Finite Group Databasebeta

← C2×#11743782 #14262201

Subgroups — C2×#11743782 #14262201

Order 1792.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D7×#41C211yesmaximal, characteristic, complemented
2C22×#6551C211yesmaximal, characteristic, complemented
3C2×C7×#548C211yesmaximal, characteristic, complemented
4C2×#90522C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊D7C211yesmaximal, characteristic, complemented
6#11743782C2132yesmaximal, direct product factor
7C2×#90367C213yesmaximal, complemented
8C2×#90366C213yesmaximal, complemented
9C2×#90322C213yesmaximal, complemented
10C2×D7×C22⋊Q8C213yesmaximal, complemented
11C2×#90303C213yesmaximal, complemented
12C2×#90299C213yesmaximal, complemented
13C2×Q8×D28C211yesmaximal, characteristic, complemented
14C2×#90265C211yesmaximal, characteristic, complemented
15C2×#90242C213yesmaximal, complemented
16C2×#90238C213yesmaximal, complemented
17C22×C7×#41C2211yescharacteristic
18C23×C7×Q8C2211yescharacteristic, complemented
19C2×D7×#41—216no—
20C2×D7×#41C22116yescomplemented
21C2×#6551—216no—
22C2×#6551C22116yescomplemented
23C22×#1161C2211yescharacteristic
24C22×#1161C2213yescomplemented
25C22×Q8×D7C2211yescharacteristic
26C22×Q8×D7C2213yescomplemented
27C22×Q8×D7C2211yescharacteristic, complemented
28C22×#1159C2213yes—
29C22×D4×D7C2213yes—
30C22×#1157C2213yes—
31C22×#1157C2213yescomplemented
32C22×#1157C2213yescomplemented
33C23×C4×D7C2213yes—
34C7×#548C22116yescomplemented
35C2×C7×#124C2213yescomplemented
36C2×C7×C22⋊Q8C2213yescomplemented
37C2×C7×#121C2213yescomplemented
38C2×C4×C7×Q8C2211yescharacteristic, complemented
39C2×C4×C7×D4C2213yescomplemented
40#90522C22116yescomplemented
41Q8×C22⋊D7C22116yescomplemented
42C2×#6509C2213yes—
43C2×Q8×Dic7C2211yescharacteristic, complemented
44C2×#6507C2213yescomplemented
45C2×#6502C2213yescomplemented
46C2×#6501C2216yescomplemented
47C2×#6501C2213yescomplemented
48C2×#6500C2213yes—
49C2×#6499C2213yescomplemented
50C2×C4×C22⋊D7C2213yes—
51C2×C4×C22⋊D7C2213yescomplemented
52C2×#6487C2213yescomplemented
53C2×#6487C2213yescomplemented
54#90367C22148yescomplemented
55#90366C22148yescomplemented
56#90322C22148yescomplemented
57D7×C22⋊Q8C22148yescomplemented
58#90303C22148yescomplemented
59#90299C22148yescomplemented
60Q8×D28C22116yescomplemented
61#90265C22116yescomplemented
62#90242C22148yescomplemented
63#90238C22148yescomplemented
64C2×#6460C2213yes—
65C2×#6460C2213yescomplemented
66C2×#6459C2213yes—
67C2×#6457C2213yescomplemented
68C2×#6456C2213yescomplemented
69C2×D7×C4⋊C4C2213yescomplemented
70C2×D7×C4⋊C4C2216yescomplemented
71C2×#6447C2211yescharacteristic
72C2×#6447C2216yescomplemented
73C2×#6446C2216yescomplemented
