Finite Group Databasebeta

← #34328879

Subgroups — #34328879

Order 20224.

922 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098785C211yesmaximal, characteristic, complemented
2C2×#19098616C211yesmaximal, characteristic, complemented
3#23771701C211yesmaximal, characteristic
4#23764596C211yesmaximal, characteristic, complemented
5#23764582C211yesmaximal, characteristic
6#23764408C211yesmaximal, characteristic, complemented
7#23764401C211yesmaximal, characteristic
8#23764332C211yesmaximal, characteristic, complemented
9#23764260C211yesmaximal, characteristic, complemented
10#23764257C211yesmaximal, characteristic, complemented
11#23764168C211yesmaximal, characteristic, complemented
12#23764082C211yesmaximal, characteristic, complemented
13#23764075C211yesmaximal, characteristic, complemented
14#23763415C211yesmaximal, characteristic, complemented
15C4×C22⋊Q8×C79C211yesmaximal, characteristic, complemented
16C22×#11929614C2211yescharacteristic
17C22×#11929611C2211yescharacteristic
18C2×#14579149C2211yescharacteristic
19C2×#14579140C2211yescharacteristic
20C2×#14579135C2211yescharacteristic
21#19098785—24no—
22#19098616—24no—
23C2×#14579094C2211yescharacteristic
24C2×#14579092C2211yescharacteristic
25C2×C4⋊(C79⋊C8)C2211yescharacteristic
26C2×C4⋊(C79⋊C8)C2211yescharacteristic
27C2×#14579085C2211yescharacteristic
28C2×#14579085C2211yescharacteristic
29C2×#14579084C2211yescharacteristic
30C2×#14579084C2211yescharacteristic
31C2×#14579084C2211yescharacteristic
32C2×#14579081C2211yescharacteristic
33C2×#14579081C2211yescharacteristic
34C2×#14579081C2211yescharacteristic
35C2×C22⋊(C79⋊C8)C2211yescharacteristic
36C2×C22⋊(C79⋊C8)C2211yescharacteristic
37C2×C4×C79⋊C8C2211yescharacteristic
38C2×C4×C79⋊C8C2211yescharacteristic
39#19098469C2211yescharacteristic
40#19098465C2211yescharacteristic
41#19098454—21no—
42#19098454—21no—
43#19098442—21no—
44#19098442—21no—
45#19098429C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098325C2211yescharacteristic
50C2×C22⋊Q8×C79C2211yescharacteristic
51C2×C4×Q8×C79C2211yescharacteristic
52C22×C42×C79C2211yescharacteristic
53#391×C79C2211yescharacteristic
54#389×C79C2211yescharacteristic
55#387×C79—21no—
56#385×C79—21no—
57#380×C79C2211yescharacteristic
58C4×C4⋊C4×C79—21no—
59C4×C4⋊C4×C79C2211yescharacteristic
60C4×C22⋊C4×C79—21no—
61C22×Dic158C2311yescharacteristic
62C22×D316C2311yescharacteristic
63C22×C22⋊D79—21no—
64C2×#11929614—22no—
65C2×#11929614—22no—
66C2×#11929614—41no—
67C2×#11929611—22no—
68C2×#11929611—22no—
69C2×#11929611—41no—
70C22×C79⋊C8C2311yescharacteristic
71C22×C79⋊C8C2311yescharacteristic
