Finite Group Databasebeta

← #13148690

Subgroups — #13148690

Order 1728.

1012 conjugacy classes of subgroups.

The subgroup lattice has 953 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721738C211yesmaximal, characteristic, complemented
2#64093⋊C3C211yesmaximal, characteristic, complemented
3#64088⋊C3C211yesmaximal, characteristic, complemented
4#11721323C211yesmaximal, characteristic, complemented
5#11721323C211yesmaximal, characteristic, complemented
6#11721312C211yesmaximal, characteristic, complemented
7#11721303C211yesmaximal, characteristic, complemented
8#11721158C211yesmaximal, characteristic, complemented
9#11721157C211yesmaximal, characteristic, complemented
10#11721156C211yesmaximal, characteristic, complemented
11#11721151C211yesmaximal, characteristic, complemented
12#11721130C211yesmaximal, characteristic, complemented
13#11721127C211yesmaximal, characteristic, complemented
14#11721100C211yesmaximal, characteristic, complemented
15#11721092C211yesmaximal, characteristic, complemented
16#10594236—31nomaximal
17#10594234—31nomaximal
18C23×#272C2211yescharacteristic
19C2×#6235C2211yescharacteristic
20C2×C4⋊#272C2211yescharacteristic
21C2×C4⋊#272C2211yescharacteristic
22C2×#638⋊C3C2211yescharacteristic
23C2×#638⋊C3C2211yescharacteristic
24C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
26C2×#6200C2211yescharacteristic
27C2×#6200C2211yescharacteristic
28C2×#6200C2211yescharacteristic
29C2×#6200C2211yescharacteristic
30C2×#6200C2211yescharacteristic, complemented
31C2×#6200C2211yescharacteristic, complemented
32C2×#6199C2211yescharacteristic, complemented
33C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
34C22⋊C4×H(3,𝔽3)C2211yescharacteristic
35#88542C2211yescharacteristic
36#88542C2211yescharacteristic
37#3757⋊C3C2211yescharacteristic
38#3757⋊C3C2211yescharacteristic
39#3752⋊C3C2211yescharacteristic, complemented
40C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
41#3750⋊C3C2211yescharacteristic, complemented
42#3750⋊C3C2211yescharacteristic, complemented
43#3750⋊C3C2211yescharacteristic, complemented
44C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
45#88451C2211yescharacteristic
46#88451C2211yescharacteristic
47#88451C2211yescharacteristic
48#88451C2211yescharacteristic
49#88451C2211yescharacteristic, complemented
50#88450C2211yescharacteristic, complemented
51#88449C2211yescharacteristic, complemented
52#88448C2211yescharacteristic, complemented
53#64093D311yescharacteristic, complemented
54#64088D311yescharacteristic, complemented
55C3×#884—31no—
56C3×#882—31no—
57C3×#882—31no—
58C3×#882—61no—
59C3×#879—31no—
60#63977—31no—
61#63977—31no—
62#63976—31no—
63#63976—31no—
64#63971—31no—
65#63970—31no—
66#63970—31no—
67#63958—31no—
68#63916—31no—
69#63914—31no—
70#63911—31no—
71#63910—31no—
72#63908—31no—
73#63905—31no—
74#63891—31no—
75#63886—31no—
76#63885—31no—
77#63885—31no—
78#63884—31no—
79#63884—31no—
80#63862—31no—
