Finite Group Databasebeta

← #13148737

Subgroups — #13148737

Order 1728.

1247 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88676C211yesmaximal, characteristic, complemented
2C2×#88672C211yesmaximal, characteristic, complemented
3#11721742C211yesmaximal, characteristic, complemented
4#64091⋊C3C211yesmaximal, characteristic, complemented
5#64090⋊C3C211yesmaximal, characteristic, complemented
6#11721322C211yesmaximal, characteristic, complemented
7C2×#88450C211yesmaximal, characteristic, complemented
8#11721162C211yesmaximal, characteristic, complemented
9#11721160C211yesmaximal, characteristic, complemented
10#11721141C211yesmaximal, characteristic, complemented
11#11721133C211yesmaximal, characteristic, complemented
12#11721132C211yesmaximal, characteristic, complemented
13#11721131C211yesmaximal, characteristic, complemented
14#11721127C211yesmaximal, characteristic, complemented
15#11721103C211yesmaximal, characteristic, complemented
16#10594294—31nomaximal
17#10594293—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
20C2×#6235C2211yescharacteristic
21C22×#1084C2211yescharacteristic, complemented
22C2×#638⋊C3C2211yescharacteristic
23C2×#638⋊C3C2211yescharacteristic, complemented
24C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
25C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
26C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
27C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
28#88676—24no—
29C2×#6200C2211yescharacteristic
30C2×#6200C2211yescharacteristic, complemented
31C2×#6198C2211yescharacteristic
32C2×#6198C2211yescharacteristic, complemented
33#88672—24no—
34C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
35C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
36C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
37C2×#6196C2211yescharacteristic, complemented
38C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
39#88542C2211yescharacteristic, complemented
40#88542C2211yescharacteristic, complemented
41C4⋊#1084C2211yescharacteristic, complemented
42C4⋊#1084C2211yescharacteristic, complemented
43#3752⋊C3C2211yescharacteristic
44#3752⋊C3C2211yescharacteristic, complemented
45#3752⋊C3C2211yescharacteristic, complemented
46#3750⋊C3C2211yescharacteristic, complemented
47C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
48#88451C2211yescharacteristic, complemented
49#88450C2211yescharacteristic
50#88450C2211yescharacteristic
51#88450C2211yescharacteristic, complemented
52#88450C2211yescharacteristic, complemented
53#88450C2211yescharacteristic, complemented
54#88448C2211yescharacteristic, complemented
55C2×#3811—31no—
56C2×D3×#67—31no—
57C2×#3804—31no—
58C2×#3804—31no—
59#64091D311yescharacteristic, complemented
60#64090D311yescharacteristic, complemented
61C3×#886—31no—
