Finite Group Databasebeta

← #13275366

Subgroups — #13275366

Order 1792.

2666 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D7C211yesmaximal, characteristic
2C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
3C2×#89729C212yesmaximal
4C2×#89421C212yesmaximal, complemented
5C2×#89438C211yesmaximal, characteristic, complemented
6C7×C22⋊#95C211yesmaximal, characteristic, complemented
7#11729299C212yesmaximal, complemented
8(C2×D7)⋊#95C211yesmaximal, characteristic, complemented
9#11727162C212yesmaximal, complemented
10Dic7⋊#95C211yesmaximal, characteristic, complemented
11Dic7×#95C211yesmaximal, characteristic, complemented
12C24×C4×C7C2211yescharacteristic
13C23×C22⋊D7C2211yescharacteristic
14C23×C4×D7C2211yescharacteristic
15C22×C7×C22⋊C4C2212yes—
16C22×C22⋊Dic7C2211yescharacteristic
17C22×C22⋊Dic7C2212yes—
18C2×C4×C22⋊D7—28no—
19C2×C4×C22⋊D7C418yescomplemented
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2212yes—
22C22×(C2×D7)⋊C4C2212yes—
23C22×Dic7⋊C4C2212yes—
24C22×Dic7⋊C4C2211yescharacteristic
25C22×C4×Dic7C2212yes—
26C22×C4×Dic7C2212yes—
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2212yes—
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2212yes—
32C4×C22⋊Dic7—24no—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2211yescharacteristic
38#89729C4116yescomplemented
39#89438—24no—
40#89421—28no—
41#13820—71nomaximal, Sylow
42C25×C7C2311yescharacteristic
43C24×D7C2311yescharacteristic
44C23×C4×C7—24no—
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7—42no—
48C23×C4×C7C2×C414yes—
49C23×C4×C7C2312yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C22×C22⋊D7—24no—
54C22×C22⋊D7—22no—
55C22×C22⋊D7—22no—
56C22×C22⋊D7C2×C414yes—
57C22×C22⋊D7C2×C418yes—
58C23×Dic7C2312yes—
59C23×Dic7C2311yescharacteristic
60C23×Dic7C2311yescharacteristic
61C23×Dic7C2312yes—
62C23×Dic7C2311yescharacteristic
63C22×C4×D7—22no—
64C22×C4×D7—22no—
65C22×C4×D7—24no—
66C22×C4×D7—42no—
67C22×C4×D7C2×C414yes—
68C2×C7×C22⋊C4—42no—
69C2×C7×C22⋊C4—42no—
70C2×C7×C22⋊C4C2×C418yescomplemented
71C2×C22⋊Dic7—24no—
72C2×C22⋊Dic7—24no—
73C2×C22⋊Dic7—24no—
74C2×C22⋊Dic7C2×C414yes—
75C2×C22⋊Dic7C2×C418yescomplemented
76C4×C22⋊D7—232no—
77C2×(C2×D7)⋊C4—24no—
78C2×(C2×D7)⋊C4—24no—
79C2×(C2×D7)⋊C4—24no—
80C2×(C2×D7)⋊C4—42no—
81C2×(C2×D7)⋊C4—42no—
82C2×(C2×D7)⋊C4C2×C414yes—
83C2×(C2×D7)⋊C4C2×C418yescomplemented
84C2×(C2×D7)⋊C4C2×C418yescomplemented
85C2×Dic7⋊C4—24no—
86C2×Dic7⋊C4—24no—
87C2×Dic7⋊C4C2×C414yes—
88C2×Dic7⋊C4C2×C418yescomplemented
89C2×Dic7⋊C4D418yes—
90C2×C4×Dic7—24no—
91C2×C4×Dic7—24no—
92C2×C4×Dic7—24no—
93C2×C4×Dic7—24no—
94C2×C4×Dic7—24no—
95C2×C4×Dic7—24no—
