Finite Group Databasebeta

← #13150719

Subgroups — #13150719

Order 1728.

942 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721824C211yesmaximal, characteristic, complemented
2C4×#638⋊C3C211yesmaximal, characteristic, complemented
3C2×#3752⋊C3C211yesmaximal, characteristic, complemented
4#11721316C211yesmaximal, characteristic
5#11721310C211yesmaximal, characteristic, complemented
6#11721306C211yesmaximal, characteristic, complemented
7#11721296C211yesmaximal, characteristic, complemented
8#11721143C211yesmaximal, characteristic, complemented
9#11721139C211yesmaximal, characteristic, complemented
10#11721135C211yesmaximal, characteristic, complemented
11#11721131C211yesmaximal, characteristic, complemented
12#11721122C211yesmaximal, characteristic, complemented
13#11721120C211yesmaximal, characteristic, complemented
14#11721111C211yesmaximal, characteristic, complemented
15#11721109C211yesmaximal, characteristic, complemented
16#10595035—31nomaximal
17#10594941—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C22×C4×H(3,𝔽3)C2211yescharacteristic
20C2×#6229C2211yescharacteristic, complemented
21C2×#638⋊C3C2211yescharacteristic
22C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
23C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
24C2×#6198C2211yescharacteristic
25C2×#6198C2211yescharacteristic
26C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
27C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
28#88552C2211yescharacteristic
29#88552C2211yescharacteristic
30C4⋊#1084C2211yescharacteristic, complemented
31#88540C2211yescharacteristic, complemented
32#88540C2211yescharacteristic, complemented
33#3757⋊C3C2211yescharacteristic
34#3752⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38#3752⋊C3C2211yescharacteristic, complemented
39#3750⋊C3C2211yescharacteristic, complemented
40C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
41#88450C2211yescharacteristic
42#88450C2211yescharacteristic
43#88450C2211yescharacteristic
44#88450C2211yescharacteristic
45#88450C2211yescharacteristic, complemented
46#88450C2211yescharacteristic, complemented
47#88449C2211yescharacteristic, complemented
48#88449C2211yescharacteristic, complemented
49#88448C2211yescharacteristic, complemented
50#88448C2211yescharacteristic, complemented
51#88447C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53C4×#638D311yescharacteristic, complemented
54C2×#3752D311yescharacteristic, complemented
55C3×C4×#67—31no—
56C2×C3×(C2×D3)⋊C4—31no—
57C3×#924—31no—
58C3×#924—31no—
59C3×#924—61no—
60#63981—31no—
61#63977—31no—
62#63974—31no—
63D3×#217—31no—
64#63966—31no—
65#63962—31no—
66#63957—31no—
67#63955—31no—
68#63907—31no—
69#63907—31no—
70#63904—31no—
71#63890—31no—
72#63888—31no—
73#63887—31no—
74#63881—31no—
75#63878—31no—
76#63868—31no—
77#63862—31no—
78#63858—31no—
79#63854—31no—
80#63853—31no—
81#63850—31no—
82#63848—31no—
