Finite Group Databasebeta

← #13148724

Subgroups — #13148724

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#11721740C211yesmaximal, characteristic, complemented
2#64095⋊C3C211yesmaximal, characteristic, complemented
3#64094⋊C3C211yesmaximal, characteristic, complemented
4#11721324C211yesmaximal, characteristic, complemented
5#11721322C211yesmaximal, characteristic, complemented
6#11721303C211yesmaximal, characteristic, complemented
7#11721293C211yesmaximal, characteristic, complemented
8#11721163C211yesmaximal, characteristic, complemented
9#11721161C211yesmaximal, characteristic, complemented
10#11721155C211yesmaximal, characteristic, complemented
11#11721149C211yesmaximal, characteristic, complemented
12#11721109C211yesmaximal, characteristic, complemented
13#11721108C211yesmaximal, characteristic, complemented
14#11721102C211yesmaximal, characteristic, complemented
15#11721094C211yesmaximal, characteristic, complemented
16#10594302—31nomaximal
17#10594301—31nomaximal
18C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
19C2×#6235C2211yescharacteristic
20C2×#6235C2211yescharacteristic, complemented
21C2×C4⋊#272C2211yescharacteristic
22C2×C4×#272C2211yescharacteristic
23C2×#638⋊C3C2211yescharacteristic
24C2×#638⋊C3C2211yescharacteristic
25C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
26C2×#634⋊C3C2211yescharacteristic, complemented
27C2×#6200C2211yescharacteristic
28C2×#6200C2211yescharacteristic
29C2×#6199C2211yescharacteristic
30C2×#6199C2211yescharacteristic, complemented
31C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
32#88542C2211yescharacteristic, complemented
33#88540C2211yescharacteristic, complemented
34#3757⋊C3C2211yescharacteristic, complemented
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38#3752⋊C3C2211yescharacteristic
39C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
40C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
41C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
42#88451C2211yescharacteristic
43#88451C2211yescharacteristic
44#88451C2211yescharacteristic, complemented
45#88450C2211yescharacteristic
46#88450C2211yescharacteristic
47#88450C2211yescharacteristic
48#88450C2211yescharacteristic
49#88449C2211yescharacteristic, complemented
50#88448C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53#64095D311yescharacteristic, complemented
54#64094D311yescharacteristic, complemented
55C3×#886—31no—
56C3×#885—31no—
57C3×#884—31no—
58C3×#884—31no—
59C3×#884—61no—
60#63983—31no—
61#63983—31no—
62#63980—31no—
63#63978—31no—
64#67⋊Dic3—31no—
65Dic3×#67—31no—
66#63971—31no—
67#63970—31no—
68#63922—31no—
69#63922—31no—
70D3×(C2×D3)⋊C4—31no—
71D3×(C2×D3)⋊C4—31no—
72#63913—31no—
73#63907—31no—
74#63898—31no—
75Dic3×D12—31no—
76#63891—31no—
77#63890—31no—
78#63868—31no—
79#63862—31no—
80#63861—31no—
81#63857—31no—
82#63856—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)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94#6235—22no—
95#6235—41no—
96C2×#1084C2311yescharacteristic
97C2×#1084C2311yescharacteristic
98C4⋊#272—22no—
99C4×#272—41no—
100#638⋊C3—41no—
101#638⋊C3—41no—
102C2×(C3⋊Dic3)⋊C3—41no—
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
108C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
109#634⋊C3—41no—
110#6200—41no—
111#6200—41no—
112#6199—41no—
113#6199—41no—
114#5678—91no—
115#5657—91no—
116#5617—91no—
117C22×D32—31no—
118C22×D32—31no—
119C2×#638C2×D311yescharacteristic
120C2×#638C2×D311yescharacteristic
