Finite Group Databasebeta

← #13148471

Subgroups — #13148471

Order 1728.

851 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721734C211yesmaximal, characteristic
2#64087⋊C3C211yesmaximal, characteristic
3#64086⋊C3C211yesmaximal, characteristic
4#11721309C211yesmaximal, characteristic
5#11721299C211yesmaximal, characteristic
6#11721296C211yesmaximal, characteristic
7C2×#88447C211yesmaximal, characteristic
8#11721087C211yesmaximal, characteristic, complemented
9#11721085C211yesmaximal, characteristic, complemented
10#11721083C211yesmaximal, characteristic, complemented
11#11721082C211yesmaximal, characteristic, complemented
12#11721080C211yesmaximal, characteristic, complemented
13#11721079C211yesmaximal, characteristic, complemented
14#11721077C211yesmaximal, characteristic, complemented
15#11721077C211yesmaximal, characteristic, complemented
16#10594030—31nomaximal
17#10594029—31nomaximal
18C22×#1084C2211yescharacteristic
19C2×#6229C2211yescharacteristic
20C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
22C2×#634⋊C3C2211yescharacteristic
23C2×#6196C2211yescharacteristic
24C2×#6196C2211yescharacteristic
25C22⋊C4×H(3,𝔽3)C2211yescharacteristic
26#88552C2211yescharacteristic
27C4⋊#1084C2211yescharacteristic
28#88540C2211yescharacteristic
29#88540C2211yescharacteristic
30#3757⋊C3C2211yescharacteristic
31#3757⋊C3C2211yescharacteristic
32C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
33#3750⋊C3C2211yescharacteristic
34#3750⋊C3C2211yescharacteristic
35#3750⋊C3C2211yescharacteristic
36#3750⋊C3C2211yescharacteristic
37C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
38C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
39#88449C2211yescharacteristic
40#88449C2211yescharacteristic
41#88448C2211yescharacteristic
42#88448C2211yescharacteristic
43#88448C2211yescharacteristic
44#88448C2211yescharacteristic
45#88448C2211yescharacteristic
46#88448C2211yescharacteristic
47#88447C2211yescharacteristic
48#88447C2211yescharacteristic
49#88447C2211yescharacteristic
50#88447C2211yescharacteristic
51#88447C2211yescharacteristic
52#88447C2211yescharacteristic
53#64087D311yescharacteristic
54#64086D311yescharacteristic
55C3×#878—31no—
56C3×#878—31no—
57C3×#878—31no—
58C3×#878—61no—
59C3×#877—31no—
60#63982—31no—
61#63964—31no—
62#63964—31no—
63#63964—31no—
64#63957—31no—
65#63955—31no—
66C2×Dic32—31no—
67C2×Dic32—31no—
68#63847—31no—
69#63847—31no—
70#63846—31no—
71#63845—31no—
72#63844—31no—
73#63843—31no—
74#63843—31no—
75Dic3×Dic6—31no—
76#63840—31no—
77#63839—31no—
78#63839—31no—
79#63839—31no—
80#63838—31no—
81#63838—31no—
82#63837—31no—
83#63837—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C2×C4×H(3,𝔽3)C2311yescharacteristic
86C2×C4×H(3,𝔽3)C2311yescharacteristic
87C2×#1084—22no—
88C2×#1084C2311yescharacteristic
89C2×#1084C2311yescharacteristic
90C2×#1084C2311yescharacteristic
91C2×#1084C2311yescharacteristic
