Finite Group Databasebeta

← #13285094

Subgroups — #13285094

Order 1792.

1630 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89744C211yesmaximal, characteristic
2C2×C42×Dic7C211yesmaximal, characteristic
3C2×#89418C211yesmaximal, characteristic
4C2×#89418C211yesmaximal, characteristic
5C2×#89418C211yesmaximal, characteristic
6C7×#1436C211yesmaximal, characteristic
7#11729318C211yesmaximal, characteristic
8#11729290C211yesmaximal, characteristic
9#11727159C211yesmaximal, characteristic
10Dic7⋊#95C211yesmaximal, characteristic
11Dic7⋊#95C211yesmaximal, characteristic
12#11727156C211yesmaximal, characteristic
13#11727156C211yesmaximal, characteristic
14#11727155C211yesmaximal, characteristic
15#11727155C211yesmaximal, characteristic
16C23×Dic14C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C22×Dic7⋊C4C2211yescharacteristic
20C22×Dic7⋊C4C2211yescharacteristic
21C22×Dic7⋊C4C2211yescharacteristic
22C22×Dic7⋊C4C2211yescharacteristic
23C22×C4×Dic7C2211yescharacteristic
24C22×C4×Dic7C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
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#89744—24no—
52C42×Dic7—24no—
53#89418—24no—
54#89418—24no—
55#89418C418yescomplemented
56#14703—71nomaximal, Sylow
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C22×Dic14—22no—
73C22×Dic14—22no—
74C22×Dic14—22no—
75C22×Dic14—22no—
76C22×Dic14—22no—
77C22×Dic14—22no—
78C22×Dic14C2×C414yes—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—22no—
82C2×C42×C7—22no—
83C2×C42×C7—22no—
84C2×C42×C7—22no—
85C2×Dic7⋊C4—22no—
86C2×Dic7⋊C4—22no—
87C2×Dic7⋊C4—22no—
88C2×Dic7⋊C4—22no—
89C2×Dic7⋊C4—22no—
90C2×Dic7⋊C4—22no—
91C2×Dic7⋊C4—22no—
92C2×Dic7⋊C4—22no—
93C2×Dic7⋊C4—22no—
94C2×Dic7⋊C4—22no—
95C2×Dic7⋊C4—22no—
96C2×Dic7⋊C4C2×C414yes—
97C2×C4×Dic7—22no—
98C2×C4×Dic7—22no—
99C2×C4×Dic7—22no—
100C2×C4×Dic7—22no—
101C2×C4×Dic7—22no—
102C2×C4×Dic7—22no—
103C2×C4×Dic7—22no—
104C2×C4×Dic7—22no—
105C2×C4×Dic7—22no—
106C2×C4×Dic7—22no—
107C2×C4×Dic7—22no—
108C2×C4×Dic7—22no—
109C2×C4×Dic7—22no—
110C2×C4×Dic7C2×C414yes—
111C2×C4×Dic7D414yes—
112C2×C4×Dic7D414yes—
113C2×C4×Dic7Q814yescomplemented
114C2×C4×Dic7Q814yescomplemented
115C7×#95—22no—
116C7×#95—22no—
117C7×#95—22no—
118C7×#95—22no—
119C7×#95C2×C414yes—
120C7⋊#95—22no—
121C7⋊#95—22no—
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⋊#95C2×C414yes—
135C7⋊#95C2×C414yes—
136C7⋊#95C2×C414yes—
137C2×#391—71no—
138C2×#391—71no—
139C2×#391—71no—
140C2×#389—71no—
141C2×C43—71no—
142#1436—71no—
143#1436—71no—
144#1436—71no—
145#1436D711yescharacteristic
146C4⋊#95—71no—
147C4⋊#95—71no—
148#1434—71no—
149#1434—71no—
150#1434—71no—
151#1434—71no—
152C24×C7C2411yescharacteristic
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
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×C7C22×C412yes—
192C22×C4×C7C22×C412yes—
193C22×C4×C7C22×C412yes—
194C22×C4×C7C2×D412yes—
195C22×C4×C7C2×D412yes—
196C22×C4×C7C2×Q812yes—
197C22×C4×C7C2×Q812yes—
