Finite Group Databasebeta

← #13370176

Subgroups — #13370176

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×#90234C211yesmaximal, characteristic
2C2×C7×#435C211yesmaximal, characteristic
3#11739780C211yesmaximal, characteristic
4#11729743C211yesmaximal, characteristic, complemented
5#11729739C211yesmaximal, characteristic, complemented
6#11729726C211yesmaximal, characteristic, complemented
7C2×#89346C211yesmaximal, characteristic, complemented
8#11728240C211yesmaximal, characteristic, complemented
9#11728214C211yesmaximal, characteristic, complemented
10#11727685C211yesmaximal, characteristic, complemented
11#11727684C211yesmaximal, characteristic, complemented
12#11727679C211yesmaximal, characteristic, complemented
13#11727678C211yesmaximal, characteristic, complemented
14#11727582C211yesmaximal, characteristic, complemented
15#11727567C211yesmaximal, characteristic, complemented
16C22×C7×M16C2211yescharacteristic
17C23×C7×C8C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C2×D4×Dic7—21no—
20C2×#6489C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23C22×C4⋊Dic7C2211yescharacteristic
24C2×#6487C2211yescharacteristic
25C2×#6487C2211yescharacteristic
26#90234—24no—
27#90234C418yescomplemented
28C2×#6453—21no—
29C2×#6441—21no—
30C2×#6441—21no—
31C2×#6432C2211yescharacteristic
32C2×C4×Dic14C2211yescharacteristic
33C7×#435—24no—
34C2×C7×C4⋊C8C2211yescharacteristic
35C2×C7×C22⋊C8C2211yescharacteristic
36C2×C7×C22⋊C8C2211yescharacteristic
37C2×C7×#97C2211yescharacteristic
38#89992—21no—
39#89984C2211yescharacteristic
40#89984C2211yescharacteristic
41C2×#6390C2211yescharacteristic
42C2×#6390C2211yescharacteristic
43C2×#6390C2211yescharacteristic
44C2×#6390C2211yescharacteristic
45#89753—21no—
46#89723—21no—
47C22⋊C4×Dic7—21no—
48#89708C2211yescharacteristic
49C4×C4⋊Dic7C2211yescharacteristic
50#89346C2211yescharacteristic
51#89346C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89346C2211yescharacteristic
57#89346C2211yescharacteristic
58#89346C2211yescharacteristic
59#89346C2211yescharacteristic
60#89346C2211yescharacteristic
61#89346C2211yescharacteristic
62#22497—71nomaximal, Sylow
63C22×C7×D4D411yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×Dic7—21no—
67C23×Dic7—21no—
68C23×Dic7—21no—
69C22×Dic14—21no—
70C22×Dic14C2311yescharacteristic
71C2×C7×M16—22no—
72C2×C7×M16—22no—
73C2×C7×M16—41no—
74C22×C7×C8—22no—
75C22×C7×C8—22no—
76C22×C7×C8—41no—
77C22×C7×C8C2311yescharacteristic
78C22×C7×C8C2311yescharacteristic
79C22×C7×C8C2311yescharacteristic
80C22×C7×C8C2311yescharacteristic
81C4×C7×D4C2×C414yes—
82C4×C7×D4D414yes—
83C2×C7×C4⋊C4D411yescharacteristic
84C2×C7×C22⋊C4D411yescharacteristic
85C2×C7×C22⋊C4D411yescharacteristic
