Finite Group Databasebeta

← #13374219

Subgroups — #13374219

Order 1792.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2363C211yesmaximal, characteristic
2C2×#89812C211yesmaximal, characteristic
3C2×#89790C211yesmaximal, characteristic, complemented
4C2×#89776C211yesmaximal, characteristic, complemented
5C22⋊C4×Dic14C211yesmaximal, characteristic, complemented
6#11729436C211yesmaximal, characteristic
7#11729366C211yesmaximal, characteristic, complemented
8#11729330C211yesmaximal, characteristic, complemented
9#11727414C211yesmaximal, characteristic, complemented
10#11727400C211yesmaximal, characteristic, complemented
11#11727386C211yesmaximal, characteristic, complemented
12#11727370C211yesmaximal, characteristic, complemented
13C4×#6384C211yesmaximal, characteristic, complemented
14#11727219C211yesmaximal, characteristic, complemented
15#11727202C211yesmaximal, characteristic, complemented
16C23×Dic14C2211yescharacteristic
17C2×C7×#121C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C2×C7×#117C2211yescharacteristic
20C22×#1142C2211yescharacteristic
21C22×#1142C2211yescharacteristic
22C22×#1136C2211yescharacteristic
23C2×C4×Dic14C2211yescharacteristic
24C2×C4×Dic14C2211yescharacteristic
25C7×#390—21no—
26C7×#390C2211yescharacteristic
27C7×#389C2211yescharacteristic
28C7×#388—21no—
29C7×#386—21no—
30C4×C7×C4⋊C4C2211yescharacteristic
31C4×C7×C22⋊C4—21no—
32C4×C7×C22⋊C4C2211yescharacteristic
33C2×#6406C2211yescharacteristic
34C2×#6406C2211yescharacteristic
35#89984C2211yescharacteristic
36C2×C22⋊(C7⋊C8)C2211yescharacteristic
37#89812C418yescomplemented
38#89790—24no—
39#89776—24no—
40C2×#6384C2211yescharacteristic
41C2×#6384C2211yescharacteristic
42C2×#6384C2211yescharacteristic
43C2×#6384C2211yescharacteristic
44C2×#6384C2211yescharacteristic
45C2×#6384C2211yescharacteristic
46C2×#6382C2211yescharacteristic
47C2×#6381C2211yescharacteristic
48#89714—21no—
49C22⋊C4×Dic7—21no—
50#89701C2211yescharacteristic
51#89701C2211yescharacteristic
52C2×#6377C2211yescharacteristic
53C2×C4×C7⋊C8C2211yescharacteristic
54#89418—21no—
55#89418—21no—
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89319C2211yescharacteristic
61#89319C2211yescharacteristic
62#22865—71nomaximal, Sylow
63C22×C7×D4—21no—
64C22×C7×D4C2311yescharacteristic
65C23×C4×C7—21no—
66C23×C4×C7C2311yescharacteristic
67C23×Dic7—21no—
68C22×Dic14—22no—
69C22×Dic14—22no—
70C22×Dic14—21no—
71C22×Dic14—22no—
72C22×Dic14—41no—
73C22×Dic14—41no—
74C22×Dic14C2×C414yescomplemented
75C22×Dic14C2311yescharacteristic
76C22×Dic14C2311yescharacteristic
77C7×#121—22no—
78C7×#121C2×C414yes—
79C4×C7×D4—22no—
80C4×C7×D4—41no—
81C7×#117—22no—
82C7×#117—41no—
83C2×C7×C4⋊C4—21no—
84C2×C7×C4⋊C4C2311yescharacteristic
85C2×C7×C4⋊C4C2311yescharacteristic
86C2×C7×C4⋊C4C2311yescharacteristic
87C2×C7×C22⋊C4—21no—
88C2×C7×C22⋊C4—21no—
89C2×C7×C22⋊C4—21no—
90C2×C7×C22⋊C4—21no—
91C2×C7×C22⋊C4—21no—
92C2×C7×C22⋊C4D411yescharacteristic
93C2×C7×C22⋊C4D411yescharacteristic
94C2×C42×C7—21no—
95C2×C42×C7—21no—
96C2×C42×C7C2311yescharacteristic
