Finite Group Databasebeta

← #13148515

Subgroups — #13148515

Order 1728.

944 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721733C211yesmaximal, characteristic, complemented
2#64091⋊C3C211yesmaximal, characteristic
3#64087⋊C3C211yesmaximal, characteristic, complemented
4#11721314C211yesmaximal, characteristic, complemented
5#11721310C211yesmaximal, characteristic, complemented
6#11721307C211yesmaximal, characteristic, complemented
7C2×#88450C211yesmaximal, characteristic, complemented
8#11721136C211yesmaximal, characteristic, complemented
9#11721128C211yesmaximal, characteristic, complemented
10#11721125C211yesmaximal, characteristic, complemented
11#11721125C211yesmaximal, characteristic, complemented
12#11721121C211yesmaximal, characteristic, complemented
13#11721113C211yesmaximal, characteristic, complemented
14#11721112C211yesmaximal, characteristic, complemented
15#11721108C211yesmaximal, characteristic, complemented
16#10594166—31nomaximal
17#10594117—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C22×#1084C2211yescharacteristic
20C2×#638⋊C3C2211yescharacteristic
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
22C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
23C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
24C2×#634⋊C3C2211yescharacteristic, complemented
25C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
26C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
27C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
28C22⋊C4×H(3,𝔽3)C2211yescharacteristic
29#88552C2211yescharacteristic
30#88540C2211yescharacteristic, complemented
31#88540C2211yescharacteristic, complemented
32C4×#1084C2211yescharacteristic, complemented
33C4×#1084C2211yescharacteristic, complemented
34#3757⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
38#3750⋊C3C2211yescharacteristic, complemented
39#3750⋊C3C2211yescharacteristic, complemented
40#88450C2211yescharacteristic
41#88450C2211yescharacteristic
42#88450C2211yescharacteristic
43#88450C2211yescharacteristic
44#88450C2211yescharacteristic
45#88450C2211yescharacteristic
46#88450C2211yescharacteristic, complemented
47#88450C2211yescharacteristic, complemented
48#88450C2211yescharacteristic, complemented
49#88448C2211yescharacteristic, complemented
50#88448C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53#64091D311yescharacteristic
54#64087D311yescharacteristic, complemented
55C3×#882—31no—
56C3×#878—31no—
57C3×#877—31no—
58C3×#877—31no—
59C3×#877—61no—
60#63974—31no—
61#67⋊Dic3—31no—
62D3×#217—31no—
63#63966—31no—
64C2×#3722—31no—
65#63961—31no—
66C2×(C2×D3)⋊Dic3—31no—
67#63952—31no—
68#63897—31no—
69#63897—31no—
70#63896—31no—
71#63894—31no—
72Dic3×D12—31no—
73#63888—31no—
74#63884—31no—
75#63884—31no—
76#63877—31no—
77#63868—31no—
78#63864—31no—
79#63861—31no—
80#63860—31no—
81#63859—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)C2311yescharacteristic
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×#1084—22no—
94C2×#1084C2311yescharacteristic
95C2×#1084C2311yescharacteristic
96C2×#1084C2311yescharacteristic
97C2×#1084C2311yescharacteristic
98#638⋊C3—22no—
99C2×(C3⋊Dic3)⋊C3—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)—22no—
