Finite Group Databasebeta

← #13148710

Subgroups — #13148710

Order 1728.

1275 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88676C211yesmaximal, characteristic
2C2×C4×((C3⋊D3)⋊C3)⋊C2C211yesmaximal, characteristic, complemented
3#11721739C211yesmaximal, characteristic, complemented
4#64092⋊C3C211yesmaximal, characteristic, complemented
5C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
6#11721319C211yesmaximal, characteristic, complemented
7#11721311C211yesmaximal, characteristic, complemented
8#11721310C211yesmaximal, characteristic, complemented
9#11721160C211yesmaximal, characteristic, complemented
10#11721139C211yesmaximal, characteristic, complemented
11#11721131C211yesmaximal, characteristic, complemented
12#11721129C211yesmaximal, characteristic, complemented
13#11721119C211yesmaximal, characteristic, complemented
14#11721104C211yesmaximal, characteristic, complemented
15#11721102C211yesmaximal, characteristic, complemented
16#10594260—31nomaximal
17D3×#883—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
20C2×#6235C2211yescharacteristic
21C2×C4×#272C2211yescharacteristic, complemented
22C2×#638⋊C3C2211yescharacteristic
23C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
24C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
26#88676—24no—
27C2×#6200C2211yescharacteristic
28C2×#6199C2211yescharacteristic, complemented
29C2×#6198C2211yescharacteristic
30C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
31C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
32C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
33C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
34C4×((C3⋊D3)⋊C3)⋊C2—24no—
35C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
36#88552C2211yescharacteristic, complemented
37#88542C2211yescharacteristic, complemented
38C4⋊#1084C2211yescharacteristic, complemented
39#88540C2211yescharacteristic, complemented
40#3757⋊C3C2211yescharacteristic, complemented
41#3757⋊C3C2211yescharacteristic, complemented
42#3752⋊C3C2211yescharacteristic, complemented
43#3752⋊C3C2211yescharacteristic, complemented
44#3752⋊C3C2211yescharacteristic, complemented
45C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
46#3750⋊C3C2211yescharacteristic, complemented
47#88451C2211yescharacteristic, complemented
48#88450C2211yescharacteristic, complemented
49#88450C2211yescharacteristic, complemented
50#88450C2211yescharacteristic, complemented
51#88449C2211yescharacteristic, complemented
52#88448C2211yescharacteristic, complemented
53#88448C2211yescharacteristic, complemented
54#88448C2211yescharacteristic, complemented
55C2×#3811—31no—
56C2×D3×#67—31no—
57C2×C4×D32—31no—
58C2×C4×D32—31no—
59#64092D311yescharacteristic, complemented
60C22⋊C4×C3⋊D3D311yescharacteristic, complemented
61C3×#883—31no—
62C3×#883—31no—
63C3×#883—31no—
64C3×#883—61no—
65C3×D3×C22⋊C4—31no—
66#63975—31no—
67#63974—31no—
68#63969—31no—
69#63969—31no—
70#63969—31no—
71D3×#217—31no—
