Finite Group Databasebeta

← #13149406

Subgroups — #13149406

Order 1728.

746 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721764C211yesmaximal, characteristic
2#64099⋊C3C211yesmaximal, characteristic, complemented
3#64098⋊C3C211yesmaximal, characteristic, complemented
4#11721096C211yesmaximal, characteristic
5#11721092C211yesmaximal, characteristic
6#11721092C211yesmaximal, characteristic
7#11721089C211yesmaximal, characteristic
8#11721088C211yesmaximal, characteristic
9#11721088C211yesmaximal, characteristic
10#11721087C211yesmaximal, characteristic, complemented
11#11721086C211yesmaximal, characteristic, complemented
12#11721086C211yesmaximal, characteristic, complemented
13#11721083C211yesmaximal, characteristic, complemented
14#11721080C211yesmaximal, characteristic, complemented
15#11721077C211yesmaximal, characteristic, complemented
16#10594336—31nomaximal
17#10594319—31nomaximal
18C2×C4×#272C2211yescharacteristic
19C2×#6229C2211yescharacteristic
20C2×#6196C2211yescharacteristic
21C4⋊C4×H(3,𝔽3)C2211yescharacteristic
22#88542C2211yescharacteristic
23#88542C2211yescharacteristic
24#88540C2211yescharacteristic
25#88540C2211yescharacteristic
26C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
27C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
28C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
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
38#88451C2211yescharacteristic
39#88451C2211yescharacteristic
40#88451C2211yescharacteristic
41#88451C2211yescharacteristic
42#88449C2211yescharacteristic
43#88449C2211yescharacteristic
44#88449C2211yescharacteristic
45#88448C2211yescharacteristic
46#88448C2211yescharacteristic
47#88448C2211yescharacteristic
48#88448C2211yescharacteristic
49#88447C2211yescharacteristic
50#88447C2211yescharacteristic
51#88447C2211yescharacteristic
52#88447C2211yescharacteristic
53#64099D311yescharacteristic, complemented
54#64098D311yescharacteristic, complemented
55C3×#896—31no—
56C3×#896—31no—
57C3×#896—61no—
58C3×#890—31no—
59C3×#889—31no—
60#63862—31no—
61#63862—31no—
62#63861—31no—
63#63861—31no—
64#63859—31no—
65#63859—31no—
66#63858—31no—
67#63858—31no—
68#63851—31no—
69#63851—31no—
70#63847—31no—
71#63846—31no—
72#63846—31no—
73#63845—31no—
74#63845—31no—
75#63845—31no—
76#63843—31no—
77Dic3×Dic6—31no—
78#63841—31no—
79#63841—31no—
80#63839—31no—
81#63839—31no—
82#63838—31no—
83#63837—31no—
84C22×#272C2311yescharacteristic
85C2×C4×H(3,𝔽3)C2311yescharacteristic
86C2×C4×H(3,𝔽3)C2311yescharacteristic
87C2×C4×H(3,𝔽3)C2311yescharacteristic
88C2×#1084C2311yescharacteristic
89C2×#1084C2311yescharacteristic
90C2×#1084C2311yescharacteristic
91C4×#272—22no—
92#6229—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#6196—22no—
102#5696—91no—
103#5696—91no—
104#5625—91no—
105C2×C3×C4×D3—31no—
