Finite Group Databasebeta

← #13148723

Subgroups — #13148723

Order 1728.

946 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721739C211yesmaximal, characteristic, complemented
2#64094⋊C3C211yesmaximal, characteristic, complemented
3#64090⋊C3C211yesmaximal, characteristic, complemented
4#11721324C211yesmaximal, characteristic
5#11721311C211yesmaximal, characteristic, complemented
6#11721306C211yesmaximal, characteristic, complemented
7#11721293C211yesmaximal, characteristic, complemented
8#11721161C211yesmaximal, characteristic, complemented
9#11721160C211yesmaximal, characteristic, complemented
10#11721148C211yesmaximal, characteristic, complemented
11#11721120C211yesmaximal, characteristic, complemented
12#11721111C211yesmaximal, characteristic, complemented
13#11721109C211yesmaximal, characteristic, complemented
14#11721106C211yesmaximal, characteristic, complemented
15#11721097C211yesmaximal, characteristic, complemented
16#10594305—31nomaximal
17#10594299—31nomaximal
18C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
19C2×#6235C2211yescharacteristic
20C2×C4×#272C2211yescharacteristic
21C2×#638⋊C3C2211yescharacteristic
22C2×#638⋊C3C2211yescharacteristic
23C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
24C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
25C2×#634⋊C3C2211yescharacteristic, complemented
26C2×#6199C2211yescharacteristic
27C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
28C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
29#88552C2211yescharacteristic, complemented
30#88542C2211yescharacteristic
31C4⋊#1084C2211yescharacteristic, complemented
32#88540C2211yescharacteristic, complemented
33#3757⋊C3C2211yescharacteristic, complemented
34#3752⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37#3750⋊C3C2211yescharacteristic, complemented
38C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
39C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
40#88451C2211yescharacteristic
41#88451C2211yescharacteristic
42#88450C2211yescharacteristic
43#88450C2211yescharacteristic
44#88450C2211yescharacteristic
45#88450C2211yescharacteristic
46#88450C2211yescharacteristic
47#88449C2211yescharacteristic, complemented
48#88449C2211yescharacteristic, complemented
49#88449C2211yescharacteristic, complemented
50#88449C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53#64094D311yescharacteristic, complemented
54#64090D311yescharacteristic, complemented
55C3×#885—31no—
56C3×#883—31no—
57C3×#883—31no—
58C3×#883—61no—
59C3×#67⋊C4—31no—
60#63983—31no—
61#63983—31no—
62#63975—31no—
63#67⋊Dic3—31no—
64Dic3×#67—31no—
65#63969—31no—
66#63966—31no—
67#63962—31no—
68#63921—31no—
69D3×(C2×D3)⋊C4—31no—
70D3×(C2×D3)⋊C4—31no—
71D3×(C2×D3)⋊C4—31no—
72#63896—31no—
73#63887—31no—
74#63878—31no—
75#63871—31no—
76#63868—31no—
77#63862—31no—
78#63858—31no—
79#63857—31no—
80#63855—31no—
81#63855—31no—
82#63848—31no—
83#63836—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×#272C2311yescharacteristic