62C3×#886—31no—
63C3×#886—61no—
64C3×#882—31no—
65C3×#67⋊C4—31no—
66#63980—31no—
67#63978—31no—
68C2×#3722—31no—
69C2×(C2×D3)⋊Dic3—31no—
70#63923—31no—
71#63922—31no—
72#63921—31no—
73D3×(C2×D3)⋊C4—31no—
74#63916—31no—
75#63915—31no—
76#63910—31no—
77#63909—31no—
78#63899—31no—
79#63898—31no—
80#63895—31no—
81#63894—31no—
82#63890—31no—
83#63885—31no—
84#63854—31no—
85#63852—31no—
86C23×H(3,𝔽3)C2311yescharacteristic
87C22×#272C2311yescharacteristic
88C22×(C3⋊D3)⋊C3—22no—
89C22×(C3⋊D3)⋊C3—22no—
90C22×(C3⋊D3)⋊C3—41no—
91C22×(C3⋊D3)⋊C3C2311yescharacteristic
92C22×(C3⋊D3)⋊C3C2311yescharacteristic
93C22×(C3⋊D3)⋊C3C2311yescharacteristic
94C22×(C3⋊D3)⋊C3C2311yescharacteristic
95C2×((C3⋊D3)⋊C3)⋊C2—22no—
96C2×((C3⋊D3)⋊C3)⋊C2—22no—
97C2×((C3⋊D3)⋊C3)⋊C2—41no—
98C2×C4×H(3,𝔽3)C2311yescharacteristic
99C2×C4×H(3,𝔽3)C2311yescharacteristic
100#6235—22no—
101C2×#1084—22no—
102C2×#1084C2311yescharacteristic
103C2×#1084C2311yescharacteristic
104C2×#1084C2311yescharacteristic
105#638⋊C3—22no—
106#638⋊C3D414yescomplemented
107C2×(C3⋊Dic3)⋊C3—41no—
108C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
109C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
110C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
111C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
112C4⋊((C3⋊D3)⋊C3)—22no—
113C4⋊((C3⋊D3)⋊C3)—41no—
114C4×(C3⋊D3)⋊C3—41no—
115#6200—22no—
116#6200—41no—
117#6198—22no—
118#6198—22no—
119((C3⋊D3)⋊C3)⋊C4—22no—
120((C3⋊D3)⋊C3)⋊C4—22no—
121((C3⋊D3)⋊C3)⋊C4—22no—
122#6196—22no—
123#5654—91no—
124#5591—91no—
125#5554—91no—
126C23×C3⋊D3C2×D311yescharacteristic
127C23×C3×D3—31no—
128C22×D32—31no—
129C22×D32—31no—
130C2×#638C2×D311yescharacteristic
131C2×#638C2×D311yescharacteristic, complemented
132C22×C3⋊Dic3C2×D311yescharacteristic, complemented
133C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
134C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
135C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
136C2×C3×#67—31no—
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C2×C3×#67—31no—
140C2×C3×#67—61no—
141C22×C3×Dic3—31no—
142C22×C3×Dic3—31no—
143C22×C3×Dic3—31no—
144C22×C3×Dic3—61no—
145C2×C3×D12—31no—
146C2×C3×D12—31no—
147C2×C3×C4×D3—31no—
148#3811—64no—
149D3×#67—64no—
150C2×#627—31no—
151C2×#627—31no—
152C2×#626—31no—
153C2×#626—31no—
154C2×#626—31no—
155C2×#626—31no—
156C2×#626—31no—
157C2×#626—31no—
158C2×#625—31no—
159C2×#625—31no—
160C2×#624—31no—
161C2×#624—31no—
162C2×#624—31no—
163#3804—64no—
164#3804—64no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—31no—
167C2×D3×Dic3—31no—
168C32×C22⋊C4—21no—
169C32×C22⋊C4C2×D311yescharacteristic, complemented
170C32×C22⋊C4C2×D311yescharacteristic, complemented
171#3752C2×D311yescharacteristic
172#3752C2×D311yescharacteristic, complemented