92#6229—22no—
93C2×(C3⋊Dic3)⋊C3—22no—
94C2×(C3⋊Dic3)⋊C3Q814yescomplemented
95C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
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#634⋊C3—22no—
104#6196—22no—
105#6196—22no—
106#5622—91no—
107#5622—91no—
108#5517—91no—
109C22×C3⋊Dic3C2×D311yescharacteristic
110C22×C3⋊Dic3C2×D311yescharacteristic
111C2×#634C2×D311yescharacteristic
112C22×C3×Dic3—31no—
113C22×C3×Dic3—31no—
114C22×C3×Dic3—31no—
115C22×C3×Dic3—31no—
116C22×C3×Dic3—61no—
117C2×C3×Dic6—31no—
118C2×C3×Dic6—31no—
119C2×C3×Dic6—31no—
120C2×C3×Dic6—61no—
121C2×#627—31no—
122C2×#627—31no—
123C2×#627—31no—
124C2×#627—31no—
125C32×C22⋊C4—21no—
126C32×C22⋊C4C2×D311yescharacteristic
127C32×C22⋊C4C2×D311yescharacteristic
128#3757C2×D311yescharacteristic
129#3757C2×D311yescharacteristic
130C4⋊(C3⋊Dic3)C2×D311yescharacteristic
131#3750C2×D311yescharacteristic
132#3750C2×D311yescharacteristic
133#3750C2×D311yescharacteristic
134#3750C2×D311yescharacteristic
135C4×C3⋊Dic3C2×D311yescharacteristic
136C4×C3⋊Dic3C2×D311yescharacteristic
137C3×#217—31no—
138C3×#217—31no—
139C3×#217—31no—
140C3×#217—31no—
141C3×#217—61no—
142C3×C4⋊Dic3—31no—
143C3×C4⋊Dic3—31no—
144C3×C4⋊Dic3—31no—
145C3×C4⋊Dic3—61no—
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×Dic3⋊C4—61no—
156C3×C4×Dic3—31no—
157C3×C4×Dic3—31no—
158#3724—31no—
159#3724—31no—
160#3724—31no—
161#3724—31no—
162#3724—31no—
163#3724—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—
173Dic3⋊Dic3—31no—
174Dic32—31no—
175Dic32—31no—
176Dic32—31no—
177Dic32—31no—
178Dic32—31no—
179Dic32—31no—
180Dic32—31no—
181Dic32—31no—
182Dic32—31no—
183Dic32—31no—
184Dic32—31no—
185Dic32—31no—
186C22×H(3,𝔽3)—21no—
187C22×H(3,𝔽3)—21no—
188C22×H(3,𝔽3)C2×Q812yes—
189C22×H(3,𝔽3)C2411yescharacteristic
190C4×H(3,𝔽3)—21no—
191C4×H(3,𝔽3)—21no—
192#1084—21no—
193#1084—21no—
194#1084—21no—
195#1084#4112yes—
196(C3⋊Dic3)⋊C3—21no—
197(C3⋊Dic3)⋊C3—21no—
198(C3⋊Dic3)⋊C3—21no—
199(C3⋊Dic3)⋊C3—21no—
200(C3⋊Dic3)⋊C3—21no—
201(C3⋊Dic3)⋊C3C2×Q812yes—
202(C3⋊Dic3)⋊C3C2×Q812yes—
203(C3⋊Dic3)⋊C3#4112yes—
204C3×C22⋊Q8—91no—
205C3×C22⋊Q8—91no—
206C3×#117—91no—
207Q8×Dic3—91no—
208Q8×Dic3—91no—
209#944—91no—
210#944—91no—
211#926—91no—
212#924—91no—
213#924—91no—
214C2×C4×Dic3—91no—
215C2×C4×Dic3—91no—
216C2×C4×Dic3—91no—
217#890—91no—
218#890—91no—
219#889—91no—
220#889—91no—
221#889—91no—
222#889—91no—
223#888—91no—
224#888—91no—
225#888—91no—
226#888—91no—
227#887—91no—
228#887—91no—
229#887—91no—
230#887—91no—
231#887—91no—
232#887—91no—
233#878—31no—
234#878—31no—
235#878—31no—
236#878—61no—
237#878—91no—
238#878—91no—
239#878—91no—
240#878—91no—
241#878—91no—
242#877—31no—
243#877—91no—
244#877—91no—
245#877—91no—
246C4×Dic6—91no—
247C4×Dic6—91no—
248C4×Dic6—91no—
249C4×Dic6—91no—
250C23×C32—21no—
251C23×C32C22×D311yescharacteristic
252C23×C32C22×D311yescharacteristic
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C3⋊Dic3—22no—
