Finite Group Databasebeta

← #13370123

Subgroups — #13370123

Order 1792.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90233C211yesmaximal, characteristic
2C7×#2352C211yesmaximal, characteristic
3C2×#89783C211yesmaximal, characteristic
4#11729339C211yesmaximal, characteristic, complemented
5#11729334C211yesmaximal, characteristic, complemented
6#11729313C211yesmaximal, characteristic, complemented
7#11729312C211yesmaximal, characteristic, complemented
8#11727313C211yesmaximal, characteristic, complemented
9#11727309C211yesmaximal, characteristic, complemented
10#11727270C211yesmaximal, characteristic, complemented
11#11727268C211yesmaximal, characteristic, complemented
12#11727257C211yesmaximal, characteristic, complemented
13#11727257C211yesmaximal, characteristic, complemented
14#11727243C211yesmaximal, characteristic, complemented
15#11727229C211yesmaximal, characteristic, complemented
16C2×C4×C7×D4C2211yescharacteristic
17C2×C7×#117C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C2×#6499—21no—
20C2×#6489C2211yescharacteristic
21C2×#6489C2211yescharacteristic
22C2×#6487C2211yescharacteristic
23C2×#6487C2211yescharacteristic
24C22×#1136C2211yescharacteristic
25C23×C7⋊C8C2211yescharacteristic
26#90233—24no—
27#90233C418yescomplemented
28C2×#6450—21no—
29C2×#6442—21no—
30C2×#6442—21no—
31C2×#6432C2211yescharacteristic
32C2×C4×Dic14C2211yescharacteristic
33C7×#388—21no—
34C7×#387—21no—
35C7×#386—21no—
36C7×#382C2211yescharacteristic
37C7×#380C2211yescharacteristic
38C7×#380C2211yescharacteristic
39C4×C7×C4⋊C4C2211yescharacteristic
40C4×C7×C22⋊C4—21no—
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42C2×C22⋊(C7⋊C8)C2211yescharacteristic
43#89783—24no—
44C2×#6384C2211yescharacteristic
45C2×#6384C2211yescharacteristic
46C2×#6384C2211yescharacteristic
47C2×#6384C2211yescharacteristic
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#22494—71nomaximal, Sylow
63C22×C7×D4D411yescharacteristic
64C23×C4×C7—21no—
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C22×Dic14—21no—
68C22×Dic14C2311yescharacteristic
69C4×C7×D4C2×C414yes—
70C4×C7×D4D414yes—
71C7×#117—22no—
72C7×#117—41no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—21no—
75C2×C7×C4⋊C4—41no—
76C2×C7×C4⋊C4D411yescharacteristic
77C2×C7×C4⋊C4C2311yescharacteristic
78C2×C7×C4⋊C4C2311yescharacteristic
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C22⋊C4—21no—
82C2×C7×C22⋊C4—21no—
83C2×C7×C22⋊C4—21no—
84C2×C7×C22⋊C4D411yescharacteristic
85C2×C7×C22⋊C4D411yescharacteristic
86C2×C42×C7—21no—
87C2×C42×C7—21no—
88C2×C42×C7C2311yescharacteristic
89C2×C22⋊Dic7—21no—
90C2×C22⋊Dic7—21no—
91C2×C22⋊Dic7—21no—
92C2×C22⋊Dic7—21no—
93#6499—28no—
94#6489—22no—
95#6489—22no—
96#6489C2×C414yes—
97#6489C2×C414yescomplemented
98C2×C4⋊Dic7—21no—
99C2×C4⋊Dic7C2311yescharacteristic