106C4⋊((C3⋊D3)⋊C3)—41no—
107#634⋊C3—41no—
108((C3⋊D3)⋊C3)⋊C4—22no—
109((C3⋊D3)⋊C3)⋊C4—41no—
110((C3⋊D3)⋊C3)⋊C4—41no—
111#5637—91no—
112#5587—91no—
113#5527—91no—
114C23×C3⋊D3C2×D311yescharacteristic
115C23×C3×D3—31no—
116C2×#638C2×D311yescharacteristic
117C22×C3⋊Dic3C2×D311yescharacteristic
118C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
119C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
120C2×#634C2×D311yescharacteristic, complemented
121C2×C3×#67—31no—
122C22×C3×Dic3—31no—
123C22×C3×Dic3—31no—
124C22×C3×Dic3—31no—
125C22×C3×Dic3—61no—
126C2×C3×D12—31no—
127C2×C3×D12—31no—
128C2×C3×Dic6—31no—
129C2×#624—31no—
130C2×#624—31no—
131C2×#624—31no—
132C2×D3×Dic3—31no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135C32×C22⋊C4—21no—
136C32×C22⋊C4C2×D311yescharacteristic
137C32×C22⋊C4C2×D311yescharacteristic
138#3757C2×D311yescharacteristic
139#3752C2×D311yescharacteristic
140#3752C2×D311yescharacteristic
141C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
142#3750C2×D311yescharacteristic, complemented
143#3750C2×D311yescharacteristic, complemented
144C3×#217—31no—
145C3×#217—31no—
146C3×#217—31no—
147C3×#217—61no—
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4—31no—
150C3×C4⋊Dic3—31no—
151C3×Dic3⋊C4—31no—
152C3×Dic3⋊C4—31no—
153C3×Dic3⋊C4—31no—
154C3×Dic3⋊C4—31no—
155C3×Dic3⋊C4—31no—
156C3×Dic3⋊C4—31no—
157C3×Dic3⋊C4—61no—
158C3×Dic3⋊C4—61no—
159C3×C4×Dic3—31no—
160C3×C4×Dic3—31no—
161C3×C4×Dic3—31no—
162C3×C4×Dic3—31no—
163C3×C4×Dic3—61no—
164C3×C4×Dic3—61no—
165#3724—31no—
166#3724—31no—
167#3724—31no—
168Dic3⋊Dic3—31no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—31no—
171#3722—31no—
172#3722—31no—
173#3722—31no—
174#3722—31no—
175#3722—31no—
176#3722—31no—
177#3722—31no—
178#3722—31no—
179#3722—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)—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×#120—91no—
218C3×#117—91no—
219C2×#217—91no—
220C2×#217—91no—
221#947—91no—
222#946—91no—
223#936—91no—
224#935—91no—
225#935—91no—
226#935—91no—
227D4×Dic3—91no—
228D4×Dic3—91no—
229#929—91no—
230C4×#67—91no—
231C2×(C2×D3)⋊C4—91no—
232C2×(C2×D3)⋊C4—91no—
233#898—91no—
234#898—91no—
235#898—91no—
236#896—91no—
237#894—91no—
238#894—91no—
239#894—91no—
240#894—91no—
241#893—91no—
242#892—91no—
243#886—91no—
244#882—31no—
245#882—91no—
246#67⋊C4—91no—
247D3×C22⋊C4—91no—
248D3×C22⋊C4—91no—
249#879—91no—
250#879—91no—
251#878—31no—
252#878—91no—
253#878—91no—
254#877—31no—
255#877—31no—
256#877—61no—
257#877—91no—
258#876—91no—
259#875—91no—
260C4×D12—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×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283#638—22no—
284C2×C3⋊Dic3—41no—
285C2×C3⋊Dic3C22×D311yescharacteristic
286C2×C3⋊Dic3C22×D311yescharacteristic
287C2×C3⋊Dic3C22×D311yescharacteristic
288C2×C3⋊Dic3C22×D311yescharacteristic
289C2×C3⋊Dic3C22×D311yescharacteristic
290C4⋊(C3⋊D3)—22no—
291C4⋊(C3⋊D3)—41no—
292#634—41no—
293C3×#67—62no—
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—31no—
305C2×C3×Dic3—31no—
306C2×C3×Dic3—31no—
307C2×C3×Dic3—61no—
308C2×C3×Dic3—61no—
309C2×C3×Dic3—61no—
310C2×C3×Dic3—61no—
311C2×C3×Dic3—64no—
312C2×C3×Dic3—62no—
