Finite Group Databasebeta

← #13150898

Subgroups — #13150898

Order 1728.

969 conjugacy classes of subgroups.

The subgroup lattice has 899 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721830C211yesmaximal, characteristic, complemented
2#64138⋊C3C211yesmaximal, characteristic, complemented
3C4×#638⋊C3C211yesmaximal, characteristic, complemented
4#11721324C211yesmaximal, characteristic, complemented
5#11721312C211yesmaximal, characteristic, complemented
6#11721303C211yesmaximal, characteristic, complemented
7#11721294C211yesmaximal, characteristic, complemented
8#11721163C211yesmaximal, characteristic, complemented
9#11721160C211yesmaximal, characteristic, complemented
10#11721154C211yesmaximal, characteristic, complemented
11#11721151C211yesmaximal, characteristic, complemented
12#11721133C211yesmaximal, characteristic, complemented
13#11721111C211yesmaximal, characteristic, complemented
14#11721103C211yesmaximal, characteristic, complemented
15#11721092C211yesmaximal, characteristic, complemented
16#10595089—31nomaximal
17#10595086—31nomaximal
18C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
19C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
20C2×#6235C2211yescharacteristic
21C2×#6235C2211yescharacteristic, complemented
22C2×C4⋊#272C2211yescharacteristic
23C2×#638⋊C3C2211yescharacteristic
24C2×#638⋊C3C2211yescharacteristic
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
26C2×#6200C2211yescharacteristic
27C2×#6200C2211yescharacteristic
28C2×#6199C2211yescharacteristic, complemented
29C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
30C2×#6196C2211yescharacteristic, complemented
31#88542C2211yescharacteristic
32#88542C2211yescharacteristic, complemented
33C4⋊#1084C2211yescharacteristic, complemented
34#3757⋊C3C2211yescharacteristic, complemented
35#3757⋊C3C2211yescharacteristic, complemented
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38#3752⋊C3C2211yescharacteristic
39#3750⋊C3C2211yescharacteristic, complemented
40#3750⋊C3C2211yescharacteristic, complemented
41#3750⋊C3C2211yescharacteristic, complemented
42C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
43#88451C2211yescharacteristic
44#88451C2211yescharacteristic
45#88451C2211yescharacteristic
46#88451C2211yescharacteristic, complemented
47#88450C2211yescharacteristic
48#88450C2211yescharacteristic
49#88450C2211yescharacteristic
50#88449C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53#64138D311yescharacteristic, complemented
54C4×#638D311yescharacteristic, complemented
55C3×#930—31no—
56C3×#930—31no—
57C3×#930—61no—
58C3×#929—31no—
59C3×C4×#67—31no—
60#63983—31no—
61#63983—31no—
62#63971—31no—
63#63970—31no—
64#63970—31no—
65#63959—31no—
66#63959—31no—
67#63958—31no—
68#63922—31no—