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—61no—
108C2×C3×Dic6—31no—
109C2×C3×Dic6—31no—
110C2×C3×Dic6—61no—
111C2×#627—31no—
112C2×#627—31no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2×D311yescharacteristic
115C32×C4⋊C4C2×D311yescharacteristic
116C4⋊(C3⋊Dic3)C2×D311yescharacteristic
117C4⋊(C3⋊Dic3)C2×D311yescharacteristic
118C4⋊(C3⋊Dic3)C2×D311yescharacteristic
119C4⋊(C3⋊Dic3)C2×D311yescharacteristic
120#3750C2×D311yescharacteristic
121#3750C2×D311yescharacteristic
122#3750C2×D311yescharacteristic
123#3750C2×D311yescharacteristic
124#3750C2×D311yescharacteristic
125#3750C2×D311yescharacteristic
126C4×C3⋊Dic3C2×D311yescharacteristic
127C4×C3⋊Dic3C2×D311yescharacteristic
128C3×(C2×D3)⋊C4—31no—
129C3×(C2×D3)⋊C4—31no—
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4—31no—
132C3×(C2×D3)⋊C4—61no—
133C3×(C2×D3)⋊C4—61no—
134C3×C4⋊Dic3—31no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—31no—
138C3×Dic3⋊C4—31no—
139C3×Dic3⋊C4—31no—
140C3×Dic3⋊C4—31no—
141C3×Dic3⋊C4—31no—
142C3×Dic3⋊C4—31no—
143C3×Dic3⋊C4—31no—
144C3×Dic3⋊C4—31no—
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4—31no—
148C3×Dic3⋊C4—61no—
149C3×Dic3⋊C4—61no—
150C3×C4×Dic3—31no—
151C3×C4×Dic3—31no—
152#3724—31no—
153#3724—31no—
154#3724—31no—
155#3724—31no—
156Dic3⋊Dic3—31no—
157Dic3⋊Dic3—31no—
158Dic3⋊Dic3—31no—
159Dic3⋊Dic3—31no—
160Dic3⋊Dic3—31no—
161Dic3⋊Dic3—31no—
162Dic3⋊Dic3—31no—
163Dic3⋊Dic3—31no—
164Dic3⋊Dic3—31no—
165Dic3⋊Dic3—31no—
166(C2×D3)⋊Dic3—31no—
167(C2×D3)⋊Dic3—31no—
168(C2×D3)⋊Dic3—31no—
169(C2×D3)⋊Dic3—31no—
170(C2×D3)⋊Dic3—31no—
171(C2×D3)⋊Dic3—31no—
172(C2×D3)⋊Dic3—31no—
173(C2×D3)⋊Dic3—31no—
174Dic32—31no—
175Dic32—31no—
176Dic32—31no—
177Dic32—31no—
178Dic32—31no—
179Dic32—31no—
180Dic32—31no—
181Dic32—31no—
182C22×H(3,𝔽3)C2411yescharacteristic
183C2×#272—21no—
184C2×#272—21no—
185C2×#272—21no—
186C4×H(3,𝔽3)—21no—
187C4×H(3,𝔽3)—21no—
188C4×H(3,𝔽3)—21no—
189#1084—21no—
190#1084—21no—
191#1084#4112yes—
192(C3⋊Dic3)⋊C3—21no—
193(C3⋊Dic3)⋊C3—21no—
194(C3⋊Dic3)⋊C3—21no—
195(C3⋊Dic3)⋊C3—21no—
196(C3⋊Dic3)⋊C3—21no—
197(C3⋊Dic3)⋊C3—21no—
198(C3⋊Dic3)⋊C3—21no—
199(C3⋊Dic3)⋊C3—21no—
200C3×#125—91no—
201C3×#125—91no—
202C3×C22⋊Q8—91no—
203Q8×Dic3—91no—
204#944—91no—
205#926—91no—
206#924—91no—
207#898—91no—
208#898—91no—
209#898—91no—
210#898—91no—
211#898—91no—
212#898—91no—
213#896—31no—
214#896—31no—
215#896—61no—
216#896—91no—
217#896—91no—
218#892—91no—
219#892—91no—
220#890—31no—
221#890—91no—
222#890—91no—
223#890—91no—
224#890—91no—
225#889—31no—
226#889—91no—
227#889—91no—
228#889—91no—
229#889—91no—
230#889—91no—
231#889—91no—
232#889—91no—
233#888—91no—
234#888—91no—
235#887—91no—
236#887—91no—
237#887—91no—
238#879—91no—
239#879—91no—
240#879—91no—
241#879—91no—
242#876—91no—
243#876—91no—
244C4×Dic6—91no—
245C4×Dic6—91no—