313C2×C3×Dic3—62no—
314C2×C3×Dic3—121no—
315C3×D12—62no—
316C3×D12—121no—
317C3×Dic6—121no—
318#624—62no—
319#624—121no—
320#624—121no—
321D3×Dic3—62no—
322D3×Dic3—121no—
323D3×Dic3—121no—
324#551—271noSylow
325C2×H(3,𝔽3)—22no—
326C2×H(3,𝔽3)C2×#4111yescharacteristic
327C2×H(3,𝔽3)C2×#4111yescharacteristic
328C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
329(C3⋊D3)⋊C3—22no—
330(C3⋊D3)⋊C3—41no—
331(C3⋊D3)⋊C3—41no—
332C24×C3—91no—
333C23×D3—31no—
334C23×D3—91no—
335C2×C3×Q8—91no—
336C2×C3×D4—91no—
337C2×C3×D4—91no—
338C2×C3×D4—91no—
339C22×C3×C4—91no—
340C22×C3×C4—91no—
341C2×#67—31no—
342C2×#67—91no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—61no—
347C22×Dic3—91no—
348C22×Dic3—91no—
349C22×Dic3—91no—
350C22×Dic3—91no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—91no—
354C2×D12—91no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×C4×D3—91no—
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×Dic6—31no—
362C2×Dic6—91no—
363C3×C4⋊C4—91no—
364C3×C4⋊C4—91no—
365C3×C4⋊C4—91no—
366C3×C4⋊C4—91no—
367C3×C4⋊C4—91no—
368C3×C22⋊C4—31no—
369C3×C22⋊C4—31no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—91no—
372C3×C22⋊C4—91no—
373C3×C22⋊C4—91no—
374C3×C22⋊C4—91no—
375C3×C22⋊C4D3211yescharacteristic
376C3×C42—91no—
377C3×C42—91no—
378#217—31no—
379#217—31no—
380#217—31no—
381#217—61no—
382#217—91no—
383#217—91no—
384#217—91no—
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—91no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—91no—
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—91no—
416C4⋊Dic3—91no—
417C4⋊Dic3—91no—
418C4⋊Dic3—91no—
419Dic3⋊C4—31no—
420Dic3⋊C4—31no—
421Dic3⋊C4—31no—
422Dic3⋊C4—31no—
423Dic3⋊C4—31no—
424Dic3⋊C4—31no—
425Dic3⋊C4—61no—
426Dic3⋊C4—61no—
427Dic3⋊C4—91no—
428Dic3⋊C4—91no—
429Dic3⋊C4—91no—
430Dic3⋊C4—91no—
431Dic3⋊C4—91no—
432Dic3⋊C4—91no—
433Dic3⋊C4—91no—
434Dic3⋊C4—91no—
435C4×Dic3—31no—
436C4×Dic3—31no—
437C4×Dic3—31no—
438C4×Dic3—31no—
439C4×Dic3—61no—
440C4×Dic3—61no—
441C4×Dic3—91no—
442C4×Dic3—91no—
443C4×Dic3—91no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—22no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32#23712yes—
453C22×C32#23912yes—
454C22×C32C23×D311yescharacteristic
455C22×C32C23×D311yescharacteristic
456C2×C3⋊D3—21no—
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—44no—
465C2×C3⋊D3#23712yes—
466C2×C3×D3—32no—
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—124no—
476C32×C4—21no—
477C32×C4—21no—
478C32×C4—21no—
479C32×C4—21no—
480C32×C4—41no—
481C32×C4—41no—
482C3⋊Dic3—21no—
483C3⋊Dic3—21no—
484C3⋊Dic3—21no—
485C3⋊Dic3—21no—
486C3⋊Dic3—21no—
487C3×Dic3—62no—
488C3×Dic3—62no—
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—61no—
502C3×Dic3—121no—
503C3×Dic3—121no—
504#126—271no—
505#126—271no—
506#124—271no—
507#123—271no—
508#123—271no—
509#123—271no—
510C22⋊Q8—91no—
511C22⋊Q8—271no—
512#120—91no—
513C4×D4—271no—
514C4×D4—271no—
515#117—91no—
516#117—271no—
517C2×C22⋊C4—271no—
518C2×C22⋊C4—271no—
519H(3,𝔽3)#55111yescharacteristic, complemented, Sylow
520C23×C3—31no—
521C23×C3—31no—
522C23×C3—61no—
523C23×C3—91no—
524C23×C3—91no—
525C23×C3—91no—
526C23×C3—182no—
527C23×C3—182no—