173#3752C2×D311yescharacteristic, complemented
174#3750C2×D311yescharacteristic, complemented
175C4×C3⋊Dic3C2×D311yescharacteristic, complemented
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×(C2×D3)⋊C4—31no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—61no—
184C3×(C2×D3)⋊C4—61no—
185C3×C4⋊Dic3—31no—
186C3×C4⋊Dic3—31no—
187C3×C4⋊Dic3—31no—
188C3×C4⋊Dic3—31no—
189C3×C4⋊Dic3—61no—
190C3×C4⋊Dic3—61no—
191C3×Dic3⋊C4—31no—
192C3×C4×Dic3—31no—
193#3724—31no—
194Dic3⋊Dic3—31no—
195#3722—31no—
196#3722—31no—
197#3722—31no—
198#3722—31no—
199#3722—31no—
200(C2×D3)⋊Dic3—31no—
201(C2×D3)⋊Dic3—31no—
202(C2×D3)⋊Dic3—31no—
203(C2×D3)⋊Dic3—31no—
204(C2×D3)⋊Dic3—31no—
205(C2×D3)⋊Dic3—31no—
206(C2×D3)⋊Dic3—31no—
207C22×H(3,𝔽3)—21no—
208C22×H(3,𝔽3)—21no—
209C22×H(3,𝔽3)C2×D412yes—
210C22×H(3,𝔽3)C2411yescharacteristic
211C2×#272—21no—
212C2×#272—21no—
213C2×#272—21no—
214C2×(C3⋊D3)⋊C3—21no—
215C2×(C3⋊D3)⋊C3—21no—
216C2×(C3⋊D3)⋊C3—21no—
217C2×(C3⋊D3)⋊C3—21no—
218C2×(C3⋊D3)⋊C3—21no—
219C2×(C3⋊D3)⋊C3—21no—
220C2×(C3⋊D3)⋊C3—21no—
221C2×(C3⋊D3)⋊C3—21no—
222C2×(C3⋊D3)⋊C3—21no—
223C2×(C3⋊D3)⋊C3—21no—
224C2×(C3⋊D3)⋊C3—44no—
225C2×(C3⋊D3)⋊C3C2×D412yes—
226C2×(C3⋊D3)⋊C3#4112yescomplemented
227((C3⋊D3)⋊C3)⋊C2—44no—
228C4×H(3,𝔽3)—21no—
229C4×H(3,𝔽3)—21no—
230#1084—21no—
231#1084—21no—
232#1084—21no—
233(C3⋊Dic3)⋊C3—21no—
234(C3⋊Dic3)⋊C3—21no—
235(C3⋊Dic3)⋊C3—21no—
236(C3⋊Dic3)⋊C3C2×D412yes—
237C22×#67—91no—
238C2×#237—91no—
239C2×#237—91no—
240C2×D3×D4—91no—
241C2×D3×D4—91no—
242C2×#235—91no—
243C3×#123—91no—
244C3×#120—91no—
245C3×C4×D4—91no—
246C2×#217—91no—
247#939—91no—
248#939—91no—
249#939—91no—
250#938—91no—
251#937—91no—
252D4×Dic3—91no—
253#930—91no—
254#930—91no—
255C2×(C2×D3)⋊C4—91no—
256C2×(C2×D3)⋊C4—91no—
257C2×(C2×D3)⋊C4—91no—
258#897—91no—
259#896—91no—
260#895—91no—
261#895—91no—
262#894—91no—
263#893—91no—
264#886—31no—
265#886—31no—
266#886—61no—
267#886—91no—
268#885—91no—
269#885—91no—
270#884—91no—
271#883—91no—
272#882—31no—
273#882—91no—
274#882—91no—
275#882—91no—
276#67⋊C4—31no—
277#67⋊C4—91no—
278D3×C22⋊C4—91no—
279D3×C22⋊C4—91no—
280#878—91no—
281#875—91no—
282C4×D12—91no—
283C23×C32—21no—
284C23×C32C22×D311yescharacteristic
285C23×C32C22×D311yescharacteristic
286C22×C3⋊D3—22no—
287C22×C3⋊D3—22no—
288C22×C3⋊D3—41no—
289C22×C3⋊D3C22×D311yescharacteristic
290C22×C3⋊D3C22×D311yescharacteristic
291C22×C3⋊D3C22×D311yescharacteristic
292C22×C3⋊D3C22×D311yescharacteristic
293C22×C3×D3—31no—
294C22×C3×D3—31no—
295C22×C3×D3—31no—
296C22×C3×D3—31no—
297C22×C3×D3—31no—
298C22×C3×D3—31no—
299C22×C3×D3—61no—
300C22×C3×D3—62no—
301C22×C3×D3—62no—
302C22×C3×D3—121no—
303C2×D32—62no—
304C2×D32—62no—
305C2×D32—62no—
306C2×D32—62no—
307C2×D32—121no—
308C2×D32—121no—
309C2×C32×C4—21no—
310C2×C32×C4—21no—
311C2×C32×C4C22×D311yescharacteristic
312C2×C32×C4C22×D311yescharacteristic