96C2×C4×Dic7—24no—
97C2×C4×Dic7—42no—
98C2×C4×Dic7—42no—
99C2×C4×Dic7C2×C414yes—
100C2×C4×Dic7C2×C418yescomplemented
101C7×#95—24no—
102C7×#95—22no—
103C7×#95—22no—
104C7⋊#95—22no—
105C7⋊#95—24no—
106C7⋊#95—24no—
107C7⋊#95—42no—
108C7⋊#95D414yescomplemented
109C22×C4×D4—71no—
110C2×#390—72no—
111C2×C4×C4⋊C4—72no—
112C2×C4×C22⋊C4—71no—
113C2×C4×C22⋊C4—71no—
114#1437—72no—
115#1437—72no—
116C4⋊#95—71no—
117C22⋊#95—71no—
118C22⋊#95D711yescharacteristic, complemented
119C4×#95—71no—
120C24×C7—21no—
121C24×C7—22no—
122C24×C7—22no—
123C24×C7—21no—
124C24×C7—21no—
125C24×C7—21no—
126C24×C7—21no—
127C24×C7—22no—
128C24×C7—21no—
129C24×C7C22×C412yes—
130C24×C7C22×C414yes—
131C24×C7C2411yescharacteristic
132C23×D7—21no—
133C23×D7—22no—
134C23×D7—22no—
135C23×D7—21no—
136C23×D7—21no—
137C23×D7—21no—
138C23×D7—21no—
139C23×D7—22no—
140C23×D7—21no—
141C23×D7C22×C412yes—
142C23×D7C22×C414yes—
143C22×C4×C7—21no—
144C22×C4×C7—22no—
145C22×C4×C7—21no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—28no—
161C22×C4×C7—28no—
162C22×C4×C7—44no—
163C22×C4×C7—48no—
164C22×C4×C7—48no—
165C22×C4×C7C22×C414yes—
166C22×C4×C7C22×C414yes—
167C22×C4×C7C22×C412yes—
168C22×C4×C7C22×C412yes—
169C22×C4×C7C2×D414yes—
170C22×C4×C7C2×D412yes—
171C22×C4×C7#4112yes—
172C2×C22⋊D7—28no—
173C2×C22⋊D7—28no—
174C2×C22⋊D7—216no—
175C2×C22⋊D7—216no—
176C2×C22⋊D7C42116yescomplemented
177C22×Dic7—22no—
178C22×Dic7—21no—
179C22×Dic7—22no—
180C22×Dic7—21no—
181C22×Dic7—22no—
182C22×Dic7—22no—
183C22×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—22no—
188C22×Dic7—22no—
189C22×Dic7—22no—
190C22×Dic7—21no—
191C22×Dic7—22no—
192C22×Dic7—22no—
193C22×Dic7—21no—
194C22×Dic7C22×C412yes—
195C22×Dic7C22×C414yes—
196C22×Dic7C22×C412yes—
197C22×Dic7C22×C414yes—
198C22×Dic7C22×C412yes—
199C22×Dic7C22×C414yes—
200C22×Dic7C2×D414yes—
201C22×Dic7C2×D414yes—
202C22×Dic7C2×D414yes—
203C22×Dic7#4114yes—
204C22×Dic7#4112yes—
205C22×Dic7#4112yes—
206C2×C4×D7—28no—
207C2×C4×D7—28no—
208C2×C4×D7—44no—
209C2×C4×D7—48no—
210C2×C4×D7—48no—
211C7×C22⋊C4—48no—
212C22⋊Dic7—28no—
213C22⋊Dic7—216no—
214(C2×D7)⋊C4—28no—
215(C2×D7)⋊C4—216no—
216(C2×D7)⋊C4—48no—
217Dic7⋊C4—216no—
218Dic7⋊C4C22⋊C4116yescomplemented
219C4×Dic7—28no—
220C4×Dic7—216no—
221C4×Dic7—48no—
222C4×Dic7—48no—
223C23×D4—71no—
224C24×C4—71no—
225C24×C4C2×D711yescharacteristic
226C2×C4×D4—78no—
227C2×C4×D4—148no—
228C22×C4⋊C4—71no—
229C22×C4⋊C4—72no—
230C22×C22⋊C4—71no—
231C22×C22⋊C4—72no—
232C22×C22⋊C4—71no—
233C22×C22⋊C4—72no—
234C22×C22⋊C4—72no—
235C22×C22⋊C4C2×D712yes—
236C22×C42—71no—
237C22×C42—72no—
238C22×C42—72no—
239C22×C42—72no—
240#390—716no—
241C4×C4⋊C4—148no—