246C22×C3×D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3—61no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C3⋊Dic3C22×D311yescharacteristic
259C2×C3⋊Dic3C22×D311yescharacteristic
260C2×C3⋊Dic3C22×D311yescharacteristic
261C2×C3⋊Dic3C22×D311yescharacteristic
262C2×C3⋊Dic3C22×D311yescharacteristic
263C2×C3⋊Dic3C22×D311yescharacteristic
264C2×C3⋊Dic3C22×D311yescharacteristic
265C2×C3⋊Dic3C22×D311yescharacteristic
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
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—61no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—61no—
283C3×C4×D3—62no—
284C3×C4×D3—62no—
285C3×C4×D3—122no—
286C3×Dic6—62no—
287C3×Dic6—62no—
288C3×Dic6—122no—
289#627—62no—
290#627—62no—
291#541—271noSylow
292C2×H(3,𝔽3)C2×#4111yescharacteristic
293C2×H(3,𝔽3)2−1+411yescharacteristic
294C2×H(3,𝔽3)2−1+411yescharacteristic
295#272—41no—
296C2×C3×Q8—91no—
297C22×C3×C4—91no—
298C2×C4×D3—31no—
299C2×C4×D3—31no—
300C2×C4×D3—61no—
301C2×Dic6—31no—
302C2×Dic6—31no—
303C2×Dic6—61no—
304C2×Dic6—91no—
305C2×Dic6—91no—
306C2×Dic6—91no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—61no—
310C3×C4⋊C4—91no—
311C3×C4⋊C4—91no—
312C3×C4⋊C4—91no—
313C3×C4⋊C4—91no—
314C3×C4⋊C4—91no—
315C3×C4⋊C4—91no—
316C3×C4⋊C4—91no—
317C3×C4⋊C4—91no—
318C3×C4⋊C4—91no—
319C3×C4⋊C4—91no—
320C3×C4⋊C4—91no—
321C3×C4⋊C4—91no—
322C3×C4⋊C4D3211yescharacteristic
323C3×C22⋊C4—91no—
324C3×C22⋊C4—91no—
325C3×C42—91no—
326C3×C42—91no—
327#217—91no—
328#217—91no—
329#217—91no—
330#217—91no—
331(C2×D3)⋊C4—31no—
332(C2×D3)⋊C4—31no—
333(C2×D3)⋊C4—31no—
334(C2×D3)⋊C4—31no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
337(C2×D3)⋊C4—91no—
338(C2×D3)⋊C4—91no—
339(C2×D3)⋊C4—91no—
340(C2×D3)⋊C4—91no—
341(C2×D3)⋊C4—91no—
342(C2×D3)⋊C4—91no—
343(C2×D3)⋊C4—91no—
344(C2×D3)⋊C4—91no—
345C4⋊Dic3—31no—
346C4⋊Dic3—31no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—91no—
350C4⋊Dic3—91no—
351C4⋊Dic3—91no—
352C4⋊Dic3—91no—
353C4⋊Dic3—91no—
354C4⋊Dic3—91no—
355C4⋊Dic3—91no—
356C4⋊Dic3—91no—
357C4⋊Dic3—91no—
358C4⋊Dic3—91no—
359C4⋊Dic3—91no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—31no—
363Dic3⋊C4—31no—
364Dic3⋊C4—31no—
365Dic3⋊C4—31no—
366Dic3⋊C4—31no—
367Dic3⋊C4—31no—
368Dic3⋊C4—31no—
369Dic3⋊C4—31no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—91no—
373Dic3⋊C4—91no—
374Dic3⋊C4—91no—
375Dic3⋊C4—91no—
376Dic3⋊C4—91no—
377Dic3⋊C4—91no—
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—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—91no—
395C4×Dic3—91no—
396C4×Dic3—91no—
397C4×Dic3—91no—
398C4×Dic3—91no—
399C4×Dic3—91no—
400C4×Dic3—91no—
401C4×Dic3—91no—
402C4×Dic3—91no—
403C4×Dic3—91no—
404C4×Dic3—91no—
405C4×Dic3—91no—
406C4×Dic3—91no—
407C4×Dic3—91no—
408C22×C32—21no—
409C22×C32C23×D311yescharacteristic
410C22×C32C23×D311yescharacteristic
411C2×C3×D3—62no—
412C2×C3×D3—61no—