198C22×C4×C7#4112yes—
199C22×C4×C7#4112yes—
200C22×C4×C7#4112yes—
201C22×C4×C7#4112yes—
202C22×Dic7—21no—
203C22×Dic7—21no—
204C22×Dic7—21no—
205C22×Dic7—21no—
206C22×Dic7—21no—
207C22×Dic7—21no—
208C22×Dic7—21no—
209C22×Dic7—21no—
210C22×Dic7—21no—
211C22×Dic7—21no—
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×Dic7C22×C412yes—
241C22×Dic7C22×C412yes—
242C22×Dic7C22×C412yes—
243C22×Dic7C22×C412yes—
244C22×Dic7C2×D412yes—
245C22×Dic7C2×D412yes—
246C22×Dic7C2×D412yes—
247C22×Dic7C2×D412yes—
248C22×Dic7C2×Q812yes—
249C22×Dic7C2×Q812yes—
250C22×Dic7C2×Q812yes—
251C22×Dic7C2×Q812yes—
252C22×Dic7#4112yes—
253C22×Dic7#4112yes—
254C22×Dic7#4112yes—
255C22×Dic7#4112yes—
256C22×Dic7#4112yes—
257C22×Dic7#4112yes—
258C2×Dic14—28no—
259C2×Dic14—28no—
260C2×Dic14—28no—
261C2×Dic14—44no—
262C2×Dic14—44no—
263C2×Dic14—44no—
264C2×Dic14—44no—
265C7×C4⋊C4—44no—
266C42×C7—28no—
267Dic7⋊C4—28no—
268Dic7⋊C4—44no—
269Dic7⋊C4—44no—
270Dic7⋊C4—44no—
271C4×Dic7—28no—
272C4×Dic7—28no—
273C4×Dic7—28no—
274C4×Dic7—28no—
275C4×Dic7—28no—
276C4×Dic7—28no—
277C23×Q8—71no—
278C22×C4⋊C4—71no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4—71no—
282C22×C4⋊C4C2×D711yescharacteristic
283C22×C42—71no—
284C22×C42—71no—
285C22×C42—71no—
286C22×C42—71no—
287C22×C42—71no—
288C22×C42—71no—
289C22×C42C2×D711yescharacteristic
290#391—78no—
291#391—144no—
292#391—144no—
293#389—144no—
294C2×#95—71no—
295C2×#95—71no—
296C2×#95—71no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
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×#95C2×D711yescharacteristic
312C2×#95C2×D711yescharacteristic
313C2×#95C2×D711yescharacteristic
314C2×#95C2×D711yescharacteristic
315C2×#95C2×D711yescharacteristic
316C43—144no—
317C23×C7C23×C411yescharacteristic
318C23×C7C22×D411yescharacteristic
319C23×C7C22×D411yescharacteristic
320C23×C7C22×Q811yescharacteristic
321C23×C7C22×Q811yescharacteristic
322C23×C7C2×#4111yescharacteristic
323C23×C7C2×#4111yescharacteristic
324C23×C7C2×#4111yescharacteristic
325C23×C7C2×#4111yescharacteristic
326C23×C7C2×#4111yescharacteristic
327C23×C7C2×#4111yescharacteristic
328C23×C7C2×#4111yescharacteristic
329C23×C7C2×#4111yescharacteristic
330C23×C7C2×#4111yescharacteristic
331C23×C7C2×#4111yescharacteristic
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
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—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
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×C7C4×Q814yes—
379C2×C4×C7C22⋊Q814yes—
380C2×C4×C7#12414yes—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
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—41no—
406C2×Dic7—41no—
407C2×Dic7—41no—
408C2×Dic7—41no—
409C2×Dic7—41no—
410C2×Dic7—41no—
411C2×Dic7—41no—
412C2×Dic7—41no—
413C2×Dic7—41no—
414C2×Dic7—41no—
415C2×Dic7—41no—
416C2×Dic7—41no—
417C2×Dic7—41no—
418C2×Dic7—41no—
419C2×Dic7—41no—
420C2×Dic7—41no—
421C2×Dic7—41no—
422C2×Dic7—41no—
