Finite Group Databasebeta

← #13149458

Subgroups — #13149458

Order 1728.

841 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊C4×#272C211yesmaximal, characteristic, complemented
2#64107⋊C3C211yesmaximal, characteristic, complemented
3#64098⋊C3C211yesmaximal, characteristic, complemented
4#11721134C211yesmaximal, characteristic, complemented
5#11721124C211yesmaximal, characteristic
6#11721120C211yesmaximal, characteristic, complemented
7#11721111C211yesmaximal, characteristic, complemented
8#11721104C211yesmaximal, characteristic
9#11721104C211yesmaximal, characteristic
10#11721097C211yesmaximal, characteristic, complemented
11#11721096C211yesmaximal, characteristic, complemented
12#11721089C211yesmaximal, characteristic, complemented
13#11721086C211yesmaximal, characteristic, complemented
14#11721085C211yesmaximal, characteristic, complemented
15#11721077C211yesmaximal, characteristic, complemented
16#10594543—31nomaximal
17#10594331—31nomaximal
18C2×C4×#272C2211yescharacteristic
19C2×C4×#272C2211yescharacteristic
20C2×C4×#272C2211yescharacteristic
21C2×#6200C2211yescharacteristic
22C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
23C2×#6196C2211yescharacteristic
24C4⋊C4×H(3,𝔽3)C2211yescharacteristic
25C4⋊#1084C2211yescharacteristic
26#88540C2211yescharacteristic
27#88540C2211yescharacteristic
28#3752⋊C3C2211yescharacteristic
29#3752⋊C3C2211yescharacteristic
30#3752⋊C3C2211yescharacteristic
31C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
32C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
33#3750⋊C3C2211yescharacteristic
34#3750⋊C3C2211yescharacteristic
35#3750⋊C3C2211yescharacteristic
36#3750⋊C3C2211yescharacteristic
37#3750⋊C3C2211yescharacteristic
38C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
39C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
40#88451C2211yescharacteristic
41#88451C2211yescharacteristic
42#88451C2211yescharacteristic
43#88450C2211yescharacteristic
44#88450C2211yescharacteristic
45#88449C2211yescharacteristic
46#88449C2211yescharacteristic
47#88449C2211yescharacteristic
48#88448C2211yescharacteristic
49#88448C2211yescharacteristic
50#88447C2211yescharacteristic
51#88447C2211yescharacteristic
52#88447C2211yescharacteristic
53#64107D311yescharacteristic, complemented
54#64098D311yescharacteristic, complemented
55C3×#898—31no—
56C3×D3×C4⋊C4—31no—
57C3×D3×C4⋊C4—31no—
58C3×D3×C4⋊C4—61no—
59C3×#889—31no—
60#63905—31no—
61#63905—31no—
62#63904—31no—
63#63895—31no—
64#63893—31no—
65#63879—31no—
66#63878—31no—
67#63858—31no—
68#63855—31no—
69#63855—31no—
70#63851—31no—
71#63851—31no—
72#63850—31no—
73#63850—31no—
74#63848—31no—
75#63847—31no—
76#63846—31no—
77#63846—31no—
78#63845—31no—
79#63841—31no—
80#63841—31no—
81#63838—31no—
82#63837—31no—
83#63836—31no—
84C22×#272C2311yescharacteristic
85C22×(C3⋊D3)⋊C3C2311yescharacteristic
86C2×C4×H(3,𝔽3)C2311yescharacteristic
87C2×C4×H(3,𝔽3)C2311yescharacteristic
88C2×C4×H(3,𝔽3)C2311yescharacteristic
89C2×#1084C2311yescharacteristic
90C2×#1084C2311yescharacteristic