72#63921—31no—
73D3×(C2×D3)⋊C4—31no—
74#63905—31no—
75#63900—31no—
76#63891—31no—
77#63890—31no—
78#63890—31no—
79D3×C4⋊Dic3—31no—
80#63883—31no—
81D3×Dic3⋊C4—31no—
82#63854—31no—
83#63853—31no—
84#63850—31no—
85#63850—31no—
86C23×H(3,𝔽3)C2311yescharacteristic
87C22×#272C2311yescharacteristic
88C22×(C3⋊D3)⋊C3—22no—
89C22×(C3⋊D3)⋊C3—22no—
90C22×(C3⋊D3)⋊C3—22no—
91C22×(C3⋊D3)⋊C3C2311yescharacteristic
92C22×(C3⋊D3)⋊C3C2311yescharacteristic
93C22×(C3⋊D3)⋊C3C2311yescharacteristic
94C2×((C3⋊D3)⋊C3)⋊C2—22no—
95C2×((C3⋊D3)⋊C3)⋊C2—22no—
96C2×((C3⋊D3)⋊C3)⋊C2D414yes—
97C2×C4×H(3,𝔽3)C2311yescharacteristic
98C2×C4×H(3,𝔽3)C2311yescharacteristic
99#6235—22no—
100C2×#1084C2311yescharacteristic
101C2×#1084C2311yescharacteristic
102C2×#1084C2311yescharacteristic
103C4×#272—22no—
104#638⋊C3—22no—
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
108C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
109C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
110C4×(C3⋊D3)⋊C3—22no—
111C4×(C3⋊D3)⋊C3—22no—
112C4×(C3⋊D3)⋊C3—22no—
113#6200—22no—
114#6199—22no—
115#6198—22no—
116((C3⋊D3)⋊C3)⋊C4—22no—
117((C3⋊D3)⋊C3)⋊C4—22no—
118((C3⋊D3)⋊C3)⋊C4—22no—
119((C3⋊D3)⋊C3)⋊C4—22no—
120D3×#123—91no—
121D3×#123—91no—
122C2×#883—91no—
123C23×C3⋊D3C2×D311yescharacteristic
124C23×C3×D3—31no—
125C22×D32—31no—
126C22×D32—31no—
127C2×#638C2×D311yescharacteristic
128C2×C4×C3⋊D3C2×D311yescharacteristic
129C2×C4×C3⋊D3C2×D311yescharacteristic
130C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C2×C3×#67—31no—
134C2×C3×#67—61no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—31no—
140C2×C3×C4×D3—61no—
141#3811—64no—
142D3×#67—64no—
143C2×#626—31no—
144C2×#626—31no—
145C2×#626—31no—
146C2×#625—31no—
147C2×#624—31no—
148C2×#624—31no—
149C2×#624—31no—
150C2×#624—31no—
151C2×D3×Dic3—31no—
152C2×D3×Dic3—31no—
153C2×D3×Dic3—31no—
154C2×D3×Dic3—31no—
155C2×D3×Dic3—31no—
156C2×D3×Dic3—31no—
157C4×D32—64no—
158C4×D32—64no—
159C32×C22⋊C4—21no—
160C32×C22⋊C4C2×D311yescharacteristic, complemented
161C32×C22⋊C4C2×D311yescharacteristic, complemented
162#3757C2×D311yescharacteristic, complemented
163#3757C2×D311yescharacteristic, complemented
164#3752C2×D311yescharacteristic, complemented
165#3752C2×D311yescharacteristic, complemented
166#3752C2×D311yescharacteristic, complemented
167C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
168#3750C2×D311yescharacteristic, complemented
169C3×#217—31no—
170C3×#217—31no—
171C3×#217—31no—
172C3×#217—31no—
173C3×#217—61no—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—61no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—61no—
184C3×Dic3⋊C4—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—61no—
188#3724—31no—
189#3724—31no—
190#3724—31no—
191Dic3⋊Dic3—31no—
192Dic3⋊Dic3—31no—
193Dic3⋊Dic3—31no—
194Dic3⋊Dic3—31no—
195Dic3⋊Dic3—31no—
196#3722—31no—
197#3722—31no—
198#3722—31no—
199(C2×D3)⋊Dic3—31no—
200(C2×D3)⋊Dic3—31no—
201(C2×D3)⋊Dic3—31no—
202(C2×D3)⋊Dic3—31no—
203(C2×D3)⋊Dic3—31no—