81#63859—31no—
82#63854—31no—
83#63853—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×#272—41no—
86C22×#272—41no—
87C22×#272—41no—
88C22×#272C2311yescharacteristic
89C22×#272C2311yescharacteristic
90C22×#272C2311yescharacteristic
91C22×(C3⋊D3)⋊C3C2311yescharacteristic
92C22×(C3⋊D3)⋊C3C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94C2×C4×H(3,𝔽3)C2311yescharacteristic
95#6235—41no—
96C2×#1084C2311yescharacteristic
97C4⋊#272—41no—
98C4⋊#272—41no—
99#638⋊C3—41no—
100#638⋊C3—41no—
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C4⋊((C3⋊D3)⋊C3)—41no—
108C4×(C3⋊D3)⋊C3—41no—
109#6200—41no—
110#6200—41no—
111#6200—41no—
112#6200—41no—
113#6200—41no—
114#6200—41no—
115#6199—41no—
116((C3⋊D3)⋊C3)⋊C4—41no—
117#5711—91no—
118#5620—91no—
119#5595—91no—
120C23×C3×D3—31no—
121C23×C3×D3—31no—
122C23×C3×D3—61no—
123C2×#638C2×D311yescharacteristic
124C2×#638C2×D311yescharacteristic
125C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
126C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
127C2×C3×#67—31no—
128C2×C3×#67—31no—
129C2×C3×#67—31no—
130C2×C3×#67—31no—
131C2×C3×#67—61no—
132C2×C3×D12—31no—
133C2×C3×D12—31no—
134C2×C3×D12—31no—
135C2×C3×D12—31no—
136C2×C3×D12—31no—
137C2×C3×D12—61no—
138C2×C3×D12—61no—
139C2×C3×C4×D3—31no—
140C2×#626—31no—
141C2×#626—31no—
142C2×#626—31no—
143C2×#626—31no—
144C2×#626—31no—
145C2×#626—31no—
146C2×#625—31no—
147C2×#625—31no—
148C2×#625—31no—
149C2×#625—31no—
150C2×#625—31no—
151C2×#625—31no—
152C2×#624—31no—
153C2×D3×Dic3—31no—
154C2×D3×Dic3—31no—
155C2×D3×Dic3—31no—
156C32×C22⋊C4—21no—
157C32×C22⋊C4C2×D311yescharacteristic
158C32×C22⋊C4C2×D311yescharacteristic
159#3757C2×D311yescharacteristic
160#3757C2×D311yescharacteristic
161#3752C2×D311yescharacteristic, complemented
162C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
163#3750C2×D311yescharacteristic, complemented
164#3750C2×D311yescharacteristic, complemented
165#3750C2×D311yescharacteristic, complemented
166C4×C3⋊Dic3C2×D311yescharacteristic, complemented
167C3×#217—31no—
168C3×#217—31no—
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4—31no—
171C3×(C2×D3)⋊C4—31no—
172C3×(C2×D3)⋊C4—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4—61no—
175C3×(C2×D3)⋊C4—61no—
176C3×C4⋊Dic3—31no—
177C3×Dic3⋊C4—31no—
178C3×Dic3⋊C4—31no—
179C3×Dic3⋊C4—31no—
180C3×C4×Dic3—31no—
181#3724—31no—
182Dic3⋊Dic3—31no—
183Dic3⋊Dic3—31no—
184Dic3⋊Dic3—31no—
185#3722—31no—
186(C2×D3)⋊Dic3—31no—
187(C2×D3)⋊Dic3—31no—
188(C2×D3)⋊Dic3—31no—
189(C2×D3)⋊Dic3—31no—
190(C2×D3)⋊Dic3—31no—
191(C2×D3)⋊Dic3—31no—
192(C2×D3)⋊Dic3—31no—
193(C2×D3)⋊Dic3—31no—
194(C2×D3)⋊Dic3—31no—
195(C2×D3)⋊Dic3—31no—
196(C2×D3)⋊Dic3—31no—
197C22×H(3,𝔽3)—21no—
198C22×H(3,𝔽3)—21no—
199C22×H(3,𝔽3)—21no—
200C22×H(3,𝔽3)C2411yescharacteristic
201C2×#272—21no—
202C2×#272—21no—
203C2×#272—21no—
204C2×#272—21no—
205C2×#272—21no—
206C2×#272—21no—
207C2×#272—21no—
208C2×#272—21no—
209C2×#272—21no—
210C2×#272—44no—