72C22×C79⋊C8C2311yescharacteristic
73C22×C79⋊C8C2311yescharacteristic
74#14579149—22no—
75#14579149—22no—
76#14579140—41no—
77#14579140—41no—
78#14579135—41no—
79#14579135—41no—
80C2×C4⋊Dic79C2311yescharacteristic
81C2×C4⋊Dic79C2311yescharacteristic
82C2×Dic79⋊C4—21no—
83C2×C22⋊Dic79—21no—
84C2×(C2×D79)⋊C4—21no—
85C2×(C2×D79)⋊C4—21no—
86C2×(C2×D79)⋊C4—21no—
87C2×(C2×D79)⋊C4—21no—
88C2×(C2×D79)⋊C4—21no—
89#14579094—41no—
90#14579092—41no—
91C4⋊(C79⋊C8)—22no—
92C4⋊(C79⋊C8)D414yescomplemented
93#14579085—41no—
94#14579085—41no—
95#14579084—22no—
96#14579084—22no—
97#14579084—41no—
98#14579081—22no—
99#14579081—22no—
100#14579081—41no—
101C22⋊(C79⋊C8)—22no—
102C22⋊(C79⋊C8)—22no—
103C4×C79⋊C8—22no—
104C4×C79⋊C8—22no—
105C79⋊#95—21no—
106C79⋊#95—21no—
107C79⋊#95—21no—
108C79⋊#95—21no—
109C22×Q8×C79C2311yescharacteristic
110C23×C4×C79D411yescharacteristic
111C23×C4×C79D411yescharacteristic
112C23×C4×C79C2311yescharacteristic
113C22⋊Q8×C79—22no—
114C22⋊Q8×C79—22no—
115C4×Q8×C79—22no—
116C4×Q8×C79—22no—
117C2×C4⋊C4×C79—21no—
118C2×C4⋊C4×C79—21no—
119C2×C4⋊C4×C79—21no—
120C2×C4⋊C4×C79C2311yescharacteristic
121C2×C4⋊C4×C79C2311yescharacteristic
122C2×C4⋊C4×C79C2311yescharacteristic
123C2×C22⋊C4×C79—21no—
124C2×C22⋊C4×C79—21no—
125C2×C42×C79—22no—
126C2×C42×C79—22no—
127C2×C42×C79—21no—
128C2×C42×C79—21no—
129C2×C42×C79D411yescharacteristic
130C2×C42×C79D411yescharacteristic
131C2×C42×C79C2311yescharacteristic
132C2×C42×C79C2311yescharacteristic
133#95×C79—21no—
134#95×C79—21no—
135#95×C79—21no—
136#95×C79—21no—
137#95×C79—21no—
138C23×D79—21no—
139C2×Dic158—21no—
140C2×Dic158—21no—
141C2×Dic158—21no—
142C2×Dic158—21no—
143C2×Dic158—21no—
144C2×Dic158—21no—
145C2×D316—21no—
146C2×D316—21no—
147C2×D316—21no—
148C2×D316—21no—
149C2×D316—21no—
150C2×D316—21no—
151C2×C22⋊D79—42no—
152C2×C22⋊D79—42no—
153C2×C22⋊D79—42no—
154C22×Dic79—21no—
155C22×Dic79—21no—
156C22×Dic79—21no—
157#11929614—44no—
158#11929611—44no—
159C2×C79⋊C8—21no—
160C2×C79⋊C8—21no—
161C2×C79⋊C8—21no—
162C2×C79⋊C8—21no—
163C2×C79⋊C8—21no—
164C2×C79⋊C8—21no—
165C2×C79⋊C8—21no—
166C2×C79⋊C8—21no—
167C2×C79⋊C8—21no—
168C2×C79⋊C8—21no—
169C2×C79⋊C8C2×D412yes—
170C2×C79⋊C8C2×D412yes—
171C4⋊Dic79—21no—
172C4⋊Dic79—21no—
173C4⋊Dic79—21no—
174C4⋊Dic79—21no—
175Dic79⋊C4—42no—
176C22⋊Dic79—42no—
177(C2×D79)⋊C4—42no—
178(C2×D79)⋊C4—42no—
179(C2×D79)⋊C4—42no—
180(C2×D79)⋊C4—42no—
181(C2×D79)⋊C4—42no—
182C24×C79C2×D411yescharacteristic
183C2×Q8×C79—21no—
184C2×Q8×C79—21no—
185C2×Q8×C79—21no—
186C2×Q8×C79—21no—
187C2×Q8×C79—21no—
188C2×Q8×C79#4112yes—
189C22×C4×C79—22no—
190C22×C4×C79—22no—
191C22×C4×C79—22no—
192C22×C4×C79—21no—
