Finite Group Databasebeta

← #13148642

Subgroups — #13148642

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×#88650C211yesmaximal, characteristic, complemented
3C22⋊C4×#272C211yesmaximal, characteristic, complemented
4#64090⋊C3C211yesmaximal, characteristic, complemented
5C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
6#11721323C211yesmaximal, characteristic, complemented
7#11721316C211yesmaximal, characteristic, complemented
8#11721299C211yesmaximal, characteristic, complemented
9C4×#6200C211yesmaximal, characteristic, complemented
10#11721142C211yesmaximal, characteristic, complemented
11#11721140C211yesmaximal, characteristic, complemented
12#11721140C211yesmaximal, characteristic, complemented
13#11721104C211yesmaximal, characteristic, complemented
14#11721103C211yesmaximal, characteristic, complemented
15#11721100C211yesmaximal, characteristic, complemented
16#10594186—31nomaximal
17#10594183—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)⋊C3C2211yescharacteristic, complemented
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
26C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
27C2×#6200—24no—
28C2×#6200C2211yescharacteristic
29C2×#6200C2211yescharacteristic
30C2×#6200C2211yescharacteristic
31C2×#6200C2211yescharacteristic
32C2×#6200C2211yescharacteristic, complemented
33C2×#6200C2211yescharacteristic, complemented
34C2×#6198C2211yescharacteristic, complemented
35C2×#6198C2211yescharacteristic, complemented
36C2×#6196C2211yescharacteristic, complemented
37#88650—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
45#3752⋊C3C2211yescharacteristic, complemented
46#3750⋊C3C2211yescharacteristic, complemented
47C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
48#88451C2211yescharacteristic, complemented
49#88451C2211yescharacteristic, complemented
50#88450C2211yescharacteristic, complemented
51#88450C2211yescharacteristic, complemented
52#88449C2211yescharacteristic, complemented
53#88448C2211yescharacteristic, complemented
54#88448C2211yescharacteristic, complemented
55C22×#626—31no—
56C22×#625—31no—
57C2×#3798—31no—
58C2×#3798—31no—
59#64090D311yescharacteristic, complemented
60C22⋊C4×C3⋊D3D311yescharacteristic, complemented
61C3×#67⋊C4—31no—
62C3×D3×C22⋊C4—31no—
63C3×D3×C22⋊C4—31no—
64C3×D3×C22⋊C4—31no—
65C3×D3×C22⋊C4—61no—
66#63982—31no—
67#63981—31no—
68#63977—31no—
69#63977—31no—
70#63976—31no—
71#63964—31no—
72#63915—31no—
73#63912—31no—
74#63912—31no—
75#63906—31no—
76#63906—31no—
77#63906—31no—
78#63906—31no—
79#63905—31no—
80#63905—31no—
81C4×#626—31no—
82C4×#625—31no—
83#63853—31no—
84#63852—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—22no—
113C4×(C3⋊D3)⋊C3—41no—
114#6200—22no—
115#6200—22no—
116#6200—22no—
117#6200—22no—
118#6200—41no—
119#6200D414yescomplemented
120#6198—22no—
121#6198—41no—
122#6196—22no—
123#5550—91no—
124#5490—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⋊D3C2×D311yescharacteristic, complemented
134C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
135C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
136C2×C3×#67—31no—
137C22×C3×Dic3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—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—31no—
145C2×C3×C4×D3—61no—
146C2×C3×C4×D3—61no—
147C2×#627—31no—
148C2×#627—31no—
149C2×#626—31no—
150C2×#626—31no—
151C2×#626—31no—
152C2×#626—31no—
153C2×#626—31no—
154C2×#626—31no—
155C2×#626—31no—
156C2×#626—31no—
157C2×#626—31no—
158C2×#626—31no—
159C2×#626—64no—
160C2×#625—31no—
161C2×#625—31no—
162C2×#625—31no—
163C2×#625—31no—
164C2×#625—31no—
165C2×#625—31no—
166C2×#625—64no—
167#3798—64no—
168#3798—64no—
169C32×C22⋊C4—21no—
170C32×C22⋊C4C2×D311yescharacteristic
171C32×C22⋊C4C2×D311yescharacteristic
172#3757C2×D311yescharacteristic
173#3752C2×D311yescharacteristic, complemented
174#3752C2×D311yescharacteristic, complemented
175#3752C2×D311yescharacteristic, complemented
