Finite Group Databasebeta

← #13148686

Subgroups — #13148686

Order 1728.

969 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721737C211yesmaximal, characteristic, complemented
2#64091⋊C3C211yesmaximal, characteristic, complemented
3#64087⋊C3C211yesmaximal, characteristic, complemented
4#11721322C211yesmaximal, characteristic, complemented
5#11721321C211yesmaximal, characteristic, complemented
6#11721315C211yesmaximal, characteristic, complemented
7C2×#88450C211yesmaximal, characteristic, complemented
8#11721159C211yesmaximal, characteristic, complemented
9#11721155C211yesmaximal, characteristic, complemented
10#11721127C211yesmaximal, characteristic, complemented
11#11721125C211yesmaximal, characteristic, complemented
12#11721113C211yesmaximal, characteristic, complemented
13#11721112C211yesmaximal, characteristic, complemented
14#11721108C211yesmaximal, characteristic, complemented
15#11721104C211yesmaximal, characteristic, complemented
16#10594243—31nomaximal
17#10594238—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C2×#6235C2211yescharacteristic
20C22×#1084C2211yescharacteristic
21C2×C4×#272C2211yescharacteristic, complemented
22C2×#638⋊C3C2211yescharacteristic
23C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
24C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
25C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
26C2×#634⋊C3C2211yescharacteristic, complemented
27C2×#6200C2211yescharacteristic
28C2×#6200C2211yescharacteristic
29C2×#6200C2211yescharacteristic, complemented
30C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
31C22⋊C4×H(3,𝔽3)C2211yescharacteristic
32#88542C2211yescharacteristic, complemented
33#88540C2211yescharacteristic, complemented
34C4×#1084C2211yescharacteristic, complemented
35#3757⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
39#3750⋊C3C2211yescharacteristic, complemented
40#3750⋊C3C2211yescharacteristic, complemented
41#88451C2211yescharacteristic, complemented
42#88450C2211yescharacteristic
43#88450C2211yescharacteristic
44#88450C2211yescharacteristic
45#88450C2211yescharacteristic
46#88450C2211yescharacteristic
47#88450C2211yescharacteristic
48#88450C2211yescharacteristic, complemented
49#88450C2211yescharacteristic, complemented
50#88448C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53#64091D311yescharacteristic, complemented
54#64087D311yescharacteristic, complemented
55C3×#882—31no—
56C3×#67⋊C4—31no—
57C3×#67⋊C4—31no—
58C3×#67⋊C4—61no—
59C3×#878—31no—
60#63981—31no—
61#63980—31no—
62#63978—31no—
63#63976—31no—
64Dic3×#67—31no—
65C2×#3722—31no—
66C2×(C2×D3)⋊Dic3—31no—
67#63952—31no—
68#63913—31no—
69#63910—31no—
70#63909—31no—
71#63908—31no—
72#63907—31no—
73#63905—31no—
74#63897—31no—
75#63885—31no—
76#63884—31no—
77#63868—31no—
78#63864—31no—
79#63861—31no—
80#63860—31no—
81#63859—31no—
