Finite Group Databasebeta

← #13149600

Subgroups — #13149600

Order 1728.

927 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721763C211yesmaximal, characteristic, complemented
2#64107⋊C3C211yesmaximal, characteristic, complemented
3#64098⋊C3C211yesmaximal, characteristic, complemented
4#11721157C211yesmaximal, characteristic, complemented
5#11721157C211yesmaximal, characteristic, complemented
6#11721157C211yesmaximal, characteristic, complemented
7#11721151C211yesmaximal, characteristic, complemented
8#11721149C211yesmaximal, characteristic, complemented
9#11721149C211yesmaximal, characteristic, complemented
10#11721147C211yesmaximal, characteristic, complemented
11#11721130C211yesmaximal, characteristic, complemented
12#11721124C211yesmaximal, characteristic, complemented
13#11721123C211yesmaximal, characteristic, complemented
14#11721088C211yesmaximal, characteristic, complemented
15#11721076C211yesmaximal, characteristic, complemented
16#10594438—31nomaximal
17#10594434—31nomaximal
18C2×C4⋊#272C2211yescharacteristic
19C2×C4⋊#272C2211yescharacteristic
20C2×C4⋊#272C2211yescharacteristic
21C2×C4×#272C2211yescharacteristic
22C2×#6200C2211yescharacteristic
23C2×#6200C2211yescharacteristic
24C2×#6200C2211yescharacteristic
25C2×#6199C2211yescharacteristic
26C2×#6199C2211yescharacteristic
27C2×#6199C2211yescharacteristic
28C2×#6199C2211yescharacteristic
29C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
30C4⋊C4×H(3,𝔽3)C2211yescharacteristic
31#88542C2211yescharacteristic
32#88542C2211yescharacteristic
33#3752⋊C3C2211yescharacteristic
34#3752⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
37C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
38#3750⋊C3C2211yescharacteristic
39#3750⋊C3C2211yescharacteristic
40#3750⋊C3C2211yescharacteristic
41#3750⋊C3C2211yescharacteristic
42#3750⋊C3C2211yescharacteristic
43C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
44C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
45#88451C2211yescharacteristic
46#88451C2211yescharacteristic
47#88451C2211yescharacteristic
48#88451C2211yescharacteristic
49#88451C2211yescharacteristic
50#88448C2211yescharacteristic
51#88448C2211yescharacteristic
52#88447C2211yescharacteristic
53#64107D311yescharacteristic, complemented
54#64098D311yescharacteristic, complemented
55C3×#898—31no—
56C3×#895—31no—
57C3×#895—31no—
58C3×#895—61no—
59C3×#889—31no—
60#63904—31no—
61#63902—31no—
62#63898—31no—
63#63898—31no—
64Dic3×D12—31no—
65Dic3×D12—31no—
66#63891—31no—
67#63886—31no—
68#63886—31no—
69#63886—31no—
70#63885—31no—
71#63885—31no—
72#63885—31no—
73#63884—31no—
74#63884—31no—
75#63880—31no—
76#63879—31no—
77#63878—31no—
78#63877—31no—
79D3×Dic3⋊C4—31no—
80D3×Dic3⋊C4—31no—
81#63861—31no—
82#63858—31no—
83#63854—31no—