97C2×C42×C7C2311yescharacteristic
98C2×C22⋊Dic7—21no—
99C2×#1142—22no—
100C2×#1142—22no—
101C2×#1142—41no—
102C2×#1142—41no—
103C2×#1142C2×C414yes—
104C2×#1142C2×C414yes—
105C2×C4⋊Dic7C2311yescharacteristic
106C2×C4⋊Dic7C2311yescharacteristic
107C2×Dic7⋊C4—21no—
108C2×Dic7⋊C4—21no—
109C2×C4×Dic7—21no—
110C2×C4×Dic7—21no—
111C2×#1136—22no—
112C2×#1136—22no—
113C2×#1136—41no—
114C22×C7⋊C8C2311yescharacteristic
115C22×C7⋊C8C2311yescharacteristic
116C22×C7⋊C8C2311yescharacteristic
117C22×C7⋊C8C2311yescharacteristic
118C4×Dic14—22no—
119C4×Dic14—22no—
120C4×Dic14—41no—
121C4×Dic14—41no—
122C7×#95—21no—
123C7×#95—21no—
124C7×#95D411yescharacteristic
125C7×#95D411yescharacteristic
126#6406—22no—
127#6406—41no—
128C7⋊#95—21no—
129C7⋊#95—21no—
130C7⋊#95—21no—
131C7⋊#95—21no—
132C7⋊#95—21no—
133C22⋊(C7⋊C8)C2×C414yescomplemented
134#6384—22no—
135#6384—22no—
136#6384—22no—
137#6384C2×C414yescomplemented
138#6384C2×C414yescomplemented
139#6384D414yescomplemented
140#6382—41no—
141#6381—22no—
142#6377—22no—
143C4×C7⋊C8—41no—
144C2×#448—71no—
145C2×#440—71no—
146C2×#419—71no—
147#2363D711yescharacteristic
148Q8×C22⋊C4—71no—
149#1968—71no—
150#1935—71no—
151#1928—71no—
152#1895—71no—
153#1880—71no—
154#1877—71no—
155#1865—71no—
156#1854—71no—
157C4×#103—71no—
158#1753—71no—
159C24×C7—21no—
160C24×C7C2×D411yescharacteristic
161C2×C7×D4—24no—
162C2×C7×D4—21no—
163C2×C7×D4—21no—
164C2×C7×D4—21no—
165C2×C7×D4—21no—
166C2×C7×D4—21no—
167C2×C7×D4—81no—
168C2×C7×D4—81no—
169C2×C7×D4C22×C412yes—
170C22×C4×C7—21no—
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—42no—
178C22×C4×C7—42no—
179C22×C4×C7—81no—
180C22×C4×C7C22×C412yes—
181C22×C4×C7C2×D411yescharacteristic
182C22×C4×C7C2×D411yescharacteristic
183C22×C4×C7C2×D411yescharacteristic
184C22×C4×C7C2×D411yescharacteristic
185C22×C4×C7C2×D411yescharacteristic
186C22×C4×C7#4112yes—
187C22×C4×C7C2411yescharacteristic
188C22×Dic7—21no—
189C22×Dic7—24no—
190C22×Dic7—21no—
191C22×Dic7—21no—
192C22×Dic7—21no—
193C22×Dic7—42no—
194C22×Dic7—42no—
195C2×Dic14—21no—
196C2×Dic14—21no—
197C2×Dic14—21no—
198C2×Dic14—21no—
199C2×Dic14—21no—
200C2×Dic14—21no—
201C2×Dic14—21no—
202C2×Dic14—28no—
203C2×Dic14—24no—
204C2×Dic14—21no—
205C2×Dic14—44no—
206C2×Dic14—44no—
207C2×Dic14—44no—
208C2×Dic14—42no—
209C2×Dic14—42no—
210C2×Dic14C22×C412yes—
211C2×Dic14C22×C412yes—
212C2×Dic14C2×D412yes—
213C2×Dic14#4112yes—
214C7×C4⋊C4—21no—
215C7×C4⋊C4—21no—
216C7×C4⋊C4—21no—
217C7×C4⋊C4—21no—
218C7×C4⋊C4—81no—
219C7×C4⋊C4C22×C412yes—
220C7×C4⋊C4C2×D412yes—
221C7×C22⋊C4—24no—
222C7×C22⋊C4—22no—
223C7×C22⋊C4—41no—
224C7×C22⋊C4—42no—
225C7×C22⋊C4—42no—
226C7×C22⋊C4—42no—
227C7×C22⋊C4—81no—
228C42×C7—21no—
229C42×C7—21no—
230C42×C7—21no—
231C42×C7—21no—
232C42×C7—42no—
233C42×C7—81no—
234C22⋊Dic7—42no—
235#1142—28no—
236#1142—44no—
237C4⋊Dic7—21no—
238C4⋊Dic7—21no—
239C4⋊Dic7—21no—
240C4⋊Dic7—21no—
241Dic7⋊C4—42no—
242Dic7⋊C4—42no—
243C4×Dic7—42no—
244C4×Dic7—42no—
245#1136—44no—
246C2×C7⋊C8—21no—
247C2×C7⋊C8—21no—
248C2×C7⋊C8—21no—
