Finite Group Databasebeta

← #13147921

Subgroups — #13147921

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
1C4×C4⋊#272C211yesmaximal, characteristic, complemented
2#11721387C211yesmaximal, characteristic, complemented
3#64084⋊C3C211yesmaximal, characteristic, complemented
4#11721163C211yesmaximal, characteristic, complemented
5#11721162C211yesmaximal, characteristic, complemented
6#11721161C211yesmaximal, characteristic, complemented
7#11721157C211yesmaximal, characteristic, complemented
8#11721155C211yesmaximal, characteristic, complemented
9#11721148C211yesmaximal, characteristic, complemented
10#11721142C211yesmaximal, characteristic, complemented
11#11721131C211yesmaximal, characteristic, complemented
12#11721127C211yesmaximal, characteristic, complemented
13#11721124C211yesmaximal, characteristic, complemented
14#11721111C211yesmaximal, characteristic, complemented
15#11721104C211yesmaximal, characteristic, complemented
16#10594013—31nomaximal
17#10594012—31nomaximal
18C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
19C2×C4⋊#272C2211yescharacteristic
20C2×C4×#272C2211yescharacteristic
21C2×C4×#272C2211yescharacteristic, complemented
22C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
23C2×#634⋊C3C2211yescharacteristic, complemented
24C2×#6200C2211yescharacteristic
25C2×#6200C2211yescharacteristic
26C2×#6200C2211yescharacteristic
27C2×#6200C2211yescharacteristic, complemented
28C2×#6199C2211yescharacteristic
29C2×#6198C2211yescharacteristic
30C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
31C42×H(3,𝔽3)C2211yescharacteristic, complemented
32#88542C2211yescharacteristic
33#88542C2211yescharacteristic, complemented
34C4⋊#1084C2211yescharacteristic, complemented
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38#3752⋊C3C2211yescharacteristic
39#3752⋊C3C2211yescharacteristic
40#3752⋊C3C2211yescharacteristic, complemented
41#3752⋊C3C2211yescharacteristic, complemented
42#3750⋊C3C2211yescharacteristic, complemented
43#3750⋊C3C2211yescharacteristic, complemented
44#3750⋊C3C2211yescharacteristic, complemented
45#88451C2211yescharacteristic
46#88451C2211yescharacteristic, complemented
47#88450C2211yescharacteristic
48#88450C2211yescharacteristic
49#88450C2211yescharacteristic
50#88449C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53#64085D311yescharacteristic, complemented
54#64084D311yescharacteristic, complemented
55C3×#876—31no—
56C3×#875—31no—
57C3×C4×D12—31no—
58C3×C4×D12—31no—
59C3×C4×D12—61no—
60#63923—31no—
61#63922—31no—
62#63922—31no—
63#63922—31no—
64D3×(C2×D3)⋊C4—31no—
65D3×(C2×D3)⋊C4—31no—
66#63913—31no—
67#63910—31no—
68#63907—31no—
69#63906—31no—
70#63906—31no—
71#63905—31no—
72#63904—31no—
73#63896—31no—
74#63890—31no—
75#63887—31no—
76#63886—31no—
77#63885—31no—
78#63885—31no—
79#63879—31no—
80#63858—31no—
81#63854—31no—
82#63850—31no—
83#63848—31no—
84C22×#272C2311yescharacteristic
85C22×#272C2311yescharacteristic
86C22×(C3⋊D3)⋊C3C2311yescharacteristic
87C22×(C3⋊D3)⋊C3C2311yescharacteristic
88C22×(C3⋊D3)⋊C3C2311yescharacteristic
89C2×((C3⋊D3)⋊C3)⋊C2—22no—
90C2×((C3⋊D3)⋊C3)⋊C2—41no—
91C2×((C3⋊D3)⋊C3)⋊C2—41no—
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94C2×C4×H(3,𝔽3)C2311yescharacteristic
95C2×#1084C2311yescharacteristic
96C2×#1084C2311yescharacteristic
97C4⋊#272—22no—
98C4×#272—41no—
99C4×#272—41no—
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C4⋊((C3⋊D3)⋊C3)—41no—
106#634⋊C3—41no—
107#6200—22no—