211C2×(C3⋊D3)⋊C3—21no—
212C2×(C3⋊D3)⋊C3—21no—
213C2×(C3⋊D3)⋊C3—21no—
214C2×(C3⋊D3)⋊C3—21no—
215C2×(C3⋊D3)⋊C3—21no—
216C2×(C3⋊D3)⋊C3—21no—
217C4×H(3,𝔽3)—21no—
218C4×H(3,𝔽3)—21no—
219#1084—21no—
220(C3⋊Dic3)⋊C3—21no—
221(C3⋊Dic3)⋊C3—21no—
222(C3⋊Dic3)⋊C3—21no—
223(C3⋊Dic3)⋊C3—21no—
224(C3⋊Dic3)⋊C3—21no—
225(C3⋊Dic3)⋊C3—21no—
226C3×#126—91no—
227C3×#121—91no—
228C3×#120—91no—
229#953—91no—
230#953—91no—
231#940—91no—
232#940—91no—
233#939—91no—
234#939—91no—
235#939—91no—
236#939—91no—
237#938—91no—
238#938—91no—
239#938—91no—
240#937—91no—
241#937—91no—
242#935—91no—
243#930—91no—
244#929—91no—
245#898—91no—
246#895—91no—
247#895—91no—
248#895—91no—
249#894—91no—
250#894—91no—
251#894—91no—
252#894—91no—
253#886—91no—
254#884—31no—
255#884—91no—
256#884—91no—
257#884—91no—
258#884—91no—
259#884—91no—
260#883—91no—
261#883—91no—
262#882—31no—
263#882—31no—
264#882—61no—
265#882—91no—
266#882—91no—
267#879—31no—
268#879—91no—
269#879—91no—
270#876—91no—
271#874—91no—
272C23×C32—21no—
273C23×C32C22×D311yescharacteristic
274C23×C32C22×D311yescharacteristic
275C22×C3⋊D3C22×D311yescharacteristic
276C22×C3⋊D3C22×D311yescharacteristic
277C22×C3×D3—31no—
278C22×C3×D3—31no—
279C22×C3×D3—31no—
280C22×C3×D3—31no—
281C22×C3×D3—31no—
282C22×C3×D3—31no—
283C22×C3×D3—31no—
284C22×C3×D3—31no—
285C22×C3×D3—61no—
286C22×C3×D3—61no—
287C22×C3×D3—61no—
288C22×C3×D3—121no—
289C22×C3×D3—121no—
290C22×C3×D3—121no—
291C22×C3×D3—121no—
292C22×C3×D3—121no—
293C22×C3×D3—121no—
294C22×C3×D3—122no—
295C22×C3×D3—122no—
296C22×C3×D3—122no—
297C2×C32×C4—21no—
298C2×C32×C4—21no—
299C2×C32×C4C22×D311yescharacteristic
300C2×C32×C4C22×D311yescharacteristic
301C2×C32×C4C22×D311yescharacteristic
302C2×C32×C4C22×D311yescharacteristic
303#638—41no—
304#638—41no—
305C2×C3⋊Dic3C22×D311yescharacteristic
306C2×C3⋊Dic3C22×D311yescharacteristic
307C2×C3⋊Dic3C22×D311yescharacteristic
308C2×C3⋊Dic3C22×D311yescharacteristic
309C2×C3⋊Dic3C22×D311yescharacteristic
310C2×C3⋊Dic3C22×D311yescharacteristic
311C4⋊(C3⋊D3)—41no—
312C4×C3⋊D3—41no—
313C3×#67—121no—
314C3×#67—121no—
315C3×#67—121no—
316C3×#67—121no—
317C3×#67—122no—
318C2×C3×Dic3—31no—
319C2×C3×Dic3—31no—
320C2×C3×Dic3—31no—
321C2×C3×Dic3—31no—
322C2×C3×Dic3—31no—
323C2×C3×Dic3—31no—
324C2×C3×Dic3—31no—
325C2×C3×Dic3—31no—
326C2×C3×Dic3—61no—
327C3×D12—121no—
328C3×D12—121no—
329C3×D12—121no—
330C3×D12—121no—
331C3×D12—121no—
332C3×D12—122no—
333C3×D12—122no—
334C3×C4×D3—121no—
335#626—121no—
336#626—121no—
337#626—121no—
338#626—121no—
339#626—121no—
340#626—121no—
341#625—121no—
342#625—121no—
343#625—121no—
344#625—121no—
345#625—121no—
346#625—121no—
347#624—121no—
348D3×Dic3—121no—
349D3×Dic3—121no—
350D3×Dic3—121no—
351#560—271noSylow
352C2×H(3,𝔽3)—41no—
353C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
354C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
355C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
356#272—41no—
357#272—41no—
358#272—41no—