204C22×H(3,𝔽3)—21no—
205C22×H(3,𝔽3)—21no—
206C22×H(3,𝔽3)—21no—
207C22×H(3,𝔽3)C2411yescharacteristic
208C2×#272—21no—
209C2×#272—21no—
210C2×#272C2×D412yes—
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—44no—
217C2×(C3⋊D3)⋊C3C2×D412yes—
218C2×(C3⋊D3)⋊C3C2×D412yes—
219C2×(C3⋊D3)⋊C3#4112yes—
220C2×(C3⋊D3)⋊C3#4112yes—
221((C3⋊D3)⋊C3)⋊C2—28no—
222C4×H(3,𝔽3)—21no—
223C4×H(3,𝔽3)—21no—
224#1084—21no—
225#1084—21no—
226#1084—21no—
227(C3⋊Dic3)⋊C3—21no—
228(C3⋊Dic3)⋊C3—21no—
229(C3⋊Dic3)⋊C3—21no—
230(C3⋊Dic3)⋊C3—21no—
231(C3⋊Dic3)⋊C3—21no—
232C22×#67—91no—
233C2×D3×D4—91no—
234C2×D3×D4—91no—
235C22×C4×D3—91no—
236C22×C4×D3—91no—
237C22×C4×D3—91no—
238C3×#123—91no—
239C3×#123—91no—
240C2×C3×C22⋊C4—91no—
241C2×#217—91no—
242#935—91no—
243#935—91no—
244#929—91no—
245#929—91no—
246C2×(C2×D3)⋊C4—91no—
247C2×C4⋊Dic3—91no—
248C2×Dic3⋊C4—91no—
249#894—91no—
250#894—91no—
251#894—91no—
252#894—91no—
253D3×C4⋊C4—91no—
254D3×C4⋊C4—91no—
255D3×C4⋊C4—91no—
256D3×C4⋊C4—91no—
257#886—91no—
258#886—91no—
259#883—31no—
260#883—31no—
261#883—31no—
262#883—61no—
263#883—91no—
264#883—91no—
265#883—91no—
266#883—91no—
267#883—91no—
268#883—91no—
269#883—91no—
270#883—91no—
271#883—91no—
272D3×C22⋊C4—31no—
273D3×C22⋊C4—91no—
274D3×C22⋊C4—91no—
275D3×C22⋊C4—91no—
276D3×C22⋊C4—91no—
277D3×C22⋊C4—91no—
278C23×C32—21no—
279C23×C32C22×D311yescharacteristic
280C23×C32C22×D311yescharacteristic
281C22×C3⋊D3—22no—
282C22×C3⋊D3—22no—
283C22×C3⋊D3—22no—
284C22×C3⋊D3C22×D311yescharacteristic
285C22×C3⋊D3C22×D311yescharacteristic
286C22×C3⋊D3C22×D311yescharacteristic
287C22×C3×D3—31no—
288C22×C3×D3—31no—
289C22×C3×D3—31no—
290C22×C3×D3—31no—
291C22×C3×D3—31no—
292C22×C3×D3—61no—
293C22×C3×D3—62no—
294C22×C3×D3—62no—
295C22×C3×D3—62no—
296C2×D32—34no—
297C2×D32—34no—
298C2×D32—62no—
299C2×D32—62no—
300C2×D32—62no—
301C2×D32—62no—
302C2×C32×C4—21no—
303C2×C32×C4—21no—
304C2×C32×C4C22×D311yescharacteristic
305C2×C32×C4C22×D311yescharacteristic
306C2×C32×C4C22×D311yescharacteristic
307C2×C32×C4C22×D311yescharacteristic
308#638—22no—
309C2×C3⋊Dic3C22×D311yescharacteristic
310C2×C3⋊Dic3C22×D311yescharacteristic
311C2×C3⋊Dic3C22×D311yescharacteristic
312C2×C3⋊Dic3C22×D311yescharacteristic
313C2×C3⋊Dic3C22×D311yescharacteristic
314C4×C3⋊D3—22no—
315C4×C3⋊D3—22no—
316C4×C3⋊D3—22no—
317C3×#67—62no—
318C3×#67—62no—
319C3×#67—62no—
320C3×#67—122no—
321C2×C3×Dic3—31no—
322C2×C3×Dic3—31no—
323C2×C3×Dic3—31no—
324C2×C3×Dic3—31no—
325C2×C3×Dic3—31no—
326C2×C3×Dic3—31no—
327C2×C3×Dic3—31no—
328C2×C3×Dic3—31no—
329C2×C3×Dic3—31no—
330C2×C3×Dic3—31no—
331C2×C3×Dic3—31no—
332C2×C3×Dic3—61no—
333C2×C3×Dic3—61no—
334C2×C3×Dic3—61no—
335C3×C4×D3—62no—
336C3×C4×D3—62no—
337C3×C4×D3—62no—
338C3×C4×D3—62no—
339C3×C4×D3—62no—
340C3×C4×D3—122no—
341#626—62no—
342#626—62no—
343#626—62no—
344#625—62no—
345#624—62no—
346#624—62no—
347#624—62no—
348#624—62no—
349D3×Dic3—62no—
350D3×Dic3—62no—
351D3×Dic3—62no—
352D3×Dic3—62no—
353D3×Dic3—62no—