69#63922—31no—
70#63921—31no—
71D3×(C2×D3)⋊C4—31no—
72#63915—31no—
73#63899—31no—
74#63895—31no—
75#63884—31no—
76#63884—31no—
77#63881—31no—
78#63879—31no—
79#63862—31no—
80#63859—31no—
81#63858—31no—
82#63852—31no—
83#63848—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×#272C2311yescharacteristic
86C22×#272C2311yescharacteristic
87C22×(C3⋊D3)⋊C3C2311yescharacteristic
88C22×(C3⋊D3)⋊C3C2311yescharacteristic
89C2×((C3⋊D3)⋊C3)⋊C2—22no—
90C2×((C3⋊D3)⋊C3)⋊C2—41no—
91C2×((C3⋊D3)⋊C3)⋊C2—41no—
92C2×C4×H(3,𝔽3)—41no—
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94C2×C4×H(3,𝔽3)C2311yescharacteristic
95#6235—41no—
96#6235—41no—
97C2×#1084C2311yescharacteristic
98C2×#1084C2311yescharacteristic
99C4⋊#272—41no—
100#638⋊C3—22no—
101#638⋊C3—41no—
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
108C4×(C3⋊D3)⋊C3—41no—
109#6200—22no—
110#6200—41no—
111#6199—41no—
112((C3⋊D3)⋊C3)⋊C4—41no—
113#6196—41no—
114#5657—91no—
115#5613—91no—
116#5560—91no—
117C22×D32—31no—
118C22×D32—31no—
119C22×C32×C4—21no—
120C22×C32×C4C2×D311yescharacteristic, complemented
121C22×C32×C4C2×D311yescharacteristic, complemented
122C2×#638C2×D311yescharacteristic
123C2×#638C2×D311yescharacteristic
124C2×C4×C3⋊D3C2×D311yescharacteristic
125C2×C3×#67—31no—
126C2×C3×#67—31no—
127C2×C3×#67—31no—
128C2×C3×#67—31no—
129C2×C3×#67—31no—
130C2×C3×#67—31no—
131C2×C3×#67—61no—
132C2×C3×#67—61no—
133C2×C3×D12—31no—
134C2×C3×D12—31no—
135C2×C3×D12—61no—
136C2×C3×C4×D3—31no—
137C2×#627—31no—
138C2×#627—31no—
139C2×#626—31no—
140C2×#626—31no—
141C2×#625—31no—
142C2×#625—31no—
143C2×#624—31no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—31no—
146C2×D3×Dic3—31no—
147#3757C2×D311yescharacteristic, complemented
148#3757C2×D311yescharacteristic, complemented
149#3752C2×D311yescharacteristic
150#3752C2×D311yescharacteristic
151#3752C2×D311yescharacteristic
152#3750C2×D311yescharacteristic, complemented
153#3750C2×D311yescharacteristic, complemented
154#3750C2×D311yescharacteristic, complemented
155C4×C3⋊Dic3C2×D311yescharacteristic, complemented
156C3×#217—31no—
157C3×#217—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4—31no—
160C3×(C2×D3)⋊C4—31no—
161C3×(C2×D3)⋊C4—31no—
162C3×(C2×D3)⋊C4—31no—
163C3×(C2×D3)⋊C4—31no—
164C3×(C2×D3)⋊C4—31no—
165C3×(C2×D3)⋊C4—61no—
166C3×(C2×D3)⋊C4—61no—
167C3×C4⋊Dic3—31no—
168C3×C4⋊Dic3—31no—
169C3×C4⋊Dic3—61no—
170C3×Dic3⋊C4—31no—
171C3×Dic3⋊C4—31no—
172C3×Dic3⋊C4—31no—
173C3×C4×Dic3—31no—
174#3724—31no—
175Dic3⋊Dic3—31no—
176Dic3⋊Dic3—31no—
177Dic3⋊Dic3—31no—
178#3722—31no—
179#3722—31no—
180#3722—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—
189(C2×D3)⋊Dic3—31no—
190(C2×D3)⋊Dic3—31no—
191(C2×D3)⋊Dic3—31no—
192Dic32—31no—
193Dic32—31no—
194C22×H(3,𝔽3)—21no—
195C22×H(3,𝔽3)—21no—