359(C3⋊D3)⋊C3—41no—
360(C3⋊D3)⋊C3—41no—
361C24×C3—91no—
362C23×D3—31no—
363C23×D3—31no—
364C23×D3—61no—
365C2×C3×D4—91no—
366C2×C3×D4—91no—
367C2×C3×D4—91no—
368C2×C3×D4—91no—
369C2×C3×D4—91no—
370C2×C3×D4—91no—
371C22×C3×C4—91no—
372C2×#67—31no—
373C2×#67—31no—
374C2×#67—31no—
375C2×#67—31no—
376C2×#67—61no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—91no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—91no—
387C2×#67—91no—
388C2×#67—91no—
389C2×#67—91no—
390C2×#67—91no—
391C22×Dic3—91no—
392C22×Dic3—91no—
393C2×D12—31no—
394C2×D12—31no—
395C2×D12—31no—
396C2×D12—31no—
397C2×D12—31no—
398C2×D12—61no—
399C2×D12—61no—
400C2×D12—91no—
401C2×D12—91no—
402C2×D12—91no—
403C2×D12—91no—
404C2×D12—91no—
405C2×D12—91no—
406C2×D12—91no—
407C2×C4×D3—31no—
408C2×C4×D3—91no—
409C2×C4×D3—91no—
410C2×C4×D3—91no—
411C2×C4×D3—91no—
412C2×C4×D3—91no—
413C3×C4⋊C4—91no—
414C3×C4⋊C4—91no—
415C3×C4⋊C4—91no—
416C3×C4⋊C4—91no—
417C3×C22⋊C4—31no—
418C3×C22⋊C4—31no—
419C3×C22⋊C4—61no—
420C3×C22⋊C4—91no—
421C3×C22⋊C4—91no—
422C3×C22⋊C4—91no—
423C3×C22⋊C4—91no—
424C3×C22⋊C4—91no—
425C3×C22⋊C4D3211yescharacteristic
426C3×C42—91no—
427#217—31no—
428#217—31no—
429#217—91no—
430#217—91no—
431#217—91no—
432#217—91no—
433#217—91no—
434#217—91no—
435#217—91no—
436#217—91no—
437(C2×D3)⋊C4—31no—
438(C2×D3)⋊C4—31no—
439(C2×D3)⋊C4—31no—
440(C2×D3)⋊C4—31no—
441(C2×D3)⋊C4—31no—
442(C2×D3)⋊C4—61no—
443(C2×D3)⋊C4—61no—
444(C2×D3)⋊C4—91no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—91no—
447(C2×D3)⋊C4—91no—
448(C2×D3)⋊C4—91no—
449(C2×D3)⋊C4—91no—
450(C2×D3)⋊C4—91no—
451(C2×D3)⋊C4—91no—
452(C2×D3)⋊C4—91no—
453(C2×D3)⋊C4—91no—
454(C2×D3)⋊C4—91no—
455(C2×D3)⋊C4—91no—
456(C2×D3)⋊C4—91no—
457C4⋊Dic3—31no—
458C4⋊Dic3—91no—
459C4⋊Dic3—91no—
460C4⋊Dic3—91no—
461Dic3⋊C4—31no—
462Dic3⋊C4—31no—
463Dic3⋊C4—31no—
464Dic3⋊C4—91no—
465Dic3⋊C4—91no—
466Dic3⋊C4—91no—
467Dic3⋊C4—91no—
468Dic3⋊C4—91no—
469Dic3⋊C4—91no—
470Dic3⋊C4—91no—
471C4×Dic3—31no—
472C4×Dic3—91no—
473C22×C32—22no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32—21no—
479C22×C32—21no—
480C22×C32—21no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32C23×D311yescharacteristic
484C22×C32C23×D311yescharacteristic
485C2×C3⋊D3—21no—
486C2×C3⋊D3—21no—
487C2×C3⋊D3—21no—
488C2×C3⋊D3—21no—
489C2×C3⋊D3—21no—
490C2×C3⋊D3—21no—
491C2×C3×D3—62no—
492C2×C3×D3—62no—
493C2×C3×D3—61no—
494C2×C3×D3—61no—
495C2×C3×D3—61no—
496C2×C3×D3—61no—
497C2×C3×D3—61no—
498C2×C3×D3—61no—
499C2×C3×D3—61no—
500C2×C3×D3—61no—
501C2×C3×D3—61no—
502C2×C3×D3—61no—
503C2×C3×D3—61no—
504C2×C3×D3—61no—
505C2×C3×D3—61no—
506C2×C3×D3—61no—
507C2×C3×D3—61no—
508C2×C3×D3—61no—
509C2×C3×D3—61no—
510C2×C3×D3—61no—
511C2×C3×D3—61no—
512C2×C3×D3—61no—
513C2×C3×D3—61no—
514C2×C3×D3—61no—
515C2×C3×D3—61no—
516C2×C3×D3—61no—
517C2×C3×D3—121no—
518C2×C3×D3—121no—
519C2×C3×D3—121no—
520C2×C3×D3—121no—
521C2×C3×D3—121no—
522C2×C3×D3—121no—
523C2×C3×D3—121no—
524C2×C3×D3—128no—
525C2×C3×D3—124no—