86C2×C42×C7C2311yescharacteristic
87C2×C22⋊Dic7—21no—
88C2×C22⋊Dic7—21no—
89C2×C22⋊Dic7—21no—
90C2×C22⋊Dic7—21no—
91C2×C22⋊Dic7—21no—
92D4×Dic7—28no—
93#6489—22no—
94#6489—41no—
95C2×C4⋊Dic7—21no—
96C2×C4⋊Dic7—21no—
97C2×C4⋊Dic7—21no—
98C2×C4⋊Dic7—22no—
99C2×C4⋊Dic7—22no—
100C2×C4⋊Dic7—22no—
101C2×C4⋊Dic7—21no—
102C2×C4⋊Dic7—41no—
103C2×C4⋊Dic7C2×C414yes—
104C2×C4⋊Dic7C2×C414yescomplemented
105C2×C4⋊Dic7C2311yescharacteristic
106C2×C4⋊Dic7C2311yescharacteristic
107C2×C4⋊Dic7C2311yescharacteristic
108C2×C4⋊Dic7C2311yescharacteristic
109C2×C4⋊Dic7C2311yescharacteristic
110C2×C4⋊Dic7C2311yescharacteristic
111C2×C4⋊Dic7C2311yescharacteristic
112#6487—22no—
113#6487—22no—
114#6487C2×C414yes—
115#6487C2×C414yescomplemented
116C2×Dic7⋊C4—21no—
117C2×Dic7⋊C4—21no—
118C2×Dic7⋊C4—21no—
119C2×C4×Dic7—21no—
120C2×C4×Dic7—21no—
121C2×C4×Dic7—21no—
122#6453—28no—
123#6441—28no—
124#6441—28no—
125#6432—22no—
126#6432C2×C414yescomplemented
127C4×Dic14—22no—
128C4×Dic14C2×C414yescomplemented
129C7×C4⋊C8—22no—
130C7×C22⋊C8—22no—
131C7×C22⋊C8—22no—
132C7×#97—22no—
133C7⋊#95—21no—
134C7⋊#95—21no—
135C7⋊#95—21no—
136C7⋊#95—21no—
137C7⋊#95—21no—
138#6390—22no—
139#6390—22no—
140#6390—41no—
141#6390—41no—
142C2×#554—71no—
143C2×#435D711yescharacteristic
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×D4—22no—
160C2×C7×D4—22no—
161C2×C7×D4C22⋊C414yes—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7C22×C412yes—
171C22×C4×C7C22×C412yes—
172C22×C4×C7C2×D411yescharacteristic
173C22×C4×C7C2×D411yescharacteristic
174C22×C4×C7C2×D411yescharacteristic
175C22×C4×C7C2×D411yescharacteristic
176C22×C4×C7C2×D412yes—
177C22×C4×C7C2×D412yes—
178C22×C4×C7C2411yescharacteristic
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C22×Dic7—21no—
184C22×Dic7—24no—
185C22×Dic7—24no—
186C22×Dic7—21no—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—42no—
190C22×Dic7—42no—
191C22×Dic7—81no—
192C22×Dic7—81no—
193C22×Dic7—81no—
194C22×Dic7—81no—
195C22×Dic7—81no—
196C2×Dic14—21no—
197C2×Dic14—21no—
198C2×Dic14—21no—
199C2×Dic14—21no—
200C2×Dic14—21no—
201C2×Dic14—24no—
202C2×Dic14—81no—
203C2×Dic14—81no—
204C2×Dic14C22×C412yes—
205C7×M16—44no—
206C2×C7×C8—21no—
207C2×C7×C8—21no—
208C2×C7×C8—21no—
209C2×C7×C8—21no—
210C2×C7×C8—21no—
211C2×C7×C8—21no—
212C2×C7×C8—21no—
213C2×C7×C8—21no—
214C2×C7×C8—21no—
215C2×C7×C8—21no—
216C2×C7×C8—21no—
217C2×C7×C8—44no—
218C2×C7×C8#4112yes—
219C7×C4⋊C4C22⋊C414yes—
220C7×C22⋊C4C22⋊C414yes—
221C7×C22⋊C4C22⋊C414yes—
222C42×C7C22×C412yes—
223C42×C7C2×D412yes—
224C22⋊Dic7—24no—
225C22⋊Dic7—24no—
226C22⋊Dic7—42no—
227C22⋊Dic7—42no—
228C22⋊Dic7—81no—
229C4⋊Dic7—24no—
230C4⋊Dic7—24no—
231C4⋊Dic7—24no—
232C4⋊Dic7—21no—
233C4⋊Dic7—21no—
234C4⋊Dic7—21no—
235C4⋊Dic7—21no—
