Finite Group Databasebeta

← #13148702

Subgroups — #13148702

Order 1728.

1007 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊C4×#272C211yesmaximal, characteristic, complemented
2#64093⋊C3C211yesmaximal, characteristic, complemented
3#64088⋊C3C211yesmaximal, characteristic, complemented
4#11721323C211yesmaximal, characteristic, complemented
5#11721323C211yesmaximal, characteristic, complemented
6#11721311C211yesmaximal, characteristic, complemented
7#11721304C211yesmaximal, characteristic, complemented
8#11721159C211yesmaximal, characteristic, complemented
9C4×#6200C211yesmaximal, characteristic, complemented
10#11721127C211yesmaximal, characteristic, complemented
11#11721124C211yesmaximal, characteristic, complemented
12#11721103C211yesmaximal, characteristic, complemented
13#11721100C211yesmaximal, characteristic, complemented
14#11721096C211yesmaximal, characteristic, complemented
15#11721088C211yesmaximal, characteristic, complemented
16#10594199—31nomaximal
17#10594195—31nomaximal
18C23×#272C2211yescharacteristic
19C2×C4×#272C2211yescharacteristic
20C2×C4×#272C2211yescharacteristic
21C2×#638⋊C3C2211yescharacteristic
22C2×#638⋊C3C2211yescharacteristic
23C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
24C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
25C2×#6200C2211yescharacteristic
26C2×#6200C2211yescharacteristic
27C2×#6200C2211yescharacteristic
28C2×#6200C2211yescharacteristic
29C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
30C2×#6196C2211yescharacteristic, complemented
31C22⋊C4×H(3,𝔽3)C2211yescharacteristic
32#88552C2211yescharacteristic
33#88542C2211yescharacteristic
34#88542C2211yescharacteristic
35#3757⋊C3C2211yescharacteristic
36#3757⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic, complemented
38C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
39#3750⋊C3C2211yescharacteristic, complemented
40#3750⋊C3C2211yescharacteristic, complemented
41#3750⋊C3C2211yescharacteristic, complemented
42C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
43#88451C2211yescharacteristic
44#88451C2211yescharacteristic
45#88451C2211yescharacteristic
46#88451C2211yescharacteristic
47#88450C2211yescharacteristic, complemented
48#88450C2211yescharacteristic, complemented
49#88450C2211yescharacteristic, complemented
50#88449C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53#64093D311yescharacteristic, complemented
54#64088D311yescharacteristic, complemented
55C3×#884—31no—
56C3×D3×C22⋊C4—31no—
57C3×D3×C22⋊C4—31no—
58C3×D3×C22⋊C4—61no—
59C3×#879—31no—
60#63977—31no—
61#63977—31no—
62#63976—31no—
63#63976—31no—
64#63975—31no—
65#63969—31no—
66#63959—31no—
67#63953—31no—
68#63915—31no—
69#63910—31no—
70#63909—31no—
71#63908—31no—
72#63905—31no—
73#63904—31no—
74C4×#626—31no—
75C4×#625—31no—
