Finite Group Databasebeta

← C2×#11727175 #13275514

Subgroups — C2×#11727175 #13275514

Order 1792.

2942 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic7⋊C4C211yesmaximal, characteristic
2C22×C7×#95C211yesmaximal, characteristic
3C22×C7⋊#95C211yesmaximal, characteristic
4C22×C7⋊#95C211yesmaximal, characteristic
5C22×C7⋊#95C211yesmaximal, characteristic
6C22×C7⋊#95C211yesmaximal, characteristic
7C22×C7⋊#95C211yesmaximal, characteristic
8#11727175C218yesmaximal, direct product factor
9C24×C4×C7C2211yescharacteristic
10C24×C4×C7C2211yescharacteristic
11C24×C4×C7C2211yescharacteristic
12C24×Dic7C2211yescharacteristic
13C24×Dic7C2211yescharacteristic
14C24×Dic7C2211yescharacteristic
15C24×Dic7C2211yescharacteristic
16C22×Dic7⋊C4—24no—
17C22×Dic7⋊C4—24no—
18C22×Dic7⋊C4C418yescomplemented
19C22×Dic7⋊C4C2214yes—
20C2×C7×#95—24no—
21C2×C7×#95C2214yes—
22C2×C7⋊#95—24no—
23C2×C7⋊#95—24no—
24C2×C7⋊#95—24no—
25C2×C7⋊#95—24no—
26C2×C7⋊#95—24no—
27C2×C7⋊#95C2214yes—
28C2×C7⋊#95C2214yes—
29C2×C7⋊#95C2214yes—
30C2×C7⋊#95C2214yes—
31C2×C7⋊#95C2214yes—
32C2×#1445—71nomaximal, Sylow
33C25×C7C2311yescharacteristic
34C23×C4×C7—22no—
35C23×C4×C7—22no—
36C23×C4×C7—22no—
37C23×C4×C7—22no—
38C23×C4×C7—22no—
39C23×C4×C7—22no—
40C23×C4×C7—22no—
41C23×C4×C7—22no—
42C23×C4×C7—22no—
43C23×C4×C7—22no—
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7—22no—
49C23×C4×C7—22no—
50C23×C4×C7—22no—
51C23×C4×C7—22no—
52C23×C4×C7C2×C414yes—
53C23×C4×C7D414yes—
54C23×C4×C7Q814yes—
55C23×C4×C7C2312yes—
56C23×C4×C7C2312yes—
57C23×C4×C7C2312yes—
58C23×Dic7—22no—
59C23×Dic7—22no—
60C23×Dic7—22no—
61C23×Dic7—22no—
62C23×Dic7—22no—
63C23×Dic7—22no—
64C23×Dic7—22no—
65C23×Dic7—22no—
66C23×Dic7—22no—
67C23×Dic7—22no—
68C23×Dic7—22no—
69C23×Dic7—22no—
70C23×Dic7—22no—
71C23×Dic7—22no—
72C23×Dic7—22no—
73C23×Dic7—22no—
74C23×Dic7—22no—
75C23×Dic7—22no—
76C23×Dic7—22no—
77C23×Dic7—22no—
78C23×Dic7—22no—
79C23×Dic7—22no—
80C23×Dic7C2×C414yes—
81C23×Dic7C2×C414yes—
82C23×Dic7D414yes—
83C23×Dic7D414yes—
84C23×Dic7D414yes—
85C23×Dic7Q814yes—
86C23×Dic7C2312yes—
87C23×Dic7C2312yes—
88C23×Dic7C2312yes—
89C23×Dic7C2312yes—
90C2×Dic7⋊C4—232no—
91C2×Dic7⋊C4—28no—
92C2×Dic7⋊C4—28no—
93C2×Dic7⋊C4C2×C4116yescomplemented
94C7×#95—28no—
95C7⋊#95—28no—
96C7⋊#95—28no—
97C7⋊#95—28no—
98C7⋊#95—28no—
99C7⋊#95—28no—
100C23×C4⋊C4—71no—
101C22×#95—71no—
102C22×#95—71no—
103C22×#95—71no—
104C22×#95—71no—
105C22×#95—71no—
106C22×#95D711yescharacteristic
107#1445—78no—
108C24×C7C22×C412yes—
109C24×C7C2×D412yes—
110C24×C7C2×D412yes—
111C24×C7C2×D412yes—
112C24×C7C2×D412yes—
113C24×C7C2×Q812yes—
114C24×C7C2×Q812yes—
115C24×C7#4112yes—
116C24×C7#4112yes—