313C2×C32×C4C22×D311yescharacteristic
314C2×C32×C4C22×D311yescharacteristic
315#638—22no—
316#638D1214yescomplemented
317C2×C3⋊Dic3—41no—
318C2×C3⋊Dic3C22×D311yescharacteristic
319C2×C3⋊Dic3C22×D311yescharacteristic
320C2×C3⋊Dic3C22×D311yescharacteristic
321C2×C3⋊Dic3C22×D311yescharacteristic
322C4⋊(C3⋊D3)—22no—
323C4⋊(C3⋊D3)—41no—
324C4×C3⋊D3—41no—
325C3×#67—34no—
326C3×#67—62no—
327C3×#67—62no—
328C3×#67—62no—
329C3×#67—122no—
330C2×C3×Dic3—31no—
331C2×C3×Dic3—31no—
332C2×C3×Dic3—31no—
333C2×C3×Dic3—31no—
334C2×C3×Dic3—31no—
335C2×C3×Dic3—31no—
336C2×C3×Dic3—31no—
337C2×C3×Dic3—31no—
338C2×C3×Dic3—31no—
339C2×C3×Dic3—31no—
340C2×C3×Dic3—61no—
341C2×C3×Dic3—61no—
342C2×C3×Dic3—61no—
343C2×C3×Dic3—62no—
344C2×C3×Dic3—62no—
345C2×C3×Dic3—122no—
346C2×C3×Dic3—121no—
347C3×D12—62no—
348C3×D12—121no—
349C3×C4×D3—121no—
350#627—62no—
351#627—62no—
352#626—62no—
353#626—62no—
354#626—62no—
355#626—62no—
356#626—62no—
357#626—121no—
358#625—62no—
359#625—121no—
360#624—62no—
361#624—62no—
362#624—62no—
363D3×Dic3—62no—
364D3×Dic3—62no—
365D3×Dic3—62no—
366#546—271noSylow
367C2×H(3,𝔽3)—22no—
368C2×H(3,𝔽3)C22×D411yescharacteristic
369C2×H(3,𝔽3)C2×#4111yescharacteristic
370C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
371#272—41no—
372(C3⋊D3)⋊C3—22no—
373(C3⋊D3)⋊C3—22no—
374(C3⋊D3)⋊C3—41no—
375(C3⋊D3)⋊C3—41no—
376C24×C3—91no—
377C23×D3—31no—
378C23×D3—91no—
379C23×D3—91no—
380C23×D3—91no—
381C23×D3—91no—
382C2×C3×D4—91no—
383C2×C3×D4—91no—
384C2×C3×D4—91no—
385C2×C3×D4—91no—
386C2×C3×D4—91no—
387C22×C3×C4—91no—
388C22×C3×C4—91no—
389C22×C3×C4—91no—
390C2×#67—31no—
391C2×#67—31no—
392C2×#67—31no—
393C2×#67—31no—
394C2×#67—61no—
395C2×#67—91no—
396C2×#67—91no—
397C2×#67—91no—
398C2×#67—91no—
399C2×#67—91no—
400C2×#67—91no—
401C2×#67—91no—
402C2×#67—91no—
403C2×#67—91no—
404C2×#67—91no—
405C2×#67—184no—
406C22×Dic3—31no—
407C22×Dic3—31no—
408C22×Dic3—31no—
409C22×Dic3—61no—
410C22×Dic3—91no—
411C22×Dic3—91no—
412C22×Dic3—91no—
413C22×Dic3—91no—
414#237—184no—
415#237—184no—
416D3×D4—184no—
417D3×D4—184no—
418#235—184no—
419C2×D12—31no—
420C2×D12—31no—
421C2×D12—91no—
422C2×D12—91no—
423C2×D12—91no—
424C2×D12—91no—
425C2×D12—91no—
426C2×D12—91no—
427C2×C4×D3—31no—
428C2×C4×D3—91no—
429C2×C4×D3—91no—
430C2×C4×D3—91no—
431C2×C4×D3—91no—
432C2×C4×D3—91no—
433C2×C4×D3—91no—
434C2×C4×D3—91no—
435C2×Dic6—91no—
436C2×Dic6—91no—
437C2×Dic6—91no—
438C3×C4⋊C4—91no—
439C3×C4⋊C4—91no—
440C3×C4⋊C4—91no—
441C3×C22⋊C4—31no—
442C3×C22⋊C4—31no—
443C3×C22⋊C4—61no—
444C3×C22⋊C4—91no—
445C3×C22⋊C4—91no—
446C3×C22⋊C4—91no—
447C3×C22⋊C4—91no—
448C3×C22⋊C4—91no—
449C3×C22⋊C4D3211yescharacteristic
450C3×C42—91no—
451#217—91no—
452#217—91no—
453#217—91no—
454#217—91no—
455#217—91no—
456#217—91no—
457(C2×D3)⋊C4—31no—
458(C2×D3)⋊C4—31no—
