Finite Group Databasebeta

← #13148648

Subgroups — #13148648

Order 1728.

1301 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6200C211yesmaximal, characteristic, complemented
2C2×#88649C211yesmaximal, characteristic, complemented
3C22⋊C4×#272C211yesmaximal, characteristic, complemented
4#64091⋊C3C211yesmaximal, characteristic, complemented
5#64087⋊C3C211yesmaximal, characteristic, complemented
6#11721323C211yesmaximal, characteristic, complemented
7#11721314C211yesmaximal, characteristic, complemented
8#11721310C211yesmaximal, characteristic, complemented
9#11721159C211yesmaximal, characteristic, complemented
10#11721155C211yesmaximal, characteristic, complemented
11#11721130C211yesmaximal, characteristic, complemented
12#11721127C211yesmaximal, characteristic, complemented
13#11721127C211yesmaximal, characteristic, complemented
14#11721124C211yesmaximal, characteristic, complemented
15#11721104C211yesmaximal, characteristic, complemented
16#10594187—31nomaximal
17#10594184—31nomaximal
18C23×#272C2211yescharacteristic
19C23×(C3⋊D3)⋊C3C2211yescharacteristic
20C2×C4×#272C2211yescharacteristic, complemented
21C2×C4×#272C2211yescharacteristic, complemented
22C2×#638⋊C3C2211yescharacteristic
23C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
24C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
25C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
26C2×#634⋊C3C2211yescharacteristic, complemented
27C2×#6200—24no—
28C2×#6200C2211yescharacteristic
29C2×#6200C2211yescharacteristic
30C2×#6200C2211yescharacteristic
31C2×#6200C2211yescharacteristic
32C2×#6200C2211yescharacteristic, complemented
33C2×#6200C2211yescharacteristic, complemented
34C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
35C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
36C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
37#88649—24no—
38C22⋊C4×H(3,𝔽3)C2211yescharacteristic
39#88552C2211yescharacteristic
40#88542C2211yescharacteristic, complemented
41#88542C2211yescharacteristic, complemented
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#88450C2211yescharacteristic, complemented
51#88450C2211yescharacteristic, complemented
52#88450C2211yescharacteristic, complemented
53#88448C2211yescharacteristic, complemented
54#88447C2211yescharacteristic, complemented
55C22×#626—31no—
56C22×#625—31no—
57C2×#3799—31no—
58C2×#3795—31no—
59#64091D311yescharacteristic, complemented
60#64087D311yescharacteristic, complemented
61C3×#882—31no—
62C3×D3×C22⋊C4—31no—
63C3×D3×C22⋊C4—31no—
64C3×D3×C22⋊C4—61no—
65C3×#878—31no—
66#63977—31no—
67#63976—31no—
68#63974—31no—
69#67⋊Dic3—31no—
70D3×#217—31no—
71#63952—31no—
72#63913—31no—
73#63910—31no—
74#63910—31no—
75#63909—31no—
76#63908—31no—
77#63907—31no—
78#63905—31no—
79#63904—31no—
80#63891—31no—
81#63885—31no—
82#63885—31no—
83#63879—31no—
84#63854—31no—
85#63850—31no—
86C23×H(3,𝔽3)C2311yescharacteristic
87C22×#272—22no—
88C22×#272—22no—
89C22×#272—41no—
90C22×#272C2311yescharacteristic
91C22×#272C2311yescharacteristic
92C22×(C3⋊D3)⋊C3—22no—
93C22×(C3⋊D3)⋊C3—22no—
94C22×(C3⋊D3)⋊C3—41no—
95C22×(C3⋊D3)⋊C3C2311yescharacteristic
96C22×(C3⋊D3)⋊C3C2311yescharacteristic