117C24×C7#4112yes—
118C24×C7#4112yes—
119C24×C7#4112yes—
120C24×C7#4112yes—
121C24×C7#4112yes—
122C24×C7#4112yes—
123C24×C7C2411yescharacteristic
124C22×C4×C7—28no—
125C22×C4×C7—28no—
126C22×C4×C7—28no—
127C22×C4×C7—28no—
128C22×C4×C7—28no—
129C22×C4×C7—28no—
130C22×C4×C7—28no—
131C22×C4×C7—28no—
132C22×C4×C7—28no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—44no—
152C22×C4×C7—44no—
153C22×C4×C7—44no—
154C22×C4×C7—44no—
155C22×C4×C7—44no—
156C22×C4×C7—44no—
157C22×C4×C7—44no—
158C22×C4×C7—44no—
159C22×C4×C7—44no—
160C22×C4×C7—44no—
161C22×C4×C7—44no—
162C22×C4×C7—44no—
163C22×C4×C7C22×C414yes—
164C22×C4×C7C2×D414yes—
165C22×C4×C7C2×Q814yes—
166C22×Dic7—28no—
167C22×Dic7—28no—
168C22×Dic7—28no—
169C22×Dic7—28no—
170C22×Dic7—28no—
171C22×Dic7—28no—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—28no—
177C22×Dic7—28no—
178C22×Dic7—28no—
179C22×Dic7—28no—
180C22×Dic7—28no—
181C22×Dic7—28no—
182C22×Dic7—28no—
183C22×Dic7—28no—
184C22×Dic7—28no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7—22no—
189C22×Dic7—22no—
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—22no—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7—22no—
203C22×Dic7—44no—
204C22×Dic7—44no—
205C22×Dic7—44no—
206C22×Dic7—44no—
207C22×Dic7—44no—
208C22×Dic7—44no—
209C22×Dic7—44no—
210C22×Dic7—44no—
211C22×Dic7—44no—
212C22×Dic7—44no—
213C22×Dic7—44no—
214C22×Dic7—44no—
215C22×Dic7C22⋊C4116yes—
216C22×Dic7C22×C414yes—
217C22×Dic7C22×C414yes—
218C22×Dic7C2×D414yes—
219C22×Dic7C2×D414yes—
220C22×Dic7C2×D414yes—
221C22×Dic7C2×Q814yes—
222Dic7⋊C4—232no—
223C24×C4—71no—
224C24×C4—71no—
225C24×C4—71no—
226C24×C4—71no—
227C24×C4C2×D711yescharacteristic
228C24×C4C2×D711yescharacteristic
229C24×C4C2×D711yescharacteristic
230C22×C4⋊C4—78no—
231C22×C4⋊C4—74no—
232C22×C4⋊C4—144no—
233C22×C4⋊C4—144no—
234C2×#95—24no—
235C2×#95—74no—
236C2×#95—74no—
237C2×#95—74no—
238C2×#95—74no—
239C2×#95—74no—
240C2×#95—144no—
241C2×#95—144no—
242C2×#95—144no—
243C2×#95—144no—
244C2×#95—144no—
245C2×#95C2×D714yes—
246C23×C7C2×C22⋊C414yes—
247C23×C7#11714yes—
248C23×C7#11714yes—
249C23×C7C4×D414yes—
250C23×C7C4×D414yes—
251C23×C7C4×Q814yes—
252C23×C7C4×Q814yes—
253C23×C7#12114yes—
254C23×C7#12114yes—
255C23×C7C22⋊Q814yes—
256C23×C7C22⋊Q814yes—
257C23×C7C22⋊Q814yes—
258C23×C7C22⋊Q814yes—
259C23×C7C22⋊Q814yes—
260C23×C7C22⋊Q814yes—
261C23×C7#12314yes—
262C23×C7#12314yes—
263C23×C7#12314yes—
264C23×C7#12314yes—
265C23×C7#12314yes—
266C23×C7#12314yes—
267C23×C7#12314yes—
268C23×C7#12314yes—
269C23×C7#12414yes—
270C23×C7#12414yes—
271C23×C7#12514yes—
272C23×C7#12514yes—
273C23×C7#12514yes—
274C23×C7#12514yes—
275C23×C7#12614yes—
276C23×C7#12614yes—