74C2×#6446C2213yescomplemented
75C2×#6446C2216yescomplemented
76C2×#6445C2213yes—
77C2×D7×C22⋊C4C2216yes—
78C2×#6441C2216yescomplemented
79C2×#6441C2213yescomplemented
80C2×C4×D28C2213yes—
81C2×C4×D28C2213yescomplemented
82C2×#6435C2213yescomplemented
83C2×#6432C2213yescomplemented
84C2×#3489—71nomaximal, Sylow
85C24×D7C2313yes—
86C2×C7×#41—28no—
87C2×C7×#41C2318yes—
88C22×C7×Q8—28no—
89C22×C7×Q8C2313yes—
90C22×C7×Q8C2311yescharacteristic
91C22×C7×Q8C2318yescomplemented
92C22×C7×D4C2313yes—
93C22×C7×D4C2313yes—
94C23×C4×C7C2313yes—
95C23×C4×C7C2313yes—
96C22×C22⋊D7C2316yes—
97C22×C22⋊D7C2313yes—
98C22×C22⋊D7C2311yescharacteristic
99C22×C22⋊D7C2311yescharacteristic
100C22×C22⋊D7C2313yes—
101C23×Dic7C2313yes—
102D7×#41—2128no—
103#6551—2128no—
104C2×#1161—224no—
105C2×#1161D4116yescomplemented
106C2×#1161C2318yes—
107C2×#1161C23124yescomplemented
108C2×Q8×D7—28no—
109C2×Q8×D7—28no—
110C2×Q8×D7—224no—
111C2×Q8×D7C2318yes—
112C2×Q8×D7C2318yescomplemented
113C2×Q8×D7C23124yescomplemented
114C2×#1159—224no—
115C2×#1159C23124yes—
116C2×D4×D7—224no—
117C2×D4×D7C23124yes—
118C2×#1157—224no—
119C2×#1157—224no—
120C2×#1157—224no—
121C2×#1157C23124yes—
122C2×#1157C23124yescomplemented
123C2×#1157C23124yescomplemented
124C22×D28C2311yescharacteristic
125C22×D28C2313yes—
126C22×D28C2313yes—
127C22×C4×D7—224no—
128C22×C4×D7C2313yes—
129C22×C4×D7C2313yes—
130C22×C4×D7C2316yes—
131C22×C4×D7C2313yes—
132C22×C4×D7C2311yescharacteristic
133C22×C4×D7C23124yes—
134C22×C4×D7C2316yes—
135C22×C4×D7C2313yes—
136C22×Dic14C2313yes—
137C22×Dic14C2313yes—
138C22×Dic14C2313yes—
139C7×#124C23124yescomplemented
140C7×C22⋊Q8C23124yescomplemented
141C7×#121C23124yescomplemented
142C4×C7×Q8C2318yescomplemented
143C4×C7×D4C23124yescomplemented
144C2×C7×C4⋊C4C2313yes—
145C2×C7×C4⋊C4C2313yes—
146C2×C7×C22⋊C4C2316yes—
147C2×C7×C22⋊C4C2313yes—
148C2×C7×C22⋊C4C2311yescharacteristic
149C2×C42×C7C2313yes—
150C2×C22⋊Dic7C2316yes—
151C2×C22⋊Dic7C2313yes—
152C2×C22⋊Dic7C2313yes—
153#6509C23124yes—
154Q8×Dic7C2318yescomplemented
155#6507C23124yescomplemented
156#6502C23124yescomplemented
157#6501C23148yescomplemented
158#6501C23124yescomplemented
159#6500C23124yes—
160#6499C23124yescomplemented
161C4×C22⋊D7C23124yes—
162C4×C22⋊D7C23124yescomplemented
163C2×(C2×D7)⋊C4C2313yes—
164C2×(C2×D7)⋊C4C2313yes—
165C2×(C2×D7)⋊C4C2313yes—
166C2×(C2×D7)⋊C4C2313yes—
167C2×(C2×D7)⋊C4C2313yes—
168C2×(C2×D7)⋊C4C2311yescharacteristic
169C2×C4⋊Dic7C2313yes—
170C2×C4⋊Dic7C2316yes—
171C2×C4⋊Dic7C2313yes—
172#6487C23124yescomplemented
173#6487C23124yescomplemented
174C2×Dic7⋊C4C2311yescharacteristic
175C2×Dic7⋊C4C2313yes—
176C2×Dic7⋊C4C2313yes—
177C2×Dic7⋊C4C2316yes—
