Finite Group Databasebeta

← #13281177

Subgroups — #13281177

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×C7×C22⋊Q8C211yesmaximal, characteristic
2C2×#90002C211yesmaximal, characteristic, complemented
3C2×#89983C211yesmaximal, characteristic
4C2×#89723C211yesmaximal, characteristic
5C2×#89723C211yesmaximal, characteristic
6#11729888C211yesmaximal, characteristic, complemented
7#11729881C211yesmaximal, characteristic
8#11729323C211yesmaximal, characteristic, complemented
9#11729319C211yesmaximal, characteristic, complemented
10#11729319C211yesmaximal, characteristic, complemented
11#11729318C211yesmaximal, characteristic, complemented
12#11729318C211yesmaximal, characteristic, complemented
13#11729317C211yesmaximal, characteristic, complemented
14#11729302C211yesmaximal, characteristic
15#11729302C211yesmaximal, characteristic
16C23×C7×Q8C2211yescharacteristic
17C24×C4×C7C2211yescharacteristic
18C2×C7×C22⋊Q8—24no—
19C2×C7×C22⋊Q8—24no—
20C2×C7×C22⋊Q8C418yescomplemented
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×C4⋊Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C22×C4×Dic7C2211yescharacteristic
34#90002—24no—
35#89983—24no—
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
55C2×C7⋊#95C2211yescharacteristic
56#89723—24no—
57#89723—24no—
58#14364—71nomaximal, Sylow
59C25×C7C2311yescharacteristic
60C22×C7×Q8—22no—
61C22×C7×Q8—22no—
62C22×C7×Q8—22no—
63C22×C7×Q8—22no—
64C22×C7×Q8—41no—
65C22×C7×Q8—41no—
66C22×C7×Q8C2×C414yes—
67C23×C4×C7—22no—
68C23×C4×C7—22no—
69C23×C4×C7—22no—
70C23×C4×C7—22no—
71C23×C4×C7—41no—
72C23×C4×C7—41no—
73C23×C4×C7C2×C414yes—
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C7×C22⋊Q8—232no—
89C2×C7×C4⋊C4—22no—
90C2×C7×C4⋊C4—22no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4—22no—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4C2×C414yes—
96C2×C7×C4⋊C4C2×C414yes—
97C2×C7×C4⋊C4C2×C414yes—
98C2×C7×C22⋊C4—22no—
99C2×C7×C22⋊C4—22no—
100C2×C7×C22⋊C4C2×C414yes—
101C2×C7×C22⋊C4C2×C414yes—
102C2×C7×C22⋊C4D414yes—
103C2×C7×C22⋊C4D414yes—
104C2×C22⋊Dic7—22no—
105C2×C22⋊Dic7—22no—
106C2×C22⋊Dic7—22no—
107C2×C22⋊Dic7—22no—
108C2×C22⋊Dic7—22no—
109C2×C22⋊Dic7—22no—
110C2×C22⋊Dic7—22no—
111C2×C22⋊Dic7—22no—
112C2×C22⋊Dic7—41no—
113C2×C22⋊Dic7—41no—
114C2×C22⋊Dic7—41no—
115C2×C22⋊Dic7—41no—
116C2×C4⋊Dic7—22no—
117C2×C4⋊Dic7—22no—
118C2×C4⋊Dic7—22no—
119C2×C4⋊Dic7—22no—
120C2×C4⋊Dic7—41no—
121C2×C4⋊Dic7—41no—
122C2×C4×Dic7—22no—
123C2×C4×Dic7—22no—
124C2×C4×Dic7—22no—
125C2×C4×Dic7—22no—
126C2×C4×Dic7—41no—
127C2×C4×Dic7—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—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⋊Q8D711yescharacteristic
149C2×#391—71no—
150C2×#388—71no—
151C2×#388—71no—
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
179C2×C7×Q8—28no—
180C2×C7×Q8—28no—
181C2×C7×Q8—44no—
182C2×C7×Q8—44no—
183C2×C7×Q8—44no—
184C2×C7×Q8—44no—
185C2×C7×Q8—44no—
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—28no—
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×C7—28no—
218C22×C4×C7—44no—
219C22×C4×C7—44no—
220C22×C4×C7—44no—
221C22×C4×C7—44no—
222C22×C4×C7—44no—
223C22×C4×C7C22×C412yes—
224C22×C4×C7C22×C412yes—
225C22×C4×C7C22×C412yes—
226C22×C4×C7C22×C412yes—
227C22×C4×C7C22×C412yes—
228C22×C4×C7C22×C412yes—
229C22×C4×C7C2×D412yes—
230C22×C4×C7C2×D412yes—
231C22×C4×C7C2×D412yes—
232C22×C4×C7C2×D412yes—
233C22×C4×C7C2×D412yes—
234C22×C4×C7#4112yes—
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×Dic7—21no—
277C22×Dic7—21no—
278C22×Dic7—21no—
279C22×Dic7—21no—
280C22×Dic7—21no—
281C22×Dic7—21no—
282C22×Dic7—21no—
283C22×Dic7—21no—
284C22×Dic7—21no—
285C22×Dic7—21no—
286C22×Dic7—21no—
287C22×Dic7C2×D412yes—
288C22×Dic7C2×D412yes—
289C22×Dic7#4112yes—
290C22×Dic7#4112yes—
291C7×C4⋊C4—28no—
