Finite Group Databasebeta

← #33108574

Subgroups — #33108574

Order 18688.

1066 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988814C211yesmaximal, characteristic
2C2×C4×#11924016C211yesmaximal, characteristic, complemented
3C22×#14556522C211yesmaximal, characteristic, complemented
4#22612934C211yesmaximal, characteristic, complemented
5#22610784C211yesmaximal, characteristic, complemented
6#22610656C211yesmaximal, characteristic, complemented
7#22610565C211yesmaximal, characteristic, complemented
8#22610555C211yesmaximal, characteristic, complemented
9#22610249C211yesmaximal, characteristic
10#22610238C211yesmaximal, characteristic, complemented
11#22610198C211yesmaximal, characteristic, complemented
12#22610192C211yesmaximal, characteristic, complemented
13C4×#14556522C211yesmaximal, characteristic, complemented
14C22⋊C4×#10596831C211yesmaximal, characteristic, complemented
15C73×#2361C211yesmaximal, characteristic
16C22×#11924016C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C2×#14556570C2211yescharacteristic
19C2×C4×Dic146C2211yescharacteristic
20C22×C4⋊Dic73C2211yescharacteristic
21#17988814C418yescomplemented
22C4×#11924016—24no—
23C2×#14556522—24no—
24C2×#14556522C2211yescharacteristic
25C2×#14556522C2211yescharacteristic
26C2×#14556522C2211yescharacteristic
27C2×#14556522C2211yescharacteristic
28C2×#14556522C2211yescharacteristic
29C2×#14556514C2211yescharacteristic
30C2×#14556514C2211yescharacteristic
31C2×#14556514C2211yescharacteristic
32C2×#14556512C2211yescharacteristic
33C2×#14556512C2211yescharacteristic
34C2×#14556512C2211yescharacteristic
35C2×C22⋊#10596831C2211yescharacteristic
36C2×C4×#10596831C2211yescharacteristic
37C2×C4×#10596831C2211yescharacteristic
38#17988493C2211yescharacteristic
39#17988485C2211yescharacteristic
40#17988484—21no—
41#17988474—21no—
42#17988459—21no—
43C4×C4⋊Dic73C2211yescharacteristic
44C22⋊C4×Dic73—21no—
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988342C2211yescharacteristic
50#17988342C2211yescharacteristic
51C2×#121×C73C2211yescharacteristic
52C2×C4×D4×C73—21no—
53C2×C4×D4×C73C2211yescharacteristic
54C22×C4⋊C4×C73C2211yescharacteristic
55#390×C73C2211yescharacteristic
56#389×C73C2211yescharacteristic
57#388×C73—21no—
58#386×C73—21no—
59#385×C73—21no—
60C4×C4⋊C4×C73C2211yescharacteristic
61C4×C22⋊C4×C73C2211yescharacteristic
62C22×Dic146C2311yescharacteristic
63C23×Dic73—21no—
64C2×#11924016—22no—
65C2×#11924016—22no—
66C2×#11924016C2×C414yescomplemented
67C22×#10596831—22no—
68C22×#10596831—22no—
69C22×#10596831C2×C414yescomplemented
70C22×#10596831C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74#14556570—22no—
75#14556570C2×C414yescomplemented
76C4×Dic146—22no—
77C4×Dic146—41no—
78C2×C4⋊Dic73—22no—
79C2×C4⋊Dic73—21no—
80C2×C4⋊Dic73—41no—
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×#11924007—21no—
85C2×#11924007—21no—
86C2×#11924007—21no—
87C2×C22⋊Dic73—21no—
88C2×C4×Dic73—21no—
89C2×C4×Dic73—21no—
90#14556522—22no—
91#14556522—22no—
92#14556522—22no—
93#14556522C2×C414yescomplemented