413C2×C3×D3—61no—
414C2×C3×D3—61no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—121no—
419C2×C3×D3—121no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4—41no—
429C3⋊Dic3—21no—
430C3⋊Dic3—21no—
431C3⋊Dic3—21no—
432C3⋊Dic3—21no—
433C3⋊Dic3—21no—
434C3⋊Dic3—21no—
435C3⋊Dic3—21no—
436C3⋊Dic3—21no—
437C3×Dic3—32no—
438C3×Dic3—32no—
439C3×Dic3—62no—
440C3×Dic3—61no—
441C3×Dic3—61no—
442C3×Dic3—61no—
443C3×Dic3—61no—
444C3×Dic3—61no—
445C3×Dic3—61no—
446C3×Dic3—61no—
447C3×Dic3—61no—
448C3×Dic3—61no—
449C3×Dic3—61no—
450C3×Dic3—61no—
451C3×Dic3—61no—
452C3×Dic3—121no—
453C3×Dic3—121no—
454C4⋊Q8—271no—
455#126—271no—
456#126—271no—
457#126—271no—
458#126—271no—
459#125—91no—
460#125—91no—
461#125—271no—
462#125—271no—
463#125—271no—
464C22⋊Q8—91no—
465C22⋊Q8—271no—
466C4×Q8—271no—
467C4×Q8—271no—
468#117—271no—
469H(3,𝔽3)#54111yescharacteristic, complemented, Sylow
470C23×C3—91no—
471C22×D3—31no—
472C22×D3—31no—
473C22×D3—61no—
474C3×Q8—182no—
475C2×C3×C4—31no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—91no—
485C2×C3×C4—91no—
486C2×C3×C4—91no—
487C2×C3×C4—91no—
488C2×C3×C4—91no—
489C2×C3×C4—91no—
490C2×C3×C4—91no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—91no—
495C2×C3×C4—182no—
496C2×C3×C4C2×D3211yescharacteristic
497C2×C3×C4C2×D3211yescharacteristic
498C2×C3×C4C2×D3211yescharacteristic
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—31no—
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—91no—
517C2×Dic3—91no—
518C2×Dic3—91no—
519C2×Dic3—91no—
520C2×Dic3—91no—
521C2×Dic3—91no—
522C2×Dic3—91no—
523C2×Dic3—91no—
524C4×D3—62no—
525C4×D3—62no—
526C4×D3—122no—
527Dic6—62no—
528Dic6—62no—
529Dic6—122no—
530Dic6—182no—
531Dic6—182no—
532Dic6—182no—
533C2×C32—21no—
534C2×C32—21no—
535C2×C32—21no—
536C2×C32#100711yescharacteristic
537C2×C32#100711yescharacteristic
538C2×C32D3×#4111yescharacteristic
539C2×C32D3×#4111yescharacteristic
540C2×C32#101011yescharacteristic
541C2×C32#101011yescharacteristic
542C3×D3—122no—
543C3×D3—121no—
544C3×D3—121no—
545C2×Q8—91no—
546C2×Q8—271no—
547C22×C4—91no—
548C4⋊C4—91no—
549C4⋊C4—91no—
550C4⋊C4—91no—
551C4⋊C4—91no—
552C4⋊C4—91no—
553C4⋊C4—91no—
554C4⋊C4—91no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—91no—
558C4⋊C4—91no—
559C4⋊C4—91no—
560C4⋊C4—271no—
561C4⋊C4—271no—
562C4⋊C4—271no—
563C4⋊C4—271no—
564C4⋊C4—271no—
565C4⋊C4—271no—
566C4⋊C4—271no—
567C4⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
568C22⋊C4—91no—
569C22⋊C4—91no—
570C22⋊C4—271no—
571C22⋊C4—271no—
572C22⋊C4—271no—
573C22⋊C4—271no—
574C42—91no—
575C42—91no—
576C42—271no—
577C42—271no—
578C42—271no—
579C42—271no—
580C22×C3—31no—
581C22×C3—31no—
582C22×C3—61no—
583C22×C3—181no—
584C22×C3—181no—
585C22×C3—181no—
586C22×C3C22×D3211yescharacteristic
587C2×D3—61no—
588C2×D3—61no—
589C2×D3—61no—
590C2×D3—61no—
