Finite Group Databasebeta

← #13148643

Subgroups — #13148643

Order 1728.

1299 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6200C211yesmaximal, characteristic, complemented
2C2×#88652C211yesmaximal, characteristic, complemented
3#11721738C211yesmaximal, characteristic, complemented
4C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
5#64087⋊C3C211yesmaximal, characteristic, complemented
6#11721321C211yesmaximal, characteristic, complemented
7#11721320C211yesmaximal, characteristic, complemented
8#11721293C211yesmaximal, characteristic, complemented
9#11721157C211yesmaximal, characteristic, complemented
10#11721157C211yesmaximal, characteristic, complemented
11#11721156C211yesmaximal, characteristic, complemented
12#11721155C211yesmaximal, characteristic, complemented
13#11721154C211yesmaximal, characteristic, complemented
14#11721102C211yesmaximal, characteristic, complemented
15#11721100C211yesmaximal, characteristic, complemented
16#10594184—31nomaximal
17#10594063—31nomaximal
18C23×#272C2211yescharacteristic
19C23×(C3⋊D3)⋊C3C2211yescharacteristic
20C2×#6235C2211yescharacteristic
21C2×C4⋊#272C2211yescharacteristic, complemented
22C2×C4⋊#272C2211yescharacteristic, complemented
23C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
24C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
26C2×#634⋊C3C2211yescharacteristic, complemented
27C2×#6200—24no—
28C2×#6200C2211yescharacteristic
29C2×#6200C2211yescharacteristic
30C2×#6200C2211yescharacteristic
31C2×#6200C2211yescharacteristic
32C2×#6200C2211yescharacteristic, complemented
33C2×#6200C2211yescharacteristic, complemented
34C2×#6199C2211yescharacteristic, complemented
35C2×#6199C2211yescharacteristic, complemented
36C2×#6199C2211yescharacteristic, complemented
37#88652—24no—
38C22⋊C4×H(3,𝔽3)C2211yescharacteristic
39#88542C2211yescharacteristic, complemented
40#88542C2211yescharacteristic, complemented
41#3757⋊C3C2211yescharacteristic
42#3757⋊C3C2211yescharacteristic
43#3752⋊C3C2211yescharacteristic, complemented
44#3752⋊C3C2211yescharacteristic, complemented
45C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
46#3750⋊C3C2211yescharacteristic, complemented
47#3750⋊C3C2211yescharacteristic, complemented
48#88451C2211yescharacteristic, complemented
49#88451C2211yescharacteristic, complemented
50#88451C2211yescharacteristic, complemented
51#88450C2211yescharacteristic, complemented
52#88450C2211yescharacteristic, complemented
53#88449C2211yescharacteristic, complemented
54#88447C2211yescharacteristic, complemented
55C22×#626—31no—
56C22×#625—31no—
57C2×#3796—31no—
58C2×#3795—31no—
59C22⋊C4×C3⋊D3D311yescharacteristic, complemented
60#64087D311yescharacteristic, complemented
61C3×#882—31no—
62C3×#882—31no—
63C3×#882—61no—
64C3×D3×C22⋊C4—31no—