82#63850—31no—
83#63848—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×#272C2311yescharacteristic
86C22×(C3⋊D3)⋊C3—22no—
87C22×(C3⋊D3)⋊C3—41no—
88C22×(C3⋊D3)⋊C3—41no—
89C22×(C3⋊D3)⋊C3C2311yescharacteristic
90C22×(C3⋊D3)⋊C3C2311yescharacteristic
91C22×(C3⋊D3)⋊C3C2311yescharacteristic
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94#6235—22no—
95C2×#1084—41no—
96C2×#1084C2311yescharacteristic
97C2×#1084C2311yescharacteristic
98C2×#1084C2311yescharacteristic
99C4×#272—41no—
100#638⋊C3—22no—
101C2×(C3⋊Dic3)⋊C3—41no—
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C4⋊((C3⋊D3)⋊C3)—41no—
108C4⋊((C3⋊D3)⋊C3)—41no—
109#634⋊C3—41no—
110#6200—41no—
111#6200—41no—
112#6200—41no—
113((C3⋊D3)⋊C3)⋊C4—41no—
114#5644—91no—
115#5593—91no—
116#5560—91no—
117C23×C3⋊D3C2×D311yescharacteristic
118C23×C3×D3—31no—
119C2×#638C2×D311yescharacteristic
120C22×C3⋊Dic3C2×D311yescharacteristic
121C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
122C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
123C2×#634C2×D311yescharacteristic, complemented
124C2×C3×#67—31no—
125C2×C3×#67—31no—
126C2×C3×#67—31no—
127C2×C3×#67—61no—
128C22×C3×Dic3—31no—
129C22×C3×Dic3—31no—
130C22×C3×Dic3—31no—
131C22×C3×Dic3—61no—
132C2×C3×D12—31no—
133C2×C3×D12—31no—
134C2×C3×C4×D3—31no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—61no—
137C2×C3×Dic6—31no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#626—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#3752C2×D311yescharacteristic
151#3752C2×D311yescharacteristic
152C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
153#3750C2×D311yescharacteristic, complemented
154#3750C2×D311yescharacteristic, complemented
155C3×#217—31no—
156C3×(C2×D3)⋊C4—31no—
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4—31no—
160C3×(C2×D3)⋊C4—61no—
161C3×C4⋊Dic3—31no—
162C3×Dic3⋊C4—31no—
163C3×Dic3⋊C4—31no—
164C3×Dic3⋊C4—31no—
165C3×Dic3⋊C4—31no—
166C3×Dic3⋊C4—61no—
167C3×C4×Dic3—31no—
168C3×C4×Dic3—31no—
169C3×C4×Dic3—61no—
170#3724—31no—
171#3724—31no—
172Dic3⋊Dic3—31no—
173Dic3⋊Dic3—31no—
174#3722—31no—
175#3722—31no—
176#3722—31no—
177#3722—31no—
178#3722—31no—
179#3722—31no—
180#3722—31no—
181#3722—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×(C3⋊D3)⋊C3—21no—
202C2×(C3⋊D3)⋊C3—21no—
203C2×(C3⋊D3)⋊C3—21no—
204C2×(C3⋊D3)⋊C3—21no—
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—44no—
211C4×H(3,𝔽3)—21no—
212C4×H(3,𝔽3)—21no—
213#1084—21no—
214#1084—21no—
215#1084—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—91no—
256#882—91no—
257#67⋊C4—31no—
258#67⋊C4—31no—
259#67⋊C4—61no—
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⋊D3—22no—
271C22×C3⋊D3—41no—
272C22×C3⋊D3—41no—
273C22×C3⋊D3C22×D311yescharacteristic
274C22×C3⋊D3C22×D311yescharacteristic
275C22×C3⋊D3C22×D311yescharacteristic
276C22×C3×D3—31no—
277C22×C3×D3—31no—