83#63836—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×(C3⋊D3)⋊C3—22no—
86C22×(C3⋊D3)⋊C3—22no—
87C22×(C3⋊D3)⋊C3—41no—
88C22×(C3⋊D3)⋊C3C2311yescharacteristic
89C22×(C3⋊D3)⋊C3C2311yescharacteristic
90C22×(C3⋊D3)⋊C3C2311yescharacteristic
91C2×C4×H(3,𝔽3)—41no—
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94C2×#1084C2311yescharacteristic
95C2×#1084C2311yescharacteristic
96C2×#1084C2311yescharacteristic
97C2×#1084C2311yescharacteristic
98#6229—41no—
99#638⋊C3—22no—
100C2×(C3⋊Dic3)⋊C3—22no—
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C4×(C3⋊D3)⋊C3—41no—
107#6198—22no—
108#6198—41no—
109((C3⋊D3)⋊C3)⋊C4—22no—
110((C3⋊D3)⋊C3)⋊C4—41no—
111#5637—91no—
112#5556—91no—
113#5495—91no—
114C23×C3⋊D3C2×D311yescharacteristic
115C23×C3×D3—31no—
116C22×C32×C4—21no—
117C22×C32×C4C2×D311yescharacteristic
118C22×C32×C4C2×D311yescharacteristic
119C2×#638C2×D311yescharacteristic
120C22×C3⋊Dic3C2×D311yescharacteristic
121C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
122C2×C3×#67—31no—
123C22×C3×Dic3—31no—
124C2×C3×C4×D3—31no—
125C2×C3×Dic6—31no—
126C2×C3×Dic6—31no—
127C2×C3×Dic6—61no—
128C2×#626—31no—
129C2×#626—31no—
130C2×#626—31no—
131C2×#626—31no—
132C2×#624—31no—
133C2×#624—31no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—31no—
136#3757C2×D311yescharacteristic
137#3752C2×D311yescharacteristic
138#3752C2×D311yescharacteristic
139#3752C2×D311yescharacteristic
140#3752C2×D311yescharacteristic
141#3752C2×D311yescharacteristic, complemented
142#3750C2×D311yescharacteristic, complemented
143C4×C3⋊Dic3C2×D311yescharacteristic, complemented
144C3×#217—31no—
145C3×#217—31no—
146C3×#217—31no—
147C3×#217—31no—
148C3×#217—31no—
149C3×#217—61no—
150C3×#217—61no—
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×C4⋊Dic3—31no—
157C3×C4⋊Dic3—31no—
158C3×C4⋊Dic3—61no—
159C3×Dic3⋊C4—31no—
160C3×Dic3⋊C4—31no—
161C3×Dic3⋊C4—31no—
162C3×Dic3⋊C4—31no—
163C3×Dic3⋊C4—31no—
164C3×Dic3⋊C4—61no—
165C3×Dic3⋊C4—61no—
166C3×C4×Dic3—31no—
167#3724—31no—
168#3724—31no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—31no—
171Dic3⋊Dic3—31no—
172Dic3⋊Dic3—31no—
173Dic3⋊Dic3—31no—
174Dic3⋊Dic3—31no—
175#3722—31no—
176#3722—31no—
177#3722—31no—
178#3722—31no—
179#3722—31no—
180#3722—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—
187Dic32—31no—
188Dic32—31no—
189Dic32—31no—
190Dic32—31no—
191C22×H(3,𝔽3)—21no—
192C22×H(3,𝔽3)—21no—
193C22×H(3,𝔽3)#4112yes—
194C22×H(3,𝔽3)C2411yescharacteristic
195C2×(C3⋊D3)⋊C3—21no—
196C2×(C3⋊D3)⋊C3—21no—
197C2×(C3⋊D3)⋊C3—21no—
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—44no—
204C2×(C3⋊D3)⋊C3#4112yes—
205C4×H(3,𝔽3)—21no—
206C4×H(3,𝔽3)—21no—
207#1084—21no—
208#1084—21no—
209#1084—21no—
210#1084—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×C22⋊Q8—91no—
217C3×C4×D4—91no—
218C2×C3×C22⋊C4—91no—
219#953—91no—
220C2×#217—91no—
221#947—91no—
222#946—91no—
223#937—91no—
224#935—91no—
225#929—91no—
