Finite Group Databasebeta

← #13149587

Subgroups — #13149587

Order 1728.

827 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721762C211yesmaximal, characteristic
2#64098⋊C3C211yesmaximal, characteristic, complemented
3#64096⋊C3C211yesmaximal, characteristic, complemented
4#11721151C211yesmaximal, characteristic
5#11721149C211yesmaximal, characteristic
6#11721148C211yesmaximal, characteristic, complemented
7#11721148C211yesmaximal, characteristic, complemented
8#11721147C211yesmaximal, characteristic, complemented
9#11721097C211yesmaximal, characteristic, complemented
10#11721092C211yesmaximal, characteristic, complemented
11#11721092C211yesmaximal, characteristic, complemented
12#11721091C211yesmaximal, characteristic, complemented
13#11721086C211yesmaximal, characteristic, complemented
14#11721076C211yesmaximal, characteristic, complemented
15#11721076C211yesmaximal, characteristic, complemented
16#10594430—31nomaximal
17#10594420—31nomaximal
18C2×C4⋊#272C2211yescharacteristic
19C2×C4×#272C2211yescharacteristic
20C2×#634⋊C3C2211yescharacteristic
21C2×#6199C2211yescharacteristic
22C2×#6199C2211yescharacteristic
23C2×#6199C2211yescharacteristic
24C4⋊C4×H(3,𝔽3)C2211yescharacteristic
25#88542C2211yescharacteristic
26#88542C2211yescharacteristic
27#88542C2211yescharacteristic
28#88540C2211yescharacteristic
29C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
30#3750⋊C3C2211yescharacteristic
31#3750⋊C3C2211yescharacteristic
32#3750⋊C3C2211yescharacteristic
33#3750⋊C3C2211yescharacteristic
34#3750⋊C3C2211yescharacteristic
35#3750⋊C3C2211yescharacteristic
36C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
37C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
38C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
39C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
40#88451C2211yescharacteristic
41#88451C2211yescharacteristic
42#88451C2211yescharacteristic
43#88451C2211yescharacteristic
44#88451C2211yescharacteristic
45#88449C2211yescharacteristic
46#88449C2211yescharacteristic
47#88449C2211yescharacteristic
48#88448C2211yescharacteristic
49#88448C2211yescharacteristic
50#88448C2211yescharacteristic
51#88448C2211yescharacteristic
52#88447C2211yescharacteristic
53#64098D311yescharacteristic, complemented
54#64096D311yescharacteristic, complemented
55C3×#894—31no—
56C3×#894—31no—
57C3×#894—61no—
58C3×#889—31no—
59C3×#887—31no—
60#63898—31no—
61#63896—31no—
62#63896—31no—
63Dic3×D12—31no—
64#63887—31no—
65#63887—31no—
66#63884—31no—
67#63884—31no—
68#63878—31no—
69#63878—31no—
70#63877—31no—
71#63877—31no—
72D3×Dic3⋊C4—31no—
73D3×Dic3⋊C4—31no—
74#63870—31no—
75#63867—31no—
76#63862—31no—
77#63862—31no—
78#63859—31no—
79#63859—31no—
80#63855—31no—
81#63855—31no—
82#63846—31no—
83#63845—31no—
84C22×#272C2311yescharacteristic
85C22×#272C2311yescharacteristic
86C2×C4×H(3,𝔽3)C2311yescharacteristic
87C2×C4×H(3,𝔽3)C2311yescharacteristic
88C2×C4×H(3,𝔽3)C2311yescharacteristic
89C2×#1084C2311yescharacteristic
90C2×#1084C2311yescharacteristic
91C4⋊#272—22no—
92C4×#272—22no—
93C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
94C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
95C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
96C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
97C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101#634⋊C3—22no—
102#6199—22no—
103#6199—22no—
104#6199—22no—
105#5693—91no—
106#5650—91no—
107#5581—91no—
108C2×#634C2×D311yescharacteristic
109C2×C3×D12—31no—
110C2×C3×D12—31no—
111C2×C3×D12—61no—
112C2×C3×C4×D3—31no—
113C2×C3×C4×D3—31no—