526C2×C3×D3—124no—
527C32×C4—21no—
528C32×C4—21no—
529C32×C4—21no—
530C32×C4—21no—
531C32×C4—41no—
532C32×C4—41no—
533C3⋊Dic3—21no—
534C3⋊Dic3—21no—
535C3⋊Dic3—21no—
536C3⋊Dic3—21no—
537C3⋊Dic3—21no—
538C3⋊Dic3—21no—
539C3×Dic3—61no—
540C3×Dic3—61no—
541C3×Dic3—61no—
542C3×Dic3—61no—
543C3×Dic3—61no—
544C3×Dic3—61no—
545C3×Dic3—61no—
546C3×Dic3—61no—
547C3×Dic3—121no—
548#127—271no—
549#126—91no—
550#126—271no—
551#123—271no—
552#123—271no—
553#123—271no—
554#121—91no—
555#121—271no—
556#121—271no—
557#121—271no—
558#121—271no—
559#121—271no—
560#120—91no—
561#120—271no—
562#120—271no—
563H(3,𝔽3)#56011yescharacteristic, complemented, Sylow
564C23×C3—31no—
565C23×C3—31no—
566C23×C3—61no—
567C23×C3—91no—
568C23×C3—91no—
569C23×C3—91no—
570C23×C3—91no—
571C23×C3—91no—
572C23×C3—361no—
573C23×C3—361no—
574C23×C3—361no—
575C23×C3C2×D3211yescharacteristic
576C22×D3—31no—
577C22×D3—31no—
578C22×D3—31no—
579C22×D3—31no—
580C22×D3—31no—
581C22×D3—31no—
582C22×D3—31no—
583C22×D3—31no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—61no—
587C22×D3—91no—
588C22×D3—91no—
589C22×D3—121no—
590C22×D3—121no—
591C22×D3—121no—
592C22×D3—121no—
593C22×D3—121no—
594C22×D3—121no—
595C22×D3—122no—
596C22×D3—122no—
597C22×D3—122no—
598C3×D4—361no—
599C3×D4—361no—
600C3×D4—361no—
601C3×D4—361no—
602C3×D4—361no—
603C3×D4—361no—
604C2×C3×C4—31no—
605C2×C3×C4—31no—
606C2×C3×C4—31no—
607C2×C3×C4—31no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—91no—
611C2×C3×C4—91no—
612C2×C3×C4—91no—
613C2×C3×C4—91no—
614C2×C3×C4—91no—
615C2×C3×C4—91no—
616C2×C3×C4—91no—
617C2×C3×C4—361no—
618C2×C3×C4C2×D3211yescharacteristic
619C2×C3×C4C2×D3211yescharacteristic
620#67—121no—
621#67—121no—
622#67—121no—
623#67—121no—
624#67—122no—
625#67—361no—
626#67—361no—
627#67—361no—
628#67—361no—
629#67—361no—
630#67—361no—
631#67—361no—
632#67—361no—
633#67—361no—
634#67—361no—
635#67—361no—
636#67—361no—
637#67—361no—
638#67—361no—
639C2×Dic3—31no—
640C2×Dic3—31no—
641C2×Dic3—31no—
642C2×Dic3—31no—
643C2×Dic3—31no—
644C2×Dic3—31no—
645C2×Dic3—31no—
646C2×Dic3—31no—
647C2×Dic3—61no—
648C2×Dic3—91no—
649C2×Dic3—91no—
650C2×Dic3—91no—
651C2×Dic3—91no—
652C2×Dic3—91no—
653C2×Dic3—91no—
654C2×Dic3—361no—
655C2×Dic3—361no—
656D12—121no—
657D12—121no—
658D12—121no—
659D12—121no—
660D12—121no—
661D12—122no—
662D12—122no—
663D12—361no—
664D12—361no—
665D12—361no—
666D12—361no—
667D12—361no—
668D12—361no—
669D12—361no—
670C4×D3—121no—
671C4×D3—361no—
672C4×D3—361no—
673C4×D3—361no—
674C4×D3—361no—
675C4×D3—361no—
676C2×C32—21no—
677C2×C32—21no—
678C2×C32—21no—
679C2×C32—42no—
680C2×C32—41no—
681C2×C32—41no—
682C2×C32#100411yescharacteristic
683C2×C32#100411yescharacteristic
684C2×C32#100911yescharacteristic
685C2×C32#100911yescharacteristic
686C2×C32#100911yescharacteristic
687C2×C32#100911yescharacteristic
688C3⋊D3—41no—
689C3⋊D3—41no—
690C3×D3—122no—
691C3×D3—122no—
692C3×D3—121no—
693C3×D3—121no—
694C3×D3—121no—