76#63885—31no—
77#63879—31no—
78#63861—31no—
79#63858—31no—
80#63853—31no—
81#63852—31no—
82#63851—31no—
83#63851—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×#272—22no—
86C22×#272—41no—
87C22×#272—41no—
88C22×#272C2311yescharacteristic
89C22×#272C2311yescharacteristic
90C22×(C3⋊D3)⋊C3C2311yescharacteristic
91C22×(C3⋊D3)⋊C3C2311yescharacteristic
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94C2×#1084C2311yescharacteristic
95C2×#1084C2311yescharacteristic
96C4×#272—41no—
97C4×#272—41no—
98#638⋊C3—41no—
99#638⋊C3—41no—
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C4⋊((C3⋊D3)⋊C3)—41no—
107C4×(C3⋊D3)⋊C3—41no—
108#6200—22no—
109#6200—22no—
110#6200—41no—
111#6200—41no—
112((C3⋊D3)⋊C3)⋊C4—41no—
113#6196—41no—
114#5704—91no—
115#5613—91no—
116#5494—91no—
117C23×C3×D3—31no—
118C23×C3×D3—31no—
119C23×C3×D3—61no—
120C2×#638C2×D311yescharacteristic
121C2×#638C2×D311yescharacteristic
122C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
123C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
124C2×C3×#67—31no—
125C2×C3×#67—31no—
126C2×C3×D12—31no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—31no—
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—61no—
133C2×C3×C4×D3—61no—
134C2×#627—31no—
135C2×#627—31no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#625—31no—
141C2×#625—31no—
142C2×#625—31no—
143C2×#625—31no—
144C2×#624—31no—
145C2×D3×Dic3—31no—
146C32×C22⋊C4—21no—
147C32×C22⋊C4C2×D311yescharacteristic
148C32×C22⋊C4C2×D311yescharacteristic
149#3757C2×D311yescharacteristic
150#3757C2×D311yescharacteristic
151#3752C2×D311yescharacteristic, complemented
152C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
153#3750C2×D311yescharacteristic, complemented
154#3750C2×D311yescharacteristic, complemented
155#3750C2×D311yescharacteristic, complemented
156C4×C3⋊Dic3C2×D311yescharacteristic, complemented
157C3×#217—31no—
158C3×#217—31no—
159C3×#217—31no—
160C3×#217—31no—
161C3×#217—61no—
162C3×(C2×D3)⋊C4—31no—
163C3×(C2×D3)⋊C4—31no—
164C3×(C2×D3)⋊C4—31no—
165C3×(C2×D3)⋊C4—31no—
166C3×(C2×D3)⋊C4—31no—
167C3×(C2×D3)⋊C4—61no—
168C3×(C2×D3)⋊C4—61no—
169C3×C4⋊Dic3—31no—
170C3×Dic3⋊C4—31no—
171C3×Dic3⋊C4—31no—
172C3×Dic3⋊C4—31no—
173C3×C4×Dic3—31no—
174#3724—31no—
175Dic3⋊Dic3—31no—
176Dic3⋊Dic3—31no—
177Dic3⋊Dic3—31no—
178#3722—31no—
179#3722—31no—
180#3722—31no—
181(C2×D3)⋊Dic3—31no—
182(C2×D3)⋊Dic3—31no—
183(C2×D3)⋊Dic3—31no—
184(C2×D3)⋊Dic3—31no—
185(C2×D3)⋊Dic3—31no—
186(C2×D3)⋊Dic3—31no—
187(C2×D3)⋊Dic3—31no—
188(C2×D3)⋊Dic3—31no—
189(C2×D3)⋊Dic3—31no—
190(C2×D3)⋊Dic3—31no—
191(C2×D3)⋊Dic3—31no—
192Dic32—31no—
193Dic32—31no—
194C22×H(3,𝔽3)—21no—
195C22×H(3,𝔽3)—21no—
196C22×H(3,𝔽3)—21no—
197C22×H(3,𝔽3)C2411yescharacteristic
198C2×#272—21no—
199C2×#272—21no—
200C2×#272—21no—
201C2×#272—21no—