84C22×#272C2311yescharacteristic
85C22×#272C2311yescharacteristic
86C22×#272C2311yescharacteristic
87C22×(C3⋊D3)⋊C3C2311yescharacteristic
88C2×C4×H(3,𝔽3)C2311yescharacteristic
89C2×C4×H(3,𝔽3)C2311yescharacteristic
90C2×C4×H(3,𝔽3)C2311yescharacteristic
91C2×#1084C2311yescharacteristic
92C4⋊#272—22no—
93C4⋊#272—22no—
94C4⋊#272—41no—
95C4×#272—41no—
96C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
97C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103#6200—22no—
104#6200—22no—
105#6200—41no—
106#6199—22no—
107#6199—22no—
108#6199—41no—
109#6199—41no—
110((C3⋊D3)⋊C3)⋊C4—41no—
111#5709—91no—
112#5695—91no—
113#5601—91no—
114C2×C3×D12—31no—
115C2×C3×D12—31no—
116C2×C3×D12—31no—
117C2×C3×D12—31no—
118C2×C3×D12—31no—
119C2×C3×D12—31no—
120C2×C3×D12—61no—
121C2×C3×D12—61no—
122C2×C3×D12—61no—
123C2×C3×C4×D3—31no—
124C2×C3×C4×D3—31no—
125C2×C3×C4×D3—61no—
126C2×#626—31no—
127C2×#626—31no—
128C2×#626—31no—
129C2×#625—31no—
130C2×#625—31no—
131C2×#625—31no—
132C2×#624—31no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137C2×D3×Dic3—31no—
138C2×D3×Dic3—31no—
139C2×D3×Dic3—31no—
140C2×D3×Dic3—31no—
141C2×D3×Dic3—31no—
142C32×C4⋊C4—21no—
143C32×C4⋊C4C2×D311yescharacteristic
144C32×C4⋊C4C2×D311yescharacteristic
145#3752C2×D311yescharacteristic
146#3752C2×D311yescharacteristic
147#3752C2×D311yescharacteristic
148C4⋊(C3⋊Dic3)C2×D311yescharacteristic
149C4⋊(C3⋊Dic3)C2×D311yescharacteristic
150#3750C2×D311yescharacteristic
151#3750C2×D311yescharacteristic
152#3750C2×D311yescharacteristic
153#3750C2×D311yescharacteristic
154#3750C2×D311yescharacteristic
155C4×C3⋊Dic3C2×D311yescharacteristic
156C4×C3⋊Dic3C2×D311yescharacteristic
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4—31no—
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—61no—
165C3×(C2×D3)⋊C4—61no—
166C3×C4⋊Dic3—31no—
167C3×C4⋊Dic3—31no—
168C3×Dic3⋊C4—31no—
169C3×Dic3⋊C4—31no—
170C3×Dic3⋊C4—31no—
171C3×Dic3⋊C4—31no—
172C3×Dic3⋊C4—31no—
173C3×C4×Dic3—31no—
174C3×C4×Dic3—31no—
175#3724—31no—
176#3724—31no—
177Dic3⋊Dic3—31no—
178Dic3⋊Dic3—31no—
179(C2×D3)⋊Dic3—31no—
180(C2×D3)⋊Dic3—31no—
181(C2×D3)⋊Dic3—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—
189Dic32—31no—
190Dic32—31no—
191C22×H(3,𝔽3)C2411yescharacteristic
192C2×#272—21no—
193C2×#272—21no—
194C2×#272—21no—
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—
204C4×H(3,𝔽3)—21no—
205C4×H(3,𝔽3)—21no—
206C4×H(3,𝔽3)—21no—
207#1084—21no—
208(C3⋊Dic3)⋊C3—21no—
209(C3⋊Dic3)⋊C3—21no—
210(C3⋊Dic3)⋊C3—21no—
211(C3⋊Dic3)⋊C3—21no—
212(C3⋊Dic3)⋊C3—21no—
213(C3⋊Dic3)⋊C3—21no—
214(C3⋊Dic3)⋊C3#4112yes—
215C3×#126—91no—
216C3×#125—91no—
217C3×#121—91no—
218#939—91no—
219#939—91no—
220#939—91no—
221#935—91no—
222D4×Dic3—91no—
223D4×Dic3—91no—
224C4×#67—91no—
225C2×Dic3⋊C4—91no—
226#898—31no—
