Finite Group Databasebeta

← C2×#11722507 #13164745

Subgroups — C2×#11722507 #13164745

Order 1728.

3379 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#272C211yesmaximal, characteristic, complemented
2C2×#3830⋊C3C211yesmaximal, characteristic, complemented
3C2×D4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
4C2×#88677C212yesmaximal, complemented
5C2×#88676C212yesmaximal, complemented
6C22×#6200C212yesmaximal, complemented
7C2×#88671C212yesmaximal, complemented
8#11722507C2116yesmaximal, direct product factor
9C2×#88654C211yesmaximal, characteristic, complemented
10C2×#88652C211yesmaximal, characteristic, complemented
11C2×#88650C211yesmaximal, characteristic, complemented
12C2×#88649C211yesmaximal, characteristic, complemented
13C2×#64314—31nomaximal
14C2×#64313—31nomaximal
15C23×#272C2212yescomplemented
16C23×(C3⋊D3)⋊C3C2212yescomplemented
17C22×((C3⋊D3)⋊C3)⋊C2C2212yescomplemented
18C2×D4×H(3,𝔽3)C2211yescharacteristic, complemented
19C2×#6235C2212yescomplemented
20D4×#272C2218yescomplemented
21C2×C4⋊#272C2211yescharacteristic, complemented
22C2×C4×#272C2211yescharacteristic, complemented
23C2×#638⋊C3C2212yescomplemented
24C2×#638⋊C3C2212yescomplemented
25C22×(C3⋊Dic3)⋊C3C2212yescomplemented
26#3830⋊C3C2218yescomplemented
27D4×(C3⋊D3)⋊C3C2218yescomplemented
28C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
29C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
30C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
31C2×#634⋊C3C2211yescharacteristic, complemented
32#88677C22116yescomplemented
33#88676C22116yescomplemented
34C2×#6200C2212yescomplemented
35C2×#6200C2211yescharacteristic, complemented
36C2×#6200C2212yescomplemented
37C2×#6200C2212yescomplemented
38C2×#6200C2211yescharacteristic, complemented
39C2×#6200C22116yescomplemented
40C2×#6199C2212yescomplemented
41C2×#6198C2211yescharacteristic, complemented
42#88671C22116yescomplemented
43C2×((C3⋊D3)⋊C3)⋊C4C2212yescomplemented
44C2×#6196C2211yescharacteristic, complemented
45#88654C2218yescomplemented
46#88652C2218yescomplemented
47#88650C2218yescomplemented
48#88649C2218yescomplemented
49C2×#3830D311yescharacteristic, complemented
50C2×D4×C3⋊D3D311yescharacteristic, complemented
51C2×C3×#237—31no—
52C2×C3×D3×D4—31no—
53C2×C3×D3×D4—31no—
54C2×C3×D3×D4—31no—
55C2×C3×D3×D4—61no—
56C2×#3811—32no—
57C2×D3×#67—32no—
58C2×D3×#67—32no—
59C2×D3×#67—32no—
60C22×#626—32no—
61C22×#625—32no—
62C2×#3805—32no—
63C2×#3804—32no—
64#64314—316no—
65#64313—316no—
66C2×#3802—31no—
67C2×D3×D12—31no—
68C2×#3799—31no—
69C2×#3798—31no—
70C2×#3798—31no—
71C2×#3796—31no—
72C2×#3795—31no—
73C2×#3795—31no—