277C23×C7#12614yes—
278C23×C7#12614yes—
279C23×C7#12714yes—
280C23×C7C4⋊Q814yes—
281C23×C7C23×C411yescharacteristic
282C23×C7C22×D411yescharacteristic
283C23×C7C22×D411yescharacteristic
284C23×C7C22×D411yescharacteristic
285C23×C7C22×D411yescharacteristic
286C23×C7C22×Q811yescharacteristic
287C23×C7C22×Q811yescharacteristic
288C23×C7C2×#4111yescharacteristic
289C23×C7C2×#4111yescharacteristic
290C23×C7C2×#4111yescharacteristic
291C23×C7C2×#4111yescharacteristic
292C23×C7C2×#4111yescharacteristic
293C23×C7C2×#4111yescharacteristic
294C23×C7C2×#4111yescharacteristic
295C23×C7C2×#4111yescharacteristic
296C2×C4×C7—24no—
297C2×C4×C7—24no—
298C2×C4×C7—24no—
299C2×C4×C7—24no—
300C2×C4×C7—24no—
301C2×C4×C7—24no—
302C2×C4×C7—24no—
303C2×C4×C7—24no—
304C2×C4×C7—24no—
305C2×C4×C7—42no—
306C2×C4×C7—42no—
307C2×C4×C7—42no—
308C2×C4×C7—42no—
309C2×C4×C7—42no—
310C2×C4×C7—42no—
311C2×C4×C7—42no—
312C2×C4×C7—42no—
313C2×C4×C7—42no—
314C2×C4×C7—42no—
315C2×C4×C7—42no—
316C2×C4×C7—42no—
317C2×C4×C7—416no—
318C2×C4×C7—416no—
319C2×C4×C7—416no—
320C2×Dic7—24no—
321C2×Dic7—24no—
322C2×Dic7—24no—
323C2×Dic7—24no—
324C2×Dic7—24no—
325C2×Dic7—24no—
326C2×Dic7—232no—
327C2×Dic7—24no—
328C2×Dic7—24no—
329C2×Dic7—24no—
330C2×Dic7—24no—
331C2×Dic7—24no—
332C2×Dic7—24no—
333C2×Dic7—24no—
334C2×Dic7—24no—
335C2×Dic7—24no—
336C2×Dic7—42no—
337C2×Dic7—42no—
338C2×Dic7—42no—
339C2×Dic7—42no—
340C2×Dic7—42no—
341C2×Dic7—42no—
342C2×Dic7—42no—
343C2×Dic7—42no—
344C2×Dic7—42no—
345C2×Dic7—42no—
346C2×Dic7—42no—
347C2×Dic7—42no—
348C2×Dic7—416no—
349C2×Dic7—416no—
350C2×Dic7—416no—
351C2×Dic7C2×C22⋊C418yes—
352C25C22×D711yescharacteristic
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—74no—
372C23×C4—74no—
373C23×C4—74no—
374C23×C4—72no—
375C23×C4—74no—
376C23×C4—74no—
377C23×C4—74no—
378C23×C4—72no—
379C23×C4—72no—
380C23×C4—72no—
381C23×C4—142no—
382C23×C4—142no—
383C23×C4—142no—
384C23×C4—142no—
385C23×C4—142no—
386C23×C4—142no—
387C23×C4—142no—
388C23×C4—142no—
389C23×C4—142no—
390C23×C4—142no—
391C23×C4—142no—
392C23×C4—142no—
393C23×C4—142no—
394C23×C4—142no—
395C23×C4—142no—
396C23×C4—142no—
397C23×C4—142no—
398C23×C4—142no—
399C23×C4—142no—
400C23×C4—142no—
401C23×C4—142no—
402C23×C4—142no—
403C23×C4Dic1414yes—
404C23×C4C4×D714yes—
405C23×C4C22⋊D714yes—
406C23×C4C22×D712yes—
407C23×C4C22×D712yes—
408C23×C4C22×D712yes—
409C2×C4⋊C4—716no—
410C2×C4⋊C4—1432no—
411C2×C4⋊C4—148no—
412C2×C4⋊C4—148no—
413#95—28no—
414#95—148no—
415#95—148no—
416#95—148no—
417#95—148no—
418#95—148no—
419C22×C7#38118yes—
420C22×C7#38718yes—
421C22×C7#38718yes—
422C22×C7#38718yes—
423C22×C7#38718yes—
424C22×C7#39018yes—
425C22×C7#39118yes—