459(C2×D3)⋊C4—31no—
460(C2×D3)⋊C4—31no—
461(C2×D3)⋊C4—31no—
462(C2×D3)⋊C4—31no—
463(C2×D3)⋊C4—31no—
464(C2×D3)⋊C4—61no—
465(C2×D3)⋊C4—61no—
466(C2×D3)⋊C4—91no—
467(C2×D3)⋊C4—91no—
468(C2×D3)⋊C4—91no—
469(C2×D3)⋊C4—91no—
470(C2×D3)⋊C4—91no—
471(C2×D3)⋊C4—91no—
472(C2×D3)⋊C4—91no—
473(C2×D3)⋊C4—91no—
474(C2×D3)⋊C4—91no—
475(C2×D3)⋊C4—91no—
476(C2×D3)⋊C4—91no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—91no—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4—91no—
481C4⋊Dic3—31no—
482C4⋊Dic3—31no—
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—61no—
486C4⋊Dic3—61no—
487C4⋊Dic3—91no—
488Dic3⋊C4—31no—
489Dic3⋊C4—91no—
490Dic3⋊C4—91no—
491Dic3⋊C4—91no—
492C4×Dic3—31no—
493C4×Dic3—91no—
494C22×C32—21no—
495C22×C32—21no—
496C22×C32—21no—
497C22×C32—21no—
498C22×C32—21no—
499C22×C32—22no—
500C22×C32—41no—
501C22×C32—41no—
502C22×C32C2×D1212yes—
503C22×C32D3×D412yes—
504C22×C32C23×D311yescharacteristic
505C22×C32C23×D311yescharacteristic
506C2×C3⋊D3—21no—
507C2×C3⋊D3—21no—
508C2×C3⋊D3—21no—
509C2×C3⋊D3—21no—
510C2×C3⋊D3—21no—
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—21no—
514C2×C3⋊D3—21no—
515C2×C3⋊D3—21no—
516C2×C3⋊D3—44no—
517C2×C3⋊D3C2×D1212yes—
518C2×C3⋊D3#23712yescomplemented
519C2×C3×D3—32no—
520C2×C3×D3—32no—
521C2×C3×D3—61no—
522C2×C3×D3—61no—
523C2×C3×D3—61no—
524C2×C3×D3—61no—
525C2×C3×D3—61no—
526C2×C3×D3—61no—
527C2×C3×D3—61no—
528C2×C3×D3—61no—
529C2×C3×D3—61no—
530C2×C3×D3—61no—
531C2×C3×D3—61no—
532C2×C3×D3—61no—
533C2×C3×D3—61no—
534C2×C3×D3—61no—
535C2×C3×D3—61no—
536C2×C3×D3—61no—
537C2×C3×D3—121no—
538C2×C3×D3—121no—
539C2×C3×D3—121no—
540C2×C3×D3—124no—
541D32—124no—
542D32—124no—
543C32×C4—21no—
544C32×C4—21no—
545C32×C4—21no—
546C32×C4—21no—
547C32×C4—41no—
548C32×C4—41no—
549C3⋊Dic3—21no—
550C3⋊Dic3—21no—
551C3⋊Dic3—21no—
552C3⋊Dic3C2×D1212yes—
553C3×Dic3—32no—
554C3×Dic3—61no—
555C3×Dic3—61no—
556C3×Dic3—61no—
557C3×Dic3—61no—
558C3×Dic3—61no—
559C3×Dic3—61no—
560C3×Dic3—61no—
561C3×Dic3—61no—
562C3×Dic3—61no—
563C3×Dic3—121no—
564C3×Dic3—121no—
565C3×Dic3—121no—
566C2×#41—271no—
567C22×D4—271no—
568#124—271no—
569#123—91no—
570#123—271no—
571C22⋊Q8—271no—
572#121—271no—
573#121—271no—
574#121—271no—
575#120—91no—
576#120—271no—
577C4×D4—91no—
578C4×D4—271no—
579C2×C22⋊C4—271no—
580C2×C22⋊C4—271no—
581H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
582C23×C3—31no—
583C23×C3—31no—
584C23×C3—61no—
585C23×C3—91no—
586C23×C3—91no—
587C23×C3—91no—
588C23×C3—91no—
589C23×C3—91no—
590C23×C3—182no—
591C23×C3—182no—
592C23×C3—361no—
593C23×C3C2×D3211yescharacteristic
594C22×D3—31no—
595C22×D3—31no—
596C22×D3—31no—
597C22×D3—31no—
598C22×D3—31no—
599C22×D3—31no—
600C22×D3—61no—
601C22×D3—62no—
602C22×D3—62no—
603C22×D3—91no—
604C22×D3—91no—
605C22×D3—91no—
606C22×D3—91no—
607C22×D3—121no—