176#3750C2×D311yescharacteristic, complemented
177C4×C3⋊Dic3C2×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—31no—
189C3×(C2×D3)⋊C4—61no—
190C3×(C2×D3)⋊C4—61no—
191C3×Dic3⋊C4—31no—
192C3×C4×Dic3—31no—
193#3724—31no—
194#3724—31no—
195Dic3⋊Dic3—31no—
196Dic3⋊Dic3—31no—
197Dic3⋊Dic3—31no—
198Dic3⋊Dic3—31no—
199#3722—31no—
200#3722—31no—
201(C2×D3)⋊Dic3—31no—
202(C2×D3)⋊Dic3—31no—
203(C2×D3)⋊Dic3—31no—
204(C2×D3)⋊Dic3—31no—
205(C2×D3)⋊Dic3—31no—
206(C2×D3)⋊Dic3—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×#235—91no—
240C2×#235—91no—
241C2×#235—91no—
242C22×D12—91no—
243C3×C4×D4—91no—
244C2×C3×C22⋊C4—91no—
245C2×C3×C22⋊C4—91no—
246#953—91no—
247#953—91no—
248#937—91no—
249#937—91no—
250#930—91no—
251#930—91no—
252#930—91no—
253#929—91no—
254#929—91no—
255C4×#67—91no—
256C4×#67—91no—
257#924—91no—
258#894—91no—
259#894—91no—
260#885—91no—
261#885—91no—
262#884—91no—
263#884—91no—
264#884—91no—
265#884—91no—
266#884—91no—
267#884—91no—
268#883—91no—
269#883—91no—
270#882—91no—
271#882—91no—
272#67⋊C4—31no—
273#67⋊C4—91no—
274D3×C22⋊C4—31no—
275D3×C22⋊C4—31no—
276D3×C22⋊C4—31no—
277D3×C22⋊C4—61no—
278D3×C22⋊C4—91no—
279#878—91no—
280#878—91no—
281#875—91no—
282C4×D12—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—22no—
328C4×C3⋊D3—41no—
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×C4×D3—62no—
343C3×C4×D3—62no—
344C3×C4×D3—62no—
345C3×C4×D3—62no—
346C3×C4×D3—122no—
347C3×C4×D3—121no—
348C3×C4×D3—121no—
349C3×C4×D3—121no—
350C3×C4×D3—122no—
351#627—62no—
352#627—62no—
353#626—34no—
354#626—62no—
355#626—62no—
356#626—62no—
357#626—62no—
358#626—62no—
359#626—62no—
360#626—121no—
361#626—121no—
362#626—121no—
363#625—34no—
364#625—62no—
365#625—62no—
366#625—62no—
367#625—62no—
368#625—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×D4—91no—
387C22×C3×C4—91no—
388C22×C3×C4—91no—
389C22×C3×C4—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—91no—
408C2×#67—91no—
409C2×#67—91no—
410C2×#67—91no—
411C2×#67—184no—
412C2×#67—184no—
413C22×Dic3—31no—
414C22×Dic3—91no—
415#235—184no—
416#235—184no—
417#235—184no—
418C2×D12—91no—
419C2×D12—91no—
420C2×D12—91no—
421C2×D12—91no—
422C2×D12—91no—
423C2×D12—91no—
424C2×D12—91no—
425C2×D12—91no—
426C2×D12—184no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—61no—
435C2×C4×D3—61no—
436C2×C4×D3—91no—
437C2×C4×D3—91no—
438C2×C4×D3—91no—
439C2×Dic6—91no—
440C2×Dic6—91no—
441C2×Dic6—91no—
442C3×C4⋊C4—91no—
443C3×C22⋊C4—31no—
444C3×C22⋊C4—31no—
445C3×C22⋊C4—61no—
446C3×C22⋊C4—91no—
447C3×C22⋊C4—91no—
448C3×C22⋊C4—91no—
449C3×C22⋊C4—91no—
450C3×C22⋊C4—91no—
451C3×C22⋊C4—91no—
452C3×C22⋊C4—91no—
453C3×C22⋊C4D3211yescharacteristic
454C3×C42—91no—
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(C2×D3)⋊C4—31no—
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—
484C4⋊Dic3—91no—
485C4⋊Dic3—91no—
486C4⋊Dic3—91no—
487Dic3⋊C4—31no—
488Dic3⋊C4—91no—
489Dic3⋊C4—91no—
490Dic3⋊C4—91no—
491Dic3⋊C4—91no—
492Dic3⋊C4—91no—
493Dic3⋊C4—91no—
494Dic3⋊C4—91no—
495C4×Dic3—31no—
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#23512yescomplemented
506C22×C32#23512yescomplemented
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—271no—
578#121—271no—
579#121—271no—
580#121—271no—
581#120—271no—
582#120—271no—
583C4×D4—91no—
584C4×D4—271no—
585C2×C22⋊C4—91no—
586C2×C22⋊C4—91no—
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×D4—182no—
631C2×C3×C4—31no—
632C2×C3×C4—31no—
633C2×C3×C4—31no—
634C2×C3×C4—31no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—91no—
638C2×C3×C4—91no—
639C2×C3×C4—91no—
640C2×C3×C4—91no—
641C2×C3×C4—91no—
642C2×C3×C4—91no—
643C2×C3×C4—91no—
644C2×C3×C4—182no—
645C2×C3×C4—182no—
646C2×C3×C4—182no—
647C2×C3×C4—182no—
648C2×C3×C4—361no—
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—182no—
665#67—182no—
666#67—361no—
667#67—361no—
668#67—361no—
669#67—361no—
670C2×Dic3—31no—
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—61no—