426C22×C7#39718yes—
427C22×C7#39718yes—
428C22×C7#39818yes—
429C22×C7#39818yes—
430C22×C7#39918yes—
431C22×C7#39918yes—
432C22×C7#40018yes—
433C22×C7#40018yes—
434C22×C7C22×C22⋊C411yescharacteristic
435C22×C7C2×#11711yescharacteristic
436C22×C7C2×#11711yescharacteristic
437C22×C7C2×C4×D411yescharacteristic
438C22×C7C2×C4×D411yescharacteristic
439C22×C7C2×C4×Q811yescharacteristic
440C22×C7C2×C4×Q811yescharacteristic
441C22×C7C2×#12111yescharacteristic
442C22×C7C2×#12111yescharacteristic
443C22×C7C2×C22⋊Q811yescharacteristic
444C22×C7C2×C22⋊Q811yescharacteristic
445C22×C7C2×C22⋊Q811yescharacteristic
446C22×C7C2×C22⋊Q811yescharacteristic
447C22×C7C2×C22⋊Q811yescharacteristic
448C22×C7C2×C22⋊Q811yescharacteristic
449C22×C7C2×#12311yescharacteristic
450C22×C7C2×#12311yescharacteristic
451C22×C7C2×#12311yescharacteristic
452C22×C7C2×#12311yescharacteristic
453C22×C7C2×#12311yescharacteristic
454C22×C7C2×#12311yescharacteristic
455C22×C7C2×#12311yescharacteristic
456C22×C7C2×#12311yescharacteristic
457C22×C7C2×#12411yescharacteristic
458C22×C7C2×#12411yescharacteristic
459C22×C7C2×#12511yescharacteristic
460C22×C7C2×#12511yescharacteristic
461C22×C7C2×#12511yescharacteristic
462C22×C7C2×#12511yescharacteristic
463C22×C7C2×#12611yescharacteristic
464C22×C7C2×#12611yescharacteristic
465C22×C7C2×#12611yescharacteristic
466C22×C7C2×#12611yescharacteristic
467C22×C7C2×#12711yescharacteristic
468C22×C7C2×C4⋊Q811yescharacteristic
469C4×C7—44no—
470C4×C7—44no—
471C4×C7—44no—
472Dic7—28no—
473Dic7—44no—
474Dic7—44no—
475Dic7—44no—
476C24C2×Dic1412yes—
477C24C2×C4×D712yes—
478C24#115712yes—
479C24#115712yes—
480C24#115712yes—
481C24#115712yes—
482C24D4×D712yes—
483C24D4×D712yes—
484C24D4×D712yes—
485C24#115912yes—
486C24#115912yes—
487C24#115912yes—
488C24Q8×D712yes—
489C24#116112yes—
490C24C2×C22⋊D712yes—
491C24C23×D711yescharacteristic
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—716no—
532C22×C4—74no—
533C22×C4—74no—
534C22×C4—74no—
535C22×C4—74no—
536C22×C4—74no—
537C22×C4—74no—
538C22×C4—148no—
539C22×C4—148no—
540C22×C4—148no—
541C22×C4—148no—
542C22×C4—148no—
543C22×C4—148no—
544C22×C4—142no—
545C22×C4—142no—
546C22×C4—142no—
547C22×C4—142no—
548C22×C4—148no—
549C22×C4—148no—
550C22×C4—148no—
551C22×C4—148no—
552C22×C4—148no—
553C22×C4—148no—
554C22×C4—148no—
555C22×C4—148no—
556C22×C4—148no—
557C22×C4—142no—
558C22×C4—142no—
559C22×C4—142no—
560C22×C4—142no—
561C22×C4—142no—
562C22×C4—142no—
563C22×C4—142no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—142no—
575C22×C4—284no—
576C22×C4—284no—
577C22×C4—284no—
578C22×C4—284no—
579C22×C4—284no—
580C22×C4—284no—
581C22×C4—284no—