242C4×C22⋊C4—144no—
243C4×C22⋊C4—144no—
244C2×#95—71no—
245C2×#95—72no—
246C2×#95—71no—
247C2×#95—72no—
248C2×#95—72no—
249C2×#95C2×D711yescharacteristic
250C2×#95C2×D711yescharacteristic
251C2×#95C2×D712yes—
252C23×C7—22no—
253C23×C7—22no—
254C23×C7—24no—
255C23×C7—24no—
256C23×C7—24no—
257C23×C7—22no—
258C23×C7—22no—
259C23×C7—24no—
260C23×C7—24no—
261C23×C7—22no—
262C23×C7—22no—
263C23×C7—24no—
264C23×C7—42no—
265C23×C7—42no—
266C23×C7—41no—
267C23×C7—42no—
268C23×C7—42no—
269C23×C7—41no—
270C23×C7—42no—
271C23×C7—41no—
272C23×C7—41no—
273C23×C7—42no—
274C23×C7C2×C4214yes—
275C23×C7C23×C411yescharacteristic
276C23×C7C23×C412yes—
277C23×C7C22×D412yes—
278C23×C7C22×D411yescharacteristic
279C23×C7C2×#4111yescharacteristic
280C23×C7C2×#4111yescharacteristic
281C23×C7C2×#4111yescharacteristic
282C23×C7C2×#4112yes—
283C23×C7H(5,𝔽2)12yes—
284C23×C7H(5,𝔽2)11yescharacteristic
285C23×C72−1+411yescharacteristic
286C22×D7—22no—
287C22×D7—22no—
288C22×D7—24no—
289C22×D7—22no—
290C22×D7—24no—
291C22×D7—24no—
292C22×D7—22no—
293C22×D7—24no—
294C22×D7—24no—
295C22×D7—22no—
296C22×D7—22no—
297C22×D7—24no—
298C22×D7—42no—
299C22×D7—42no—
300C22×D7—41no—
301C22×D7—42no—
302C22×D7—42no—
303C22×D7—41no—
304C22×D7—42no—
305C22×D7—41no—
306C22×D7—41no—
307C22×D7—42no—
308C22×D7C2×C4214yes—
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—24no—
314C2×C4×C7—24no—
315C2×C4×C7—24no—
316C2×C4×C7—24no—
317C2×C4×C7—24no—
318C2×C4×C7—24no—
319C2×C4×C7—24no—
320C2×C4×C7—24no—
321C2×C4×C7—24no—
322C2×C4×C7—24no—
323C2×C4×C7—416no—
324C2×C4×C7—42no—
325C2×C4×C7—42no—
326C2×C4×C7—42no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7—42no—
330C2×C4×C7—42no—
331C2×C4×C7—42no—
332C2×C4×C7C2×C22⋊C414yes—
333C2×C4×C7C4×D414yes—
334C22⋊D7—232no—
335C2×Dic7—24no—
336C2×Dic7—22no—
337C2×Dic7—22no—
338C2×Dic7—24no—
339C2×Dic7—24no—
340C2×Dic7—24no—
341C2×Dic7—24no—
342C2×Dic7—24no—
343C2×Dic7—24no—
344C2×Dic7—24no—
345C2×Dic7—22no—
346C2×Dic7—24no—
347C2×Dic7—24no—
348C2×Dic7—22no—
349C2×Dic7—24no—
350C2×Dic7—22no—
351C2×Dic7—42no—
352C2×Dic7—42no—
353C2×Dic7—42no—
354C2×Dic7—42no—
355C2×Dic7—42no—
356C2×Dic7—42no—
357C2×Dic7C2×C4214yes—
358C2×Dic7C2×C22⋊C414yes—
359C2×Dic7C2×C22⋊C414yes—
360C2×Dic7#11714yes—
361C2×Dic7C4×D418yes—
362C2×Dic7C4×D418yes—
363C2×Dic7C4×D418yescomplemented
364C4×D7—416no—
365C25—71no—
366C25C22×D711yescharacteristic
367C22×D4—74no—
368C22×D4—78no—
369C22×D4—144no—
370C22×D4—142no—
371C22×D4—142no—
372C23×C4—24no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—42no—
376C23×C4—71no—
377C23×C4—72no—
378C23×C4—71no—
379C23×C4—72no—
380C23×C4—71no—
381C23×C4—74no—
382C23×C4—144no—