74C23×H(3,𝔽3)C2312yes—
75C22×#272—44no—
76C22×#272C2312yes—
77C22×#272C2311yescharacteristic
78C22×#272C2318yescomplemented
79C22×(C3⋊D3)⋊C3—44no—
80C22×(C3⋊D3)⋊C3C2311yescharacteristic
81C22×(C3⋊D3)⋊C3C2312yes—
82C22×(C3⋊D3)⋊C3C2311yescharacteristic
83C22×(C3⋊D3)⋊C3C2318yescomplemented
84C2×((C3⋊D3)⋊C3)⋊C2—44no—
85C2×((C3⋊D3)⋊C3)⋊C2C2318yescomplemented
86D4×H(3,𝔽3)C2314yescomplemented
87C2×C4×H(3,𝔽3)C2311yescharacteristic
88#6235C2318yescomplemented
89C2×#1084C2311yescharacteristic
90C4⋊#272C2314yescomplemented
91C4×#272C2314yescomplemented
92#638⋊C3C2318yescomplemented
93#638⋊C3C2318yescomplemented
94C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
95C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
96C2×(C3⋊Dic3)⋊C3C2312yes—
97C2×(C3⋊Dic3)⋊C3C2318yescomplemented
98C4⋊((C3⋊D3)⋊C3)C2314yescomplemented
99C4×(C3⋊D3)⋊C3C2314yescomplemented
100C4×(C3⋊D3)⋊C3C2314yescomplemented
101#634⋊C3C2314yescomplemented
102#6200C2318yescomplemented
103#6200C2314yescomplemented
104#6200C2314yescomplemented
105#6200C2318yescomplemented
106#6200C2318yescomplemented
107#6199C2318yescomplemented
108#6198C2314yescomplemented
109((C3⋊D3)⋊C3)⋊C4C2318yescomplemented
110#6196C2314yescomplemented
111C2×#1009—91no—
112C2×#1004—91no—
113C2×#1004—91no—
114C23×C3⋊D3C2×D312yescomplemented
115C23×C3×D3—32no—
116C23×C3×D3—32no—
117C23×C3×D3—32no—
118C23×C3×D3—62no—
119C22×D32—32no—
120C22×D32—32no—
121C2×C32×D4—21no—
122C2×C32×D4C2×D311yescharacteristic, complemented
123C2×C32×D4C2×D311yescharacteristic, complemented
124C2×#638C2×D312yescomplemented
125C2×#638C2×D312yescomplemented
126C22×C3⋊Dic3C2×D312yescomplemented
127#3830C2×D318yescomplemented
128D4×C3⋊D3C2×D318yescomplemented
129C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
130C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
131C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
132C2×#634C2×D311yescharacteristic, complemented
133C2×C3×#67—32no—
134C2×C3×#67—32no—
135C2×C3×#67—32no—
136C2×C3×#67—32no—
137C2×C3×#67—62no—
138C22×C3×Dic3—32no—
139C3×#237—38no—
140C3×D3×D4—38no—
141C3×D3×D4—38no—
142C3×D3×D4—38no—
143C3×D3×D4—68no—
144C2×C3×D12—31no—
145C2×C3×D12—31no—
146C2×C3×D12—31no—
147C2×C3×D12—61no—
148C2×C3×C4×D3—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—61no—
153C2×C3×Dic6—31no—
154#3811—316no—
155D3×#67—316no—
156D3×#67—316no—
157D3×#67—316no—
158C2×#627—31no—
159C2×#627—31no—
160C2×#626—32no—
161C2×#626—31no—
162C2×#626—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626—32no—
166C2×#626—32no—
167C2×#626—316no—
168C2×#625—32no—
169C2×#625—32no—
170C2×#625—31no—
171C2×#625—31no—