528C23×C3—361no—
529C23×C3C2×D3211yescharacteristic
530C22×D3—31no—
531C22×D3—31no—
532C22×D3—31no—
533C22×D3—62no—
534C22×D3—62no—
535C22×D3—91no—
536C22×D3—91no—
537C22×D3—91no—
538C22×D3—121no—
539C22×D3—182no—
540C22×D3—182no—
541C22×D3—361no—
542C3×Q8—361no—
543C3×D4—182no—
544C3×D4—182no—
545C3×D4—361no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—31no—
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—182no—
562C2×C3×C4—361no—
563C2×C3×C4C2×D3211yescharacteristic
564C2×C3×C4C2×D3211yescharacteristic
565#67—62no—
566#67—182no—
567C2×Dic3—31no—
568C2×Dic3—31no—
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—31no—
579C2×Dic3—31no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—62no—
585C2×Dic3—62no—
586C2×Dic3—64no—
587C2×Dic3—91no—
588C2×Dic3—91no—
589C2×Dic3—91no—
590C2×Dic3—91no—
591C2×Dic3—91no—
592C2×Dic3—121no—
593C2×Dic3—182no—
594C2×Dic3—361no—
595C2×Dic3—361no—
596C2×Dic3—361no—
597D12—62no—
598D12—121no—
599D12—182no—
600D12—361no—
601C4×D3—182no—
602C4×D3—182no—
603C4×D3—361no—
604C4×D3—361no—
605C4×D3—361no—
606C4×D3—361no—
607Dic6—121no—
608Dic6—361no—
609C2×C32—22no—
610C2×C32—22no—
611C2×C32—21no—
612C2×C32—21no—
613C2×C32—21no—
614C2×C32—42no—
615C2×C32C2×#23711yescharacteristic
616C2×C32C2×#23711yescharacteristic
617C2×C32#100411yescharacteristic
618C2×C32#100411yescharacteristic
619C2×C32C2×#23911yescharacteristic
620C2×C32D3×#4111yescharacteristic
621C3⋊D3—22no—
622C3⋊D3—41no—
623C3⋊D3—41no—
624C3×D3—62no—
625C3×D3—121no—
626C3×D3—121no—
627C24—91no—
628C2×Q8—91no—
629C2×D4—91no—
630C2×D4—91no—
631C2×D4—91no—
632C22×C4—91no—
633C22×C4—91no—
634C22×C4—271no—
635C22×C4—271no—
636C22×C4—271no—
637C4⋊C4—91no—
638C4⋊C4—91no—
639C4⋊C4—91no—
640C4⋊C4—91no—
641C4⋊C4—91no—
642C4⋊C4—271no—
643C4⋊C4—271no—
644C4⋊C4—271no—
645C22⋊C4—91no—
646C22⋊C4—91no—
647C22⋊C4—91no—
648C22⋊C4—91no—
649C22⋊C4—271no—
650C22⋊C4—271no—
651C22⋊C4—271no—
652C22⋊C4—271no—
653C22⋊C4—271no—
654C22⋊C4—271no—
655C22⋊C4—271no—
656C22⋊C4—271no—
657C22⋊C4—271no—
658C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
659C42—91no—
660C42—91no—
661C42—271no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—31no—
665C22×C3—31no—
666C22×C3—32no—
667C22×C3—32no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3—62no—
674C22×C3—92no—
675C22×C3—121no—
676C22×C3—121no—
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—364no—
686C22×C3#379612yes—
687C22×C3C22×D3211yescharacteristic
688C2×D3—32no—
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—92no—
698C2×D3—124no—
699C2×D3—181no—
700C2×D3—181no—
701C2×D3—181no—
702C2×D3—181no—
703C2×D3—181no—
704C2×D3—181no—
705C2×D3—181no—
706C2×D3—181no—
707C2×D3—364no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—61no—
711C3×C4—61no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—121no—
715C3×C4—121no—
716C3×C4—181no—
717C3×C4—181no—
718C3×C4—181no—
719C3×C4—181no—
720C3×C4—181no—
721C3×C4—181no—
722C3×C4—181no—
723C3×C4—181no—
724C3×C4—181no—
725Dic3—61no—
726Dic3—61no—
727Dic3—61no—
728Dic3—61no—
729Dic3—61no—
730Dic3—61no—
731Dic3—61no—
732Dic3—61no—
733Dic3—62no—
734Dic3—62no—
735Dic3—61no—
736Dic3—61no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—121no—