278C22×C3×D3—31no—
279C22×C3×D3—31no—
280C22×C3×D3—31no—
281C22×C3×D3—61no—
282C22×C3×D3—62no—
283C22×C3×D3—121no—
284C22×C3×D3—121no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291#638—22no—
292C2×C3⋊Dic3—41no—
293C2×C3⋊Dic3C22×D311yescharacteristic
294C2×C3⋊Dic3C22×D311yescharacteristic
295C2×C3⋊Dic3C22×D311yescharacteristic
296C2×C3⋊Dic3C22×D311yescharacteristic
297C2×C3⋊Dic3C22×D311yescharacteristic
298C4⋊(C3⋊D3)—41no—
299C4⋊(C3⋊D3)—41no—
300#634—41no—
301C3×#67—64no—
302C3×#67—62no—
303C3×#67—62no—
304C3×#67—62no—
305C2×C3×Dic3—31no—
306C2×C3×Dic3—31no—
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—61no—
317C2×C3×Dic3—61no—
318C2×C3×Dic3—61no—
319C2×C3×Dic3—121no—
320C2×C3×Dic3—121no—
321C2×C3×Dic3—121no—
322C2×C3×Dic3—122no—
323C3×D12—121no—
324C3×D12—121no—
325C3×C4×D3—121no—
326C3×C4×D3—121no—
327C3×C4×D3—122no—
328C3×Dic6—121no—
329#626—121no—
330#626—121no—
331#626—121no—
332#625—121no—
333#625—121no—
334#625—121no—
335#624—121no—
336D3×Dic3—121no—
337#538—271noSylow
338C2×H(3,𝔽3)—22no—
339C2×H(3,𝔽3)C2×#4111yescharacteristic
340C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
341C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
342#272—41no—
343(C3⋊D3)⋊C3—41no—
344(C3⋊D3)⋊C3—41no—
345(C3⋊D3)⋊C3—41no—
346C24×C3—91no—
347C23×D3—31no—
348C23×D3—91no—
349C2×C3×Q8—91no—
350C2×C3×D4—91no—
351C2×C3×D4—91no—
352C2×C3×D4—91no—
353C2×C3×D4—91no—
354C22×C3×C4—91no—
355C22×C3×C4—91no—
356C22×C3×C4—91no—
357C2×#67—31no—
358C2×#67—31no—
359C2×#67—31no—
360C2×#67—61no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67—91no—
365C2×#67—91no—
366C2×#67—91no—
367C2×#67—91no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—61no—
372C22×Dic3—91no—
373C22×Dic3—91no—
374C2×D12—31no—
375C2×D12—31no—
376C2×D12—91no—
377C2×D12—91no—
378C2×D12—91no—
379C2×D12—91no—
380C2×D12—91no—
381C2×C4×D3—31no—
382C2×C4×D3—31no—
383C2×C4×D3—61no—
384C2×C4×D3—91no—
385C2×C4×D3—91no—
386C2×Dic6—31no—
387C2×Dic6—91no—
388C3×C4⋊C4—91no—
389C3×C4⋊C4—91no—
390C3×C4⋊C4—91no—
391C3×C4⋊C4—91no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4—91no—
399C3×C22⋊C4D3211yescharacteristic
400C3×C42—91no—
401#217—31no—
402#217—91no—
403#217—91no—
404#217—91no—
405#217—91no—
406#217—91no—
407#217—91no—
408#217—91no—
409#217—91no—
410#217—91no—
411#217—91no—
412(C2×D3)⋊C4—31no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—31no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—91no—
418(C2×D3)⋊C4—91no—
419(C2×D3)⋊C4—91no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—91no—
422(C2×D3)⋊C4—91no—
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—
437C4⋊Dic3—31no—
438C4⋊Dic3—91no—
439C4⋊Dic3—91no—
440C4⋊Dic3—91no—
441Dic3⋊C4—31no—
442Dic3⋊C4—31no—
443Dic3⋊C4—31no—
444Dic3⋊C4—31no—
445Dic3⋊C4—61no—
446Dic3⋊C4—91no—
447Dic3⋊C4—91no—
448Dic3⋊C4—91no—
449Dic3⋊C4—91no—
450Dic3⋊C4—91no—
