Finite Group Databasebeta

← #13371111

Subgroups — #13371111

Order 1792.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×D4×C22⋊C4C211yesmaximal, characteristic
2C2×#89987C211yesmaximal, characteristic
3#11730904C211yesmaximal, characteristic, complemented
4#11729882C211yesmaximal, characteristic
5#11729363C211yesmaximal, characteristic, complemented
6C4×#6406C211yesmaximal, characteristic, complemented
7#11729361C211yesmaximal, characteristic, complemented
8#11729360C211yesmaximal, characteristic, complemented
9#11727399C211yesmaximal, characteristic, complemented
10#11727398C211yesmaximal, characteristic, complemented
11#11727391C211yesmaximal, characteristic, complemented
12#11727390C211yesmaximal, characteristic, complemented
13#11727267C211yesmaximal, characteristic, complemented
14#11727257C211yesmaximal, characteristic, complemented
15#11727202C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C2×C4×C7×D4C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C22×C7×C22⋊C4—21no—
20C2×#6489C2211yescharacteristic
21C22×#1136C2211yescharacteristic
22C7×#390C2211yescharacteristic
23C7×#390C2211yescharacteristic
24C7×#386—21no—
25C7×#386—21no—
26C7×#380C2211yescharacteristic
27C7×#379—21no—
28C4×C7×C22⋊C4C2211yescharacteristic
29#89987C418yescomplemented
30C2×#6406C2211yescharacteristic
31C2×#6406C2211yescharacteristic
32C2×#6406C2211yescharacteristic
33C2×#6406C2211yescharacteristic
34C2×#6406C2211yescharacteristic
35C2×#6406C2211yescharacteristic
36C2×#6406C2211yescharacteristic
37C2×#6406C2211yescharacteristic
38#89984C2211yescharacteristic
39C2×C22⋊(C7⋊C8)C2211yescharacteristic
40C2×#6382C2211yescharacteristic, complemented
41C2×#6381C2211yescharacteristic, complemented
42#89716—21no—
43#89716—21no—
44C4×C4⋊Dic7C2211yescharacteristic, complemented
45C4×C4⋊Dic7C2211yescharacteristic, complemented
46#89700C2211yescharacteristic, complemented
47#89700C2211yescharacteristic, complemented
48C2×#6377C2211yescharacteristic, complemented
49C2×C4×C7⋊C8C2211yescharacteristic, complemented
50#89422—21no—
51#89420—21no—
52#89324C2211yescharacteristic, complemented
53#89324C2211yescharacteristic, complemented
54#89324C2211yescharacteristic, complemented
55#89324C2211yescharacteristic, complemented
56#89324C2211yescharacteristic, complemented
57#89324C2211yescharacteristic, complemented
58#89319C2211yescharacteristic, complemented
59#89319C2211yescharacteristic, complemented
60#22584—71nomaximal, Sylow
61C25×C7—21no—
62C22×C7×D4—22no—
63C22×C7×D4—22no—
64C22×C7×D4—21no—
65C22×C7×D4—22no—
66C22×C7×D4—41no—
67C22×C7×D4—41no—
68C22×C7×D4C2×C414yes—
69C22×C7×D4C2311yescharacteristic
70C22×C7×D4C2311yescharacteristic
71C23×C4×C7—21no—
72C23×C4×C7—21no—
73C23×C4×C7C2311yescharacteristic
74C4×C7×D4—22no—
75C4×C7×D4—22no—
76C4×C7×D4—41no—
77C4×C7×D4—41no—
78C2×C7×C4⋊C4C2311yescharacteristic
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C7×C22⋊C4—21no—
81C2×C7×C22⋊C4—21no—
82C2×C7×C22⋊C4—21no—
83C2×C7×C22⋊C4—21no—
84C2×C7×C22⋊C4—21no—
85C2×C7×C22⋊C4—21no—
86C2×C7×C22⋊C4—21no—
87C2×C7×C22⋊C4—44no—
88C2×C7×C22⋊C4D411yescharacteristic
