Finite Group Databasebeta

← #13148685

Subgroups — #13148685

Order 1728.

1005 conjugacy classes of subgroups.

The subgroup lattice has 911 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721738C211yesmaximal, characteristic, complemented
2#64090⋊C3C211yesmaximal, characteristic, complemented
3#64087⋊C3C211yesmaximal, characteristic, complemented
4#11721323C211yesmaximal, characteristic, complemented
5#11721322C211yesmaximal, characteristic, complemented
6C2×#88451C211yesmaximal, characteristic, complemented
7#11721293C211yesmaximal, characteristic, complemented
8#11721157C211yesmaximal, characteristic, complemented
9#11721156C211yesmaximal, characteristic, complemented
10#11721155C211yesmaximal, characteristic, complemented
11#11721151C211yesmaximal, characteristic, complemented
12#11721114C211yesmaximal, characteristic, complemented
13#11721100C211yesmaximal, characteristic, complemented
14#11721092C211yesmaximal, characteristic, complemented
15#11721088C211yesmaximal, characteristic, complemented
16#10594238—31nomaximal
17#10594173—31nomaximal
18C23×#272C2211yescharacteristic
19C2×#6235C2211yescharacteristic
20C2×C4⋊#272C2211yescharacteristic
21C2×C4⋊#272C2211yescharacteristic
22C2×#638⋊C3C2211yescharacteristic
23C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
24C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
26C2×#634⋊C3C2211yescharacteristic, complemented
27C2×#6200C2211yescharacteristic
28C2×#6200C2211yescharacteristic
29C2×#6200C2211yescharacteristic, complemented
30C2×#6199C2211yescharacteristic, complemented
31C22⋊C4×H(3,𝔽3)C2211yescharacteristic
32#88542C2211yescharacteristic
33#88542C2211yescharacteristic
34#3757⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic, complemented
36C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
37#3750⋊C3C2211yescharacteristic, complemented
38#3750⋊C3C2211yescharacteristic, complemented
39#3750⋊C3C2211yescharacteristic, complemented
40C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
41#88451C2211yescharacteristic
42#88451C2211yescharacteristic
43#88451C2211yescharacteristic
44#88451C2211yescharacteristic
45#88451C2211yescharacteristic
46#88451C2211yescharacteristic
47#88451C2211yescharacteristic, complemented
48#88451C2211yescharacteristic, complemented
49#88450C2211yescharacteristic, complemented
50#88449C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53#64090D311yescharacteristic, complemented
54#64087D311yescharacteristic, complemented
55C3×#882—31no—
56C3×#882—31no—
57C3×#882—61no—
58C3×#67⋊C4—31no—
59C3×#878—31no—
60#63980—31no—
61#63978—31no—
62#63977—31no—
63#63976—31no—
64#67⋊Dic3—31no—
65Dic3×#67—31no—
66C2×(C2×D3)⋊Dic3—31no—
67C2×(C2×D3)⋊Dic3—31no—
68#63916—31no—
69#63913—31no—
70#63908—31no—
71#63907—31no—
72#63905—31no—
73#63886—31no—
74#63885—31no—
75#63884—31no—
76#63884—31no—
77#63863—31no—
78#63862—31no—
79#63861—31no—
80#63860—31no—
81#63859—31no—
82#63858—31no—
83#63853—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×#272—22no—
86C22×#272—41no—
87C22×#272—41no—
88C22×#272C2311yescharacteristic