423C2×Dic7—41no—
424C2×Dic7—41no—
425C2×Dic7—41no—
426C2×Dic7—41no—
427C2×Dic7#11714yes—
428C2×Dic7C4×D414yes—
429C2×Dic7C4×D414yes—
430C2×Dic7C4×Q814yes—
431C2×Dic7#12114yes—
432C2×Dic7C22⋊Q814yes—
433C2×Dic7#12314yes—
434C2×Dic7#12414yes—
435C2×Dic7#12614yes—
436C2×Dic7C4⋊Q814yes—
437Dic14—416no—
438C22×Q8—74no—
439C22×Q8—142no—
440C22×Q8—142no—
441C22×Q8—142no—
442C22×Q8—142no—
443C22×Q8—142no—
444C22×Q8—142no—
445C23×C4—71no—
446C23×C4—71no—
447C23×C4—71no—
448C23×C4—71no—
449C23×C4—71no—
450C23×C4—71no—
451C23×C4—71no—
452C23×C4—71no—
453C23×C4C22×D711yescharacteristic
454C23×C4C22×D711yescharacteristic
455C23×C4C22×D711yescharacteristic
456C23×C4C22×D711yescharacteristic
457C23×C4C22×D711yescharacteristic
458C23×C4C22×D711yescharacteristic
459C23×C4C22×D711yescharacteristic
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—74no—
464C2×C4⋊C4—142no—
465C2×C4⋊C4—142no—
466C2×C4⋊C4—142no—
467C2×C4⋊C4—142no—
468C2×C4⋊C4—142no—
469C2×C4⋊C4—142no—
470C2×C4⋊C4—142no—
471C2×C4⋊C4—142no—
472C2×C4⋊C4—142no—
473C2×C4⋊C4—142no—
474C2×C4⋊C4—142no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42—74no—
479C2×C42—74no—
480C2×C42—74no—
481C2×C42—74no—
482C2×C42—74no—
483C2×C42—142no—
484C2×C42—142no—
485C2×C42—142no—
486C2×C42—142no—
487C2×C42—142no—
488C2×C42—142no—
489C2×C42—142no—
490C2×C42—142no—
491C2×C42—142no—
492C2×C42—142no—
493C2×C42—142no—
494C2×C42—142no—
495C2×C42—142no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—74no—
501#95—74no—
502#95—74no—
503#95—142no—
504#95—142no—
505#95—142no—
506#95—142no—
507#95—142no—
508#95—142no—
509#95—142no—
510#95—142no—
511#95—142no—
512#95—142no—
513#95—142no—
514#95—142no—
515#95—142no—
516#95—142no—
517#95C4×D714yes—
518C22×C7C2×#11711yescharacteristic
519C22×C7C2×C4×D411yescharacteristic
520C22×C7C2×C4×D411yescharacteristic
521C22×C7C2×C4×Q811yescharacteristic
522C22×C7C2×C4×Q811yescharacteristic
523C22×C7C4×#4111yescharacteristic
524C22×C7C4×#4111yescharacteristic
525C22×C7C2×#12111yescharacteristic
526C22×C7C2×C22⋊Q811yescharacteristic
527C22×C7C2×C22⋊Q811yescharacteristic
528C22×C7C2×#12311yescharacteristic
529C22×C7#52511yescharacteristic
530C22×C7#52511yescharacteristic
531C22×C7C2×#12411yescharacteristic
532C22×C7C2×#12411yescharacteristic
533C22×C7C2×#12611yescharacteristic
534C22×C7#52911yescharacteristic
535C22×C7#52911yescharacteristic
536C22×C7#52911yescharacteristic
537C22×C7#52911yescharacteristic
538C22×C7#52911yescharacteristic
539C22×C7#52911yescharacteristic
540C22×C7#52911yescharacteristic
541C22×C7#52911yescharacteristic
542C22×C7C2×C4⋊Q811yescharacteristic
543C22×C7#53211yescharacteristic
544C22×C7#53211yescharacteristic
545C22×C7#53311yescharacteristic
546C22×C7#53311yescharacteristic
547C22×C7#53311yescharacteristic
548C22×C7#53311yescharacteristic
549C22×C7#53311yescharacteristic
550C22×C7#53311yescharacteristic
551C22×C7#53311yescharacteristic
552C22×C7#53311yescharacteristic
553C4×C7—24no—