172C2×#625—32no—
173C2×#625—316no—
174C2×#624—32no—
175#3805—316no—
176#3804—316no—
177C2×D3×Dic3—32no—
178C2×D3×Dic3—32no—
179C2×D3×Dic3—32no—
180#3802—38no—
181D3×D12—38no—
182#3799—38no—
183#3798—38no—
184#3798—38no—
185#3796—38no—
186#3795—38no—
187#3795—38no—
188C22×H(3,𝔽3)—24no—
189C22×H(3,𝔽3)C2414yes—
190C22×H(3,𝔽3)C2411yescharacteristic
191C2×#272—22no—
192C2×#272—24no—
193C2×#272—48no—
194C2×#272C2414yes—
195C2×#272C2412yes—
196C2×(C3⋊D3)⋊C3—22no—
197C2×(C3⋊D3)⋊C3—24no—
198C2×(C3⋊D3)⋊C3—22no—
199C2×(C3⋊D3)⋊C3—48no—
200C2×(C3⋊D3)⋊C3C2414yes—
201C2×(C3⋊D3)⋊C3C2412yes—
202C2×(C3⋊D3)⋊C3C2412yes—
203((C3⋊D3)⋊C3)⋊C2—48no—
204C4×H(3,𝔽3)C2412yes—
205#1084C2412yes—
206(C3⋊Dic3)⋊C3C2412yes—
207(C3⋊Dic3)⋊C3C2412yes—
208(C3⋊Dic3)⋊C3C2414yes—
209C2×C3×#41—91no—
210C22×C3×D4—91no—
211C22×C3×D4—91no—
212C22×#67—92no—
213C22×#67—92no—
214C22×#67—92no—
215C22×#67—92no—
216#1009—916no—
217C2×#239—91no—
218C2×#239—91no—
219#1004—916no—
220#1004—916no—
221C2×#237—31no—
222C2×#237—91no—
223C2×#237—91no—
224C2×#237—91no—
225C2×#237—92no—
226C2×#237—92no—
227C2×D3×D4—31no—
228C2×D3×D4—31no—
229C2×D3×D4—31no—
230C2×D3×D4—61no—
231C2×D3×D4—91no—
232C2×D3×D4—91no—
233C2×D3×D4—91no—
234C2×D3×D4—92no—
235C2×D3×D4—92no—
236C2×D3×D4—92no—
237C2×D3×D4—92no—
238C2×#235—91no—
239C2×#235—91no—
240C2×#235—91no—
241C2×#235—91no—
242C2×#235—91no—
243C2×#235—92no—
244C22×D12—91no—
245C22×D12—92no—
246C23×C32—22no—
247C23×C32C22×D312yes—
248C23×C32C22×D312yes—
249C22×C3⋊D3—44no—
250C22×C3⋊D3C22×D311yescharacteristic
251C22×C3⋊D3C22×D312yes—
252C22×C3⋊D3C22×D311yescharacteristic
253C22×C3⋊D3C22×D318yescomplemented
254C22×C3×D3—31no—
255C22×C3×D3—32no—
256C22×C3×D3—32no—
257C22×C3×D3—32no—
258C22×C3×D3—31no—
259C22×C3×D3—31no—
260C22×C3×D3—31no—
261C22×C3×D3—38no—
262C22×C3×D3—38no—
263C22×C3×D3—38no—
264C22×C3×D3—61no—
265C22×C3×D3—62no—
266C22×C3×D3—68no—
267C22×C3×D3—124no—
268C22×C3×D3—124no—
269C22×C3×D3—124no—
270C22×C3×D3—128no—
271C2×D32—38no—
272C2×D32—38no—
273C2×D32—124no—
274C2×D32—124no—
275C32×D4—24no—
276C32×D4C22×D314yescomplemented
277C32×D4C22×D314yescomplemented
278C2×C32×C4—21no—
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281#638C22×D318yescomplemented
282#638C22×D318yescomplemented
283C2×C3⋊Dic3C22×D312yes—
284C2×C3⋊Dic3C22×D311yescharacteristic
285C2×C3⋊Dic3C22×D311yescharacteristic
286C2×C3⋊Dic3C22×D318yescomplemented
287C4⋊(C3⋊D3)C22×D314yescomplemented
288C4×C3⋊D3C22×D314yescomplemented
289C4×C3⋊D3C22×D314yescomplemented
290#634C22×D314yescomplemented
291C3×#67—38no—
292C3×#67—38no—
293C3×#67—38no—
294C3×#67—38no—