196C22×H(3,𝔽3)—21no—
197C22×H(3,𝔽3)C2411yescharacteristic
198C2×#272—21no—
199C2×#272—21no—
200C2×#272—21no—
201C2×#272—21no—
202C2×#272—21no—
203C2×#272—21no—
204C2×(C3⋊D3)⋊C3—21no—
205C2×(C3⋊D3)⋊C3—21no—
206C2×(C3⋊D3)⋊C3—21no—
207C2×(C3⋊D3)⋊C3—21no—
208C2×(C3⋊D3)⋊C3—21no—
209C2×(C3⋊D3)⋊C3#4112yes—
210((C3⋊D3)⋊C3)⋊C2—44no—
211C4×H(3,𝔽3)—21no—
212C4×H(3,𝔽3)—21no—
213#1084—21no—
214#1084—21no—
215(C3⋊Dic3)⋊C3—21no—
216(C3⋊Dic3)⋊C3—21no—
217(C3⋊Dic3)⋊C3—21no—
218(C3⋊Dic3)⋊C3—21no—
219(C3⋊Dic3)⋊C3—21no—
220(C3⋊Dic3)⋊C3—21no—
221C3×#123—91no—
222C3×#121—91no—
223C3×C4×D4—91no—
224#939—91no—
225#939—91no—
226#938—91no—
227#938—91no—
228#937—91no—
229#937—91no—
230#937—91no—
231#937—91no—
232#936—91no—
233#935—91no—
234#930—31no—
235#930—31no—
236#930—61no—
237#929—31no—
238#929—91no—
239C4×#67—31no—
240C4×#67—91no—
241C4×#67—91no—
242C2×(C2×D3)⋊C4—91no—
243#898—91no—
244#898—91no—
245#898—91no—
246#897—91no—
247#896—91no—
248#894—91no—
249#894—91no—
250#893—91no—
251#885—91no—
252#885—91no—
253#885—91no—
254#885—91no—
255#884—91no—
256#884—91no—
257#882—91no—
258#882—91no—
259#67⋊C4—91no—
260D3×C22⋊C4—91no—
261D3×C22⋊C4—91no—
262#879—91no—
263#879—91no—
264#878—91no—
265#876—91no—
266#875—91no—
267C23×C32—21no—
268C23×C32C22×D311yescharacteristic
269C23×C32C22×D311yescharacteristic
270C22×C3⋊D3C22×D311yescharacteristic
271C22×C3⋊D3C22×D311yescharacteristic
272C22×C3×D3—31no—
273C22×C3×D3—31no—
274C22×C3×D3—31no—
275C22×C3×D3—31no—
276C22×C3×D3—31no—
277C22×C3×D3—31no—
278C22×C3×D3—61no—
279C22×C3×D3—61no—
280C2×D32—62no—
281C2×D32—62no—
282C2×D32—121no—
283C2×D32—121no—
284C2×D32—121no—
285C2×D32—121no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—41no—
289C2×C32×C4—41no—
290C2×C32×C4—42no—
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C22×D311yescharacteristic
294C2×C32×C4C22×D311yescharacteristic
295#638—22no—
296#638—41no—
297C2×C3⋊Dic3C22×D311yescharacteristic
298C2×C3⋊Dic3C22×D311yescharacteristic
299C2×C3⋊Dic3C22×D311yescharacteristic
300C2×C3⋊Dic3C22×D311yescharacteristic
301C2×C3⋊Dic3C22×D311yescharacteristic
302C2×C3⋊Dic3C22×D311yescharacteristic
303C4×C3⋊D3—41no—
304C3×#67—62no—
305C3×#67—121no—
306C3×#67—121no—
307C3×#67—121no—
308C3×#67—121no—
309C3×#67—121no—
310C3×#67—122no—
311C3×#67—122no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3—31no—
314C2×C3×Dic3—31no—
315C2×C3×Dic3—31no—
316C2×C3×Dic3—31no—
317C2×C3×Dic3—31no—
318C2×C3×Dic3—31no—
319C2×C3×Dic3—31no—
320C2×C3×Dic3—31no—
321C2×C3×Dic3—31no—
322C2×C3×Dic3—61no—
323C2×C3×Dic3—61no—
324C3×D12—121no—
325C3×D12—121no—
326C3×D12—122no—
327C3×C4×D3—121no—
328#627—121no—
329#627—121no—
330#626—62no—
331#626—121no—
332#625—62no—
333#625—121no—
334#624—121no—
335D3×Dic3—121no—
336D3×Dic3—121no—
337D3×Dic3—121no—