86C22×(C3⋊D3)⋊C3C2311yescharacteristic
87C22×(C3⋊D3)⋊C3C2311yescharacteristic
88C2×((C3⋊D3)⋊C3)⋊C2—22no—
89C2×((C3⋊D3)⋊C3)⋊C2—22no—
90C2×((C3⋊D3)⋊C3)⋊C2—41no—
91C2×C4×H(3,𝔽3)C2311yescharacteristic
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93#6235—22no—
94C2×#1084C2311yescharacteristic
95C2×#1084C2311yescharacteristic
96C2×#1084C2311yescharacteristic
97C4×#272—22no—
98#638⋊C3—22no—
99#638⋊C3—41no—
100C2×(C3⋊Dic3)⋊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—
108#634⋊C3—41no—
109#6199—41no—
110((C3⋊D3)⋊C3)⋊C4—22no—
111#5679—91no—
112#5658—91no—
113#5556—91no—
114C22×D32—31no—
115C22×D32—31no—
116C2×#638C2×D311yescharacteristic
117C2×#638C2×D311yescharacteristic
118C22×C3⋊Dic3C2×D311yescharacteristic, complemented
119C2×C4×C3⋊D3C2×D311yescharacteristic
120C2×#634C2×D311yescharacteristic, complemented
121C2×C3×#67—31no—
122C2×C3×#67—31no—
123C2×C3×#67—31no—
124C2×C3×#67—31no—
125C2×C3×#67—61no—
126C22×C3×Dic3—31no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—31no—
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3—61no—
131C2×C3×Dic6—31no—
132C2×#624—31no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—31no—
136C32×C22⋊C4—21no—
137C32×C22⋊C4C2×D311yescharacteristic, complemented
138C32×C22⋊C4C2×D311yescharacteristic, complemented
139#3757C2×D311yescharacteristic, complemented
140#3752C2×D311yescharacteristic
141#3752C2×D311yescharacteristic
142#3752C2×D311yescharacteristic
143#3750C2×D311yescharacteristic, complemented
144C4×C3⋊Dic3C2×D311yescharacteristic, complemented
145C4×C3⋊Dic3C2×D311yescharacteristic, complemented
146C3×#217—31no—
147C3×#217—31no—
148C3×#217—31no—
149C3×#217—61no—
150C3×(C2×D3)⋊C4—31no—
151C3×(C2×D3)⋊C4—31no—
152C3×(C2×D3)⋊C4—31no—
153C3×(C2×D3)⋊C4—31no—
154C3×(C2×D3)⋊C4—31no—
155C3×(C2×D3)⋊C4—61no—
156C3×C4⋊Dic3—31no—
157C3×C4⋊Dic3—31no—
158C3×C4⋊Dic3—61no—
159C3×Dic3⋊C4—31no—
160C3×Dic3⋊C4—31no—
161C3×Dic3⋊C4—31no—
162C3×Dic3⋊C4—61no—
163C3×C4×Dic3—31no—
164C3×C4×Dic3—31no—
165#3724—31no—
166Dic3⋊Dic3—31no—
167Dic3⋊Dic3—31no—
168Dic3⋊Dic3—31no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—31no—
171Dic3⋊Dic3—31no—
172Dic3⋊Dic3—31no—
173Dic3⋊Dic3—31no—
174Dic3⋊Dic3—31no—
175#3722—31no—
176#3722—31no—
177#3722—31no—
178#3722—31no—
179#3722—31no—
180(C2×D3)⋊Dic3—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—
189Dic32—31no—
190Dic32—31no—
191C22×H(3,𝔽3)—21no—
192C22×H(3,𝔽3)—21no—
193C22×H(3,𝔽3)—21no—
194C22×H(3,𝔽3)C2411yescharacteristic
195C2×#272—21no—
196C2×#272—21no—
197C2×#272#4112yes—
198C2×(C3⋊D3)⋊C3—21no—
199C2×(C3⋊D3)⋊C3—21no—
200C2×(C3⋊D3)⋊C3—21no—
201C2×(C3⋊D3)⋊C3—21no—
202C2×(C3⋊D3)⋊C3—21no—
203C2×(C3⋊D3)⋊C3#4112yes—
204((C3⋊D3)⋊C3)⋊C2—44no—
205C4×H(3,𝔽3)—21no—
206C4×H(3,𝔽3)—21no—
207#1084—21no—
208#1084—21no—
209#1084—21no—
210(C3⋊Dic3)⋊C3—21no—
211(C3⋊Dic3)⋊C3—21no—
212(C3⋊Dic3)⋊C3—21no—
213(C3⋊Dic3)⋊C3—21no—
214(C3⋊Dic3)⋊C3—21no—
215(C3⋊Dic3)⋊C3—21no—
216C3×#124—91no—
217C3×#123—91no—
218C3×C4×D4—91no—
219#946—91no—
220#946—91no—
221#937—91no—
222#937—91no—
