Finite Group Databasebeta

← #13147919

Subgroups — #13147919

Order 1728.

962 conjugacy classes of subgroups.

The subgroup lattice has 849 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#64081⋊C3C211yesmaximal, characteristic, complemented
4#11721163C211yesmaximal, characteristic
5#11721161C211yesmaximal, characteristic, complemented
6#11721160C211yesmaximal, characteristic, complemented
7#11721151C211yesmaximal, characteristic, complemented
8#11721133C211yesmaximal, characteristic, complemented
9#11721124C211yesmaximal, characteristic, complemented
10#11721111C211yesmaximal, characteristic, complemented
11#11721104C211yesmaximal, characteristic, complemented
12#11721103C211yesmaximal, characteristic, complemented
13#11721100C211yesmaximal, characteristic, complemented
14#11721096C211yesmaximal, characteristic, complemented
15#11721076C211yesmaximal, characteristic, complemented
16#10594018—31nomaximal
17#10594015—31nomaximal
18C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
19C2×C4⋊#272C2211yescharacteristic
20C2×C4×#272C2211yescharacteristic
21C2×C4×#272C2211yescharacteristic, complemented
22C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
23C2×#6200C2211yescharacteristic
24C2×#6200C2211yescharacteristic
25C2×#6199C2211yescharacteristic
26C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
27C2×#6196C2211yescharacteristic, complemented
28C42×H(3,𝔽3)C2211yescharacteristic, complemented
29#88542C2211yescharacteristic
30#88542C2211yescharacteristic, complemented
31C4⋊#1084C2211yescharacteristic, complemented
32#3752⋊C3C2211yescharacteristic
33#3752⋊C3C2211yescharacteristic
34#3752⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37#3750⋊C3C2211yescharacteristic, complemented
38#3750⋊C3C2211yescharacteristic, complemented
39#3750⋊C3C2211yescharacteristic, complemented
40#3750⋊C3C2211yescharacteristic, complemented
41#3750⋊C3C2211yescharacteristic, complemented
42C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
43#88451C2211yescharacteristic
44#88451C2211yescharacteristic
45#88451C2211yescharacteristic, complemented
46#88451C2211yescharacteristic, complemented
47#88450C2211yescharacteristic
48#88450C2211yescharacteristic
49#88450C2211yescharacteristic
50#88449C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53#64085D311yescharacteristic, complemented
54#64081D311yescharacteristic, complemented
55C3×#876—31no—
56C3×C4×D12—31no—
57C3×C4×D12—31no—
58C3×C4×D12—61no—
59C3×#872—31no—
60#63922—31no—
61#63922—31no—
62#63921—31no—
63D3×(C2×D3)⋊C4—31no—
64D3×(C2×D3)⋊C4—31no—
65D3×(C2×D3)⋊C4—31no—
66#63915—31no—
67#63905—31no—
68#63905—31no—
69#63904—31no—
70#63899—31no—
71#63895—31no—
72#63884—31no—
73#63884—31no—
74#63879—31no—
75#63878—31no—
76#63877—31no—
77#63858—31no—
78#63853—31no—
79#63852—31no—
80#63851—31no—
81#63851—31no—
82#63850—31no—
83#63848—31no—
84C22×#272C2311yescharacteristic
85C22×#272C2311yescharacteristic
86C22×(C3⋊D3)⋊C3C2311yescharacteristic
87C22×(C3⋊D3)⋊C3C2311yescharacteristic
88C2×((C3⋊D3)⋊C3)⋊C2—22no—
89C2×((C3⋊D3)⋊C3)⋊C2—22no—
90C2×((C3⋊D3)⋊C3)⋊C2—41no—
91C2×C4×H(3,𝔽3)C2311yescharacteristic
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94C2×#1084C2311yescharacteristic
95C2×#1084C2311yescharacteristic
96C4⋊#272—22no—
97C4×#272—41no—
98C4×#272—41no—
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C4×(C3⋊D3)⋊C3—22no—