100C2×C4⋊Dic7C2311yescharacteristic
101C2×C4⋊Dic7C2311yescharacteristic
102#6487—22no—
103#6487—22no—
104#6487C2×C414yes—
105#6487C2×C414yescomplemented
106C2×Dic7⋊C4—21no—
107C2×Dic7⋊C4—21no—
108C2×Dic7⋊C4—21no—
109C2×C4×Dic7—21no—
110C2×C4×Dic7—21no—
111C2×C4×Dic7—21no—
112C2×#1136—22no—
113C2×#1136—22no—
114C2×#1136—41no—
115C22×C7⋊C8—22no—
116C22×C7⋊C8—22no—
117C22×C7⋊C8—41no—
118C22×C7⋊C8C2311yescharacteristic
119C22×C7⋊C8C2311yescharacteristic
120C22×C7⋊C8C2311yescharacteristic
121C22×C7⋊C8C2311yescharacteristic
122#6450—28no—
123#6442—28no—
124#6442—28no—
125#6432—22no—
126#6432C2×C414yescomplemented
127C4×Dic14—22no—
128C4×Dic14C2×C414yescomplemented
129C7×#95—21no—
130C7×#95—21no—
131C7×#95—21no—
132C7×#95—21no—
133C7×#95—21no—
134C22⋊(C7⋊C8)—22no—
135C22⋊(C7⋊C8)—22no—
136#6384—22no—
137#6384—22no—
138#6384—41no—
139#6384—41no—
140C4⋊(C7⋊C8)—22no—
141#6377—22no—
142C2×#556—71no—
143C2×#435—71no—
144#2352D711yescharacteristic
145#1993—71no—
146#1987—71no—
147#1894—71no—
148#1892—71no—
149#1873—71no—
150#1872—71no—
151#1825—71no—
152#1825—71no—
153#1805—71no—
154#1763—71no—
155#1736—71no—
156#1735—71no—
157C24×C7C2×D411yescharacteristic
158C24×C7C2×D411yescharacteristic
159C2×C7×D4—41no—
160C2×C7×D4—41no—
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×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—42no—
175C22×C4×C7—42no—
176C22×C4×C7—81no—
177C22×C4×C7C22×C412yes—
178C22×C4×C7C22×C412yes—
179C22×C4×C7C2×D411yescharacteristic
180C22×C4×C7C2×D411yescharacteristic
181C22×C4×C7C2×D411yescharacteristic
182C22×C4×C7C2×D411yescharacteristic
183C22×C4×C7C2×D412yes—
184C22×C4×C7C2×D412yes—
185C22×C4×C7C2411yescharacteristic
186C22×Dic7—21no—
187C22×Dic7—21no—
188C22×Dic7—21no—
189C22×Dic7—21no—
190C2×Dic14—21no—
191C2×Dic14—21no—
192C2×Dic14—21no—
193C2×Dic14—21no—
194C2×Dic14—24no—
195C2×Dic14—21no—
196C2×Dic14—42no—
197C2×Dic14—42no—
198C2×Dic14C22×C412yes—
199C7×C4⋊C4—21no—
200C7×C4⋊C4—21no—
201C7×C4⋊C4—21no—
202C7×C4⋊C4—21no—
203C7×C4⋊C4—21no—
204C7×C4⋊C4—21no—
205C7×C4⋊C4—21no—
206C7×C4⋊C4—42no—
207C7×C4⋊C4C22⋊C414yes—
208C7×C4⋊C4#4112yes—
209C7×C22⋊C4—42no—
210C7×C22⋊C4—42no—
211C7×C22⋊C4—81no—
212C7×C22⋊C4C22⋊C414yes—
213C7×C22⋊C4C22⋊C414yes—
214C42×C7—42no—
215C42×C7—81no—
216C42×C7C22×C412yes—
217C42×C7C2×D412yes—
218C22⋊Dic7—24no—
219C22⋊Dic7—24no—
220C22⋊Dic7—24no—
221C22⋊Dic7—24no—
222C4⋊Dic7—24no—
223C4⋊Dic7—21no—
224C4⋊Dic7—21no—
225C4⋊Dic7—21no—
226C4⋊Dic7C22×C412yes—
227C4⋊Dic7C22×C412yes—
228C4⋊Dic7C22×C412yes—
229Dic7⋊C4—24no—
230Dic7⋊C4—24no—
231Dic7⋊C4—24no—
232C4×Dic7—24no—
233C4×Dic7—24no—
234C4×Dic7—24no—
235#1136—44no—
236C2×C7⋊C8—21no—
237C2×C7⋊C8—21no—
238C2×C7⋊C8—21no—
239C2×C7⋊C8—21no—
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—44no—
248C2×C7⋊C8#4112yes—
249C22×M16—71no—
250C23×C8—71no—