97C22×(C3⋊D3)⋊C3C2311yescharacteristic
98C2×C4×H(3,𝔽3)C2311yescharacteristic
99C2×C4×H(3,𝔽3)C2311yescharacteristic
100C2×#1084C2311yescharacteristic
101C2×#1084C2311yescharacteristic
102C4×#272—22no—
103C4×#272—41no—
104#638⋊C3—22no—
105C2×(C3⋊Dic3)⋊C3—22no—
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((C3⋊D3)⋊C3)⋊C4—22no—
121((C3⋊D3)⋊C3)⋊C4—22no—
122((C3⋊D3)⋊C3)⋊C4—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—
131C2×#638C2×D311yescharacteristic
132C22×C3⋊Dic3C2×D311yescharacteristic
133C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
134C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
135C2×#634C2×D311yescharacteristic, complemented
136C2×C3×#67—31no—
137C22×C3×Dic3—31no—
138C2×C3×D12—31no—
139C2×C3×D12—31no—
140C2×C3×C4×D3—31no—
141C2×C3×C4×D3—31no—
142C2×C3×C4×D3—31no—
143C2×C3×C4×D3—31no—
144C2×C3×C4×D3—61no—
145C2×C3×C4×D3—61no—
146C2×C3×Dic6—31no—
147C2×#626—31no—
148C2×#626—31no—
149C2×#626—31no—
150C2×#626—31no—
151C2×#626—31no—
152C2×#626—31no—
153C2×#626—64no—
154C2×#625—31no—
155C2×#625—31no—
156C2×#625—31no—
157C2×#625—31no—
158C2×#625—31no—
159C2×#625—31no—
160C2×#625—64no—
161C2×#624—31no—
162C2×#624—31no—
163C2×#624—31no—
164C2×D3×Dic3—31no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—31no—
167#3799—64no—
168#3795—64no—
169C32×C22⋊C4—21no—
170C32×C22⋊C4C2×D311yescharacteristic
171C32×C22⋊C4C2×D311yescharacteristic
172#3757C2×D311yescharacteristic
173#3752C2×D311yescharacteristic, complemented
174#3752C2×D311yescharacteristic, complemented
175C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
176#3750C2×D311yescharacteristic, complemented
177#3750C2×D311yescharacteristic, complemented
178C3×#217—31no—
179C3×#217—31no—
180C3×#217—31no—
181C3×#217—61no—
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—
193#3724—31no—
194Dic3⋊Dic3—31no—
195#3722—31no—
196#3722—31no—
197#3722—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—44no—
217C2×#272C2×D412yes—
218C2×(C3⋊D3)⋊C3—21no—
219C2×(C3⋊D3)⋊C3—21no—
220C2×(C3⋊D3)⋊C3—21no—
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#1084—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—91no—
273#882—91no—
274#67⋊C4—91no—
275#67⋊C4—91no—
276D3×C22⋊C4—31no—
277D3×C22⋊C4—31no—
278D3×C22⋊C4—61no—
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⋊D3C22×D311yescharacteristic
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—62no—
302C22×C3×D3—62no—
303C22×C3×D3—62no—
304C22×C3×D3—64no—
305C22×C3×D3—62no—
306C22×C3×D3—62no—
307C22×C3×D3—62no—
308C22×C3×D3—122no—
309C22×C3×D3—121no—
310C22×C3×D3—121no—
311C22×C3×D3—121no—
312C22×C3×D3—122no—
313C2×C32×C4—21no—
314C2×C32×C4—21no—
315C2×C32×C4C22×D311yescharacteristic
316C2×C32×C4C22×D311yescharacteristic
317C2×C32×C4C22×D311yescharacteristic
318C2×C32×C4C22×D311yescharacteristic
319#638—22no—
320C2×C3⋊Dic3—22no—
321C2×C3⋊Dic3C22×D311yescharacteristic
322C2×C3⋊Dic3C22×D311yescharacteristic
323C2×C3⋊Dic3C22×D311yescharacteristic
324C2×C3⋊Dic3C22×D311yescharacteristic
325C2×C3⋊Dic3C22×D311yescharacteristic
326C4⋊(C3⋊D3)—22no—
327C4⋊(C3⋊D3)—41no—
328#634—22no—
329C3×#67—62no—
330C2×C3×Dic3—31no—
331C2×C3×Dic3—31no—
