Finite Group Databasebeta

← #13370174

Subgroups — #13370174

Order 1792.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#554C211yesmaximal, characteristic
2#11739780C211yesmaximal, characteristic
3C2×#89783C211yesmaximal, characteristic
4#11729542C211yesmaximal, characteristic, complemented
5#11729534C211yesmaximal, characteristic, complemented
6#11729451C211yesmaximal, characteristic, complemented
7#11729450C211yesmaximal, characteristic, complemented
8#11729447C211yesmaximal, characteristic, complemented
9#11729446C211yesmaximal, characteristic, complemented
10#11729385C211yesmaximal, characteristic, complemented
11#11729381C211yesmaximal, characteristic, complemented
12#11729312C211yesmaximal, characteristic, complemented
13C2×#89324C211yesmaximal, characteristic, complemented
14#11729308C211yesmaximal, characteristic, complemented
15#11729307C211yesmaximal, characteristic, complemented
16C7×#554—24no—
17C7×#554C418yescomplemented
18C2×C7×C4⋊Q8C2211yescharacteristic
19C2×C7×#125—21no—
20C2×C7×C22⋊Q8—21no—
21C2×C7×C22⋊Q8—21no—
22C2×C7×C22⋊Q8C2211yescharacteristic
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C4×C7×Q8C2211yescharacteristic
25C2×C4×C7×D4—21no—
26C2×C4×C7×D4C2211yescharacteristic
27C22×C7×C4⋊C4C2211yescharacteristic
28C22×C7×C4⋊C4C2211yescharacteristic
29C2×#6489C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×#1136C2211yescharacteristic
32C23×C7⋊C8C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37#89992—21no—
38#89984C2211yescharacteristic
39#89984C2211yescharacteristic
40C2×C22⋊(C7⋊C8)C2211yescharacteristic
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42#89783—24no—
43#89753—21no—
44#89723—21no—
45C22⋊C4×Dic7—21no—
46#89708C2211yescharacteristic
47C4×C4⋊Dic7C2211yescharacteristic
48C2×C4⋊(C7⋊C8)C2211yescharacteristic
49C2×#6377C2211yescharacteristic
50#89324C2211yescharacteristic
51#89324C2211yescharacteristic
52#89324C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#22497—71nomaximal, Sylow
63C22×C7×Q8—21no—
64C22×C7×Q8C2311yescharacteristic
65C22×C7×D4D411yescharacteristic
66C23×C4×C7—21no—
67C23×C4×C7—21no—
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×Dic7—21no—
71C7×C4⋊Q8—22no—
72C7×C4⋊Q8C2×C414yescomplemented
73C7×#125—28no—
74C7×C22⋊Q8—22no—
75C7×C22⋊Q8—22no—
76C7×C22⋊Q8—28no—
77C7×C22⋊Q8—28no—
78C7×C22⋊Q8C2×C414yes—
79C7×C22⋊Q8C2×C414yescomplemented
80C4×C7×Q8—22no—
81C4×C7×Q8C2×C414yescomplemented
82C4×C7×D4—28no—
83C4×C7×D4C2×C414yes—
84C4×C7×D4D414yes—
85C2×C7×C4⋊C4—21no—
86C2×C7×C4⋊C4—21no—
87C2×C7×C4⋊C4—22no—
88C2×C7×C4⋊C4—22no—
89C2×C7×C4⋊C4—21no—
90C2×C7×C4⋊C4—21no—
91C2×C7×C4⋊C4—21no—
92C2×C7×C4⋊C4—21no—
93C2×C7×C4⋊C4C2×C414yes—
94C2×C7×C4⋊C4C2×C414yescomplemented
95C2×C7×C4⋊C4D411yescharacteristic
96C2×C7×C4⋊C4C2311yescharacteristic
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C22⋊C4—21no—
100C2×C7×C22⋊C4—21no—
101C2×C7×C22⋊C4D411yescharacteristic
102C2×C7×C22⋊C4D411yescharacteristic