292C7×C4⋊C4—28no—
293C7×C4⋊C4—28no—
294C7×C22⋊C4—28no—
295C7×C22⋊C4C22⋊C4116yes—
296C22⋊Dic7—44no—
297C22⋊Dic7—44no—
298C22⋊Dic7—44no—
299C22⋊Dic7—44no—
300C4⋊Dic7—44no—
301C4⋊Dic7—44no—
302C4×Dic7—44no—
303C4×Dic7—44no—
304C23×Q8C2×D711yescharacteristic
305C24×C4C2×D711yescharacteristic
306C2×C22⋊Q8—24no—
307C2×C22⋊Q8—24no—
308C2×C22⋊Q8Dic718yescomplemented
309C22×C4⋊C4—71no—
310C22×C4⋊C4—71no—
311C22×C4⋊C4C2×D711yescharacteristic
312C22×C4⋊C4C2×D711yescharacteristic
313C22×C4⋊C4C2×D711yescharacteristic
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C22⋊C4—71no—
317C22×C22⋊C4—71no—
318C22×C22⋊C4C2×D711yescharacteristic
319C22×C22⋊C4C2×D711yescharacteristic
320C22×C42—71no—
321C22×C42—71no—
322#391—144no—
323#388—144no—
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×#95—71no—
345C2×#95—71no—
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
396C7×Q8—416no—
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—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—416no—
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×C7C2×C22⋊C414yes—
438C2×C4×C7C2×C22⋊C414yes—
439C2×C4×C7C4×D414yes—
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—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—
488C2×Dic7—41no—
489C2×Dic7—41no—
490C2×Dic7—41no—
491C2×Dic7—41no—
492C2×Dic7—41no—
493C2×Dic7—41no—
494C2×Dic7—41no—
495C2×Dic7—41no—
496C25C22×D711yescharacteristic
497C22×Q8—22no—
498C22×Q8—22no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8C2×Dic714yes—
504C23×C4—22no—
505C23×C4—22no—
506C23×C4—22no—
507C23×C4—22no—
508C23×C4—41no—
509C23×C4—41no—
510C23×C4—71no—
511C23×C4—71no—
512C23×C4—71no—
513C23×C4—71no—
514C23×C4—71no—
515C23×C4—71no—
516C23×C4—71no—
517C23×C4—71no—
518C23×C4C2×Dic714yes—
519C23×C4C22×D711yescharacteristic
520C23×C4C22×D711yescharacteristic
521C23×C4C22×D711yescharacteristic
522C23×C4C22×D711yescharacteristic
523C23×C4C22×D711yescharacteristic
524C23×C4C22×D711yescharacteristic
525C22⋊Q8—232no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—142no—
533C2×C4⋊C4—142no—
534C2×C4⋊C4—142no—
535C2×C4⋊C4—142no—
536C2×C4⋊C4—281no—
537C2×C4⋊C4—281no—
538C2×C4⋊C4C2×Dic714yes—
539C2×C4⋊C4C2×Dic714yes—
540C2×C4⋊C4C2×Dic714yes—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
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—142no—
550C2×C22⋊C4—142no—
551C2×C22⋊C4—281no—
552C2×C22⋊C4—281no—
553C2×C22⋊C4—281no—
554C2×C22⋊C4—281no—
555C2×C22⋊C4C2×Dic714yes—
556C2×C22⋊C4C2×Dic714yes—
557C2×C22⋊C4C22⋊D714yes—
558C2×C22⋊C4C22⋊D714yes—
559C2×C42—142no—
560C2×C42—142no—
561C2×C42—142no—
562C2×C42—142no—
563C2×C42—281no—
564C2×C42—281no—
565#95—74no—
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—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—24no—
638C4×C7—42no—
639C4×C7—42no—
640C4×C7—42no—
641Dic7—42no—
642Dic7—42no—
643Dic7—42no—
644Dic7—42no—
645Dic7—81no—
646Dic7—81no—
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—
661C24C22×Dic712yes—
662C24C2×C22⋊D712yes—
663C24C2×C22⋊D712yes—
664C24C23×D711yescharacteristic
665C2×Q8—28no—
666C2×Q8—28no—
667C2×Q8—44no—
668C2×Q8—44no—
669C2×Q8—44no—
670C2×Q8—44no—
671C2×Q8—44no—
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—28no—
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—28no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—72no—
710C22×C4—72no—
711C22×C4—72no—
712C22×C4—72no—
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×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—141no—
765C22×C4D4×D712yes—
766C22×C4#115912yes—
767C22×C4C22×Dic712yes—
768C22×C4C22×Dic712yes—
769C22×C4C22×Dic712yes—
770C22×C4C22×Dic712yes—
771C22×C4C22×Dic712yes—
772C22×C4C22×Dic712yes—
773C22×C4C2×C22⋊D712yes—
774C22×C4C2×C22⋊D712yes—
775C22×C4C2×C22⋊D712yes—
776C22×C4C2×C22⋊D712yes—