89C22×#272C2311yescharacteristic
90C22×#272C2311yescharacteristic
91C22×(C3⋊D3)⋊C3C2311yescharacteristic
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94#6235—22no—
95C2×#1084C2311yescharacteristic
96C4⋊#272—41no—
97C4⋊#272—41no—
98#638⋊C3—22no—
99C2×(C3⋊Dic3)⋊C3—41no—
100C2×(C3⋊Dic3)⋊C3—41no—
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
108C4×(C3⋊D3)⋊C3—41no—
109#634⋊C3—41no—
110#6200—41no—
111#6200—41no—
112#6200—41no—
113#6199—41no—
114#5644—91no—
115#5593—91no—
116#5560—91no—
117C23×C3×D3—31no—
118C23×C3×D3—31no—
119C23×C3×D3—61no—
120C2×#638C2×D311yescharacteristic
121C22×C3⋊Dic3C2×D311yescharacteristic
122C22×C3⋊Dic3C2×D311yescharacteristic
123C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
124C2×#634C2×D311yescharacteristic, complemented
125C2×C3×#67—31no—
126C2×C3×#67—31no—
127C2×C3×#67—31no—
128C2×C3×#67—61no—
129C22×C3×Dic3—31no—
130C22×C3×Dic3—31no—
131C2×C3×D12—31no—
132C2×C3×D12—31no—
133C2×C3×D12—31no—
134C2×C3×D12—31no—
135C2×C3×D12—61no—
136C2×C3×D12—61no—
137C2×C3×C4×D3—31no—
138C2×C3×Dic6—31no—
139C2×#626—31no—
140C2×#626—31no—
141C2×#626—31no—
142C2×#625—31no—
143C2×#625—31no—
144C2×#625—31no—
145C2×D3×Dic3—31no—
146C2×D3×Dic3—31no—
147C32×C22⋊C4—21no—
148C32×C22⋊C4C2×D311yescharacteristic
149C32×C22⋊C4C2×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×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4—31no—
160C3×(C2×D3)⋊C4—31no—
161C3×(C2×D3)⋊C4—31no—
162C3×(C2×D3)⋊C4—31no—
163C3×(C2×D3)⋊C4—61no—
164C3×(C2×D3)⋊C4—61no—
165C3×C4⋊Dic3—31no—
166C3×Dic3⋊C4—31no—
167C3×Dic3⋊C4—31no—
168C3×Dic3⋊C4—31no—
169C3×C4×Dic3—31no—
170#3724—31no—
171Dic3⋊Dic3—31no—
172Dic3⋊Dic3—31no—
173Dic3⋊Dic3—31no—
174#3722—31no—
175(C2×D3)⋊Dic3—31no—
176(C2×D3)⋊Dic3—31no—
177(C2×D3)⋊Dic3—31no—
178(C2×D3)⋊Dic3—31no—
179(C2×D3)⋊Dic3—31no—
180(C2×D3)⋊Dic3—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)#4112yes—
197C22×H(3,𝔽3)C2411yescharacteristic
198C2×#272—21no—
199C2×#272—21no—
200C2×#272—21no—
201C2×#272—21no—
202C2×#272—21no—
203C2×#272—21no—
204C2×#272—21no—
205C2×#272—21no—
206C2×#272—21no—
207C2×#272—44no—
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(C3⋊Dic3)⋊C3—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×C22⋊Q8—91no—
222C3×#120—91no—
223C3×C4×D4—91no—
224#953—91no—
225C2×#217—91no—
226#947—91no—
227#947—91no—
228#939—91no—
229#939—91no—
230#939—91no—
231#938—91no—
232#937—91no—
233#936—91no—
234#935—91no—
235D4×Dic3—91no—
236#930—91no—
237#930—91no—
238#929—91no—
239C4×#67—91no—
240C2×(C2×D3)⋊C4—91no—
241C2×(C2×D3)⋊C4—91no—
242#898—91no—
243#898—91no—
244#898—91no—
245#895—91no—
246#895—91no—
247#894—91no—
248#894—91no—
249#894—91no—
250#885—91no—
251#885—91no—
252#884—91no—
253#883—91no—
254#882—31no—
255#882—31no—
256#882—61no—
257#882—91no—
258#67⋊C4—31no—
259#67⋊C4—91no—
260#67⋊C4—91no—
261#879—91no—
262#879—91no—
263#878—31no—
264#878—91no—
265#876—91no—
266#875—91no—
267C23×C32—21no—
268C23×C32C22×D311yescharacteristic
269C23×C32C22×D311yescharacteristic
270C22×C3⋊D3C22×D311yescharacteristic
271C22×C3×D3—31no—