106#6200—22no—
107#6200—41no—
108#6199—22no—
109((C3⋊D3)⋊C3)⋊C4—41no—
110#6196—41no—
111#5705—91no—
112#5556—91no—
113#5527—91no—
114C22×D32—31no—
115C22×D32—31no—
116C2×C4×C3⋊D3C2×D311yescharacteristic
117C2×C3×D12—31no—
118C2×C3×D12—31no—
119C2×C3×D12—61no—
120C2×C3×C4×D3—31no—
121C2×C3×C4×D3—31no—
122C2×C3×C4×D3—31no—
123C2×C3×C4×D3—31no—
124C2×C3×C4×D3—31no—
125C2×C3×C4×D3—61no—
126C2×C3×C4×D3—61no—
127C2×#627—31no—
128C2×#627—31no—
129C2×#626—31no—
130C2×#626—31no—
131C2×#625—31no—
132C2×#625—31no—
133C2×#624—31no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137C32×C42—21no—
138C32×C42C2×D311yescharacteristic, complemented
139C32×C42C2×D311yescharacteristic, complemented
140#3752C2×D311yescharacteristic
141#3752C2×D311yescharacteristic
142#3752C2×D311yescharacteristic
143#3752C2×D311yescharacteristic
144#3752C2×D311yescharacteristic
145#3750C2×D311yescharacteristic, complemented
146#3750C2×D311yescharacteristic, complemented
147#3750C2×D311yescharacteristic, complemented
148#3750C2×D311yescharacteristic, complemented
149#3750C2×D311yescharacteristic, complemented
150C4×C3⋊Dic3C2×D311yescharacteristic, complemented
151C3×(C2×D3)⋊C4—31no—
152C3×(C2×D3)⋊C4—31no—
153C3×(C2×D3)⋊C4—31no—
154C3×(C2×D3)⋊C4—31no—
155C3×(C2×D3)⋊C4—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×(C2×D3)⋊C4—61no—
162C3×C4⋊Dic3—31no—
163C3×C4⋊Dic3—31no—
164C3×C4⋊Dic3—61no—
165C3×Dic3⋊C4—31no—
166C3×Dic3⋊C4—31no—
167C3×Dic3⋊C4—31no—
168C3×Dic3⋊C4—31no—
169C3×Dic3⋊C4—31no—
170C3×C4×Dic3—31no—
171#3724—31no—
172Dic3⋊Dic3—31no—
173Dic3⋊Dic3—31no—
174Dic3⋊Dic3—31no—
175#3722—31no—
176#3722—31no—
177#3722—31no—
178(C2×D3)⋊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#4112yes—
198C2×(C3⋊D3)⋊C3—21no—
199C2×(C3⋊D3)⋊C3—21no—
200C2×(C3⋊D3)⋊C3—21no—
201C2×(C3⋊D3)⋊C3—21no—
202C2×(C3⋊D3)⋊C3—21no—
203C2×(C3⋊D3)⋊C3#4112yes—
204((C3⋊D3)⋊C3)⋊C2—44no—
205C4×H(3,𝔽3)—21no—
206C4×H(3,𝔽3)—21no—
207C4×H(3,𝔽3)—21no—
208#1084—21no—
209#1084—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—21no—
215(C3⋊Dic3)⋊C3—21no—
216C3×#126—91no—
217C3×C4×D4—91no—
218C3×#117—91no—
219#937—91no—
220#935—91no—
221#929—91no—
222#929—91no—
223C4×#67—91no—
224C2×(C2×D3)⋊C4—91no—
225C2×(C2×D3)⋊C4—91no—
226#924—91no—
227#898—91no—
228#898—91no—
229#897—91no—
230#896—91no—
231#896—91no—
232#896—91no—
233#894—91no—
234#894—91no—
235#894—91no—
236#894—91no—
237#893—91no—
238#892—91no—
239#885—91no—
240#885—91no—
241#883—91no—
242#883—91no—
243#882—91no—
244#882—91no—
245#67⋊C4—91no—
246D3×C22⋊C4—91no—
247D3×C22⋊C4—91no—
248D3×C22⋊C4—91no—
249D3×C22⋊C4—91no—
250#879—91no—
251#878—91no—
252#877—91no—
253#876—31no—
254#876—91no—
255#875—91no—
256C4×D12—31no—
257C4×D12—31no—
258C4×D12—61no—
259#872—31no—
260#872—91no—
261#872—91no—
262C22×C3⋊D3C22×D311yescharacteristic
263C22×C3⋊D3C22×D311yescharacteristic
264C22×C3×D3—31no—
265C22×C3×D3—31no—
266C22×C3×D3—31no—
267C22×C3×D3—31no—
268C22×C3×D3—31no—
269C22×C3×D3—31no—
270C22×C3×D3—61no—
271C22×C3×D3—61no—
272C2×D32—62no—
273C2×D32—62no—
274C2×D32—62no—
275C2×D32—62no—
276C2×D32—121no—
277C2×D32—121no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283C2×C32×C4C22×D311yescharacteristic
284C2×C32×C4C22×D311yescharacteristic
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287C2×C3⋊Dic3C22×D311yescharacteristic