227#898—91no—
228#898—91no—
229#898—91no—
230#895—31no—
231#895—31no—
232#895—61no—
233#895—91no—
234#895—91no—
235#895—91no—
236#894—91no—
237#894—91no—
238#894—91no—
239#893—91no—
240#893—91no—
241#893—91no—
242#892—91no—
243D3×C4⋊C4—91no—
244D3×C4⋊C4—91no—
245#889—31no—
246#889—91no—
247#886—91no—
248#884—91no—
249#884—91no—
250#884—91no—
251#883—91no—
252#67⋊C4—91no—
253#67⋊C4—91no—
254#67⋊C4—91no—
255#879—91no—
256#877—91no—
257C4×D12—91no—
258C4×D12—91no—
259C4×D12—91no—
260#872—91no—
261C22×C3⋊D3C22×D311yescharacteristic
262C22×C3×D3—31no—
263C22×C3×D3—31no—
264C22×C3×D3—31no—
265C22×C3×D3—31no—
266C22×C3×D3—31no—
267C22×C3×D3—31no—
268C22×C3×D3—31no—
269C22×C3×D3—61no—
270C22×C3×D3—61no—
271C22×C3×D3—61no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C22×D311yescharacteristic
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281C2×C3⋊Dic3C22×D311yescharacteristic
282C2×C3⋊Dic3C22×D311yescharacteristic
283C2×C3⋊Dic3C22×D311yescharacteristic
284C2×C3⋊Dic3C22×D311yescharacteristic
285C2×C3⋊Dic3C22×D311yescharacteristic
286C2×C3⋊Dic3C22×D311yescharacteristic
287C2×C3⋊Dic3C22×D311yescharacteristic
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—61no—
298C3×D12—62no—
299C3×D12—62no—
300C3×D12—62no—
301C3×D12—62no—
302C3×D12—122no—
303C3×D12—122no—
304C3×D12—121no—
305C3×D12—121no—
306C3×D12—122no—
307C3×C4×D3—121no—
308C3×C4×D3—121no—
309C3×C4×D3—122no—
310#626—62no—
311#626—62no—
312#626—121no—
313#625—62no—
314#625—62no—
315#625—121no—
316#624—121no—
317D3×Dic3—62no—
318D3×Dic3—62no—
319D3×Dic3—62no—
320D3×Dic3—62no—
321D3×Dic3—121no—
322D3×Dic3—121no—
323D3×Dic3—121no—
324D3×Dic3—121no—
325D3×Dic3—121no—
326#553—271noSylow
327C2×H(3,𝔽3)C2×#4111yescharacteristic
328C2×H(3,𝔽3)C2×#4111yescharacteristic
329C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
330#272—22no—
331#272—41no—
332#272—41no—
333(C3⋊D3)⋊C3—41no—
334C2×C3×D4—91no—
335C2×C3×D4—91no—
336C2×C3×D4—91no—
337C22×C3×C4—91no—
338C2×#67—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C22×Dic3—91no—
345C22×Dic3—91no—
346C22×Dic3—91no—
347C22×Dic3—91no—
348C22×Dic3—91no—
349C2×D12—31no—
350C2×D12—31no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—91no—
359C2×D12—91no—
360C2×D12—91no—
361C2×C4×D3—31no—
362C2×C4×D3—31no—
363C2×C4×D3—61no—
364C2×C4×D3—91no—
365C2×C4×D3—91no—
366C2×C4×D3—91no—
367C2×C4×D3—91no—
368C2×C4×D3—91no—
369C2×C4×D3—91no—
370C2×C4×D3—91no—
371C2×C4×D3—91no—
372C2×C4×D3—91no—
373C2×C4×D3—91no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—61no—
377C3×C4⋊C4—91no—
378C3×C4⋊C4—91no—
379C3×C4⋊C4—91no—
380C3×C4⋊C4—91no—
381C3×C4⋊C4—91no—
382C3×C4⋊C4—91no—
383C3×C4⋊C4—91no—
384C3×C4⋊C4D3211yescharacteristic
385C3×C22⋊C4—91no—
386C3×C22⋊C4—91no—
387C3×C22⋊C4—91no—
388C3×C22⋊C4—91no—
389C3×C22⋊C4—91no—