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—61no—
281C22×C3×D3—62no—
282C22×C3×D3—62no—
283C22×C3×D3—122no—
284C22×C3×D3—121no—
285C22×C3×D3—121no—
286C22×C3×D3—121no—
287C22×C3×D3—121no—
288C22×C3×D3—122no—
289C22×C3×D3—122no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C22×D311yescharacteristic
294C2×C32×C4C22×D311yescharacteristic
295C2×C32×C4C22×D311yescharacteristic
296#638—22no—
297C2×C3⋊Dic3—41no—
298C2×C3⋊Dic3—41no—
299C2×C3⋊Dic3C22×D311yescharacteristic
300C2×C3⋊Dic3C22×D311yescharacteristic
301C2×C3⋊Dic3C22×D311yescharacteristic
302C2×C3⋊Dic3C22×D311yescharacteristic
303C2×C3⋊Dic3C22×D311yescharacteristic
304C2×C3⋊Dic3C22×D311yescharacteristic
305C2×C3⋊Dic3C22×D311yescharacteristic
306C4×C3⋊D3—41no—
307#634—41no—
308C3×#67—62no—
309C3×#67—62no—
310C3×#67—62no—
311C3×#67—122no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3—31no—
314C2×C3×Dic3—31no—
315C2×C3×Dic3—31no—
316C2×C3×Dic3—31no—
317C2×C3×Dic3—31no—
318C2×C3×Dic3—31no—
319C2×C3×Dic3—31no—
320C2×C3×Dic3—31no—
321C2×C3×Dic3—61no—
322C2×C3×Dic3—121no—
323C2×C3×Dic3—121no—
324C3×D12—121no—
325C3×D12—121no—
326C3×D12—121no—
327C3×D12—121no—
328C3×D12—122no—
329C3×D12—122no—
330C3×C4×D3—121no—
331C3×Dic6—121no—
332#626—121no—
333#626—121no—
334#626—121no—
335#625—121no—
336#625—121no—
337#625—121no—
338D3×Dic3—121no—
339D3×Dic3—121no—
340#538—271noSylow
341C2×H(3,𝔽3)—22no—
342C2×H(3,𝔽3)C2×#4111yescharacteristic
343C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
344C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
345#272—41no—
346#272—41no—
347#272—41no—
348(C3⋊D3)⋊C3—41no—
349C24×C3—91no—
350C23×D3—31no—
351C23×D3—31no—
352C23×D3—61no—
353C2×C3×Q8—91no—
354C2×C3×D4—91no—
355C2×C3×D4—91no—
356C2×C3×D4—91no—
357C2×C3×D4—91no—
358C22×C3×C4—91no—
359C22×C3×C4—91no—
360C22×C3×C4—91no—
361C2×#67—31no—
362C2×#67—31no—
363C2×#67—31no—
364C2×#67—61no—
365C2×#67—91no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—91no—
369C2×#67—91no—
370C2×#67—91no—
371C2×#67—91no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—91no—
375C22×Dic3—91no—
376C22×Dic3—91no—
377C2×D12—31no—
378C2×D12—31no—
379C2×D12—31no—
380C2×D12—31no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12—91no—
384C2×D12—91no—
385C2×D12—91no—
386C2×C4×D3—31no—
387C2×C4×D3—91no—
388C2×C4×D3—91no—
389C2×C4×D3—91no—
390C2×Dic6—31no—
391C2×Dic6—91no—
392C3×C4⋊C4—91no—
393C3×C4⋊C4—91no—
394C3×C4⋊C4—91no—
395C3×C4⋊C4—91no—
396C3×C22⋊C4—31no—
397C3×C22⋊C4—31no—
398C3×C22⋊C4—61no—
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—91no—
407#217—91no—
408#217—91no—
409#217—91no—
410#217—91no—
411#217—91no—
412#217—91no—
413#217—91no—
414#217—91no—
415#217—91no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—31no—
419(C2×D3)⋊C4—31no—
420(C2×D3)⋊C4—31no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—91no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
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—
441(C2×D3)⋊C4—91no—
442C4⋊Dic3—31no—
443C4⋊Dic3—91no—
444C4⋊Dic3—91no—
445C4⋊Dic3—91no—
446Dic3⋊C4—31no—
447Dic3⋊C4—31no—