121C22×C3⋊Dic3C2×D311yescharacteristic, complemented
122C2×#634C2×D311yescharacteristic, complemented
123C2×C3×#67—31no—
124C2×C3×#67—31no—
125C2×C3×#67—31no—
126C2×C3×#67—31no—
127C2×C3×#67—31no—
128C2×C3×#67—31no—
129C2×C3×#67—61no—
130C2×C3×#67—61no—
131C22×C3×Dic3—31no—
132C2×C3×D12—31no—
133C2×C3×D12—31no—
134C2×C3×D12—61no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—61no—
138C2×C3×Dic6—31no—
139C2×#626—31no—
140C2×#626—31no—
141C2×#625—31no—
142C2×#625—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—31no—
146C2×D3×Dic3—31no—
147C32×C22⋊C4—21no—
148C32×C22⋊C4C2×D311yescharacteristic, complemented
149C32×C22⋊C4C2×D311yescharacteristic, complemented
150#3757C2×D311yescharacteristic, complemented
151#3752C2×D311yescharacteristic
152#3752C2×D311yescharacteristic
153#3752C2×D311yescharacteristic
154#3752C2×D311yescharacteristic
155C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
156C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
157C4×C3⋊Dic3C2×D311yescharacteristic, complemented
158C3×#217—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×C4⋊Dic3—31no—
167C3×C4⋊Dic3—31no—
168C3×Dic3⋊C4—31no—
169C3×Dic3⋊C4—31no—
170C3×Dic3⋊C4—61no—
171C3×C4×Dic3—31no—
172#3724—31no—
173#3724—31no—
174Dic3⋊Dic3—31no—
175Dic3⋊Dic3—31no—
176Dic3⋊Dic3—31no—
177Dic3⋊Dic3—31no—
178#3722—31no—
179#3722—31no—
180#3722—31no—
181#3722—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#4112yes—
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—21no—
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×#124—91no—
222C3×#123—91no—
223C3×#121—91no—
224#947—91no—
225#946—91no—
226#939—91no—
227#939—91no—
228#939—91no—
229#938—91no—
230#937—91no—
231#937—91no—
232#937—91no—
233#937—91no—
234D4×Dic3—91no—
235D4×Dic3—91no—
236#930—91no—
237C4×#67—91no—
238C2×(C2×D3)⋊C4—91no—
239#924—91no—
240#898—91no—
241#898—91no—
242#898—91no—
243#897—91no—
244#894—91no—
245#893—91no—
246#886—31no—
247#886—91no—
248#886—91no—
249#885—31no—
250#885—91no—
251#885—91no—
252#885—91no—
253#884—31no—
254#884—31no—
255#884—61no—
256#884—91no—
257#883—91no—
258#882—91no—
259#882—91no—
260#67⋊C4—91no—
261D3×C22⋊C4—91no—
262D3×C22⋊C4—91no—
263#879—91no—
264#879—91no—
265#876—91no—
266C4×D12—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×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C22×D311yescharacteristic
292#638—41no—
293#638—41no—
294C2×C3⋊Dic3—41no—
295C2×C3⋊Dic3C22×D311yescharacteristic
296C2×C3⋊Dic3C22×D311yescharacteristic
297C2×C3⋊Dic3C22×D311yescharacteristic
298C2×C3⋊Dic3C22×D311yescharacteristic
299C2×C3⋊Dic3C22×D311yescharacteristic
300C2×C3⋊Dic3C22×D311yescharacteristic
301#634—41no—
302C3×#67—62no—
303C3×#67—62no—
304C3×#67—122no—
305C3×#67—121no—
306C3×#67—121no—
307C3×#67—121no—
308C3×#67—121no—
309C3×#67—122no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3—31no—
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—61no—
321C2×C3×Dic3—61no—
322C2×C3×Dic3—121no—
323C3×D12—62no—
324C3×D12—62no—
325C3×D12—122no—
326C3×C4×D3—121no—
327C3×C4×D3—121no—
328C3×C4×D3—122no—
329C3×Dic6—121no—
330#626—121no—
331#626—121no—
332#625—121no—
333#625—121no—
334D3×Dic3—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—22no—
344#272—41no—
345(C3⋊D3)⋊C3—41no—
346(C3⋊D3)⋊C3—41no—
347C23×D3—91no—
348C23×D3—91no—
349C23×D3—91no—
350C2×C3×Q8—91no—
351C2×C3×D4—91no—
352C2×C3×D4—91no—
353C2×C3×D4—91no—
354C2×C3×D4—91no—
355C2×C3×D4—91no—
356C22×C3×C4—91no—
357C22×C3×C4—91no—
358C2×#67—31no—
359C2×#67—31no—
360C2×#67—31no—