251#556—78no—
252#556—144no—
253C2×C4⋊Q8—71no—
254C2×#126—141no—
255C2×#126—141no—
256C2×#124—141no—
257C2×C22⋊Q8—71no—
258C2×C22⋊Q8—71no—
259C2×C4×Q8—71no—
260C2×C4×Q8—141no—
261C2×C4×D4C2×D711yescharacteristic
262C2×#117—71no—
263C2×#117—71no—
264C2×#117C2×D711yescharacteristic
265C22×C4⋊C4C2×D711yescharacteristic
266#435—144no—
267C2×C4⋊C8—71no—
268C2×#103—71no—
269C2×#103—71no—
270C2×#103—71no—
271C2×#103—71no—
272C2×C22⋊C8—71no—
273C2×C22⋊C8—71no—
274C2×#97—71no—
275#388—21no—
276#387—21no—
277#386—21no—
278#382C2×D711yescharacteristic
279#380C2×D711yescharacteristic
280#380C2×D711yescharacteristic
281C4×C4⋊C4C2×D711yescharacteristic
282C4×C22⋊C4—21no—
283#340—71no—
284#340—71no—
285#340—71no—
286#340—71no—
287#340—71no—
288#340—71no—
289#340—71no—
290#340—71no—
291#340—71no—
292#340—71no—
293#340—71no—
294#340—71no—
295C23×C7—21no—
296C23×C7—21no—
297C23×C7—21no—
298C23×C7—21no—
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×C7C2×C22⋊C412yes—
308C23×C7C2×C22⋊C412yes—
309C23×C7C22×D411yescharacteristic
310C7×D4—44no—
311C2×C4×C7—21no—
312C2×C4×C7—21no—
313C2×C4×C7—21no—
314C2×C4×C7—21no—
315C2×C4×C7—21no—
316C2×C4×C7—21no—
317C2×C4×C7—21no—
318C2×C4×C7—21no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—41no—
339C2×C4×C7—84no—
340C2×C4×C7C2×C22⋊C412yes—
341C2×C4×C7C2×C22⋊C412yes—
342C2×C4×C7C2×C22⋊C412yes—
343C2×C4×C7C2×C22⋊C412yes—
344C2×C4×C7C23×C411yescharacteristic
345C2×C4×C7C22×D411yescharacteristic
346C2×C4×C7C2×#4111yescharacteristic
347C2×C4×C7C2×#4111yescharacteristic
348C2×C4×C7H(5,𝔽2)11yescharacteristic
349C2×C4×C72−1+411yescharacteristic
350C2×Dic7—22no—
351C2×Dic7—22no—
352C2×Dic7—22no—
353C2×Dic7—22no—
354C2×Dic7—41no—
355C2×Dic7—41no—
356C2×Dic7—41no—
357C2×Dic7—41no—
358C2×Dic7—41no—
359C2×Dic7—41no—
360C2×Dic7—41no—
361C2×Dic7—41no—
362Dic14—22no—
363Dic14—22no—
364Dic14—48no—
365Dic14—41no—
366Dic14—41no—
367C7⋊C8—22no—
368C7⋊C8—41no—
369C7⋊C8—41no—
370C7⋊C8—41no—
371C22×Q8—71no—
372C22×Q8—141no—
373C22×D4C22⋊D711yescharacteristic
374C23×C4—21no—
375C23×C4C22×D711yescharacteristic
376C23×C4C22×D711yescharacteristic
377C2×M16—142no—
378C2×M16—142no—
379C2×M16—281no—
380C22×C8—71no—
381C22×C8—71no—
382C22×C8—71no—
383C22×C8—71no—
384C22×C8—142no—
385C22×C8—142no—
386C22×C8—281no—
387C4⋊Q8—74no—
388C4⋊Q8—142no—
389#126—148no—
390#126—148no—
391#124—148no—
392C22⋊Q8—74no—
393C22⋊Q8—74no—
394C22⋊Q8—142no—
395C22⋊Q8—142no—
396C4×Q8—74no—
397C4×Q8—148no—
398C4×Q8—142no—
399C4×D4C4×D714yes—
400C4×D4D2814yes—
401#117—22no—
402#117—41no—
403#117—74no—
404#117—74no—
405#117—142no—
406#117—142no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—41no—
410C2×C4⋊C4—71no—
411C2×C4⋊C4—71no—
412C2×C4⋊C4—71no—
413C2×C4⋊C4—141no—
414C2×C4⋊C4—141no—
415C2×C4⋊C4—141no—
416C2×C4⋊C4—141no—
417C2×C4⋊C4C22⋊D711yescharacteristic