65C3×#878—31no—
66#63981—31no—
67#63976—31no—
68#67⋊Dic3—31no—
69Dic3×#67—31no—
70D3×#217—31no—
71D3×#217—31no—
72#63916—31no—
73#63913—31no—
74#63908—31no—
75#63907—31no—
76#63905—31no—
77#63891—31no—
78#63890—31no—
79#63886—31no—
80#63886—31no—
81#63885—31no—
82#63885—31no—
83#63881—31no—
84#63879—31no—
85#63853—31no—
86C23×H(3,𝔽3)C2311yescharacteristic
87C22×#272—22no—
88C22×#272—22no—
89C22×#272—41no—
90C22×#272C2311yescharacteristic
91C22×#272C2311yescharacteristic
92C22×#272C2311yescharacteristic
93C22×(C3⋊D3)⋊C3—22no—
94C22×(C3⋊D3)⋊C3—22no—
95C22×(C3⋊D3)⋊C3—41no—
96C22×(C3⋊D3)⋊C3C2311yescharacteristic
97C22×(C3⋊D3)⋊C3C2311yescharacteristic
98C2×C4×H(3,𝔽3)C2311yescharacteristic
99C2×C4×H(3,𝔽3)C2311yescharacteristic
100#6235—22no—
101C2×#1084C2311yescharacteristic
102C4⋊#272—22no—
103C4⋊#272—41no—
104C2×(C3⋊Dic3)⋊C3—22no—
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
108C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
109C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
110C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
111C4×(C3⋊D3)⋊C3—22no—
112C4×(C3⋊D3)⋊C3—41no—
113#634⋊C3—22no—
114#6200—22no—
115#6200—22no—
116#6200—22no—
117#6200—22no—
118#6200—41no—
119#6200D414yescomplemented
120#6199—22no—
121#6199—22no—
122#6199—41no—
123#5630—91no—
124#5591—91no—
125#5490—91no—
126C23×C3⋊D3C2×D311yescharacteristic
127C23×C3×D3—31no—
128C23×C3×D3—31no—
129C23×C3×D3—31no—
130C23×C3×D3—61no—
131C22×C3⋊Dic3C2×D311yescharacteristic
132C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
133C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
134C2×#634C2×D311yescharacteristic, complemented
135C2×C3×#67—31no—
136C2×C3×#67—31no—
137C2×C3×#67—61no—
138C22×C3×Dic3—31no—
139C2×C3×D12—31no—
140C2×C3×D12—31no—
141C2×C3×D12—31no—
142C2×C3×D12—31no—
143C2×C3×D12—61no—
144C2×C3×D12—61no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×Dic6—31no—
148C2×#626—31no—
149C2×#626—31no—
150C2×#626—31no—
151C2×#626—31no—
152C2×#626—31no—
153C2×#626—31no—
154C2×#626—64no—
155C2×#625—31no—
156C2×#625—31no—
157C2×#625—31no—
158C2×#625—31no—
159C2×#625—31no—
160C2×#625—31no—
161C2×#625—64no—
162C2×D3×Dic3—31no—
163C2×D3×Dic3—31no—
164C2×D3×Dic3—31no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—31no—
167C2×D3×Dic3—31no—
168#3796—64no—
169#3795—64no—
170C32×C22⋊C4—21no—
171C32×C22⋊C4C2×D311yescharacteristic
172C32×C22⋊C4C2×D311yescharacteristic
173#3757C2×D311yescharacteristic
174#3757C2×D311yescharacteristic
175#3752C2×D311yescharacteristic, complemented
176#3752C2×D311yescharacteristic, complemented
177C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
178#3750C2×D311yescharacteristic, complemented
179#3750C2×D311yescharacteristic, complemented
180C3×#217—31no—
181C3×#217—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—61no—