226#929—91no—
227C4×#67—31no—
228C4×#67—91no—
229C4×#67—91no—
230C2×(C2×D3)⋊C4—31no—
231C2×(C2×D3)⋊C4—91no—
232#926—91no—
233#924—31no—
234#924—31no—
235#924—61no—
236#898—91no—
237#898—91no—
238#898—91no—
239#896—91no—
240#894—91no—
241#894—91no—
242#893—91no—
243#892—91no—
244#886—91no—
245#886—91no—
246#885—91no—
247#885—91no—
248#883—91no—
249#883—91no—
250#882—91no—
251#67⋊C4—91no—
252D3×C22⋊C4—91no—
253D3×C22⋊C4—91no—
254#879—91no—
255#879—91no—
256#878—91no—
257#877—91no—
258#877—91no—
259#877—91no—
260#876—91no—
261#872—91no—
262C23×C32—21no—
263C23×C32C22×D311yescharacteristic
264C23×C32C22×D311yescharacteristic
265C22×C3⋊D3—22no—
266C22×C3⋊D3—22no—
267C22×C3⋊D3—41no—
268C22×C3⋊D3C22×D311yescharacteristic
269C22×C3⋊D3C22×D311yescharacteristic
270C22×C3⋊D3C22×D311yescharacteristic
271C22×C3×D3—31no—
272C22×C3×D3—31no—
273C22×C3×D3—31no—
274C22×C3×D3—62no—
275C22×C3×D3—62no—
276C22×C3×D3—121no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—41no—
280C2×C32×C4—41no—
281C2×C32×C4—42no—
282C2×C32×C4C22×D311yescharacteristic
283C2×C32×C4C22×D311yescharacteristic
284C2×C32×C4C22×D311yescharacteristic
285C2×C32×C4C22×D311yescharacteristic
286#638—22no—
287C2×C3⋊Dic3—22no—
288C2×C3⋊Dic3C22×D311yescharacteristic
289C2×C3⋊Dic3C22×D311yescharacteristic
290C2×C3⋊Dic3C22×D311yescharacteristic
291C2×C3⋊Dic3C22×D311yescharacteristic
292C2×C3⋊Dic3C22×D311yescharacteristic
293C4×C3⋊D3—41no—
294C3×#67—62no—
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—31no—
305C2×C3×Dic3—31no—
306C2×C3×Dic3—31no—
307C2×C3×Dic3—31no—
308C2×C3×Dic3—61no—
309C2×C3×Dic3—61no—
310C2×C3×Dic3—61no—
311C2×C3×Dic3—61no—
312C2×C3×Dic3—62no—
313C3×C4×D3—121no—
314C3×Dic6—121no—
315C3×Dic6—121no—
316C3×Dic6—122no—
317#626—62no—
318#626—62no—
319#626—121no—
320#626—121no—
321#624—62no—
322#624—121no—
323D3×Dic3—62no—
324D3×Dic3—121no—
325#551—271noSylow
326C2×H(3,𝔽3)—22no—
327C2×H(3,𝔽3)C2×#4111yescharacteristic
328C2×H(3,𝔽3)C2×#4111yescharacteristic
329C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
330(C3⋊D3)⋊C3—22no—
331(C3⋊D3)⋊C3—41no—
332(C3⋊D3)⋊C3—41no—
333C24×C3—91no—
334C23×D3—31no—
335C23×D3—91no—
336C2×C3×Q8—91no—
337C2×C3×D4—91no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—61no—
341C22×C3×C4—91no—
342C22×C3×C4—91no—
343C22×C3×C4D3211yescharacteristic
344C2×#67—31no—
345C2×#67—91no—
346C2×#67—91no—
347C2×#67—91no—
348C2×#67—91no—
349C2×#67—91no—
350C22×Dic3—31no—
351C22×Dic3—91no—
352C22×Dic3—91no—
353C22×Dic3—91no—
354C2×D12—91no—
355C2×D12—91no—
356C2×C4×D3—31no—
357C2×C4×D3—91no—
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×Dic6—31no—
363C2×Dic6—31no—
364C2×Dic6—61no—
365C3×C4⋊C4—91no—
366C3×C4⋊C4—91no—
367C3×C4⋊C4—91no—
368C3×C4⋊C4—91no—
369C3×C22⋊C4—91no—
370C3×C22⋊C4—91no—
371C3×C22⋊C4—91no—
372C3×C22⋊C4—91no—
373C3×C22⋊C4—91no—
374C3×C22⋊C4—91no—
375C3×C22⋊C4—91no—
376C3×C22⋊C4—91no—
377C3×C42—91no—
378#217—31no—