383C23×C4—142no—
384C23×C4—142no—
385C23×C4—282no—
386C23×C4C4×D714yes—
387C23×C4C22×D712yes—
388C23×C4C22×D712yes—
389C23×C4C22×D711yescharacteristic
390C23×C4C22×D711yescharacteristic
391C4×D4—1432no—
392C2×C4⋊C4—74no—
393C2×C4⋊C4—78no—
394C2×C4⋊C4—78no—
395C2×C4⋊C4—144no—
396C2×C4⋊C4—144no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—74no—
400C2×C22⋊C4—78no—
401C2×C22⋊C4—74no—
402C2×C22⋊C4—78no—
403C2×C22⋊C4—78no—
404C2×C22⋊C4—144no—
405C2×C22⋊C4—144no—
406C2×C22⋊C4—144no—
407C2×C22⋊C4—144no—
408C2×C22⋊C4—144no—
409C2×C22⋊C4—144no—
410C2×C22⋊C4—282no—
411C2×C22⋊C4—282no—
412C2×C22⋊C4C4×D718yescomplemented
413C2×C42—74no—
414C2×C42—78no—
415C2×C42—144no—
416C2×C42—144no—
417C2×C42—144no—
418C2×C42—144no—
419C2×C42—144no—
420C2×C42—144no—
421C2×C42—144no—
422C2×C42—282no—
423C2×C42—282no—
424#95—22no—
425#95—24no—
426#95—22no—
427#95—74no—
428#95—144no—
429#95—144no—
430#95—142no—
431#95—282no—
432C22×C7—24no—
433C22×C7—24no—
434C22×C7—24no—
435C22×C7—42no—
436C22×C7—42no—
437C22×C7—42no—
438C22×C7—42no—
439C22×C7—44no—
440C22×C7—44no—
441C22×C7—44no—
442C22×C7—44no—
443C22×C7C22×C4211yescharacteristic
444C22×C7C22×C22⋊C411yescharacteristic
445C22×C7C2×#11711yescharacteristic
446C22×C7C2×C4×D411yescharacteristic
447C22×C7C2×C4×D412yes—
448C22×C7C2×C4×D412yes—
449C22×C7C2×C4×D412yes—
450C22×C7C4×#4111yescharacteristic
451C22×C7C4×#4112yes—
452C22×C7#51811yescharacteristic
453C22×C7#51812yes—
454C22×C7#52011yescharacteristic
455C22×C7#52012yes—
456C22×C7D4212yes—
457C22×C7#54612yes—
458C22×C7#54711yescharacteristic
459C22×C7#54812yes—
460C22×C7#55012yes—
461C22×C7#55011yescharacteristic
462C22×C7#55312yes—
463C22×C7#55511yescharacteristic
464C22×C7#55611yescharacteristic
465C22×C7#55912yes—
466C2×D7—24no—
467C2×D7—24no—
468C2×D7—24no—
469C2×D7—42no—
470C2×D7—42no—
471C2×D7—42no—
472C2×D7—42no—
473C2×D7—44no—
474C2×D7—44no—
475C2×D7—44no—
476C2×D7—44no—
477C4×C7—24no—
478C4×C7—24no—
479C4×C7—44no—
480C4×C7—44no—
481Dic7—24no—
482Dic7—28no—
483Dic7—42no—
484Dic7—44no—
485Dic7C4×C22⋊C418yescomplemented
486C24—21no—
487C24—22no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24—21no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—74no—
496C24—72no—
497C24—141no—
498C24—142no—
499C24—141no—
500C24—141no—
501C24—142no—
502C24—141no—
503C24—142no—
504C24—141no—
505C24—141no—
506C24C2×C4×D714yes—
507C24C2×C4×D712yes—
508C24C23×D711yescharacteristic
509C2×D4—716no—
510C2×D4—148no—
511C2×D4—148no—
512C2×D4—1416no—
513C2×D4—1416no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—44no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—72no—
537C22×C4—74no—
538C22×C4—74no—