390C3×C42—91no—
391C3×C42—91no—
392#217—91no—
393#217—91no—
394#217—91no—
395#217—91no—
396#217—91no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—31no—
400(C2×D3)⋊C4—31no—
401(C2×D3)⋊C4—31no—
402(C2×D3)⋊C4—31no—
403(C2×D3)⋊C4—31no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—91no—
415(C2×D3)⋊C4—91no—
416(C2×D3)⋊C4—91no—
417(C2×D3)⋊C4—91no—
418(C2×D3)⋊C4—91no—
419C4⋊Dic3—31no—
420C4⋊Dic3—31no—
421C4⋊Dic3—91no—
422C4⋊Dic3—91no—
423C4⋊Dic3—91no—
424C4⋊Dic3—91no—
425Dic3⋊C4—31no—
426Dic3⋊C4—31no—
427Dic3⋊C4—31no—
428Dic3⋊C4—31no—
429Dic3⋊C4—31no—
430Dic3⋊C4—91no—
431Dic3⋊C4—91no—
432Dic3⋊C4—91no—
433Dic3⋊C4—91no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439C4×Dic3—31no—
440C4×Dic3—31no—
441C4×Dic3—91no—
442C4×Dic3—91no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C4×Dic3—91no—
446C22×C32—21no—
447C22×C32C23×D311yescharacteristic
448C22×C32C23×D311yescharacteristic
449C2×C3⋊D3—21no—
450C2×C3⋊D3—21no—
451C2×C3⋊D3—21no—
452C2×C3×D3—32no—
453C2×C3×D3—32no—
454C2×C3×D3—62no—
455C2×C3×D3—61no—
456C2×C3×D3—61no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3—61no—
463C2×C3×D3—61no—
464C2×C3×D3—61no—
465C2×C3×D3—61no—
466C2×C3×D3—61no—
467C2×C3×D3—61no—
468C2×C3×D3—61no—
469C2×C3×D3—61no—
470C2×C3×D3—61no—
471C2×C3×D3—61no—
472C2×C3×D3—61no—
473C2×C3×D3—61no—
474C2×C3×D3—121no—
475C2×C3×D3—121no—
476C2×C3×D3—121no—
477C2×C3×D3—121no—
478C2×C3×D3—121no—
479C2×C3×D3—121no—
480C2×C3×D3—121no—
481C2×C3×D3—121no—
482C32×C4—22no—
483C32×C4—21no—
484C32×C4—21no—
485C32×C4—21no—
486C32×C4—21no—
487C32×C4—21no—
488C32×C4—21no—
489C32×C4—41no—
490C32×C4—41no—
491C3⋊Dic3—21no—
492C3⋊Dic3—21no—
493C3⋊Dic3—21no—
494C3⋊Dic3—21no—
495C3⋊Dic3—21no—
496C3⋊Dic3—21no—
497C3⋊Dic3#23912yes—
498C3×Dic3—32no—
499C3×Dic3—61no—
500C3×Dic3—61no—
501C3×Dic3—61no—
502C3×Dic3—61no—
503C3×Dic3—61no—
504C3×Dic3—61no—
505C3×Dic3—61no—
506C3×Dic3—61no—
507C3×Dic3—121no—
508#126—91no—
509#126—271no—
510#125—91no—
511#123—271no—
512#123—271no—
513#121—91no—
514#121—271no—
515#121—271no—
516#121—271no—
517C4×D4—271no—
518C4×D4—271no—
519C4×D4—271no—
520C4×D4—271no—
521#117—271no—
522C2×C4⋊C4—271no—
523H(3,𝔽3)#55311yescharacteristic, complemented, Sylow
524C23×C3—91no—
525C23×C3—91no—
526C23×C3—91no—
527C23×C3—91no—
528C22×D3—31no—
529C22×D3—31no—
530C22×D3—31no—
531C22×D3—31no—
532C22×D3—31no—
533C22×D3—31no—
534C22×D3—31no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—91no—
539C3×D4—182no—
540C3×D4—182no—
541C3×D4—361no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—91no—
552C2×C3×C4—91no—
553C2×C3×C4—91no—
554C2×C3×C4—91no—
555C2×C3×C4—91no—
556C2×C3×C4—91no—
557C2×C3×C4—91no—
558C2×C3×C4—91no—
559C2×C3×C4—361no—
560C2×C3×C4C2×D3211yescharacteristic
561C2×C3×C4C2×D3211yescharacteristic