89C2×C7×C22⋊C4D411yescharacteristic
90C2×C42×C7C2311yescharacteristic
91C2×C42×C7C2311yescharacteristic
92C2×C22⋊Dic7—21no—
93C2×C22⋊Dic7—21no—
94#6489—22no—
95#6489C2×C414yescomplemented
96C2×C4⋊Dic7C2311yescharacteristic
97C2×C4⋊Dic7C2311yescharacteristic
98C2×C4⋊Dic7C2311yescharacteristic
99C2×C4⋊Dic7C2311yescharacteristic
100C2×Dic7⋊C4—21no—
101C2×Dic7⋊C4—21no—
102C2×C4×Dic7—21no—
103C2×C4×Dic7—21no—
104C2×C4×Dic7—21no—
105C2×#1136—41no—
106C2×#1136—41no—
107C2×#1136C2×C414yescomplemented
108C22×C7⋊C8C2311yescharacteristic
109C22×C7⋊C8C2311yescharacteristic
110C22×C7⋊C8C2311yescharacteristic
111C22×C7⋊C8C2311yescharacteristic
112C7×#95—21no—
113C7×#95D411yescharacteristic
114C7×#95D411yescharacteristic
115#6406—22no—
116#6406—22no—
117#6406—41no—
118#6406—41no—
119#6406C2×C414yes—
120#6406C2×C414yes—
121#6406C2×C414yescomplemented
122#6406C2×C414yescomplemented
123C7⋊#95—21no—
124C7⋊#95—21no—
125C7⋊#95—21no—
126C7⋊#95—21no—
127C7⋊#95—21no—
128C22⋊(C7⋊C8)—22no—
129#6382—41no—
130#6381—41no—
131#6377—41no—
132C4×C7⋊C8—41no—
133C2×#418—71no—
134#2346—71no—
135D4×C22⋊C4D711yescharacteristic
136#1936—71no—
137#1934—71no—
138#1926—71no—
139#1925—71no—
140#1864—71no—
141#1862—71no—
142#1825—71no—
143#1809—71no—
144#1786—71no—
145#1762—71no—
146C4×#102—71no—
147#1753—71no—
148C24×C7—21no—
149C24×C7—21no—
150C24×C7—24no—
151C24×C7—42no—
152C24×C7—42no—
153C24×C7—42no—
154C24×C7—42no—
155C24×C7—81no—
156C24×C7—81no—
157C24×C7C2×D411yescharacteristic
158C2×C7×D4—28no—
159C2×C7×D4—24no—
160C2×C7×D4—21no—
161C2×C7×D4—21no—
162C2×C7×D4—21no—
163C2×C7×D4—21no—
164C2×C7×D4—21no—
165C2×C7×D4—21no—
166C2×C7×D4—21no—
167C2×C7×D4—21no—
168C2×C7×D4—44no—
169C2×C7×D4—44no—
170C2×C7×D4—44no—
171C2×C7×D4—42no—
172C2×C7×D4—42no—
173C2×C7×D4C22×C412yes—
174C2×C7×D4C22×C412yes—
175C2×C7×D4#4112yes—
176C2×C7×D4#4112yes—
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—42no—
184C22×C4×C7—42no—
185C22×C4×C7—42no—
186C22×C4×C7—42no—
187C22×C4×C7—81no—
188C22×C4×C7—81no—
189C22×C4×C7C22×C412yes—
190C22×C4×C7C2×D411yescharacteristic
191C22×C4×C7C2×D411yescharacteristic
192C22×C4×C7C2×D411yescharacteristic
193C22×C4×C7C2×D411yescharacteristic
194C22×C4×C7C2×D411yescharacteristic
195C22×C4×C7#4112yes—
196C22×C4×C7C2411yescharacteristic
197C22×Dic7—21no—
198C22×Dic7—21no—
199C22×Dic7—21no—
200C22×Dic7—21no—
201C7×C4⋊C4—21no—
202C7×C4⋊C4—21no—
203C7×C4⋊C4—21no—
204C7×C4⋊C4—21no—
205C7×C22⋊C4—22no—
206C7×C22⋊C4—41no—
207C7×C22⋊C4—42no—
208C7×C22⋊C4—42no—
209C7×C22⋊C4—42no—
210C7×C22⋊C4—42no—
211C7×C22⋊C4—42no—
212C7×C22⋊C4—81no—
213C7×C22⋊C4—81no—
214C42×C7—21no—
215C42×C7—21no—
216C42×C7—21no—
217C42×C7—21no—
218C22⋊Dic7—24no—
219C22⋊Dic7—81no—
220C4⋊Dic7—21no—
221C4⋊Dic7—21no—
222C4⋊Dic7—21no—
223C4⋊Dic7—21no—
224C4⋊Dic7—21no—
225C4⋊Dic7—21no—
226C4⋊Dic7C22×C412yes—
227C4⋊Dic7C22×C412yes—
228Dic7⋊C4—81no—
229Dic7⋊C4—81no—
230C4×Dic7—24no—
231C4×Dic7—42no—
232C4×Dic7—42no—
233#1136—44no—
234C2×C7⋊C8—21no—
235C2×C7⋊C8—21no—
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⋊C8C22×C412yes—
245C2×C7⋊C8C22×C412yes—
246C23×D4C2×D711yescharacteristic