295C3×#67—68no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—32no—
298C2×C3×Dic3—31no—
299C2×C3×Dic3—38no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—61no—
303C3×D12—34no—
304C3×D12—34no—
305C3×D12—34no—
306C3×D12—64no—
307C3×C4×D3—34no—
308C3×C4×D3—34no—
309C3×C4×D3—34no—
310C3×C4×D3—34no—
311C3×C4×D3—64no—
312C3×Dic6—34no—
313#627—34no—
314#627—34no—
315#626—34no—
316#626—34no—
317#626—38no—
318#626—34no—
319#626—34no—
320#626—38no—
321#626—38no—
322#625—38no—
323#625—38no—
324#625—34no—
325#625—34no—
326#625—38no—
327#624—38no—
328D3×Dic3—38no—
329D3×Dic3—38no—
330D3×Dic3—38no—
331C2×H(5,𝔽2)—271noSylow
332C2×H(3,𝔽3)—24no—
333C2×H(3,𝔽3)H(5,𝔽2)12yescomplemented
334C2×H(3,𝔽3)C2511yescharacteristic
335#272—22no—
336#272—24no—
337(C3⋊D3)⋊C3—22no—
338(C3⋊D3)⋊C3—24no—
339(C3⋊D3)⋊C3—22no—
340C24×C3—92no—
341C24×C3—92no—
342C23×D3—32no—
343C23×D3—32no—
344C23×D3—32no—
345C23×D3—62no—
346C23×D3—92no—
347C23×D3—92no—
348C23×D3—92no—
349C23×D3—92no—
350C3×#41—98no—
351C2×C3×Q8—91no—
352C2×C3×D4—31no—
353C2×C3×D4—31no—
354C2×C3×D4—61no—
355C2×C3×D4—91no—
356C2×C3×D4—98no—
357C2×C3×D4—92no—
358C2×C3×D4—92no—
359C2×C3×D4—92no—
360C2×C3×D4—98no—
361C2×C3×D4—91no—
362C2×C3×D4D3211yescharacteristic
363C22×C3×C4—91no—
364C22×C3×C4—91no—
365C22×C3×C4—92no—
366C22×C3×C4—91no—
367C2×#67—32no—
368C2×#67—32no—
369C2×#67—32no—
370C2×#67—32no—
371C2×#67—62no—
372C2×#67—92no—
373C2×#67—92no—
374C2×#67—92no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—92no—
378C2×#67—92no—
379C2×#67—916no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—916no—
383C2×#67—916no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—92no—
387C2×#67—92no—
388C2×#67—92no—
389C2×#67—916no—
390C22×Dic3—32no—
391C22×Dic3—92no—
392C22×Dic3—92no—
393C22×Dic3—92no—
394#239—98no—
395#239—98no—
396#237—38no—
397#237—98no—
398#237—98no—
399#237—98no—
400#237—916no—
401#237—916no—
402D3×D4—38no—
403D3×D4—38no—
404D3×D4—38no—
405D3×D4—68no—
406D3×D4—98no—
407D3×D4—98no—
408D3×D4—98no—
409D3×D4—916no—
410D3×D4—916no—
411D3×D4—916no—
412D3×D4—916no—
413#235—98no—
414#235—98no—
415#235—98no—
416#235—98no—
417#235—98no—
418#235—916no—
419C2×D12—31no—
420C2×D12—31no—
421C2×D12—31no—
422C2×D12—61no—
423C2×D12—91no—
424C2×D12—98no—
425C2×D12—91no—
426C2×D12—91no—
427C2×D12—92no—
428C2×D12—92no—
429C2×D12—92no—
430C2×D12—916no—
431C2×D12—91no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—31no—
435C2×C4×D3—31no—
436C2×C4×D3—61no—
437C2×C4×D3—91no—
438C2×C4×D3—91no—
439C2×C4×D3—92no—
440C2×C4×D3—92no—
441C2×C4×D3—92no—
442C2×C4×D3—92no—
443C2×Dic6—31no—
444C2×Dic6—91no—
445C2×Dic6—91no—
446C2×Dic6—91no—
447C2×Dic6—91no—