562C2×C3×C4C2×D3211yescharacteristic
563#67—182no—
564#67—182no—
565#67—182no—
566#67—182no—
567#67—361no—
568#67—361no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—61no—
579C2×Dic3—91no—
580C2×Dic3—91no—
581C2×Dic3—91no—
582C2×Dic3—91no—
583C2×Dic3—91no—
584C2×Dic3—91no—
585C2×Dic3—91no—
586C2×Dic3—182no—
587C2×Dic3—182no—
588C2×Dic3—361no—
589C2×Dic3—361no—
590C2×Dic3—361no—
591D12—62no—
592D12—62no—
593D12—62no—
594D12—62no—
595D12—122no—
596D12—122no—
597D12—121no—
598D12—121no—
599D12—122no—
600D12—182no—
601D12—182no—
602D12—361no—
603C4×D3—121no—
604C4×D3—121no—
605C4×D3—122no—
606C4×D3—182no—
607C4×D3—182no—
608C4×D3—182no—
609C4×D3—182no—
610C4×D3—361no—
611C4×D3—361no—
612C4×D3—361no—
613C4×D3—361no—
614C4×D3—361no—
615C4×D3—361no—
616C2×C32—21no—
617C2×C32—21no—
618C2×C32—21no—
619C2×C32C2×#23911yescharacteristic
620C2×C32D3×#4111yescharacteristic
621C2×C32D3×#4111yescharacteristic
622C2×C32D3×#4111yescharacteristic
623C2×C32#100911yescharacteristic
624C2×C32#100911yescharacteristic
625C3⋊D3—41no—
626C3×D3—62no—
627C3×D3—62no—
628C3×D3—122no—
629C3×D3—121no—
630C3×D3—121no—
631C3×D3—121no—
632C3×D3—121no—
633C3×D3—121no—
634C3×D3—241no—
635C3×D3—241no—
636C2×D4—91no—
637C2×D4—91no—
638C2×D4—91no—
639C2×D4—271no—
640C2×D4—271no—
641C2×D4—271no—
642C22×C4—91no—
643C22×C4—271no—
644C22×C4—271no—
645C22×C4—271no—
646C22×C4—271no—
647C22×C4—271no—
648C4⋊C4—91no—
649C4⋊C4—91no—
650C4⋊C4—91no—
651C4⋊C4—91no—
652C4⋊C4—91no—
653C4⋊C4—91no—
654C4⋊C4—91no—
655C4⋊C4—271no—
656C4⋊C4—271no—
657C4⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
658C22⋊C4—91no—
659C22⋊C4—91no—
660C22⋊C4—91no—
661C22⋊C4—91no—
662C22⋊C4—91no—
663C22⋊C4—271no—
664C22⋊C4—271no—
665C22⋊C4—271no—
666C22⋊C4—271no—
667C22⋊C4—271no—
668C42—91no—
669C42—91no—
670C42—271no—
671C22×C3—31no—
672C22×C3—31no—
673C22×C3—61no—
674C22×C3—92no—
675C22×C3—181no—
676C22×C3—181no—
677C22×C3—181no—
678C22×C3—181no—
679C22×C3—181no—
680C22×C3—181no—
681C22×C3—181no—
682C22×C3—181no—
683C22×C3—181no—
684C22×C3—181no—
685C22×C3—181no—
686C22×C3C22×D3211yescharacteristic
687C2×D3—32no—
688C2×D3—32no—
689C2×D3—62no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—61no—
699C2×D3—61no—
700C2×D3—61no—
701C2×D3—61no—
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—61no—
705C2×D3—61no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—181no—
718C2×D3—181no—
719C2×D3—181no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—61no—
724C3×C4—61no—
725C3×C4—61no—
726C3×C4—61no—
727C3×C4—61no—
728C3×C4—61no—
729C3×C4—62no—
730C3×C4—92no—
731C3×C4—121no—
732C3×C4—121no—
733C3×C4—181no—
734C3×C4—181no—
735C3×C4—181no—
736C3×C4—181no—
737C3×C4—181no—
738C3×C4—181no—
739C3×C4—181no—
740Dic3—32no—
741Dic3—61no—
742Dic3—61no—
743Dic3—61no—
744Dic3—61no—