202C2×#272—21no—
203C2×#272—44no—
204C2×#272#4112yes—
205C2×(C3⋊D3)⋊C3—21no—
206C2×(C3⋊D3)⋊C3—21no—
207C2×(C3⋊D3)⋊C3—21no—
208C2×(C3⋊D3)⋊C3—21no—
209C2×(C3⋊D3)⋊C3—21no—
210C2×(C3⋊D3)⋊C3—21no—
211C4×H(3,𝔽3)—21no—
212C4×H(3,𝔽3)—21no—
213#1084—21no—
214#1084—21no—
215(C3⋊Dic3)⋊C3—21no—
216(C3⋊Dic3)⋊C3—21no—
217(C3⋊Dic3)⋊C3—21no—
218(C3⋊Dic3)⋊C3—21no—
219(C3⋊Dic3)⋊C3—21no—
220(C3⋊Dic3)⋊C3—21no—
221C3×#126—91no—
222C3×#121—91no—
223C2×C3×C22⋊C4—91no—
224#953—91no—
225#953—91no—
226#939—91no—
227#938—91no—
228#937—91no—
229#937—91no—
230#936—91no—
231#935—91no—
232#930—91no—
233#929—91no—
234C4×#67—91no—
235C4×#67—91no—
236C4×#67—91no—
237#924—91no—
238#898—91no—
239#898—91no—
240#896—91no—
241#896—91no—
242#895—91no—
243#895—91no—
244#894—91no—
245#893—91no—
246#885—91no—
247#885—91no—
248#885—91no—
249#885—91no—
250#884—31no—
251#884—91no—
252#884—91no—
253#883—91no—
254#883—91no—
255#883—91no—
256#882—91no—
257#882—91no—
258#67⋊C4—91no—
259D3×C22⋊C4—31no—
260D3×C22⋊C4—31no—
261D3×C22⋊C4—61no—
262#879—31no—
263#879—91no—
264#879—91no—
265#875—91no—
266C4×D12—91no—
267C23×C32—21no—
268C23×C32C22×D311yescharacteristic
269C23×C32C22×D311yescharacteristic
270C22×C3⋊D3C22×D311yescharacteristic
271C22×C3⋊D3C22×D311yescharacteristic
272C22×C3×D3—31no—
273C22×C3×D3—31no—
274C22×C3×D3—31no—
275C22×C3×D3—31no—
276C22×C3×D3—31no—
277C22×C3×D3—31no—
278C22×C3×D3—61no—
279C22×C3×D3—61no—
280C22×C3×D3—62no—
281C22×C3×D3—62no—
282C22×C3×D3—64no—
283C22×C3×D3—121no—
284C22×C3×D3—121no—
285C22×C3×D3—121no—
286C22×C3×D3—121no—
287C22×C3×D3—122no—
288C22×C3×D3—122no—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C22×D311yescharacteristic
294C2×C32×C4C22×D311yescharacteristic
295#638—41no—
296#638—41no—
297C2×C3⋊Dic3C22×D311yescharacteristic
298C2×C3⋊Dic3C22×D311yescharacteristic
299C2×C3⋊Dic3C22×D311yescharacteristic
300C2×C3⋊Dic3C22×D311yescharacteristic
301C2×C3⋊Dic3C22×D311yescharacteristic
302C2×C3⋊Dic3C22×D311yescharacteristic
303C4⋊(C3⋊D3)—41no—
304C4×C3⋊D3—41no—
305C3×#67—121no—
306C3×#67—121no—
307C2×C3×Dic3—31no—
308C2×C3×Dic3—31no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3—31no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3—31no—
314C2×C3×Dic3—31no—
315C2×C3×Dic3—31no—
316C2×C3×Dic3—31no—
317C2×C3×Dic3—61no—
318C2×C3×Dic3—61no—
319C3×D12—121no—
320C3×C4×D3—121no—
321C3×C4×D3—121no—
322C3×C4×D3—121no—
323C3×C4×D3—121no—
324C3×C4×D3—121no—
325C3×C4×D3—122no—
326C3×C4×D3—122no—
327#627—121no—
328#627—121no—
329#626—62no—
330#626—62no—
331#626—121no—
332#626—121no—
333#625—62no—
334#625—62no—
335#625—121no—
336#625—121no—
337#624—121no—
338D3×Dic3—121no—
339#538—271noSylow
340C2×H(3,𝔽3)—41no—
341C2×H(3,𝔽3)C2×#4111yescharacteristic
342C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
