Finite Group Databasebeta

← #13369381

Subgroups — #13369381

Order 1792.

1458 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
1C2×C7×#548C211yesmaximal, characteristic
2C2×#90005C211yesmaximal, characteristic, complemented
3C2×#89997C211yesmaximal, characteristic, complemented
4#11739782C211yesmaximal, characteristic, complemented
5C2×#89783C211yesmaximal, characteristic, complemented
6#11729889C211yesmaximal, characteristic, complemented
7#11729886C211yesmaximal, characteristic, complemented
8#11729480C211yesmaximal, characteristic, complemented
9#11729475C211yesmaximal, characteristic, complemented
10#11729450C211yesmaximal, characteristic, complemented
11#11729447C211yesmaximal, characteristic, complemented
12#11729436C211yesmaximal, characteristic, complemented
13#11729432C211yesmaximal, characteristic, complemented
14#11729385C211yesmaximal, characteristic, complemented
15#11729380C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C23×C7×Q8C2211yescharacteristic
18C7×#548—24no—
19C7×#548C418yescomplemented
20C2×C7×#124—21no—
21C2×C7×#124C2211yescharacteristic
22C2×C7×C22⋊Q8—21no—
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C7×#121—21no—
25C2×C7×#121C2211yescharacteristic
26C2×C4×C7×Q8C2211yescharacteristic
27C2×C4×C7×D4—21no—
28C2×C4×C7×D4C2211yescharacteristic
29C2×#6489C2211yescharacteristic
30C2×#6489C2211yescharacteristic
31C22×#1136C2211yescharacteristic
32C23×C7⋊C8C2211yescharacteristic
33#90005—24no—
34#89997—24no—
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38C2×#6409C2211yescharacteristic
39C2×#6409C2211yescharacteristic
40C2×#6409C2211yescharacteristic
41C2×#6409C2211yescharacteristic
42C2×#6409C2211yescharacteristic
43#89993—21no—
44C2×#6406C2211yescharacteristic
45C2×#6406C2211yescharacteristic
46C2×#6406C2211yescharacteristic
47C2×#6406C2211yescharacteristic
48#89984C2211yescharacteristic
49#89984C2211yescharacteristic
50C2×C22⋊(C7⋊C8)C2211yescharacteristic
51C2×C22⋊(C7⋊C8)C2211yescharacteristic
52#89783—24no—
53C4⋊C4×Dic7—21no—
54#89723—21no—
55#89723—21no—
56#89707C2211yescharacteristic
57C4×C4⋊Dic7C2211yescharacteristic
58C2×C4⋊(C7⋊C8)C2211yescharacteristic
59C2×#6377C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#89324C2211yescharacteristic
63#89324C2211yescharacteristic
64#22426—71nomaximal, Sylow
65C2×C7×#41—22no—
66C2×C7×#41—22no—
67C2×C7×#41—22no—
68C2×C7×#41—41no—
69C2×C7×#41—41no—
70C2×C7×#41C2×C414yes—
71C22×C7×Q8—21no—
72C22×C7×Q8—22no—
73C22×C7×Q8—22no—
74C22×C7×Q8—22no—
75C22×C7×Q8—41no—
76C22×C7×Q8—41no—
77C22×C7×Q8C2×C414yes—
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4—21no—
81C22×C7×D4—21no—
82C22×C7×D4D411yescharacteristic
83C22×C7×D4C2311yescharacteristic
84C23×C4×C7—21no—
85C23×C4×C7—21no—
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C7×#124—28no—