91C2×#1084C2311yescharacteristic
92C4×#272—22no—
93C4×#272—22no—
94C4×#272—22no—
95C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
96C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
97C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102#6200—22no—
103((C3⋊D3)⋊C3)⋊C4—22no—
104#6196—22no—
105#5708—91no—
106#5693—91no—
107#5513—91no—
108C2×C3×C4×D3—31no—
109C2×C3×C4×D3—31no—
110C2×C3×C4×D3—31no—
111C2×C3×C4×D3—31no—
112C2×C3×C4×D3—31no—
113C2×C3×C4×D3—31no—
114C2×C3×C4×D3—61no—
115C2×C3×C4×D3—61no—
116C2×C3×C4×D3—61no—
117C2×#627—31no—
118C2×#627—31no—
119C2×#626—31no—
120C2×#625—31no—
121C2×#624—31no—
122C2×D3×Dic3—31no—
123C32×C4⋊C4—21no—
124C32×C4⋊C4C2×D311yescharacteristic
125C32×C4⋊C4C2×D311yescharacteristic
126#3752C2×D311yescharacteristic
127#3752C2×D311yescharacteristic
128#3752C2×D311yescharacteristic
129C4⋊(C3⋊Dic3)C2×D311yescharacteristic
130C4⋊(C3⋊Dic3)C2×D311yescharacteristic
131#3750C2×D311yescharacteristic
132#3750C2×D311yescharacteristic
133#3750C2×D311yescharacteristic
134#3750C2×D311yescharacteristic
135#3750C2×D311yescharacteristic
136C4×C3⋊Dic3C2×D311yescharacteristic
137C4×C3⋊Dic3C2×D311yescharacteristic
138C3×(C2×D3)⋊C4—31no—
139C3×(C2×D3)⋊C4—31no—
140C3×(C2×D3)⋊C4—31no—
141C3×C4⋊Dic3—31no—
142C3×C4⋊Dic3—31no—
143C3×C4⋊Dic3—31no—
144C3×C4⋊Dic3—31no—
145C3×C4⋊Dic3—61no—
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4—31no—
148C3×Dic3⋊C4—31no—
149C3×Dic3⋊C4—31no—
150C3×Dic3⋊C4—31no—
151C3×Dic3⋊C4—31no—
152C3×Dic3⋊C4—31no—
153C3×Dic3⋊C4—31no—
154C3×Dic3⋊C4—31no—
155C3×Dic3⋊C4—61no—
156C3×Dic3⋊C4—61no—
157C3×C4×Dic3—31no—
158C3×C4×Dic3—31no—
159#3724—31no—
160#3724—31no—
161Dic3⋊Dic3—31no—
162Dic3⋊Dic3—31no—
163Dic3⋊Dic3—31no—
164Dic3⋊Dic3—31no—
165Dic3⋊Dic3—31no—
166Dic3⋊Dic3—31no—
167Dic3⋊Dic3—31no—
168Dic3⋊Dic3—31no—
169#3722—31no—
170#3722—31no—
171(C2×D3)⋊Dic3—31no—
172(C2×D3)⋊Dic3—31no—
173(C2×D3)⋊Dic3—31no—
174(C2×D3)⋊Dic3—31no—
175(C2×D3)⋊Dic3—31no—
176(C2×D3)⋊Dic3—31no—
177(C2×D3)⋊Dic3—31no—
178(C2×D3)⋊Dic3—31no—
179Dic32—31no—
180Dic32—31no—
181Dic32—31no—
182Dic32—31no—
183Dic32—31no—
184Dic32—31no—
185C22×H(3,𝔽3)C2411yescharacteristic
186C2×#272—21no—
187C2×#272—21no—
188C2×#272#4112yes—
189C2×(C3⋊D3)⋊C3—21no—
190C2×(C3⋊D3)⋊C3—21no—
191C2×(C3⋊D3)⋊C3—21no—
192C4×H(3,𝔽3)—21no—
193C4×H(3,𝔽3)—21no—
194C4×H(3,𝔽3)—21no—
195#1084—21no—
196#1084—21no—
197#1084#4112yes—
198(C3⋊Dic3)⋊C3—21no—
199(C3⋊Dic3)⋊C3—21no—
200(C3⋊Dic3)⋊C3—21no—
201(C3⋊Dic3)⋊C3—21no—
202(C3⋊Dic3)⋊C3—21no—
203(C3⋊Dic3)⋊C3—21no—
204(C3⋊Dic3)⋊C3—21no—
205C3×#126—91no—
206C3×#125—91no—
207C2×C3×C4⋊C4—91no—
208#929—91no—
209#929—91no—
210C4×#67—91no—
211#926—91no—
212#926—91no—
213#924—91no—
214#898—31no—
215#898—91no—
216#898—91no—
217#898—91no—
218#897—91no—
219#896—91no—
220#896—91no—
221#896—91no—
222#894—91no—
223#894—91no—
224#893—91no—
225#892—91no—
226#892—91no—
227#892—91no—
228D3×C4⋊C4—31no—
229D3×C4⋊C4—31no—
230D3×C4⋊C4—61no—
231#890—91no—
232#890—91no—
233#889—31no—
234#889—91no—
235#889—91no—
236#889—91no—