343C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
344#272—22no—
345#272—41no—
346(C3⋊D3)⋊C3—41no—
347(C3⋊D3)⋊C3—41no—
348C24×C3—91no—
349C23×D3—31no—
350C23×D3—31no—
351C23×D3—61no—
352C2×C3×D4—91no—
353C2×C3×D4—91no—
354C2×C3×D4—91no—
355C22×C3×C4—91no—
356C22×C3×C4—91no—
357C22×C3×C4—91no—
358C2×#67—31no—
359C2×#67—31no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67—91no—
365C2×#67—91no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—91no—
369C2×#67—91no—
370C22×Dic3—91no—
371C2×D12—31no—
372C2×D12—91no—
373C2×D12—91no—
374C2×D12—91no—
375C2×D12—91no—
376C2×D12—91no—
377C2×C4×D3—31no—
378C2×C4×D3—31no—
379C2×C4×D3—31no—
380C2×C4×D3—31no—
381C2×C4×D3—31no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—91no—
385C2×C4×D3—91no—
386C2×C4×D3—91no—
387C2×Dic6—91no—
388C2×Dic6—91no—
389C2×Dic6—91no—
390C3×C4⋊C4—91no—
391C3×C4⋊C4—91no—
392C3×C4⋊C4—91no—
393C3×C4⋊C4—91no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4—91no—
399C3×C22⋊C4—91no—
400C3×C22⋊C4—91no—
401C3×C22⋊C4—91no—
402C3×C22⋊C4—91no—
403C3×C22⋊C4D3211yescharacteristic
404C3×C42—91no—
405#217—31no—
406#217—31no—
407#217—31no—
408#217—31no—
409#217—61no—
410#217—91no—
411#217—91no—
412#217—91no—
413#217—91no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—91no—
418#217—91no—
419(C2×D3)⋊C4—31no—
420(C2×D3)⋊C4—31no—
421(C2×D3)⋊C4—31no—
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—31no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—91no—
435(C2×D3)⋊C4—91no—
436(C2×D3)⋊C4—91no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441C4⋊Dic3—31no—
442C4⋊Dic3—91no—
443C4⋊Dic3—91no—
444C4⋊Dic3—91no—
445Dic3⋊C4—31no—
446Dic3⋊C4—31no—
447Dic3⋊C4—31no—
448Dic3⋊C4—91no—
449Dic3⋊C4—91no—
450Dic3⋊C4—91no—
451Dic3⋊C4—91no—
452Dic3⋊C4—91no—
453Dic3⋊C4—91no—
454Dic3⋊C4—91no—
455C4×Dic3—31no—
456C4×Dic3—91no—
457C4×Dic3—91no—
458C4×Dic3—91no—
459C4×Dic3—91no—
460C22×C32—22no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—21no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32C23×D311yescharacteristic
471C22×C32C23×D311yescharacteristic
472C2×C3⋊D3—21no—
473C2×C3⋊D3—21no—
474C2×C3⋊D3—21no—
475C2×C3⋊D3—21no—
476C2×C3⋊D3—21no—
477C2×C3⋊D3—21no—
478C2×C3×D3—32no—
479C2×C3×D3—32no—
480C2×C3×D3—62no—
481C2×C3×D3—62no—
482C2×C3×D3—62no—
483C2×C3×D3—61no—
484C2×C3×D3—61no—
485C2×C3×D3—61no—
486C2×C3×D3—61no—
487C2×C3×D3—62no—
488C2×C3×D3—61no—
489C2×C3×D3—61no—
490C2×C3×D3—61no—
491C2×C3×D3—61no—
492C2×C3×D3—61no—
493C2×C3×D3—61no—
494C2×C3×D3—61no—
495C2×C3×D3—61no—
496C2×C3×D3—61no—
497C2×C3×D3—61no—
498C2×C3×D3—61no—
499C2×C3×D3—61no—
500C2×C3×D3—121no—
501C2×C3×D3—121no—
502C2×C3×D3—128no—
503C2×C3×D3—124no—
504C2×C3×D3—124no—
505C32×C4—21no—
506C32×C4—21no—
507C32×C4—21no—
508C32×C4—21no—
509C32×C4—41no—
510C32×C4—41no—
511C3⋊Dic3—21no—
512C3⋊Dic3—21no—