89C7×#124—22no—
90C7×#124C2×C414yes—
91C7×C22⋊Q8—22no—
92C7×C22⋊Q8—28no—
93C7×C22⋊Q8C2×C414yes—
94C7×#121—28no—
95C7×#121—22no—
96C7×#121C2×C414yes—
97C4×C7×Q8—22no—
98C4×C7×Q8C2×C414yes—
99C4×C7×D4—28no—
100C4×C7×D4C2×C414yes—
101C4×C7×D4D414yes—
102C2×C7×C4⋊C4—21no—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4D411yescharacteristic
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C22⋊C4—21no—
107C2×C7×C22⋊C4—21no—
108C2×C7×C22⋊C4—21no—
109C2×C7×C22⋊C4—21no—
110C2×C7×C22⋊C4D411yescharacteristic
111C2×C7×C22⋊C4D411yescharacteristic
112C2×C42×C7—21no—
113C2×C42×C7C2311yescharacteristic
114C2×C22⋊Dic7—21no—
115C2×C22⋊Dic7—21no—
116C2×C22⋊Dic7—21no—
117C2×C22⋊Dic7—21no—
118#6489—22no—
119#6489—22no—
120#6489—41no—
121#6489—41no—
122C2×C4⋊Dic7—21no—
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7C2311yescharacteristic
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4⋊Dic7C2311yescharacteristic
128C2×C4×Dic7—21no—
129C2×C4×Dic7—21no—
130C2×C4×Dic7—21no—
131C2×#1136—22no—
132C2×#1136—22no—
133C2×#1136—41no—
134C22×C7⋊C8—22no—
135C22×C7⋊C8—22no—
136C22×C7⋊C8—41no—
137C22×C7⋊C8C2311yescharacteristic
138C22×C7⋊C8C2311yescharacteristic
139C22×C7⋊C8C2311yescharacteristic
140C22×C7⋊C8C2311yescharacteristic
141#6409—22no—
142#6409—22no—
143#6409—22no—
144#6409—22no—
145#6409—22no—
146#6409—41no—
147#6409—41no—
148#6409D414yescomplemented
149#6406—22no—
150#6406—22no—
151#6406—41no—
152#6406—41no—
153C7⋊#95—21no—
154C7⋊#95—21no—
155C7⋊#95—21no—
156C22⋊(C7⋊C8)—22no—
157C22⋊(C7⋊C8)—22no—
158C4⋊(C7⋊C8)—22no—
159#6377—22no—
160C2×#548D711yescharacteristic
161C2×#435—71no—
162C2×#419—71no—
163C2×#416—71no—
164#2354—71no—
165#1983—71no—
166#1959—71no—
167#1895—71no—
168#1892—71no—
169#1875—71no—
170#1873—71no—
171#1803—71no—
172#1788—71no—
173#1787—71no—
174#1763—71no—
175C24×C7—21no—
176C24×C7C2×D411yescharacteristic
177C24×C7C2×D411yescharacteristic
178C7×#41—28no—
179C7×#41—44no—
180C7×#41—44no—
181C7×#41—44no—
182C2×C7×Q8—24no—
183C2×C7×Q8—21no—
184C2×C7×Q8—21no—
185C2×C7×Q8—21no—
186C2×C7×Q8—21no—
187C2×C7×Q8—28no—
188C2×C7×Q8—21no—
189C2×C7×Q8—21no—
190C2×C7×Q8—21no—
191C2×C7×Q8—21no—
192C2×C7×Q8—42no—
193C2×C7×Q8—42no—
194C2×C7×Q8—44no—
195C2×C7×Q8—44no—
196C2×C7×Q8—44no—
197C2×C7×Q8C22×C412yes—
198C2×C7×Q8C22×C412yes—
199C2×C7×Q8C2×D412yes—
200C2×C7×Q8#4112yes—
201C2×C7×D4—24no—
202C2×C7×D4—24no—
203C2×C7×D4—21no—
204C2×C7×D4—21no—
205C2×C7×D4—21no—
206C2×C7×D4—21no—
207C2×C7×D4—21no—
208C2×C7×D4—41no—
209C2×C7×D4—41no—
210C2×C7×D4—42no—
211C2×C7×D4—42no—
212C2×C7×D4—42no—
213C2×C7×D4—42no—
214C2×C7×D4C22⋊C414yes—
215C2×C7×D4C22×C412yes—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—24no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—24no—
229C22×C4×C7—42no—