94#14556522D414yescomplemented
95#14556514—22no—
96#14556514—41no—
97#14556514C2×C414yescomplemented
98#14556512—22no—
99#14556512—41no—
100#14556512C2×C414yescomplemented
101C22⋊#10596831—22no—
102C4×#10596831—22no—
103C4×#10596831—22no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107#14556498—21no—
108C22×D4×C73—21no—
109C22×D4×C73C2311yescharacteristic
110C23×C4×C73—21no—
111C23×C4×C73—21no—
112C23×C4×C73C2311yescharacteristic
113#121×C73—22no—
114#121×C73C2×C414yes—
115C4×D4×C73—22no—
116C4×D4×C73—41no—
117C4×D4×C73—44no—
118C2×C4⋊C4×C73—22no—
119C2×C4⋊C4×C73—21no—
120C2×C4⋊C4×C73—21no—
121C2×C4⋊C4×C73—41no—
122C2×C4⋊C4×C73C2311yescharacteristic
123C2×C4⋊C4×C73C2311yescharacteristic
124C2×C4⋊C4×C73C2311yescharacteristic
125C2×C22⋊C4×C73—21no—
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73D411yescharacteristic
130C2×C22⋊C4×C73D411yescharacteristic
131C2×C42×C73—21no—
132C2×C42×C73C2311yescharacteristic
133C2×C42×C73C2311yescharacteristic
134#95×C73—21no—
135#95×C73—21no—
136#95×C73D411yescharacteristic
137#95×C73D411yescharacteristic
138C2×Dic146—21no—
139C2×Dic146—21no—
140C2×Dic146—21no—
141C2×Dic146—21no—
142C2×Dic146—21no—
143C2×Dic146C22×C412yes—
144C22×Dic73—21no—
145C22×Dic73—21no—
146C22×Dic73—21no—
147C22×Dic73—21no—
148C22×Dic73—42no—
149C22×Dic73—42no—
150C22×Dic73—81no—
151#11924016—28no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—28no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831C22×C412yes—
162C2×#10596831C22×C412yes—
163C2×#10596831C2×D412yes—
164C2×#10596831#4112yes—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73—42no—
170C4⋊Dic73C22×C412yes—
171C4⋊Dic73C2×D412yes—
172#11924007—24no—
173#11924007—42no—
174#11924007—81no—
175C22⋊Dic73—24no—
176C4×Dic73—42no—
177C4×Dic73—81no—
178C24×C73—21no—
179C24×C73C2×D411yescharacteristic
180C2×D4×C73—24no—
181C2×D4×C73—21no—
182C2×D4×C73—21no—
183C2×D4×C73—21no—
184C2×D4×C73—21no—
185C2×D4×C73—21no—
186C2×D4×C73—42no—
187C2×D4×C73—42no—
188C2×D4×C73C22×C412yes—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—42no—
197C22×C4×C73—42no—
198C22×C4×C73—42no—
199C22×C4×C73—42no—
200C22×C4×C73—81no—
201C22×C4×C73—81no—
202C22×C4×C73C22×C412yes—
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2×D411yescharacteristic
205C22×C4×C73C2×D411yescharacteristic
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73C2×D411yescharacteristic
208C22×C4×C73#4112yes—
209C22×C4×C73C2411yescharacteristic
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—42no—
215C4⋊C4×C73—42no—
216C4⋊C4×C73C22×C412yes—
217C4⋊C4×C73C2×D412yes—
218C22⋊C4×C73—22no—
219C22⋊C4×C73—24no—
220C22⋊C4×C73—42no—
221C22⋊C4×C73—42no—
222C22⋊C4×C73—81no—
223C22⋊C4×C73SD1614yescomplemented
224C42×C73—21no—
225C42×C73—21no—
226C42×C73—21no—
227C42×C73—21no—
228C42×C73—42no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—22no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73C4×D412yes—
241C23×C73C2×SD1612yes—
242C23×C73#13512yes—
243C23×C73C22×D411yescharacteristic
244D4×C73—22no—
245D4×C73—22no—
246D4×C73—48no—
247D4×C73—41no—