591C2×D3—61no—
592C2×D3—61no—
593C2×D3—62no—
594C2×D3—121no—
595C2×D3—121no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—61no—
600C3×C4—61no—
601C3×C4—61no—
602C3×C4—61no—
603C3×C4—61no—
604C3×C4—61no—
605C3×C4—92no—
606C3×C4—121no—
607C3×C4—121no—
608C3×C4—121no—
609C3×C4—181no—
610C3×C4—181no—
611C3×C4—181no—
612C3×C4—181no—
613C3×C4—181no—
614C3×C4—181no—
615C3×C4—181no—
616C3×C4—181no—
617C3×C4—181no—
618C3×C4—181no—
619Dic3—32no—
620Dic3—32no—
621Dic3—62no—
622Dic3—61no—
623Dic3—61no—
624Dic3—61no—
625Dic3—61no—
626Dic3—61no—
627Dic3—61no—
628Dic3—61no—
629Dic3—61no—
630Dic3—61no—
631Dic3—61no—
632Dic3—61no—
633Dic3—61no—
634Dic3—121no—
635Dic3—121no—
636Dic3—181no—
637Dic3—181no—
638Dic3—181no—
639Dic3—181no—
640Dic3—181no—
641Dic3—181no—
642Dic3—181no—
643Dic3—181no—
644C32—21no—
645C32#569611yescharacteristic, complemented
646C32#569611yescharacteristic, complemented
647C23—91no—
648Q8—182no—
649Q8—542no—
650C2×C4—91no—
651C2×C4—91no—
652C2×C4—91no—
653C2×C4—91no—
654C2×C4—91no—
655C2×C4—91no—
656C2×C4—91no—
657C2×C4—91no—
658C2×C4—91no—
659C2×C4—91no—
660C2×C4—91no—
661C2×C4—182no—
662C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
663C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
664C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
665C2×C3—31no—
666C2×C3—31no—
667C2×C3—31no—
668C2×C3—31no—
669C2×C3—31no—
670C2×C3—31no—
671C2×C3—61no—
672C2×C3—61no—
673C2×C3—61no—
674C2×C3—361no—
675C2×C3#6429711yescharacteristic
676C2×C3#6431211yescharacteristic
677C2×C3#6431511yescharacteristic
678D3—121no—
679D3—121no—
680D3—122no—
681C22—181no—
682C22—181no—
683C22—181no—
684C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
685C4—21no—
686C4—21no—
687C4—21no—
688C4—92no—
689C4—181no—
690C4—181no—
691C4—181no—
692C4—181no—
693C4—181no—
694C4—181no—
695C4—181no—
696C4—181no—
697C4—181no—
698C4—181no—
699C3—31no—
700C3—31no—
701C3—61no—
702C3#1059432311yescharacteristic
703C2—361no—
704C2#1172248211yescharacteristic
705C2#1172250511yescharacteristic
706C2#1172251611yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC4⋊C4×H(3,𝔽3)C22
prime radicalC22×#272C23
hypercenterC4⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#541
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. #64099⋊C3C2semidirect
3. #64098⋊C3C2semidirect
10. #11721087C2semidirect
11. #11721086C2semidirect
12. #11721086C2semidirect
13. #11721083C2semidirect
14. #11721080C2semidirect
15. #11721077C2semidirect
53. #64099D3semidirect
54. #64098D3semidirect
469. H(3,𝔽3)#541semidirect
645. C32#5696semidirect
646. C32#5696semidirect

Maximal subgroups

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

subgroupindex
#117217642
#64099⋊C32
#64098⋊C32
#117210962
#117210922
#117210892
#117210882
#117210872
#117210862
#117210832
#117210802
#117210772
#105943363
#105943193