608C22×D3—182no—
609C22×D3—182no—
610C22×D3—182no—
611C22×D3—182no—
612C22×D3—182no—
613C22×D3—182no—
614C22×D3—182no—
615C22×D3—182no—
616C22×D3—361no—
617C22×D3—361no—
618C22×D3—361no—
619C22×D3—361no—
620C3×D4—94no—
621C3×D4—182no—
622C3×D4—182no—
623C3×D4—182no—
624C3×D4—361no—
625C2×C3×C4—31no—
626C2×C3×C4—31no—
627C2×C3×C4—31no—
628C2×C3×C4—31no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—91no—
632C2×C3×C4—91no—
633C2×C3×C4—91no—
634C2×C3×C4—91no—
635C2×C3×C4—91no—
636C2×C3×C4—91no—
637C2×C3×C4—91no—
638C2×C3×C4—182no—
639C2×C3×C4—361no—
640C2×C3×C4—361no—
641C2×C3×C4C2×D3211yescharacteristic
642C2×C3×C4C2×D3211yescharacteristic
643#67—34no—
644#67—62no—
645#67—62no—
646#67—62no—
647#67—94no—
648#67—122no—
649#67—182no—
650#67—182no—
651#67—182no—
652#67—182no—
653#67—182no—
654#67—182no—
655#67—182no—
656#67—361no—
657#67—361no—
658C2×Dic3—31no—
659C2×Dic3—31no—
660C2×Dic3—31no—
661C2×Dic3—31no—
662C2×Dic3—31no—
663C2×Dic3—31no—
664C2×Dic3—31no—
665C2×Dic3—31no—
666C2×Dic3—31no—
667C2×Dic3—31no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—62no—
672C2×Dic3—62no—
673C2×Dic3—91no—
674C2×Dic3—91no—
675C2×Dic3—91no—
676C2×Dic3—91no—
677C2×Dic3—122no—
678C2×Dic3—121no—
679C2×Dic3—182no—
680C2×Dic3—182no—
681C2×Dic3—182no—
682C2×Dic3—361no—
683D12—62no—
684D12—121no—
685D12—182no—
686D12—182no—
687D12—182no—
688D12—182no—
689D12—361no—
690D12—361no—
691C4×D3—121no—
692C4×D3—182no—
693C4×D3—182no—
694C4×D3—182no—
695C4×D3—182no—
696C4×D3—182no—
697C4×D3—182no—
698C4×D3—361no—
699Dic6—182no—
700Dic6—182no—
701Dic6—182no—
702C2×C32—22no—
703C2×C32—22no—
704C2×C32—21no—
705C2×C32—21no—
706C2×C32—21no—
707C2×C32—42no—
708C2×C32C22×D1211yescharacteristic
709C2×C32C2×D3×D411yescharacteristic
710C2×C32C2×#23711yescharacteristic
711C2×C32#100411yescharacteristic
712C2×C32#100411yescharacteristic
713C2×C32D3×#4111yescharacteristic
714C3⋊D3—22no—
715C3⋊D3—22no—
716C3⋊D3—41no—
717C3⋊D3—41no—
718C3×D3—62no—
719C3×D3—62no—
720C3×D3—121no—
721C3×D3—121no—
722C3×D3—121no—
723C3×D3—121no—
724C3×D3—241no—
725C24—91no—
726C24—271no—
727#41—544no—
728C2×Q8—271no—
729C2×D4—91no—
730C2×D4—91no—
731C2×D4—91no—
732C2×D4—91no—
733C2×D4—91no—
734C2×D4—271no—
735C2×D4—271no—
736C2×D4—271no—
737C2×D4—271no—
738C2×D4—544no—
739C22×C4—91no—
740C22×C4—91no—
741C22×C4—91no—
742C22×C4—271no—
743C22×C4—271no—
744C22×C4—271no—
745C4⋊C4—91no—
746C4⋊C4—91no—
747C4⋊C4—91no—
748C4⋊C4—271no—
749C22⋊C4—91no—
750C22⋊C4—91no—
751C22⋊C4—91no—
752C22⋊C4—91no—
753C22⋊C4—91no—
754C22⋊C4—271no—
755C22⋊C4—271no—
756C22⋊C4—271no—
757C22⋊C4—271no—
758C22⋊C4—271no—
759C22⋊C4—271no—
760C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
761C42—91no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—31no—
765C22×C3—31no—
766C22×C3—32no—
767C22×C3—32no—
768C22×C3—61no—