741Dic3—121no—
742Dic3—181no—
743Dic3—181no—
744Dic3—181no—
745Dic3—181no—
746Dic3—181no—
747C32—21no—
748C32#558711yescharacteristic, complemented
749C32#563711yescharacteristic, complemented
750C23—91no—
751C23—91no—
752C23—91no—
753C23—182no—
754C23—182no—
755C23—361no—
756C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
757Q8—361no—
758D4—182no—
759D4—182no—
760D4—361no—
761C2×C4—91no—
762C2×C4—91no—
763C2×C4—91no—
764C2×C4—91no—
765C2×C4—91no—
766C2×C4—91no—
767C2×C4—91no—
768C2×C4—91no—
769C2×C4—91no—
770C2×C4—182no—
771C2×C4—361no—
772C2×C4—542no—
773C2×C4—1081no—
774C2×C4—1081no—
775C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
776C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
777C2×C3—22no—
778C2×C3—31no—
779C2×C3—31no—
780C2×C3—31no—
781C2×C3—31no—
782C2×C3—31no—
783C2×C3—31no—
784C2×C3—62no—
785C2×C3—62no—
786C2×C3—61no—
787C2×C3—61no—
788C2×C3—61no—
789C2×C3—122no—
790C2×C3—182no—
791C2×C3—361no—
792C2×C3—361no—
793C2×C3C2×#379611yescharacteristic
794C2×C3D3×#23711yescharacteristic
795C2×C3#6431311yescharacteristic
796D3—62no—
797D3—121no—
798D3—121no—
799D3—182no—
800D3—361no—
801D3—361no—
802C22—21no—
803C22—21no—
804C22—92no—
805C22—181no—
806C22—181no—
807C22—181no—
808C22—181no—
809C22—181no—
810C22—181no—
811C22—181no—
812C22—181no—
813C22—364no—
814C22#8864912yes—
815C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
816C4—21no—
817C4—21no—
818C4—181no—
819C4—181no—
820C4—181no—
821C4—181no—
822C4—181no—
823C4—181no—
824C4—181no—
825C4—181no—
826C4—181no—
827C3—31no—
828C3—31no—
829C3—61no—
830C3#1059411911yescharacteristic
831C2—22no—
832C2—182no—
833C2—361no—
834C2—361no—
835C2C2×#8864911yescharacteristic
836C2#1172250411yescharacteristic
837C2#1172250611yescharacteristic
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#64091⋊C3C2
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. #11721733C2semidirect
3. #64087⋊C3C2semidirect
4. #11721314C2semidirect
5. #11721310C2semidirect
6. #11721307C2semidirect
7. C2×#88450C2semidirect
8. #11721136C2semidirect
9. #11721128C2semidirect
10. #11721125C2semidirect
11. #11721125C2semidirect
12. #11721121C2semidirect
13. #11721113C2semidirect
14. #11721112C2semidirect
15. #11721108C2semidirect
24. C2×#634⋊C3C22semidirect
27. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
30. #88540C22semidirect
31. #88540C22semidirect
32. C4×#1084C22semidirect
33. C4×#1084C22semidirect
37. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
38. #3750⋊C3C22semidirect
39. #3750⋊C3C22semidirect
46. #88450C22semidirect
47. #88450C22semidirect
48. #88450C22semidirect
49. #88448C22semidirect
50. #88448C22semidirect
51. #88448C22semidirect
52. #88447C22semidirect
54. #64087D3semidirect
120. C2×#634C2×D3semidirect
141. C4⋊(C3⋊Dic3)C2×D3semidirect
142. #3750C2×D3semidirect
143. #3750C2×D3semidirect
519. H(3,𝔽3)#551semidirect
748. C32#5587semidirect
749. C32#5637semidirect

Maximal subgroups

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

subgroupindex
#117217332
#64091⋊C32
#64087⋊C32
#117213142
#117213102
#117213072
C2×#884502
#117211362
#117211282
#117211252
#117211212
#117211132
#117211122
#117211082
#105941663
#105941173