338#538—271noSylow
339C2×H(3,𝔽3)—41no—
340C2×H(3,𝔽3)C2×#4111yescharacteristic
341C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
342C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
343#272—41no—
344#272—41no—
345(C3⋊D3)⋊C3—22no—
346(C3⋊D3)⋊C3—41no—
347C23×D3—91no—
348C23×D3—91no—
349C23×D3—91no—
350C2×C3×D4—91no—
351C2×C3×D4—91no—
352C2×C3×D4—91no—
353C2×C3×D4—91no—
354C2×C3×D4—91no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—61no—
358C22×C3×C4—91no—
359C22×C3×C4D3211yescharacteristic
360C2×#67—31no—
361C2×#67—31no—
362C2×#67—31no—
363C2×#67—31no—
364C2×#67—31no—
365C2×#67—31no—
366C2×#67—61no—
367C2×#67—61no—
368C2×#67—91no—
369C2×#67—91no—
370C2×#67—91no—
371C2×#67—91no—
372C2×#67—91no—
373C2×#67—91no—
374C22×Dic3—91no—
375C22×Dic3—91no—
376C2×D12—31no—
377C2×D12—31no—
378C2×D12—61no—
379C2×D12—91no—
380C2×D12—91no—
381C2×C4×D3—31no—
382C2×C4×D3—91no—
383C2×C4×D3—91no—
384C2×C4×D3—91no—
385C2×C4×D3—91no—
386C2×C4×D3—91no—
387C2×Dic6—91no—
388C2×Dic6—91no—
389C2×Dic6—91no—
390C3×C4⋊C4—91no—
391C3×C4⋊C4—91no—
392C3×C4⋊C4—91no—
393C3×C4⋊C4—91no—
394C3×C22⋊C4—91no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4—91no—
399C3×C22⋊C4—91no—
400C3×C22⋊C4—91no—
401C3×C42—91no—
402#217—31no—
403#217—31no—
404#217—91no—
405#217—91no—
406#217—91no—
407#217—91no—
408#217—91no—
409#217—91no—
410#217—91no—
411#217—91no—
412#217—91no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—31no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—31no—
419(C2×D3)⋊C4—31no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—91no—
423(C2×D3)⋊C4—91no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—91no—
435(C2×D3)⋊C4—91no—
436(C2×D3)⋊C4—91no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—91no—
439C4⋊Dic3—31no—
440C4⋊Dic3—31no—
441C4⋊Dic3—61no—
442C4⋊Dic3—91no—
443C4⋊Dic3—91no—
444Dic3⋊C4—31no—
445Dic3⋊C4—31no—
446Dic3⋊C4—31no—
447Dic3⋊C4—91no—
448Dic3⋊C4—91no—
449Dic3⋊C4—91no—
450Dic3⋊C4—91no—
451Dic3⋊C4—91no—
452Dic3⋊C4—91no—
453Dic3⋊C4—91no—
454C4×Dic3—31no—
455C4×Dic3—91no—
456C4×Dic3—91no—
457C4×Dic3—91no—
458C4×Dic3—91no—
459C22×C32—22no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C23×D311yescharacteristic
470C22×C32C23×D311yescharacteristic
471C2×C3⋊D3—21no—
472C2×C3⋊D3—21no—
473C2×C3⋊D3—21no—
474C2×C3⋊D3—21no—
475C2×C3⋊D3—21no—
476C2×C3⋊D3#23512yes—
477C2×C3×D3—32no—
478C2×C3×D3—61no—
479C2×C3×D3—61no—
480C2×C3×D3—61no—
481C2×C3×D3—61no—
482C2×C3×D3—61no—
483C2×C3×D3—61no—
484C2×C3×D3—61no—
485C2×C3×D3—61no—
486C2×C3×D3—61no—
487C2×C3×D3—61no—
488C2×C3×D3—61no—
489C2×C3×D3—61no—
490C2×C3×D3—61no—
491C2×C3×D3—61no—
492C2×C3×D3—61no—
493C2×C3×D3—61no—
494C2×C3×D3—61no—
495C2×C3×D3—121no—
496C2×C3×D3—121no—
497C2×C3×D3—121no—
498C2×C3×D3—121no—
499C2×C3×D3—121no—