236C4⋊Dic7—21no—
237C4⋊Dic7—21no—
238C4⋊Dic7—21no—
239C4⋊Dic7—21no—
240C4⋊Dic7—21no—
241C4⋊Dic7—21no—
242C4⋊Dic7—42no—
243C4⋊Dic7C22×C412yes—
244C4⋊Dic7C22×C412yes—
245C4⋊Dic7C22×C412yes—
246C4⋊Dic7#4112yes—
247Dic7⋊C4—24no—
248Dic7⋊C4—24no—
249Dic7⋊C4—24no—
250C4×Dic7—24no—
251C4×Dic7—42no—
252C4×Dic7—81no—
253C22×M16C2×D711yescharacteristic
254C23×C8C2×D711yescharacteristic
255#554—78no—
256#554—144no—
257C2×C4⋊Q8—71no—
258C2×#125—141no—
259C2×C22⋊Q8—71no—
260C2×C22⋊Q8—71no—
261C2×C22⋊Q8—141no—
262C2×C22⋊Q8—141no—
263C2×C4×Q8—71no—
264C2×C4×D4—141no—
265C2×C4×D4C2×D711yescharacteristic
266C2×#117—71no—
267C22×C4⋊C4—71no—
268C22×C4⋊C4—71no—
269C22×C4⋊C4—71no—
270#435—24no—
271C2×C4⋊C8C2×D711yescharacteristic
272C2×#103—71no—
273C2×#103—71no—
274C2×#103—71no—
275C2×#103—71no—
276C2×C22⋊C8C2×D711yescharacteristic
277C2×C22⋊C8C2×D711yescharacteristic
278C2×#97C2×D711yescharacteristic
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×D4—28no—
315C2×C4×C7—21no—
316C2×C4×C7—21no—
317C2×C4×C7—21no—
318C2×C4×C7—21no—
319C2×C4×C7—21no—
320C2×C4×C7—21no—
321C2×C4×C7—21no—
322C2×C4×C7—21no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7C2×C22⋊C412yes—
332C2×C4×C7C2×C22⋊C412yes—
333C2×C4×C7C2×C22⋊C412yes—
334C2×C4×C7C2×C22⋊C412yes—
335C2×C4×C7C23×C411yescharacteristic
336C2×C4×C7C22×D411yescharacteristic
337C2×C4×C7C2×#4111yescharacteristic
338C2×C4×C7C2×#4111yescharacteristic
339C2×C4×C7H(5,𝔽2)11yescharacteristic
340C2×C4×C72−1+411yescharacteristic
341C2×Dic7—22no—
342C2×Dic7—22no—
343C2×Dic7—22no—
344C2×Dic7—22no—
345C2×Dic7—22no—
346C2×Dic7—41no—
347C2×Dic7—41no—
348C2×Dic7—41no—
349C2×Dic7—41no—
350C2×Dic7—41no—
351C2×Dic7—41no—
352C2×Dic7—41no—
353C2×Dic7—41no—
354C2×Dic7—41no—
355C2×Dic7—41no—
356C2×Dic7—41no—
357C2×Dic7—41no—
358C2×Dic7—41no—
359C2×Dic7—41no—
360C2×Dic7—41no—
361C2×Dic7—41no—
362C2×Dic7—41no—
363C2×Dic7—41no—
364C2×Dic7—41no—
365C2×Dic7—84no—
366C2×Dic7—84no—
367C2×Dic7—84no—
368Dic14—22no—
369Dic14—22no—
370Dic14—41no—
371Dic14—41no—
372Dic14—84no—
373C7×C8—22no—
374C7×C8—41no—
375C7×C8—41no—
376C7×C8—41no—
377C22×Q8—71no—
378C22×Q8—141no—
379C22×D4D2811yescharacteristic
380C23×C4—141no—
381C23×C4—141no—
382C23×C4—141no—
383C23×C4C22×D711yescharacteristic
384C23×C4C22×D711yescharacteristic
385C2×M16—22no—
386C2×M16—22no—
387C2×M16—41no—
388C22×C8—22no—
389C22×C8—22no—
390C22×C8—41no—
391C22×C8C22×D711yescharacteristic
392C22×C8C22×D711yescharacteristic
393C22×C8C22×D711yescharacteristic
394C22×C8C22×D711yescharacteristic
395C4⋊Q8—74no—
396C4⋊Q8—142no—
397#125—148no—
398C22⋊Q8—74no—
399C22⋊Q8—74no—
400C22⋊Q8—142no—
401C22⋊Q8—142no—
402C22⋊Q8—148no—
403C22⋊Q8—148no—
404C4×Q8—74no—
405C4×Q8—142no—
406C4×D4—148no—
407C4×D4C4×D714yes—
408C4×D4C22⋊D714yes—