189C3×(C2×D3)⋊C4—61no—
190C3×C4⋊Dic3—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193Dic3⋊Dic3—31no—
194Dic3⋊Dic3—31no—
195#3722—31no—
196#3722—31no—
197(C2×D3)⋊Dic3—31no—
198(C2×D3)⋊Dic3—31no—
199(C2×D3)⋊Dic3—31no—
200(C2×D3)⋊Dic3—31no—
201(C2×D3)⋊Dic3—31no—
202(C2×D3)⋊Dic3—31no—
203(C2×D3)⋊Dic3—31no—
204(C2×D3)⋊Dic3—31no—
205Dic32—31no—
206Dic32—31no—
207C22×H(3,𝔽3)—21no—
208C22×H(3,𝔽3)—21no—
209C22×H(3,𝔽3)#4112yescomplemented
210C22×H(3,𝔽3)C2411yescharacteristic
211C2×#272—21no—
212C2×#272—21no—
213C2×#272—21no—
214C2×#272—21no—
215C2×#272—21no—
216C2×#272—21no—
217C2×#272—21no—
218C2×#272—21no—
219C2×#272—44no—
220C2×#272C2×D412yes—
221C2×(C3⋊D3)⋊C3—21no—
222C2×(C3⋊D3)⋊C3—21no—
223C2×(C3⋊D3)⋊C3—21no—
224C2×(C3⋊D3)⋊C3—21no—
225C2×(C3⋊D3)⋊C3—21no—
226C2×(C3⋊D3)⋊C3—44no—
227C2×(C3⋊D3)⋊C3C2×D412yes—
228C4×H(3,𝔽3)—21no—
229C4×H(3,𝔽3)—21no—
230#1084—21no—
231(C3⋊Dic3)⋊C3—21no—
232(C3⋊Dic3)⋊C3—21no—
233(C3⋊Dic3)⋊C3—21no—
234(C3⋊Dic3)⋊C3—21no—
235(C3⋊Dic3)⋊C3—21no—
236(C3⋊Dic3)⋊C3C2×D412yes—
237C22×#67—91no—
238C22×#67—91no—
239C2×#239—91no—
240C2×#237—91no—
241C2×#235—91no—
242C22×D12—91no—
243C3×C22⋊Q8—91no—
244C3×#120—91no—
245C2×C3×C22⋊C4—91no—
246#953—91no—
247C2×#217—91no—
248#947—91no—
249#939—91no—
250#939—91no—
251#938—91no—
252#937—91no—
253D4×Dic3—91no—
254#930—91no—
255#929—91no—
256C4×#67—91no—
257C4×#67—91no—
258#895—91no—
259#895—91no—
260#895—91no—
261#894—91no—
262#894—91no—
263#893—91no—
264#886—91no—
265#885—91no—
266#885—91no—
267#884—91no—
268#884—91no—
269#883—91no—
270#883—91no—
271#882—31no—
272#882—31no—
273#882—61no—
274#882—91no—
275#67⋊C4—91no—
276#67⋊C4—91no—
277D3×C22⋊C4—31no—
278D3×C22⋊C4—91no—
279D3×C22⋊C4—91no—
280D3×C22⋊C4—91no—
281#878—31no—
282#878—91no—
283C23×C32—21no—
284C23×C32C22×D311yescharacteristic
285C23×C32C22×D311yescharacteristic
286C22×C3⋊D3—22no—
287C22×C3⋊D3—22no—
288C22×C3⋊D3—41no—
289C22×C3⋊D3C22×D311yescharacteristic
290C22×C3⋊D3C22×D311yescharacteristic
291C22×C3×D3—31no—
292C22×C3×D3—31no—
293C22×C3×D3—31no—
294C22×C3×D3—31no—
295C22×C3×D3—31no—
296C22×C3×D3—31no—
297C22×C3×D3—31no—
298C22×C3×D3—31no—
299C22×C3×D3—61no—
300C22×C3×D3—61no—
301C22×C3×D3—61no—
302C22×C3×D3—62no—
303C22×C3×D3—62no—
304C22×C3×D3—62no—
305C22×C3×D3—62no—
306C22×C3×D3—62no—
307C22×C3×D3—62no—
308C22×C3×D3—122no—
309C22×C3×D3—122no—
310C22×C3×D3—121no—
311C22×C3×D3—121no—
312C22×C3×D3—121no—
313C22×C3×D3—122no—
314C2×C32×C4—21no—
315C2×C32×C4—21no—
316C2×C32×C4C22×D311yescharacteristic
317C2×C32×C4C22×D311yescharacteristic
318C2×C32×C4C22×D311yescharacteristic
319C2×C32×C4C22×D311yescharacteristic
320C2×C3⋊Dic3—22no—
321C2×C3⋊Dic3C22×D311yescharacteristic
322C2×C3⋊Dic3C22×D311yescharacteristic
323C2×C3⋊Dic3C22×D311yescharacteristic