379#217—31no—
380#217—31no—
381#217—31no—
382#217—31no—
383#217—61no—
384#217—61no—
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—91no—
398(C2×D3)⋊C4—91no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
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—
414C4⋊Dic3—31no—
415C4⋊Dic3—31no—
416C4⋊Dic3—61no—
417C4⋊Dic3—91no—
418C4⋊Dic3—91no—
419C4⋊Dic3—91no—
420C4⋊Dic3—91no—
421Dic3⋊C4—31no—
422Dic3⋊C4—31no—
423Dic3⋊C4—31no—
424Dic3⋊C4—31no—
425Dic3⋊C4—31no—
426Dic3⋊C4—61no—
427Dic3⋊C4—61no—
428Dic3⋊C4—91no—
429Dic3⋊C4—91no—
430Dic3⋊C4—91no—
431Dic3⋊C4—91no—
432Dic3⋊C4—91no—
433Dic3⋊C4—91no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437C4×Dic3—31no—
438C4×Dic3—91no—
439C4×Dic3—91no—
440C4×Dic3—91no—
441C4×Dic3—91no—
442C4×Dic3—91no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—22no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32#23512yes—
454C22×C32#23712yes—
455C22×C32C23×D311yescharacteristic
456C22×C32C23×D311yescharacteristic
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—21no—
465C2×C3⋊D3—44no—
466C2×C3⋊D3#23512yes—
467C2×C3×D3—32no—
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—61no—
476C2×C3×D3—124no—
477C32×C4—22no—
478C32×C4—21no—
479C32×C4—21no—
480C32×C4—21no—
481C32×C4—21no—
482C32×C4—41no—
483C3⋊Dic3—21no—
484C3⋊Dic3—21no—
485C3⋊Dic3—21no—
486C3⋊Dic3—21no—
487C3⋊Dic3—21no—
488C3×Dic3—61no—
489C3×Dic3—61no—
490C3×Dic3—61no—
491C3×Dic3—61no—
492C3×Dic3—61no—
493C3×Dic3—61no—
494C3×Dic3—61no—
495C3×Dic3—61no—
496C3×Dic3—61no—
497C3×Dic3—61no—
498C3×Dic3—61no—
499C3×Dic3—61no—
500C3×Dic3—61no—
501C3×Dic3—121no—
502C3×Dic3—121no—
503C3×Dic3—121no—
504C3×Dic3—121no—
505#126—271no—
506#126—271no—
507#124—271no—
508#123—271no—
509#123—271no—
510#123—271no—
511C22⋊Q8—91no—
512C22⋊Q8—271no—
513#120—271no—
514C4×D4—91no—
515C4×D4—271no—
516#117—271no—
517#117—271no—
518C2×C22⋊C4—91no—
519C2×C22⋊C4—271no—
520H(3,𝔽3)#55111yescharacteristic, complemented, Sylow
521C23×C3—31no—
522C23×C3—31no—
523C23×C3—61no—
524C23×C3—91no—
525C23×C3—91no—
526C23×C3—91no—
527C23×C3—182no—
528C23×C3—182no—
529C23×C3—361no—
530C23×C3C2×D3211yescharacteristic
531C22×D3—31no—
532C22×D3—31no—
533C22×D3—31no—
534C22×D3—62no—
535C22×D3—62no—
536C22×D3—91no—
537C22×D3—91no—
538C22×D3—91no—
539C22×D3—121no—
540C22×D3—182no—
541C22×D3—182no—
542C22×D3—361no—
543C3×Q8—361no—
544C3×D4—182no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—41no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
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—91no—
560C2×C3×C4—91no—
561C2×C3×C4—121no—
562C2×C3×C4—121no—
563C2×C3×C4—122no—
564C2×C3×C4—182no—
565C2×C3×C4—361no—
566C2×C3×C4C2×D3211yescharacteristic
567C2×C3×C4C2×D3211yescharacteristic
568#67—62no—
569#67—182no—
570#67—182no—
571#67—182no—
572#67—361no—
573#67—361no—
574C2×Dic3—31no—
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—31no—