230C22×C4×C7—42no—
231C22×C4×C7—42no—
232C22×C4×C7—42no—
233C22×C4×C7C22×C412yes—
234C22×C4×C7C22×C412yes—
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2×D411yescharacteristic
237C22×C4×C7C2×D411yescharacteristic
238C22×C4×C7C2×D411yescharacteristic
239C22×C4×C7C2×D412yes—
240C22×C4×C7C2×D412yes—
241C22×C4×C7C2411yescharacteristic
242C22×Dic7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C7×C4⋊C4—24no—
247C7×C4⋊C4—24no—
248C7×C4⋊C4—21no—
249C7×C4⋊C4C22⋊C414yes—
250C7×C4⋊C4C22×C412yes—
251C7×C22⋊C4—24no—
252C7×C22⋊C4—24no—
253C7×C22⋊C4—24no—
254C7×C22⋊C4—24no—
255C7×C22⋊C4C22⋊C414yes—
256C7×C22⋊C4C22⋊C414yes—
257C42×C7—24no—
258C42×C7C22×C412yes—
259C42×C7C2×D412yes—
260C22⋊Dic7—42no—
261C22⋊Dic7—42no—
262C22⋊Dic7—81no—
263C22⋊Dic7—81no—
264C4⋊Dic7—21no—
265C4⋊Dic7—21no—
266C4⋊Dic7—21no—
267C4⋊Dic7—21no—
268C4⋊Dic7—21no—
269C4⋊Dic7—21no—
270C4⋊Dic7—21no—
271C4⋊Dic7—42no—
272C4⋊Dic7—81no—
273C4⋊Dic7C2×D412yes—
274C4×Dic7—42no—
275C4×Dic7—42no—
276C4×Dic7—42no—
277#1136—44no—
278C2×C7⋊C8—21no—
279C2×C7⋊C8—21no—
280C2×C7⋊C8—21no—
281C2×C7⋊C8—21no—
282C2×C7⋊C8—21no—
283C2×C7⋊C8—21no—
284C2×C7⋊C8—21no—
285C2×C7⋊C8—21no—
286C2×C7⋊C8—21no—
287C2×C7⋊C8—21no—
288C2×C7⋊C8—21no—
289C2×C7⋊C8—44no—
290C2×C7⋊C8C2×D412yes—
291C22×#41C2×D711yescharacteristic
292C23×Q8C2×D711yescharacteristic
293C22×M16—71no—
294C23×C8—71no—
295#548—24no—
296#548Dic718yescomplemented
297C2×#124—21no—
298C2×#124C2×D711yescharacteristic
299C2×C22⋊Q8—21no—
300C2×C22⋊Q8C2×D711yescharacteristic
301C2×#121—21no—
302C2×#121C2×D711yescharacteristic
303C2×C4×Q8C2×D711yescharacteristic
304C2×C4×D4—21no—
305C2×C4×D4C2×D711yescharacteristic
306C2×#117—71no—
307C2×#117—71no—
308#435—144no—
309C2×C4⋊C8—71no—
310#419—144no—
311#416—144no—
312C2×#103—71no—
313C2×#103—71no—
314C2×#103—71no—
315C2×#103—71no—
316C2×#103—71no—
317C2×#103—71no—
318C2×#103—71no—
319C2×#103—71no—
320C2×#102—71no—
321C2×#102—71no—
322C2×#102—71no—
323C2×#102—71no—
324C2×C22⋊C8—71no—
325C2×C22⋊C8—71no—
326C2×#97—71no—
327#390—141no—
328#388—141no—
329#388—141no—
330#384—71no—
331#380—71no—
332#380—71no—
333C4×C4⋊C4—71no—
334C4×C4⋊C4—141no—
335#340—71no—
336#340—71no—
337#340—71no—
338#340—71no—
339C23×C7—21no—
340C23×C7—21no—
341C23×C7—21no—
342C23×C7—21no—
343C23×C7—21no—
344C23×C7—21no—
345C23×C7—21no—
346C23×C7—21no—
347C23×C7—21no—
348C23×C7—21no—
349C23×C7—21no—
350C23×C7—21no—
351C23×C7—22no—
352C23×C7—41no—
353C23×C7—41no—
354C23×C7—41no—
355C23×C7—41no—
356C23×C7—41no—
357C23×C7—41no—
358C23×C7C2×C22⋊C412yes—
359C23×C7C2×C22⋊C412yes—
360C23×C7C22×D411yescharacteristic
361C7×Q8—22no—
362C7×Q8—22no—
363C7×Q8—22no—
364C7×Q8—22no—
365C7×Q8—22no—
366C7×Q8—48no—
367C7×Q8—41no—
368C7×Q8—41no—
369C7×Q8C4×D414yes—
370C7×D4—22no—
371C7×D4—22no—
372C7×D4—44no—
373C7×D4—48no—