108#6200—41no—
109#6200—41no—
110#6200—41no—
111#6199—41no—
112#6198—41no—
113((C3⋊D3)⋊C3)⋊C4—41no—
114#5704—91no—
115#5678—91no—
116#5560—91no—
117C22×D32—31no—
118C22×D32—31no—
119C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
120C2×#634C2×D311yescharacteristic, complemented
121C2×C3×D12—31no—
122C2×C3×D12—31no—
123C2×C3×D12—31no—
124C2×C3×D12—61no—
125C2×C3×C4×D3—31no—
126C2×C3×C4×D3—31no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—31no—
129C2×C3×C4×D3—61no—
130C2×C3×C4×D3—61no—
131C2×C3×Dic6—31no—
132C2×#626—31no—
133C2×#626—31no—
134C2×#626—31no—
135C2×#626—31no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#625—31no—
139C2×#625—31no—
140C2×#625—31no—
141C2×#625—31no—
142C2×#624—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—31no—
146C32×C42—21no—
147C32×C42C2×D311yescharacteristic, complemented
148C32×C42C2×D311yescharacteristic, complemented
149#3752C2×D311yescharacteristic
150#3752C2×D311yescharacteristic
151#3752C2×D311yescharacteristic
152#3752C2×D311yescharacteristic
153#3752C2×D311yescharacteristic
154#3752C2×D311yescharacteristic, complemented
155#3752C2×D311yescharacteristic, complemented
156#3750C2×D311yescharacteristic, complemented
157#3750C2×D311yescharacteristic, complemented
158#3750C2×D311yescharacteristic, complemented
159C3×(C2×D3)⋊C4—31no—
160C3×(C2×D3)⋊C4—31no—
161C3×(C2×D3)⋊C4—31no—
162C3×(C2×D3)⋊C4—31no—
163C3×(C2×D3)⋊C4—31no—
164C3×(C2×D3)⋊C4—31no—
165C3×(C2×D3)⋊C4—31no—
166C3×(C2×D3)⋊C4—31no—
167C3×(C2×D3)⋊C4—31no—
168C3×(C2×D3)⋊C4—31no—
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4—61no—
171C3×(C2×D3)⋊C4—61no—
172C3×C4⋊Dic3—31no—
173C3×C4⋊Dic3—31no—
174C3×C4⋊Dic3—61no—
175C3×Dic3⋊C4—31no—
176C3×Dic3⋊C4—31no—
177C3×Dic3⋊C4—31no—
178#3724—31no—
179Dic3⋊Dic3—31no—
180Dic3⋊Dic3—31no—
181Dic3⋊Dic3—31no—
182#3722—31no—
183#3722—31no—
184#3722—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)C2411yescharacteristic
195C2×#272—21no—
196C2×#272—21no—
197C2×#272—21no—
198C2×#272—21no—
199C2×#272—21no—
200C2×#272#4112yes—
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—
210((C3⋊D3)⋊C3)⋊C2—44no—
211C4×H(3,𝔽3)—21no—
212C4×H(3,𝔽3)—21no—
213C4×H(3,𝔽3)—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×#126—91no—
222C3×#124—91no—
223C3×C4×D4—91no—
224#947—91no—
225#946—91no—
226#939—91no—
227#939—91no—
228#937—91no—
229#937—91no—
230#930—91no—
231#929—91no—
232C4×#67—91no—
233C2×(C2×D3)⋊C4—91no—
234#898—91no—
235#898—91no—
236#896—91no—
237#895—91no—
238#895—91no—
239#894—91no—
240#894—91no—
241#893—91no—
242#886—91no—
243#885—91no—
244#885—91no—
245#884—91no—
246#884—91no—
247#884—91no—
248#884—91no—
249#883—91no—
250#883—91no—
251#882—91no—
252#882—91no—
253#882—91no—
254#882—91no—
255#67⋊C4—91no—
256D3×C22⋊C4—91no—
257D3×C22⋊C4—91no—
258#879—91no—
259#878—91no—
260#876—31no—
261#876—91no—
262#875—31no—
263#875—91no—
264C4×D12—31no—
265C4×D12—31no—
266C4×D12—61no—
267C22×C3⋊D3C22×D311yescharacteristic
268C22×C3⋊D3C22×D311yescharacteristic
269C22×C3⋊D3C22×D311yescharacteristic
270C22×C3×D3—31no—
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—61no—
278C22×C3×D3—61no—
279C2×D32—62no—
280C2×D32—62no—
281C2×D32—121no—
282C2×D32—121no—
283C2×D32—121no—
284C2×D32—121no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C22×D311yescharacteristic
294C2×C3⋊Dic3C22×D311yescharacteristic
295C2×C3⋊Dic3C22×D311yescharacteristic
296C2×C3⋊Dic3C22×D311yescharacteristic
297C2×C3⋊Dic3C22×D311yescharacteristic