114C2×C3×C4×D3—61no—
115C2×C3×Dic6—31no—
116C2×D3×Dic3—31no—
117C2×D3×Dic3—31no—
118C2×D3×Dic3—31no—
119C2×D3×Dic3—31no—
120C2×D3×Dic3—31no—
121C2×D3×Dic3—31no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4C2×D311yescharacteristic
124C32×C4⋊C4C2×D311yescharacteristic
125C4⋊(C3⋊Dic3)C2×D311yescharacteristic
126#3750C2×D311yescharacteristic
127#3750C2×D311yescharacteristic
128#3750C2×D311yescharacteristic
129#3750C2×D311yescharacteristic
130#3750C2×D311yescharacteristic
131#3750C2×D311yescharacteristic
132C4×C3⋊Dic3C2×D311yescharacteristic
133C4×C3⋊Dic3C2×D311yescharacteristic
134C4×C3⋊Dic3C2×D311yescharacteristic
135C4×C3⋊Dic3C2×D311yescharacteristic
136C3×(C2×D3)⋊C4—31no—
137C3×(C2×D3)⋊C4—31no—
138C3×(C2×D3)⋊C4—31no—
139C3×(C2×D3)⋊C4—31no—
140C3×(C2×D3)⋊C4—31no—
141C3×(C2×D3)⋊C4—31no—
142C3×(C2×D3)⋊C4—61no—
143C3×(C2×D3)⋊C4—61no—
144C3×(C2×D3)⋊C4—61no—
145C3×C4⋊Dic3—31no—
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—61no—
155C3×C4×Dic3—31no—
156C3×C4×Dic3—31no—
157C3×C4×Dic3—31no—
158C3×C4×Dic3—31no—
159#3724—31no—
160#3724—31no—
161#3724—31no—
162#3724—31no—
163Dic3⋊Dic3—31no—
164Dic3⋊Dic3—31no—
165Dic3⋊Dic3—31no—
166Dic3⋊Dic3—31no—
167Dic3⋊Dic3—31no—
168Dic3⋊Dic3—31no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—31no—
171Dic3⋊Dic3—31no—
172Dic3⋊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—
179(C2×D3)⋊Dic3—31no—
180(C2×D3)⋊Dic3—31no—
181(C2×D3)⋊Dic3—31no—
182(C2×D3)⋊Dic3—31no—
183Dic32—31no—
184Dic32—31no—
185C22×H(3,𝔽3)C2411yescharacteristic
186C2×#272—21no—
187C2×#272—21no—
188C2×#272—21no—
189C2×#272—21no—
190C2×#272—21no—
191C2×#272#4112yes—
192C4×H(3,𝔽3)—21no—
193C4×H(3,𝔽3)—21no—
194C4×H(3,𝔽3)—21no—
195#1084—21no—
196#1084—21no—
197(C3⋊Dic3)⋊C3—21no—
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#4112yes—
205C3×#125—91no—
206C3×#123—91no—
207C3×C4×Q8—91no—
208#946—91no—
209#946—91no—
210#935—91no—
211D4×Dic3—91no—
212#926—91no—
213C2×Dic3⋊C4—91no—
214#898—91no—
215#898—91no—
216#896—91no—
217#896—91no—
218#894—31no—
219#894—31no—
220#894—61no—
221#894—91no—
222#894—91no—
223#893—91no—
224#892—91no—
225#892—91no—
226D3×C4⋊C4—91no—
227D3×C4⋊C4—91no—
228#890—91no—
229#889—31no—
230#889—91no—
231#889—91no—
232#889—91no—
233#889—91no—
234#889—91no—
235#887—31no—
236#887—91no—
237#879—91no—
238#879—91no—
239#878—91no—
240#878—91no—
241#877—91no—
242#877—91no—
243#876—91no—
244#876—91no—
245C4×D12—91no—
246#872—91no—
247#872—91no—
248#872—91no—
249#872—91no—
250#870—91no—
251C22×C3×D3—31no—
252C22×C3×D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C22×C3×D3—61no—
256C22×C3×D3—61no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×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⋊Dic3C22×D311yescharacteristic
273C2×C3⋊Dic3C22×D311yescharacteristic
274#634—22no—
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—31no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—61no—
289C3×D12—62no—
290C3×D12—62no—
291C3×D12—122no—
292C3×C4×D3—62no—
293C3×C4×D3—62no—
294C3×C4×D3—122no—
295C3×Dic6—62no—
296D3×Dic3—62no—
297D3×Dic3—62no—
298D3×Dic3—62no—
299D3×Dic3—62no—
300D3×Dic3—62no—
301D3×Dic3—62no—
302#552—271noSylow
303C2×H(3,𝔽3)C2×#4111yescharacteristic
304C2×H(3,𝔽3)C2×#4111yescharacteristic
305C2×H(3,𝔽3)2−1+411yescharacteristic
306#272—22no—
307#272—41no—
308C2×C3×Q8—91no—
309C2×C3×D4—91no—
310C22×C3×C4—91no—
311C22×Dic3—91no—
312C22×Dic3—91no—
313C22×Dic3—91no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—61no—
320C2×C4×D3—91no—
321C2×C4×D3—91no—
322C2×C4×D3—91no—
323C2×C4×D3—91no—
324C2×C4×D3—91no—
325C2×C4×D3—91no—
326C2×Dic6—31no—