374C7×D4—48no—
375C7×D4—41no—
376C7×D4—41no—
377C2×C4×C7—22no—
378C2×C4×C7—21no—
379C2×C4×C7—21no—
380C2×C4×C7—22no—
381C2×C4×C7—21no—
382C2×C4×C7—21no—
383C2×C4×C7—22no—
384C2×C4×C7—21no—
385C2×C4×C7—21no—
386C2×C4×C7—21no—
387C2×C4×C7—21no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—48no—
399C2×C4×C7—48no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7C2×C22⋊C412yes—
405C2×C4×C7C2×C22⋊C412yes—
406C2×C4×C7C2×C22⋊C412yes—
407C2×C4×C7C2×C22⋊C412yes—
408C2×C4×C7C23×C411yescharacteristic
409C2×C4×C7C22×D411yescharacteristic
410C2×C4×C7C22×D411yescharacteristic
411C2×C4×C7C2×#4111yescharacteristic
412C2×C4×C7H(5,𝔽2)11yescharacteristic
413C2×C4×C7H(5,𝔽2)11yescharacteristic
414C2×Dic7—22no—
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—
426C7⋊C8—22no—
427C7⋊C8—41no—
428C7⋊C8—41no—
429C7⋊C8—41no—
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—41no—
434C2×#41—41no—
435C2×#41C2×Dic714yes—
436C22×Q8—21no—
437C22×Q8—22no—
438C22×Q8—22no—
439C22×Q8—22no—
440C22×Q8—41no—
441C22×Q8—41no—
442C22×Q8C2×Dic714yes—
443C22×Q8C22×D711yescharacteristic
444C22×Q8C22×D711yescharacteristic
445C22×D4—21no—
446C22×D4—21no—
447C22×D4C22⋊D711yescharacteristic
448C22×D4C22×D711yescharacteristic
449C23×C4—21no—
450C23×C4—21no—
451C23×C4C22×D711yescharacteristic
452C23×C4C22×D711yescharacteristic
453C2×M16—142no—
454C2×M16—142no—
455C2×M16—281no—
456C22×C8—71no—
457C22×C8—71no—
458C22×C8—71no—
459C22×C8—71no—
460C22×C8—142no—
461C22×C8—142no—
462C22×C8—281no—
463#124—28no—
464#124—22no—
465#124C2×Dic714yes—
466C22⋊Q8—22no—
467C22⋊Q8—28no—
468C22⋊Q8C2×Dic714yes—
469#121—28no—
470#121—22no—
471#121C2×Dic714yes—
472C4×Q8—22no—
473C4×Q8C2×Dic714yes—
474C4×D4—28no—
475C4×D4C2×Dic714yes—
476C4×D4C22⋊D714yes—
477#117—142no—
478#117—142no—
479#117—281no—
480#117—281no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—71no—
484C2×C4⋊C4—71no—
485C2×C4⋊C4—71no—
486C2×C4⋊C4—71no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4—141no—
489C2×C4⋊C4C22⋊D711yescharacteristic
490C2×C4⋊C4C22×D711yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—141no—
496C2×C22⋊C4—141no—
497C2×C22⋊C4—141no—
498C2×C22⋊C4—141no—
499C2×C22⋊C4C22⋊D711yescharacteristic
500C2×C22⋊C4C22⋊D711yescharacteristic
501C2×C42—21no—
502C2×C42—141no—
503C2×C42—141no—
504C2×C42—141no—
505C2×C42C22×D711yescharacteristic
506C4⋊C8—142no—
507#103—74no—
508#103—142no—
509#103—142no—
510#103—142no—
511#103—142no—
512#103—142no—
513#103—281no—
514#103—281no—
515#102—142no—
516#102—142no—
517#102—281no—
518#102—281no—
519C22⋊C8—142no—
520C22⋊C8—142no—
521#97—142no—
522#95—141no—
523#95—141no—
524#95—141no—
525C22×C7—22no—
526C22×C7—22no—
527C22×C7—22no—
528C22×C7—22no—
529C22×C7—22no—
530C22×C7—22no—
531C22×C7—41no—
532C22×C7—41no—
533C22×C7—41no—
534C22×C7—41no—