554C4×C7—24no—
555C4×C7—24no—
556C4×C7—42no—
557C4×C7—42no—
558C4×C7—81no—
559C4×C7—81no—
560Dic7—24no—
561Dic7—24no—
562Dic7—24no—
563Dic7—42no—
564Dic7—42no—
565Dic7—81no—
566Dic7—81no—
567Dic7#38818yes—
568C24C23×D711yescharacteristic
569C2×Q8—148no—
570C2×Q8—148no—
571C2×Q8—148no—
572C2×Q8—284no—
573C2×Q8—284no—
574C2×Q8—284no—
575C2×Q8—284no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
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—72no—
615C22×C4—72no—
616C22×C4—72no—
617C22×C4—72no—
618C22×C4—72no—
619C22×C4—72no—
620C22×C4—72no—
621C22×C4—72no—
622C22×C4—72no—
623C22×C4—72no—
624C22×C4—72no—
625C22×C4—72no—
626C22×C4—72no—
627C22×C4—72no—
628C22×C4—72no—
629C22×C4—72no—
630C22×C4—72no—
631C22×C4—72no—
632C22×C4—141no—
633C22×C4—141no—
634C22×C4—141no—
635C22×C4—141no—
636C22×C4—141no—
637C22×C4—141no—
638C22×C4—141no—
639C22×C4—141no—
640C22×C4—141no—
641C22×C4—141no—
642C22×C4—141no—
643C22×C4—141no—
644C22×C4—141no—
645C22×C4—141no—
646C22×C4—141no—
647C22×C4—141no—
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×C4C2×C4×D712yes—
671C22×C4C2×C4×D712yes—
672C22×C4C2×C4×D712yes—
673C22×C4#115712yes—
674C22×C4#115712yes—
675C22×C4D4×D712yes—
676C22×C4D4×D712yes—
677C22×C4#115912yes—
678C22×C4#115912yes—
679C22×C4Q8×D712yes—
680C22×C4Q8×D712yes—
681C4⋊C4—44no—
682C4⋊C4—148no—
683C4⋊C4—284no—
684C4⋊C4—284no—
685C4⋊C4—284no—
686C42—28no—
687C42—148no—
688C42—148no—
689C42—148no—
690C42—148no—
691C42—148no—
692C42—148no—
693C2×C7C2×#38811yescharacteristic
694C2×C7#229511yescharacteristic
695C2×C7#229511yescharacteristic
696C2×C7C4×C22⋊Q811yescharacteristic
697C2×C7C4×C22⋊Q811yescharacteristic
698C2×C7C4×#12411yescharacteristic
699C2×C7C4×C4⋊Q811yescharacteristic
700C2×C7#285011yescharacteristic
701C2×C7#285511yescharacteristic
702C2×C7#285511yescharacteristic
703C2×C7#285711yescharacteristic
704C2×C7#286111yescharacteristic
705C2×C7#286211yescharacteristic
706C2×C7#286311yescharacteristic
707C2×C7#286311yescharacteristic
708C23C22×C4×D711yescharacteristic
709C23C2×#115711yescharacteristic
710C23C2×#115711yescharacteristic
711C23C2×D4×D711yescharacteristic
712C23C2×D4×D711yescharacteristic
713C23C2×#115911yescharacteristic
714C23C2×#115911yescharacteristic
715C23C2×Q8×D711yescharacteristic
716C23C2×Q8×D711yescharacteristic
717C23D7×#4111yescharacteristic
718C23D7×#4111yescharacteristic
719C23D7×#4111yescharacteristic
720C23D7×#4111yescharacteristic
721C23D7×#4111yescharacteristic
722C23D7×#4111yescharacteristic
723Q8—2816no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
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—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
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—74no—
771C2×C4—74no—
772C2×C4—74no—
773C2×C4—74no—
774C2×C4—74no—
775C2×C4—74no—
776C2×C4—74no—
777C2×C4—74no—
778C2×C4—74no—
779C2×C4—74no—
780C2×C4—142no—
781C2×C4—142no—
782C2×C4—142no—
783C2×C4—142no—