248D4×C73—41no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
260C2×C4×C73—21no—
261C2×C4×C73—22no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—84no—
275C2×C4×C73—84no—
276C2×C4×C73C4×D412yes—
277C2×C4×C73C2×SD1612yes—
278C2×C4×C73C2×SD1612yes—
279C2×C4×C73C23×C411yescharacteristic
280C2×C4×C73C22×D411yescharacteristic
281C2×C4×C73C2×#4111yescharacteristic
282C2×C4×C73C2×#4111yescharacteristic
283C2×C4×C73H(5,𝔽2)11yescharacteristic
284C2×C4×C732−1+411yescharacteristic
285C2×Dic73—22no—
286C2×Dic73—22no—
287C2×Dic73—22no—
288C2×Dic73—41no—
289C2×Dic73—41no—
290C2×Dic73—41no—
291C2×Dic73—41no—
292C2×Dic73—41no—
293C2×Dic73—41no—
294C2×Dic73—41no—
295C2×Dic73—41no—
296C2×Dic73—41no—
297C2×Dic73—84no—
298Dic146—22no—
299Dic146—22no—
300Dic146—41no—
301Dic146—41no—
302#10596831—22no—
303#10596831—41no—
304#10596831—41no—
305#10596831C4×D414yescomplemented
306C22×C73—22no—
307C22×C73—22no—
308C22×C73—22no—
309C22×C73—22no—
310C22×C73—22no—
311C22×C73—22no—
312C22×C73—42no—
313C22×C73—42no—
314C22×C73—42no—
315C22×C73—81no—
316C22×C73—81no—
317C22×C73—81no—
318C22×C73—81no—
319C22×C73C4×SD1614yescomplemented
320C22×C73C2×C4×D411yescharacteristic
321C22×C73D4211yescharacteristic
322C22×C73#54711yescharacteristic
323C22×C73C22×SD1611yescharacteristic
324C22×C73C2×#13511yescharacteristic
325C22×C73#57711yescharacteristic
326C22×C73#57711yescharacteristic
327C4×C73—22no—
328C4×C73—22no—
329C4×C73—22no—
330C4×C73—41no—
331C4×C73—42no—
332C4×C73—42no—
333C4×C73—41no—
334C4×C73—81no—
335C4×C73C2×C4×D411yescharacteristic
336C4×C73#52011yescharacteristic
337C4×C73#54811yescharacteristic
338C4×C73#55311yescharacteristic
339Dic73—42no—
340Dic73—42no—
341Dic73—42no—
342Dic73—81no—
343#23022—731nomaximal, Sylow
344C2×C73—24no—
345C2×C73—82no—
346C2×C73#236111yescharacteristic
347C2×C73C2×C4×SD1611yescharacteristic
348C2×C73#295211yescharacteristic
349C2×C73D4×SD1611yescharacteristic
350C2×C73#328211yescharacteristic
351C2×C73#333511yescharacteristic
352C2×C73#333711yescharacteristic
353C2×#465—731no—
354C2×C4×SD16—731no—
355C22×#106—731no—
356#2361D7311yescharacteristic
357#2360—731no—
358#1968—731no—
359#1941—731no—
360#1927—731no—
361#1926—731no—
362#1874—731no—
363#1872—731no—
364#1865—731no—
365#1864—731no—
366C4×#106—731no—
367C8×C22⋊C4—731no—
368C73#2302211yescharacteristic, complemented, Sylow
369C22×SD16—731no—
370C23×C8—731no—
371C2×C22⋊Q8—731no—
372C2×#121C2×D7311yescharacteristic
373C2×C4×Q8—731no—
374C2×C4×D4—21no—
375C2×C4×D4C2×D7311yescharacteristic
376C22×C4⋊C4—731no—
377C22×C4⋊C4C2×D7311yescharacteristic
378#465—738no—
379C4×SD16—1464no—
380C2×#106—731no—
381C2×#106—731no—
382C2×#106—731no—
383C2×#106—731no—
384C2×#106—731no—
385C2×#106—1464no—
386C2×#103—731no—
387C2×#103—731no—
388C2×#103—731no—
389C2×#102—731no—
390C2×#102—731no—
391C2×#102—731no—
392C2×C22⋊C8—731no—
393C2×C4×C8—731no—
394C2×C4×C8—731no—
395#391—731no—
396#390C2×D7311yescharacteristic
397#389—731no—
398#389—1461no—
399#389C2×D7311yescharacteristic
400#388—21no—
401#387—1461no—
402#386—21no—