448Dic3⋊C4—31no—
449Dic3⋊C4—91no—
450Dic3⋊C4—91no—
451Dic3⋊C4—91no—
452Dic3⋊C4—91no—
453Dic3⋊C4—91no—
454Dic3⋊C4—91no—
455Dic3⋊C4—91no—
456C4×Dic3—31no—
457C4×Dic3—91no—
458C4×Dic3—91no—
459C4×Dic3—91no—
460C4×Dic3—91no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32—22no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32#23512yes—
470C22×C32#23912yes—
471C22×C32C23×D311yescharacteristic
472C22×C32C23×D311yescharacteristic
473C2×C3⋊D3—21no—
474C2×C3⋊D3—21no—
475C2×C3⋊D3—21no—
476C2×C3×D3—62no—
477C2×C3×D3—62no—
478C2×C3×D3—61no—
479C2×C3×D3—61no—
480C2×C3×D3—61no—
481C2×C3×D3—61no—
482C2×C3×D3—61no—
483C2×C3×D3—61no—
484C2×C3×D3—61no—
485C2×C3×D3—61no—
486C2×C3×D3—61no—
487C2×C3×D3—61no—
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—121no—
500C2×C3×D3—121no—
501C2×C3×D3—121no—
502C2×C3×D3—121no—
503C2×C3×D3—121no—
504C2×C3×D3—121no—
505C2×C3×D3—121no—
506C2×C3×D3—124no—
507C2×C3×D3—124no—
508C2×C3×D3—128no—
509C32×C4—21no—
510C32×C4—21no—
511C32×C4—21no—
512C32×C4—21no—
513C32×C4—41no—
514C32×C4—41no—
515C3⋊Dic3—21no—
516C3⋊Dic3—21no—
517C3⋊Dic3—21no—
518C3⋊Dic3—21no—
519C3⋊Dic3—21no—
520C3⋊Dic3—21no—
521C3⋊Dic3—21no—
522C3×Dic3—61no—
523C3×Dic3—61no—
524C3×Dic3—61no—
525C3×Dic3—61no—
526C3×Dic3—61no—
527C3×Dic3—61no—
528C3×Dic3—61no—
529C3×Dic3—61no—
530C3×Dic3—61no—
531C3×Dic3—121no—
532#126—271no—
533#126—271no—
534#124—271no—
535#124—271no—
536#123—271no—
537#123—271no—
538C22⋊Q8—91no—
539#121—271no—
540#121—271no—
541#121—271no—
542#120—91no—
543#120—271no—
544C4×D4—91no—
545C4×D4—271no—
546C2×C22⋊C4—271no—
547H(3,𝔽3)#53811yescharacteristic, complemented, Sylow
548C23×C3—31no—
549C23×C3—31no—
550C23×C3—61no—
551C23×C3—91no—
552C23×C3—91no—
553C23×C3—91no—
554C23×C3—91no—
555C23×C3—182no—
556C23×C3—361no—
557C23×C3—361no—
558C23×C3C2×D3211yescharacteristic
559C22×D3—31no—
560C22×D3—31no—
561C22×D3—31no—
562C22×D3—31no—
563C22×D3—31no—
564C22×D3—31no—
565C22×D3—31no—
566C22×D3—61no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—62no—
570C22×D3—62no—
571C22×D3—91no—
572C22×D3—122no—
573C22×D3—121no—
574C22×D3—121no—
575C22×D3—121no—
576C22×D3—121no—
577C22×D3—122no—
578C22×D3—122no—
579C3×Q8—361no—
580C3×D4—182no—
581C3×D4—182no—
582C3×D4—361no—
583C3×D4—361no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—31no—
587C2×C3×C4—31no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—91no—
591C2×C3×C4—91no—
592C2×C3×C4—91no—
593C2×C3×C4—91no—
594C2×C3×C4—91no—
595C2×C3×C4—91no—
596C2×C3×C4—91no—
597C2×C3×C4—91no—
598C2×C3×C4—361no—
599C2×C3×C4—361no—
600C2×C3×C4—361no—
601C2×C3×C4C2×D3211yescharacteristic
602C2×C3×C4C2×D3211yescharacteristic
603#67—62no—
604#67—62no—
605#67—62no—
606#67—122no—
607#67—182no—
608#67—361no—
609#67—361no—
610#67—361no—
611#67—361no—
612#67—361no—
613#67—361no—
614C2×Dic3—31no—
615C2×Dic3—31no—
616C2×Dic3—31no—
617C2×Dic3—31no—
618C2×Dic3—31no—
619C2×Dic3—31no—
620C2×Dic3—31no—
621C2×Dic3—31no—
622C2×Dic3—31no—
623C2×Dic3—61no—
624C2×Dic3—91no—
625C2×Dic3—91no—
626C2×Dic3—91no—
627C2×Dic3—91no—
628C2×Dic3—91no—
629C2×Dic3—91no—