260C2×C3⋊Dic3Dic614yescomplemented
261C2×C3⋊Dic3C22×D311yescharacteristic
262C2×C3⋊Dic3C22×D311yescharacteristic
263C2×C3⋊Dic3C22×D311yescharacteristic
264C2×C3⋊Dic3C22×D311yescharacteristic
265C2×C3⋊Dic3C22×D311yescharacteristic
266C2×C3⋊Dic3C22×D311yescharacteristic
267C2×C3⋊Dic3C22×D311yescharacteristic
268C2×C3⋊Dic3C22×D311yescharacteristic
269#634—22no—
270C2×C3×Dic3—34no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
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—
289C2×C3×Dic3—61no—
290C2×C3×Dic3—61no—
291C2×C3×Dic3—62no—
292C2×C3×Dic3—62no—
293C2×C3×Dic3—62no—
294C2×C3×Dic3—122no—
295C3×Dic6—62no—
296C3×Dic6—62no—
297C3×Dic6—62no—
298C3×Dic6—122no—
299#627—62no—
300#627—62no—
301#627—62no—
302#627—62no—
303#533—271noSylow
304C2×H(3,𝔽3)—22no—
305C2×H(3,𝔽3)C22×Q811yescharacteristic
306C2×H(3,𝔽3)C2×#4111yescharacteristic
307C2×H(3,𝔽3)C2×#4111yescharacteristic
308C2×C3×Q8—91no—
309C2×C3×Q8—91no—
310C22×C3×C4—91no—
311C22×C3×C4—91no—
312C22×C3×C4—91no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—61no—
318C22×Dic3—91no—
319C22×Dic3—91no—
320C2×Dic6—31no—
321C2×Dic6—31no—
322C2×Dic6—31no—
323C2×Dic6—61no—
324C2×Dic6—91no—
325C2×Dic6—91no—
326C2×Dic6—91no—
327C2×Dic6—91no—
328C2×Dic6—91no—
329C2×Dic6—91no—
330C2×Dic6—91no—
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×C22⋊C4—31no—
340C3×C22⋊C4—31no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—91no—
343C3×C22⋊C4—91no—
344C3×C22⋊C4—91no—
345C3×C22⋊C4D3211yescharacteristic
346C3×C42—91no—
347C3×C42—91no—
348#217—31no—
349#217—31no—
350#217—31no—
351#217—31no—
352#217—61no—
353#217—91no—
354#217—91no—
355C4⋊Dic3—31no—
356C4⋊Dic3—31no—
357C4⋊Dic3—31no—
358C4⋊Dic3—61no—
359C4⋊Dic3—91no—
360C4⋊Dic3—91no—
361C4⋊Dic3—91no—
362C4⋊Dic3—91no—
363C4⋊Dic3—91no—
364C4⋊Dic3—91no—
365C4⋊Dic3—91no—
366C4⋊Dic3—91no—
367C4⋊Dic3—91no—
368Dic3⋊C4—31no—
369Dic3⋊C4—31no—
370Dic3⋊C4—31no—
371Dic3⋊C4—31no—
372Dic3⋊C4—31no—
373Dic3⋊C4—31no—
374Dic3⋊C4—31no—
375Dic3⋊C4—31no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—91no—
379Dic3⋊C4—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
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—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—91no—
401C4×Dic3—91no—
402C4×Dic3—91no—
403C4×Dic3—91no—
404C4×Dic3—91no—
405C4×Dic3—91no—
406C4×Dic3—91no—
407C4×Dic3—91no—
408C4×Dic3—91no—
409C4×Dic3—91no—
410C4×Dic3—91no—
411C4×Dic3—91no—
412C4×Dic3—91no—
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×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—22no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32C2×Dic612yes—
429C22×C32D3×Q812yes—
430C22×C32C23×D311yescharacteristic
431C22×C32C23×D311yescharacteristic
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4—21no—
436C32×C4—41no—
437C32×C4—41no—
438C3⋊Dic3—21no—
439C3⋊Dic3—21no—
440C3⋊Dic3—21no—
441C3⋊Dic3—21no—
442C3⋊Dic3—21no—