448C22×C32—24no—
449C22×C32—24no—
450C22×C32—21no—
451C22×C32—24no—
452C22×C32—44no—
453C22×C32C23×D314yes—
454C22×C32C23×D314yes—
455C22×C32C23×D311yescharacteristic
456C22×C32C23×D311yescharacteristic
457C2×C3⋊D3—24no—
458C2×C3⋊D3—22no—
459C2×C3⋊D3—22no—
460C2×C3⋊D3—48no—
461C2×C3⋊D3C23×D314yes—
462C2×C3⋊D3C23×D312yes—
463C2×C3⋊D3C23×D312yes—
464C2×C3×D3—34no—
465C2×C3×D3—32no—
466C2×C3×D3—32no—
467C2×C3×D3—34no—
468C2×C3×D3—34no—
469C2×C3×D3—32no—
470C2×C3×D3—32no—
471C2×C3×D3—62no—
472C2×C3×D3—64no—
473C2×C3×D3—64no—
474C2×C3×D3—62no—
475C2×C3×D3—64no—
476C2×C3×D3—62no—
477C2×C3×D3—64no—
478C2×C3×D3—62no—
479C2×C3×D3—64no—
480C2×C3×D3—62no—
481C2×C3×D3—124no—
482C2×C3×D3—128no—
483C2×C3×D3—128no—
484C2×C3×D3—128no—
485C2×C3×D3—1216no—
486D32—128no—
487D32—128no—
488C32×C4—22no—
489C32×C4C23×D312yes—
490C32×C4C23×D312yes—
491C3⋊Dic3C23×D314yes—
492C3⋊Dic3C23×D312yes—
493C3⋊Dic3C23×D312yes—
494C3×Dic3—32no—
495C3×Dic3—34no—
496C3×Dic3—32no—
497C3×Dic3—32no—
498C3×Dic3—32no—
499C3×Dic3—62no—
500H(5,𝔽2)—2716no—
501C2×#41—91no—
502C2×#41—271no—
503C2×#41—272no—
504C2×#41—271no—
505C2×#41—271no—
506C22×D4—91no—
507C22×D4—91no—
508C22×D4—271no—
509C22×D4—272no—
510C22×D4—272no—
511C22×D4—272no—
512H(3,𝔽3)C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
513C23×C3—32no—
514C23×C3—32no—
515C23×C3—62no—
516C23×C3—92no—
517C23×C3—91no—
518C23×C3—91no—
519C23×C3—98no—
520C23×C3—92no—
521C23×C3—91no—
522C23×C3—98no—
523C23×C3—364no—
524C23×C3—364no—
525C23×C3C2×D3212yes—
526C22×D3—31no—
527C22×D3—31no—
528C22×D3—32no—
529C22×D3—32no—
530C22×D3—31no—
531C22×D3—31no—
532C22×D3—32no—
533C22×D3—38no—
534C22×D3—38no—
535C22×D3—38no—
536C22×D3—61no—
537C22×D3—62no—
538C22×D3—68no—
539C22×D3—91no—
540C22×D3—92no—
541C22×D3—91no—
542C22×D3—98no—
543C22×D3—98no—
544C22×D3—98no—
545C22×D3—98no—
546C22×D3—124no—
547C22×D3—124no—
548C22×D3—124no—
549C22×D3—128no—
550C22×D3—364no—
551C22×D3—364no—
552C22×D3—364no—
553C22×D3—364no—
554C3×Q8—94no—
555C3×D4—34no—
556C3×D4—34no—
557C3×D4—64no—
558C3×D4—94no—
559C3×D4—98no—
560C3×D4—98no—
561C3×D4—98no—
562C3×D4—94no—
563C3×D4C2×D3214yes—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—61no—
567C2×C3×C4—94no—
568C2×C3×C4—94no—
569C2×C3×C4—91no—
570C2×C3×C4—91no—
571C2×C3×C4—92no—
572C2×C3×C4—98no—
573C2×C3×C4—91no—
574C2×C3×C4—94no—
575C2×C3×C4C2×D3211yescharacteristic
576#67—38no—
577#67—38no—
578#67—38no—
579#67—38no—
580#67—68no—
581#67—98no—
582#67—98no—
583#67—98no—
584#67—94no—
585#67—94no—
586#67—98no—
587#67—98no—
588#67—94no—
589#67—94no—
590#67—94no—
591#67—94no—
592#67—98no—
593#67—98no—