500C2×C3×D3—121no—
501D32—124no—
502D32—124no—
503C32×C4—22no—
504C32×C4—21no—
505C32×C4—21no—
506C32×C4—21no—
507C32×C4—21no—
508C32×C4—41no—
509C3⋊Dic3—21no—
510C3⋊Dic3—21no—
511C3⋊Dic3—21no—
512C3⋊Dic3—21no—
513C3⋊Dic3—21no—
514C3⋊Dic3—21no—
515C3×Dic3—61no—
516C3×Dic3—61no—
517C3×Dic3—61no—
518C3×Dic3—61no—
519C3×Dic3—61no—
520C3×Dic3—61no—
521C3×Dic3—61no—
522C3×Dic3—61no—
523C3×Dic3—61no—
524C3×Dic3—61no—
525C3×Dic3—121no—
526C3×Dic3—121no—
527#126—271no—
528#126—271no—
529#124—271no—
530#124—271no—
531#123—91no—
532#123—271no—
533C22⋊Q8—271no—
534#121—91no—
535#121—271no—
536#121—271no—
537#120—271no—
538#120—271no—
539C4×D4—91no—
540C4×D4—271no—
541C2×C22⋊C4—271no—
542H(3,𝔽3)#53811yescharacteristic, complemented, Sylow
543C23×C3—31no—
544C23×C3—31no—
545C23×C3—61no—
546C23×C3—91no—
547C23×C3—91no—
548C23×C3—91no—
549C23×C3—91no—
550C23×C3C2×D3211yescharacteristic
551C22×D3—31no—
552C22×D3—31no—
553C22×D3—31no—
554C22×D3—31no—
555C22×D3—31no—
556C22×D3—31no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—91no—
560C22×D3—91no—
561C22×D3—182no—
562C22×D3—182no—
563C22×D3—182no—
564C22×D3—361no—
565C22×D3—361no—
566C22×D3—361no—
567C22×D3—361no—
568C22×D3—361no—
569C22×D3—361no—
570C3×D4—182no—
571C3×D4—361no—
572C3×D4—361no—
573C3×D4—361no—
574C3×D4—361no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—41no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—91no—
583C2×C3×C4—91no—
584C2×C3×C4—91no—
585C2×C3×C4—91no—
586C2×C3×C4—91no—
587C2×C3×C4—91no—
588C2×C3×C4—91no—
589C2×C3×C4—91no—
590C2×C3×C4—121no—
591C2×C3×C4—121no—
592C2×C3×C4—122no—
593C2×C3×C4—361no—
594C2×C3×C4C2×D3211yescharacteristic
595C2×C3×C4C2×D3211yescharacteristic
596#67—62no—
597#67—121no—
598#67—121no—
599#67—121no—
600#67—121no—
601#67—121no—
602#67—122no—
603#67—122no—
604#67—182no—
605#67—182no—
606#67—182no—
607#67—361no—
608#67—361no—
609#67—361no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—31no—
613C2×Dic3—31no—
614C2×Dic3—31no—
615C2×Dic3—31no—
616C2×Dic3—31no—
617C2×Dic3—31no—
618C2×Dic3—31no—
619C2×Dic3—31no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—91no—
623C2×Dic3—91no—
624C2×Dic3—91no—
625C2×Dic3—91no—
626C2×Dic3—91no—
627C2×Dic3—91no—
628C2×Dic3—361no—
629C2×Dic3—361no—
630D12—121no—
631D12—121no—
632D12—122no—
633D12—182no—
634D12—361no—
635C4×D3—121no—
636C4×D3—361no—
637C4×D3—361no—
638C4×D3—361no—
639C4×D3—361no—
640C4×D3—361no—
641Dic6—361no—
642Dic6—361no—
643Dic6—361no—
644C2×C32—21no—
645C2×C32—21no—
646C2×C32—21no—
647C2×C32—42no—
648C2×C32—41no—
649C2×C32—41no—
650C2×C32C2×#23511yescharacteristic
651C2×C32#100411yescharacteristic
652C2×C32#100411yescharacteristic
653C2×C32D3×#4111yescharacteristic
654C2×C32#100911yescharacteristic
655C2×C32#100911yescharacteristic