769C22×C3—61no—
770C22×C3—61no—
771C22×C3—61no—
772C22×C3—61no—
773C22×C3—62no—
774C22×C3—92no—
775C22×C3—92no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3—181no—
779C22×C3—181no—
780C22×C3—181no—
781C22×C3—181no—
782C22×C3—181no—
783C22×C3—181no—
784C22×C3—181no—
785C22×C3—181no—
786C22×C3—181no—
787C22×C3—181no—
788C22×C3—181no—
789C22×C3—181no—
790C22×C3—181no—
791C22×C3—364no—
792C22×C3D3×D1212yes—
793C22×C3C22×D3211yescharacteristic
794C2×D3—32no—
795C2×D3—32no—
796C2×D3—61no—
797C2×D3—61no—
798C2×D3—61no—
799C2×D3—61no—
800C2×D3—61no—
801C2×D3—61no—
802C2×D3—61no—
803C2×D3—61no—
804C2×D3—61no—
805C2×D3—61no—
806C2×D3—61no—
807C2×D3—61no—
808C2×D3—61no—
809C2×D3—61no—
810C2×D3—61no—
811C2×D3—61no—
812C2×D3—92no—
813C2×D3—92no—
814C2×D3—121no—
815C2×D3—121no—
816C2×D3—121no—
817C2×D3—124no—
818C2×D3—181no—
819C2×D3—181no—
820C2×D3—181no—
821C2×D3—181no—
822C2×D3—181no—
823C2×D3—181no—
824C2×D3—181no—
825C2×D3—181no—
826C2×D3—181no—
827C2×D3—181no—
828C2×D3—364no—
829C2×D3—364no—
830C2×D3—364no—
831C2×D3—364no—
832C3×C4—21no—
833C3×C4—21no—
834C3×C4—61no—
835C3×C4—61no—
836C3×C4—61no—
837C3×C4—61no—
838C3×C4—92no—
839C3×C4—121no—
840C3×C4—121no—
841C3×C4—181no—
842C3×C4—181no—
843C3×C4—181no—
844C3×C4—181no—
845C3×C4—181no—
846C3×C4—181no—
847Dic3—32no—
848Dic3—61no—
849Dic3—61no—
850Dic3—61no—
851Dic3—61no—
852Dic3—61no—
853Dic3—61no—
854Dic3—61no—
855Dic3—61no—
856Dic3—61no—
857Dic3—92no—
858Dic3—121no—
859Dic3—121no—
860Dic3—121no—
861Dic3—181no—
862Dic3—181no—
863Dic3—181no—
864C32—21no—
865C32#555411yescharacteristic, complemented
866C32#559111yescharacteristic, complemented
867C23—91no—
868C23—91no—
869C23—91no—
870C23—91no—
871C23—91no—
872C23—182no—
873C23—182no—
874C23—361no—
875C23—542no—
876C23—542no—
877C23—1081no—
878C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
879Q8—542no—
880D4—94no—
881D4—182no—
882D4—182no—
883D4—182no—
884D4—361no—
885D4—542no—
886D4—542no—
887D4—542no—
888D4—1081no—
889C2×C4—91no—
890C2×C4—91no—
891C2×C4—91no—
892C2×C4—91no—
893C2×C4—91no—
894C2×C4—91no—
895C2×C4—91no—
896C2×C4—182no—
897C2×C4—361no—
898C2×C4—361no—
899C2×C4—542no—
900C2×C4—542no—
901C2×C4—542no—
902C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
903C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
904C2×C3—22no—
905C2×C3—31no—
906C2×C3—31no—
907C2×C3—31no—
908C2×C3—31no—
909C2×C3—31no—
910C2×C3—31no—
911C2×C3—62no—
912C2×C3—62no—
913C2×C3—61no—
914C2×C3—61no—
915C2×C3—61no—
916C2×C3—122no—
917C2×C3—182no—
918C2×C3—182no—
919C2×C3—361no—
920C2×C3—361no—
921C2×C3—361no—
922C2×C3C2×D3×D1211yescharacteristic
923C2×C3D3×#23711yescharacteristic
924C2×C3#6431311yescharacteristic
925D3—62no—
926D3—62no—
927D3—121no—
928D3—121no—
929D3—121no—
930D3—121no—
931D3—182no—
932D3—182no—
933D3—241no—
934D3—361no—