288C2×C3⋊Dic3C22×D311yescharacteristic
289C2×C3⋊Dic3C22×D311yescharacteristic
290C2×C3⋊Dic3C22×D311yescharacteristic
291C2×C3⋊Dic3C22×D311yescharacteristic
292C2×C3⋊Dic3C22×D311yescharacteristic
293C4×C3⋊D3—22no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—31no—
298C2×C3×Dic3—31no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—61no—
305C2×C3×Dic3—61no—
306C3×D12—62no—
307C3×D12—62no—
308C3×D12—64no—
309C3×C4×D3—62no—
310C3×C4×D3—121no—
311C3×C4×D3—121no—
312C3×C4×D3—121no—
313C3×C4×D3—121no—
314C3×C4×D3—122no—
315C3×C4×D3—122no—
316#627—121no—
317#627—121no—
318#626—62no—
319#626—121no—
320#625—62no—
321#625—121no—
322#624—121no—
323D3×Dic3—62no—
324D3×Dic3—62no—
325D3×Dic3—121no—
326#551—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(C3⋊D3)⋊C3—22no—
333(C3⋊D3)⋊C3—41no—
334C23×D3—91no—
335C23×D3—91no—
336C23×D3—91no—
337C2×C3×D4—91no—
338C22×C3×C4—91no—
339C22×C3×C4—91no—
340C22×C3×C4—91no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345C22×Dic3—91no—
346C22×Dic3—91no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—61no—
350C2×D12—91no—
351C2×D12—91no—
352C2×C4×D3—31no—
353C2×C4×D3—31no—
354C2×C4×D3—31no—
355C2×C4×D3—31no—
356C2×C4×D3—31no—
357C2×C4×D3—61no—
358C2×C4×D3—61no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3—91no—
363C2×C4×D3—91no—
364C2×Dic6—91no—
365C2×Dic6—91no—
366C2×Dic6—91no—
367C3×C4⋊C4—91no—
368C3×C4⋊C4—91no—
369C3×C4⋊C4—91no—
370C3×C4⋊C4—91no—
371C3×C4⋊C4—91no—
372C3×C4⋊C4—91no—
373C3×C22⋊C4—91no—
374C3×C22⋊C4—91no—
375C3×C22⋊C4—91no—
376C3×C22⋊C4—91no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380C3×C42—31no—
381C3×C42—31no—
382C3×C42—61no—
383C3×C42—91no—
384C3×C42D3211yescharacteristic
385#217—91no—
386#217—91no—
387#217—91no—
388#217—91no—
389#217—91no—
390#217—91no—
391#217—91no—
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—31no—
400(C2×D3)⋊C4—31no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
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—
419(C2×D3)⋊C4—91no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—91no—
422C4⋊Dic3—31no—
423C4⋊Dic3—31no—
424C4⋊Dic3—61no—
425C4⋊Dic3—91no—
426C4⋊Dic3—91no—
427Dic3⋊C4—31no—
428Dic3⋊C4—31no—
429Dic3⋊C4—31no—
430Dic3⋊C4—31no—
431Dic3⋊C4—31no—
432Dic3⋊C4—91no—
433Dic3⋊C4—91no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4—91no—
441C4×Dic3—31no—
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—21no—
453C2×C3⋊D3—21no—
454C2×C3⋊D3#23512yes—
455C2×C3×D3—32no—
456C2×C3×D3—32no—
457C2×C3×D3—32no—
458C2×C3×D3—62no—
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—62no—
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—61no—
475C2×C3×D3—121no—
476C2×C3×D3—121no—
477C2×C3×D3—121no—
478C2×C3×D3—121no—
479D32—124no—
480D32—124no—
481C32×C4—22no—
482C32×C4—22no—
483C32×C4—21no—
484C32×C4—21no—
485C32×C4—21no—
486C32×C4—21no—
487C32×C4—21no—
488C32×C4—21no—
489C32×C4—41no—
490C3⋊Dic3—21no—
491C3⋊Dic3—21no—
492C3⋊Dic3—21no—
493C3⋊Dic3—21no—
494C3⋊Dic3—21no—
495C3⋊Dic3—21no—
496C3×Dic3—61no—
497C3×Dic3—61no—
498C3×Dic3—61no—
499C3×Dic3—61no—
500C3×Dic3—61no—
501C3×Dic3—61no—
502C3×Dic3—61no—
503C3×Dic3—61no—
504C3×Dic3—61no—
505C3×Dic3—61no—
506C3×Dic3—121no—
507C3×Dic3—121no—
508#126—91no—
509#126—271no—
510#124—271no—
511#123—271no—
512#123—271no—
513#123—271no—
514C22⋊Q8—271no—
515C22⋊Q8—271no—
516#120—271no—