539C22×C4—72no—
540C22×C4—72no—
541C22×C4—74no—
542C22×C4—72no—
543C22×C4—74no—
544C22×C4—74no—
545C22×C4—74no—
546C22×C4—72no—
547C22×C4—74no—
548C22×C4—148no—
549C22×C4—142no—
550C22×C4—141no—
551C22×C4—141no—
552C22×C4—142no—
553C22×C4—142no—
554C22×C4—142no—
555C22×C4—142no—
556C22×C4—142no—
557C22×C4—142no—
558C22×C4—142no—
559C22×C4—141no—
560C22×C4—142no—
561C22×C4—142no—
562C22×C4—141no—
563C22×C4—142no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—148no—
567C22×C4—284no—
568C22×C4—288no—
569C22×C4—288no—
570C22×C4C2×C4×D714yes—
571C22×C4C2×C4×D714yes—
572C22×C4C2×C4×D712yes—
573C22×C4C2×C4×D712yes—
574C22×C4D4×D714yes—
575C22×C4D4×D712yes—
576C22×C4#115912yes—
577C4⋊C4—716no—
578C4⋊C4—1416no—
579C22⋊C4—48no—
580C22⋊C4—1416no—
581C22⋊C4—148no—
582C22⋊C4—1416no—
583C22⋊C4—148no—
584C22⋊C4—288no—
585C42—1416no—
586C42—148no—
587C42—288no—
588C42—288no—
589C2×C7—44no—
590C2×C7C2×C4×C22⋊C411yescharacteristic
591C2×C7C42×D411yescharacteristic
592C2×C7#227511yescharacteristic
593C2×C7D4×C22⋊C411yescharacteristic
594C2×C7#234111yescharacteristic
595C2×C7#235411yescharacteristic
596C2×C7#235711yescharacteristic
597C2×C7#236112yes—
598C2×C7#236312yes—
599C2×C7#236612yes—
600C2×C7#236712yes—
601D7—44no—
602C23—22no—
603C23—22no—
604C23—24no—
605C23—22no—
606C23—22no—
607C23—24no—
608C23—22no—
609C23—22no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—42no—
621C23—41no—
622C23—42no—
623C23—42no—
624C23—74no—
625C23—142no—
626C23—142no—
627C23—144no—
628C23—142no—
629C23—142no—
630C23—144no—
631C23—142no—
632C23—142no—
633C23—144no—
634C23—144no—
635C23—144no—
636C23—144no—
637C23—282no—
638C23—282no—
639C23—282no—
640C23—281no—
641C23—281no—
642C23—281no—
643C23—282no—
644C23—281no—
645C23—282no—
646C23—282no—
647C23C42×D714yes—
648C23C22×C4×D711yescharacteristic
649C23C22×C4×D712yes—
650C23C2×D4×D712yes—
651C23C2×D4×D711yescharacteristic
652C23C2×#115911yescharacteristic
653C23#654812yes—
654C23#654811yescharacteristic
655C23#655111yescharacteristic
656C23D7×#4111yescharacteristic
657C23D7×#4111yescharacteristic
658C23D7×#4112yes—
659D4—1432no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—416no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—74no—
684C2×C4—74no—
685C2×C4—74no—
686C2×C4—78no—
687C2×C4—78no—
688C2×C4—74no—
689C2×C4—78no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—144no—
693C2×C4—144no—
694C2×C4—144no—
695C2×C4—144no—
696C2×C4—144no—
697C2×C4—144no—
698C2×C4—144no—
699C2×C4—144no—
700C2×C4—142no—
701C2×C4—144no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—144no—
705C2×C4—144no—
706C2×C4—2816no—
707C2×C4—282no—