443C3⋊Dic3C2×Dic612yes—
444C3⋊Dic3C2×Dic612yes—
445C3⋊Dic3#23712yes—
446C3×Dic3—32no—
447C3×Dic3—32no—
448C3×Dic3—32no—
449C3×Dic3—32no—
450C3×Dic3—32no—
451C3×Dic3—62no—
452C3×Dic3—61no—
453C3×Dic3—61no—
454C3×Dic3—61no—
455C3×Dic3—61no—
456C3×Dic3—61no—
457C3×Dic3—61no—
458C3×Dic3—61no—
459C3×Dic3—61no—
460C3×Dic3—61no—
461C3×Dic3—61no—
462C3×Dic3—61no—
463C3×Dic3—121no—
464C3×Dic3—121no—
465C3×Dic3—121no—
466C4⋊Q8—271no—
467C4⋊Q8—271no—
468#125—271no—
469#125—271no—
470C22⋊Q8—91no—
471C22⋊Q8—91no—
472C22⋊Q8—271no—
473C22⋊Q8—271no—
474C4×Q8—271no—
475C4×Q8—271no—
476C4×Q8—271no—
477C4×Q8—271no—
478#117—91no—
479#117—271no—
480C2×C42—271no—
481H(3,𝔽3)#53311yescharacteristic, complemented, Sylow
482C23×C3—31no—
483C23×C3—31no—
484C23×C3—61no—
485C23×C3C2×D3211yescharacteristic
486C3×Q8—182no—
487C3×Q8—182no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—91no—
495C2×C3×C4—91no—
496C2×C3×C4—91no—
497C2×C3×C4—94no—
498C2×C3×C4—91no—
499C2×C3×C4—91no—
500C2×C3×C4—91no—
501C2×C3×C4—91no—
502C2×C3×C4—91no—
503C2×C3×C4—91no—
504C2×C3×C4—91no—
505C2×C3×C4—91no—
506C2×C3×C4—91no—
507C2×C3×C4—182no—
508C2×C3×C4—182no—
509C2×C3×C4C2×D3211yescharacteristic
510C2×C3×C4C2×D3211yescharacteristic
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—34no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—62no—
533C2×Dic3—62no—
534C2×Dic3—62no—
535C2×Dic3—94no—
536C2×Dic3—91no—
537C2×Dic3—91no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—91no—
543C2×Dic3—91no—
544C2×Dic3—122no—
545C2×Dic3—182no—
546Dic6—62no—
547Dic6—62no—
548Dic6—62no—
549Dic6—122no—
550Dic6—182no—
551Dic6—182no—
552Dic6—182no—
553Dic6—182no—
554Dic6—182no—
555Dic6—182no—
556Dic6—182no—
557C2×C32—22no—
558C2×C32—22no—
559C2×C32—21no—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—42no—
563C2×C32C22×Dic611yescharacteristic
564C2×C32C2×#23711yescharacteristic
565C2×C32C2×D3×Q811yescharacteristic
566C2×C32D3×#4111yescharacteristic
567C2×C32D3×#4111yescharacteristic
568C2×C32D3×#4111yescharacteristic
569C2×Q8—91no—
570C2×Q8—91no—
571C2×Q8—271no—
572C2×Q8—271no—
573C22×C4—91no—
574C22×C4—91no—
575C22×C4—91no—
576C4⋊C4—91no—
577C4⋊C4—91no—
578C4⋊C4—91no—
579C4⋊C4—91no—
580C4⋊C4—91no—
581C4⋊C4—91no—
582C4⋊C4—91no—
583C4⋊C4—91no—
584C4⋊C4—271no—
585C4⋊C4—271no—
586C4⋊C4—271no—
587C4⋊C4—271no—
588C4⋊C4—271no—
589C4⋊C4—271no—
590C4⋊C4—271no—
591C4⋊C4—271no—
592C22⋊C4—91no—
593C22⋊C4—91no—
594C22⋊C4—91no—
595C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
596C42—91no—
597C42—91no—
598C42—271no—
599C42—271no—
600C42—271no—
601C42—271no—
602C42—271no—
603C42—271no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—31no—
607C22×C3—31no—
608C22×C3—32no—
609C22×C3—32no—
610C22×C3—61no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—61no—
614C22×C3—61no—
615C22×C3—62no—
616C22×C3—121no—
617C22×C3—121no—
618C22×C3D3×Dic612yes—
619C22×C3C22×D3211yescharacteristic