582C22×C4—284no—
583C22×C4—284no—
584C22×C4—284no—
585C22×C4—284no—
586C22×C4—284no—
587C22×C4C2×Dic1414yes—
588C22×C4C2×C4×D714yes—
589C22×C4C2×C22⋊D714yes—
590C4⋊C4—1432no—
591C2×C7#1445116yescomplemented
592C2×C7C2×#38111yescharacteristic
593C2×C7C2×#38711yescharacteristic
594C2×C7C2×#38711yescharacteristic
595C2×C7C2×#38711yescharacteristic
596C2×C7C2×#38711yescharacteristic
597C2×C7C2×#39011yescharacteristic
598C2×C7C2×#39111yescharacteristic
599C2×C7C2×#39711yescharacteristic
600C2×C7C2×#39711yescharacteristic
601C2×C7C2×#39811yescharacteristic
602C2×C7C2×#39811yescharacteristic
603C2×C7C2×#39911yescharacteristic
604C2×C7C2×#39911yescharacteristic
605C2×C7C2×#40011yescharacteristic
606C2×C7C2×#40011yescharacteristic
607C23C4×Dic1414yes—
608C23#643314yes—
609C23#643514yes—
610C23#643914yes—
611C23#644114yes—
612C23#644114yes—
613C23#644214yes—
614C23#644214yes—
615C23D7×C22⋊C414yes—
616C23(C22⋊D7)⋊C414yes—
617C23#644614yes—
618C23#644614yes—
619C23#644614yes—
620C23#644714yes—
621C23#644814yes—
622C23#644814yes—
623C23#645014yes—
624C23#645114yes—
625C23#645214yes—
626C23#645214yes—
627C23#645314yes—
628C23#645514yes—
629C23#645714yes—
630C23#645714yes—
631C23#645714yes—
632C23#645914yes—
633C23#645914yes—
634C23#646114yes—
635C23#648714yes—
636C23C4×C22⋊D714yes—
637C23#649214yes—
638C23#649814yes—
639C23#650214yes—
640C23#650314yes—
641C23#650914yes—
642C23C22×Dic1411yescharacteristic
643C23C22×C4×D711yescharacteristic
644C23C2×#115711yescharacteristic
645C23C2×#115711yescharacteristic
646C23C2×#115711yescharacteristic
647C23C2×#115711yescharacteristic
648C23C2×D4×D711yescharacteristic
649C23C2×D4×D711yescharacteristic
650C23C2×D4×D711yescharacteristic
651C23C2×#115911yescharacteristic
652C23C2×#115911yescharacteristic
653C23C2×#115911yescharacteristic
654C23C2×Q8×D711yescharacteristic
655C23C2×#116111yescharacteristic
656C23C22×C22⋊D711yescharacteristic
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—416no—
676C2×C4—416no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—416no—
681C2×C4—78no—
682C2×C4—144no—
683C2×C4—144no—
684C2×C4—144no—
685C2×C4—144no—
686C2×C4—144no—
687C2×C4—144no—
688C2×C4—1432no—
689C2×C4—144no—
690C2×C4—144no—
691C2×C4—144no—
692C2×C4—144no—
693C2×C4—144no—
694C2×C4—144no—
695C2×C4—144no—
696C2×C4—144no—
697C2×C4—144no—
698C2×C4—282no—
699C2×C4—282no—
700C2×C4—282no—
701C2×C4—282no—
702C2×C4—282no—
703C2×C4—282no—
704C2×C4—282no—
705C2×C4—282no—
706C2×C4—2816no—
707C2×C4—282no—
708C2×C4—282no—
709C2×C4—282no—
710C2×C4—282no—
711C2×C4—2816no—
712C2×C4—2816no—
713C7C2×#144511yescharacteristic, complemented, Sylow
714C22#8941818yes—
715C22#8942418yes—
716C22#8942718yes—