178C2×Dic7⋊C4C2313yes—
179C2×C4×Dic7C2313yes—
180#6460C23124yes—
181#6460C23124yescomplemented
182#6459C23124yes—
183#6457C23124yescomplemented
184#6456C23124yescomplemented
185D7×C4⋊C4C23148yescomplemented
186D7×C4⋊C4C23124yescomplemented
187#6447C2318yes—
188#6447C23148yescomplemented
189#6446C23124yescomplemented
190#6446C23148yescomplemented
191#6446C23148yescomplemented
192#6445C23124yes—
193D7×C22⋊C4C23148yes—
194#6441C23124yescomplemented
195#6441C23148yescomplemented
196C4×D28C23124yes—
197C4×D28C23124yescomplemented
198#6435C23124yescomplemented
199#6432C23124yescomplemented
200C22×2−1+4—71no—
201C23×#41—71no—
202#3489—732no—
203C2×D4×Q8—71no—
204C2×D4×Q8—71no—
205C2×#548—71no—
206C2×#548D711yescharacteristic, complemented
207C2×#547—73no—
208C2×#547—73no—
209C2×#546—73no—
210C2×#546—73no—
211C2×#537—73no—
212C2×#536—73no—
213C2×#525—73no—
214C22×C22⋊Q8—73no—
215C2×#520—71no—
216C24×C7C2413yes—
217C24×C7C2411yescharacteristic
218C23×D7—212no—
219C23×D7—212no—
220C23×D7—46no—
221C23×D7C2411yescharacteristic
222C23×D7C24112yes—
223C23×D7C2413yes—
224C23×D7C2411yescharacteristic
225C7×#41—232no—
226C2×C7×Q8—232no—
227C2×C7×Q8—212no—
228C2×C7×Q8C2×D418yes—
229C2×C7×Q8C24112yes—
230C2×C7×Q8C2414yes—
231C2×C7×D4—212no—
232C2×C7×D4—46no—
233C2×C7×D4C24112yes—
234C2×C7×D4C24112yes—
235C22×C4×C7—212no—
236C22×C4×C7—212no—
237C22×C4×C7C2413yes—
238C22×C4×C7C2411yescharacteristic
239C22×C4×C7C2411yescharacteristic
240C22×C4×C7C2413yes—
241C22×C4×C7C24112yes—
242C22×C4×C7C24112yes—
243C22×C4×C7C2413yes—
244C2×C22⋊D7—212no—
245C2×C22⋊D7—224no—
246C2×C22⋊D7—24no—
247C2×C22⋊D7—24no—
248C2×C22⋊D7—46no—
249C2×C22⋊D7C24124yes—
250C2×C22⋊D7C24112yes—
251C2×C22⋊D7C2414yes—
252C2×C22⋊D7C2414yes—
253C2×C22⋊D7C24112yes—
254C22×Dic7—212no—
255C22×Dic7C24112yes—
256C22×Dic7C2411yescharacteristic
257C22×Dic7C2413yes—
258C22×Dic7C2413yes—
259C22×Dic7C2413yes—
260C22×Dic7C2411yescharacteristic
261#1161—296no—
262#1161C2×D4164yescomplemented
263Q8×D7—232no—
264Q8×D7—232no—
265Q8×D7—296no—
266#1159—296no—
267D4×D7—296no—
268#1157—296no—
269#1157—296no—
270#1157—296no—
271C2×D28—212no—
272C2×D28—24no—
273C2×D28C2×D4124yes—
274C2×D28C2414yes—
275C2×D28C24112yes—
276C2×D28C24112yes—
277C2×C4×D7—212no—
278C2×C4×D7—224no—
279C2×C4×D7—212no—
280C2×C4×D7—212no—
281C2×C4×D7—24no—
282C2×C4×D7—296no—
283C2×C4×D7—412no—
284C2×C4×D7C2×D4124yes—
285C2×C4×D7C24112yes—
286C2×C4×D7C24112yes—
287C2×C4×D7C24124yes—
288C2×C4×D7C24112yes—
289C2×C4×D7C2414yes—
290C2×C4×D7C24124yes—
291C2×C4×D7C24112yes—
292C2×Dic14—212no—
293C2×Dic14—212no—
294C2×Dic14—212no—
295C2×Dic14C24112yes—
296C2×Dic14C24112yes—
297C2×Dic14C24112yes—
298C7×C4⋊C4C24112yes—
299C7×C4⋊C4C24112yes—