249C2×C7⋊C8—21no—
250C2×C7⋊C8—21no—
251C2×C7⋊C8—21no—
252C2×C7⋊C8—21no—
253C2×C7⋊C8—21no—
254C2×C7⋊C8—21no—
255C2×C7⋊C8C22×C412yes—
256C2×C7⋊C8C22×C412yes—
257C2×C7⋊C8C2×D412yes—
258C23×Q8—71no—
259C22×SD16—71no—
260C22×SD16—71no—
261C22×M16—71no—
262C2×#121C2×D711yescharacteristic
263C2×C4×Q8—71no—
264C2×C4×Q8—71no—
265C2×C4×D4C2×D711yescharacteristic
266C2×#117C2×D711yescharacteristic
267#448—78no—
268#440—144no—
269C2×#107—71no—
270C2×#106—71no—
271#419—144no—
272C2×#103—71no—
273C2×#103—71no—
274C2×#103—71no—
275C2×#103—71no—
276C2×#103—71no—
277C2×#103—71no—
278C2×#102—71no—
279C2×#102—71no—
280C2×C22⋊C8—71no—
281C2×#97—71no—
282C2×C4×C8—71no—
283#391—71no—
284#391—71no—
285#391—141no—
286#391—141no—
287#390—21no—
288#390C2×D711yescharacteristic
289#389C2×D711yescharacteristic
290#388—21no—
291#386—21no—
292#380—71no—
293#380—141no—
294C4×C4⋊C4C2×D711yescharacteristic
295C4×C22⋊C4—21no—
296C4×C22⋊C4—141no—
297C4×C22⋊C4C2×D711yescharacteristic
298#340—71no—
299#340—71no—
300#340—71no—
301#340—71no—
302#336—71no—
303#336—71no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7—22no—
311C23×C7—41no—
312C23×C7—41no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7C4×D412yes—
318C23×C7C22×D411yescharacteristic
319C7×D4—22no—
320C7×D4—22no—
321C7×D4—41no—
322C7×D4—41no—
323C7×D4—84no—
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—21no—
334C2×C4×C7—21no—
335C2×C4×C7—22no—
336C2×C4×C7—21no—
337C2×C4×C7—21no—
338C2×C4×C7—21no—
339C2×C4×C7—21no—
340C2×C4×C7—21no—
341C2×C4×C7—21no—
342C2×C4×C7—21no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—84no—
351C2×C4×C7C4×D412yes—
352C2×C4×C7#13712yes—
353C2×C4×C7C23×C411yescharacteristic
354C2×C4×C7C22×D411yescharacteristic
355C2×C4×C7C2×#4111yescharacteristic
356C2×C4×C7C2×#4111yescharacteristic
357C2×C4×C7H(5,𝔽2)11yescharacteristic
358C2×C4×C7H(5,𝔽2)11yescharacteristic
359C2×Dic7—22no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—48no—
364C2×Dic7—41no—
365C2×Dic7—41no—
366C2×Dic7—41no—
367C2×Dic7—41no—
368C2×Dic7—41no—
369C2×Dic7—41no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372Dic14—22no—
373Dic14—22no—
374Dic14—22no—
375Dic14—22no—
376Dic14—22no—
377Dic14—48no—
378Dic14—41no—
379Dic14—41no—
380Dic14C4×D414yes—
381C7⋊C8—22no—
382C7⋊C8—22no—
383C7⋊C8—22no—
384C7⋊C8—41no—
385C22×Q8—74no—
386C22×Q8—71no—
387C22×Q8—71no—
388C22×Q8—142no—
389C22×Q8—142no—
390C22×Q8—142no—
391C22×Q8—141no—
392C22×Q8—281no—
393C22×Q8—281no—
394C22×D4—21no—
395C22×D4C22×D711yescharacteristic
396C23×C4—21no—
397C23×C4—141no—
398C23×C4C22×D711yescharacteristic
399C2×SD16—74no—
400C2×SD16—74no—
401C2×SD16—142no—
402C2×SD16—142no—
403C2×SD16—281no—
404C2×SD16—281no—
405C2×M16—142no—
406C2×M16—142no—
407C2×M16—281no—
408C22×C8—71no—
409C22×C8—71no—
410C22×C8—71no—
411C22×C8—71no—
412#121—22no—
413#121C4×D714yes—
414C4×Q8—142no—
415C4×Q8—142no—
416C4×Q8—281no—
417C4×Q8—281no—
418C4×D4—22no—
419C4×D4—41no—
420#117—22no—
421#117—41no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—71no—
424C2×C4⋊C4—71no—
425C2×C4⋊C4—141no—