327C2×Dic6—91no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—91no—
332C3×C4⋊C4—91no—
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⋊C4D3211yescharacteristic
340C3×C22⋊C4—91no—
341C3×C22⋊C4—91no—
342C3×C22⋊C4—91no—
343C3×C42—91no—
344C3×C42—91no—
345C3×C42—91no—
346C3×C42—91no—
347#217—91no—
348#217—91no—
349#217—91no—
350#217—91no—
351#217—91no—
352(C2×D3)⋊C4—31no—
353(C2×D3)⋊C4—31no—
354(C2×D3)⋊C4—31no—
355(C2×D3)⋊C4—31no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
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—
370(C2×D3)⋊C4—91no—
371C4⋊Dic3—31no—
372C4⋊Dic3—91no—
373C4⋊Dic3—91no—
374C4⋊Dic3—91no—
375C4⋊Dic3—91no—
376C4⋊Dic3—91no—
377C4⋊Dic3—91no—
378C4⋊Dic3—91no—
379C4⋊Dic3—91no—
380Dic3⋊C4—31no—
381Dic3⋊C4—31no—
382Dic3⋊C4—31no—
383Dic3⋊C4—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
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—
408Dic3⋊C4—91no—
409C4×Dic3—31no—
410C4×Dic3—31no—
411C4×Dic3—31no—
412C4×Dic3—31no—
413C4×Dic3—91no—
414C4×Dic3—91no—
415C4×Dic3—91no—
416C4×Dic3—91no—
417C4×Dic3—91no—
418C4×Dic3—91no—
419C4×Dic3—91no—
420C22×C32—21no—
421C22×C32C23×D311yescharacteristic
422C22×C32C23×D311yescharacteristic
423C2×C3×D3—32no—
424C2×C3×D3—32no—
425C2×C3×D3—62no—
426C2×C3×D3—61no—
427C2×C3×D3—61no—
428C2×C3×D3—61no—
429C2×C3×D3—61no—
430C2×C3×D3—61no—
431C2×C3×D3—61no—
432C2×C3×D3—61no—
433C2×C3×D3—61no—
434C2×C3×D3—61no—
435C2×C3×D3—61no—
436C2×C3×D3—121no—
437C2×C3×D3—121no—
438C2×C3×D3—121no—
439C2×C3×D3—121no—
440C2×C3×D3—121no—
441C32×C4—21no—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—41no—
448C32×C4—41no—
449C32×C4—41no—
450C3⋊Dic3—21no—
451C3⋊Dic3—21no—
452C3⋊Dic3—21no—
453C3⋊Dic3—21no—
454C3⋊Dic3—21no—
455C3⋊Dic3—21no—
456C3⋊Dic3—21no—
457C3⋊Dic3#23512yes—
458C3×Dic3—32no—
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—61no—
470C3×Dic3—121no—
471C3×Dic3—121no—
472#126—271no—
473#126—271no—
474#125—91no—
475#125—271no—
476#125—271no—
477#123—91no—
478#123—271no—
479C22⋊Q8—271no—
480C22⋊Q8—271no—
481C4×Q8—91no—
482C4×D4—271no—
483#117—271no—
484#117—271no—
485#117—271no—
486C2×C4⋊C4—271no—
487H(3,𝔽3)#55211yescharacteristic, complemented, Sylow
488C23×C3—91no—
489C23×C3—91no—
490C22×D3—31no—
491C22×D3—31no—
492C22×D3—31no—
493C22×D3—31no—
494C22×D3—61no—
495C22×D3—61no—
496C3×Q8—182no—
497C3×D4—182no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
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—91no—
514C2×C3×C4—91no—
515C2×C3×C4—91no—
516C2×C3×C4—91no—
517C2×C3×C4—182no—
518C2×C3×C4C2×D3211yescharacteristic
519C2×C3×C4C2×D3211yescharacteristic
520C2×C3×C4C2×D3211yescharacteristic
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—61no—
534C2×Dic3—61no—
535C2×Dic3—91no—
536C2×Dic3—91no—
537C2×Dic3—91no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—91no—
543C2×Dic3—182no—
544C2×Dic3—182no—
545C2×Dic3—182no—
546D12—62no—
547D12—62no—
548D12—122no—
549C4×D3—62no—
550C4×D3—62no—
551C4×D3—122no—
552C4×D3—182no—
553C4×D3—182no—
554C4×D3—182no—
555C4×D3—182no—
556C4×D3—182no—
557C4×D3—182no—
558Dic6—62no—
559Dic6—182no—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—21no—
563C2×C32C2×#23511yescharacteristic
564C2×C32#100711yescharacteristic
565C2×C32#100711yescharacteristic
566C2×C32D3×#4111yescharacteristic
567C2×C32D3×#4111yescharacteristic
568C2×C32D3×#4111yescharacteristic
569C3×D3—62no—
570C3×D3—62no—
571C3×D3—122no—
572C3×D3—121no—
573C3×D3—121no—
574C3×D3—241no—
575C2×Q8—91no—
576C2×D4—91no—
577C22×C4—91no—
578C22×C4—271no—
579C22×C4—271no—
580C22×C4—271no—
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—271no—