300C7×C22⋊C4C24124yes—
301C7×C22⋊C4C24112yes—
302C7×C22⋊C4C2414yes—
303C42×C7C24112yes—
304C22⋊Dic7C24124yes—
305C22⋊Dic7C24112yes—
306C22⋊Dic7C24112yes—
307(C2×D7)⋊C4C24112yes—
308(C2×D7)⋊C4C24112yes—
309(C2×D7)⋊C4C24112yes—
310(C2×D7)⋊C4C24112yes—
311(C2×D7)⋊C4C24112yes—
312(C2×D7)⋊C4C2414yes—
313C4⋊Dic7C24112yes—
314C4⋊Dic7C24124yes—
315C4⋊Dic7C24112yes—
316Dic7⋊C4C2414yes—
317Dic7⋊C4C24112yes—
318Dic7⋊C4C24112yes—
319Dic7⋊C4C24124yes—
320Dic7⋊C4C24112yes—
321C4×Dic7C24112yes—
322C2×2−1+4—716no—
323C2×2−1+4—1416no—
324C22×#41—716no—
325C22×#41—71no—
326C22×#41—73no—
327C22×#41—73no—
328C22×#41—73no—
329C22×#41—73no—
330C22×#41—73no—
331C22×#41—1416no—
332C22×#41C2×D711yescharacteristic
333C23×Q8—71no—
334C23×Q8—73no—
335C23×Q8—71no—
336C23×Q8C2×D711yescharacteristic, complemented
337C23×D4—73no—
338C24×C4—73no—
339D4×Q8—716no—
340D4×Q8—716no—
341#548—716no—
342#548C2×D7116yescomplemented
343#547—748no—
344#547—748no—
345#546—748no—
346#546—748no—
347#537—748no—
348#536—748no—
349C2×C4⋊Q8—73no—
350C2×C4⋊Q8—73no—
351C2×#124—73no—
352C2×#124C2×D713yescomplemented
353#525—748no—
354C2×#123—73no—
355C2×#123—73no—
356C2×#123—76no—
357C2×#123—76no—
358C2×C22⋊Q8—73no—
359C2×C22⋊Q8—73no—
360C2×C22⋊Q8—73no—
361C2×C22⋊Q8—748no—
362C2×C22⋊Q8—73no—
363C2×C22⋊Q8—73no—
364C2×C22⋊Q8—73no—
365C2×C22⋊Q8—76no—
366C2×C22⋊Q8—73no—
367C2×C22⋊Q8C2×D713yescomplemented
368C2×#121—73no—
369C2×#121—76no—
370C2×#121—73no—
371C2×#121—71no—
372C2×#121—76no—
373C2×#121C2×D713yescomplemented
374C2×#120—73no—
375C2×#120—73no—
376#520—716no—
377C2×C4×Q8—71no—
378C2×C4×Q8C2×D711yescharacteristic, complemented
379C2×C4×D4—73no—
380C2×C4×D4—73no—
381C2×C4×D4—73no—
382C2×C4×D4—73no—
383C2×C4×D4—73no—
384C2×C4×D4C2×D713yescomplemented
385C2×#117—73no—
386C22×C4⋊C4—73no—
387C22×C4⋊C4—76no—
388C22×C22⋊C4—76no—
389C23×C7—26no—
390C23×C7—22no—
391C23×C7—22no—
392C23×C7—26no—
393C23×C7—26no—
394C23×C7—22no—
395C23×C7C2516yes—
396C23×C7C2512yes—
397C23×C7C2511yescharacteristic
398C22×D7—22no—
399C22×D7—26no—
400C22×D7—26no—
401C22×D7—22no—
402C22×D7—22no—
403C22×D7—22no—
404C22×D7—22no—
405C22×D7—224no—
406C22×D7—224no—
407C22×D7—412no—
408C22×D7—448no—
409C22×D7C22×D4112yes—
410C22×D72−1+414yescomplemented
411C22×D7C2512yes—
412C22×D7C2516yes—
413C22×D7C2512yes—
414C7×Q8—224no—
415C7×Q8C22×D4116yes—
416C7×D4—224no—
417C7×D4—412no—
418C2×C4×C7—26no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—26no—
422C2×C4×C7—224no—
423C2×C4×C7—224no—
424C2×C4×C7C22×D4112yes—
425C2×C4×C7C2516yes—
426C2×C4×C7C2512yes—
427C2×C4×C7C2512yes—
428C2×C4×C7C2516yes—
429C2×C4×C7C2516yes—
430C22⋊D7—224no—
431C22⋊D7—248no—
432C22⋊D7—28no—
433C22⋊D7—28no—