517C4×D4—91no—
518C4×D4—271no—
519#117—91no—
520#117—271no—
521C2×C22⋊C4—271no—
522C2×C22⋊C4—271no—
523H(3,𝔽3)#55111yescharacteristic, 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—61no—
535C22×D3—61no—
536C22×D3—91no—
537C22×D3—91no—
538C22×D3—182no—
539C22×D3—182no—
540C22×D3—182no—
541C22×D3—182no—
542C22×D3—182no—
543C22×D3—182no—
544C22×D3—361no—
545C22×D3—361no—
546C22×D3—361no—
547C3×D4—182no—
548C2×C3×C4—31no—
549C2×C3×C4—31no—
550C2×C3×C4—31no—
551C2×C3×C4—31no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—91no—
558C2×C3×C4—91no—
559C2×C3×C4—91no—
560C2×C3×C4—91no—
561C2×C3×C4—91no—
562C2×C3×C4—91no—
563C2×C3×C4—91no—
564C2×C3×C4—91no—
565C2×C3×C4—182no—
566C2×C3×C4—361no—
567C2×C3×C4—361no—
568C2×C3×C4C2×D3211yescharacteristic
569C2×C3×C4C2×D3211yescharacteristic
570C2×C3×C4C2×D3211yescharacteristic
571#67—182no—
572#67—182no—
573#67—361no—
574#67—361no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—31no—
580C2×Dic3—31no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—91no—
588C2×Dic3—91no—
589C2×Dic3—91no—
590C2×Dic3—91no—
591C2×Dic3—91no—
592C2×Dic3—91no—
593C2×Dic3—182no—
594C2×Dic3—361no—
595D12—62no—
596D12—62no—
597D12—64no—
598D12—182no—
599D12—361no—
600C4×D3—62no—
601C4×D3—121no—
602C4×D3—121no—
603C4×D3—121no—
604C4×D3—121no—
605C4×D3—122no—
606C4×D3—122no—
607C4×D3—182no—
608C4×D3—182no—
609C4×D3—182no—
610C4×D3—361no—
611C4×D3—361no—
612Dic6—361no—
613Dic6—361no—
614Dic6—361no—
615C2×C32—21no—
616C2×C32—21no—
617C2×C32—21no—
618C2×C32C2×#23511yescharacteristic
619C2×C32D3×#4111yescharacteristic
620C2×C32D3×#4111yescharacteristic
621C2×C32D3×#4111yescharacteristic
622C2×C32#100911yescharacteristic
623C2×C32#100911yescharacteristic
624C3⋊D3—22no—
625C3⋊D3—41no—
626C3×D3—62no—
627C3×D3—62no—
628C3×D3—62no—
629C3×D3—122no—
630C3×D3—122no—
631C3×D3—121no—
632C3×D3—121no—
633C3×D3—121no—
634C24—271no—
635C2×Q8—271no—
636C2×D4—91no—
637C2×D4—271no—
638C2×D4—271no—
639C22×C4—91no—
640C22×C4—91no—
641C22×C4—91no—
642C22×C4—271no—
643C22×C4—271no—
644C4⋊C4—91no—
645C4⋊C4—91no—
646C4⋊C4—91no—
647C4⋊C4—91no—
648C4⋊C4—91no—
649C4⋊C4—91no—
650C4⋊C4—271no—
651C4⋊C4—271no—
652C22⋊C4—91no—
653C22⋊C4—91no—
654C22⋊C4—91no—
655C22⋊C4—91no—
656C22⋊C4—91no—
657C22⋊C4—91no—
658C22⋊C4—91no—
659C22⋊C4—271no—
660C22⋊C4—271no—
661C22⋊C4—271no—
662C22⋊C4—271no—
663C22⋊C4—271no—
664C22⋊C4—271no—
665C22⋊C4—271no—
666C42—91no—
667C42—271no—
668C42((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
669C22×C3—31no—
670C22×C3—31no—
671C22×C3—61no—
672C22×C3—92no—
673C22×C3—92no—
674C22×C3—181no—
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×C3C22×D3211yescharacteristic
685C2×D3—32no—
686C2×D3—32no—
687C2×D3—32no—
688C2×D3—62no—
689C2×D3—61no—
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—62no—
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—61no—
705C2×D3—92no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—181no—
711C2×D3—181no—
712C2×D3—181no—
713C2×D3—181no—
714C2×D3—181no—
715C2×D3—364no—
716C2×D3—364no—
717C2×D3—364no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—61no—
722C3×C4—61no—
723C3×C4—61no—
724C3×C4—61no—
725C3×C4—61no—
726C3×C4—61no—
727C3×C4—62no—
728C3×C4—62no—
729C3×C4—121no—
730C3×C4—181no—
731C3×C4—181no—
732C3×C4—181no—
733C3×C4—181no—
734C3×C4—181no—
735C3×C4—181no—
736C3×C4—181no—
