteristic, complemented, Sylow
846C22C2×D7×C22⋊C411yescharacteristic
847C22C2×(C22⋊D7)⋊C411yescharacteristic
848C22#9017711yescharacteristic
849C22C4×Q8×D711yescharacteristic
850C22#9026311yescharacteristic
851C22#9026311yescharacteristic
852C22#9026311yescharacteristic
853C22#9028111yescharacteristic
854C22#9028111yescharacteristic
855C22#9028211yescharacteristic
856C22#9028211yescharacteristic
857C22#9031411yescharacteristic
858C22#9031611yescharacteristic
859C22#9031611yescharacteristic
860C22#9031911yescharacteristic
861C22#9031911yescharacteristic
862C22#9032211yescharacteristic
863C22#9032311yescharacteristic
864C22#9032311yescharacteristic
865C22#9032411yescharacteristic
866C22#9033111yescharacteristic
867C22#9033711yescharacteristic
868C22#9033711yescharacteristic
869C22#9036011yescharacteristic
870C22#9036211yescharacteristic
871C22#9036311yescharacteristic
872C22#9036611yescharacteristic
873C22#9036611yescharacteristic
874C22#9036811yescharacteristic
875C22#9041211yescharacteristic
876C22#9041511yescharacteristic
877C22#9041511yescharacteristic
878C22#9041811yescharacteristic
879C22#9042011yescharacteristic
880C22#9042611yescharacteristic
881C4—24no—
882C4—24no—
883C4—42no—
884C4—42no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4—144no—
889C4—144no—
890C4—144no—
891C4—282no—
892C4—282no—
893C4—282no—
894C4—282no—
895C4—561no—
896C2#1173129511yescharacteristic
897C2#1173393011yescharacteristic
898C2#1173393111yescharacteristic
899C2#1173393711yescharacteristic
900C2#1173394211yescharacteristic
901C2#1173405511yescharacteristic
902C2#1173405911yescharacteristic
903C2#1173426811yescharacteristic
904C2#1173427511yescharacteristic
905C2#1173427611yescharacteristic
906C2#1173431911yescharacteristic
907C2#1173466211yescharacteristic
908C2#1173466311yescharacteristic
909C2#1173470511yescharacteristic
910C2#1173470611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1446C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1446D7
hypocenterC7#14420
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
20. C2×#6507C4semidirect
139. C7⋊#95Q8semidirect
845. C7#14420semidirect

Maximal subgroups

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

subgroupindex
C22×#65072
C2×#900022
C2×#894182
C2×#894272
C2×#894242
C7×#14462
#117271782
#117271752
#117271642
#117271632
#117271602
#117271592
#117271572
#117271552
#144207