324C2×C3⋊Dic3C22×D311yescharacteristic
325C2×C3⋊Dic3C22×D311yescharacteristic
326C2×C3⋊Dic3C22×D311yescharacteristic
327C4×C3⋊D3—22no—
328C4×C3⋊D3—41no—
329#634—22no—
330C3×#67—62no—
331C3×#67—62no—
332C3×#67—122no—
333C2×C3×Dic3—31no—
334C2×C3×Dic3—31no—
335C2×C3×Dic3—31no—
336C2×C3×Dic3—31no—
337C2×C3×Dic3—31no—
338C2×C3×Dic3—31no—
339C2×C3×Dic3—31no—
340C2×C3×Dic3—31no—
341C2×C3×Dic3—61no—
342C2×C3×Dic3—62no—
343C3×D12—62no—
344C3×D12—62no—
345C3×D12—122no—
346C3×D12—121no—
347C3×D12—121no—
348C3×D12—122no—
349C3×C4×D3—62no—
350C3×C4×D3—121no—
351C3×Dic6—62no—
352#626—34no—
353#626—62no—
354#626—62no—
355#626—62no—
356#626—62no—
357#626—121no—
358#625—34no—
359#625—62no—
360#625—62no—
361#625—62no—
362#625—62no—
363#625—121no—
364D3×Dic3—62no—
365D3×Dic3—62no—
366D3×Dic3—62no—
367D3×Dic3—62no—
368D3×Dic3—121no—
369D3×Dic3—121no—
370#546—271noSylow
371C2×H(3,𝔽3)—22no—
372C2×H(3,𝔽3)C22×D411yescharacteristic
373C2×H(3,𝔽3)C2×#4111yescharacteristic
374C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
375#272—22no—
376#272—41no—
377#272—41no—
378(C3⋊D3)⋊C3—22no—
379(C3⋊D3)⋊C3—41no—
380C24×C3—91no—
381C24×C3—91no—
382C23×D3—31no—
383C23×D3—31no—
384C23×D3—31no—
385C23×D3—61no—
386C23×D3—91no—
387C2×C3×Q8—91no—
388C2×C3×D4—91no—
389C2×C3×D4—91no—
390C2×C3×D4—91no—
391C22×C3×C4—91no—
392C22×C3×C4—91no—
393C22×C3×C4—91no—
394C2×#67—31no—
395C2×#67—31no—
396C2×#67—61no—
397C2×#67—91no—
398C2×#67—91no—
399C2×#67—91no—
400C2×#67—91no—
401C2×#67—91no—
402C2×#67—91no—
403C2×#67—91no—
404C2×#67—91no—
405C2×#67—91no—
406C2×#67—91no—
407C2×#67—91no—
408C2×#67—91no—
409C2×#67—184no—
410C2×#67—184no—
411C22×Dic3—31no—
412C22×Dic3—91no—
413C22×Dic3—91no—
414C22×Dic3—91no—
415C22×Dic3—91no—
416#239—184no—
417#237—184no—
418#235—184no—
419C2×D12—31no—
420C2×D12—31no—
421C2×D12—31no—
422C2×D12—31no—
423C2×D12—61no—
424C2×D12—61no—
425C2×D12—91no—
426C2×D12—91no—
427C2×D12—91no—
428C2×D12—91no—
429C2×D12—91no—
430C2×D12—91no—
431C2×D12—184no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—91no—
435C2×C4×D3—91no—
436C2×C4×D3—91no—
437C2×C4×D3—91no—
438C2×C4×D3—91no—
439C2×C4×D3—91no—
440C2×C4×D3—91no—
441C2×C4×D3—91no—
442C2×Dic6—31no—
443C2×Dic6—91no—
444C3×C4⋊C4—91no—
445C3×C4⋊C4—91no—
446C3×C4⋊C4—91no—
447C3×C22⋊C4—31no—
448C3×C22⋊C4—31no—
449C3×C22⋊C4—61no—
450C3×C22⋊C4—91no—
451C3×C22⋊C4—91no—
452C3×C22⋊C4—91no—
453C3×C22⋊C4—91no—
454C3×C22⋊C4—91no—
455C3×C22⋊C4—91no—
456C3×C22⋊C4D3211yescharacteristic
457#217—31no—
458#217—31no—
459#217—91no—
460#217—91no—
461#217—91no—
462#217—91no—
463#217—91no—
464#217—91no—
465#217—91no—
466(C2×D3)⋊C4—31no—
467(C2×D3)⋊C4—31no—
468(C2×D3)⋊C4—31no—
469(C2×D3)⋊C4—31no—
470(C2×D3)⋊C4—31no—
471(C2×D3)⋊C4—31no—
472(C2×D3)⋊C4—61no—
473(C2×D3)⋊C4—61no—
474(C2×D3)⋊C4—91no—
475(C2×D3)⋊C4—91no—