237#889—91no—
238#889—91no—
239#887—91no—
240#887—91no—
241#883—91no—
242#883—91no—
243#67⋊C4—91no—
244#879—91no—
245#878—91no—
246#877—91no—
247#872—91no—
248#872—91no—
249#872—91no—
250C4×Dic6—91no—
251C22×C3⋊D3C22×D311yescharacteristic
252C22×C3×D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C22×C3×D3—61no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C3⋊Dic3C22×D311yescharacteristic
266C2×C3⋊Dic3C22×D311yescharacteristic
267C2×C3⋊Dic3C22×D311yescharacteristic
268C2×C3⋊Dic3C22×D311yescharacteristic
269C2×C3⋊Dic3C22×D311yescharacteristic
270C2×C3⋊Dic3C22×D311yescharacteristic
271C2×C3⋊Dic3C22×D311yescharacteristic
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—61no—
288C3×C4×D3—62no—
289C3×C4×D3—62no—
290C3×C4×D3—62no—
291C3×C4×D3—62no—
292C3×C4×D3—62no—
293C3×C4×D3—62no—
294C3×C4×D3—64no—
295C3×C4×D3—122no—
296C3×C4×D3—122no—
297#627—62no—
298#627—62no—
299#626—62no—
300#625—62no—
301#624—62no—
302D3×Dic3—62no—
303#552—271noSylow
304C2×H(3,𝔽3)C2×#4111yescharacteristic
305C2×H(3,𝔽3)C2×#4111yescharacteristic
306C2×H(3,𝔽3)2−1+411yescharacteristic
307#272—22no—
308(C3⋊D3)⋊C3—41no—
309C22×C3×C4—91no—
310C22×C3×C4—91no—
311C22×C3×C4—91no—
312C2×#67—91no—
313C2×#67—91no—
314C22×Dic3—91no—
315C2×D12—91no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—91no—
326C2×C4×D3—91no—
327C2×Dic6—91no—
328C2×Dic6—91no—
329C2×Dic6—91no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—91no—
334C3×C4⋊C4—91no—
335C3×C4⋊C4—91no—
336C3×C4⋊C4—91no—
337C3×C4⋊C4—91no—
338C3×C4⋊C4—91no—
339C3×C4⋊C4—91no—
340C3×C4⋊C4—91no—
341C3×C4⋊C4—91no—
342C3×C4⋊C4—91no—
343C3×C4⋊C4D3211yescharacteristic
344C3×C22⋊C4—91no—
345C3×C22⋊C4—91no—
346C3×C22⋊C4—91no—
347C3×C42—91no—
348C3×C42—91no—
349#217—91no—
350#217—91no—
351#217—91no—
352#217—91no—
353#217—91no—
354(C2×D3)⋊C4—31no—
355(C2×D3)⋊C4—31no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—91no—
358(C2×D3)⋊C4—91no—
359(C2×D3)⋊C4—91no—
360(C2×D3)⋊C4—91no—
361(C2×D3)⋊C4—91no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—91no—
368(C2×D3)⋊C4—91no—
369(C2×D3)⋊C4—91no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3—91no—
376C4⋊Dic3—91no—
377C4⋊Dic3—91no—
378C4⋊Dic3—91no—
379C4⋊Dic3—91no—
380C4⋊Dic3—91no—
381C4⋊Dic3—91no—
382Dic3⋊C4—31no—
383Dic3⋊C4—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—31no—
389Dic3⋊C4—31no—
390Dic3⋊C4—31no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—91no—
394Dic3⋊C4—91no—
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408C4×Dic3—31no—
409C4×Dic3—31no—
410C4×Dic3—91no—
411C4×Dic3—91no—
412C4×Dic3—91no—
413C4×Dic3—91no—
414C4×Dic3—91no—
415C4×Dic3—91no—
416C4×Dic3—91no—
417C4×Dic3—91no—
418C4×Dic3—91no—
419C4×Dic3—91no—
420C4×Dic3—91no—
421C22×C32—21no—
422C22×C32C23×D311yescharacteristic
423C22×C32C23×D311yescharacteristic
424C2×C3⋊D3—21no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3—21no—
427C2×C3×D3—32no—
428C2×C3×D3—32no—
429C2×C3×D3—62no—
430C2×C3×D3—62no—
431C2×C3×D3—62no—
432C2×C3×D3—61no—
433C2×C3×D3—61no—
434C2×C3×D3—61no—