717C22#8942918yes—
718C22#8943018yes—
719C22#8943218yes—
720C22#8943618yes—
721C22#8944718yes—
722C22#8970518yes—
723C22#8972118yes—
724C22#8972418yes—
725C22#8972918yes—
726C22#8975018yes—
727C22#8975618yes—
728C22#8976418yes—
729C22C2×C4×Dic1411yescharacteristic
730C22C2×#643311yescharacteristic
731C22C2×#643511yescharacteristic
732C22C2×#643911yescharacteristic
733C22C2×#644111yescharacteristic
734C22C2×#644111yescharacteristic
735C22C2×#644211yescharacteristic
736C22C2×#644211yescharacteristic
737C22C2×D7×C22⋊C411yescharacteristic
738C22C2×(C22⋊D7)⋊C411yescharacteristic
739C22C2×#644611yescharacteristic
740C22C2×#644611yescharacteristic
741C22C2×#644611yescharacteristic
742C22C2×#644711yescharacteristic
743C22C2×#644811yescharacteristic
744C22C2×#644811yescharacteristic
745C22C2×#645011yescharacteristic
746C22C2×#645111yescharacteristic
747C22C2×#645211yescharacteristic
748C22C2×#645211yescharacteristic
749C22C2×#645311yescharacteristic
750C22C2×#645511yescharacteristic
751C22C2×#645711yescharacteristic
752C22C2×#645711yescharacteristic
753C22C2×#645711yescharacteristic
754C22C2×#645911yescharacteristic
755C22C2×#645911yescharacteristic
756C22C2×#646111yescharacteristic
757C22C2×#648711yescharacteristic
758C22C2×C4×C22⋊D711yescharacteristic
759C22C2×#649211yescharacteristic
760C22C2×#649811yescharacteristic
761C22C2×#650211yescharacteristic
762C22C2×#650311yescharacteristic
763C22C2×#650911yescharacteristic
764C4—44no—
765C4—44no—
766C4—44no—
767C4—148no—
768C4—284no—
769C4—284no—
770C4—284no—
771C2#11727175116yesdirect product factor
772C2C2×#8942411yescharacteristic
773C2C2×#8942711yescharacteristic
774C2C2×#8941811yescharacteristic
775C2C2×#8942911yescharacteristic
776C2C2×#8943011yescharacteristic
777C2C2×#8943211yescharacteristic
778C2C2×#8943611yescharacteristic
779C2C2×#8944711yescharacteristic
780C2C2×#8970511yescharacteristic
781C2C2×#8972911yescharacteristic
782C2C2×#8972411yescharacteristic
783C2C2×#8972111yescharacteristic
784C2C2×#8975011yescharacteristic
785C2C2×#8975611yescharacteristic
786C2C2×#8976411yescharacteristic
subgroupG/H
centerC25C22×D7
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC22×C7×#95C2
socle, prime radicalC25×C7C23
cosocleC24×C7C24
hypercenterC22×#95D7
hypocenterC7C2×#1445
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C25 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
8. #11727175C2direct (N × H)
18. C22×Dic7⋊C4C4semidirect
93. C2×Dic7⋊C4C2×C4semidirect
591. C2×C7#1445semidirect
713. C7C2×#1445semidirect
771. C2#11727175direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Dic7⋊C42
C22×C7×#952
C22×C7⋊#952
#117271752
C2×#14457