223#937—91no—
224#935—91no—
225#935—91no—
226D4×Dic3—91no—
227#929—91no—
228C4×#67—91no—
229C2×(C2×D3)⋊C4—91no—
230C2×(C2×D3)⋊C4—91no—
231#926—91no—
232#924—91no—
233#898—91no—
234#898—91no—
235#898—91no—
236#897—91no—
237#896—91no—
238#892—91no—
239#886—91no—
240#885—31no—
241#885—91no—
242#883—31no—
243#883—31no—
244#883—61no—
245#883—91no—
246#883—91no—
247#67⋊C4—31no—
248#67⋊C4—91no—
249#67⋊C4—91no—
250D3×C22⋊C4—91no—
251D3×C22⋊C4—91no—
252D3×C22⋊C4—91no—
253D3×C22⋊C4—91no—
254#879—91no—
255#879—91no—
256#878—91no—
257#877—91no—
258#876—91no—
259#872—91no—
260#872—91no—
261#872—91no—
262C23×C32—21no—
263C23×C32C22×D311yescharacteristic
264C23×C32C22×D311yescharacteristic
265C22×C3⋊D3C22×D311yescharacteristic
266C22×C3⋊D3C22×D311yescharacteristic
267C22×C3×D3—31no—
268C22×C3×D3—31no—
269C22×C3×D3—31no—
270C22×C3×D3—31no—
271C22×C3×D3—61no—
272C2×D32—62no—
273C2×D32—62no—
274C2×D32—62no—
275C2×D32—62no—
276C2×D32—121no—
277C2×D32—121no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283C2×C32×C4C22×D311yescharacteristic
284#638—22no—
285#638—41no—
286C2×C3⋊Dic3—41no—
287C2×C3⋊Dic3C22×D311yescharacteristic
288C2×C3⋊Dic3C22×D311yescharacteristic
289C2×C3⋊Dic3C22×D311yescharacteristic
290C2×C3⋊Dic3C22×D311yescharacteristic
291C2×C3⋊Dic3C22×D311yescharacteristic
292C2×C3⋊Dic3C22×D311yescharacteristic
293C4×C3⋊D3—41no—
294#634—41no—
295C3×#67—62no—
296C3×#67—62no—
297C3×#67—62no—
298C3×#67—122no—
299C3×#67—121no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—31no—
305C2×C3×Dic3—31no—
306C2×C3×Dic3—31no—
307C2×C3×Dic3—31no—
308C2×C3×Dic3—31no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3—31no—
312C2×C3×Dic3—61no—
313C2×C3×Dic3—61no—
314C2×C3×Dic3—61no—
315C2×C3×Dic3—121no—
316C3×C4×D3—62no—
317C3×C4×D3—62no—
318C3×C4×D3—122no—
319C3×C4×D3—121no—
320C3×Dic6—121no—
321#624—62no—
322D3×Dic3—62no—
323D3×Dic3—121no—
324D3×Dic3—121no—
325#551—271noSylow
326C2×H(3,𝔽3)—41no—
327C2×H(3,𝔽3)C2×#4111yescharacteristic
328C2×H(3,𝔽3)C2×#4111yescharacteristic
329C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
330#272—22no—
331(C3⋊D3)⋊C3—22no—
332(C3⋊D3)⋊C3—41no—
333C23×D3—91no—
334C23×D3—91no—
335C23×D3—91no—
336C2×C3×Q8—91no—
337C2×C3×D4—91no—
338C2×C3×D4—91no—
339C2×C3×D4—91no—
340C22×C3×C4—91no—
341C22×C3×C4—91no—
342C22×C3×C4—91no—
343C2×#67—31no—
344C2×#67—31no—
345C2×#67—31no—
346C2×#67—31no—
347C2×#67—61no—
348C2×#67—91no—
349C2×#67—91no—
350C22×Dic3—31no—
351C22×Dic3—91no—
352C22×Dic3—91no—
353C22×Dic3—91no—
354C2×C4×D3—31no—
355C2×C4×D3—31no—
356C2×C4×D3—31no—
357C2×C4×D3—61no—
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3—91no—
363C2×Dic6—31no—
364C2×Dic6—91no—
365C3×C4⋊C4—91no—
366C3×C4⋊C4—91no—
367C3×C4⋊C4—91no—
368C3×C22⋊C4—31no—
369C3×C22⋊C4—31no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—91no—
372C3×C22⋊C4—91no—
373C3×C22⋊C4—91no—
374C3×C22⋊C4—91no—
375C3×C22⋊C4—91no—
376C3×C22⋊C4—91no—
377C3×C22⋊C4D3211yescharacteristic
378C3×C42—91no—
379C3×C42—91no—
380#217—31no—
381#217—31no—
382#217—31no—