451Dic3⋊C4—91no—
452C4×Dic3—31no—
453C4×Dic3—31no—
454C4×Dic3—61no—
455C4×Dic3—91no—
456C4×Dic3—91no—
457C4×Dic3—91no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—22no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32#23712yes—
467C22×C32#23912yes—
468C22×C32C23×D311yescharacteristic
469C22×C32C23×D311yescharacteristic
470C2×C3⋊D3—21no—
471C2×C3⋊D3—21no—
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—21no—
479C2×C3⋊D3—44no—
480C2×C3×D3—62no—
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—121no—
497C2×C3×D3—121no—
498C2×C3×D3—124no—
499C32×C4—21no—
500C32×C4—21no—
501C32×C4—21no—
502C32×C4—21no—
503C32×C4—41no—
504C32×C4—41no—
505C3⋊Dic3—21no—
506C3⋊Dic3—21no—
507C3⋊Dic3—21no—
508C3⋊Dic3—21no—
509C3⋊Dic3—21no—
510C3×Dic3—62no—
511C3×Dic3—62no—
512C3×Dic3—61no—
513C3×Dic3—61no—
514C3×Dic3—61no—
515C3×Dic3—61no—
516C3×Dic3—61no—
517C3×Dic3—61no—
518C3×Dic3—61no—
519C3×Dic3—61no—
520C3×Dic3—61no—
521C3×Dic3—61no—
522C3×Dic3—61no—
523C3×Dic3—121no—
524#126—271no—
525#126—271no—
526#124—271no—
527#124—271no—
528#123—271no—
529#123—271no—
530C22⋊Q8—91no—
531#121—271no—
532#121—271no—
533#121—271no—
534#120—91no—
535#120—271no—
536C4×D4—91no—
537C4×D4—271no—
538C2×C22⋊C4—271no—
539H(3,𝔽3)#53811yescharacteristic, complemented, Sylow
540C23×C3—31no—
541C23×C3—31no—
542C23×C3—61no—
543C23×C3—91no—
544C23×C3—91no—
545C23×C3—91no—
546C23×C3—91no—
547C23×C3—182no—
548C23×C3—361no—
549C23×C3—361no—
550C23×C3C2×D3211yescharacteristic
551C22×D3—31no—
552C22×D3—31no—
553C22×D3—31no—
554C22×D3—31no—
555C22×D3—31no—
556C22×D3—61no—
557C22×D3—62no—
558C22×D3—91no—
559C22×D3—91no—
560C22×D3—91no—
561C22×D3—121no—
562C22×D3—121no—
563C22×D3—182no—
564C22×D3—361no—
565C22×D3—361no—
566C3×Q8—361no—
567C3×D4—182no—
568C3×D4—182no—
569C3×D4—361no—
570C3×D4—361no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—91no—
578C2×C3×C4—91no—
579C2×C3×C4—91no—
580C2×C3×C4—91no—
581C2×C3×C4—91no—
582C2×C3×C4—91no—
583C2×C3×C4—91no—
584C2×C3×C4—91no—
585C2×C3×C4—361no—
586C2×C3×C4—361no—
587C2×C3×C4—361no—
588C2×C3×C4C2×D3211yescharacteristic
589C2×C3×C4C2×D3211yescharacteristic
590#67—62no—
591#67—62no—
592#67—64no—
593#67—62no—
594#67—182no—
595#67—361no—
596#67—361no—
597#67—361no—
598#67—361no—
599#67—361no—
600#67—361no—
601C2×Dic3—31no—
602C2×Dic3—31no—
603C2×Dic3—31no—
604C2×Dic3—31no—
605C2×Dic3—31no—
606C2×Dic3—31no—
607C2×Dic3—31no—
608C2×Dic3—31no—
609C2×Dic3—31no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—91no—
616C2×Dic3—91no—
617C2×Dic3—91no—
618C2×Dic3—91no—
619C2×Dic3—91no—
620C2×Dic3—121no—
621C2×Dic3—121no—
622C2×Dic3—121no—
623C2×Dic3—122no—
624C2×Dic3—361no—
625C2×Dic3—361no—
626D12—121no—
627D12—121no—
628D12—361no—
629D12—361no—
630D12—361no—
631D12—361no—
632D12—361no—
633C4×D3—121no—
634C4×D3—121no—
635C4×D3—122no—
636C4×D3—361no—
637C4×D3—361no—