476(C2×D3)⋊C4—91no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—91no—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—91no—
482(C2×D3)⋊C4—91no—
483(C2×D3)⋊C4—91no—
484(C2×D3)⋊C4—91no—
485(C2×D3)⋊C4—91no—
486C4⋊Dic3—31no—
487C4⋊Dic3—91no—
488C4⋊Dic3—91no—
489Dic3⋊C4—31no—
490Dic3⋊C4—31no—
491Dic3⋊C4—91no—
492Dic3⋊C4—91no—
493Dic3⋊C4—91no—
494Dic3⋊C4—91no—
495C4×Dic3—91no—
496C4×Dic3—91no—
497C4×Dic3—91no—
498C22×C32—21no—
499C22×C32—21no—
500C22×C32—21no—
501C22×C32—21no—
502C22×C32—21no—
503C22×C32—22no—
504C22×C32—41no—
505C22×C32—41no—
506C22×C32#23512yescomplemented
507C22×C32#23912yescomplemented
508C22×C32C23×D311yescharacteristic
509C22×C32C23×D311yescharacteristic
510C2×C3⋊D3—21no—
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—21no—
514C2×C3⋊D3—21no—
515C2×C3⋊D3—44no—
516C2×C3⋊D3D3×D412yes—
517C2×C3×D3—32no—
518C2×C3×D3—32no—
519C2×C3×D3—32no—
520C2×C3×D3—62no—
521C2×C3×D3—61no—
522C2×C3×D3—61no—
523C2×C3×D3—61no—
524C2×C3×D3—61no—
525C2×C3×D3—61no—
526C2×C3×D3—61no—
527C2×C3×D3—62no—
528C2×C3×D3—61no—
529C2×C3×D3—61no—
530C2×C3×D3—61no—
531C2×C3×D3—61no—
532C2×C3×D3—61no—
533C2×C3×D3—61no—
534C2×C3×D3—61no—
535C2×C3×D3—61no—
536C2×C3×D3—61no—
537C2×C3×D3—61no—
538C2×C3×D3—61no—
539C2×C3×D3—61no—
540C2×C3×D3—61no—
541C2×C3×D3—61no—
542C2×C3×D3—61no—
543C2×C3×D3—121no—
544C2×C3×D3—121no—
545C2×C3×D3—121no—
546C2×C3×D3—121no—
547C2×C3×D3—121no—
548C2×C3×D3—121no—
549C2×C3×D3—121no—
550C2×C3×D3—124no—
551C2×C3×D3—124no—
552C2×C3×D3—124no—
553C2×C3×D3—128no—
554C32×C4—21no—
555C32×C4—21no—
556C32×C4—21no—
557C32×C4—21no—
558C32×C4—41no—
559C32×C4—41no—
560C3⋊Dic3—21no—
561C3⋊Dic3—21no—
562C3⋊Dic3—21no—
563C3⋊Dic3—21no—
564C3⋊Dic3—21no—
565C3⋊Dic3D3×D412yes—
566C3×Dic3—32no—
567C3×Dic3—61no—
568C3×Dic3—61no—
569C3×Dic3—61no—
570C3×Dic3—61no—
571C3×Dic3—61no—
572C3×Dic3—61no—
573C3×Dic3—61no—
574C3×Dic3—121no—
575C2×#41—271no—
576C22×D4—271no—
577#124—271no—
578#123—271no—
579#123—271no—
580C22⋊Q8—91no—
581#121—271no—
582#121—271no—
583#121—271no—
584#120—91no—
585#120—271no—
586C4×D4—271no—
587C4×D4—271no—
588C2×C22⋊C4—91no—
589C2×C22⋊C4—271no—
590H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
591C23×C3—31no—
592C23×C3—31no—
593C23×C3—61no—
594C23×C3—91no—
595C23×C3—91no—
596C23×C3—91no—
597C23×C3—91no—
598C23×C3—91no—
599C23×C3—182no—
600C23×C3—182no—
601C23×C3—182no—
602C23×C3—182no—
603C23×C3—361no—
604C23×C3—361no—
605C23×C3C2×D3211yescharacteristic
606C22×D3—31no—
607C22×D3—31no—
608C22×D3—31no—
609C22×D3—31no—
610C22×D3—31no—
611C22×D3—31no—
612C22×D3—31no—
613C22×D3—31no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—61no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—62no—
620C22×D3—62no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—91no—