426C2×C4⋊C4—141no—
427C2×C4⋊C4C22×D711yescharacteristic
428C2×C4⋊C4C22×D711yescharacteristic
429C2×C4⋊C4C22×D711yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—141no—
436C2×C22⋊C4C22⋊D711yescharacteristic
437C2×C22⋊C4C22⋊D711yescharacteristic
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—141no—
441C2×C42—141no—
442C2×C42C22×D711yescharacteristic
443C2×C42C22×D711yescharacteristic
444#107—142no—
445#106—281no—
446#103—74no—
447#103—74no—
448#103—74no—
449#103—142no—
450#103—142no—
451#103—142no—
452#102—142no—
453#102—281no—
454C22⋊C8—74no—
455#97—142no—
456C4×C8—281no—
457#95—21no—
458#95—21no—
459#95—141no—
460#95—141no—
461#95—141no—
462#95—141no—
463#95—141no—
464#95C22⋊D711yescharacteristic
465#95C22⋊D711yescharacteristic
466C22×C7—22no—
467C22×C7—22no—
468C22×C7—22no—
469C22×C7—41no—
470C22×C7—41no—
471C22×C7—41no—
472C22×C7—41no—
473C22×C7—42no—
474C22×C7—42no—
475C22×C7—42no—
476C22×C7—81no—
477C22×C7—81no—
478C22×C7—81no—
479C22×C7—81no—
480C22×C7C2×C4×D411yescharacteristic
481C22×C7D4211yescharacteristic
482C22×C7#54611yescharacteristic
483C22×C7C2×#13711yescharacteristic
484C22×C7#57511yescharacteristic
485C22×C7#57711yescharacteristic
486C22×C7#57711yescharacteristic
487C4×C7—22no—
488C4×C7—22no—
489C4×C7—42no—
490C4×C7—41no—
491C4×C7—42no—
492C4×C7—41no—
493C4×C7—41no—
494C4×C7—81no—
495C4×C7C2×C4×D411yescharacteristic
496C4×C7#51811yescharacteristic
497C4×C7#54611yescharacteristic
498C4×C7#55111yescharacteristic
499Dic7—24no—
500Dic7—42no—
501Dic7—81no—
502Dic7—81no—
503C24—21no—
504C24C2×C22⋊D711yescharacteristic
505C2×Q8—72no—
506C2×Q8—72no—
507C2×Q8—72no—
508C2×Q8—72no—
509C2×Q8—148no—
510C2×Q8—144no—
511C2×Q8—141no—
512C2×Q8—141no—
513C2×Q8—141no—
514C2×Q8—141no—
515C2×Q8—141no—
516C2×Q8—141no—
517C2×Q8—141no—
518C2×Q8—141no—
519C2×Q8—282no—
520C2×Q8—282no—
521C2×Q8—284no—
522C2×Q8—284no—
523C2×Q8—284no—
524C2×D4—24no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—81no—
531C2×D4—81no—
532C2×D4C2×C4×D712yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—81no—
543C22×C4—141no—
544C22×C4—144no—
545C22×C4—141no—
546C22×C4—141no—
547C22×C4—141no—
548C22×C4—282no—
549C22×C4—282no—
550C22×C4C2×C4×D712yes—
551C22×C4#115712yes—
552C22×C4C2×C22⋊D711yescharacteristic
553C22×C4C2×C22⋊D711yescharacteristic
554C22×C4C2×C22⋊D711yescharacteristic
555C22×C4C2×C22⋊D711yescharacteristic
556C22×C4C2×C22⋊D711yescharacteristic
557C22×C4C23×D711yescharacteristic
558SD16—148no—
559SD16—284no—
560M16—284no—
561C2×C8—72no—
562C2×C8—72no—
563C2×C8—72no—
564C2×C8—141no—
565C2×C8—141no—
566C2×C8—141no—
567C2×C8—141no—
568C2×C8—141no—
569C2×C8—141no—
570C2×C8—141no—
571C2×C8—141no—
572C2×C8—141no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—81no—
578C4⋊C4—141no—
579C4⋊C4—141no—
580C4⋊C4—141no—
581C4⋊C4—141no—
582C4⋊C4—282no—
583C4⋊C4—282no—
584C4⋊C4C2×C4×D712yes—
585C4⋊C4D4×D712yes—
586C22⋊C4—24no—
587C22⋊C4—22no—
588C22⋊C4—41no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—81no—
593C22⋊C4—282no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—42no—