247C22×M16—71no—
248C2×C4×D4C2×D711yescharacteristic
249C2×C4×D4C2×D711yescharacteristic
250C2×#117—71no—
251C22×C22⋊C4—21no—
252C2×#107—71no—
253C2×#106—71no—
254#418—78no—
255C2×#102—71no—
256C2×#102—71no—
257C2×#102—71no—
258C2×#102—71no—
259C2×#102—71no—
260C2×#102—71no—
261C2×#102—71no—
262C2×#102—71no—
263C2×C22⋊C8—71no—
264C2×#97—71no—
265C2×C4×C8—71no—
266#390C2×D711yescharacteristic
267#390C2×D711yescharacteristic
268#389—71no—
269#389—71no—
270#388—141no—
271#388—141no—
272#386—21no—
273#386—21no—
274#382—141no—
275#380—71no—
276#380C2×D711yescharacteristic
277#379—21no—
278C4×C4⋊C4—71no—
279C4×C4⋊C4—71no—
280C4×C22⋊C4C2×D711yescharacteristic
281#376—141no—
282#340—71no—
283#340—71no—
284#340—71no—
285#340—71no—
286#340—71no—
287#340—71no—
288#336—71no—
289#336—71no—
290C23×C7—22no—
291C23×C7—22no—
292C23×C7—22no—
293C23×C7—21no—
294C23×C7—21no—
295C23×C7—21no—
296C23×C7—21no—
297C23×C7—21no—
298C23×C7—21no—
299C23×C7—22no—
300C23×C7—48no—
301C23×C7—48no—
302C23×C7—41no—
303C23×C7—41no—
304C23×C7—41no—
305C23×C7—41no—
306C23×C7—41no—
307C23×C7—41no—
308C23×C7—41no—
309C23×C7—41no—
310C23×C7—41no—
311C23×C7—41no—
312C23×C7—84no—
313C23×C7—84no—
314C23×C7—84no—
315C23×C7—84no—
316C23×C7—84no—
317C23×C7C4×D412yes—
318C23×C7C22×D411yescharacteristic
319C7×D4—22no—
320C7×D4—22no—
321C7×D4—22no—
322C7×D4—22no—
323C7×D4—22no—
324C7×D4—48no—
325C7×D4—41no—
326C7×D4—41no—
327C7×D4#11714yes—
328C2×C4×C7—21no—
329C2×C4×C7—21no—
330C2×C4×C7—21no—
331C2×C4×C7—21no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
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—21no—
344C2×C4×C7—21no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—84no—
352C2×C4×C7—84no—
353C2×C4×C7C4×D412yes—
354C2×C4×C7AGL(1,ℤ/8)12yes—
355C2×C4×C7C23×C411yescharacteristic
356C2×C4×C7C2×#4111yescharacteristic
357C2×C4×C7C2×#4111yescharacteristic
358C2×C4×C7C2×#4111yescharacteristic
359C2×C4×C7H(5,𝔽2)11yescharacteristic
360C2×C4×C7H(5,𝔽2)11yescharacteristic
361C2×Dic7—22no—
362C2×Dic7—22no—
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—41no—
373C7⋊C8—22no—
374C7⋊C8—22no—
375C7⋊C8—41no—
376C7⋊C8—41no—
377C25—21no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4—21no—
382C22×D4—41no—
383C22×D4—41no—
384C22×D4C4×D714yes—
385C22×D4C22×D711yescharacteristic
386C22×D4C22×D711yescharacteristic
387C23×C4—21no—
388C23×C4—21no—
389C23×C4C22×D711yescharacteristic
390C2×M16—74no—
391C2×M16—281no—
392C2×M16—281no—
393C22×C8—71no—
394C22×C8—71no—
395C22×C8—71no—
396C22×C8—71no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—41no—
400C4×D4—41no—
401#117—74no—
402#117—142no—
403C2×C4⋊C4—71no—
404C2×C4⋊C4—71no—
405C2×C4⋊C4—71no—
406C2×C4⋊C4—71no—
407C2×C4⋊C4—141no—
408C2×C4⋊C4—141no—
409C2×C4⋊C4C22×D711yescharacteristic
410C2×C4⋊C4C22×D711yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—141no—
420C2×C22⋊C4—141no—
421C2×C22⋊C4C22⋊D711yescharacteristic
422C2×C22⋊C4C22⋊D711yescharacteristic
423C2×C42—141no—
424C2×C42—141no—
425C2×C42—141no—
426C2×C42C22×D711yescharacteristic
427C2×C42C22×D711yescharacteristic
428#107—281no—
429#106—281no—