361C2×#67—31no—
362C2×#67—31no—
363C2×#67—31no—
364C2×#67—61no—
365C2×#67—61no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—91no—
369C2×#67—91no—
370C2×#67—91no—
371C2×#67—91no—
372C22×Dic3—31no—
373C22×Dic3—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—31no—
383C2×C4×D3—61no—
384C2×C4×D3—91no—
385C2×C4×D3—91no—
386C2×C4×D3—91no—
387C2×C4×D3—91no—
388C2×Dic6—31no—
389C2×Dic6—91no—
390C3×C4⋊C4—91no—
391C3×C4⋊C4—91no—
392C3×C4⋊C4—91no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—91no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4—91no—
399C3×C22⋊C4—91no—
400C3×C22⋊C4—91no—
401C3×C22⋊C4—91no—
402C3×C22⋊C4D3211yescharacteristic
403C3×C42—91no—
404#217—31no—
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—61no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—91no—
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—
438C4⋊Dic3—31no—
439C4⋊Dic3—31no—
440C4⋊Dic3—91no—
441C4⋊Dic3—91no—
442C4⋊Dic3—91no—
443C4⋊Dic3—91no—
444C4⋊Dic3—91no—
445Dic3⋊C4—31no—
446Dic3⋊C4—31no—
447Dic3⋊C4—61no—
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—21no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32—41no—
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—21no—
477C2×C3×D3—32no—
478C2×C3×D3—32no—
479C2×C3×D3—62no—
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—61no—
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—21no—
504C32×C4—21no—
505C32×C4—21no—
506C32×C4—21no—
507C32×C4—41no—
508C32×C4—41no—
509C3⋊Dic3—21no—
510C3⋊Dic3—21no—
511C3⋊Dic3—21no—
512C3⋊Dic3—21no—
513C3⋊Dic3—21no—
514C3⋊Dic3—21no—
515C3×Dic3—62no—
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—61no—
526C3×Dic3—121no—
527#126—271no—
528#126—271no—
529#124—91no—
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—271no—
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×Q8—361no—
571C3×D4—182no—
572C3×D4—182no—
573C3×D4—361no—
574C3×D4—361no—
575C3×D4—361no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
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—361no—
591C2×C3×C4—361no—
592C2×C3×C4C2×D3211yescharacteristic
593C2×C3×C4C2×D3211yescharacteristic
594#67—62no—
595#67—62no—
596#67—122no—
597#67—121no—
598#67—121no—
599#67—121no—
600#67—121no—
601#67—122no—
602#67—361no—
603#67—361no—
604#67—361no—
605#67—361no—
606#67—361no—
607#67—361no—
608C2×Dic3—31no—
609C2×Dic3—31no—
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—61no—
619C2×Dic3—61no—
620C2×Dic3—91no—
621C2×Dic3—91no—
622C2×Dic3—91no—
623C2×Dic3—91no—
624C2×Dic3—91no—
625C2×Dic3—91no—
626C2×Dic3—121no—
627C2×Dic3—361no—
628C2×Dic3—361no—
629C2×Dic3—361no—
630D12—62no—
631D12—62no—
632D12—122no—
633D12—361no—
634D12—361no—
635C4×D3—121no—
636C4×D3—121no—
637C4×D3—122no—
638C4×D3—361no—
639C4×D3—361no—
640C4×D3—361no—
641C4×D3—361no—
642Dic6—121no—
643Dic6—361no—
644C2×C32—21no—
645C2×C32—21no—
646C2×C32—21no—
647C2×C32—41no—
648C2×C32—41no—
649C2×C32—81no—
650C2×C32#100411yescharacteristic
651C2×C32#100411yescharacteristic
652C2×C32D3×#4111yescharacteristic
653C2×C32D3×#4111yescharacteristic
654C2×C32#100911yescharacteristic
655C2×C32#100911yescharacteristic
656C3⋊D3—41no—
657C3⋊D3—41no—
658C3×D3—62no—
659C3×D3—62no—
660C3×D3—122no—
661C3×D3—121no—
662C3×D3—121no—
663C3×D3—121no—
664C3×D3—121no—
665C3×D3—241no—
666C24—271no—
667C2×Q8—91no—
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—91no—
677C22×C4—271no—
678C22×C4—271no—
679C4⋊C4—91no—
680C4⋊C4—91no—
681C4⋊C4—91no—
682C4⋊C4—271no—