695C3×D3—121no—
696C3×D3—121no—
697C3×D3—121no—
698C3×D3—121no—
699C3×D3—121no—
700C3×D3—241no—
701C24—91no—
702C2×D4—91no—
703C2×D4—91no—
704C2×D4—91no—
705C2×D4—91no—
706C2×D4—91no—
707C2×D4—91no—
708C2×D4—271no—
709C2×D4—271no—
710C2×D4—271no—
711C2×D4—271no—
712C2×D4—271no—
713C2×D4—271no—
714C22×C4—91no—
715C22×C4—271no—
716C22×C4—271no—
717C4⋊C4—91no—
718C4⋊C4—91no—
719C4⋊C4—91no—
720C4⋊C4—91no—
721C4⋊C4—271no—
722C4⋊C4—271no—
723C22⋊C4—91no—
724C22⋊C4—91no—
725C22⋊C4—91no—
726C22⋊C4—91no—
727C22⋊C4—91no—
728C22⋊C4—271no—
729C22⋊C4—271no—
730C22⋊C4—271no—
731C22⋊C4—271no—
732C22⋊C4—271no—
733C22⋊C4—271no—
734C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
735C42—91no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—31no—
740C22×C3—31no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3—62no—
748C22×C3—61no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—181no—
752C22×C3—181no—
753C22×C3—181no—
754C22×C3—181no—
755C22×C3—181no—
756C22×C3—181no—
757C22×C3—181no—
758C22×C3—181no—
759C22×C3—181no—
760C22×C3—181no—
761C22×C3—181no—
762C22×C3—181no—
763C22×C3—181no—
764C22×C3—181no—
765C22×C3—181no—
766C22×C3—364no—
767C22×C3C22×D3211yescharacteristic
768C2×D3—61no—
769C2×D3—61no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—61no—
778C2×D3—61no—
779C2×D3—61no—
780C2×D3—61no—
781C2×D3—61no—
782C2×D3—61no—
783C2×D3—61no—
784C2×D3—61no—
785C2×D3—61no—
786C2×D3—62no—
787C2×D3—62no—
788C2×D3—61no—
789C2×D3—61no—
790C2×D3—61no—
791C2×D3—61no—
792C2×D3—61no—
793C2×D3—61no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—121no—
798C2×D3—121no—
799C2×D3—121no—
800C2×D3—121no—
801C2×D3—124no—
802C2×D3—124no—
803C2×D3—128no—
804C2×D3—181no—
805C2×D3—181no—
806C2×D3—181no—
807C2×D3—181no—
808C2×D3—181no—
809C2×D3—181no—
810C3×C4—21no—
811C3×C4—21no—
812C3×C4—61no—
813C3×C4—61no—
814C3×C4—61no—
815C3×C4—61no—
816C3×C4—121no—
817C3×C4—121no—
818C3×C4—181no—
819C3×C4—181no—
820C3×C4—181no—
821C3×C4—181no—
822C3×C4—181no—
823C3×C4—181no—
824C3×C4—181no—
825Dic3—61no—
826Dic3—61no—
827Dic3—61no—
828Dic3—61no—
829Dic3—61no—
830Dic3—61no—
831Dic3—61no—
832Dic3—61no—
833Dic3—121no—
834Dic3—181no—
835Dic3—181no—
836Dic3—181no—
837Dic3—181no—
838Dic3—181no—
839Dic3—181no—
840C32—21no—
841C32#562011yescharacteristic, complemented
842C32#571111yescharacteristic, complemented
843C23—91no—
844C23—91no—
845C23—91no—
846C23—91no—
847C23—91no—
848C23—361no—
849C23—361no—
850C23—361no—
851C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
852D4—361no—
853D4—361no—
854D4—361no—
855D4—361no—
856D4—361no—
857D4—361no—
858D4—1081no—
859D4—1081no—
860D4—1081no—
861D4—1081no—
862D4—1081no—
863D4—1081no—
864C2×C4—91no—
865C2×C4—91no—
866C2×C4—91no—
867C2×C4—91no—
868C2×C4—91no—
869C2×C4—91no—
870C2×C4—91no—
871C2×C4—361no—
872C2×C4—1081no—
873C2×C4—1081no—
874C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
875C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
876C2×C3—31no—