784C2×C4—142no—
785C2×C4—142no—
786C2×C4—142no—
787C2×C4—142no—
788C2×C4—142no—
789C2×C4—142no—
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—281no—
805C2×C4—281no—
806C2×C4—281no—
807C2×C4—281no—
808C2×C4—281no—
809C2×C4—281no—
810C2×C4—281no—
811C2×C4—281no—
812C2×C4—281no—
813C2×C4—281no—
814C2×C4—281no—
815C2×C4—281no—
816C2×C4—281no—
817C2×C4—281no—
818C2×C4—281no—
819C2×C4—281no—
820C2×C4—281no—
821C2×C4—281no—
822C2×C4—281no—
823C2×C4—281no—
824C2×C4—281no—
825C2×C4—281no—
826C2×C4#644814yes—
827C2×C4#645014yes—
828C2×C4#645914yes—
829C7#1470311yescharacteristic, complemented, Sylow
830C22C4×#115711yescharacteristic
831C22C2×#644811yescharacteristic
832C22C2×#645011yescharacteristic
833C22C2×#645911yescharacteristic
834C22D7×#11711yescharacteristic
835C22#9021911yescharacteristic
836C22#9021911yescharacteristic
837C22C4×#115911yescharacteristic
838C22#9022911yescharacteristic
839C22#9022911yescharacteristic
840C22#9022911yescharacteristic
841C22C4×D4×D711yescharacteristic
842C22C4×D4×D711yescharacteristic
843C22#9023811yescharacteristic
844C22#9023911yescharacteristic
845C22C4×Q8×D711yescharacteristic
846C22#9026911yescharacteristic
847C22#9026911yescharacteristic
848C22#9026911yescharacteristic
849C22#9027711yescharacteristic
850C22#9028711yescharacteristic
851C22D7×#12111yescharacteristic
852C22#9031311yescharacteristic
853C22#9031311yescharacteristic
854C22#9031311yescharacteristic
855C22D7×C22⋊Q811yescharacteristic
856C22#9034011yescharacteristic
857C22#9034011yescharacteristic
858C22D7×#12311yescharacteristic
859C22D7×#12411yescharacteristic
860C22#9037911yescharacteristic
861C22#9037911yescharacteristic
862C22D7×#12611yescharacteristic
863C22#9039711yescharacteristic
864C22D7×C4⋊Q811yescharacteristic
865C4—24no—
866C4—24no—
867C4—24no—
868C4—42no—
869C4—42no—
870C4—78no—
871C4—81no—
872C4—81no—
873C4—144no—
874C4—144no—
875C4—144no—
876C4—282no—
877C4—282no—
878C4—561no—
879C4—561no—
880C2C4×#644811yescharacteristic
881C2#1173106411yescharacteristic
882C2C4×#645911yescharacteristic
883C2#1173182611yescharacteristic
884C2#1173203411yescharacteristic
885C2#1173231411yescharacteristic
886C2#1173238311yescharacteristic
887C2#1173273611yescharacteristic
888C2#1173273611yescharacteristic
889C2#1173289311yescharacteristic
890C2#1173326611yescharacteristic
891C2D7×#38811yescharacteristic
892C2#1173341211yescharacteristic
893C2#1173373311yescharacteristic
894C2#1173405211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1436C2
socle, prime radical, cosocleC24×C7C24
hypercenter#1436D7
hypocenterC7#14703
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
55. #89418C4semidirect
113. C2×C4×Dic7Q8semidirect
114. C2×C4×Dic7Q8semidirect
829. C7#14703semidirect

Maximal subgroups

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

subgroupindex
C2×#897442
C2×C42×Dic72
C2×#894182
C7×#14362
#117293182
#117292902
#117271592
Dic7⋊#952
#117271562
#117271552
#147037