586C2×Dic3—31no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—62no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—91no—
596C2×Dic3—91no—
597C2×Dic3—182no—
598C2×Dic3—182no—
599C2×Dic3—361no—
600D12—182no—
601D12—361no—
602C4×D3—121no—
603C4×D3—182no—
604C4×D3—182no—
605C4×D3—361no—
606C4×D3—361no—
607C4×D3—361no—
608Dic6—121no—
609Dic6—121no—
610Dic6—122no—
611C2×C32—22no—
612C2×C32—22no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—42no—
617C2×C32C2×#23511yescharacteristic
618C2×C32C2×#23511yescharacteristic
619C2×C32C2×#23711yescharacteristic
620C2×C32#100411yescharacteristic
621C2×C32#100411yescharacteristic
622C2×C32D3×#4111yescharacteristic
623C3⋊D3—22no—
624C3⋊D3—41no—
625C3⋊D3—41no—
626C3×D3—62no—
627C3×D3—121no—
628C3×D3—121no—
629C24—91no—
630C2×Q8—91no—
631C2×D4—91no—
632C2×D4—271no—
633C2×D4—271no—
634C22×C4—91no—
635C22×C4—91no—
636C22×C4—271no—
637C22×C4—271no—
638C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
639C4⋊C4—91no—
640C4⋊C4—91no—
641C4⋊C4—91no—
642C4⋊C4—91no—
643C4⋊C4—271no—
644C4⋊C4—271no—
645C4⋊C4—271no—
646C4⋊C4—271no—
647C22⋊C4—91no—
648C22⋊C4—91no—
649C22⋊C4—91no—
650C22⋊C4—91no—
651C22⋊C4—91no—
652C22⋊C4—91no—
653C22⋊C4—91no—
654C22⋊C4—91no—
655C22⋊C4—271no—
656C22⋊C4—271no—
657C22⋊C4—271no—
658C22⋊C4—271no—
659C22⋊C4—271no—
660C22⋊C4—271no—
661C42—91no—
662C42—271no—
663C42—271no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—31no—
667C22×C3—31no—
668C22×C3—32no—
669C22×C3—32no—
670C22×C3—61no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—62no—
676C22×C3—92no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—181no—
680C22×C3—181no—
681C22×C3—181no—
682C22×C3—181no—
683C22×C3—181no—
684C22×C3—181no—
685C22×C3—181no—
686C22×C3—181no—
687C22×C3—364no—
688C22×C3#379512yes—
689C22×C3C22×D3211yescharacteristic
690C2×D3—32no—
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—92no—
700C2×D3—124no—
701C2×D3—181no—
702C2×D3—181no—
703C2×D3—181no—
704C2×D3—181no—
705C2×D3—181no—
706C2×D3—181no—
707C2×D3—181no—
708C2×D3—181no—
709C2×D3—364no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—61no—
715C3×C4—61no—
716C3×C4—62no—
717C3×C4—121no—
718C3×C4—181no—
719C3×C4—181no—
720C3×C4—181no—
721C3×C4—181no—
722C3×C4—181no—
723C3×C4—181no—
724C3×C4—181no—
725C3×C4—181no—
726C3×C4—181no—
727Dic3—61no—
728Dic3—61no—
729Dic3—61no—
730Dic3—61no—
731Dic3—61no—
732Dic3—61no—
733Dic3—61no—
734Dic3—61no—
735Dic3—61no—
736Dic3—61no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—121no—
741Dic3—121no—
742Dic3—121no—
743Dic3—121no—
744Dic3—181no—
745Dic3—181no—
746Dic3—181no—
747Dic3—181no—
748Dic3—181no—
749C32—21no—
750C32#549511yescharacteristic, complemented
751C32#555611yescharacteristic, complemented
752C23—91no—
753C23—91no—
754C23—91no—
755C23—182no—
756C23—182no—
757C23—361no—
758C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
759Q8—361no—
760D4—182no—
761D4—542no—