383#217—61no—
384#217—91no—
385#217—91no—
386#217—91no—
387#217—91no—
388#217—91no—
389#217—91no—
390#217—91no—
391#217—91no—
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—91no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—91no—
415C4⋊Dic3—31no—
416C4⋊Dic3—31no—
417C4⋊Dic3—61no—
418C4⋊Dic3—91no—
419C4⋊Dic3—91no—
420C4⋊Dic3—91no—
421C4⋊Dic3—91no—
422C4⋊Dic3—91no—
423Dic3⋊C4—31no—
424Dic3⋊C4—31no—
425Dic3⋊C4—31no—
426Dic3⋊C4—61no—
427Dic3⋊C4—91no—
428Dic3⋊C4—91no—
429Dic3⋊C4—91no—
430Dic3⋊C4—91no—
431Dic3⋊C4—91no—
432Dic3⋊C4—91no—
433Dic3⋊C4—91no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438C4×Dic3—31no—
439C4×Dic3—31no—
440C4×Dic3—91no—
441C4×Dic3—91no—
442C4×Dic3—91no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32C23×D311yescharacteristic
456C22×C32C23×D311yescharacteristic
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3⋊D3#23512yes—
463C2×C3×D3—32no—
464C2×C3×D3—32no—
465C2×C3×D3—32no—
466C2×C3×D3—62no—
467C2×C3×D3—61no—
468C2×C3×D3—61no—
469C2×C3×D3—61no—
470C2×C3×D3—61no—
471C2×C3×D3—61no—
472C2×C3×D3—61no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—121no—
477C2×C3×D3—121no—
478D32—124no—
479D32—124no—
480C32×C4—21no—
481C32×C4—21no—
482C32×C4—21no—
483C32×C4—21no—
484C32×C4—41no—
485C32×C4—41no—
486C3⋊Dic3—21no—
487C3⋊Dic3—21no—
488C3⋊Dic3—21no—
489C3⋊Dic3—21no—
490C3⋊Dic3—21no—
491C3⋊Dic3—21no—
492C3×Dic3—61no—
493C3×Dic3—61no—
494C3×Dic3—61no—
495C3×Dic3—61no—
496C3×Dic3—61no—
497C3×Dic3—61no—
498C3×Dic3—61no—
499C3×Dic3—61no—
500C3×Dic3—61no—
501C3×Dic3—61no—
502C3×Dic3—61no—
503C3×Dic3—61no—
504C3×Dic3—121no—
505C3×Dic3—121no—
506C3×Dic3—121no—
507#126—271no—
508#126—271no—
509#124—91no—
510#123—91no—
511#123—271no—
512#123—271no—
513C22⋊Q8—271no—
514C22⋊Q8—271no—
515#120—271no—
516C4×D4—91no—
517C4×D4—271no—
518#117—271no—
519#117—271no—
520C2×C22⋊C4—271no—
521C2×C22⋊C4—271no—
522H(3,𝔽3)#55111yescharacteristic, complemented, Sylow
523C23×C3—31no—
524C23×C3—31no—
525C23×C3—61no—
526C23×C3—91no—
527C23×C3—91no—
528C23×C3—91no—
529C23×C3C2×D3211yescharacteristic
530C22×D3—31no—
531C22×D3—31no—
532C22×D3—31no—
533C22×D3—31no—
534C22×D3—61no—
535C22×D3—91no—
536C22×D3—91no—
537C22×D3—182no—
538C22×D3—182no—
539C22×D3—182no—
540C22×D3—182no—
541C22×D3—182no—
542C22×D3—182no—
543C22×D3—361no—
544C22×D3—361no—
545C22×D3—361no—
546C3×Q8—361no—
547C3×D4—182no—
548C3×D4—182no—
549C3×D4—361no—
550C2×C3×C4—31no—
551C2×C3×C4—31no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—91no—
557C2×C3×C4—91no—
558C2×C3×C4—91no—
559C2×C3×C4—91no—
560C2×C3×C4—91no—
561C2×C3×C4—91no—
562C2×C3×C4—91no—
563C2×C3×C4—91no—
564C2×C3×C4—91no—
565C2×C3×C4—182no—
566C2×C3×C4—361no—
567C2×C3×C4—361no—
568C2×C3×C4C2×D3211yescharacteristic
569C2×C3×C4C2×D3211yescharacteristic
570#67—62no—
571#67—62no—
572#67—62no—
573#67—122no—
574#67—121no—
575#67—182no—
576#67—361no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—31no—
580C2×Dic3—31no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—91no—