594#67—98no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—32no—
598C2×Dic3—31no—
599C2×Dic3—31no—
600C2×Dic3—38no—
601C2×Dic3—61no—
602C2×Dic3—91no—
603C2×Dic3—91no—
604C2×Dic3—92no—
605C2×Dic3—98no—
606C2×Dic3—98no—
607C2×Dic3—98no—
608D12—34no—
609D12—34no—
610D12—34no—
611D12—64no—
612D12—94no—
613D12—94no—
614D12—94no—
615D12—98no—
616D12—98no—
617D12—98no—
618D12—94no—
619C4×D3—34no—
620C4×D3—34no—
621C4×D3—34no—
622C4×D3—34no—
623C4×D3—64no—
624C4×D3—94no—
625C4×D3—94no—
626C4×D3—98no—
627C4×D3—98no—
628C4×D3—98no—
629C4×D3—98no—
630Dic6—34no—
631Dic6—94no—
632Dic6—94no—
633Dic6—94no—
634Dic6—94no—
635C2×C32—24no—
636C2×C32—24no—
637C2×C32—22no—
638C2×C32—21no—
639C2×C32—44no—
640C2×C32#100412yescomplemented
641C2×C32#100912yescomplemented
642C2×C32C24×D311yescharacteristic
643C2×C32C24×D311yescharacteristic
644C3⋊D3—24no—
645C3⋊D3—22no—
646C3⋊D3—22no—
647C3×D3—64no—
648C3×D3—62no—
649C3×D3—64no—
650C3×D3—62no—
651C3×D3—64no—
652C3×D3—62no—
653C3×D3—64no—
654C3×D3—62no—
655C3×D3—124no—
656C24—92no—
657C24—92no—
658C24—272no—
659#41—98no—
660#41—278no—
661#41—2716no—
662#41—278no—
663#41—278no—
664C2×Q8—91no—
665C2×Q8—271no—
666C2×D4—92no—
667C2×D4—92no—
668C2×D4—92no—
669C2×D4—98no—
670C2×D4—98no—
671C2×D4—91no—
672C2×D4—91no—
673C2×D4—278no—
674C2×D4—271no—
675C2×D4—272no—
676C2×D4—271no—
677C2×D4—271no—
678C2×D4—272no—
679C2×D4—272no—
680C2×D4—2716no—
681C2×D4—2716no—
682C2×D4—2716no—
683C2×D4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
684C22×C4—92no—
685C22×C4—91no—
686C22×C4—91no—
687C22×C4—91no—
688C22×C4—272no—
689C22×C4—272no—
690C22×C3—24no—
691C22×C3—34no—
692C22×C3—34no—
693C22×C3—31no—
694C22×C3—31no—
695C22×C3—64no—
696C22×C3—64no—
697C22×C3—64no—
698C22×C3—61no—
699C22×C3—94no—
700C22×C3—92no—
701C22×C3—92no—
702C22×C3—94no—
703C22×C3—92no—
704C22×C3—124no—
705C22×C3—182no—
706C22×C3—184no—
707C22×C3—182no—
708C22×C3—184no—
709C22×C3—182no—
710C22×C3—368no—
711C22×C3—368no—
712C22×C3C22×D3214yes—
713C22×C3C22×D3211yescharacteristic
714C2×D3—32no—
715C2×D3—32no—
716C2×D3—34no—
717C2×D3—34no—
718C2×D3—32no—
719C2×D3—32no—
720C2×D3—34no—
721C2×D3—62no—
722C2×D3—64no—
723C2×D3—62no—
724C2×D3—62no—
725C2×D3—64no—
726C2×D3—64no—
727C2×D3—64no—
728C2×D3—62no—
729C2×D3—64no—
730C2×D3—62no—
731C2×D3—92no—
732C2×D3—94no—
733C2×D3—92no—
734C2×D3—124no—
735C2×D3—128no—
736C2×D3—128no—
737C2×D3—128no—
738C2×D3—1216no—
739C2×D3—182no—
740C2×D3—184no—
741C2×D3—182no—
742C2×D3—368no—
743C2×D3—368no—
744C2×D3—368no—
745C2×D3—368no—
746C3×C4—32no—
747C3×C4—32no—
748C3×C4—62no—
749C3×C4—92no—
750C3×C4—92no—
751C3×C4—94no—
752C3×C4—92no—
753C3×C4C22×D3212yes—