103C2×C42×C7—21no—
104C2×C42×C7C2311yescharacteristic
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108#6489—22no—
109#6489—41no—
110C2×C4⋊Dic7—22no—
111C2×C4⋊Dic7—21no—
112C2×C4⋊Dic7—41no—
113C2×C4⋊Dic7C2311yescharacteristic
114C2×C4⋊Dic7C2311yescharacteristic
115C2×C4⋊Dic7C2311yescharacteristic
116C2×C4⋊Dic7C2311yescharacteristic
117C2×C4×Dic7—21no—
118C2×C4×Dic7—21no—
119C2×#1136—22no—
120C2×#1136—22no—
121C2×#1136—41no—
122C22×C7⋊C8—22no—
123C22×C7⋊C8—22no—
124C22×C7⋊C8—41no—
125C22×C7⋊C8C2311yescharacteristic
126C22×C7⋊C8C2311yescharacteristic
127C22×C7⋊C8C2311yescharacteristic
128C22×C7⋊C8C2311yescharacteristic
129#6409—22no—
130#6409—22no—
131#6409—41no—
132#6409—41no—
133C7⋊#95—21no—
134C7⋊#95—21no—
135C7⋊#95—21no—
136C7⋊#95—21no—
137C7⋊#95—21no—
138C22⋊(C7⋊C8)—22no—
139C22⋊(C7⋊C8)—22no—
140C4⋊(C7⋊C8)—22no—
141#6377—22no—
142C2×#554D711yescharacteristic
143C2×#435—71no—
144#2352—71no—
145#1993—71no—
146#1988—71no—
147#1894—71no—
148#1892—71no—
149#1873—71no—
150#1872—71no—
151#1824—71no—
152#1823—71no—
153#1805—71no—
154#1763—71no—
155#1736—71no—
156C2×#340—71no—
157C24×C7C2×D411yescharacteristic
158C24×C7C2×D411yescharacteristic
159C2×C7×Q8—24no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8—21no—
165C2×C7×Q8—81no—
166C2×C7×Q8—81no—
167C2×C7×Q8C22×C412yes—
168C2×C7×D4—22no—
169C2×C7×D4—22no—
170C2×C7×D4C22⋊C414yes—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—24no—
184C22×C4×C7—24no—
185C22×C4×C7—81no—
186C22×C4×C7—81no—
187C22×C4×C7—81no—
188C22×C4×C7—81no—
189C22×C4×C7C22×C412yes—
190C22×C4×C7C22×C412yes—
191C22×C4×C7C2×D411yescharacteristic
192C22×C4×C7C2×D411yescharacteristic
193C22×C4×C7C2×D411yescharacteristic
194C22×C4×C7C2×D411yescharacteristic
195C22×C4×C7C2×D412yes—
196C22×C4×C7C2×D412yes—
197C22×C4×C7C2411yescharacteristic
198C22×Dic7—21no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7—42no—
203C22×Dic7—42no—
204C22×Dic7—81no—
205C7×C4⋊C4—24no—
206C7×C4⋊C4—24no—
207C7×C4⋊C4—24no—
208C7×C4⋊C4—24no—
209C7×C4⋊C4—24no—
210C7×C4⋊C4—24no—
211C7×C4⋊C4—21no—
212C7×C4⋊C4—21no—
213C7×C4⋊C4—21no—
214C7×C4⋊C4C22⋊C414yes—
215C7×C4⋊C4C22×C412yes—
216C7×C4⋊C4C22×C412yes—
217C7×C4⋊C4C22×C412yes—
218C7×C22⋊C4—24no—
219C7×C22⋊C4—24no—
220C7×C22⋊C4C22⋊C414yes—
221C7×C22⋊C4C22⋊C414yes—
222C42×C7—24no—
223C42×C7C22×C412yes—
224C42×C7C2×D412yes—
225C22⋊Dic7—42no—
226C22⋊Dic7—42no—
227C22⋊Dic7—81no—
228C4⋊Dic7—21no—
229C4⋊Dic7—21no—
230C4⋊Dic7—21no—
231C4⋊Dic7—21no—
232C4⋊Dic7—21no—
233C4⋊Dic7—21no—
234C4⋊Dic7—21no—
235C4⋊Dic7—42no—
236C4⋊Dic7#4112yes—
237C4×Dic7—42no—
238C4×Dic7—81no—
239#1136—44no—
240C2×C7⋊C8—21no—
241C2×C7⋊C8—21no—
242C2×C7⋊C8—21no—
243C2×C7⋊C8—21no—
244C2×C7⋊C8—21no—
245C2×C7⋊C8—21no—
246C2×C7⋊C8—21no—
247C2×C7⋊C8—21no—
248C2×C7⋊C8—21no—
249C2×C7⋊C8—21no—
250C2×C7⋊C8—21no—
251C2×C7⋊C8—44no—
252C2×C7⋊C8#4112yes—
253C22×M16—71no—
254C23×C8—71no—
255#554—24no—
256#554Dic718yescomplemented
257C2×C4⋊Q8C2×D711yescharacteristic