193C22×C4×C79—21no—
194C22×C4×C79—22no—
195C22×C4×C79—22no—
196C22×C4×C79—21no—
197C22×C4×C79—21no—
198C22×C4×C79—21no—
199C22×C4×C79—21no—
200C22×C4×C79—21no—
201C22×C4×C79—21no—
202C22×C4×C79—21no—
203C22×C4×C79—21no—
204C22×C4×C79—41no—
205C22×C4×C79C2×D411yescharacteristic
206C22×C4×C79C2×D411yescharacteristic
207C22×C4×C79C2×D411yescharacteristic
208C22×C4×C79C2×D411yescharacteristic
209C22×C4×C79C2×D411yescharacteristic
210C22×C4×C79C2411yescharacteristic
211C4⋊C4×C79—24no—
212C4⋊C4×C79—21no—
213C4⋊C4×C79—21no—
214C4⋊C4×C79—21no—
215C4⋊C4×C79—21no—
216C4⋊C4×C79—21no—
217C4⋊C4×C79—42no—
218C4⋊C4×C79—42no—
219C4⋊C4×C79#4112yes—
220C22⋊C4×C79—24no—
221C22⋊C4×C79—42no—
222C42×C79—22no—
223C42×C79—22no—
224C42×C79—21no—
225C42×C79—21no—
226C42×C79—42no—
227C42×C79—42no—
228C42×C79C2×D412yes—
229C42×C79#4112yes—
230C23×C79—21no—
231C23×C79—21no—
232C23×C79—21no—
233C23×C79—21no—
234C23×C79—21no—
235C23×C79—21no—
236C23×C79#13512yes—
237C23×C79C22×D411yescharacteristic
238C22×D79—41no—
239C22×D79—41no—
240C22×D79—41no—
241C22×D79—41no—
242C22×D79—41no—
243C22×D79—41no—
244C22×D79—41no—
245Q8×C79—22no—
246Q8×C79—22no—
247Q8×C79—41no—
248Q8×C79—41no—
249C2×C4×C79—28no—
250C2×C4×C79—21no—
251C2×C4×C79—21no—
252C2×C4×C79—21no—
253C2×C4×C79—21no—
254C2×C4×C79—21no—
255C2×C4×C79—21no—
256C2×C4×C79—21no—
257C2×C4×C79—21no—
258C2×C4×C79—21no—
259C2×C4×C79—22no—
260C2×C4×C79—22no—
261C2×C4×C79—21no—
262C2×C4×C79—21no—
263C2×C4×C79—44no—
264C2×C4×C79—41no—
265C2×C4×C79—41no—
266C2×C4×C79—41no—
267C2×C4×C79—41no—
268C2×C4×C79—41no—
269C2×C4×C79—41no—
270C2×C4×C79—41no—
271C2×C4×C79—41no—
272C2×C4×C79—41no—
273C2×C4×C79—41no—
274C2×C4×C79—41no—
275C2×C4×C79—41no—
276C2×C4×C79—41no—
277C2×C4×C79—41no—
278C2×C4×C79#12112yes—
279C2×C4×C79#12112yes—
280C2×C4×C79#13512yes—
281C2×C4×C79#13712yes—
282C2×C4×C79C22×D411yescharacteristic
283C2×C4×C79C2×#4111yescharacteristic
284C2×C4×C79C2×#4111yescharacteristic
285C2×C4×C79C2×#4111yescharacteristic
286C2×C4×C79H(5,𝔽2)11yescharacteristic
287C2×C4×C79H(5,𝔽2)11yescharacteristic
288C22⋊D79—84no—
289C2×Dic79—41no—
290C2×Dic79—41no—
291C2×Dic79—41no—
292C2×Dic79—41no—
293C2×Dic79—41no—
294C2×Dic79—41no—
295C2×Dic79—41no—
296C2×Dic79—41no—
297C2×Dic79—41no—
298D316—41no—
299D316—41no—
300D316—41no—
301D316—41no—
302Dic158—41no—
303Dic158—41no—
304Dic158—41no—
305Dic158—41no—
306C79⋊C8—22no—
307C79⋊C8—22no—
308C79⋊C8—41no—
309C79⋊C8—41no—
310C22×C79—22no—
311C22×C79—22no—
312C22×C79—22no—
313C22×C79—41no—
314C22×C79—41no—
315C22×C79—41no—
316C22×C79—41no—
317C22×C79C2×#12111yescharacteristic
318C22×C79#52511yescharacteristic