430#102—74no—
431#102—74no—
432#102—74no—
433#102—74no—
434#102—142no—
435#102—142no—
436#102—281no—
437#102—281no—
438C22⋊C8—142no—
439#97—281no—
440C4×C8—281no—
441#95—21no—
442#95—141no—
443#95—141no—
444#95—141no—
445#95—141no—
446#95—141no—
447#95C22⋊D711yescharacteristic
448#95C22⋊D711yescharacteristic
449C22×C7—22no—
450C22×C7—24no—
451C22×C7—22no—
452C22×C7—22no—
453C22×C7—42no—
454C22×C7—42no—
455C22×C7—42no—
456C22×C7—41no—
457C22×C7—41no—
458C22×C7—42no—
459C22×C7—41no—
460C22×C7—42no—
461C22×C7—42no—
462C22×C7—41no—
463C22×C7—42no—
464C22×C7—42no—
465C22×C7—42no—
466C22×C7—816no—
467C22×C7—81no—
468C22×C7—81no—
469C22×C7—81no—
470C22×C7—81no—
471C22×C7C2×C4×D411yescharacteristic
472C22×C7#54611yescharacteristic
473C22×C7#54611yescharacteristic
474C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
475C22×C7#57511yescharacteristic
476C22×C7#57611yescharacteristic
477C22×C7#57711yescharacteristic
478C4×C7—22no—
479C4×C7—22no—
480C4×C7—41no—
481C4×C7—41no—
482C4×C7—41no—
483C4×C7—81no—
484C4×C7—81no—
485C4×C7C2×#11711yescharacteristic
486C4×C7#51811yescharacteristic
487C4×C7#55111yescharacteristic
488C4×C7#55111yescharacteristic
489Dic7—42no—
490Dic7—42no—
491Dic7—81no—
492Dic7—81no—
493C24—21no—
494C24—21no—
495C24—24no—
496C24—42no—
497C24—42no—
498C24—42no—
499C24—42no—
500C24—81no—
501C24—81no—
502C24C2×C22⋊D711yescharacteristic
503C2×D4—28no—
504C2×D4—24no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4C2×C4×D712yes—
519C2×D4C2×C4×D712yes—
520C2×D4#115912yes—
521C2×D4#115912yes—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—141no—
535C22×C4—141no—
536C22×C4—141no—
537C22×C4—141no—
538C22×C4C2×C4×D712yes—
539C22×C4#115712yes—
540C22×C4C2×C22⋊D711yescharacteristic
541C22×C4C2×C22⋊D711yescharacteristic
542C22×C4C2×C22⋊D711yescharacteristic
543C22×C4C2×C22⋊D711yescharacteristic
544C22×C4C2×C22⋊D711yescharacteristic
545C22×C4C23×D711yescharacteristic
546M16—284no—
547C2×C8—72no—
548C2×C8—72no—
549C2×C8—141no—
550C2×C8—141no—
551C2×C8—141no—
552C2×C8—141no—
553C2×C8—141no—
554C2×C8—141no—
555C2×C8—141no—
556C2×C8—141no—
557C2×C8—141no—
558C2×C8—141no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—72no—
564C4⋊C4—72no—
565C4⋊C4—141no—
566C4⋊C4—141no—
567C4⋊C4—141no—
568C4⋊C4—141no—
569C4⋊C4—141no—
570C4⋊C4—141no—
571C4⋊C4—561no—
572C4⋊C4—561no—
573C22⋊C4—22no—
574C22⋊C4—41no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—81no—
581C22⋊C4—81no—
582C22⋊C4—144no—
583C22⋊C4—561no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—144no—
589C42—282no—
590C42—282no—
591C2×C7—42no—
592C2×C7—44no—
593C2×C7—82no—
594C2×C7#234211yescharacteristic
595C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
596C2×C7#294611yescharacteristic
597C2×C7#331011yescharacteristic
598C2×C7#331911yescharacteristic
599C2×C7#332311yescharacteristic
600C2×C7#332511yescharacteristic
601C23—22no—
602C23—21no—
603C23—22no—
604C23—22no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—22no—
611C23—48no—
612C23—48no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—84no—
624C23—84no—
625C23—84no—
626C23—84no—