332C2×C3×Dic3—31no—
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—61no—
340C2×C3×Dic3—61no—
341C2×C3×Dic3—62no—
342C3×D12—62no—
343C3×D12—121no—
344C3×C4×D3—62no—
345C3×C4×D3—62no—
346C3×C4×D3—122no—
347C3×C4×D3—121no—
348C3×C4×D3—121no—
349C3×C4×D3—122no—
350C3×Dic6—62no—
351#626—34no—
352#626—62no—
353#626—62no—
354#626—62no—
355#626—62no—
356#626—121no—
357#625—34no—
358#625—62no—
359#625—62no—
360#625—62no—
361#625—62no—
362#625—121no—
363#624—62no—
364#624—62no—
365#624—121no—
366D3×Dic3—62no—
367D3×Dic3—62no—
368D3×Dic3—121no—
369#546—271noSylow
370C2×H(3,𝔽3)—22no—
371C2×H(3,𝔽3)C22×D411yescharacteristic
372C2×H(3,𝔽3)C2×#4111yescharacteristic
373C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
374#272—22no—
375#272—41no—
376(C3⋊D3)⋊C3—22no—
377(C3⋊D3)⋊C3—41no—
378(C3⋊D3)⋊C3—41no—
379C24×C3—91no—
380C24×C3—91no—
381C23×D3—31no—
382C23×D3—31no—
383C23×D3—31no—
384C23×D3—61no—
385C23×D3—91no—
386C2×C3×Q8—91no—
387C2×C3×D4—91no—
388C2×C3×D4—91no—
389C2×C3×D4—91no—
390C22×C3×C4—91no—
391C22×C3×C4—91no—
392C22×C3×C4—91no—
393C2×#67—31no—
394C2×#67—91no—
395C2×#67—91no—
396C2×#67—91no—
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—184no—
408C2×#67—184no—
409C22×Dic3—31no—
410C22×Dic3—91no—
411C22×Dic3—91no—
412C22×Dic3—91no—
413C22×Dic3—91no—
414#239—184no—
415#237—184no—
416#235—184no—
417C2×D12—31no—
418C2×D12—31no—
419C2×D12—91no—
420C2×D12—91no—
421C2×D12—91no—
422C2×D12—91no—
423C2×D12—91no—
424C2×D12—91no—
425C2×D12—91no—
426C2×D12—91no—
427C2×D12—184no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—61no—
433C2×C4×D3—61no—
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×Dic6—31no—
441C2×Dic6—91no—
442C3×C4⋊C4—91no—
443C3×C4⋊C4—91no—
444C3×C4⋊C4—91no—
445C3×C22⋊C4—31no—
446C3×C22⋊C4—31no—
447C3×C22⋊C4—61no—
448C3×C22⋊C4—91no—
449C3×C22⋊C4—91no—
450C3×C22⋊C4—91no—
451C3×C22⋊C4—91no—
452C3×C22⋊C4—91no—
453C3×C22⋊C4—91no—
454C3×C22⋊C4D3211yescharacteristic
455#217—31no—
456#217—31no—
457#217—31no—
458#217—61no—
459#217—91no—
460#217—91no—
461#217—91no—
462#217—91no—
463#217—91no—
464#217—91no—
465(C2×D3)⋊C4—31no—
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—61no—
472(C2×D3)⋊C4—61no—
473(C2×D3)⋊C4—91no—
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—
485C4⋊Dic3—31no—
486C4⋊Dic3—91no—
487C4⋊Dic3—91no—
488Dic3⋊C4—31no—
489Dic3⋊C4—31no—
490Dic3⋊C4—91no—
491Dic3⋊C4—91no—
492Dic3⋊C4—91no—
493Dic3⋊C4—91no—
494C4×Dic3—91no—
495C4×Dic3—91no—
496C4×Dic3—91no—
497C22×C32—21no—
498C22×C32—21no—
499C22×C32—21no—
500C22×C32—21no—
501C22×C32—21no—
502C22×C32—22no—
503C22×C32—41no—
504C22×C32—41no—
505C22×C32#23712yescomplemented
506C22×C32#23912yescomplemented
507C22×C32C23×D311yescharacteristic
508C22×C32C23×D311yescharacteristic
509C2×C3⋊D3—21no—
510C2×C3⋊D3—21no—
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—21no—
514C2×C3⋊D3—21no—
515C2×C3⋊D3—21no—
516C2×C3⋊D3—21no—
517C2×C3⋊D3—44no—
518C2×C3⋊D3D3×D412yes—
519C2×C3×D3—32no—
520C2×C3×D3—32no—
521C2×C3×D3—32no—
522C2×C3×D3—62no—
523C2×C3×D3—62no—
524C2×C3×D3—62no—
525C2×C3×D3—61no—
526C2×C3×D3—61no—
527C2×C3×D3—61no—
528C2×C3×D3—61no—
529C2×C3×D3—61no—
530C2×C3×D3—61no—
531C2×C3×D3—62no—