596C2×Dic3—91no—
597C2×Dic3—91no—
598C2×Dic3—121no—
599C2×Dic3—182no—
600C2×Dic3—361no—
601C2×Dic3—361no—
602C4×D3—62no—
603C4×D3—62no—
604C4×D3—122no—
605C4×D3—121no—
606C4×D3—182no—
607C4×D3—182no—
608C4×D3—361no—
609C4×D3—361no—
610C4×D3—361no—
611Dic6—121no—
612Dic6—361no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—41no—
617C2×C32—41no—
618C2×C32—81no—
619C2×C32C2×#23511yescharacteristic
620C2×C32#100411yescharacteristic
621C2×C32#100411yescharacteristic
622C2×C32D3×#4111yescharacteristic
623C2×C32D3×#4111yescharacteristic
624C2×C32D3×#4111yescharacteristic
625C3⋊D3—22no—
626C3⋊D3—41no—
627C3×D3—62no—
628C3×D3—62no—
629C3×D3—62no—
630C3×D3—122no—
631C3×D3—121no—
632C24—271no—
633C2×Q8—91no—
634C2×D4—91no—
635C2×D4—91no—
636C2×D4—91no—
637C22×C4—91no—
638C22×C4—91no—
639C22×C4—91no—
640C22×C4—271no—
641C22×C4—271no—
642C4⋊C4—91no—
643C4⋊C4—91no—
644C4⋊C4—91no—
645C4⋊C4—271no—
646C4⋊C4—271no—
647C4⋊C4—271no—
648C4⋊C4—271no—
649C4⋊C4—271no—
650C22⋊C4—91no—
651C22⋊C4—91no—
652C22⋊C4—91no—
653C22⋊C4—91no—
654C22⋊C4—91no—
655C22⋊C4—91no—
656C22⋊C4—271no—
657C22⋊C4—271no—
658C22⋊C4—271no—
659C22⋊C4—271no—
660C22⋊C4—271no—
661C22⋊C4—271no—
662C22⋊C4—271no—
663C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
664C42—91no—
665C42—91no—
666C42—271no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—31no—
671C22×C3—31no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—61no—
679C22×C3—92no—
680C22×C3—92no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—181no—
685C22×C3—181no—
686C22×C3—181no—
687C22×C3—181no—
688C22×C3—181no—
689C22×C3—181no—
690C22×C3—181no—
691C22×C3C22×D3211yescharacteristic
692C2×D3—32no—
693C2×D3—32no—
694C2×D3—32no—
695C2×D3—62no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—61no—
699C2×D3—61no—
700C2×D3—61no—
701C2×D3—61no—
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—61no—
705C2×D3—92no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—181no—
709C2×D3—181no—
710C2×D3—181no—
711C2×D3—181no—
712C2×D3—181no—
713C2×D3—364no—
714C2×D3—364no—
715C2×D3—364no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—61no—
719C3×C4—61no—
720C3×C4—61no—
721C3×C4—61no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4—181no—
725C3×C4—181no—
726C3×C4—181no—
727C3×C4—181no—
728C3×C4—181no—
729C3×C4—181no—
730C3×C4—181no—
731C3×C4—181no—
732C3×C4—181no—
733Dic3—61no—
734Dic3—61no—
735Dic3—61no—
736Dic3—61no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—61no—
741Dic3—61no—
742Dic3—61no—
743Dic3—61no—
744Dic3—61no—
745Dic3—121no—
746Dic3—121no—
747Dic3—121no—
748Dic3—181no—
749Dic3—181no—
750Dic3—181no—
751Dic3—181no—
752Dic3—181no—
753Dic3—181no—
754C32—21no—
755C32#555611yescharacteristic, complemented
756C32#567911yescharacteristic, complemented
757C23—91no—
758C23—91no—
759C23—91no—
760C23—542no—
761C23—542no—
762C23—1081no—
763C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
764Q8—361no—
765D4—182no—
766D4—182no—
767D4—361no—
768C2×C4—91no—
769C2×C4—91no—