630C2×Dic3—91no—
631C2×Dic3—121no—
632C2×Dic3—121no—
633C2×Dic3—361no—
634C2×Dic3—361no—
635C2×Dic3—361no—
636D12—121no—
637D12—121no—
638D12—121no—
639D12—121no—
640D12—122no—
641D12—122no—
642D12—361no—
643D12—361no—
644D12—361no—
645C4×D3—121no—
646C4×D3—361no—
647C4×D3—361no—
648C4×D3—361no—
649Dic6—121no—
650Dic6—361no—
651C2×C32—22no—
652C2×C32—22no—
653C2×C32—21no—
654C2×C32—21no—
655C2×C32—21no—
656C2×C32—42no—
657C2×C32C2×#23511yescharacteristic
658C2×C32#100411yescharacteristic
659C2×C32#100411yescharacteristic
660C2×C32C2×#23911yescharacteristic
661C2×C32#100911yescharacteristic
662C2×C32#100911yescharacteristic
663C3⋊D3—41no—
664C3×D3—122no—
665C3×D3—122no—
666C3×D3—121no—
667C3×D3—121no—
668C3×D3—121no—
669C3×D3—121no—
670C3×D3—121no—
671C3×D3—121no—
672C3×D3—121no—
673C3×D3—241no—
674C24—91no—
675C2×Q8—91no—
676C2×D4—91no—
677C2×D4—91no—
678C2×D4—91no—
679C2×D4—91no—
680C2×D4—271no—
681C2×D4—271no—
682C2×D4—271no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—91no—
686C22×C4—271no—
687C4⋊C4—91no—
688C4⋊C4—91no—
689C4⋊C4—91no—
690C4⋊C4—91no—
691C4⋊C4—271no—
692C4⋊C4—271no—
693C22⋊C4—91no—
694C22⋊C4—91no—
695C22⋊C4—91no—
696C22⋊C4—91no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4—271no—
701C22⋊C4—271no—
702C22⋊C4—271no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4—271no—
706C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
707C42—91no—
708C42—271no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—31no—
712C22×C3—31no—
713C22×C3—32no—
714C22×C3—32no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—62no—
721C22×C3—121no—
722C22×C3—121no—
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—181no—
732C22×C3—181no—
733C22×C3—181no—
734C22×C3—181no—
735C22×C3—364no—
736C22×C3#379912yes—
737C22×C3C22×D3211yescharacteristic
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—61no—
743C2×D3—61no—
744C2×D3—61no—
745C2×D3—61no—
746C2×D3—61no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—61no—
751C2×D3—61no—
752C2×D3—61no—
753C2×D3—61no—
754C2×D3—61no—
755C2×D3—61no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—61no—
759C2×D3—61no—
760C2×D3—61no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—124no—
769C2×D3—124no—
770C2×D3—128no—
771C2×D3—181no—
772C2×D3—181no—
773C2×D3—181no—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—61no—
777C3×C4—61no—
778C3×C4—61no—
779C3×C4—61no—
780C3×C4—121no—
781C3×C4—121no—
782C3×C4—181no—
783C3×C4—181no—
784C3×C4—181no—
785C3×C4—181no—
786C3×C4—181no—
787C3×C4—181no—
788C3×C4—181no—
789C3×C4—181no—
790Dic3—61no—
791Dic3—61no—
792Dic3—61no—
793Dic3—61no—
794Dic3—61no—
795Dic3—61no—
796Dic3—61no—
797Dic3—61no—
798Dic3—61no—
799Dic3—121no—
800Dic3—181no—
801Dic3—181no—
802Dic3—181no—
803Dic3—181no—
804Dic3—181no—
805Dic3—181no—
806Dic3—181no—
807C32—21no—
808C32#556011yescharacteristic, complemented
809C32#564411yescharacteristic, complemented
810C23—91no—
811C23—91no—
812C23—91no—
813C23—91no—
814C23—182no—
815C23—361no—
816C23—361no—
817C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