418C2×C4⋊C4C22×D711yescharacteristic
419C2×C4⋊C4C22×D711yescharacteristic
420C2×C4⋊C4C22×D711yescharacteristic
421C2×C4⋊C4C22×D711yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—141no—
426C2×C22⋊C4—141no—
427C2×C22⋊C4—141no—
428C2×C22⋊C4—141no—
429C2×C22⋊C4C22⋊D711yescharacteristic
430C2×C22⋊C4C22⋊D711yescharacteristic
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—141no—
434C2×C42—141no—
435C2×C42—141no—
436C2×C42C22×D711yescharacteristic
437C4⋊C8—142no—
438#103—142no—
439#103—142no—
440#103—281no—
441#103—281no—
442C22⋊C8—142no—
443C22⋊C8—142no—
444#97—142no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450C22×C7—22no—
451C22×C7—22no—
452C22×C7—22no—
453C22×C7—22no—
454C22×C7—22no—
455C22×C7—22no—
456C22×C7—41no—
457C22×C7—41no—
458C22×C7—41no—
459C22×C7—41no—
460C22×C7—41no—
461C22×C7—41no—
462C22×C7—41no—
463C22×C7—41no—
464C22×C7C22×C22⋊C411yescharacteristic
465C22×C7#54611yescharacteristic
466C22×C7#54711yescharacteristic
467C22×C7#57511yescharacteristic
468C22×C7#57511yescharacteristic
469C22×C7#57711yescharacteristic
470C22×C7#57811yescharacteristic
471C4×C7—22no—
472C4×C7—22no—
473C4×C7—22no—
474C4×C7—22no—
475C4×C7—42no—
476C4×C7—81no—
477C4×C7—81no—
478C4×C7—81no—
479C4×C7C4×#4111yescharacteristic
480C4×C7#52011yescharacteristic
481C4×C7#54611yescharacteristic
482C4×C7#54711yescharacteristic
483Dic7—42no—
484Dic7—42no—
485Dic7—42no—
486Dic7—42no—
487C24C2×C22⋊D711yescharacteristic
488C24C2×C22⋊D711yescharacteristic
489C2×Q8—72no—
490C2×Q8—144no—
491C2×Q8—141no—
492C2×Q8—141no—
493C2×Q8—141no—
494C2×Q8—141no—
495C2×Q8—141no—
496C2×Q8—282no—
497C2×Q8—282no—
498C2×D4—41no—
499C2×D4—41no—
500C2×D4(C2×D7)⋊C414yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—81no—
516C22×C4—141no—
517C22×C4—141no—
518C22×C4—141no—
519C22×C4—141no—
520C22×C4C2×C4×D712yes—
521C22×C4C2×C4×D712yes—
522C22×C4C2×D2812yes—
523C22×C4C2×D2812yes—
524C22×C4C2×C22⋊D711yescharacteristic
525C22×C4C2×C22⋊D711yescharacteristic
526C22×C4C2×C22⋊D711yescharacteristic
527C22×C4C2×C22⋊D711yescharacteristic
528C22×C4C23×D711yescharacteristic
529M16—284no—
530C2×C8—72no—
531C2×C8—141no—
532C2×C8—141no—
533C2×C8—141no—
534C2×C8—141no—
535C2×C8—141no—
536C2×C8—141no—
537C2×C8—141no—
538C2×C8—141no—
539C2×C8—141no—
540C2×C8—141no—
541C2×C8—141no—
542C2×C8—284no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—72no—
552C4⋊C4—72no—
553C4⋊C4—72no—
554C4⋊C4—144no—
555C4⋊C4—144no—
556C4⋊C4—144no—
557C4⋊C4—144no—
558C4⋊C4—141no—
559C4⋊C4—141no—
560C4⋊C4—141no—
561C4⋊C4(C2×D7)⋊C414yes—
562C4⋊C4#115912yes—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C22⋊C4—144no—
567C22⋊C4—144no—
568C22⋊C4—144no—
569C22⋊C4—144no—
570C22⋊C4(C2×D7)⋊C414yes—
571C22⋊C4(C2×D7)⋊C414yes—
572C42—42no—
573C42—81no—
574C42—144no—
575C42—144no—
576C42—144no—
577C42C2×C4×D712yes—