298C2×C3⋊Dic3C22×D311yescharacteristic
299C4⋊(C3⋊D3)—41no—
300#634—41no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—31no—
305C2×C3×Dic3—31no—
306C2×C3×Dic3—31no—
307C2×C3×Dic3—31no—
308C2×C3×Dic3—31no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—61no—
311C2×C3×Dic3—61no—
312C3×D12—62no—
313C3×D12—62no—
314C3×D12—64no—
315C3×D12—121no—
316C3×C4×D3—121no—
317C3×C4×D3—121no—
318C3×C4×D3—121no—
319C3×C4×D3—121no—
320C3×C4×D3—122no—
321C3×C4×D3—122no—
322C3×Dic6—121no—
323#626—62no—
324#626—121no—
325#626—121no—
326#626—121no—
327#626—121no—
328#626—121no—
329#625—62no—
330#625—121no—
331#625—121no—
332#625—121no—
333#624—121no—
334D3×Dic3—121no—
335D3×Dic3—121no—
336D3×Dic3—121no—
337#538—271noSylow
338C2×H(3,𝔽3)C2×#4111yescharacteristic
339C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
340C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
341#272—22no—
342#272—41no—
343(C3⋊D3)⋊C3—41no—
344(C3⋊D3)⋊C3—41no—
345(C3⋊D3)⋊C3—41no—
346C23×D3—91no—
347C23×D3—91no—
348C23×D3—91no—
349C2×C3×Q8—91no—
350C2×C3×D4—91no—
351C2×C3×D4—91no—
352C22×C3×C4—91no—
353C22×C3×C4—91no—
354C2×#67—91no—
355C2×#67—91no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—91no—
364C22×Dic3—91no—
365C22×Dic3—91no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—61no—
370C2×D12—91no—
371C2×D12—91no—
372C2×D12—91no—
373C2×D12—91no—
374C2×D12—91no—
375C2×D12—91no—
376C2×C4×D3—31no—
377C2×C4×D3—31no—
378C2×C4×D3—31no—
379C2×C4×D3—31no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—91no—
383C2×C4×D3—91no—
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—91no—
393C3×C22⋊C4—91no—
394C3×C22⋊C4—91no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4—91no—
399C3×C22⋊C4—91no—
400C3×C22⋊C4—91no—
401C3×C42—31no—
402C3×C42—31no—
403C3×C42—61no—
404C3×C42D3211yescharacteristic
405#217—91no—
406#217—91no—
407#217—91no—
408#217—91no—
409#217—91no—
410(C2×D3)⋊C4—31no—
411(C2×D3)⋊C4—31no—
412(C2×D3)⋊C4—31no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—31no—
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—
440C4⋊Dic3—31no—
441C4⋊Dic3—31no—
442C4⋊Dic3—61no—
443C4⋊Dic3—91no—
444C4⋊Dic3—91no—
445Dic3⋊C4—31no—
446Dic3⋊C4—31no—
447Dic3⋊C4—31no—
448Dic3⋊C4—91no—
449Dic3⋊C4—91no—
450Dic3⋊C4—91no—
451Dic3⋊C4—91no—
452Dic3⋊C4—91no—
453Dic3⋊C4—91no—
454Dic3⋊C4—91no—
455C4×Dic3—91no—
456C4×Dic3—91no—
457C4×Dic3—91no—
458C22×C32—21no—
459C22×C32C23×D311yescharacteristic
460C22×C32C23×D311yescharacteristic
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—21no—
470C2×C3×D3—32no—
471C2×C3×D3—32no—
472C2×C3×D3—62no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—61no—
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—121no—
494C2×C3×D3—121no—
495C2×C3×D3—121no—
496C2×C3×D3—121no—
497D32—124no—
498D32—124no—
499C32×C4—22no—
500C32×C4—22no—
501C32×C4—21no—
502C32×C4—21no—
503C32×C4—21no—
504C32×C4—21no—
505C32×C4—21no—
506C32×C4—21no—
507C32×C4—41no—
508C3⋊Dic3—21no—
509C3⋊Dic3—21no—
510C3⋊Dic3—21no—
511C3⋊Dic3—21no—
512C3⋊Dic3—21no—
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—121no—
523C3×Dic3—121no—
524#126—91no—
525#126—271no—
526#124—91no—
527#124—271no—
528#123—271no—
529#123—271no—
530C22⋊Q8—271no—
531#121—271no—
532#121—271no—
533#121—271no—
534#120—271no—
535#120—271no—
536C4×D4—91no—
537C4×D4—271no—
538C2×C22⋊C4—271no—
539H(3,𝔽3)#53811yescharacteristic, complemented, Sylow
540C23×C3—91no—
541C23×C3—91no—
542C23×C3—91no—
543C23×C3—91no—
544C23×C3—91no—