319C22×C79#53511yescharacteristic
320C22×C79C2×#13511yescharacteristic
321C22×C79C2×#13511yescharacteristic
322C22×C79C2×#13711yescharacteristic
323C22×C79#57511yescharacteristic
324C2×D79—81no—
325C2×D79—81no—
326C2×D79—81no—
327C2×D79—81no—
328C2×D79—81no—
329C2×D79—81no—
330C2×D79—81no—
331C4×C79—22no—
332C4×C79—22no—
333C4×C79—22no—
334C4×C79—22no—
335C4×C79—42no—
336C4×C79—41no—
337C4×C79—42no—
338C4×C79—81no—
339C4×C79—81no—
340C4×C79#54611yescharacteristic
341C4×C79#55011yescharacteristic
342C4×C79#55311yescharacteristic
343C4×C79#55511yescharacteristic
344Dic79—81no—
345Dic79—81no—
346Dic79—81no—
347#24655—791nomaximal, Sylow
348C2×C79—42no—
349C2×C79#241411yescharacteristic
350C2×C79#305011yescharacteristic
351C2×C79#305611yescharacteristic
352C2×C79#310211yescharacteristic
353C2×C79#310811yescharacteristic
354C2×C79#321011yescharacteristic
355C2×C79#321111yescharacteristic
356D79—161no—
357C2×#464—791no—
358C2×#431—791no—
359#2850—791no—
360C4×C22⋊Q8D7911yescharacteristic, complemented
361#2035—791no—
362#2033—791no—
363#2001—791no—
364#2000—791no—
365#1983—791no—
366#1969—791no—
367#1968—791no—
368#1949—791no—
369#1934—791no—
370#1933—791no—
371#1805—791no—
372C79#2465511yescharacteristic, complemented, Sylow
373C22×Q16—791no—
374C22×SD16—791no—
375C2×#124—791no—
376C2×C22⋊Q8—791no—
377C2×C22⋊Q8C2×D7911yescharacteristic
378C2×#121—791no—
379C2×C4×Q8C2×D7911yescharacteristic
380C22×C42C2×D7911yescharacteristic
381#464—1584no—
382#431—1584no—
383C2×#107—791no—
384C2×#106—791no—
385C2×C4⋊C8—791no—
386C2×C4⋊C8—791no—
387C2×#103—791no—
388C2×#103—791no—
389C2×#103—791no—
390C2×#103—791no—
391C2×#103—791no—
392C2×#102—791no—
393C2×#102—791no—
394C2×#102—791no—
395C2×C22⋊C8—791no—
396C2×C22⋊C8—791no—
397C2×C4×C8—791no—
398C2×C4×C8—791no—
399#391—791no—
400#391C2×D7911yescharacteristic
401#390—791no—
402#389C2×D7911yescharacteristic
403#388—1581no—
404#388—1581no—
405#387—21no—
406#386—1581no—
407#386—1581no—
408#385—21no—
409#382—791no—
410#380C2×D7911yescharacteristic
411C4×C4⋊C4—21no—
412C4×C4⋊C4C2×D7911yescharacteristic
413C4×C22⋊C4—21no—
414#340—791no—
415#340—791no—
416#340—791no—
417#340—791no—
418C22×Q8—791no—
419C22×Q8C22×D7911yescharacteristic
420C22×D4—791no—
421C22×D4—1581no—
422C23×C4C22⋊D7911yescharacteristic
423C23×C4C22⋊D7911yescharacteristic
424C23×C4C22×D7911yescharacteristic
425C2×Q16—3161no—
426C2×Q16—1582no—
427C2×Q16—1582no—
428C2×SD16—3161no—
429C2×SD16—1582no—
430C2×SD16—1582no—
431C22×C8—791no—
432C22×C8—791no—
433C22×C8—791no—
434C22×C8—791no—
435#124—1582no—
436#124—1582no—
437C22⋊Q8—22no—
438C22⋊Q8—22no—
439C22⋊Q8—3161no—
440C22⋊Q8—3161no—