737C3×C4—181no—
738Dic3—61no—
739Dic3—61no—
740Dic3—61no—
741Dic3—61no—
742Dic3—61no—
743Dic3—61no—
744Dic3—61no—
745Dic3—61no—
746Dic3—61no—
747Dic3—61no—
748Dic3—121no—
749Dic3—121no—
750Dic3—181no—
751Dic3—181no—
752Dic3—181no—
753Dic3—181no—
754Dic3—181no—
755Dic3—181no—
756C32—21no—
757C32#552711yescharacteristic, complemented
758C32#570511yescharacteristic, complemented
759C23—91no—
760C23—91no—
761C23—91no—
762C23—91no—
763C23—542no—
764C23—542no—
765C23—1081no—
766Q8—1081no—
767D4—182no—
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—182no—
779C2×C4—361no—
780C2×C4—361no—
781C2×C4—542no—
782C2×C4—1081no—
783C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
784C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
785C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
786C2×C3—31no—
787C2×C3—31no—
788C2×C3—31no—
789C2×C3—31no—
790C2×C3—31no—
791C2×C3—31no—
792C2×C3—61no—
793C2×C3—61no—
794C2×C3—61no—
795C2×C3—182no—
796C2×C3—182no—
797C2×C3—361no—
798C2×C3—361no—
799C2×C3D3×#23511yescharacteristic
800C2×C3#6430611yescharacteristic
801C2×C3#6430811yescharacteristic
802D3—62no—
803D3—62no—
804D3—62no—
805D3—122no—
806D3—121no—
807D3—121no—
808D3—122no—
809D3—121no—
810D3—182no—
811D3—361no—
812C22—92no—
813C22—92no—
814C22—181no—
815C22—181no—
816C22—181no—
817C22—181no—
818C22—181no—
819C22—181no—
820C22—181no—
821C22—181no—
822C22—181no—
823C22—181no—
824C22—1084no—
825C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—181no—
830C4—181no—
831C4—181no—
832C4—181no—
833C4—181no—
834C4—181no—
835C4—181no—
836C4—181no—
837C3—31no—
838C3—31no—
839C3—61no—
840C3#1059401711yescharacteristic
841C2—182no—
842C2—182no—
843C2—361no—
844C2—361no—
845C2#1172249011yescharacteristic
846C2#1172249111yescharacteristic
847C2#1172249311yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC42×H(3,𝔽3)C22
prime radical#11721163C2
hypercenterC42((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#551
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. #64081⋊C3C2semidirect
5. #11721161C2semidirect
6. #11721160C2semidirect
7. #11721151C2semidirect
8. #11721133C2semidirect
9. #11721124C2semidirect
10. #11721111C2semidirect
11. #11721104C2semidirect
12. #11721103C2semidirect
13. #11721100C2semidirect
14. #11721096C2semidirect
15. #11721076C2semidirect
21. C2×C4×#272C22semidirect
27. C2×#6196C22semidirect
28. C42×H(3,𝔽3)C22semidirect
30. #88542C22semidirect
31. C4⋊#1084C22semidirect
37. #3750⋊C3C22semidirect
38. #3750⋊C3C22semidirect
39. #3750⋊C3C22semidirect
40. #3750⋊C3C22semidirect
41. #3750⋊C3C22semidirect
42. C4×(C3⋊Dic3)⋊C3C22semidirect
45. #88451C22semidirect
46. #88451C22semidirect
50. #88449C22semidirect
51. #88448C22semidirect
52. #88447C22semidirect
53. #64085D3semidirect
54. #64081D3semidirect
138. C32×C42C2×D3semidirect
139. C32×C42C2×D3semidirect
145. #3750C2×D3semidirect
146. #3750C2×D3semidirect
147. #3750C2×D3semidirect
148. #3750C2×D3semidirect
149. #3750C2×D3semidirect
150. C4×C3⋊Dic3C2×D3semidirect
523. H(3,𝔽3)#551semidirect
668. C42((C3⋊D3)⋊C3)⋊C2semidirect
757. C32#5527semidirect
758. C32#5705semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#2722
#117213872
#64081⋊C32
#117211632
#117211612
#117211602
#117211512
#117211332
#117211242
#117211112
#117211042
#117211032
#117211002
#117210962
#117210762
#105940183
#105940153