708C2×C4—282no—
709C2×C4—282no—
710C2×C4—282no—
711C2×C4—282no—
712C2×C4—282no—
713C2×C4D7×C22⋊C414yes—
714C2×C4(C22⋊D7)⋊C414yes—
715C7#1382011yescharacteristic, complemented, Sylow
716C22—24no—
717C22—24no—
718C22—24no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—44no—
724C22—44no—
725C22—44no—
726C22—44no—
727C22—144no—
728C22—144no—
729C22—144no—
730C22—282no—
731C22—282no—
732C22—282no—
733C22—282no—
734C22—284no—
735C22—284no—
736C22—284no—
737C22—284no—
738C22C2×C42×D711yescharacteristic
739C22C2×D7×C22⋊C411yescharacteristic
740C22C2×(C22⋊D7)⋊C411yescharacteristic
741C22#9017711yescharacteristic
742C22#9017712yes—
743C22#9019511yescharacteristic
744C22#9019512yes—
745C22D7×#11711yescharacteristic
746C22#9021311yescharacteristic
747C22C4×#115912yes—
748C22C4×D4×D712yes—
749C22C4×D4×D712yes—
750C22C4×D4×D712yes—
751C22#9028112yes—
752C22#9028212yes—
753C22#9029012yes—
754C22#9029011yescharacteristic
755C22#9030711yescharacteristic
756C22#9032211yescharacteristic
757C22#9032412yes—
758C22#9033211yescharacteristic
759C22#9035212yes—
760C22#9035512yes—
761C4—24no—
762C4—24no—
763C4—44no—
764C4—44no—
765C4—78no—
766C4—144no—
767C4—148no—
768C4—282no—
769C4—284no—
770C2—44no—
771C2—284no—
772C2#1173076711yescharacteristic
773C2C4×(C22⋊D7)⋊C411yescharacteristic
774C2C4×D7×C22⋊C411yescharacteristic
775C2#1173129511yescharacteristic
776C2#1173132211yescharacteristic
777C2#1173133011yescharacteristic
778C2#1173150611yescharacteristic
779C2#1173184212yes—
780C2#1173184312yes—
781C2#1173212212yes—
782C2#1173212412yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC22×C7C22×C42
FittingC7×C22⋊#95C2
socle, cosocleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC22⋊#95D7
hypocenterC7#13820
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊Dic7C2semidirect
4. C2×#89421C2semidirect
5. C2×#89438C2semidirect
6. C7×C22⋊#95C2semidirect
7. #11729299C2semidirect
8. (C2×D7)⋊#95C2semidirect
9. #11727162C2semidirect
10. Dic7⋊#95C2semidirect
11. Dic7×#95C2semidirect
19. C2×C4×C22⋊D7C4semidirect
38. #89729C4semidirect
70. C2×C7×C22⋊C4C2×C4semidirect
75. C2×C22⋊Dic7C2×C4semidirect
83. C2×(C2×D7)⋊C4C2×C4semidirect
84. C2×(C2×D7)⋊C4C2×C4semidirect
88. C2×Dic7⋊C4C2×C4semidirect
100. C2×C4×Dic7C2×C4semidirect
108. C7⋊#95D4semidirect
118. C22⋊#95D7semidirect
176. C2×C22⋊D7C42semidirect
218. Dic7⋊C4C22⋊C4semidirect
363. C2×Dic7C4×D4semidirect
412. C2×C22⋊C4C4×D7semidirect
485. Dic7C4×C22⋊C4semidirect
715. C7#13820semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D72
C2×C4×C22⋊Dic72
C2×#897292
C2×#894212
C2×#894382
C7×C22⋊#952
#117292992
(C2×D7)⋊#952
#117271622
Dic7⋊#952
Dic7×#952
#138207