434C22⋊D7—412no—
435C2×Dic7—26no—
436C2×Dic7—26no—
437C2×Dic7—22no—
438C2×Dic7—26no—
439C2×Dic7—224no—
440C2×Dic7C22×D414yes—
441C2×Dic7C2512yes—
442C2×Dic7C2516yes—
443C2×Dic7C2516yes—
444C2×Dic7C2516yes—
445C2×Dic7C2512yes—
446D28—224no—
447D28—28no—
448D28C22×D4148yes—
449C4×D7—224no—
450C4×D7—248no—
451C4×D7—224no—
452C4×D7—224no—
453C4×D7—28no—
454C4×D7—424no—
455C4×D7C22×D4148yes—
456Dic14—224no—
457Dic14—224no—
458Dic14—224no—
459C25—73no—
4602−1+4—14128no—
461C2×#41—28no—
462C2×#41—716no—
463C2×#41—78no—
464C2×#41—724no—
465C2×#41—724no—
466C2×#41—724no—
467C2×#41—724no—
468C2×#41—724no—
469C2×#41—1424no—
470C2×#41—1424no—
471C2×#41—1424no—
472C2×#41—1424no—
473C2×#41—1424no—
474C2×#41—14128no—
475C2×#41C22×D718yes—
476C22×Q8—28no—
477C22×Q8—724no—
478C22×Q8—78no—
479C22×Q8—78no—
480C22×Q8—73no—
481C22×Q8—73no—
482C22×Q8—73no—
483C22×Q8—1424no—
484C22×Q8—148no—
485C22×Q8—148no—
486C22×Q8C22×D713yes—
487C22×Q8C22×D711yescharacteristic
488C22×Q8C22×D718yescomplemented
489C22×D4—71no—
490C22×D4—73no—
491C22×D4—71no—
492C22×D4—76no—
493C22×D4—73no—
494C22×D4—724no—
495C22×D4—73no—
496C22×D4—71no—
497C22×D4—73no—
498C22×D4—1424no—
499C22×D4C22×D713yes—
500C22×D4C22×D713yes—
501C23×C4—73no—
502C23×C4—73no—
503C23×C4—76no—
504C23×C4—73no—
505C23×C4—73no—
506C23×C4—73no—
507C23×C4—71no—
508C23×C4—724no—
509C23×C4—76no—
510C23×C4—1424no—
511C23×C4C22×D713yes—
512C23×C4C22×D713yes—
513C4⋊Q8—724no—
514C4⋊Q8—724no—
515#124—724no—
516#124C22×D7124yescomplemented
517#123—724no—
518#123—724no—
519#123—748no—
520#123—748no—
521C22⋊Q8—724no—
522C22⋊Q8—724no—
523C22⋊Q8—724no—
524C22⋊Q8—724no—
525C22⋊Q8—724no—
526C22⋊Q8—724no—
527C22⋊Q8—748no—
528C22⋊Q8—724no—
529C22⋊Q8C22×D7124yescomplemented
530#121—724no—
531#121—748no—
532#121—724no—
533#121—78no—
534#121—748no—
535#121C22×D7124yescomplemented
536#120—724no—
537#120—724no—
538C4×Q8—78no—
539C4×Q8C22×D718yescomplemented
540C4×D4—724no—
541C4×D4—724no—
542C4×D4—724no—
543C4×D4—724no—
544C4×D4—724no—
545C4×D4C22×D7124yescomplemented
546#117—724no—
547C2×C4⋊C4—73no—
548C2×C4⋊C4—73no—
549C2×C4⋊C4—73no—
550C2×C4⋊C4—76no—
551C2×C4⋊C4—76no—
552C2×C4⋊C4—71no—
553C2×C4⋊C4—73no—
554C2×C4⋊C4—73no—
555C2×C4⋊C4—724no—
556C2×C4⋊C4—748no—
557C2×C4⋊C4C22×D713yes—
558C2×C4⋊C4C22×D713yes—
559C2×C22⋊C4—76no—
560C2×C22⋊C4—73no—
561C2×C22⋊C4—73no—
562C2×C22⋊C4—73no—
563C2×C22⋊C4—73no—
564C2×C22⋊C4—73no—
565C2×C22⋊C4—73no—
566C2×C22⋊C4—71no—
567C2×C22⋊C4—73no—
568C2×C22⋊C4—748no—
569C2×C22⋊C4C22×D716yes—
570C2×C22⋊C4C22×D711yescharacteristic
571C2×C22⋊C4C22×D713yes—
572C2×C42—73no—
573C2×C42C22×D713yes—
574C22×C7—26no—
575C22×C7—22no—
576C22×C7—22no—
577C22×C7—26no—
578C22×C7—26no—
579C22×C7—22no—