545C22×D3—31no—
546C22×D3—31no—
547C22×D3—31no—
548C22×D3—31no—
549C22×D3—31no—
550C22×D3—31no—
551C22×D3—31no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—91no—
555C22×D3—91no—
556C22×D3—91no—
557C22×D3—182no—
558C22×D3—182no—
559C22×D3—182no—
560C22×D3—361no—
561C22×D3—361no—
562C22×D3—361no—
563C22×D3—361no—
564C22×D3—361no—
565C22×D3—361no—
566C3×Q8—361no—
567C3×D4—182no—
568C3×D4—361no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
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—61no—
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×C4C2×D3211yescharacteristic
588C2×C3×C4C2×D3211yescharacteristic
589C2×C3×C4C2×D3211yescharacteristic
590#67—182no—
591#67—182no—
592#67—361no—
593#67—361no—
594#67—361no—
595#67—361no—
596#67—361no—
597#67—361no—
598#67—361no—
599#67—361no—
600C2×Dic3—31no—
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—61no—
610C2×Dic3—61no—
611C2×Dic3—91no—
612C2×Dic3—91no—
613C2×Dic3—91no—
614C2×Dic3—91no—
615C2×Dic3—91no—
616C2×Dic3—361no—
617C2×Dic3—361no—
618D12—62no—
619D12—62no—
620D12—64no—
621D12—121no—
622D12—182no—
623D12—361no—
624D12—361no—
625D12—361no—
626D12—361no—
627D12—361no—
628C4×D3—121no—
629C4×D3—121no—
630C4×D3—121no—
631C4×D3—121no—
632C4×D3—122no—
633C4×D3—122no—
634C4×D3—361no—
635C4×D3—361no—
636C4×D3—361no—
637C4×D3—361no—
638Dic6—121no—
639Dic6—361no—
640C2×C32—21no—
641C2×C32—21no—
642C2×C32—21no—
643C2×C32#100411yescharacteristic
644C2×C32D3×#4111yescharacteristic
645C2×C32D3×#4111yescharacteristic
646C2×C32#100911yescharacteristic
647C2×C32#100911yescharacteristic
648C2×C32#100911yescharacteristic
649C3⋊D3—41no—
650C3⋊D3—41no—
651C3⋊D3—41no—
652C3×D3—62no—
653C3×D3—62no—
654C3×D3—122no—
655C3×D3—122no—
656C3×D3—121no—
657C3×D3—121no—
658C3×D3—121no—
659C3×D3—121no—
660C3×D3—121no—
661C24—271no—
662C2×Q8—91no—
663C2×D4—91no—
664C2×D4—91no—
665C2×D4—271no—
666C2×D4—271no—
667C2×D4—271no—
668C2×D4—271no—
669C2×D4—271no—
670C22×C4—91no—
671C22×C4—91no—
672C22×C4—271no—
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—91no—
685C22⋊C4—91no—
686C22⋊C4—91no—
687C22⋊C4—91no—
688C22⋊C4—91no—
689C22⋊C4—271no—
690C22⋊C4—271no—
691C22⋊C4—271no—
692C22⋊C4—271no—
693C22⋊C4—271no—
694C42—271no—
695C42((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
696C22×C3—31no—
697C22×C3—31no—
698C22×C3—61no—
699C22×C3—92no—
700C22×C3—181no—
701C22×C3—181no—
702C22×C3—181no—
703C22×C3—181no—
704C22×C3—181no—
705C22×C3—181no—
706C22×C3—181no—
707C22×C3—181no—
708C22×C3—181no—
709C22×C3—181no—
710C22×C3—181no—
711C22×C3—181no—
712C22×C3—181no—
713C22×C3—181no—
714C22×C3C22×D3211yescharacteristic
715C2×D3—32no—
716C2×D3—32no—
717C2×D3—62no—
718C2×D3—61no—
719C2×D3—61no—
720C2×D3—61no—
721C2×D3—61no—
722C2×D3—61no—
723C2×D3—61no—
724C2×D3—61no—
725C2×D3—61no—
726C2×D3—61no—
727C2×D3—61no—
728C2×D3—62no—
729C2×D3—61no—
730C2×D3—61no—
731C2×D3—61no—
732C2×D3—61no—
733C2×D3—61no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—61no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—181no—
743C2×D3—181no—
744C2×D3—181no—
745C2×D3—181no—
746C2×D3—181no—
747C2×D3—181no—
748C2×D3—181no—
749C2×D3—181no—
750C2×D3—181no—
751C2×D3—364no—
752C2×D3—364no—
753C2×D3—364no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—61no—
758C3×C4—61no—
759C3×C4—61no—
760C3×C4—61no—
761C3×C4—61no—
762C3×C4—61no—
763C3×C4—62no—
764C3×C4—62no—
765C3×C4—121no—
766C3×C4—181no—
767C3×C4—181no—
768C3×C4—181no—
769C3×C4—181no—