590C4⋊C4—271no—
591C4⋊C4—271no—
592C4⋊C4—271no—
593C4⋊C4—271no—
594C4⋊C4—271no—
595C4⋊C4—271no—
596C4⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
597C22⋊C4—91no—
598C22⋊C4—91no—
599C22⋊C4—91no—
600C22⋊C4—271no—
601C22⋊C4—271no—
602C22⋊C4—271no—
603C22⋊C4—271no—
604C22⋊C4—271no—
605C42—91no—
606C42—91no—
607C42—91no—
608C42—91no—
609C42—271no—
610C22×C3—31no—
611C22×C3—31no—
612C22×C3—61no—
613C22×C3—92no—
614C22×C3—181no—
615C22×C3—181no—
616C22×C3—181no—
617C22×C3—181no—
618C22×C3—181no—
619C22×C3C22×D3211yescharacteristic
620C2×D3—32no—
621C2×D3—32no—
622C2×D3—62no—
623C2×D3—61no—
624C2×D3—61no—
625C2×D3—61no—
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—121no—
634C2×D3—121no—
635C2×D3—121no—
636C2×D3—121no—
637C2×D3—121no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—61no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—92no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4—181no—
652C3×C4—181no—
653C3×C4—181no—
654C3×C4—181no—
655C3×C4—181no—
656C3×C4—181no—
657C3×C4—181no—
658C3×C4—181no—
659C3×C4—181no—
660Dic3—32no—
661Dic3—61no—
662Dic3—61no—
663Dic3—61no—
664Dic3—61no—
665Dic3—61no—
666Dic3—61no—
667Dic3—61no—
668Dic3—61no—
669Dic3—61no—
670Dic3—61no—
671Dic3—61no—
672Dic3—92no—
673Dic3—121no—
674Dic3—121no—
675Dic3—181no—
676Dic3—181no—
677Dic3—181no—
678Dic3—181no—
679Dic3—181no—
680Dic3—181no—
681Dic3—181no—
682C32—21no—
683C32#558111yescharacteristic, complemented
684C32#569311yescharacteristic, complemented
685C23—91no—
686C23—91no—
687Q8—182no—
688D4—182no—
689C2×C4—91no—
690C2×C4—91no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—91no—
694C2×C4—91no—
695C2×C4—91no—
696C2×C4—91no—
697C2×C4—91no—
698C2×C4—91no—
699C2×C4—182no—
700C2×C4—542no—
701C2×C4—542no—
702C2×C4—542no—
703C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
704C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
705C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
706C2×C3—31no—
707C2×C3—31no—
708C2×C3—31no—
709C2×C3—31no—
710C2×C3—31no—
711C2×C3—31no—
712C2×C3—61no—
713C2×C3—61no—
714C2×C3—61no—
715C2×C3—182no—
716C2×C3—361no—
717C2×C3D3×#23511yescharacteristic
718C2×C3#6431211yescharacteristic
719C2×C3#6431611yescharacteristic
720D3—62no—
721D3—62no—
722D3—122no—
723D3—121no—
724D3—121no—
725D3—241no—
726C22—92no—
727C22—181no—
728C22—181no—
729C22—181no—
730C22—181no—
731C22—181no—
732C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
733C4—21no—
734C4—21no—
735C4—21no—
736C4—92no—
737C4—181no—
738C4—181no—
739C4—181no—
740C4—181no—
741C4—181no—
742C4—181no—
743C4—181no—
744C4—181no—
745C4—181no—
746C3—31no—
747C3—31no—
748C3—61no—
749C3#1059434911yescharacteristic
750C2—182no—
751C2—361no—
752C2#1172249011yescharacteristic
753C2#1172250511yescharacteristic
754C2#1172251711yescharacteristic
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×C4⋊#272C22
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
2. #64098⋊C3C2semidirect
3. #64096⋊C3C2semidirect
6. #11721148C2semidirect
7. #11721148C2semidirect
8. #11721147C2semidirect
9. #11721097C2semidirect
10. #11721092C2semidirect
11. #11721092C2semidirect
12. #11721091C2semidirect
13. #11721086C2semidirect
14. #11721076C2semidirect
15. #11721076C2semidirect
53. #64098D3semidirect
54. #64096D3semidirect
487. H(3,𝔽3)#552semidirect
683. C32#5581semidirect
684. C32#5693semidirect

Maximal subgroups

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

subgroupindex
#117217622
#64098⋊C32
#64096⋊C32
#117211512
#117211492
#117211482
#117211472
#117210972
#117210922
#117210912
#117210862
#117210762
#105944303
#105944203