624C22×D3—91no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—121no—
628C22×D3—121no—
629C22×D3—121no—
630C22×D3—122no—
631C22×D3—182no—
632C22×D3—182no—
633C22×D3—361no—
634C3×Q8—182no—
635C3×D4—182no—
636C3×D4—182no—
637C3×D4—361no—
638C2×C3×C4—31no—
639C2×C3×C4—31no—
640C2×C3×C4—31no—
641C2×C3×C4—31no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—91no—
645C2×C3×C4—91no—
646C2×C3×C4—91no—
647C2×C3×C4—91no—
648C2×C3×C4—91no—
649C2×C3×C4—91no—
650C2×C3×C4—91no—
651C2×C3×C4—182no—
652C2×C3×C4—182no—
653C2×C3×C4—361no—
654C2×C3×C4C2×D3211yescharacteristic
655C2×C3×C4C2×D3211yescharacteristic
656#67—62no—
657#67—62no—
658#67—94no—
659#67—94no—
660#67—122no—
661#67—182no—
662#67—182no—
663#67—182no—
664#67—182no—
665#67—182no—
666#67—182no—
667#67—182no—
668#67—182no—
669#67—361no—
670#67—361no—
671C2×Dic3—31no—
672C2×Dic3—31no—
673C2×Dic3—31no—
674C2×Dic3—31no—
675C2×Dic3—31no—
676C2×Dic3—31no—
677C2×Dic3—31no—
678C2×Dic3—31no—
679C2×Dic3—61no—
680C2×Dic3—62no—
681C2×Dic3—91no—
682C2×Dic3—91no—
683C2×Dic3—91no—
684C2×Dic3—91no—
685C2×Dic3—91no—
686C2×Dic3—91no—
687C2×Dic3—182no—
688C2×Dic3—182no—
689C2×Dic3—182no—
690C2×Dic3—361no—
691D12—62no—
692D12—62no—
693D12—94no—
694D12—122no—
695D12—121no—
696D12—121no—
697D12—122no—
698D12—182no—
699D12—182no—
700D12—182no—
701D12—182no—
702D12—361no—
703C4×D3—62no—
704C4×D3—121no—
705C4×D3—182no—
706C4×D3—182no—
707C4×D3—182no—
708C4×D3—182no—
709C4×D3—182no—
710C4×D3—361no—
711C4×D3—361no—
712C4×D3—361no—
713Dic6—62no—
714Dic6—182no—
715C2×C32—22no—
716C2×C32—22no—
717C2×C32—21no—
718C2×C32—21no—
719C2×C32—21no—
720C2×C32—42no—
721C2×C32C2×#23511yescharacteristic
722C2×C32C2×D3×D411yescharacteristic
723C2×C32C2×D3×D411yescharacteristic
724C2×C32#100411yescharacteristic
725C2×C32C2×#23911yescharacteristic
726C2×C32#100911yescharacteristic
727C3⋊D3—22no—
728C3⋊D3—41no—
729C3×D3—62no—
730C3×D3—62no—
731C3×D3—62no—
732C3×D3—122no—
733C3×D3—122no—
734C3×D3—121no—
735C3×D3—121no—
736C3×D3—121no—
737C3×D3—121no—
738C3×D3—121no—
739C3×D3—241no—
740C24—91no—
741C24—91no—
742#41—544no—
743C2×Q8—91no—
744C2×D4—91no—
745C2×D4—91no—
746C2×D4—91no—
747C2×D4—271no—
748C2×D4—271no—
749C2×D4—271no—
750C2×D4—271no—
751C2×D4—271no—
752C2×D4—271no—
753C2×D4—544no—
754C22×C4—91no—
755C22×C4—91no—
756C22×C4—91no—
757C22×C4—271no—
758C22×C4—271no—
759C22×C4—271no—
760C4⋊C4—91no—
761C4⋊C4—91no—
762C4⋊C4—91no—
763C4⋊C4—271no—
764C22⋊C4—91no—
765C22⋊C4—91no—
766C22⋊C4—91no—
767C22⋊C4—91no—
768C22⋊C4—91no—
769C22⋊C4—91no—
770C22⋊C4—271no—
771C22⋊C4—271no—
772C22⋊C4—271no—
773C22⋊C4—271no—
774C22⋊C4—271no—
775C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
776C42—271no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—31no—
780C22×C3—31no—
781C22×C3—32no—
782C22×C3—32no—
783C22×C3—61no—
784C22×C3—61no—