578C42C2×D2812yes—
579C2×C7—42no—
580C2×C7—42no—
581C2×C7#233911yescharacteristic
582C2×C7#289611yescharacteristic
583C2×C7#289811yescharacteristic
584C2×C7#331111yescharacteristic
585C2×C7#331311yescharacteristic
586C2×C7#334911yescharacteristic
587C2×C7#335011yescharacteristic
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23C2×(C2×D7)⋊C412yes—
601C23C2×(C2×D7)⋊C412yes—
602C23C22×C22⋊D711yescharacteristic
603Q8—142no—
604Q8—142no—
605Q8—288no—
606Q8—281no—
607Q8—281no—
608D4—44no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—84no—
638C2×C4—142no—
639C2×C4—142no—
640C2×C4—142no—
641C2×C4—142no—
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×C4C2×(C2×D7)⋊C412yes—
651C2×C4C2×(C2×D7)⋊C412yes—
652C2×C4C2×(C2×D7)⋊C412yes—
653C2×C4C2×(C2×D7)⋊C412yes—
654C2×C4C22×C4×D711yescharacteristic
655C2×C4C22×D2811yescharacteristic
656C2×C4C2×#115911yescharacteristic
657C2×C4#654811yescharacteristic
658C2×C4D7×#4111yescharacteristic
659C2×C4#655411yescharacteristic
660C8—142no—
661C8—281no—
662C8—281no—
663C8—281no—
664C7#2249411yescharacteristic, complemented, Sylow
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22C22×(C2×D7)⋊C411yescharacteristic
680C22#9049711yescharacteristic
681C22#9051311yescharacteristic
682C22#9051311yescharacteristic
683C22#9051511yescharacteristic
684C22#9052711yescharacteristic
685C22#9052911yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—42no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—282no—
695C4—282no—
696C4—282no—
697C4—282no—
698C4C4×#115911yescharacteristic
699C4#9023711yescharacteristic
700C4#9024511yescharacteristic
701C4#9024611yescharacteristic
702C2—42no—
703C2—42no—
704C2#1173965811yescharacteristic
705C2#1173977511yescharacteristic
706C2#1174001511yescharacteristic
707C2#1174094211yescharacteristic
708C2#1174098211yescharacteristic
709C2#1174104011yescharacteristic
710C2#1174105611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2352C2
socleC23×C7C22×D4
prime radicalC22×C7×D4D4
cosocleC22×C4×C7C24
hypercenter#2352D7
hypocenterC7#22494
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
4. #11729339C2semidirect
5. #11729334C2semidirect
6. #11729313C2semidirect
7. #11729312C2semidirect
8. #11727313C2semidirect
9. #11727309C2semidirect
10. #11727270C2semidirect
11. #11727268C2semidirect
12. #11727257C2semidirect
13. #11727257C2semidirect
14. #11727243C2semidirect
15. #11727229C2semidirect
27. #90233C4semidirect
97. #6489C2×C4semidirect
105. #6487C2×C4semidirect
126. #6432C2×C4semidirect
128. C4×Dic14C2×C4semidirect
664. C7#22494semidirect

Maximal subgroups

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

subgroupindex
C2×#902332
C7×#23522
C2×#897832
#117293392
#117293342
#117293132
#117293122
#117273132
#117273092
#117272702
#117272682
#117272572
#117272432
#117272292
#224947