762D4—1081no—
763C2×C4—41no—
764C2×C4—91no—
765C2×C4—91no—
766C2×C4—91no—
767C2×C4—91no—
768C2×C4—91no—
769C2×C4—91no—
770C2×C4—91no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—182no—
774C2×C4—361no—
775C2×C4—542no—
776C2×C4—1081no—
777C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
778C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
779C2×C3—22no—
780C2×C3—31no—
781C2×C3—31no—
782C2×C3—31no—
783C2×C3—31no—
784C2×C3—31no—
785C2×C3—31no—
786C2×C3—62no—
787C2×C3—62no—
788C2×C3—61no—
789C2×C3—61no—
790C2×C3—61no—
791C2×C3—122no—
792C2×C3—182no—
793C2×C3—361no—
794C2×C3—361no—
795C2×C3C2×#379511yescharacteristic
796C2×C3D3×#23511yescharacteristic
797C2×C3#6433011yescharacteristic
798D3—62no—
799D3—121no—
800D3—121no—
801D3—182no—
802D3—361no—
803D3—361no—
804C22—21no—
805C22—21no—
806C22—92no—
807C22—181no—
808C22—181no—
809C22—181no—
810C22—181no—
811C22—181no—
812C22—181no—
813C22—181no—
814C22—181no—
815C22—364no—
816C22#8864812yes—
817C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
818C4—21no—
819C4—21no—
820C4—181no—
821C4—181no—
822C4—181no—
823C4—181no—
824C4—181no—
825C4—181no—
826C4—181no—
827C4—181no—
828C4—181no—
829C3—31no—
830C3—31no—
831C3—61no—
832C3#1059493811yescharacteristic
833C2—22no—
834C2—182no—
835C2—361no—
836C2—361no—
837C2C2×#8864811yescharacteristic
838C2#1172249011yescharacteristic
839C2#1172254511yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC22×C4×H(3,𝔽3)C22
prime radical#11721316C2
hypercenterC22×C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#551
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. #11721824C2semidirect
2. C4×#638⋊C3C2semidirect
3. C2×#3752⋊C3C2semidirect
5. #11721310C2semidirect
6. #11721306C2semidirect
7. #11721296C2semidirect
8. #11721143C2semidirect
9. #11721139C2semidirect
10. #11721135C2semidirect
11. #11721131C2semidirect
12. #11721122C2semidirect
13. #11721120C2semidirect
14. #11721111C2semidirect
15. #11721109C2semidirect
20. C2×#6229C22semidirect
23. C2×C4×(C3⋊D3)⋊C3C22semidirect
30. C4⋊#1084C22semidirect
31. #88540C22semidirect
32. #88540C22semidirect
38. #3752⋊C3C22semidirect
39. #3750⋊C3C22semidirect
40. C4×(C3⋊Dic3)⋊C3C22semidirect
45. #88450C22semidirect
46. #88450C22semidirect
47. #88449C22semidirect
48. #88449C22semidirect
49. #88448C22semidirect
50. #88448C22semidirect
51. #88447C22semidirect
52. #88447C22semidirect
53. C4×#638D3semidirect
54. C2×#3752D3semidirect
121. C2×C4×C3⋊D3C2×D3semidirect
141. #3752C2×D3semidirect
142. #3750C2×D3semidirect
143. C4×C3⋊Dic3C2×D3semidirect
520. H(3,𝔽3)#551semidirect
750. C32#5495semidirect
751. C32#5556semidirect

Maximal subgroups

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

subgroupindex
#117218242
C4×#638⋊C32
C2×#3752⋊C32
#117213162
#117213102
#117213062
#117212962
#117211432
#117211392
#117211352
#117211312
#117211222
#117211202
#117211112
#117211092
#105950353
#105949413