770C3×C4—181no—
771C3×C4—181no—
772C3×C4—181no—
773Dic3—61no—
774Dic3—61no—
775Dic3—61no—
776Dic3—61no—
777Dic3—61no—
778Dic3—61no—
779Dic3—61no—
780Dic3—61no—
781Dic3—61no—
782Dic3—121no—
783Dic3—121no—
784Dic3—181no—
785Dic3—181no—
786Dic3—181no—
787Dic3—181no—
788Dic3—181no—
789C32—21no—
790C32#567811yescharacteristic, complemented
791C32#570411yescharacteristic, complemented
792C23—91no—
793C23—91no—
794C23—91no—
795C23—91no—
796C23—91no—
797C23—542no—
798C23—1081no—
799C23—1081no—
800Q8—361no—
801D4—182no—
802D4—361no—
803D4—542no—
804D4—1081no—
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—361no—
816C2×C4—361no—
817C2×C4—1081no—
818C2×C4—1081no—
819C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
820C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
821C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
822C2×C3—31no—
823C2×C3—31no—
824C2×C3—31no—
825C2×C3—31no—
826C2×C3—31no—
827C2×C3—31no—
828C2×C3—61no—
829C2×C3—61no—
830C2×C3—61no—
831C2×C3—182no—
832C2×C3—361no—
833C2×C3—361no—
834C2×C3—361no—
835C2×C3—361no—
836C2×C3#6430611yescharacteristic
837C2×C3#6430711yescharacteristic
838C2×C3#6430811yescharacteristic
839D3—62no—
840D3—62no—
841D3—122no—
842D3—121no—
843D3—121no—
844D3—122no—
845D3—121no—
846D3—121no—
847D3—121no—
848D3—361no—
849D3—361no—
850D3—361no—
851C22—92no—
852C22—181no—
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—181no—
866C22—1084no—
867C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
868C4—21no—
869C4—21no—
870C4—21no—
871C4—181no—
872C4—181no—
873C4—181no—
874C4—181no—
875C4—181no—
876C4—181no—
877C4—181no—
878C3—31no—
879C3—31no—
880C3—61no—
881C3#1059401911yescharacteristic
882C2—182no—
883C2—361no—
884C2—361no—
885C2—361no—
886C2—361no—
887C2#1172249111yescharacteristic
888C2#1172249211yescharacteristic
889C2#1172249311yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC42×H(3,𝔽3)C22
hypercenterC42((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#538
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C4×C4⋊#272C2semidirect
2. #11721387C2semidirect
3. #64084⋊C3C2semidirect
4. #11721163C2semidirect
5. #11721162C2semidirect
6. #11721161C2semidirect
7. #11721157C2semidirect
8. #11721155C2semidirect
9. #11721148C2semidirect
10. #11721142C2semidirect
11. #11721131C2semidirect
12. #11721127C2semidirect
13. #11721124C2semidirect
14. #11721111C2semidirect
15. #11721104C2semidirect
21. C2×C4×#272C22semidirect
23. C2×#634⋊C3C22semidirect
27. C2×#6200C22semidirect
30. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
31. C42×H(3,𝔽3)C22semidirect
33. #88542C22semidirect
34. C4⋊#1084C22semidirect
40. #3752⋊C3C22semidirect
41. #3752⋊C3C22semidirect
42. #3750⋊C3C22semidirect
43. #3750⋊C3C22semidirect
44. #3750⋊C3C22semidirect
46. #88451C22semidirect
50. #88449C22semidirect
51. #88448C22semidirect
52. #88447C22semidirect
53. #64085D3semidirect
54. #64084D3semidirect
120. C2×#634C2×D3semidirect
147. C32×C42C2×D3semidirect
148. C32×C42C2×D3semidirect
154. #3752C2×D3semidirect
155. #3752C2×D3semidirect
156. #3750C2×D3semidirect
157. #3750C2×D3semidirect
158. #3750C2×D3semidirect
539. H(3,𝔽3)#538semidirect
695. C42((C3⋊D3)⋊C3)⋊C2semidirect
790. C32#5678semidirect
791. C32#5704semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#2722
#117213872
#64084⋊C32
#117211632
#117211622
#117211612
#117211572
#117211552
#117211482
#117211422
#117211312
#117211272
#117211242
#117211112
#117211042
#105940133
#105940123