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—61no—
544C2×C3×D3—121no—
545C2×C3×D3—121no—
546C2×C3×D3—124no—
547C2×C3×D3—124no—
548C2×C3×D3—124no—
549C2×C3×D3—128no—
550C32×C4—21no—
551C32×C4—21no—
552C32×C4—21no—
553C32×C4—21no—
554C32×C4—41no—
555C32×C4—41no—
556C3⋊Dic3—21no—
557C3⋊Dic3—21no—
558C3⋊Dic3—21no—
559C3⋊Dic3—21no—
560C3⋊Dic3D3×D412yes—
561C3×Dic3—32no—
562C3×Dic3—61no—
563C3×Dic3—61no—
564C3×Dic3—61no—
565C3×Dic3—61no—
566C3×Dic3—61no—
567C3×Dic3—61no—
568C3×Dic3—61no—
569C3×Dic3—61no—
570C3×Dic3—121no—
571C3×Dic3—121no—
572C2×#41—271no—
573C22×D4—271no—
574#124—271no—
575#123—271no—
576#123—271no—
577C22⋊Q8—91no—
578#121—271no—
579#121—271no—
580#121—271no—
581#120—91no—
582#120—271no—
583C4×D4—271no—
584C4×D4—271no—
585C2×C22⋊C4—91no—
586C2×C22⋊C4—271no—
587H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
588C23×C3—31no—
589C23×C3—31no—
590C23×C3—61no—
591C23×C3—91no—
592C23×C3—91no—
593C23×C3—91no—
594C23×C3—91no—
595C23×C3—91no—
596C23×C3—182no—
597C23×C3—182no—
598C23×C3—182no—
599C23×C3—182no—
600C23×C3—361no—
601C23×C3—361no—
602C23×C3C2×D3211yescharacteristic
603C22×D3—31no—
604C22×D3—31no—
605C22×D3—31no—
606C22×D3—31no—
607C22×D3—31no—
608C22×D3—31no—
609C22×D3—31no—
610C22×D3—61no—
611C22×D3—61no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—62no—
616C22×D3—62no—
617C22×D3—64no—
618C22×D3—62no—
619C22×D3—91no—
620C22×D3—91no—
621C22×D3—91no—
622C22×D3—122no—
623C22×D3—121no—
624C22×D3—121no—
625C22×D3—121no—
626C22×D3—122no—
627C22×D3—182no—
628C22×D3—182no—
629C22×D3—361no—
630C3×Q8—182no—
631C3×D4—182no—
632C3×D4—182no—
633C3×D4—361no—
634C2×C3×C4—31no—
635C2×C3×C4—31no—
636C2×C3×C4—31no—
637C2×C3×C4—31no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—91no—
641C2×C3×C4—91no—
642C2×C3×C4—91no—
643C2×C3×C4—91no—
644C2×C3×C4—91no—
645C2×C3×C4—91no—
646C2×C3×C4—91no—
647C2×C3×C4—182no—
648C2×C3×C4—182no—
649C2×C3×C4—361no—
650C2×C3×C4C2×D3211yescharacteristic
651C2×C3×C4C2×D3211yescharacteristic
652#67—62no—
653#67—94no—
654#67—94no—
655#67—182no—
656#67—182no—
657#67—182no—
658#67—182no—
659#67—182no—
660#67—182no—
661#67—182no—
662#67—182no—
663#67—182no—
664#67—361no—
665#67—361no—
666C2×Dic3—31no—
667C2×Dic3—31no—
668C2×Dic3—31no—
669C2×Dic3—31no—
670C2×Dic3—31no—
671C2×Dic3—31no—
672C2×Dic3—31no—
673C2×Dic3—31no—
674C2×Dic3—31no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—62no—
678C2×Dic3—91no—
679C2×Dic3—91no—
680C2×Dic3—91no—
681C2×Dic3—91no—
682C2×Dic3—91no—
683C2×Dic3—182no—
684C2×Dic3—182no—
685C2×Dic3—182no—
686C2×Dic3—361no—
687D12—62no—
688D12—94no—
689D12—121no—
690D12—182no—
691D12—182no—
692D12—182no—
693D12—182no—
694D12—182no—
695D12—361no—
696D12—361no—
697C4×D3—62no—
698C4×D3—62no—
699C4×D3—122no—
700C4×D3—121no—
701C4×D3—121no—
702C4×D3—122no—
703C4×D3—182no—
704C4×D3—182no—
705C4×D3—182no—
706C4×D3—182no—
707C4×D3—361no—
708C4×D3—361no—
709Dic6—62no—
710Dic6—182no—
711C2×C32—22no—
712C2×C32—22no—
713C2×C32—21no—
714C2×C32—21no—
715C2×C32—21no—
716C2×C32—42no—
717C2×C32C2×D3×D411yescharacteristic
718C2×C32C2×D3×D411yescharacteristic
719C2×C32C2×#23711yescharacteristic
720C2×C32#100411yescharacteristic