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—271no—
692C22⋊C4—271no—
693C22⋊C4—271no—
694C22⋊C4—271no—
695C22⋊C4—271no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
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—61no—
713C22×C3—92no—
714C22×C3—121no—
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—32no—
731C2×D3—62no—
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—61no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—181no—
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—121no—
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—62no—
783Dic3—61no—
784Dic3—61no—
785Dic3—61no—
786Dic3—61no—
787Dic3—61no—
788Dic3—61no—
789Dic3—121no—
790Dic3—181no—
791Dic3—181no—
792Dic3—181no—
793Dic3—181no—
794Dic3—181no—
795Dic3—181no—
796C32—21no—
797C32#565711yescharacteristic, complemented
798C32#567811yescharacteristic, complemented
799C23—91no—
800C23—91no—
801C23—91no—
802C23—91no—
803C23—542no—
804C23—1081no—
805C23—1081no—
806C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
807Q8—361no—
808D4—182no—
809D4—182no—
810D4—361no—
811D4—361no—
812D4—361no—
813D4—1081no—
814D4—1081no—
815C2×C4—91no—
816C2×C4—91no—
817C2×C4—91no—
818C2×C4—91no—
819C2×C4—91no—
820C2×C4—91no—
821C2×C4—91no—
822C2×C4—91no—
823C2×C4—361no—
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—182no—
842C2×C3—241no—
843C2×C3—361no—
844C2×C3—361no—
845C2×C3—361no—
846C2×C3#6430711yescharacteristic
847C2×C3#6431211yescharacteristic
848C2×C3#6431411yescharacteristic
849D3—62no—
850D3—62no—
851D3—122no—
852D3—121no—
853D3—121no—
854D3—121no—
855D3—121no—
856D3—241no—
857D3—361no—
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#1059430711yescharacteristic
890C2—41no—
891C2—182no—
892C2—361no—
893C2—361no—
894C2—361no—
895C2#1172249211yescharacteristic
896C2#1172250511yescharacteristic
897C2#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)#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. #11721740C2semidirect
2. #64095⋊C3C2semidirect
3. #64094⋊C3C2semidirect
4. #11721324C2semidirect
5. #11721322C2semidirect
6. #11721303C2semidirect
7. #11721293C2semidirect
8. #11721163C2semidirect
9. #11721161C2semidirect
10. #11721155C2semidirect
11. #11721149C2semidirect
12. #11721109C2semidirect
13. #11721108C2semidirect
14. #11721102C2semidirect
15. #11721094C2semidirect
20. C2×#6235C22semidirect
25. C22×(C3⋊Dic3)⋊C3C22semidirect
26. C2×#634⋊C3C22semidirect
30. C2×#6199C22semidirect
31. C22⋊C4×H(3,𝔽3)C22semidirect
32. #88542C22semidirect
33. #88540C22semidirect
34. #3757⋊C3C22semidirect
39. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
40. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
41. C4×(C3⋊Dic3)⋊C3C22semidirect
44. #88451C22semidirect
49. #88449C22semidirect
50. #88448C22semidirect
51. #88448C22semidirect
52. #88447C22semidirect
53. #64095D3semidirect
54. #64094D3semidirect
121. C22×C3⋊Dic3C2×D3semidirect
122. C2×#634C2×D3semidirect
148. C32×C22⋊C4C2×D3semidirect
149. C32×C22⋊C4C2×D3semidirect
150. #3757C2×D3semidirect
155. C4⋊(C3⋊Dic3)C2×D3semidirect
156. C4⋊(C3⋊Dic3)C2×D3semidirect
157. C4×C3⋊Dic3C2×D3semidirect
542. H(3,𝔽3)#538semidirect
698. C22⋊C4((C3⋊D3)⋊C3)⋊C2semidirect
797. C32#5657semidirect
798. C32#5678semidirect

Maximal subgroups

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

subgroupindex
#117217402
#64095⋊C32
#64094⋊C32
#117213242
#117213222
#117213032
#117212932
#117211632
#117211612
#117211552
#117211492
#117211092
#117211082
#117211022
#117210942
#105943023
#105943013