580C22×C7—412no—
581C22×C7—44no—
582C22×C7C23×D412yes—
583C22×C7C2×2−1+412yes—
584C22×C7#58512yes—
585C22×C7C2611yescharacteristic
586C2×D7—22no—
587C2×D7—26no—
588C2×D7—26no—
589C2×D7—22no—
590C2×D7—28no—
591C2×D7—224no—
592C2×D7—22no—
593C2×D7—22no—
594C2×D7—22no—
595C2×D7—448no—
596C2×D7—44no—
597C2×D7C23×D4112yes—
598C2×D7C2×2−1+414yescomplemented
599C4×C7—26no—
600C4×C7—22no—
601C4×C7—22no—
602C4×C7—26no—
603C4×C7C23×D4112yes—
604Dic7—26no—
605Dic7—26no—
606Dic7—22no—
607Dic7—26no—
608Dic7C23×D414yes—
609C24—71no—
610C24—73no—
611C24—71no—
612C24—712no—
613C24—1412no—
614C24—1412no—
615C24—286no—
616C24C23×D713yes—
617C24C23×D711yescharacteristic
618#41—232no—
619#41—764no—
620#41—1496no—
621#41—1496no—
622#41—1496no—
623#41—1496no—
624#41—1496no—
625C2×Q8—232no—
626C2×Q8—212no—
627C2×Q8—712no—
628C2×Q8—712no—
629C2×Q8—712no—
630C2×Q8—1412no—
631C2×Q8—1496no—
632C2×Q8—1432no—
633C2×Q8—1432no—
634C2×Q8—1412no—
635C2×Q8—1412no—
636C2×Q8D4×D718yes—
637C2×Q8C23×D7112yes—
638C2×Q8C23×D714yes—
639C2×D4—212no—
640C2×D4—46no—
641C2×D4—74no—
642C2×D4—712no—
643C2×D4—74no—
644C2×D4—724no—
645C2×D4—712no—
646C2×D4—724no—
647C2×D4—712no—
648C2×D4—74no—
649C2×D4—712no—
650C2×D4—144no—
651C2×D4—1412no—
652C2×D4—144no—
653C2×D4—1496no—
654C2×D4—1424no—
655C2×D4—144no—
656C2×D4—1412no—
657C2×D4—286no—
658C2×D4C23×D7112yes—
659C2×D4C23×D7112yes—
660C22×C4—212no—
661C22×C4—212no—
662C22×C4—71no—
663C22×C4—724no—
664C22×C4—712no—
665C22×C4—712no—
666C22×C4—71no—
667C22×C4—73no—
668C22×C4—73no—
669C22×C4—73no—
670C22×C4—724no—
671C22×C4—712no—
672C22×C4—712no—
673C22×C4—712no—
674C22×C4—74no—
675C22×C4—724no—
676C22×C4—144no—
677C22×C4—1496no—
678C22×C4—1412no—
679C22×C4—1424no—
680C22×C4—1412no—
681C22×C4—1412no—
682C22×C4—1412no—
683C22×C4—2812no—
684C22×C4C23×D7112yes—
685C22×C4C23×D7112yes—
686C22×C4C23×D711yescharacteristic
687C22×C4C23×D713yes—
688C22×C4C23×D713yes—
689C22×C4C23×D711yescharacteristic
690C22×C4C23×D713yes—
691C4⋊C4—712no—
692C4⋊C4—712no—
693C4⋊C4—724no—
694C4⋊C4—74no—
695C4⋊C4—712no—
696C4⋊C4—712no—
697C4⋊C4—724no—
698C4⋊C4—712no—
699C4⋊C4C23×D7112yes—
700C4⋊C4C23×D7112yes—
701C22⋊C4—724no—
702C22⋊C4—712no—
703C22⋊C4—712no—
704C22⋊C4—712no—
705C22⋊C4—712no—
706C22⋊C4—712no—
707C22⋊C4—712no—
708C22⋊C4—74no—
709C22⋊C4—712no—
710C22⋊C4C23×D7124yes—
711C22⋊C4C23×D714yes—
712C22⋊C4C23×D7112yes—
713C42—712no—
714C42C23×D7112yes—
715C2×C7—46no—
716C2×C7—42no—
717C2×C7#348914yescomplemented
718C2×C7C24×D411yescharacteristic
719C2×C7C22×2−1+411yescharacteristic
720C2×C7C2×#58511yescharacteristic
721D7—24no—
722D7—212no—
723D7—42no—
724C23—22no—
725C23—26no—
726C23—22no—
727C23—26no—
728C23—22no—
729C23—26no—