441#121—3161no—
442#121—3161no—
443C4×Q8—22no—
444C4×Q8—22no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—791no—
449C2×C4⋊C4—791no—
450C2×C4⋊C4—1581no—
451C2×C4⋊C4C22×D7911yescharacteristic
452C2×C4⋊C4C22×D7911yescharacteristic
453C2×C4⋊C4C22×D7911yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—1581no—
457C2×C22⋊C4—1581no—
458C2×C22⋊C4—1581no—
459C2×C22⋊C4—1581no—
460C2×C22⋊C4—1581no—
461C2×C22⋊C4—1581no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42C22⋊D7911yescharacteristic
467C2×C42C22⋊D7911yescharacteristic
468C2×C42C22×D7911yescharacteristic
469C2×C42C22×D7911yescharacteristic
470#107—3161no—
471#106—3161no—
472C4⋊C8—794no—
473C4⋊C8—1582no—
474#103—3161no—
475#103—3161no—
476#103—3161no—
477#103—1582no—
478#103—1582no—
479#102—3161no—
480#102—1582no—
481#102—1582no—
482C22⋊C8—1582no—
483C22⋊C8—1582no—
484C4×C8—1582no—
485C4×C8—1582no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—1581no—
492#95—1581no—
493#95—1581no—
494#95—1581no—
495C24—1581no—
496C24C2×C22⋊D7911yescharacteristic
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—1581no—
503C2×Q8—1581no—
504C2×Q8—1581no—
505C2×Q8—1581no—
506C2×Q8—1581no—
507C2×Q8—1581no—
508C2×Q8#1192962412yes—
509C2×D4—3162no—
510C2×D4—3162no—
511C2×D4—3162no—
512C2×D4—1581no—
513C2×D4—1581no—
514C2×D4—1581no—
515C2×D4—1581no—
516C2×D4—1581no—
517C2×D4—1581no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—41no—
534C22×C4—1581no—
535C22×C4—1581no—
536C22×C4—1581no—
537C22×C4C2×C22⋊D7911yescharacteristic
538C22×C4C2×C22⋊D7911yescharacteristic
539C22×C4C2×C22⋊D7911yescharacteristic
540C22×C4C2×C22⋊D7911yescharacteristic
541C22×C4C2×C22⋊D7911yescharacteristic
542C22×C4C23×D7911yescharacteristic
543Q16—3164no—
544SD16—3164no—
545C2×C8—792no—
546C2×C8—792no—
547C2×C8—1581no—
548C2×C8—1581no—
549C2×C8—1581no—
550C2×C8—1581no—
551C2×C8—1581no—
552C2×C8—1581no—
553C2×C8—1581no—
554C2×C8—1581no—
555C2×C8—1581no—
556C2×C8—1581no—
557C4⋊C4—24no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—3162no—
566C4⋊C4—1581no—
567C4⋊C4—1581no—
568C4⋊C4—1581no—
569C4⋊C4—1581no—
570C4⋊C4#1192962412yes—
571C22⋊C4—24no—
572C22⋊C4—42no—
573C22⋊C4—3162no—
574C22⋊C4—3162no—
575C22⋊C4—3162no—
576C22⋊C4—3162no—
577C22⋊C4—3162no—
578C22⋊C4—3162no—
579C42—21no—
580C42—22no—
581C42—22no—
582C42—21no—
583C42—42no—
584C42—42no—
585C42D4×D7912yes—
586C42#1192962312yes—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—3161no—
594C23—3161no—
595C23—3161no—
596C23—3161no—
597C23—3161no—
598C23—3161no—
599C23—3161no—
600C23#1457918112yes—
601C23C22×C22⋊D7911yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606Q8—3161no—