513C3⋊Dic3—21no—
514C3⋊Dic3—21no—
515C3⋊Dic3—21no—
516C3⋊Dic3—21no—
517C3×Dic3—61no—
518C3×Dic3—61no—
519C3×Dic3—61no—
520C3×Dic3—61no—
521C3×Dic3—61no—
522C3×Dic3—61no—
523C3×Dic3—61no—
524C3×Dic3—61no—
525C3×Dic3—61no—
526C3×Dic3—61no—
527C3×Dic3—121no—
528C3×Dic3—121no—
529#126—91no—
530#126—271no—
531#124—271no—
532#124—271no—
533#123—271no—
534#123—271no—
535C22⋊Q8—271no—
536#121—91no—
537#121—271no—
538#121—271no—
539#120—271no—
540#120—271no—
541C4×D4—271no—
542C4×D4—271no—
543C2×C22⋊C4—91no—
544H(3,𝔽3)#53811yescharacteristic, complemented, Sylow
545C23×C3—31no—
546C23×C3—31no—
547C23×C3—61no—
548C23×C3—91no—
549C23×C3—91no—
550C23×C3—91no—
551C23×C3—91no—
552C23×C3—182no—
553C23×C3—361no—
554C23×C3—361no—
555C23×C3C2×D3211yescharacteristic
556C22×D3—31no—
557C22×D3—31no—
558C22×D3—31no—
559C22×D3—31no—
560C22×D3—31no—
561C22×D3—31no—
562C22×D3—61no—
563C22×D3—61no—
564C22×D3—62no—
565C22×D3—62no—
566C22×D3—64no—
567C22×D3—91no—
568C22×D3—91no—
569C22×D3—121no—
570C22×D3—121no—
571C22×D3—121no—
572C22×D3—121no—
573C22×D3—122no—
574C22×D3—122no—
575C3×D4—361no—
576C3×D4—361no—
577C3×D4—361no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—31no—
581C2×C3×C4—31no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—91no—
585C2×C3×C4—91no—
586C2×C3×C4—91no—
587C2×C3×C4—91no—
588C2×C3×C4—91no—
589C2×C3×C4—91no—
590C2×C3×C4—91no—
591C2×C3×C4—91no—
592C2×C3×C4—361no—
593C2×C3×C4—361no—
594C2×C3×C4—361no—
595C2×C3×C4C2×D3211yescharacteristic
596C2×C3×C4C2×D3211yescharacteristic
597#67—121no—
598#67—121no—
599#67—182no—
600#67—182no—
601#67—182no—
602#67—182no—
603#67—361no—
604#67—361no—
605#67—361no—
606#67—361no—
607#67—361no—
608#67—361no—
609C2×Dic3—31no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—31no—
613C2×Dic3—31no—
614C2×Dic3—31no—
615C2×Dic3—31no—
616C2×Dic3—31no—
617C2×Dic3—31no—
618C2×Dic3—31no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—91no—
622C2×Dic3—91no—
623C2×Dic3—91no—
624C2×Dic3—91no—
625C2×Dic3—91no—
626C2×Dic3—91no—
627C2×Dic3—361no—
628D12—121no—
629D12—182no—
630D12—182no—
631D12—361no—
632D12—361no—
633D12—361no—
634C4×D3—121no—
635C4×D3—121no—
636C4×D3—121no—
637C4×D3—121no—
638C4×D3—121no—
639C4×D3—122no—
640C4×D3—122no—
641C4×D3—361no—
642C4×D3—361no—
643C4×D3—361no—
644Dic6—361no—
645Dic6—361no—
646Dic6—361no—
647C2×C32—21no—
648C2×C32—21no—
649C2×C32—21no—
650C2×C32—42no—
651C2×C32—41no—
652C2×C32—41no—
653C2×C32#100411yescharacteristic
654C2×C32#100411yescharacteristic
655C2×C32D3×#4111yescharacteristic
656C2×C32D3×#4111yescharacteristic
657C2×C32#100911yescharacteristic
658C2×C32#100911yescharacteristic
659C3⋊D3—41no—
660C3⋊D3—41no—
661C3×D3—64no—
662C3×D3—62no—
663C3×D3—62no—
664C3×D3—122no—
665C3×D3—121no—
666C3×D3—121no—
667C3×D3—121no—
668C3×D3—121no—