785C22×C3—61no—
786C22×C3—61no—
787C22×C3—61no—
788C22×C3—62no—
789C22×C3—92no—
790C22×C3—92no—
791C22×C3—121no—
792C22×C3—121no—
793C22×C3—181no—
794C22×C3—181no—
795C22×C3—181no—
796C22×C3—181no—
797C22×C3—181no—
798C22×C3—181no—
799C22×C3—181no—
800C22×C3—181no—
801C22×C3—181no—
802C22×C3—181no—
803C22×C3—181no—
804C22×C3—181no—
805C22×C3—181no—
806C22×C3—364no—
807C22×C3—364no—
808C22×C3#379912yes—
809C22×C3C22×D3211yescharacteristic
810C2×D3—32no—
811C2×D3—32no—
812C2×D3—32no—
813C2×D3—62no—
814C2×D3—61no—
815C2×D3—61no—
816C2×D3—61no—
817C2×D3—61no—
818C2×D3—61no—
819C2×D3—61no—
820C2×D3—61no—
821C2×D3—61no—
822C2×D3—61no—
823C2×D3—61no—
824C2×D3—61no—
825C2×D3—61no—
826C2×D3—61no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—61no—
831C2×D3—61no—
832C2×D3—62no—
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—61no—
836C2×D3—92no—
837C2×D3—121no—
838C2×D3—121no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—121no—
842C2×D3—121no—
843C2×D3—121no—
844C2×D3—124no—
845C2×D3—124no—
846C2×D3—124no—
847C2×D3—128no—
848C2×D3—181no—
849C2×D3—181no—
850C2×D3—181no—
851C2×D3—181no—
852C2×D3—181no—
853C2×D3—364no—
854C3×C4—21no—
855C3×C4—21no—
856C3×C4—61no—
857C3×C4—61no—
858C3×C4—61no—
859C3×C4—61no—
860C3×C4—92no—
861C3×C4—121no—
862C3×C4—121no—
863C3×C4—181no—
864C3×C4—181no—
865C3×C4—181no—
866C3×C4—181no—
867C3×C4—181no—
868C3×C4—181no—
869Dic3—32no—
870Dic3—61no—
871Dic3—61no—
872Dic3—61no—
873Dic3—61no—
874Dic3—61no—
875Dic3—61no—
876Dic3—61no—
877Dic3—92no—
878Dic3—121no—
879Dic3—181no—
880Dic3—181no—
881Dic3—181no—
882Dic3—181no—
883Dic3—181no—
884C32—21no—
885C32#549011yescharacteristic, complemented
886C32#563011yescharacteristic, complemented
887C23—91no—
888C23—91no—
889C23—91no—
890C23—91no—
891C23—91no—
892C23—182no—
893C23—182no—
894C23—182no—
895C23—182no—
896C23—361no—
897C23—361no—
898C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
899Q8—182no—
900D4—182no—
901D4—182no—
902D4—274no—
903D4—361no—
904D4—542no—
905D4—542no—
906D4—542no—
907D4—542no—
908D4—1081no—
909C2×C4—91no—
910C2×C4—91no—
911C2×C4—91no—
912C2×C4—91no—
913C2×C4—91no—
914C2×C4—91no—
915C2×C4—91no—
916C2×C4—182no—
917C2×C4—182no—
918C2×C4—361no—
919C2×C4—542no—
920C2×C4—542no—
921C2×C4—1081no—
922C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
923C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
924C2×C3—22no—
925C2×C3—31no—
926C2×C3—31no—
927C2×C3—31no—
928C2×C3—31no—
929C2×C3—31no—
930C2×C3—31no—
931C2×C3—62no—
932C2×C3—62no—
933C2×C3—61no—
934C2×C3—61no—
935C2×C3—61no—
936C2×C3—122no—
937C2×C3—182no—
938C2×C3—182no—
939C2×C3—361no—
940C2×C3—361no—
941C2×C3—361no—
942C2×C3C2×#379911yescharacteristic
943C2×C3D32×D411yescharacteristic
944C2×C3#6431411yescharacteristic
945D3—62no—
946D3—62no—
947D3—62no—