681C2×Dic3—62no—
682C2×Dic3—91no—
683C2×Dic3—91no—
684C2×Dic3—91no—
685C2×Dic3—91no—
686C2×Dic3—91no—
687C2×Dic3—182no—
688D12—94no—
689D12—182no—
690D12—182no—
691D12—182no—
692D12—182no—
693D12—182no—
694D12—361no—
695D12—361no—
696C4×D3—62no—
697C4×D3—62no—
698C4×D3—62no—
699C4×D3—62no—
700C4×D3—122no—
701C4×D3—121no—
702C4×D3—121no—
703C4×D3—121no—
704C4×D3—122no—
705C4×D3—182no—
706C4×D3—182no—
707C4×D3—361no—
708Dic6—182no—
709Dic6—182no—
710Dic6—182no—
711C2×C32—22no—
712C2×C32—22no—
713C2×C32—21no—
714C2×C32—21no—
715C2×C32—21no—
716C2×C32—42no—
717C2×C32C2×#23511yescharacteristic
718C2×C32C2×#23511yescharacteristic
719C2×C32C2×D3×D411yescharacteristic
720C2×C32C2×D3×D411yescharacteristic
721C2×C32#100411yescharacteristic
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—271no—
739C2×D4—91no—
740C2×D4—271no—
741C2×D4—271no—
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—91no—
753C22×C4—91no—
754C22×C4—91no—
755C4⋊C4—91no—
756C4⋊C4—271no—
757C4⋊C4—271no—
758C4⋊C4—271no—
759C22⋊C4—91no—
760C22⋊C4—91no—
761C22⋊C4—91no—
762C22⋊C4—91no—
763C22⋊C4—91no—
764C22⋊C4—91no—
765C22⋊C4—91no—
766C22⋊C4—271no—
767C22⋊C4—271no—
768C22⋊C4—271no—
769C22⋊C4—271no—
770C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
771C42—91no—
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#379812yes—
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#549011yescharacteristic, complemented
879C32#555011yescharacteristic, 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—542no—
893D4—182no—
894D4—274no—
895D4—542no—
896D4—542no—
897D4—542no—
898D4—542no—
899D4—542no—
900D4—1081no—
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—182no—
912C2×C4—182no—
913C2×C4—361no—
914C2×C4—361no—
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×#379811yescharacteristic
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#8865012yescomplemented
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#1059418611yescharacteristic
984C2—22no—
985C2—182no—
986C2—182no—
987C2—361no—
988C2—361no—
989C2—361no—
990C2C2×#8865011yescharacteristic
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×#88650C2semidirect
3. C22⋊C4×#272C2semidirect
4. #64090⋊C3C2semidirect
5. C22⋊C4×(C3⋊D3)⋊C3C2semidirect
6. #11721323C2semidirect
7. #11721316C2semidirect
8. #11721299C2semidirect
9. C4×#6200C2semidirect
10. #11721142C2semidirect
11. #11721140C2semidirect
12. #11721140C2semidirect
13. #11721104C2semidirect
14. #11721103C2semidirect
15. #11721100C2semidirect
20. C2×C4×#272C22semidirect
21. C2×C4×#272C22semidirect
24. C2×C4×(C3⋊D3)⋊C3C22semidirect
25. C2×C4×(C3⋊D3)⋊C3C22semidirect
26. C2×C4×(C3⋊D3)⋊C3C22semidirect
32. C2×#6200C22semidirect
33. C2×#6200C22semidirect
34. C2×#6198C22semidirect
35. C2×#6198C22semidirect
36. C2×#6196C22semidirect
40. #88542C22semidirect
41. #88542C22semidirect
43. #3752⋊C3C22semidirect
44. #3752⋊C3C22semidirect
45. #3752⋊C3C22semidirect
46. #3750⋊C3C22semidirect
47. C4×(C3⋊Dic3)⋊C3C22semidirect
48. #88451C22semidirect
49. #88451C22semidirect
50. #88450C22semidirect
51. #88450C22semidirect
52. #88449C22semidirect
53. #88448C22semidirect
54. #88448C22semidirect
59. #64090D3semidirect
60. C22⋊C4×C3⋊D3D3semidirect
119. #6200D4semidirect
133. C2×C4×C3⋊D3C2×D3semidirect
134. C2×C4×C3⋊D3C2×D3semidirect
135. C2×C4×C3⋊D3C2×D3semidirect
173. #3752C2×D3semidirect
174. #3752C2×D3semidirect
175. #3752C2×D3semidirect
176. #3750C2×D3semidirect
177. C4×C3⋊Dic3C2×D3semidirect
209. C22×H(3,𝔽3)#41semidirect
505. C22×C32#235semidirect
506. C22×C32#235semidirect
587. H(3,𝔽3)#546semidirect
878. C32#5490semidirect
879. C32#5550semidirect
969. C22#88650semidirect

Maximal subgroups

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

subgroupindex
C22×#62002
C2×#886502
C22⋊C4×#2722
#64090⋊C32
C22⋊C4×(C3⋊D3)⋊C32
#117213232
#117213162
#117212992
C4×#62002
#117211422
#117211402
#117211042
#117211032
#117211002
#105941863
#105941833