656C3⋊D3—22no—
657C3⋊D3—41no—
658C3×D3—62no—
659C3×D3—121no—
660C3×D3—121no—
661C3×D3—121no—
662C3×D3—121no—
663C3×D3—121no—
664C3×D3—241no—
665C3×D3—241no—
666C24—271no—
667C2×Q8—271no—
668C2×D4—91no—
669C2×D4—91no—
670C2×D4—91no—
671C2×D4—91no—
672C2×D4—91no—
673C2×D4—271no—
674C2×D4—271no—
675C22×C4—91no—
676C22×C4—271no—
677C22×C4—271no—
678C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
679C4⋊C4—91no—
680C4⋊C4—91no—
681C4⋊C4—91no—
682C4⋊C4—91no—
683C4⋊C4—271no—
684C4⋊C4—271no—
685C22⋊C4—91no—
686C22⋊C4—91no—
687C22⋊C4—91no—
688C22⋊C4—91no—
689C22⋊C4—91no—
690C22⋊C4—91no—
691C22⋊C4—91no—
692C22⋊C4—271no—
693C22⋊C4—271no—
694C22⋊C4—271no—
695C22⋊C4—271no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C42—91no—
700C42—271no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—31no—
705C22×C3—31no—
706C22×C3—61no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3—62no—
713C22×C3—61no—
714C22×C3—92no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—181no—
718C22×C3—181no—
719C22×C3—181no—
720C22×C3—181no—
721C22×C3—181no—
722C22×C3—181no—
723C22×C3—181no—
724C22×C3—181no—
725C22×C3—181no—
726C22×C3—181no—
727C22×C3—181no—
728C22×C3C22×D3211yescharacteristic
729C2×D3—32no—
730C2×D3—61no—
731C2×D3—61no—
732C2×D3—61no—
733C2×D3—61no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—61no—
743C2×D3—61no—
744C2×D3—61no—
745C2×D3—61no—
746C2×D3—61no—
747C2×D3—92no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—181no—
755C2×D3—181no—
756C2×D3—181no—
757C2×D3—181no—
758C2×D3—181no—
759C2×D3—364no—
760C2×D3—364no—
761C2×D3—364no—
762C3×C4—21no—
763C3×C4—21no—
764C3×C4—61no—
765C3×C4—61no—
766C3×C4—61no—
767C3×C4—61no—
768C3×C4—62no—
769C3×C4—121no—
770C3×C4—181no—
771C3×C4—181no—
772C3×C4—181no—
773C3×C4—181no—
774C3×C4—181no—
775C3×C4—181no—
776C3×C4—181no—
777C3×C4—181no—
778Dic3—61no—
779Dic3—61no—
780Dic3—61no—
781Dic3—61no—
782Dic3—61no—
783Dic3—61no—
784Dic3—61no—
785Dic3—61no—
786Dic3—61no—
787Dic3—61no—
788Dic3—121no—
789Dic3—121no—
790Dic3—181no—
791Dic3—181no—
792Dic3—181no—
793Dic3—181no—
794Dic3—181no—
795Dic3—181no—
796C32—21no—
797C32#556011yescharacteristic, complemented
798C32#565711yescharacteristic, complemented
799C23—91no—
800C23—91no—
801C23—91no—
802C23—91no—
803C23—542no—
804C23—1081no—
805C23—1081no—
806C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
807Q8—1081no—
808D4—182no—
809D4—361no—
810D4—361no—
811D4—361no—
812D4—361no—
813D4—542no—
814D4—1081no—
815C2×C4—41no—
816C2×C4—91no—
817C2×C4—91no—
818C2×C4—91no—
819C2×C4—91no—
820C2×C4—91no—
821C2×C4—91no—
822C2×C4—91no—
823C2×C4—91no—
824C2×C4—361no—
825C2×C4—1081no—
826C2×C4—1081no—
827C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
828C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