935D3—361no—
936C22—21no—
937C22—21no—
938C22—92no—
939C22—92no—
940C22—181no—
941C22—181no—
942C22—181no—
943C22—181no—
944C22—181no—
945C22—181no—
946C22—181no—
947C22—181no—
948C22—181no—
949C22—181no—
950C22—181no—
951C22—181no—
952C22—181no—
953C22—364no—
954C22—1084no—
955C22#8865412yes—
956C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
957C4—21no—
958C4—21no—
959C4—92no—
960C4—181no—
961C4—181no—
962C4—181no—
963C4—181no—
964C4—181no—
965C4—181no—
966C3—31no—
967C3—31no—
968C3—61no—
969C3#1059429211yescharacteristic
970C2—22no—
971C2—182no—
972C2—182no—
973C2—361no—
974C2—361no—
975C2—361no—
976C2C2×#8865411yescharacteristic
977C2#1172250411yescharacteristic
978C2#1172250611yescharacteristic
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)#546
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. C2×#88676C2semidirect
2. C2×#88672C2semidirect
3. #11721742C2semidirect
4. #64091⋊C3C2semidirect
5. #64090⋊C3C2semidirect
6. #11721322C2semidirect
7. C2×#88450C2semidirect
8. #11721162C2semidirect
9. #11721160C2semidirect
10. #11721141C2semidirect
11. #11721133C2semidirect
12. #11721132C2semidirect
13. #11721131C2semidirect
14. #11721127C2semidirect
15. #11721103C2semidirect
21. C22×#1084C22semidirect
23. C2×#638⋊C3C22semidirect
24. C22×(C3⋊Dic3)⋊C3C22semidirect
26. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
27. C2×C4×(C3⋊D3)⋊C3C22semidirect
30. C2×#6200C22semidirect
32. C2×#6198C22semidirect
35. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
36. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
37. C2×#6196C22semidirect
38. C22⋊C4×H(3,𝔽3)C22semidirect
39. #88542C22semidirect
40. #88542C22semidirect
41. C4⋊#1084C22semidirect
42. C4⋊#1084C22semidirect
44. #3752⋊C3C22semidirect
45. #3752⋊C3C22semidirect
46. #3750⋊C3C22semidirect
47. C4×(C3⋊Dic3)⋊C3C22semidirect
48. #88451C22semidirect
51. #88450C22semidirect
52. #88450C22semidirect
53. #88450C22semidirect
54. #88448C22semidirect
59. #64091D3semidirect
60. #64090D3semidirect
106. #638⋊C3D4semidirect
131. C2×#638C2×D3semidirect
132. C22×C3⋊Dic3C2×D3semidirect
134. C2×C4⋊(C3⋊D3)C2×D3semidirect
135. C2×C4×C3⋊D3C2×D3semidirect
169. C32×C22⋊C4C2×D3semidirect
170. C32×C22⋊C4C2×D3semidirect
172. #3752C2×D3semidirect
173. #3752C2×D3semidirect
174. #3750C2×D3semidirect
175. C4×C3⋊Dic3C2×D3semidirect
226. C2×(C3⋊D3)⋊C3#41semidirect
316. #638D12semidirect
518. C2×C3⋊D3#237semidirect
581. H(3,𝔽3)#546semidirect
760. C22⋊C4((C3⋊D3)⋊C3)⋊C2semidirect
865. C32#5554semidirect
866. C32#5591semidirect

Maximal subgroups

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

subgroupindex
C2×#886762
C2×#886722
#117217422
#64091⋊C32
#64090⋊C32
#117213222
C2×#884502
#117211622
#117211602
#117211412
#117211332
#117211322
#117211312
#117211272
#117211032
#105942943
#105942933