730C23—72no—
731C23—76no—
732C23—712no—
733C23—74no—
734C23—72no—
735C23—1424no—
736C23—1424no—
737C23—142no—
738C23—146no—
739C23—142no—
740C23—146no—
741C23—142no—
742C23—142no—
743C23—142no—
744C23—2812no—
745C23—2848no—
746C23C24×D716yes—
747C23C24×D712yes—
748C23C24×D711yescharacteristic
749Q8—224no—
750Q8—1424no—
751Q8—1424no—
752Q8—1424no—
753Q8C2×D4×D7116yes—
754D4—224no—
755D4—412no—
756D4—748no—
757D4—148no—
758D4—1424no—
759D4—148no—
760D4—148no—
761D4—1448no—
762D4—1424no—
763D4—2812no—
764C2×C4—22no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—22no—
768C2×C4—224no—
769C2×C4—224no—
770C2×C4—72no—
771C2×C4—74no—
772C2×C4—748no—
773C2×C4—72no—
774C2×C4—76no—
775C2×C4—76no—
776C2×C4—76no—
777C2×C4—148no—
778C2×C4—1424no—
779C2×C4—1448no—
780C2×C4—1424no—
781C2×C4—146no—
782C2×C4—146no—
783C2×C4—146no—
784C2×C4—142no—
785C2×C4—1424no—
786C2×C4—1424no—
787C2×C4—2824no—
788C2×C4C2×D4×D7112yes—
789C2×C4C24×D712yes—
790C2×C4C24×D716yes—
791C2×C4C24×D716yes—
792C2×C4C24×D712yes—
793C2×C4C24×D716yes—
794C7C2×#348911yescharacteristic, complemented, Sylow
795C22—22no—
796C22—26no—
797C22—22no—
798C22—26no—
799C22—22no—
800C22—26no—
801C22—412no—
802C22—44no—
803C22—712no—
804C22—74no—
805C22—142no—
806C22—148no—
807C22—1424no—
808C22—146no—
809C22—142no—
810C22—146no—
811C22—142no—
812C22—142no—
813C22—142no—
814C22—2848no—
815C22—284no—
816C22C22×D4×D712yes—
817C22#9061612yes—
818C22D7×2−1+412yes—
819C22C25×D711yescharacteristic
820C4—22no—
821C4—26no—
822C4—26no—
823C4—22no—
824C4—74no—
825C4—146no—
826C4—146no—
827C4—146no—
828C4—142no—
829C4C22×D4×D7112yes—
830C2—46no—
831C2—42no—
832C2—144no—
833C2—1412no—
834C2—282no—
835C2#1174378214yesdirect product factor
836C2C23×D4×D711yescharacteristic
837C2C2×#9061611yescharacteristic
838C2C2×D7×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×#548C2
socleC23×C7C25
hypercenterC2×#548D7
hypocenterC7C2×#3489
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×D7×#41C2semidirect
2. C22×#6551C2semidirect
3. C2×C7×#548C2semidirect
4. C2×#90522C2semidirect
5. C2×Q8×C22⋊D7C2semidirect
6. #11743782C2direct (N × H)
7. C2×#90367C2semidirect
8. C2×#90366C2semidirect
9. C2×#90322C2semidirect
10. C2×D7×C22⋊Q8C2semidirect
11. C2×#90303C2semidirect
12. C2×#90299C2semidirect
13. C2×Q8×D28C2semidirect
14. C2×#90265C2semidirect
15. C2×#90242C2semidirect
16. C2×#90238C2semidirect
18. C23×C7×Q8C22semidirect
20. C2×D7×#41C22semidirect
22. C2×#6551C22semidirect
24. C22×#1161C22semidirect
26. C22×Q8×D7C22semidirect
27. C22×Q8×D7C22semidirect
31. C22×#1157C22semidirect
32. C22×#1157C22semidirect
34. C7×#548C22semidirect
35. C2×C7×#124C22semidirect
36. C2×C7×C22⋊Q8C22semidirect