669C24—91no—
670C2×Q8—271no—
671C2×D4—91no—
672C2×D4—91no—
673C2×D4—91no—
674C2×D4—271no—
675C2×D4—271no—
676C2×D4—271no—
677C2×D4—271no—
678C22×C4—91no—
679C22×C4—91no—
680C22×C4—91no—
681C22×C4—271no—
682C4⋊C4—91no—
683C4⋊C4—91no—
684C4⋊C4—91no—
685C4⋊C4—91no—
686C4⋊C4—271no—
687C4⋊C4—271no—
688C22⋊C4—91no—
689C22⋊C4—91no—
690C22⋊C4—91no—
691C22⋊C4—91no—
692C22⋊C4—91no—
693C22⋊C4—91no—
694C22⋊C4—271no—
695C22⋊C4—271no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4—271no—
701C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
702C42—91no—
703C42—271no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—31no—
708C22×C3—31no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—62no—
716C22×C3—61no—
717C22×C3—92no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—181no—
721C22×C3—181no—
722C22×C3—181no—
723C22×C3—181no—
724C22×C3—181no—
725C22×C3—181no—
726C22×C3—181no—
727C22×C3—181no—
728C22×C3—181no—
729C22×C3—181no—
730C22×C3—181no—
731C22×C3—364no—
732C22×C3C22×D3211yescharacteristic
733C2×D3—32no—
734C2×D3—32no—
735C2×D3—62no—
736C2×D3—61no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—62no—
741C2×D3—62no—
742C2×D3—61no—
743C2×D3—61no—
744C2×D3—61no—
745C2×D3—61no—
746C2×D3—61no—
747C2×D3—61no—
748C2×D3—62no—
749C2×D3—61no—
750C2×D3—61no—
751C2×D3—61no—
752C2×D3—61no—
753C2×D3—61no—
754C2×D3—61no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—124no—
758C2×D3—124no—
759C2×D3—128no—
760C2×D3—181no—
761C2×D3—181no—
762C2×D3—181no—
763C2×D3—181no—
764C2×D3—181no—
765C2×D3—181no—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—61no—
769C3×C4—61no—
770C3×C4—61no—
771C3×C4—61no—
772C3×C4—121no—
773C3×C4—121no—
774C3×C4—181no—
775C3×C4—181no—
776C3×C4—181no—
777C3×C4—181no—
778C3×C4—181no—
779C3×C4—181no—
780C3×C4—181no—
781C3×C4—181no—
782Dic3—61no—
783Dic3—61no—
784Dic3—61no—
785Dic3—61no—
786Dic3—61no—
787Dic3—61no—
788Dic3—61no—
789Dic3—61no—
790Dic3—61no—
791Dic3—61no—
792Dic3—121no—
793Dic3—121no—
794Dic3—181no—
795Dic3—181no—
796Dic3—181no—
797Dic3—181no—
798Dic3—181no—
799Dic3—181no—
800C32—21no—
801C32#561311yescharacteristic, complemented
802C32#570411yescharacteristic, complemented
803C23—91no—
804C23—91no—
805C23—91no—
806C23—91no—
807C23—182no—
808C23—361no—
809C23—361no—
810C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
811Q8—1081no—
812D4—361no—
813D4—361no—
814D4—361no—
815D4—542no—
816D4—542no—
817D4—1081no—
818D4—1081no—
819C2×C4—91no—
820C2×C4—91no—
821C2×C4—91no—
822C2×C4—91no—
823C2×C4—91no—
824C2×C4—91no—
825C2×C4—91no—
826C2×C4—91no—
827C2×C4—361no—
828C2×C4—361no—
829C2×C4—361no—
830C2×C4—1081no—
831C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
832C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
833C2×C3—31no—
834C2×C3—31no—
835C2×C3—31no—
836C2×C3—31no—