409#117—142no—
410#117—281no—
411C2×C4⋊C4—74no—
412C2×C4⋊C4—74no—
413C2×C4⋊C4—71no—
414C2×C4⋊C4—71no—
415C2×C4⋊C4—71no—
416C2×C4⋊C4—71no—
417C2×C4⋊C4—71no—
418C2×C4⋊C4—71no—
419C2×C4⋊C4—71no—
420C2×C4⋊C4—142no—
421C2×C4⋊C4—141no—
422C2×C4⋊C4—141no—
423C2×C4⋊C4—141no—
424C2×C4⋊C4—141no—
425C2×C4⋊C4—141no—
426C2×C4⋊C4—141no—
427C2×C4⋊C4—142no—
428C2×C4⋊C4—142no—
429C2×C4⋊C4—141no—
430C2×C4⋊C4—281no—
431C2×C4⋊C4D2811yescharacteristic
432C2×C22⋊C4—141no—
433C2×C22⋊C4—141no—
434C2×C22⋊C4—141no—
435C2×C22⋊C4—141no—
436C2×C22⋊C4—141no—
437C2×C22⋊C4D2811yescharacteristic
438C2×C22⋊C4D2811yescharacteristic
439C2×C42—141no—
440C2×C42—141no—
441C2×C42—141no—
442C2×C42C22×D711yescharacteristic
443C4⋊C8—22no—
444#103—142no—
445#103—142no—
446#103—281no—
447#103—281no—
448C22⋊C8—22no—
449C22⋊C8—22no—
450#97—22no—
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×C7C4×#4111yescharacteristic
482C4×C7#52011yescharacteristic
483C4×C7#54611yescharacteristic
484C4×C7#54711yescharacteristic
485Dic7—42no—
486Dic7—42no—
487Dic7—42no—
488Dic7—42no—
489Dic7—42no—
490Dic7—81no—
491Dic7—81no—
492Dic7—81no—
493C24C2×D2811yescharacteristic
494C24C2×D2811yescharacteristic
495C2×Q8—72no—
496C2×Q8—144no—
497C2×Q8—141no—
498C2×Q8—141no—
499C2×Q8—141no—
500C2×Q8—141no—
501C2×Q8—141no—
502C2×Q8—561no—
503C2×Q8—561no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4(C2×D7)⋊C414yes—
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—141no—
516C22×C4—141no—
517C22×C4—141no—
518C22×C4—141no—
519C22×C4—141no—
520C22×C4—144no—
521C22×C4—144no—
522C22×C4—141no—
523C22×C4—141no—
524C22×C4—141no—
525C22×C4—282no—
526C22×C4—282no—
527C22×C4—561no—
528C22×C4—561no—
529C22×C4—561no—
530C22×C4—561no—
531C22×C4—561no—
532C22×C4C2×C4×D712yes—
533C22×C4C2×C4×D712yes—
534C22×C4C2×D2811yescharacteristic
535C22×C4C2×D2811yescharacteristic
536C22×C4C2×D2811yescharacteristic
537C22×C4C2×D2811yescharacteristic
538C22×C4C2×C22⋊D712yes—
539C22×C4C2×C22⋊D712yes—
540C22×C4C23×D711yescharacteristic
541M16—44no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—44no—
554C2×C8#115912yes—
555C4⋊C4—72no—
556C4⋊C4—72no—
557C4⋊C4—72no—
558C4⋊C4—72no—
559C4⋊C4—144no—
560C4⋊C4—144no—
561C4⋊C4—144no—
562C4⋊C4—144no—
563C4⋊C4—144no—
564C4⋊C4—144no—
565C4⋊C4—141no—
566C4⋊C4—141no—
567C4⋊C4—141no—
568C4⋊C4—141no—
569C4⋊C4—141no—
570C4⋊C4—141no—
571C4⋊C4—141no—
572C4⋊C4—141no—
573C4⋊C4—141no—
574C4⋊C4—141no—
575C4⋊C4—282no—
576C4⋊C4(C2×D7)⋊C414yes—
577C22⋊C4—144no—
578C22⋊C4—144no—
579C22⋊C4—282no—
580C22⋊C4—282no—
581C22⋊C4—561no—
582C22⋊C4(C2×D7)⋊C414yes—
583C22⋊C4(C2×D7)⋊C414yes—
584C42—144no—
585C42—282no—
586C42—561no—
587C42C2×C4×D712yes—
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#647212yes—