599C42—81no—
600C42—282no—
601C42—282no—
602C2×C7—42no—
603C2×C7—82no—
604C2×C7#235811yescharacteristic
605C2×C7C4×#13711yescharacteristic
606C2×C7#294911yescharacteristic
607C2×C7#327511yescharacteristic
608C2×C7#327811yescharacteristic
609C2×C7#332011yescharacteristic
610C2×C7#332111yescharacteristic
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23C4×C22⋊D712yes—
625C23C22×C22⋊D711yescharacteristic
626Q8—74no—
627Q8—142no—
628Q8—142no—
629Q8—142no—
630Q8—142no—
631Q8—142no—
632Q8—288no—
633Q8—281no—
634Q8—281no—
635D4—22no—
636D4—22no—
637D4—41no—
638D4—41no—
639D4—84no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—84no—
667C2×C4—142no—
668C2×C4—142no—
669C2×C4—142no—
670C2×C4—142no—
671C2×C4—288no—
672C2×C4—281no—
673C2×C4—281no—
674C2×C4—281no—
675C2×C4—281no—
676C2×C4—281no—
677C2×C4—281no—
678C2×C4—281no—
679C2×C4—281no—
680C2×C4C4×C22⋊D712yes—
681C2×C4#651412yes—
682C2×C4C22×C4×D711yescharacteristic
683C2×C4C2×#115711yescharacteristic
684C2×C4C2×D4×D711yescharacteristic
685C2×C4#654811yescharacteristic
686C2×C4D7×#4111yescharacteristic
687C2×C4#655311yescharacteristic
688C8—142no—
689C8—142no—
690C8—142no—
691C8—281no—
692C7#2286511yescharacteristic, complemented, Sylow
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22C2×C4×C22⋊D711yescharacteristic
708C22D4×C22⋊D711yescharacteristic
709C22#9051311yescharacteristic
710C22C2×#651411yescharacteristic
711C22#9052011yescharacteristic
712C22#9052711yescharacteristic
713C22#9052711yescharacteristic
714C4—22no—
715C4—22no—
716C4—41no—
717C4—42no—
718C4—42no—
719C4—41no—
720C4—41no—
721C4—81no—
722C4—144no—
723C4—282no—
724C4—561no—
725C4—561no—
726C4C4×D4×D711yescharacteristic
727C4#9023611yescharacteristic
728C4#9024111yescharacteristic
729C4#9024711yescharacteristic
730C2—42no—
731C2—82no—
732C2#1173984311yescharacteristic
733C2C4×#651411yescharacteristic
734C2#1173998811yescharacteristic
735C2#1174095311yescharacteristic
736C2#1174102911yescharacteristic
737C2#1174106511yescharacteristic
738C2#1174110111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2363C2
socleC23×C7C22×D4
prime radicalC2×C7×#121C22
cosocleC22×C4×C7C24
hypercenter#2363D7
hypocenterC7#22865
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
3. C2×#89790C2semidirect
4. C2×#89776C2semidirect
5. C22⋊C4×Dic14C2semidirect
7. #11729366C2semidirect
8. #11729330C2semidirect
9. #11727414C2semidirect
10. #11727400C2semidirect
11. #11727386C2semidirect
12. #11727370C2semidirect
13. C4×#6384C2semidirect
14. #11727219C2semidirect
15. #11727202C2semidirect
37. #89812C4semidirect
74. C22×Dic14C2×C4semidirect
133. C22⋊(C7⋊C8)C2×C4semidirect
137. #6384C2×C4semidirect
138. #6384C2×C4semidirect
139. #6384D4semidirect
692. C7#22865semidirect

Maximal subgroups

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

subgroupindex
C7×#23632
C2×#898122
C2×#897902
C2×#897762
C22⋊C4×Dic142
#117294362
#117293662
#117293302
#117274142
#117274002
#117273862
#117273702
C4×#63842
#117272192
#117272022
#228657