607Q8—3161no—
608Q8—3161no—
609Q8—3161no—
610D4—3161no—
611D4—3161no—
612D4—3161no—
613D4—3161no—
614D4—6324no—
615C2×C4—28no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—44no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—3161no—
645C2×C4—3161no—
646C2×C4—3161no—
647C2×C4—3161no—
648C2×C4—3161no—
649C2×C4—3161no—
650C2×C4—3161no—
651C2×C4—3161no—
652C2×C4—3161no—
653C2×C4#1457913312yes—
654C2×C4#1457913312yes—
655C2×C4#1457918112yes—
656C2×C4#1457919212yes—
657C2×C4C2×D4×D7911yescharacteristic
658C2×C4C2×#1192962311yescharacteristic
659C2×C4C2×#1192962411yescharacteristic
660C2×C4C2×#1192962411yescharacteristic
661C2×C4#1457920711yescharacteristic
662C2×C4#1457920711yescharacteristic
663C8—3161no—
664C8—3161no—
665C8—1582no—
666C8—1582no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—6321no—
675C22—6321no—
676C22—6321no—
677C22—6321no—
678C22—6321no—
679C22—6321no—
680C22—6321no—
681C22C2×#1457913311yescharacteristic
682C22#1909907411yescharacteristic
683C22#1909912711yescharacteristic
684C22C2×#1457918111yescharacteristic
685C22C2×#1457918111yescharacteristic
686C22C2×#1457919211yescharacteristic
687C22#1909936111yescharacteristic
688C4—22no—
689C4—22no—
690C4—22no—
691C4—22no—
692C4—41no—
693C4—42no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—6321no—
698C4—6321no—
699C4—6321no—
700C4#1909920911yescharacteristic
701C4#1909923411yescharacteristic
702C4#1909925911yescharacteristic
703C4#1909927811yescharacteristic
704C2—42no—
705C2—12641no—
706C2#2376681811yescharacteristic
707C2#2377297811yescharacteristic
708C2#2377302611yescharacteristic
709C2#2377341811yescharacteristic
710C2#2377348011yescharacteristic
711C2#2377435211yescharacteristic
712C2#2377436111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
FittingC4×C22⋊Q8×C79C2
socleC23×C79C22×D4
prime radicalC2×#14579135C22
hypercenterC4×C22⋊Q8D79
hypocenterC79#24655
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#19098785C2semidirect
2. C2×#19098616C2semidirect
4. #23764596C2semidirect
6. #23764408C2semidirect
8. #23764332C2semidirect
9. #23764260C2semidirect
10. #23764257C2semidirect
11. #23764168C2semidirect
12. #23764082C2semidirect
13. #23764075C2semidirect
14. #23763415C2semidirect
15. C4×C22⋊Q8×C79C2semidirect
92. C4⋊(C79⋊C8)D4semidirect
360. C4×C22⋊Q8D79semidirect
372. C79#24655semidirect

Maximal subgroups

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

subgroupindex
C2×#190987852
C2×#190986162
#237717012
#237645962
#237645822
#237644082
#237644012
#237643322
#237642602
#237642572
#237641682
#237640822
#237640752
#237634152
C4×C22⋊Q8×C792
#2465579