829C2×C3—31no—
830C2×C3—31no—
831C2×C3—31no—
832C2×C3—31no—
833C2×C3—31no—
834C2×C3—31no—
835C2×C3—41no—
836C2×C3—61no—
837C2×C3—61no—
838C2×C3—61no—
839C2×C3—121no—
840C2×C3—121no—
841C2×C3—122no—
842C2×C3—182no—
843C2×C3—361no—
844C2×C3—361no—
845C2×C3—361no—
846C2×C3D3×#23511yescharacteristic
847C2×C3#6430811yescharacteristic
848C2×C3#6433011yescharacteristic
849D3—62no—
850D3—121no—
851D3—121no—
852D3—121no—
853D3—121no—
854D3—121no—
855D3—182no—
856D3—241no—
857D3—241no—
858D3—361no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—92no—
863C22—181no—
864C22—181no—
865C22—181no—
866C22—181no—
867C22—181no—
868C22—181no—
869C22—181no—
870C22—181no—
871C22—181no—
872C22—181no—
873C22—181no—
874C22—1084no—
875C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
876C4—21no—
877C4—21no—
878C4—181no—
879C4—181no—
880C4—181no—
881C4—181no—
882C4—181no—
883C4—181no—
884C4—181no—
885C4—181no—
886C3—31no—
887C3—31no—
888C3—61no—
889C3#1059508511yescharacteristic
890C2—41no—
891C2—182no—
892C2—361no—
893C2—361no—
894C2—361no—
895C2#1172249011yescharacteristic
896C2#1172249311yescharacteristic
897C2#1172254511yescharacteristic
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)#538
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. #11721830C2semidirect
2. #64138⋊C3C2semidirect
3. C4×#638⋊C3C2semidirect
4. #11721324C2semidirect
5. #11721312C2semidirect
6. #11721303C2semidirect
7. #11721294C2semidirect
8. #11721163C2semidirect
9. #11721160C2semidirect
10. #11721154C2semidirect
11. #11721151C2semidirect
12. #11721133C2semidirect
13. #11721111C2semidirect
14. #11721103C2semidirect
15. #11721092C2semidirect
19. C22×C4×H(3,𝔽3)C22semidirect
21. C2×#6235C22semidirect
28. C2×#6199C22semidirect
30. C2×#6196C22semidirect
32. #88542C22semidirect
33. C4⋊#1084C22semidirect
34. #3757⋊C3C22semidirect
35. #3757⋊C3C22semidirect
39. #3750⋊C3C22semidirect
40. #3750⋊C3C22semidirect
41. #3750⋊C3C22semidirect
42. C4×(C3⋊Dic3)⋊C3C22semidirect
46. #88451C22semidirect
50. #88449C22semidirect
51. #88448C22semidirect
52. #88447C22semidirect
53. #64138D3semidirect
54. C4×#638D3semidirect
120. C22×C32×C4C2×D3semidirect
121. C22×C32×C4C2×D3semidirect
147. #3757C2×D3semidirect
148. #3757C2×D3semidirect
152. #3750C2×D3semidirect
153. #3750C2×D3semidirect
154. #3750C2×D3semidirect
155. C4×C3⋊Dic3C2×D3semidirect
542. H(3,𝔽3)#538semidirect
678. C22×C4((C3⋊D3)⋊C3)⋊C2semidirect
797. C32#5560semidirect
798. C32#5657semidirect

Maximal subgroups

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

subgroupindex
#117218302
#64138⋊C32
C4×#638⋊C32
#117213242
#117213122
#117213032
#117212942
#117211632
#117211602
#117211542
#117211512
#117211332
#117211112
#117211032
#117210922
#105950893
#105950863