258C2×#125—21no—
259C2×C22⋊Q8—21no—
260C2×C22⋊Q8—21no—
261C2×C22⋊Q8C2×D711yescharacteristic
262C2×C22⋊Q8C2×D711yescharacteristic
263C2×C4×Q8C2×D711yescharacteristic
264C2×C4×D4—21no—
265C2×C4×D4C2×D711yescharacteristic
266C2×#117—71no—
267C22×C4⋊C4—71no—
268C22×C4⋊C4C2×D711yescharacteristic
269C22×C4⋊C4C2×D711yescharacteristic
270#435—144no—
271C2×C4⋊C8—71no—
272C2×#103—71no—
273C2×#103—71no—
274C2×#103—71no—
275C2×#103—71no—
276C2×C22⋊C8—71no—
277C2×C22⋊C8—71no—
278C2×#97—71no—
279#388—141no—
280#387—141no—
281#386—141no—
282#382—71no—
283#380—71no—
284#380—71no—
285C4×C4⋊C4—71no—
286C4×C22⋊C4—141no—
287#340—71no—
288#340—71no—
289#340—71no—
290#340—71no—
291#340—71no—
292#340—71no—
293#340—71no—
294#340—71no—
295#340—71no—
296#340—71no—
297#340—71no—
298#340—71no—
299C23×C7—21no—
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—21no—
303C23×C7—21no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—21no—
309C23×C7C2×C22⋊C412yes—
310C23×C7C2×C22⋊C412yes—
311C23×C7#13712yes—
312C23×C7#13712yes—
313C23×C7C22×D411yescharacteristic
314C7×Q8—22no—
315C7×Q8—22no—
316C7×Q8—41no—
317C7×Q8—41no—
318C7×Q8—84no—
319C7×D4—28no—
320C2×C4×C7—21no—
321C2×C4×C7—21no—
322C2×C4×C7—21no—
323C2×C4×C7—21no—
324C2×C4×C7—21no—
325C2×C4×C7—21no—
326C2×C4×C7—21no—
327C2×C4×C7—21no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—84no—
349C2×C4×C7—84no—
350C2×C4×C7C2×C22⋊C412yes—
351C2×C4×C7C2×C22⋊C412yes—
352C2×C4×C7C2×C22⋊C412yes—
353C2×C4×C7C2×C22⋊C412yes—
354C2×C4×C7C23×C411yescharacteristic
355C2×C4×C7C22×D411yescharacteristic
356C2×C4×C7C2×#4111yescharacteristic
357C2×C4×C7C2×#4111yescharacteristic
358C2×C4×C7H(5,𝔽2)11yescharacteristic
359C2×C4×C72−1+411yescharacteristic
360C2×Dic7—22no—
361C2×Dic7—41no—
362C2×Dic7—41no—
363C2×Dic7—41no—
364C2×Dic7—41no—
365C2×Dic7—41no—
366C2×Dic7—41no—
367C2×Dic7—41no—
368C2×Dic7—41no—
369C2×Dic7—41no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372C2×Dic7—84no—
373C7⋊C8—22no—
374C7⋊C8—41no—
375C7⋊C8—41no—
376C7⋊C8—41no—
377C22×Q8—21no—
378C22×Q8C22×D711yescharacteristic
379C22×D4C22⋊D711yescharacteristic
380C23×C4—21no—
381C23×C4—21no—
382C23×C4—141no—
383C23×C4C22×D711yescharacteristic
384C23×C4C22×D711yescharacteristic
385C2×M16—142no—
386C2×M16—142no—
387C2×M16—281no—
388C22×C8—71no—
389C22×C8—71no—
390C22×C8—71no—
391C22×C8—71no—
392C22×C8—142no—
393C22×C8—142no—
394C22×C8—281no—
395C4⋊Q8—22no—
396C4⋊Q8C2×Dic714yescomplemented
397#125—28no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—28no—
401C22⋊Q8—28no—
402C22⋊Q8C2×Dic714yes—
403C22⋊Q8C2×Dic714yescomplemented
404C4×Q8—22no—
405C4×Q8C2×Dic714yescomplemented
406C4×D4—28no—
407C4×D4C2×Dic714yes—
408C4×D4C22⋊D714yes—
409#117—142no—
410#117—281no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—71no—
420C2×C4⋊C4—71no—
421C2×C4⋊C4—71no—
422C2×C4⋊C4—71no—
423C2×C4⋊C4—142no—
424C2×C4⋊C4—141no—
425C2×C4⋊C4—281no—
426C2×C4⋊C4C2×Dic714yes—
427C2×C4⋊C4C2×Dic714yescomplemented