403#385—21no—
404#385—1461no—
405C4×C4⋊C4—731no—
406C4×C4⋊C4C2×D7311yescharacteristic
407C4×C22⋊C4—1461no—
408C4×C22⋊C4C2×D7311yescharacteristic
409#340—731no—
410#340—731no—
411#340—731no—
412#340—731no—
413#336—731no—
414#336—731no—
415C22×Q8—731no—
416C22×D4—21no—
417C22×D4C22×D7311yescharacteristic
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—1461no—
421C23×C4C22×D7311yescharacteristic
422C2×SD16—734no—
423C2×SD16—1462no—
424C2×SD16—1462no—
425C22×C8—731no—
426C22×C8—734no—
427C22×C8—731no—
428C22×C8—731no—
429C22×C8—731no—
430C22×C8—1462no—
431C22×C8—1462no—
432C22⋊Q8—734no—
433C22⋊Q8—1462no—
434#121—22no—
435#121C4×D7314yes—
436C4×Q8—2921no—
437C4×Q8—1462no—
438C4×D4—22no—
439C4×D4—41no—
440C4×D4—44no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—2921no—
446C2×C4⋊C4—731no—
447C2×C4⋊C4—731no—
448C2×C4⋊C4—731no—
449C2×C4⋊C4—1461no—
450C2×C4⋊C4—1461no—
451C2×C4⋊C4—1462no—
452C2×C4⋊C4—1461no—
453C2×C4⋊C4—1461no—
454C2×C4⋊C4C22×D7311yescharacteristic
455C2×C4⋊C4C22×D7311yescharacteristic
456C2×C4⋊C4C22×D7311yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—1461no—
462C2×C22⋊C4C22⋊D7311yescharacteristic
463C2×C22⋊C4C22⋊D7311yescharacteristic
464C2×C42—21no—
465C2×C42—1461no—
466C2×C42—1461no—
467C2×C42C22×D7311yescharacteristic
468C2×C42C22×D7311yescharacteristic
469#106—734no—
470#106—734no—
471#106—1462no—
472#106—1462no—
473#106—1462no—
474#103—2921no—
475#103—734no—
476#103—1462no—
477#102—2921no—
478#102—734no—
479#102—1462no—
480C22⋊C8—1462no—
481C4×C8—1462no—
482C4×C8—1462no—
483#95—21no—
484#95—21no—
485#95—1461no—
486#95—1461no—
487#95—1461no—
488#95—1461no—
489#95C22⋊D7311yescharacteristic
490#95C22⋊D7311yescharacteristic
491C24—21no—
492C24C2×C22⋊D7311yescharacteristic
493C2×Q8—732no—
494C2×Q8—1461no—
495C2×Q8—1461no—
496C2×Q8—1461no—
497C2×Q8—1461no—
498C2×Q8—1461no—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4C2×C4×D7312yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4—2922no—
522C22×C4—2922no—
523C22×C4—5841no—
524C22×C4—1461no—
525C22×C4—1461no—
526C22×C4—1461no—
527C22×C4—1461no—
528C22×C4C2×C4×D7312yes—
529C22×C4C2×C22⋊D7311yescharacteristic
530C22×C4C2×C22⋊D7311yescharacteristic
531C22×C4C2×C22⋊D7311yescharacteristic
532C22×C4C2×C22⋊D7311yescharacteristic
533C22×C4C2×C22⋊D7311yescharacteristic
534C22×C4#1192402812yes—
535C22×C4C23×D7311yescharacteristic
536SD16—1468no—
537C2×C8—732no—
538C2×C8—732no—
539C2×C8—732no—
540C2×C8—732no—
541C2×C8—1461no—
542C2×C8—1461no—
543C2×C8—1461no—
544C2×C8—1461no—
545C2×C8—1461no—
546C2×C8—1461no—
547C2×C8—1468no—
548C2×C8—1461no—
549C2×C8—1461no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—2922no—
557C4⋊C4—2922no—
558C4⋊C4—5841no—
559C4⋊C4—732no—
560C4⋊C4—732no—
561C4⋊C4—1461no—
562C4⋊C4—1461no—
563C4⋊C4—1464no—
564C4⋊C4—1461no—
565C4⋊C4—1461no—
566C4⋊C4C2×C4×D7312yes—
567C4⋊C4D4×D7312yes—
568C22⋊C4—22no—
569C22⋊C4—24no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C22⋊C4—1464no—
574C22⋊C4#1192401614yescomplemented
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—2922no—