745Dic3—61no—
746Dic3—61no—
747Dic3—61no—
748Dic3—61no—
749Dic3—92no—
750Dic3—121no—
751Dic3—181no—
752Dic3—181no—
753Dic3—181no—
754Dic3—181no—
755Dic3—181no—
756Dic3—181no—
757C32—21no—
758C32#569511yescharacteristic, complemented
759C32#570911yescharacteristic, complemented
760C23—91no—
761C23—91no—
762C23—91no—
763C23—91no—
764D4—182no—
765D4—182no—
766D4—361no—
767D4—542no—
768D4—542no—
769D4—1081no—
770C2×C4—91no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—91no—
775C2×C4—91no—
776C2×C4—91no—
777C2×C4—91no—
778C2×C4—361no—
779C2×C4—542no—
780C2×C4—542no—
781C2×C4—1081no—
782C2×C4—1081no—
783C2×C4—1081no—
784C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
785C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
786C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
787C2×C3—31no—
788C2×C3—31no—
789C2×C3—31no—
790C2×C3—31no—
791C2×C3—31no—
792C2×C3—31no—
793C2×C3—61no—
794C2×C3—61no—
795C2×C3—61no—
796C2×C3—182no—
797C2×C3—361no—
798C2×C3—361no—
799C2×C3—361no—
800C2×C3#6430811yescharacteristic
801C2×C3#6431211yescharacteristic
802C2×C3D3×#23911yescharacteristic
803D3—62no—
804D3—62no—
805D3—122no—
806D3—121no—
807D3—121no—
808D3—121no—
809D3—121no—
810D3—121no—
811D3—241no—
812D3—241no—
813D3—361no—
814C22—92no—
815C22—181no—
816C22—181no—
817C22—181no—
818C22—181no—
819C22—181no—
820C22—181no—
821C22—181no—
822C22—181no—
823C22—181no—
824C22—181no—
825C22—181no—
826C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
827C4—21no—
828C4—21no—
829C4—21no—
830C4—92no—
831C4—181no—
832C4—181no—
833C4—181no—
834C4—181no—
835C4—181no—
836C4—181no—
837C4—181no—
838C3—31no—
839C3—31no—
840C3—61no—
841C3#1059446811yescharacteristic
842C2—182no—
843C2—361no—
844C2—361no—
845C2—361no—
846C2#1172249311yescharacteristic
847C2#1172250511yescharacteristic
848C2#1172251911yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC4⋊C4×H(3,𝔽3)C22
hypercenterC4⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#553
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. #11721763C2semidirect
2. #64107⋊C3C2semidirect
3. #64098⋊C3C2semidirect
4. #11721157C2semidirect
5. #11721157C2semidirect
6. #11721157C2semidirect
7. #11721151C2semidirect
8. #11721149C2semidirect
9. #11721149C2semidirect
10. #11721147C2semidirect
11. #11721130C2semidirect
12. #11721124C2semidirect
13. #11721123C2semidirect
14. #11721088C2semidirect
15. #11721076C2semidirect
53. #64107D3semidirect
54. #64098D3semidirect
523. H(3,𝔽3)#553semidirect
758. C32#5695semidirect
759. C32#5709semidirect

Maximal subgroups

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

subgroupindex
#117217632
#64107⋊C32
#64098⋊C32
#117211572
#117211512
#117211492
#117211472
#117211302
#117211242
#117211232
#117210882
#117210762
#105944383
#105944343