435C2×C3×D3—61no—
436C2×C3×D3—61no—
437C2×C3×D3—61no—
438C2×C3×D3—61no—
439C32×C4—22no—
440C32×C4—21no—
441C32×C4—21no—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—21no—
446C32×C4—41no—
447C32×C4—41no—
448C3⋊Dic3—21no—
449C3⋊Dic3—21no—
450C3⋊Dic3—21no—
451C3⋊Dic3—21no—
452C3⋊Dic3—21no—
453C3⋊Dic3—21no—
454C3⋊Dic3—21no—
455C3×Dic3—32no—
456C3×Dic3—32no—
457C3×Dic3—62no—
458C3×Dic3—61no—
459C3×Dic3—61no—
460C3×Dic3—61no—
461C3×Dic3—61no—
462C3×Dic3—61no—
463C3×Dic3—61no—
464C3×Dic3—61no—
465C3×Dic3—61no—
466C3×Dic3—61no—
467C3×Dic3—61no—
468C3×Dic3—61no—
469C3×Dic3—121no—
470C3×Dic3—121no—
471#126—91no—
472#126—271no—
473#125—91no—
474#125—271no—
475#125—271no—
476#123—271no—
477#123—271no—
478C22⋊Q8—271no—
479C22⋊Q8—271no—
480C4×Q8—271no—
481C4×D4—271no—
482#117—271no—
483#117—271no—
484#117—271no—
485C2×C4⋊C4—91no—
486H(3,𝔽3)#55211yescharacteristic, complemented, Sylow
487C23×C3—91no—
488C23×C3—91no—
489C22×D3—31no—
490C22×D3—31no—
491C22×D3—31no—
492C22×D3—61no—
493C22×D3—91no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—91no—
504C2×C3×C4—91no—
505C2×C3×C4—91no—
506C2×C3×C4—91no—
507C2×C3×C4—91no—
508C2×C3×C4—91no—
509C2×C3×C4—91no—
510C2×C3×C4—91no—
511C2×C3×C4—91no—
512C2×C3×C4—91no—
513C2×C3×C4—182no—
514C2×C3×C4—182no—
515C2×C3×C4—182no—
516C2×C3×C4C2×D3211yescharacteristic
517C2×C3×C4C2×D3211yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519#67—182no—
520#67—182no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—91no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—91no—
543C2×Dic3—91no—
544C2×Dic3—182no—
545D12—182no—
546C4×D3—62no—
547C4×D3—62no—
548C4×D3—62no—
549C4×D3—62no—
550C4×D3—62no—
551C4×D3—62no—
552C4×D3—64no—
553C4×D3—122no—
554C4×D3—122no—
555C4×D3—182no—
556C4×D3—182no—
557Dic6—182no—
558Dic6—182no—
559Dic6—182no—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—21no—
563C2×C32#100711yescharacteristic
564C2×C32D3×#4111yescharacteristic
565C2×C32D3×#4111yescharacteristic
566C2×C32D3×#4111yescharacteristic
567C2×C32D3×#4111yescharacteristic
568C2×C32#101011yescharacteristic
569C3⋊D3—41no—
570C3×D3—64no—
571C3×D3—62no—
572C3×D3—62no—
573C3×D3—121no—
574C2×Q8—271no—
575C2×D4—271no—
576C22×C4—91no—
577C22×C4—91no—
578C22×C4—91no—
579C22×C4—271no—
580C4⋊C4—91no—
581C4⋊C4—91no—
582C4⋊C4—91no—
583C4⋊C4—91no—
584C4⋊C4—91no—
585C4⋊C4—91no—
586C4⋊C4—91no—
587C4⋊C4—91no—
588C4⋊C4—91no—
589C4⋊C4—91no—
590C4⋊C4—271no—
591C4⋊C4—271no—
592C4⋊C4—271no—
593C4⋊C4—271no—
594C4⋊C4—271no—
595C4⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
596C22⋊C4—91no—
597C22⋊C4—91no—
598C22⋊C4—91no—
599C22⋊C4—271no—
600C22⋊C4—271no—
601C22⋊C4—271no—
602C22⋊C4—271no—
603C22⋊C4—271no—
604C42—91no—
605C42—91no—
606C42—271no—
607C42—271no—
608C42—271no—
609C22×C3—31no—
610C22×C3—31no—
611C22×C3—61no—
612C22×C3—92no—
613C22×C3—181no—
614C22×C3—181no—
615C22×C3—181no—
616C22×C3—181no—
617C22×C3—181no—
618C22×C3C22×D3211yescharacteristic
619C2×D3—32no—
620C2×D3—32no—
621C2×D3—62no—
622C2×D3—61no—
623C2×D3—61no—
624C2×D3—61no—