535C22×C7—41no—
536C22×C7—41no—
537C22×C7—41no—
538C22×C7—41no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—42no—
542C22×C7—81no—
543C22×C7—81no—
544C22×C7—81no—
545C22×C7—81no—
546C22×C7C22×C22⋊C411yescharacteristic
547C22×C7D4211yescharacteristic
548C22×C7#54611yescharacteristic
549C22×C7#57511yescharacteristic
550C22×C7#57511yescharacteristic
551C22×C7#57711yescharacteristic
552C22×C7#57811yescharacteristic
553C4×C7—22no—
554C4×C7—22no—
555C4×C7—24no—
556C4×C7—22no—
557C4×C7—22no—
558C4×C7—42no—
559C4×C7—42no—
560C4×C7C2×C4×D411yescharacteristic
561C4×C7#51811yescharacteristic
562C4×C7D4211yescharacteristic
563C4×C7#54611yescharacteristic
564Dic7—42no—
565Dic7—81no—
566Dic7—81no—
567Dic7—81no—
568C24—21no—
569C24C2×C22⋊D711yescharacteristic
570C24C2×C22⋊D711yescharacteristic
571#41—28no—
572#41—44no—
573#41—44no—
574#41—44no—
575C2×Q8—24no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—28no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—42no—
586C2×Q8—42no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—44no—
590C2×Q8D4×D712yes—
591C2×Q8#115912yes—
592C2×Q8C22×Dic712yes—
593C2×Q8C22×Dic712yes—
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—41no—
602C2×D4—41no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4C22⋊Dic714yes—
608C2×D4C22×Dic712yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—24no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—141no—
627C22×C4—141no—
628C22×C4—141no—
629C22×C4—141no—
630C22×C4C22×Dic712yes—
631C22×C4C22×Dic712yes—
632C22×C4C2×C22⋊D711yescharacteristic
633C22×C4C2×C22⋊D711yescharacteristic
634C22×C4C2×C22⋊D711yescharacteristic
635C22×C4C2×C22⋊D711yescharacteristic
636C22×C4C2×C22⋊D712yes—
637C22×C4C2×C22⋊D712yes—
638C22×C4C23×D711yescharacteristic
639M16—284no—
640C2×C8—72no—
641C2×C8—141no—
642C2×C8—141no—
643C2×C8—141no—
644C2×C8—141no—
645C2×C8—141no—
646C2×C8—141no—
647C2×C8—141no—
648C2×C8—141no—
649C2×C8—141no—
650C2×C8—141no—
651C2×C8—141no—
652C2×C8—284no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—21no—
656C4⋊C4—72no—
657C4⋊C4—141no—
658C4⋊C4—141no—
659C4⋊C4—141no—
660C4⋊C4—141no—
661C4⋊C4—141no—
662C4⋊C4—141no—
663C4⋊C4—141no—
664C4⋊C4—282no—
665C4⋊C4—561no—
666C4⋊C4C22⋊Dic714yes—
667C4⋊C4C22×Dic712yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—282no—
673C22⋊C4—282no—
674C22⋊C4—561no—
675C22⋊C4—561no—
676C22⋊C4C22⋊Dic714yes—
677C22⋊C4C22⋊Dic714yes—
678C42—24no—
679C42—282no—
680C42—282no—
681C42—282no—
682C42C22×Dic712yes—
683C42C2×C22⋊D712yes—
684C2×C7—42no—
685C2×C7—42no—
686C2×C7—82no—
687C2×C7D4×C22⋊C411yescharacteristic
688C2×C7#289611yescharacteristic
689C2×C7#289811yescharacteristic
690C2×C7#326911yescharacteristic
691C2×C7#327111yescharacteristic
692C2×C7#331311yescharacteristic
693C2×C7#332111yescharacteristic