638Dic6—121no—
639Dic6—361no—
640C2×C32—22no—
641C2×C32—22no—
642C2×C32—21no—
643C2×C32—21no—
644C2×C32—21no—
645C2×C32—42no—
646C2×C32C2×#23711yescharacteristic
647C2×C32#100411yescharacteristic
648C2×C32#100411yescharacteristic
649C2×C32#100411yescharacteristic
650C2×C32C2×#23911yescharacteristic
651C2×C32#100911yescharacteristic
652C3⋊D3—41no—
653C3⋊D3—41no—
654C3⋊D3—41no—
655C3×D3—122no—
656C3×D3—121no—
657C3×D3—121no—
658C3×D3—121no—
659C3×D3—121no—
660C3×D3—121no—
661C24—91no—
662C2×Q8—91no—
663C2×D4—91no—
664C2×D4—91no—
665C2×D4—91no—
666C2×D4—91no—
667C2×D4—271no—
668C2×D4—271no—
669C2×D4—271no—
670C22×C4—91no—
671C22×C4—91no—
672C22×C4—91no—
673C22×C4—271no—
674C4⋊C4—91no—
675C4⋊C4—91no—
676C4⋊C4—91no—
677C4⋊C4—91no—
678C4⋊C4—271no—
679C4⋊C4—271no—
680C22⋊C4—91no—
681C22⋊C4—91no—
682C22⋊C4—91no—
683C22⋊C4—91no—
684C22⋊C4—271no—
685C22⋊C4—271no—
686C22⋊C4—271no—
687C22⋊C4—271no—
688C22⋊C4—271no—
689C22⋊C4—271no—
690C22⋊C4—271no—
691C22⋊C4—271no—
692C22⋊C4—271no—
693C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
694C42—91no—
695C42—271no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—31no—
699C22×C3—31no—
700C22×C3—32no—
701C22×C3—32no—
702C22×C3—61no—
703C22×C3—61no—
704C22×C3—61no—
705C22×C3—61no—
706C22×C3—61no—
707C22×C3—62no—
708C22×C3—121no—
709C22×C3—121no—
710C22×C3—181no—
711C22×C3—181no—
712C22×C3—181no—
713C22×C3—181no—
714C22×C3—181no—
715C22×C3—181no—
716C22×C3—181no—
717C22×C3—181no—
718C22×C3—181no—
719C22×C3—181no—
720C22×C3—181no—
721C22×C3—181no—
722C22×C3—364no—
723C22×C3#379612yes—
724C22×C3C22×D3211yescharacteristic
725C2×D3—61no—
726C2×D3—61no—
727C2×D3—61no—
728C2×D3—61no—
729C2×D3—61no—
730C2×D3—61no—
731C2×D3—62no—
732C2×D3—61no—
733C2×D3—61no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—124no—
744C2×D3—181no—
745C2×D3—181no—
746C2×D3—181no—
747C2×D3—181no—
748C2×D3—181no—
749C2×D3—181no—
750C2×D3—181no—
751C2×D3—181no—
752C2×D3—181no—
753C2×D3—364no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—61no—
757C3×C4—61no—
758C3×C4—61no—
759C3×C4—61no—
760C3×C4—121no—
761C3×C4—121no—
762C3×C4—181no—
763C3×C4—181no—
764C3×C4—181no—
765C3×C4—181no—
766C3×C4—181no—
767C3×C4—181no—
768C3×C4—181no—
769C3×C4—181no—
770Dic3—61no—
771Dic3—61no—
772Dic3—61no—
773Dic3—61no—
774Dic3—61no—
775Dic3—61no—
776Dic3—62no—
777Dic3—62no—
778Dic3—61no—
779Dic3—61no—
780Dic3—61no—
781Dic3—61no—
782Dic3—61no—
783Dic3—121no—
784Dic3—181no—
785Dic3—181no—
786Dic3—181no—
787Dic3—181no—
788Dic3—181no—
789C32—21no—
790C32#559311yescharacteristic, complemented
791C32#564411yescharacteristic, complemented
792C23—91no—
793C23—91no—
794C23—91no—
795C23—91no—
796C23—182no—
797C23—361no—
798C23—361no—
799C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
800Q8—361no—
801D4—182no—
802D4—182no—
803D4—361no—
804D4—361no—
805D4—1081no—
806D4—1081no—