625C2×D3—61no—
626C2×D3—62no—
627C2×D3—62no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—181no—
632C2×D3—181no—
633C2×D3—181no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—61no—
638C3×C4—61no—
639C3×C4—61no—
640C3×C4—61no—
641C3×C4—61no—
642C3×C4—61no—
643C3×C4—62no—
644C3×C4—92no—
645C3×C4—121no—
646C3×C4—121no—
647C3×C4—181no—
648C3×C4—181no—
649C3×C4—181no—
650C3×C4—181no—
651C3×C4—181no—
652C3×C4—181no—
653C3×C4—181no—
654C3×C4—181no—
655C3×C4—181no—
656Dic3—32no—
657Dic3—32no—
658Dic3—62no—
659Dic3—61no—
660Dic3—61no—
661Dic3—61no—
662Dic3—61no—
663Dic3—61no—
664Dic3—61no—
665Dic3—61no—
666Dic3—61no—
667Dic3—61no—
668Dic3—61no—
669Dic3—61no—
670Dic3—121no—
671Dic3—121no—
672Dic3—181no—
673Dic3—181no—
674Dic3—181no—
675Dic3—181no—
676Dic3—181no—
677Dic3—181no—
678Dic3—181no—
679C32—21no—
680C32#569311yescharacteristic, complemented
681C32#570811yescharacteristic, complemented
682C23—91no—
683C23—91no—
684Q8—542no—
685D4—542no—
686C2×C4—91no—
687C2×C4—91no—
688C2×C4—91no—
689C2×C4—91no—
690C2×C4—91no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—91no—
694C2×C4—91no—
695C2×C4—91no—
696C2×C4—182no—
697C2×C4—182no—
698C2×C4—182no—
699C2×C4—542no—
700C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
701C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
702C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
703C2×C3—31no—
704C2×C3—31no—
705C2×C3—31no—
706C2×C3—31no—
707C2×C3—31no—
708C2×C3—31no—
709C2×C3—61no—
710C2×C3—61no—
711C2×C3—61no—
712C2×C3—182no—
713C2×C3—361no—
714C2×C3#6430611yescharacteristic
715C2×C3#6431211yescharacteristic
716C2×C3#6431511yescharacteristic
717D3—62no—
718D3—62no—
719D3—64no—
720D3—121no—
721D3—361no—
722C22—92no—
723C22—181no—
724C22—181no—
725C22—181no—
726C22—181no—
727C22—181no—
728C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—92no—
733C4—181no—
734C4—181no—
735C4—181no—
736C4—181no—
737C4—181no—
738C4—181no—
739C4—181no—
740C4—181no—
741C4—181no—
742C3—31no—
743C3—31no—
744C3—61no—
745C3#1059447111yescharacteristic
746C2—182no—
747C2—361no—
748C2#1172249111yescharacteristic
749C2#1172250511yescharacteristic
750C2#1172251611yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC4⋊C4×H(3,𝔽3)C22
prime radicalC2×#6200C22
hypercenterC4⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#552
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C4⋊C4×#272C2semidirect
2. #64107⋊C3C2semidirect
3. #64098⋊C3C2semidirect
4. #11721134C2semidirect
6. #11721120C2semidirect
7. #11721111C2semidirect
10. #11721097C2semidirect
11. #11721096C2semidirect
12. #11721089C2semidirect
13. #11721086C2semidirect
14. #11721085C2semidirect
15. #11721077C2semidirect
53. #64107D3semidirect
54. #64098D3semidirect
486. H(3,𝔽3)#552semidirect
680. C32#5693semidirect
681. C32#5708semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×#2722
#64107⋊C32
#64098⋊C32
#117211342
#117211242
#117211202
#117211112
#117211042
#117210972
#117210962
#117210892
#117210862
#117210852
#117210772
#105945433
#105943313