354D3×Dic3—62no—
355C2×#123—271noSylow
356C2×H(3,𝔽3)—41no—
357C2×H(3,𝔽3)C22×D411yescharacteristic
358C2×H(3,𝔽3)C2×#4111yescharacteristic
359C2×H(3,𝔽3)C2×#4111yescharacteristic
360#272—22no—
361(C3⋊D3)⋊C3—22no—
362(C3⋊D3)⋊C3—41no—
363(C3⋊D3)⋊C3#12314yescomplemented
364C24×C3—91no—
365C23×D3—31no—
366C23×D3—91no—
367C23×D3—91no—
368C23×D3—91no—
369C23×D3—91no—
370C2×C3×D4—91no—
371C2×C3×D4—91no—
372C22×C3×C4—91no—
373C22×C3×C4—91no—
374C22×C3×C4—91no—
375C22×C3×C4—91no—
376C2×#67—31no—
377C2×#67—31no—
378C2×#67—31no—
379C2×#67—61no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—91no—
384C2×#67—91no—
385C2×#67—184no—
386C22×Dic3—91no—
387C22×Dic3—91no—
388C22×Dic3—91no—
389C22×Dic3—91no—
390C22×Dic3—91no—
391D3×D4—184no—
392D3×D4—184no—
393C2×D12—91no—
394C2×D12—91no—
395C2×C4×D3—31no—
396C2×C4×D3—31no—
397C2×C4×D3—31no—
398C2×C4×D3—31no—
399C2×C4×D3—31no—
400C2×C4×D3—61no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×C4×D3—91no—
406C2×C4×D3—91no—
407C2×C4×D3—91no—
408C2×C4×D3—91no—
409C2×C4×D3—91no—
410C2×C4×D3—91no—
411C2×C4×D3—91no—
412C2×C4×D3—91no—
413C2×C4×D3—91no—
414C2×C4×D3—184no—
415C2×C4×D3—184no—
416C2×C4×D3—184no—
417C3×C4⋊C4—91no—
418C3×C4⋊C4—91no—
419C3×C4⋊C4—91no—
420C3×C4⋊C4—91no—
421C3×C22⋊C4—31no—
422C3×C22⋊C4—31no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4—91no—
425C3×C22⋊C4—91no—
426C3×C22⋊C4—91no—
427C3×C22⋊C4—91no—
428C3×C22⋊C4—91no—
429C3×C22⋊C4—91no—
430C3×C22⋊C4—91no—
431C3×C22⋊C4D3211yescharacteristic
432#217—31no—
433#217—31no—
434#217—31no—
435#217—31no—
436#217—61no—
437#217—91no—
438#217—91no—
439#217—91no—
440#217—91no—
441#217—91no—
442#217—91no—
443(C2×D3)⋊C4—31no—
444(C2×D3)⋊C4—31no—
445(C2×D3)⋊C4—31no—
446(C2×D3)⋊C4—31no—
447(C2×D3)⋊C4—31no—
448(C2×D3)⋊C4—61no—
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—
457(C2×D3)⋊C4—91no—
458(C2×D3)⋊C4—91no—
459(C2×D3)⋊C4—91no—
460C4⋊Dic3—31no—
461C4⋊Dic3—31no—
462C4⋊Dic3—31no—
463C4⋊Dic3—61no—
464C4⋊Dic3—91no—
465C4⋊Dic3—91no—
466C4⋊Dic3—91no—
467C4⋊Dic3—91no—
468C4⋊Dic3—91no—
469Dic3⋊C4—31no—
470Dic3⋊C4—31no—
471Dic3⋊C4—31no—
472Dic3⋊C4—61no—
473Dic3⋊C4—91no—
474Dic3⋊C4—91no—
475Dic3⋊C4—91no—
476Dic3⋊C4—91no—
477Dic3⋊C4—91no—
478Dic3⋊C4—91no—
479Dic3⋊C4—91no—
480Dic3⋊C4—91no—
481Dic3⋊C4—91no—
482C22×C32—21no—
483C22×C32—21no—
484C22×C32—21no—
485C22×C32—21no—
486C22×C32—21no—
487C22×C32—21no—
488C22×C32—21no—
489C22×C32—41no—
490C22×C32—41no—
491C22×C32—41no—
492C22×C32C23×D311yescharacteristic
493C22×C32C23×D311yescharacteristic
494C2×C3⋊D3—21no—
495C2×C3⋊D3—21no—
496C2×C3⋊D3—21no—
497C2×C3⋊D3—21no—
498C2×C3⋊D3—21no—
499C2×C3⋊D3—44no—
500C2×C3⋊D3#23512yes—
501C2×C3⋊D3D3×D412yes—
502C2×C3⋊D3D3×D412yes—
503C2×C3⋊D3#23712yes—
504C2×C3×D3—32no—
505C2×C3×D3—32no—
506C2×C3×D3—32no—
507C2×C3×D3—32no—
508C2×C3×D3—32no—
509C2×C3×D3—32no—
510C2×C3×D3—62no—
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—61no—
518C2×C3×D3—61no—
519C2×C3×D3—61no—
520C2×C3×D3—121no—
521C2×C3×D3—121no—
522C2×C3×D3—124no—