754Dic3—32no—
755Dic3—32no—
756Dic3—34no—
757Dic3—32no—
758Dic3—32no—
759Dic3—62no—
760Dic3—92no—
761Dic3—92no—
762Dic3—94no—
763C32—21no—
764C32C2×#100411yescharacteristic, complemented
765C32C2×#100911yescharacteristic, complemented
766C23—91no—
767C23—91no—
768C23—91no—
769C23—92no—
770C23—92no—
771C23—98no—
772C23—98no—
773C23—278no—
774C23—364no—
775C23—364no—
776C23—1084no—
777C23C2×((C3⋊D3)⋊C3)⋊C212yes—
778Q8—94no—
779Q8—274no—
780D4—98no—
781D4—98no—
782D4—98no—
783D4—94no—
784D4—94no—
785D4—274no—
786D4—278no—
787D4—274no—
788D4—274no—
789D4—278no—
790D4—278no—
791D4C2×((C3⋊D3)⋊C3)⋊C214yescomplemented
792C2×C4—98no—
793C2×C4—91no—
794C2×C4—91no—
795C2×C4—91no—
796C2×C4—92no—
797C2×C4—94no—
798C2×C4—94no—
799C2×C4—94no—
800C2×C4—278no—
801C2×C4—278no—
802C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
803C2×C3—24no—
804C2×C3—32no—
805C2×C3—32no—
806C2×C3—31no—
807C2×C3—31no—
808C2×C3—64no—
809C2×C3—64no—
810C2×C3—62no—
811C2×C3—61no—
812C2×C3—124no—
813C2×C3—182no—
814C2×C3—184no—
815C2×C3—182no—
816C2×C3—184no—
817C2×C3—182no—
818C2×C3#6431412yes—
819C2×C3C23×D3211yescharacteristic
820D3—62no—
821D3—62no—
822D3—64no—
823D3—64no—
824D3—64no—
825D3—62no—
826D3—64no—
827D3—62no—
828D3—124no—
829D3—182no—
830D3—184no—
831D3—182no—
832C22—24no—
833C22—92no—
834C22—92no—
835C22—92no—
836C22—94no—
837C22—94no—
838C22—182no—
839C22—182no—
840C22—184no—
841C22—184no—
842C22—182no—
843C22—368no—
844C22—368no—
845C22—1088no—
846C22C22×((C3⋊D3)⋊C3)⋊C214yes—
847C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
848C4—92no—
849C4—92no—
850C4—92no—
851C4—94no—
852C4C22×((C3⋊D3)⋊C3)⋊C212yes—
853C3—31no—
854C3—31no—
855C3—61no—
856C3C2×#6431411yescharacteristic
857C2—24no—
858C2—182no—
859C2—182no—
860C2—184no—
861C2—184no—
862C2—182no—
863C2#1172250712yesdirect product factor
864C2C23×((C3⋊D3)⋊C3)⋊C211yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC2×H(3,𝔽3)C25
FrattiniC2×C3C23×D32
FittingC2×D4×H(3,𝔽3)C22
socleC22×C3C22×D32
hypercenterC2×D4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C2×H(5,𝔽2)
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×#272C2semidirect
2. C2×#3830⋊C3C2semidirect
3. C2×D4×(C3⋊D3)⋊C3C2semidirect
4. C2×#88677C2semidirect
5. C2×#88676C2semidirect
6. C22×#6200C2semidirect
7. C2×#88671C2semidirect
8. #11722507C2direct (N × H)
9. C2×#88654C2semidirect
10. C2×#88652C2semidirect
11. C2×#88650C2semidirect
12. C2×#88649C2semidirect
15. C23×#272C22semidirect
16. C23×(C3⋊D3)⋊C3C22semidirect
17. C22×((C3⋊D3)⋊C3)⋊C2C22semidirect
18. C2×D4×H(3,𝔽3)C22semidirect
19. C2×#6235C22semidirect
20. D4×#272C22semidirect
21. C2×C4⋊#272C22semidirect