807D4—1081no—
808C2×C4—91no—
809C2×C4—91no—
810C2×C4—91no—
811C2×C4—91no—
812C2×C4—91no—
813C2×C4—91no—
814C2×C4—91no—
815C2×C4—91no—
816C2×C4—361no—
817C2×C4—361no—
818C2×C4—361no—
819C2×C4—1081no—
820C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
821C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
822C2×C3—22no—
823C2×C3—31no—
824C2×C3—31no—
825C2×C3—31no—
826C2×C3—31no—
827C2×C3—31no—
828C2×C3—31no—
829C2×C3—62no—
830C2×C3—62no—
831C2×C3—61no—
832C2×C3—61no—
833C2×C3—61no—
834C2×C3—122no—
835C2×C3—361no—
836C2×C3—361no—
837C2×C3—361no—
838C2×C3—361no—
839C2×C3C2×#379611yescharacteristic
840C2×C3#6431311yescharacteristic
841C2×C3#6431411yescharacteristic
842D3—121no—
843D3—121no—
844D3—122no—
845D3—121no—
846D3—121no—
847D3—121no—
848D3—361no—
849D3—361no—
850D3—361no—
851C22—21no—
852C22—21no—
853C22—181no—
854C22—181no—
855C22—181no—
856C22—181no—
857C22—181no—
858C22—181no—
859C22—181no—
860C22—181no—
861C22—181no—
862C22—181no—
863C22—181no—
864C22—181no—
865C22—364no—
866C22#8864912yes—
867C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
868C4—21no—
869C4—21no—
870C4—181no—
871C4—181no—
872C4—181no—
873C4—181no—
874C4—181no—
875C4—181no—
876C4—181no—
877C4—181no—
878C3—31no—
879C3—31no—
880C3—61no—
881C3#1059417311yescharacteristic
882C2—22no—
883C2—361no—
884C2—361no—
885C2—361no—
886C2—361no—
887C2C2×#8864911yescharacteristic
888C2#1172250611yescharacteristic
889C2#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. #11721737C2semidirect
2. #64091⋊C3C2semidirect
3. #64087⋊C3C2semidirect
4. #11721322C2semidirect
5. #11721321C2semidirect
6. #11721315C2semidirect
7. C2×#88450C2semidirect
8. #11721159C2semidirect
9. #11721155C2semidirect
10. #11721127C2semidirect
11. #11721125C2semidirect
12. #11721113C2semidirect
13. #11721112C2semidirect
14. #11721108C2semidirect
15. #11721104C2semidirect
21. C2×C4×#272C22semidirect
26. C2×#634⋊C3C22semidirect
29. C2×#6200C22semidirect
30. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
32. #88542C22semidirect
33. #88540C22semidirect
34. C4×#1084C22semidirect
38. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
39. #3750⋊C3C22semidirect
40. #3750⋊C3C22semidirect
41. #88451C22semidirect
48. #88450C22semidirect
49. #88450C22semidirect
50. #88448C22semidirect
51. #88448C22semidirect
52. #88447C22semidirect
53. #64091D3semidirect
54. #64087D3semidirect
123. C2×#634C2×D3semidirect
152. C4⋊(C3⋊Dic3)C2×D3semidirect
153. #3750C2×D3semidirect
154. #3750C2×D3semidirect
539. H(3,𝔽3)#538semidirect
790. C32#5593semidirect
791. C32#5644semidirect

Maximal subgroups

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

subgroupindex
#117217372
#64091⋊C32
#64087⋊C32
#117213222
#117213212
#117213152
C2×#884502
#117211592
#117211552
#117211272
#117211252
#117211132
#117211122
#117211082
#117211042
#105942433
#105942383