523D32—68no—
524D32—68no—
525C32×C4—21no—
526C32×C4—21no—
527C32×C4—21no—
528C32×C4—21no—
529C32×C4—41no—
530C32×C4—41no—
531C3⋊Dic3—21no—
532C3⋊Dic3—21no—
533C3⋊Dic3—21no—
534C3⋊Dic3—21no—
535C3⋊Dic3—21no—
536C3×Dic3—61no—
537C3×Dic3—61no—
538C3×Dic3—61no—
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—
548C3×Dic3—121no—
549C3×Dic3—121no—
550C22×D4—271no—
551C23×C4—271no—
552#123—91no—
553#123—91no—
554#123—271no—
555#123—271no—
556#123—271no—
557#123—271no—
558#123—271no—
559#123—271no—
560C2×C4⋊C4—271no—
561C2×C4⋊C4—271no—
562C2×C22⋊C4—91no—
563C2×C22⋊C4—271no—
564C2×C22⋊C4—271no—
565H(3,𝔽3)C2×#12311yescharacteristic, complemented, Sylow
566C23×C3—31no—
567C23×C3—31no—
568C23×C3—61no—
569C23×C3—91no—
570C23×C3—91no—
571C23×C3—91no—
572C23×C3—91no—
573C23×C3—182no—
574C23×C3—182no—
575C23×C3—182no—
576C23×C3C2×D3211yescharacteristic
577C22×D3—31no—
578C22×D3—31no—
579C22×D3—31no—
580C22×D3—31no—
581C22×D3—31no—
582C22×D3—61no—
583C22×D3—62no—
584C22×D3—62no—
585C22×D3—62no—
586C22×D3—91no—
587C22×D3—91no—
588C22×D3—91no—
589C22×D3—94no—
590C22×D3—94no—
591C22×D3—94no—
592C22×D3—182no—
593C22×D3—182no—
594C22×D3—182no—
595C22×D3—182no—
596C22×D3—182no—
597C22×D3—182no—
598C22×D3—182no—
599C22×D3—182no—
600C22×D3—182no—
601C3×D4—182no—
602C3×D4—182no—
603C2×C3×C4—31no—
604C2×C3×C4—31no—
605C2×C3×C4—31no—
606C2×C3×C4—31no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—91no—
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—182no—
618C2×C3×C4—182no—
619C2×C3×C4—182no—
620C2×C3×C4—182no—
621C2×C3×C4C2×D3211yescharacteristic
622C2×C3×C4C2×D3211yescharacteristic
623#67—62no—
624#67—62no—
625#67—62no—
626#67—122no—
627#67—182no—
628#67—182no—
629#67—182no—
630#67—182no—
631#67—182no—
632C2×Dic3—31no—
633C2×Dic3—31no—
634C2×Dic3—31no—
635C2×Dic3—31no—
636C2×Dic3—31no—
637C2×Dic3—31no—
638C2×Dic3—31no—
639C2×Dic3—31no—
640C2×Dic3—31no—
641C2×Dic3—31no—
642C2×Dic3—31no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—91no—
647C2×Dic3—91no—
648C2×Dic3—91no—
649C2×Dic3—91no—
650C2×Dic3—91no—
651C2×Dic3—182no—
652C2×Dic3—182no—
653C2×Dic3—182no—
654C2×Dic3—182no—
655C2×Dic3—182no—
656D12—182no—
657D12—182no—
658C4×D3—62no—
659C4×D3—62no—
660C4×D3—62no—
661C4×D3—62no—
662C4×D3—62no—
663C4×D3—122no—
664C4×D3—182no—
665C4×D3—182no—
666C4×D3—182no—
667C4×D3—182no—
668C4×D3—182no—
669C4×D3—182no—
670C4×D3—182no—
671C4×D3—182no—
672C4×D3—182no—
673C4×D3—182no—
674C4×D3—182no—
675C4×D3—182no—
676C4×D3—182no—
677C2×C32—21no—
678C2×C32—21no—
679C2×C32—21no—
680C2×C32—41no—
681C2×C32—41no—
682C2×C32—81no—
683C2×C32C2×#23511yescharacteristic
684C2×C32C2×D3×D411yescharacteristic
685C2×C32C2×D3×D411yescharacteristic
686C2×C32C2×#23711yescharacteristic
687C2×C32D3×#4111yescharacteristic
688C2×C32D3×#4111yescharacteristic
689C3⋊D3—22no—
690C3⋊D3—41no—
691C3⋊D3#88314yescomplemented
692C3×D3—34no—
693C3×D3—62no—
694C3×D3—62no—
695C3×D3—62no—
696C3×D3—122no—
697C3×D3—121no—
698C24—91no—