721C2×C32C2×#23911yescharacteristic
722C2×C32#100911yescharacteristic
723C3⋊D3—22no—
724C3⋊D3—41no—
725C3⋊D3—41no—
726C3×D3—64no—
727C3×D3—62no—
728C3×D3—62no—
729C3×D3—62no—
730C3×D3—122no—
731C3×D3—121no—
732C3×D3—121no—
733C3×D3—121no—
734C3×D3—121no—
735C24—91no—
736C24—91no—
737#41—544no—
738C2×Q8—91no—
739C2×D4—91no—
740C2×D4—91no—
741C2×D4—91no—
742C2×D4—271no—
743C2×D4—271no—
744C2×D4—271no—
745C2×D4—271no—
746C2×D4—271no—
747C2×D4—271no—
748C2×D4—544no—
749C22×C4—91no—
750C22×C4—91no—
751C22×C4—91no—
752C22×C4—271no—
753C22×C4—271no—
754C22×C4—271no—
755C4⋊C4—91no—
756C4⋊C4—91no—
757C4⋊C4—91no—
758C4⋊C4—271no—
759C22⋊C4—91no—
760C22⋊C4—91no—
761C22⋊C4—91no—
762C22⋊C4—91no—
763C22⋊C4—91no—
764C22⋊C4—91no—
765C22⋊C4—271no—
766C22⋊C4—271no—
767C22⋊C4—271no—
768C22⋊C4—271no—
769C22⋊C4—271no—
770C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
771C42—271no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—31no—
775C22×C3—31no—
776C22×C3—32no—
777C22×C3—32no—
778C22×C3—61no—
779C22×C3—61no—
780C22×C3—61no—
781C22×C3—61no—
782C22×C3—61no—
783C22×C3—62no—
784C22×C3—92no—
785C22×C3—92no—
786C22×C3—121no—
787C22×C3—121no—
788C22×C3—181no—
789C22×C3—181no—
790C22×C3—181no—
791C22×C3—181no—
792C22×C3—181no—
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—364no—
802C22×C3—364no—
803C22×C3#379612yes—
804C22×C3C22×D3211yescharacteristic
805C2×D3—32no—
806C2×D3—32no—
807C2×D3—32no—
808C2×D3—62no—
809C2×D3—61no—
810C2×D3—61no—
811C2×D3—61no—
812C2×D3—61no—
813C2×D3—62no—
814C2×D3—62no—
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—62no—
824C2×D3—61no—
825C2×D3—61no—
826C2×D3—61no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—92no—
831C2×D3—121no—
832C2×D3—121no—
833C2×D3—124no—
834C2×D3—124no—
835C2×D3—124no—
836C2×D3—128no—
837C2×D3—181no—
838C2×D3—181no—
839C2×D3—181no—
840C2×D3—181no—
841C2×D3—181no—
842C2×D3—181no—
843C2×D3—181no—
844C2×D3—181no—
845C2×D3—364no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—92no—
853C3×C4—121no—
854C3×C4—121no—
855C3×C4—181no—
856C3×C4—181no—
857C3×C4—181no—
858C3×C4—181no—
859C3×C4—181no—
860C3×C4—181no—
861Dic3—32no—
862Dic3—61no—
863Dic3—61no—
864Dic3—61no—
865Dic3—61no—
866Dic3—61no—
867Dic3—61no—
868Dic3—61no—
869Dic3—61no—
870Dic3—92no—
871Dic3—121no—
872Dic3—121no—
873Dic3—181no—
874Dic3—181no—
875Dic3—181no—
876Dic3—181no—
877C32—21no—
878C32#559111yescharacteristic, complemented
879C32#563011yescharacteristic, complemented
880C23—91no—
881C23—91no—
882C23—91no—
883C23—91no—
884C23—91no—
885C23—182no—
886C23—182no—
887C23—182no—
888C23—182no—
889C23—361no—
890C23—361no—
891C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
892Q8—182no—
893D4—182no—
894D4—182no—
895D4—274no—
896D4—361no—
897D4—542no—
898D4—542no—
899D4—542no—
900D4—542no—
901D4—1081no—
902C2×C4—91no—
903C2×C4—91no—
904C2×C4—91no—
905C2×C4—91no—
906C2×C4—91no—
907C2×C4—91no—
908C2×C4—91no—
909C2×C4—182no—
910C2×C4—182no—
911C2×C4—361no—
912C2×C4—542no—
913C2×C4—542no—
914C2×C4—1081no—
915C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
916C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
917C2×C3—22no—
918C2×C3—31no—
919C2×C3—31no—
920C2×C3—31no—