627C23—84no—
628C23C4×C22⋊D712yes—
629C23C22×C22⋊D711yescharacteristic
630D4—22no—
631D4—22no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—48no—
636D4—41no—
637D4—41no—
638D4#644014yes—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—84no—
663C2×C4—84no—
664C2×C4—142no—
665C2×C4—142no—
666C2×C4—281no—
667C2×C4—281no—
668C2×C4—281no—
669C2×C4—281no—
670C2×C4—281no—
671C2×C4—281no—
672C2×C4—281no—
673C2×C4—281no—
674C2×C4—281no—
675C2×C4—281no—
676C2×C4C4×C22⋊D712yes—
677C2×C4#649512yes—
678C2×C4C22×C4×D711yescharacteristic
679C2×C4C2×#115711yescharacteristic
680C2×C4C2×#115911yescharacteristic
681C2×C4C2×#115911yescharacteristic
682C2×C4#654811yescharacteristic
683C2×C4#654811yescharacteristic
684C8—142no—
685C8—142no—
686C8—281no—
687C8—281no—
688C7#2258411yescharacteristic, complemented, Sylow
689C22—22no—
690C22—22no—
691C22—22no—
692C22—24no—
693C22—42no—
694C22—41no—
695C22—42no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—816no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×C4×C22⋊D711yescharacteristic
712C22C2×#649511yescharacteristic
713C22#9049711yescharacteristic
714C22#9049711yescharacteristic
715C22#9051311yescharacteristic
716C22#9052611yescharacteristic
717C22#9052711yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—81no—
724C4—81no—
725C4—282no—
726C4—282no—
727C4—561no—
728C4—561no—
729C4C2×#644011yescharacteristic
730C4#9017711yescharacteristic
731C4#9018611yescharacteristic
732C4#9018611yescharacteristic
733C2—42no—
734C2—44no—
735C2—82no—
736C2#1173954311yescharacteristic
737C2C4×#649511yescharacteristic
738C2#1173998211yescharacteristic
739C2#1174092911yescharacteristic
740C2#1174093211yescharacteristic
741C2#1174094411yescharacteristic
742C2#1174094611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×D4×C22⋊C4C2
socleC23×C7C22×D4
prime radicalC23×C7×D4C22
cosocleC22×C4×C7C24
hypercenterD4×C22⋊C4D7
hypocenterC7#22584
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #11730904C2semidirect
5. #11729363C2semidirect
6. C4×#6406C2semidirect
7. #11729361C2semidirect
8. #11729360C2semidirect
9. #11727399C2semidirect
10. #11727398C2semidirect
11. #11727391C2semidirect
12. #11727390C2semidirect
13. #11727267C2semidirect
14. #11727257C2semidirect
15. #11727202C2semidirect
29. #89987C4semidirect
40. C2×#6382C22semidirect
41. C2×#6381C22semidirect
44. C4×C4⋊Dic7C22semidirect
45. C4×C4⋊Dic7C22semidirect
46. #89700C22semidirect
47. #89700C22semidirect
48. C2×#6377C22semidirect
49. C2×C4×C7⋊C8C22semidirect
52. #89324C22semidirect
53. #89324C22semidirect
54. #89324C22semidirect
55. #89324C22semidirect
56. #89324C22semidirect
57. #89324C22semidirect
58. #89319C22semidirect
59. #89319C22semidirect
95. #6489C2×C4semidirect
107. C2×#1136C2×C4semidirect
121. #6406C2×C4semidirect
122. #6406C2×C4semidirect
688. C7#22584semidirect

Maximal subgroups

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

subgroupindex
C7×D4×C22⋊C42
C2×#899872
#117309042
#117298822
#117293632
C4×#64062
#117293612
#117293602
#117273992
#117273982
#117273912
#117273902
#117272672
#117272572
#117272022
#225847