699C24—271no—
700C2×D4—91no—
701C2×D4—91no—
702C2×D4—271no—
703C2×D4—271no—
704C2×D4—544no—
705C22×C4—91no—
706C22×C4—91no—
707C22×C4—91no—
708C22×C4—91no—
709C22×C4—271no—
710C22×C4—271no—
711C22×C4—271no—
712C22×C4—271no—
713C22×C4—271no—
714C22×C4—544no—
715C4⋊C4—91no—
716C4⋊C4—91no—
717C4⋊C4—91no—
718C4⋊C4—91no—
719C4⋊C4—271no—
720C4⋊C4—271no—
721C4⋊C4—271no—
722C4⋊C4—271no—
723C22⋊C4—91no—
724C22⋊C4—91no—
725C22⋊C4—91no—
726C22⋊C4—91no—
727C22⋊C4—91no—
728C22⋊C4—91no—
729C22⋊C4—91no—
730C22⋊C4—271no—
731C22⋊C4—271no—
732C22⋊C4—271no—
733C22⋊C4—271no—
734C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—31no—
739C22×C3—31no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3—92no—
748C22×C3—92no—
749C22×C3—92no—
750C22×C3—92no—
751C22×C3—92no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—181no—
756C22×C3—181no—
757C22×C3—181no—
758C22×C3—181no—
759C22×C3—181no—
760C22×C3—181no—
761C22×C3—181no—
762C22×C3—364no—
763C22×C3C22×D3211yescharacteristic
764C2×D3—32no—
765C2×D3—32no—
766C2×D3—32no—
767C2×D3—32no—
768C2×D3—32no—
769C2×D3—32no—
770C2×D3—62no—
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—92no—
781C2×D3—92no—
782C2×D3—92no—
783C2×D3—92no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—124no—
787C2×D3—181no—
788C2×D3—181no—
789C2×D3—181no—
790C2×D3—181no—
791C2×D3—181no—
792C2×D3—188no—
793C2×D3—188no—
794C2×D3—188no—
795C2×D3—364no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—61no—
799C3×C4—61no—
800C3×C4—61no—
801C3×C4—61no—
802C3×C4—121no—
803C3×C4—121no—
804C3×C4—181no—
805C3×C4—181no—
806C3×C4—181no—
807C3×C4—181no—
808C3×C4—181no—
809C3×C4—181no—
810C3×C4—181no—
811C3×C4—181no—
812Dic3—61no—
813Dic3—61no—
814Dic3—61no—
815Dic3—61no—
816Dic3—61no—
817Dic3—61no—
818Dic3—61no—
819Dic3—61no—
820Dic3—61no—
821Dic3—61no—
822Dic3—61no—
823Dic3—121no—
824Dic3—121no—
825Dic3—121no—
826Dic3—181no—
827Dic3—181no—
828Dic3—181no—
829Dic3—181no—
830Dic3—181no—
831C32—21no—
832C32C2×#88311yescharacteristic, complemented
833C32D3×#12311yescharacteristic, complemented
834C23—91no—
835C23—91no—
836C23—91no—
837C23—91no—
838C23—182no—
839C23—182no—
840C23—182no—
841C23—274no—
842C23—542no—
843C23—542no—
844C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
845D4—182no—
846D4—182no—
847D4—542no—
848D4—542no—
849C2×C4—91no—
850C2×C4—91no—
851C2×C4—91no—
852C2×C4—91no—
853C2×C4—91no—
854C2×C4—91no—
855C2×C4—91no—
856C2×C4—91no—
857C2×C4—182no—
858C2×C4—182no—
859C2×C4—182no—
860C2×C4—182no—
861C2×C4—542no—
862C2×C4—542no—
863C2×C4—542no—
864C2×C4—542no—
865C2×C4—542no—
866C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
867C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
868C2×C3—31no—
869C2×C3—31no—
870C2×C3—31no—
871C2×C3—31no—
872C2×C3—31no—
873C2×C3—31no—
874C2×C3—41no—
875C2×C3—61no—
876C2×C3—61no—
877C2×C3—61no—
878C2×C3—94no—
879C2×C3—121no—
880C2×C3—121no—
881C2×C3—182no—
882C2×C3—182no—
883C2×C3—241no—
884C2×C3—361no—
885C2×C3D3×#23511yescharacteristic