37. C2×C7×#121C22semidirect
38. C2×C4×C7×Q8C22semidirect
39. C2×C4×C7×D4C22semidirect
40. #90522C22semidirect
41. Q8×C22⋊D7C22semidirect
43. C2×Q8×Dic7C22semidirect
44. C2×#6507C22semidirect
45. C2×#6502C22semidirect
46. C2×#6501C22semidirect
47. C2×#6501C22semidirect
49. C2×#6499C22semidirect
51. C2×C4×C22⋊D7C22semidirect
52. C2×#6487C22semidirect
53. C2×#6487C22semidirect
54. #90367C22semidirect
55. #90366C22semidirect
56. #90322C22semidirect
57. D7×C22⋊Q8C22semidirect
58. #90303C22semidirect
59. #90299C22semidirect
60. Q8×D28C22semidirect
61. #90265C22semidirect
62. #90242C22semidirect
63. #90238C22semidirect
65. C2×#6460C22semidirect
67. C2×#6457C22semidirect
68. C2×#6456C22semidirect
69. C2×D7×C4⋊C4C22semidirect
70. C2×D7×C4⋊C4C22semidirect
72. C2×#6447C22semidirect
73. C2×#6446C22semidirect
74. C2×#6446C22semidirect
75. C2×#6446C22semidirect
78. C2×#6441C22semidirect
79. C2×#6441C22semidirect
81. C2×C4×D28C22semidirect
82. C2×#6435C22semidirect
83. C2×#6432C22semidirect
91. C22×C7×Q8C23semidirect
105. C2×#1161D4semidirect
107. C2×#1161C23semidirect
112. C2×Q8×D7C23semidirect
113. C2×Q8×D7C23semidirect
122. C2×#1157C23semidirect
123. C2×#1157C23semidirect
139. C7×#124C23semidirect
140. C7×C22⋊Q8C23semidirect
141. C7×#121C23semidirect
142. C4×C7×Q8C23semidirect
143. C4×C7×D4C23semidirect
154. Q8×Dic7C23semidirect
155. #6507C23semidirect
156. #6502C23semidirect
157. #6501C23semidirect
158. #6501C23semidirect
160. #6499C23semidirect
162. C4×C22⋊D7C23semidirect
172. #6487C23semidirect
173. #6487C23semidirect
181. #6460C23semidirect
183. #6457C23semidirect
184. #6456C23semidirect
185. D7×C4⋊C4C23semidirect
186. D7×C4⋊C4C23semidirect
188. #6447C23semidirect
189. #6446C23semidirect
190. #6446C23semidirect
191. #6446C23semidirect
194. #6441C23semidirect
195. #6441C23semidirect
197. C4×D28C23semidirect
198. #6435C23semidirect
199. #6432C23semidirect
206. C2×#548D7semidirect
262. #1161C2×D4semidirect
336. C23×Q8C2×D7semidirect
342. #548C2×D7semidirect
352. C2×#124C2×D7semidirect
367. C2×C22⋊Q8C2×D7semidirect
373. C2×#121C2×D7semidirect
378. C2×C4×Q8C2×D7semidirect
384. C2×C4×D4C2×D7semidirect
410. C22×D72−1+4semidirect
488. C22×Q8C22×D7semidirect
516. #124C22×D7semidirect
529. C22⋊Q8C22×D7semidirect
535. #121C22×D7semidirect
539. C4×Q8C22×D7semidirect
545. C4×D4C22×D7semidirect
598. C2×D7C2×2−1+4semidirect
717. C2×C7#3489semidirect
794. C7C2×#3489semidirect
835. C2#11743782direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D7×#412
C22×#65512
C2×C7×#5482
C2×#905222
C2×Q8×C22⋊D72
#117437822
C2×#903672
C2×#903662
C2×#903222
C2×D7×C22⋊Q82
C2×#903032
C2×#902992
C2×Q8×D282
C2×#902652
C2×#902422
C2×#902382
C2×#34897