818Q8—361no—
819D4—182no—
820D4—182no—
821D4—361no—
822D4—361no—
823D4—1081no—
824D4—1081no—
825D4—1081no—
826C2×C4—91no—
827C2×C4—91no—
828C2×C4—91no—
829C2×C4—91no—
830C2×C4—91no—
831C2×C4—91no—
832C2×C4—91no—
833C2×C4—91no—
834C2×C4—361no—
835C2×C4—361no—
836C2×C4—361no—
837C2×C4—1081no—
838C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
839C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
840C2×C3—22no—
841C2×C3—31no—
842C2×C3—31no—
843C2×C3—31no—
844C2×C3—31no—
845C2×C3—31no—
846C2×C3—31no—
847C2×C3—62no—
848C2×C3—62no—
849C2×C3—61no—
850C2×C3—61no—
851C2×C3—61no—
852C2×C3—122no—
853C2×C3—361no—
854C2×C3—361no—
855C2×C3—361no—
856C2×C3—361no—
857C2×C3C2×#379911yescharacteristic
858C2×C3#6431411yescharacteristic
859C2×C3#6431411yescharacteristic
860D3—121no—
861D3—121no—
862D3—121no—
863D3—121no—
864D3—121no—
865D3—121no—
866D3—122no—
867D3—122no—
868D3—121no—
869D3—241no—
870D3—361no—
871C22—21no—
872C22—21no—
873C22—181no—
874C22—181no—
875C22—181no—
876C22—181no—
877C22—181no—
878C22—181no—
879C22—181no—
880C22—181no—
881C22—181no—
882C22—181no—
883C22—181no—
884C22—181no—
885C22—364no—
886C22#8865212yes—
887C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
888C4—21no—
889C4—21no—
890C4—181no—
891C4—181no—
892C4—181no—
893C4—181no—
894C4—181no—
895C4—181no—
896C4—181no—
897C4—181no—
898C3—31no—
899C3—31no—
900C3—61no—
901C3#1059424311yescharacteristic
902C2—22no—
903C2—361no—
904C2—361no—
905C2—361no—
906C2—361no—
907C2C2×#8865211yescharacteristic
908C2#1172250711yescharacteristic
909C2#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. #11721738C2semidirect
2. #64090⋊C3C2semidirect
3. #64087⋊C3C2semidirect
4. #11721323C2semidirect
5. #11721322C2semidirect
6. C2×#88451C2semidirect
7. #11721293C2semidirect
8. #11721157C2semidirect
9. #11721156C2semidirect
10. #11721155C2semidirect
11. #11721151C2semidirect
12. #11721114C2semidirect
13. #11721100C2semidirect
14. #11721092C2semidirect
15. #11721088C2semidirect
25. C2×C4×(C3⋊D3)⋊C3C22semidirect
26. C2×#634⋊C3C22semidirect
29. C2×#6200C22semidirect
30. C2×#6199C22semidirect
35. #3752⋊C3C22semidirect
36. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
37. #3750⋊C3C22semidirect
38. #3750⋊C3C22semidirect
39. #3750⋊C3C22semidirect
40. C4×(C3⋊Dic3)⋊C3C22semidirect
47. #88451C22semidirect
48. #88451C22semidirect
49. #88450C22semidirect
50. #88449C22semidirect
51. #88448C22semidirect
52. #88447C22semidirect
53. #64090D3semidirect
54. #64087D3semidirect
123. C2×C4×C3⋊D3C2×D3semidirect
124. C2×#634C2×D3semidirect
151. #3752C2×D3semidirect
152. C4⋊(C3⋊Dic3)C2×D3semidirect
153. #3750C2×D3semidirect
154. #3750C2×D3semidirect
155. #3750C2×D3semidirect
156. C4×C3⋊Dic3C2×D3semidirect
547. H(3,𝔽3)#538semidirect
808. C32#5560semidirect
809. C32#5644semidirect

Maximal subgroups

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

subgroupindex
#117217382
#64090⋊C32
#64087⋊C32
#117213232
#117213222
C2×#884512
#117212932
#117211572
#117211562
#117211552
#117211512
#117211142
#117211002
#117210922
#117210882
#105942383
#105941733