948D3—122no—
949D3—121no—
950D3—121no—
951D3—121no—
952D3—121no—
953D3—122no—
954D3—121no—
955D3—182no—
956D3—241no—
957D3—361no—
958C22—21no—
959C22—21no—
960C22—92no—
961C22—92no—
962C22—181no—
963C22—181no—
964C22—181no—
965C22—181no—
966C22—181no—
967C22—181no—
968C22—181no—
969C22—181no—
970C22—181no—
971C22—181no—
972C22—181no—
973C22—181no—
974C22—181no—
975C22—364no—
976C22—364no—
977C22#8865212yescomplemented
978C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
979C4—21no—
980C4—21no—
981C4—92no—
982C4—181no—
983C4—181no—
984C4—181no—
985C4—181no—
986C4—181no—
987C4—181no—
988C3—31no—
989C3—31no—
990C3—61no—
991C3#1059418711yescharacteristic
992C2—22no—
993C2—182no—
994C2—182no—
995C2—361no—
996C2—361no—
997C2—361no—
998C2C2×#8865211yescharacteristic
999C2D4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
1000C2#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)#546
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×#6200C2semidirect
2. C2×#88652C2semidirect
3. #11721738C2semidirect
4. C22⋊C4×(C3⋊D3)⋊C3C2semidirect
5. #64087⋊C3C2semidirect
6. #11721321C2semidirect
7. #11721320C2semidirect
8. #11721293C2semidirect
9. #11721157C2semidirect
10. #11721157C2semidirect
11. #11721156C2semidirect
12. #11721155C2semidirect
13. #11721154C2semidirect
14. #11721102C2semidirect
15. #11721100C2semidirect
21. C2×C4⋊#272C22semidirect
22. C2×C4⋊#272C22semidirect
24. C2×C4×(C3⋊D3)⋊C3C22semidirect
25. C2×C4×(C3⋊D3)⋊C3C22semidirect
26. C2×#634⋊C3C22semidirect
32. C2×#6200C22semidirect
33. C2×#6200C22semidirect
34. C2×#6199C22semidirect
35. C2×#6199C22semidirect
36. C2×#6199C22semidirect
39. #88542C22semidirect
40. #88542C22semidirect
43. #3752⋊C3C22semidirect
44. #3752⋊C3C22semidirect
45. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
46. #3750⋊C3C22semidirect
47. #3750⋊C3C22semidirect
48. #88451C22semidirect
49. #88451C22semidirect
50. #88451C22semidirect
51. #88450C22semidirect
52. #88450C22semidirect
53. #88449C22semidirect
54. #88447C22semidirect
59. C22⋊C4×C3⋊D3D3semidirect
60. #64087D3semidirect
119. #6200D4semidirect
132. C2×C4×C3⋊D3C2×D3semidirect
133. C2×C4×C3⋊D3C2×D3semidirect
134. C2×#634C2×D3semidirect
175. #3752C2×D3semidirect
176. #3752C2×D3semidirect
177. C4⋊(C3⋊Dic3)C2×D3semidirect
178. #3750C2×D3semidirect
179. #3750C2×D3semidirect
209. C22×H(3,𝔽3)#41semidirect
506. C22×C32#235semidirect
507. C22×C32#239semidirect
590. H(3,𝔽3)#546semidirect
885. C32#5490semidirect
886. C32#5630semidirect
977. C22#88652semidirect

Maximal subgroups

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

subgroupindex
C22×#62002
C2×#886522
#117217382
C22⋊C4×(C3⋊D3)⋊C32
#64087⋊C32
#117213212
#117213202
#117212932
#117211572
#117211562
#117211552
#117211542
#117211022
#117211002
#105941843
#105940633