921C2×C3—31no—
922C2×C3—31no—
923C2×C3—31no—
924C2×C3—62no—
925C2×C3—62no—
926C2×C3—61no—
927C2×C3—61no—
928C2×C3—61no—
929C2×C3—122no—
930C2×C3—182no—
931C2×C3—182no—
932C2×C3—361no—
933C2×C3—361no—
934C2×C3—361no—
935C2×C3C2×#379611yescharacteristic
936C2×C3D32×D411yescharacteristic
937C2×C3#6431411yescharacteristic
938D3—62no—
939D3—62no—
940D3—64no—
941D3—62no—
942D3—121no—
943D3—121no—
944D3—122no—
945D3—121no—
946D3—121no—
947D3—182no—
948D3—361no—
949D3—361no—
950C22—21no—
951C22—21no—
952C22—92no—
953C22—92no—
954C22—181no—
955C22—181no—
956C22—181no—
957C22—181no—
958C22—181no—
959C22—181no—
960C22—181no—
961C22—181no—
962C22—181no—
963C22—181no—
964C22—181no—
965C22—181no—
966C22—181no—
967C22—364no—
968C22—364no—
969C22#8864912yescomplemented
970C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
971C4—21no—
972C4—21no—
973C4—92no—
974C4—181no—
975C4—181no—
976C4—181no—
977C4—181no—
978C4—181no—
979C4—181no—
980C3—31no—
981C3—31no—
982C3—61no—
983C3#1059406311yescharacteristic
984C2—22no—
985C2—182no—
986C2—182no—
987C2—361no—
988C2—361no—
989C2—361no—
990C2C2×#8864911yescharacteristic
991C2D4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
992C2#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×#88649C2semidirect
3. C22⋊C4×#272C2semidirect
4. #64091⋊C3C2semidirect
5. #64087⋊C3C2semidirect
6. #11721323C2semidirect
7. #11721314C2semidirect
8. #11721310C2semidirect
9. #11721159C2semidirect
10. #11721155C2semidirect
11. #11721130C2semidirect
12. #11721127C2semidirect
13. #11721127C2semidirect
14. #11721124C2semidirect
15. #11721104C2semidirect
20. C2×C4×#272C22semidirect
21. C2×C4×#272C22semidirect
24. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
25. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
26. C2×#634⋊C3C22semidirect
32. C2×#6200C22semidirect
33. C2×#6200C22semidirect
34. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
35. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
36. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
40. #88542C22semidirect
41. #88542C22semidirect
43. #3752⋊C3C22semidirect
44. #3752⋊C3C22semidirect
45. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
46. #3750⋊C3C22semidirect
47. #3750⋊C3C22semidirect
48. #88451C22semidirect
49. #88451C22semidirect
50. #88450C22semidirect
51. #88450C22semidirect
52. #88450C22semidirect
53. #88448C22semidirect
54. #88447C22semidirect
59. #64091D3semidirect
60. #64087D3semidirect
119. #6200D4semidirect
133. C2×C4⋊(C3⋊D3)C2×D3semidirect
134. C2×C4⋊(C3⋊D3)C2×D3semidirect
135. C2×#634C2×D3semidirect
173. #3752C2×D3semidirect
174. #3752C2×D3semidirect
175. C4⋊(C3⋊Dic3)C2×D3semidirect
176. #3750C2×D3semidirect
177. #3750C2×D3semidirect
209. C22×H(3,𝔽3)#41semidirect
505. C22×C32#237semidirect
506. C22×C32#239semidirect
587. H(3,𝔽3)#546semidirect
878. C32#5591semidirect
879. C32#5630semidirect
969. C22#88649semidirect

Maximal subgroups

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

subgroupindex
C22×#62002
C2×#886492
C22⋊C4×#2722
#64091⋊C32
#64087⋊C32
#117213232
#117213142
#117213102
#117211592
#117211552
#117211302
#117211272
#117211242
#117211042
#105941873
#105941843