609C23#647212yes—
610C23C2×(C2×D7)⋊C412yes—
611C23C2×(C2×D7)⋊C412yes—
612C23C22×D2811yescharacteristic
613Q8—142no—
614Q8—142no—
615Q8—281no—
616Q8—281no—
617Q8—564no—
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—142no—
636C2×C4—142no—
637C2×C4—142no—
638C2×C4—142no—
639C2×C4—142no—
640C2×C4—281no—
641C2×C4—281no—
642C2×C4—281no—
643C2×C4—281no—
644C2×C4—281no—
645C2×C4—281no—
646C2×C4—281no—
647C2×C4—281no—
648C2×C4—281no—
649C2×C4—281no—
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—564no—
660C2×C4—564no—
661C2×C4—564no—
662C2×C4C2×(C2×D7)⋊C412yes—
663C2×C4C2×(C2×D7)⋊C412yes—
664C2×C4C2×(C2×D7)⋊C412yes—
665C2×C4C2×(C2×D7)⋊C412yes—
666C2×C4C22×C4×D711yescharacteristic
667C2×C4C2×#115911yescharacteristic
668C2×C4#654811yescharacteristic
669C2×C4D7×#4111yescharacteristic
670C2×C4#655411yescharacteristic
671C2×C4C22×C22⋊D711yescharacteristic
672C8—22no—
673C8—41no—
674C8—41no—
675C8—41no—
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#8989214yes—
691C22#9024511yescharacteristic
692C22#9024611yescharacteristic
693C22C2×#647211yescharacteristic
694C22C2×#647211yescharacteristic
695C22#9044211yescharacteristic
696C22#9044311yescharacteristic
697C22C22×(C2×D7)⋊C411yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—282no—
703C4—282no—
704C4—282no—
705C4—282no—
706C4—282no—
707C4—561no—
708C4—561no—
709C4—561no—
710C4C4×#115911yescharacteristic
711C4#9023711yescharacteristic
712C4#9049711yescharacteristic
713C4#9051511yescharacteristic
714C2—24no—
715C2—42no—
716C2#1173691511yescharacteristic
717C2#1173691711yescharacteristic
718C2#1173694811yescharacteristic
719C2#1173695811yescharacteristic
720C2#1173977511yescharacteristic
721C2C2×#8989211yescharacteristic
722C2#1174124211yescharacteristic
subgroupG/H
centerC23C22×D28
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#435C2
socleC23×C7C22×D4
prime radicalC22×C7×D4D4
cosocleC22×C4×C7C24
hypercenterC2×#435D7
hypocenterC7#22497
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
4. #11729743C2semidirect
5. #11729739C2semidirect
6. #11729726C2semidirect
7. C2×#89346C2semidirect
8. #11728240C2semidirect
9. #11728214C2semidirect
10. #11727685C2semidirect
11. #11727684C2semidirect
12. #11727679C2semidirect
13. #11727678C2semidirect
14. #11727582C2semidirect
15. #11727567C2semidirect
27. #90234C4semidirect
104. C2×C4⋊Dic7C2×C4semidirect
115. #6487C2×C4semidirect
126. #6432C2×C4semidirect
128. C4×Dic14C2×C4semidirect
676. C7#22497semidirect

Maximal subgroups

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

subgroupindex
C2×#902342
C2×C7×#4352
#117397802
#117297432
#117297392
#117297262
C2×#893462
#117282402
#117282142
#117276852
#117276842
#117276792
#117276782
#117275822
#117275672
#224977