581C42—5841no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C4×C22⋊D7312yes—
594C23C2×#1192401612yes—
595C23#1455661112yes—
596C23C22×C22⋊D7311yescharacteristic
597Q8—2921no—
598Q8—2921no—
599Q8—1462no—
600Q8—1462no—
601D4—22no—
602D4—22no—
603D4—48no—
604D4—41no—
605D4—41no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—84no—
632C2×C4—84no—
633C2×C4—2921no—
634C2×C4—2921no—
635C2×C4—2921no—
636C2×C4—2921no—
637C2×C4—2921no—
638C2×C4—2921no—
639C2×C4—2921no—
640C2×C4—2921no—
641C2×C4—2921no—
642C2×C4—5844no—
643C2×C4—1462no—
644C2×C4—1462no—
645C2×C4—1462no—
646C2×C4C4×C22⋊D7312yes—
647C2×C4C2×#1192401612yes—
648C2×C4C2×#1192401612yes—
649C2×C4C22×C4×D7311yescharacteristic
650C2×C4C2×D4×D7311yescharacteristic
651C2×C4#41×D7311yescharacteristic
652C2×C4C2×#1192402811yescharacteristic
653C2×C4#1455663611yescharacteristic
654C2×C4#1455663811yescharacteristic
655C8—2921no—
656C8—2921no—
657C8—734no—
658C8—1462no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22C4×#1192401614yescomplemented
673C22C2×C4×C22⋊D7311yescharacteristic
674C22D4×C22⋊D7311yescharacteristic
675C22#1798923611yescharacteristic
676C22C22×#1192401611yescharacteristic
677C22C2×#1455661111yescharacteristic
678C22#1798939511yescharacteristic
679C22#1798939811yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—42no—
684C4—41no—
685C4—42no—
686C4—41no—
687C4—81no—
688C4—2922no—
689C4—2922no—
690C4—2922no—
691C4—5841no—
692C4C4×D4×D7311yescharacteristic
693C4#1798906611yescharacteristic
694C4#1798924611yescharacteristic
695C4#1798928611yescharacteristic
696C2—24no—
697C2—82no—
698C2#2261294811yescharacteristic
699C2C2×C4×#1192401611yescharacteristic
700C2#2261881211yescharacteristic
701C2D4×#1192401611yescharacteristic
702C2#2262163911yescharacteristic
703C2#2262228811yescharacteristic
704C2#2262230411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2361C2
socleC23×C73C22×D4
prime radicalC2×#121×C73C22
cosocleC22×C4×C73C24
hypercenter#2361D73
hypocenterC73#23022
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11924016C2semidirect
3. C22×#14556522C2semidirect
4. #22612934C2semidirect
5. #22610784C2semidirect
6. #22610656C2semidirect
7. #22610565C2semidirect
8. #22610555C2semidirect
10. #22610238C2semidirect
11. #22610198C2semidirect
12. #22610192C2semidirect
13. C4×#14556522C2semidirect
14. C22⋊C4×#10596831C2semidirect
21. #17988814C4semidirect
66. C2×#11924016C2×C4semidirect
69. C22×#10596831C2×C4semidirect
75. #14556570C2×C4semidirect
93. #14556522C2×C4semidirect
94. #14556522D4semidirect
97. #14556514C2×C4semidirect
100. #14556512C2×C4semidirect
223. C22⋊C4×C73SD16semidirect
305. #10596831C4×D4semidirect
319. C22×C73C4×SD16semidirect
368. C73#23022semidirect
574. C22⋊C4#11924016semidirect
672. C22C4×#11924016semidirect

Maximal subgroups

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

subgroupindex
C2×#179888142
C2×C4×#119240162
C22×#145565222
#226129342
#226107842
#226106562
#226105652
#226105552
#226102492
#226102382
#226101982
#226101922
C4×#145565222
C22⋊C4×#105968312
C73×#23612
#2302273