770C2×C4—91no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—91no—
775C2×C4—91no—
776C2×C4—91no—
777C2×C4—182no—
778C2×C4—361no—
779C2×C4—361no—
780C2×C4—542no—
781C2×C4—1081no—
782C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
783C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
784C2×C3—31no—
785C2×C3—31no—
786C2×C3—31no—
787C2×C3—31no—
788C2×C3—31no—
789C2×C3—31no—
790C2×C3—41no—
791C2×C3—61no—
792C2×C3—61no—
793C2×C3—61no—
794C2×C3—121no—
795C2×C3—121no—
796C2×C3—182no—
797C2×C3—182no—
798C2×C3—241no—
799C2×C3—361no—
800C2×C3D3×#23511yescharacteristic
801C2×C3#6431211yescharacteristic
802C2×C3#6431311yescharacteristic
803D3—62no—
804D3—62no—
805D3—62no—
806D3—122no—
807D3—121no—
808D3—182no—
809D3—361no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—92no—
814C22—92no—
815C22—181no—
816C22—181no—
817C22—181no—
818C22—181no—
819C22—181no—
820C22—181no—
821C22—181no—
822C22—1084no—
823C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
824C4—21no—
825C4—21no—
826C4—181no—
827C4—181no—
828C4—181no—
829C4—181no—
830C4—181no—
831C4—181no—
832C4—181no—
833C4—181no—
834C4—181no—
835C3—31no—
836C3—31no—
837C3—61no—
838C3#1059430011yescharacteristic
839C2—41no—
840C2—182no—
841C2—182no—
842C2—361no—
843C2#1172249011yescharacteristic
844C2#1172250511yescharacteristic
845C2#1172250611yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC22⋊C4×H(3,𝔽3)C22
prime radical#11721324C2
hypercenterC22⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#551
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. #11721739C2semidirect
2. #64094⋊C3C2semidirect
3. #64090⋊C3C2semidirect
5. #11721311C2semidirect
6. #11721306C2semidirect
7. #11721293C2semidirect
8. #11721161C2semidirect
9. #11721160C2semidirect
10. #11721148C2semidirect
11. #11721120C2semidirect
12. #11721111C2semidirect
13. #11721109C2semidirect
14. #11721106C2semidirect
15. #11721097C2semidirect
23. C22×(C3⋊Dic3)⋊C3C22semidirect
25. C2×#634⋊C3C22semidirect
28. C22⋊C4×H(3,𝔽3)C22semidirect
29. #88552C22semidirect
31. C4⋊#1084C22semidirect
32. #88540C22semidirect
33. #3757⋊C3C22semidirect
37. #3750⋊C3C22semidirect
38. C4×(C3⋊Dic3)⋊C3C22semidirect
39. C4×(C3⋊Dic3)⋊C3C22semidirect
47. #88449C22semidirect
48. #88449C22semidirect
49. #88449C22semidirect
50. #88449C22semidirect
51. #88448C22semidirect
52. #88447C22semidirect
53. #64094D3semidirect
54. #64090D3semidirect
118. C22×C3⋊Dic3C2×D3semidirect
120. C2×#634C2×D3semidirect
137. C32×C22⋊C4C2×D3semidirect
138. C32×C22⋊C4C2×D3semidirect
139. #3757C2×D3semidirect
143. #3750C2×D3semidirect
144. C4×C3⋊Dic3C2×D3semidirect
145. C4×C3⋊Dic3C2×D3semidirect
522. H(3,𝔽3)#551semidirect
663. C22⋊C4((C3⋊D3)⋊C3)⋊C2semidirect
755. C32#5556semidirect
756. C32#5679semidirect

Maximal subgroups

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

subgroupindex
#117217392
#64094⋊C32
#64090⋊C32
#117213242
#117213112
#117213062
#117212932
#117211612
#117211602
#117211482
#117211202
#117211112
#117211092
#117211062
#117210972
#105943053
#105942993