837C2×C3—31no—
838C2×C3—31no—
839C2×C3—41no—
840C2×C3—61no—
841C2×C3—61no—
842C2×C3—61no—
843C2×C3—121no—
844C2×C3—121no—
845C2×C3—122no—
846C2×C3—182no—
847C2×C3—361no—
848C2×C3—361no—
849C2×C3—361no—
850C2×C3#6430611yescharacteristic
851C2×C3#6431411yescharacteristic
852C2×C3#6431411yescharacteristic
853D3—62no—
854D3—62no—
855D3—64no—
856D3—121no—
857D3—121no—
858D3—122no—
859D3—121no—
860D3—121no—
861D3—361no—
862D3—361no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—92no—
867C22—181no—
868C22—181no—
869C22—181no—
870C22—181no—
871C22—181no—
872C22—181no—
873C22—181no—
874C22—181no—
875C22—181no—
876C22—181no—
877C22—181no—
878C22—364no—
879C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
880C4—21no—
881C4—21no—
882C4—181no—
883C4—181no—
884C4—181no—
885C4—181no—
886C4—181no—
887C4—181no—
888C4—181no—
889C4—181no—
890C3—31no—
891C3—31no—
892C3—61no—
893C3#1059422611yescharacteristic
894C2—41no—
895C2—182no—
896C2—361no—
897C2—361no—
898C2—361no—
899C2#1172249111yescharacteristic
900C2#1172250711yescharacteristic
901C2#1172250711yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC22⋊C4×H(3,𝔽3)C22
hypercenterC22⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#538
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22⋊C4×#272C2semidirect
2. #64093⋊C3C2semidirect
3. #64088⋊C3C2semidirect
4. #11721323C2semidirect
5. #11721323C2semidirect
6. #11721311C2semidirect
7. #11721304C2semidirect
8. #11721159C2semidirect
9. C4×#6200C2semidirect
10. #11721127C2semidirect
11. #11721124C2semidirect
12. #11721103C2semidirect
13. #11721100C2semidirect
14. #11721096C2semidirect
15. #11721088C2semidirect
23. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
24. C2×C4×(C3⋊D3)⋊C3C22semidirect
29. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
30. C2×#6196C22semidirect
37. #3752⋊C3C22semidirect
38. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
39. #3750⋊C3C22semidirect
40. #3750⋊C3C22semidirect
41. #3750⋊C3C22semidirect
42. C4×(C3⋊Dic3)⋊C3C22semidirect
47. #88450C22semidirect
48. #88450C22semidirect
49. #88450C22semidirect
50. #88449C22semidirect
51. #88448C22semidirect
52. #88447C22semidirect
53. #64093D3semidirect
54. #64088D3semidirect
122. C2×C4⋊(C3⋊D3)C2×D3semidirect
123. C2×C4×C3⋊D3C2×D3semidirect
151. #3752C2×D3semidirect
152. C4⋊(C3⋊Dic3)C2×D3semidirect
153. #3750C2×D3semidirect
154. #3750C2×D3semidirect
155. #3750C2×D3semidirect
156. C4×C3⋊Dic3C2×D3semidirect
544. H(3,𝔽3)#538semidirect
801. C32#5613semidirect
802. C32#5704semidirect

Maximal subgroups

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

subgroupindex
C22⋊C4×#2722
#64093⋊C32
#64088⋊C32
#117213232
#117213112
#117213042
#117211592
C4×#62002
#117211272
#117211242
#117211032
#117211002
#117210962
#117210882
#105941993
#105941953