777C4⋊C4—28no—
778C4⋊C4—28no—
779C4⋊C4—28no—
780C4⋊C4—284no—
781C4⋊C4—284no—
782C22⋊C4—28no—
783C22⋊C4—284no—
784C22⋊C4—284no—
785C22⋊C4—284no—
786C22⋊C4—284no—
787C22⋊C4C22⋊Dic7116yes—
788C42—284no—
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×C22⋊Dic714yes—
841C23C2×D4×D711yescharacteristic
842C23C2×#115911yescharacteristic
843C23#654811yescharacteristic
844C23#654811yescharacteristic
845C23#655111yescharacteristic
846C23#655111yescharacteristic
847C23#655111yescharacteristic
848C23#655111yescharacteristic
849C23D7×#4111yescharacteristic
850C23D7×#4111yescharacteristic
851C23#655311yescharacteristic
852C23#655411yescharacteristic
853C23C23×Dic711yescharacteristic
854C23C22×C22⋊D711yescharacteristic
855C23C22×C22⋊D711yescharacteristic
856Q8—416no—
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—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—416no—
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—142no—
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—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—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×C4D4×Dic714yes—
954C2×C4C2×C22⋊Dic714yes—
955C2×C4C2×C22⋊Dic714yes—
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#9031611yescharacteristic
973C22#9031911yescharacteristic
974C22#9032011yescharacteristic
975C22#9032211yescharacteristic
976C22#9032411yescharacteristic
977C22#9032911yescharacteristic
978C22#9032911yescharacteristic
979C22#9033011yescharacteristic
980C22#9033111yescharacteristic
981C22#9033111yescharacteristic
982C22#9033211yescharacteristic
983C22#9033411yescharacteristic
984C22#9033711yescharacteristic
985C22#9033711yescharacteristic
986C22#9033811yescharacteristic
987C22#9033811yescharacteristic
988C22C2×D4×Dic711yescharacteristic
989C22#9048911yescharacteristic
990C22D4×C22⋊D711yescharacteristic
991C22D4×C22⋊D711yescharacteristic
992C22#9049711yescharacteristic
993C22#9049711yescharacteristic
994C22#9050311yescharacteristic
995C22#9050311yescharacteristic
996C22#9050711yescharacteristic
997C22#9050711yescharacteristic
998C22#9050711yescharacteristic
999C22#9050711yescharacteristic
1000C22#9051511yescharacteristic
1001C22#9051511yescharacteristic
1002C22#41×Dic711yescharacteristic
1003C22#9051811yescharacteristic
1004C22#9052011yescharacteristic
1005C22#9052011yescharacteristic
1006C22C22×C22⋊Dic711yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—282no—
1014C4—282no—
1015C4—282no—
1016C4—282no—
1017C4—561no—
1018C4—561no—
1019C4—561no—
1020C4—561no—
1021C2—44no—
1022C2#1174018911yescharacteristic
1023C2#1174019111yescharacteristic
1024C2#1174019311yescharacteristic
1025C2#1174019511yescharacteristic
1026C2#1174023511yescharacteristic
1027C2#1174023711yescharacteristic
1028C2#1174023911yescharacteristic
1029C2#1174024011yescharacteristic
1030C2#1174024411yescharacteristic
1031C2#1174024511yescharacteristic
1032C2#1174027111yescharacteristic
1033C2#1174027311yescharacteristic
1034C2D4×C22⋊Dic711yescharacteristic
1035C2#1174150711yescharacteristic
1036C2#1174153311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC22×C7×C22⋊Q8C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC22×C22⋊Q8D7
hypocenterC7#14364
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#90002C2semidirect
6. #11729888C2semidirect
8. #11729323C2semidirect
9. #11729319C2semidirect
10. #11729319C2semidirect
11. #11729318C2semidirect
12. #11729318C2semidirect
13. #11729317C2semidirect
20. C2×C7×C22⋊Q8C4semidirect
308. C2×C22⋊Q8Dic7semidirect
956. C7#14364semidirect

Maximal subgroups

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

subgroupindex
C22×C7×C22⋊Q82
C2×#900022
C2×#899832
C2×#897232
#117298882
#117298812
#117293232
#117293192
#117293182
#117293172
#117293022
#143647