22. C2×C4×#272C22semidirect
23. C2×#638⋊C3C22semidirect
24. C2×#638⋊C3C22semidirect
25. C22×(C3⋊Dic3)⋊C3C22semidirect
26. #3830⋊C3C22semidirect
27. D4×(C3⋊D3)⋊C3C22semidirect
28. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
29. C2×C4×(C3⋊D3)⋊C3C22semidirect
30. C2×C4×(C3⋊D3)⋊C3C22semidirect
31. C2×#634⋊C3C22semidirect
32. #88677C22semidirect
33. #88676C22semidirect
34. C2×#6200C22semidirect
35. C2×#6200C22semidirect
36. C2×#6200C22semidirect
37. C2×#6200C22semidirect
38. C2×#6200C22semidirect
39. C2×#6200C22semidirect
40. C2×#6199C22semidirect
41. C2×#6198C22semidirect
42. #88671C22semidirect
43. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
44. C2×#6196C22semidirect
45. #88654C22semidirect
46. #88652C22semidirect
47. #88650C22semidirect
48. #88649C22semidirect
49. C2×#3830D3semidirect
50. C2×D4×C3⋊D3D3semidirect
78. C22×#272C23semidirect
83. C22×(C3⋊D3)⋊C3C23semidirect
85. C2×((C3⋊D3)⋊C3)⋊C2C23semidirect
86. D4×H(3,𝔽3)C23semidirect
88. #6235C23semidirect
90. C4⋊#272C23semidirect
91. C4×#272C23semidirect
92. #638⋊C3C23semidirect
93. #638⋊C3C23semidirect
97. C2×(C3⋊Dic3)⋊C3C23semidirect
98. C4⋊((C3⋊D3)⋊C3)C23semidirect
99. C4×(C3⋊D3)⋊C3C23semidirect
100. C4×(C3⋊D3)⋊C3C23semidirect
101. #634⋊C3C23semidirect
102. #6200C23semidirect
103. #6200C23semidirect
104. #6200C23semidirect
105. #6200C23semidirect
106. #6200C23semidirect
107. #6199C23semidirect
108. #6198C23semidirect
109. ((C3⋊D3)⋊C3)⋊C4C23semidirect
110. #6196C23semidirect
114. C23×C3⋊D3C2×D3semidirect
122. C2×C32×D4C2×D3semidirect
123. C2×C32×D4C2×D3semidirect
124. C2×#638C2×D3semidirect
125. C2×#638C2×D3semidirect
126. C22×C3⋊Dic3C2×D3semidirect
127. #3830C2×D3semidirect
128. D4×C3⋊D3C2×D3semidirect
129. C2×C4⋊(C3⋊D3)C2×D3semidirect
130. C2×C4×C3⋊D3C2×D3semidirect
131. C2×C4×C3⋊D3C2×D3semidirect
132. C2×#634C2×D3semidirect
253. C22×C3⋊D3C22×D3semidirect
276. C32×D4C22×D3semidirect
277. C32×D4C22×D3semidirect
281. #638C22×D3semidirect
282. #638C22×D3semidirect
286. C2×C3⋊Dic3C22×D3semidirect
287. C4⋊(C3⋊D3)C22×D3semidirect
288. C4×C3⋊D3C22×D3semidirect
289. C4×C3⋊D3C22×D3semidirect
290. #634C22×D3semidirect
333. C2×H(3,𝔽3)H(5,𝔽2)semidirect
512. H(3,𝔽3)C2×H(5,𝔽2)semidirect
640. C2×C32#1004semidirect
641. C2×C32#1009semidirect
683. C2×D4((C3⋊D3)⋊C3)⋊C2semidirect
764. C32C2×#1004semidirect
765. C32C2×#1009semidirect
791. D4C2×((C3⋊D3)⋊C3)⋊C2semidirect
863. C2#11722507direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×#2722
C2×#3830⋊C32
C2×D4×(C3⋊D3)⋊C32
C2×#886772
C2×#886762
C22×#62002
C2×#886712
#117225072
C2×#886542
C2×#886522
C2×#886502
C2×#886492
C2×#643143
C2×#643133