877C2×C3—31no—
878C2×C3—31no—
879C2×C3—31no—
880C2×C3—31no—
881C2×C3—31no—
882C2×C3—41no—
883C2×C3—61no—
884C2×C3—61no—
885C2×C3—61no—
886C2×C3—121no—
887C2×C3—121no—
888C2×C3—122no—
889C2×C3—361no—
890C2×C3—361no—
891C2×C3—361no—
892C2×C3—361no—
893C2×C3—361no—
894C2×C3#6430811yescharacteristic
895C2×C3#6431411yescharacteristic
896C2×C3#6431411yescharacteristic
897D3—121no—
898D3—121no—
899D3—121no—
900D3—121no—
901D3—121no—
902D3—121no—
903D3—122no—
904D3—122no—
905D3—121no—
906D3—121no—
907D3—241no—
908D3—361no—
909D3—361no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—181no—
914C22—181no—
915C22—181no—
916C22—181no—
917C22—181no—
918C22—181no—
919C22—181no—
920C22—181no—
921C22—181no—
922C22—181no—
923C22—181no—
924C22—181no—
925C22—181no—
926C22—181no—
927C22—181no—
928C22—364no—
929C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
930C4—21no—
931C4—21no—
932C4—181no—
933C4—181no—
934C4—181no—
935C4—181no—
936C4—181no—
937C4—181no—
938C4—181no—
939C3—31no—
940C3—31no—
941C3—61no—
942C3#1059424211yescharacteristic
943C2—41no—
944C2—361no—
945C2—361no—
946C2—361no—
947C2—361no—
948C2—361no—
949C2#1172249311yescharacteristic
950C2#1172250711yescharacteristic
951C2#1172250711yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC22⋊C4×H(3,𝔽3)C22
hypercenterC22⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#560
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. #11721738C2semidirect
2. #64093⋊C3C2semidirect
3. #64088⋊C3C2semidirect
4. #11721323C2semidirect
5. #11721323C2semidirect
6. #11721312C2semidirect
7. #11721303C2semidirect
8. #11721158C2semidirect
9. #11721157C2semidirect
10. #11721156C2semidirect
11. #11721151C2semidirect
12. #11721130C2semidirect
13. #11721127C2semidirect
14. #11721100C2semidirect
15. #11721092C2semidirect
24. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
25. C2×C4×(C3⋊D3)⋊C3C22semidirect
30. C2×#6200C22semidirect
31. C2×#6200C22semidirect
32. C2×#6199C22semidirect
33. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
39. #3752⋊C3C22semidirect
40. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
41. #3750⋊C3C22semidirect
42. #3750⋊C3C22semidirect
43. #3750⋊C3C22semidirect
44. C4×(C3⋊Dic3)⋊C3C22semidirect
49. #88451C22semidirect
50. #88450C22semidirect
51. #88449C22semidirect
52. #88448C22semidirect
53. #64093D3semidirect
54. #64088D3semidirect
125. C2×C4⋊(C3⋊D3)C2×D3semidirect
126. C2×C4×C3⋊D3C2×D3semidirect
161. #3752C2×D3semidirect
162. C4⋊(C3⋊Dic3)C2×D3semidirect
163. #3750C2×D3semidirect
164. #3750C2×D3semidirect
165. #3750C2×D3semidirect
166. C4×C3⋊Dic3C2×D3semidirect
563. H(3,𝔽3)#560semidirect
841. C32#5620semidirect
842. C32#5711semidirect

Maximal subgroups

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

subgroupindex
#117217382
#64093⋊C32
#64088⋊C32
#117213232
#117213122
#117213032
#117211582
#117211572
#117211562
#117211512
#117211302
#117211272
#117211002
#117210922
#105942363
#105942343