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—61no—
623C3×C4—61no—
624C3×C4—61no—
625C3×C4—61no—
626C3×C4—92no—
627C3×C4—92no—
628C3×C4—92no—
629C3×C4—92no—
630C3×C4—121no—
631C3×C4—121no—
632C3×C4—181no—
633C3×C4—181no—
634C3×C4—181no—
635C3×C4—181no—
636C3×C4—181no—
637C3×C4—181no—
638C3×C4—181no—
639C3×C4—181no—
640Dic3—32no—
641Dic3—32no—
642Dic3—32no—
643Dic3—32no—
644Dic3—32no—
645Dic3—62no—
646Dic3—61no—
647Dic3—61no—
648Dic3—61no—
649Dic3—61no—
650Dic3—61no—
651Dic3—61no—
652Dic3—61no—
653Dic3—61no—
654Dic3—61no—
655Dic3—61no—
656Dic3—61no—
657Dic3—92no—
658Dic3—92no—
659Dic3—92no—
660Dic3—121no—
661Dic3—121no—
662Dic3—121no—
663Dic3—181no—
664Dic3—181no—
665Dic3—181no—
666Dic3—181no—
667Dic3—181no—
668C32—21no—
669C32#551711yescharacteristic, complemented
670C32#562211yescharacteristic, complemented
671C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
672Q8—182no—
673Q8—182no—
674Q8—542no—
675Q8—542no—
676C2×C4—91no—
677C2×C4—91no—
678C2×C4—91no—
679C2×C4—91no—
680C2×C4—94no—
681C2×C4—91no—
682C2×C4—91no—
683C2×C4—91no—
684C2×C4—91no—
685C2×C4—91no—
686C2×C4—91no—
687C2×C4—91no—
688C2×C4—91no—
689C2×C4—182no—
690C2×C4—182no—
691C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
692C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
693C2×C3—22no—
694C2×C3—31no—
695C2×C3—31no—
696C2×C3—31no—
697C2×C3—31no—
698C2×C3—31no—
699C2×C3—31no—
700C2×C3—62no—
701C2×C3—62no—
702C2×C3—61no—
703C2×C3—61no—
704C2×C3—61no—
705C2×C3—122no—
706C2×C3C2×D3×Dic611yescharacteristic
707C2×C3D3×#23711yescharacteristic
708C2×C3#6431211yescharacteristic
709C22—21no—
710C22—21no—
711C22((C3⋊D3)⋊C3)⋊Q812yes—
712C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
713C4—21no—
714C4—21no—
715C4—92no—
716C4—92no—
717C4—92no—
718C4—92no—
719C4—181no—
720C4—181no—
721C4—181no—
722C4—181no—
723C4—181no—
724C4—181no—
725C4—181no—
726C4—181no—
727C3—31no—
728C3—31no—
729C3—61no—
730C3#1059402911yescharacteristic
731C2—22no—
732C2C2×((C3⋊D3)⋊C3)⋊Q811yescharacteristic
733C2#1172250411yescharacteristic
734C2#1172250511yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC22⋊C4×H(3,𝔽3)C22
prime radicalC23×H(3,𝔽3)C23
hypercenterC22⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#533
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
8. #11721087C2semidirect
9. #11721085C2semidirect
10. #11721083C2semidirect
11. #11721082C2semidirect
12. #11721080C2semidirect
13. #11721079C2semidirect
14. #11721077C2semidirect
15. #11721077C2semidirect
94. C2×(C3⋊Dic3)⋊C3Q8semidirect
260. C2×C3⋊Dic3Dic6semidirect
481. H(3,𝔽3)#533semidirect
669. C32#5517semidirect
670. C32#5622semidirect

Maximal subgroups

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

subgroupindex
#117217342
#64087⋊C32
#64086⋊C32
#117213092
#117212992
#117212962
C2×#884472
#117210872
#117210852
#117210832
#117210822
#117210802
#117210792
#117210772
#105940303
#105940293