428C2×C4⋊C4C22⋊D711yescharacteristic
429C2×C4⋊C4C22×D711yescharacteristic
430C2×C4⋊C4C22×D711yescharacteristic
431C2×C4⋊C4C22×D711yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—141no—
435C2×C22⋊C4—141no—
436C2×C22⋊C4—141no—
437C2×C22⋊C4C22⋊D711yescharacteristic
438C2×C22⋊C4C22⋊D711yescharacteristic
439C2×C42—21no—
440C2×C42—141no—
441C2×C42—141no—
442C2×C42C22×D711yescharacteristic
443C4⋊C8—142no—
444#103—142no—
445#103—142no—
446#103—281no—
447#103—281no—
448C22⋊C8—142no—
449C22⋊C8—142no—
450#97—142no—
451#95—141no—
452#95—141no—
453#95—141no—
454#95—141no—
455#95—141no—
456C22×C7—22no—
457C22×C7—22no—
458C22×C7—22no—
459C22×C7—22no—
460C22×C7—22no—
461C22×C7—22no—
462C22×C7—22no—
463C22×C7—22no—
464C22×C7—22no—
465C22×C7—41no—
466C22×C7—41no—
467C22×C7—41no—
468C22×C7—41no—
469C22×C7#41914yes—
470C22×C7C22×C22⋊C411yescharacteristic
471C22×C7#54611yescharacteristic
472C22×C7#54711yescharacteristic
473C22×C7C2×#13711yescharacteristic
474C22×C7C2×#13711yescharacteristic
475C22×C7#57611yescharacteristic
476C22×C7#57711yescharacteristic
477C4×C7—22no—
478C4×C7—22no—
479C4×C7—22no—
480C4×C7—22no—
481C4×C7—42no—
482C4×C7—42no—
483C4×C7—42no—
484C4×C7—42no—
485C4×C7C4×#4111yescharacteristic
486C4×C7#52011yescharacteristic
487C4×C7#54611yescharacteristic
488C4×C7#54711yescharacteristic
489Dic7—42no—
490Dic7—81no—
491Dic7—81no—
492Dic7—81no—
493C24C2×C22⋊D711yescharacteristic
494C24C2×C22⋊D711yescharacteristic
495C2×Q8—24no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—81no—
502C2×Q8—81no—
503C2×Q8C22×Dic712yes—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4C22⋊Dic714yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—81no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4—141no—
526C22×C4—141no—
527C22×C4—141no—
528C22×C4—141no—
529C22×C4—282no—
530C22×C4—282no—
531C22×C4—561no—
532C22×C4C22×Dic712yes—
533C22×C4C22×Dic712yes—
534C22×C4C2×C22⋊D711yescharacteristic
535C22×C4C2×C22⋊D711yescharacteristic
536C22×C4C2×C22⋊D711yescharacteristic
537C22×C4C2×C22⋊D711yescharacteristic
538C22×C4C2×C22⋊D712yes—
539C22×C4C2×C22⋊D712yes—
540C22×C4C23×D711yescharacteristic
541M16—284no—
542C2×C8—72no—
543C2×C8—141no—
544C2×C8—141no—
545C2×C8—141no—
546C2×C8—141no—
547C2×C8—141no—
548C2×C8—141no—
549C2×C8—141no—
550C2×C8—141no—
551C2×C8—141no—
552C2×C8—141no—
553C2×C8—141no—
554C2×C8—284no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—72no—
565C4⋊C4—141no—
566C4⋊C4—141no—
567C4⋊C4—141no—
568C4⋊C4—141no—
569C4⋊C4—141no—
570C4⋊C4—141no—
571C4⋊C4—141no—
572C4⋊C4—282no—
573C4⋊C4C22⋊Dic714yes—
574C4⋊C4C22×Dic712yes—
575C4⋊C4C22×Dic712yes—
576C4⋊C4C22×Dic712yes—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—282no—
580C22⋊C4—282no—
581C22⋊C4—561no—
582C22⋊C4C22⋊Dic714yes—
583C22⋊C4C22⋊Dic714yes—
584C42—24no—
585C42—282no—
586C42—561no—
587C42C22×Dic712yes—
588C42C2×C22⋊D712yes—
589C2×C7—24no—
590C2×C7—42no—
591C2×C7#233911yescharacteristic