886C2×C3D32×D411yescharacteristic
887C2×C3D3×#23711yescharacteristic
888D3—34no—
889D3—62no—
890D3—62no—
891D3—62no—
892D3—94no—
893D3—122no—
894D3—121no—
895D3—182no—
896D3—361no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—92no—
901C22—92no—
902C22—92no—
903C22—92no—
904C22—92no—
905C22—181no—
906C22—181no—
907C22—181no—
908C22—181no—
909C22—181no—
910C22—181no—
911C22—181no—
912C22—364no—
913C22—548no—
914C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
915C4—21no—
916C4—21no—
917C4—181no—
918C4—181no—
919C4—181no—
920C4—181no—
921C4—181no—
922C4—181no—
923C4—181no—
924C4—181no—
925C3—31no—
926C3—31no—
927C3—61no—
928C3D3×#88311yescharacteristic
929C2—41no—
930C2—94no—
931C2—182no—
932C2—182no—
933C2—361no—
934C2#1172249011yescharacteristic
935C2D4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
936C2#1172250411yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC22⋊C4×H(3,𝔽3)C22
prime radicalC2×#88676C2
hypercenterC22⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C2×#123
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
2. C2×C4×((C3⋊D3)⋊C3)⋊C2C2semidirect
3. #11721739C2semidirect
4. #64092⋊C3C2semidirect
5. C22⋊C4×(C3⋊D3)⋊C3C2semidirect
6. #11721319C2semidirect
7. #11721311C2semidirect
8. #11721310C2semidirect
9. #11721160C2semidirect
10. #11721139C2semidirect
11. #11721131C2semidirect
12. #11721129C2semidirect
13. #11721119C2semidirect
14. #11721104C2semidirect
15. #11721102C2semidirect
21. C2×C4×#272C22semidirect
25. C2×C4×(C3⋊D3)⋊C3C22semidirect
28. C2×#6199C22semidirect
33. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
35. C22⋊C4×H(3,𝔽3)C22semidirect
36. #88552C22semidirect
37. #88542C22semidirect
38. C4⋊#1084C22semidirect
39. #88540C22semidirect
40. #3757⋊C3C22semidirect
41. #3757⋊C3C22semidirect
42. #3752⋊C3C22semidirect
43. #3752⋊C3C22semidirect
44. #3752⋊C3C22semidirect
45. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
46. #3750⋊C3C22semidirect
47. #88451C22semidirect
48. #88450C22semidirect
49. #88450C22semidirect
50. #88450C22semidirect
51. #88449C22semidirect
52. #88448C22semidirect
53. #88448C22semidirect
54. #88448C22semidirect
59. #64092D3semidirect
60. C22⋊C4×C3⋊D3D3semidirect
130. C2×C4×C3⋊D3C2×D3semidirect
160. C32×C22⋊C4C2×D3semidirect
161. C32×C22⋊C4C2×D3semidirect
162. #3757C2×D3semidirect
163. #3757C2×D3semidirect
164. #3752C2×D3semidirect
165. #3752C2×D3semidirect
166. #3752C2×D3semidirect
167. C4⋊(C3⋊Dic3)C2×D3semidirect
168. #3750C2×D3semidirect
363. (C3⋊D3)⋊C3#123semidirect
565. H(3,𝔽3)C2×#123semidirect
691. C3⋊D3#883semidirect
734. C22⋊C4((C3⋊D3)⋊C3)⋊C2semidirect
832. C32C2×#883semidirect
833. C32D3×#123semidirect

Maximal subgroups

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

subgroupindex
C2×#886762
C2×C4×((C3⋊D3)⋊C3)⋊C22
#117217392
#64092⋊C32
C22⋊C4×(C3⋊D3)⋊C32
#117213192
#117213112
#117213102
#117211602
#117211392
#117211312
#117211292
#117211192
#117211042
#117211022
#105942603
D3×#8833