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23C2×C22⋊Dic712yes—
714C23C2×C22⋊Dic712yes—
715C23C22×C22⋊D711yescharacteristic
716Q8—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—48no—
722Q8—41no—
723Q8—41no—
724Q8D4×Dic714yes—
725D4—22no—
726D4—22no—
727D4—44no—
728D4—48no—
729D4—48no—
730D4—41no—
731D4—41no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—48no—
754C2×C4—48no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—142no—
760C2×C4—281no—
761C2×C4—281no—
762C2×C4—281no—
763C2×C4—281no—
764C2×C4—281no—
765C2×C4—281no—
766C2×C4—281no—
767C2×C4—281no—
768C2×C4—281no—
769C2×C4—281no—
770C2×C4—281no—
771C2×C4C2×C22⋊Dic712yes—
772C2×C4C2×C22⋊Dic712yes—
773C2×C4C2×C22⋊Dic712yes—
774C2×C4C2×C22⋊Dic712yes—
775C2×C4C2×D4×D711yescharacteristic
776C2×C4C2×#115911yescharacteristic
777C2×C4#654811yescharacteristic
778C2×C4#654811yescharacteristic
779C2×C4C23×Dic711yescharacteristic
780C2×C4C22×C22⋊D711yescharacteristic
781C8—142no—
782C8—281no—
783C8—281no—
784C8—281no—
785C7#2242611yescharacteristic, complemented, Sylow
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22D4×C22⋊D711yescharacteristic
808C22#9049711yescharacteristic
809C22#9051311yescharacteristic
810C22#9051311yescharacteristic
811C22#9052811yescharacteristic
812C22#9052911yescharacteristic
813C22C22×C22⋊Dic711yescharacteristic
814C4—22no—
815C4—22no—
816C4—24no—
817C4—22no—
818C4—22no—
819C4—42no—
820C4—42no—
821C4—282no—
822C4—561no—
823C4—561no—
824C4—561no—
825C4C2×D4×Dic711yescharacteristic
826C4#9048911yescharacteristic
827C4D4×C22⋊D711yescharacteristic
828C4#9049711yescharacteristic
829C2—42no—
830C2—42no—
831C2—82no—
832C2#1174098211yescharacteristic
833C2#1174098411yescharacteristic
834C2#1174098811yescharacteristic
835C2#1174099211yescharacteristic
836C2D4×C22⋊Dic711yescharacteristic
837C2#1174151711yescharacteristic
838C2#1174155611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
Fitting, prime radicalC2×C7×#548C2
socleC23×C7C22×D4
cosocleC22×C4×C7C24
hypercenterC2×#548D7
hypocenterC7#22426
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
2. C2×#90005C2semidirect
3. C2×#89997C2semidirect
4. #11739782C2semidirect
5. C2×#89783C2semidirect
6. #11729889C2semidirect
7. #11729886C2semidirect
8. #11729480C2semidirect
9. #11729475C2semidirect
10. #11729450C2semidirect
11. #11729447C2semidirect
12. #11729436C2semidirect
13. #11729432C2semidirect
14. #11729385C2semidirect
15. #11729380C2semidirect
19. C7×#548C4semidirect
148. #6409D4semidirect
296. #548Dic7semidirect
785. C7#22426semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5482
C2×#900052
C2×#899972
#117397822
C2×#897832
#117298892
#117298862
#117294802
#117294752
#117294502
#117294472
#117294362
#117294322
#117293852
#117293802
#224267