592C2×C7C2×#41911yescharacteristic
593C2×C7#289711yescharacteristic
594C2×C7#331411yescharacteristic
595C2×C7#331611yescharacteristic
596C2×C7#334411yescharacteristic
597C2×C7#334611yescharacteristic
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23#650512yes—
609C23#650512yes—
610C23C2×C22⋊Dic712yes—
611C23C2×C22⋊Dic712yes—
612C23C22×C22⋊D711yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—41no—
616Q8—41no—
617Q8—84no—
618D4—28no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—84no—
648C2×C4—84no—
649C2×C4—142no—
650C2×C4—281no—
651C2×C4—281no—
652C2×C4—281no—
653C2×C4—281no—
654C2×C4—281no—
655C2×C4—281no—
656C2×C4—281no—
657C2×C4—281no—
658C2×C4—281no—
659C2×C4—281no—
660C2×C4—281no—
661C2×C4—564no—
662C2×C4C2×C22⋊Dic712yes—
663C2×C4C2×C22⋊Dic712yes—
664C2×C4C2×C22⋊Dic712yes—
665C2×C4C2×C22⋊Dic712yes—
666C2×C4D7×#4111yescharacteristic
667C2×C4D7×#4111yescharacteristic
668C2×C4#655311yescharacteristic
669C2×C4#655411yescharacteristic
670C2×C4C23×Dic711yescharacteristic
671C2×C4C22×C22⋊D711yescharacteristic
672C8—142no—
673C8—281no—
674C8—281no—
675C8—281no—
676C7#2249711yescharacteristic, complemented, Sylow
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#8999714yes—
691C22C2×#650511yescharacteristic
692C22C2×#650511yescharacteristic
693C22#9051511yescharacteristic
694C22#9052011yescharacteristic
695C22#9052611yescharacteristic
696C22#9052711yescharacteristic
697C22C22×C22⋊Dic711yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—282no—
707C4—561no—
708C4—561no—
709C4—561no—
710C4#9051511yescharacteristic
711C4#41×Dic711yescharacteristic
712C4#9051811yescharacteristic
713C4#9052011yescharacteristic
714C2—24no—
715C2—42no—
716C2#1174106911yescharacteristic
717C2#1174107011yescharacteristic
718C2#1174108011yescharacteristic
719C2#1174108611yescharacteristic
720C2C2×#8999711yescharacteristic
721C2#1174153311yescharacteristic
722C2#1174154411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#554C2
socleC23×C7C22×D4
prime radicalC22×C7×D4D4
cosocleC22×C4×C7C24
hypercenterC2×#554D7
hypocenterC7#22497
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
4. #11729542C2semidirect
5. #11729534C2semidirect
6. #11729451C2semidirect
7. #11729450C2semidirect
8. #11729447C2semidirect
9. #11729446C2semidirect
10. #11729385C2semidirect
11. #11729381C2semidirect
12. #11729312C2semidirect
13. C2×#89324C2semidirect
14. #11729308C2semidirect
15. #11729307C2semidirect
17. C7×#554C4semidirect
72. C7×C4⋊Q8C2×C4semidirect
79. C7×C22⋊Q8C2×C4semidirect
81. C4×C7×Q8C2×C4semidirect
94. C2×C7×C4⋊C4C2×C4semidirect
256. #554Dic7semidirect
396. C4⋊Q8C2×Dic7semidirect
403. C22⋊Q8C2×Dic7semidirect
405. C4×Q8C2×Dic7semidirect
427. C2×C4⋊C4C2×Dic7semidirect
676. C7#22497semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5542
#117397802
C2×#897832
#117295422
#117295342
#117294512
#117294502
#117294472
#117294462
#117293852
#117293812
#117293122
C2×#893242
#117293082
#117293072
#224977