Finite Group Databasebeta

← #13150854

Subgroups — #13150854

Order 1728.

1000 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88542C211yesmaximal, characteristic, complemented
2#64138⋊C3C211yesmaximal, characteristic, complemented
3#64135⋊C3C211yesmaximal, characteristic, complemented
4#11721323C211yesmaximal, characteristic
5#11721320C211yesmaximal, characteristic, complemented
6#11721315C211yesmaximal, characteristic, complemented
7#11721309C211yesmaximal, characteristic, complemented
8#11721150C211yesmaximal, characteristic, complemented
9#11721130C211yesmaximal, characteristic, complemented
10#11721123C211yesmaximal, characteristic, complemented
11#11721103C211yesmaximal, characteristic, complemented
12#11721102C211yesmaximal, characteristic, complemented
13#11721092C211yesmaximal, characteristic, complemented
14#11721088C211yesmaximal, characteristic, complemented
15#11721076C211yesmaximal, characteristic, complemented
16#10594940—31nomaximal
17#10594937—31nomaximal
18C23×#272C2211yescharacteristic
19C22×C4×H(3,𝔽3)C2211yescharacteristic
20C22×#1084C2211yescharacteristic
21C2×#638⋊C3C2211yescharacteristic
22C2×#6200C2211yescharacteristic
23C2×#6200C2211yescharacteristic
24C2×#6199C2211yescharacteristic
25C2×#6199C2211yescharacteristic
26C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
27C2×#6196C2211yescharacteristic, complemented
28#88542C2211yescharacteristic
29#88542C2211yescharacteristic
30#88542C2211yescharacteristic
31#88542C2211yescharacteristic
32#3757⋊C3C2211yescharacteristic
33#3757⋊C3C2211yescharacteristic
34#3757⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic, complemented
36#3752⋊C3C2211yescharacteristic, complemented
37C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
38C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
39#3750⋊C3C2211yescharacteristic, complemented
40#3750⋊C3C2211yescharacteristic, complemented
41C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
42C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
43#88451C2211yescharacteristic
44#88451C2211yescharacteristic
45#88451C2211yescharacteristic
46#88451C2211yescharacteristic
47#88450C2211yescharacteristic, complemented
48#88449C2211yescharacteristic, complemented
49#88448C2211yescharacteristic, complemented
50#88448C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53#64138D311yescharacteristic, complemented
54#64135D311yescharacteristic, complemented
55C3×#929—31no—
56C2×C3×(C2×D3)⋊C4—31no—
57C2×C3×(C2×D3)⋊C4—31no—
58C2×C3×(C2×D3)⋊C4—61no—
59C3×#926—31no—
60#63977—31no—
61#63976—31no—
62Dic3×#67—31no—
63D3×#217—31no—
64D3×#217—31no—
65#63964—31no—
66#63964—31no—
67#63952—31no—
68#63915—31no—
69#63902—31no—
70#63899—31no—
71#63893—31no—
72#63891—31no—
73#63891—31no—
74#63890—31no—
75#63880—31no—
76#63878—31no—
77#63877—31no—
78#63862—31no—
79#63861—31no—
80#63859—31no—
81#63858—31no—
82#63854—31no—
83#63852—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×#272—22no—
86C22×#272—22no—
87C22×#272—41no—
88C22×#272C2311yescharacteristic
89C22×#272C2311yescharacteristic
90C22×(C3⋊D3)⋊C3C2311yescharacteristic
91C2×C4×H(3,𝔽3)—22no—
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94C2×#1084—41no—
95C2×#1084C2311yescharacteristic
96C2×#1084C2311yescharacteristic
97#638⋊C3—22no—
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105#6200—22no—
106#6200—41no—
107#6199—22no—
108#6199—41no—
109((C3⋊D3)⋊C3)⋊C4—41no—
110#6196—41no—
111#5658—91no—
112#5527—91no—
113#5495—91no—
114C23×C3×D3—31no—
115C23×C3×D3—31no—
116C23×C3×D3—61no—
117C22×C32×C4—21no—
118C22×C32×C4C2×D311yescharacteristic
119C22×C32×C4C2×D311yescharacteristic
120C2×#638C2×D311yescharacteristic
121C2×C3×#67—31no—
122C22×C3×Dic3—31no—
123C22×C3×Dic3—31no—
124C22×C3×Dic3—61no—
125C2×#627—31no—
126C2×#627—31no—
127C2×#626—31no—
128C2×#626—31no—
129C2×#625—31no—
130C2×#625—31no—
131C2×#624—31no—
132C2×D3×Dic3—31no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137#3757C2×D311yescharacteristic
138#3757C2×D311yescharacteristic
139#3757C2×D311yescharacteristic
140#3752C2×D311yescharacteristic, complemented
141#3752C2×D311yescharacteristic, complemented
142C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
143C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
144#3750C2×D311yescharacteristic, complemented
145#3750C2×D311yescharacteristic, complemented
146C4×C3⋊Dic3C2×D311yescharacteristic, complemented
147C4×C3⋊Dic3C2×D311yescharacteristic, complemented
148C3×#217—31no—
149C3×#217—31no—
150C3×#217—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—31no—
156C3×(C2×D3)⋊C4—31no—
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4—31no—
160C3×(C2×D3)⋊C4—31no—
161C3×(C2×D3)⋊C4—61no—
162C3×(C2×D3)⋊C4—61no—
163C3×(C2×D3)⋊C4—61no—
164C3×(C2×D3)⋊C4—61no—
165C3×C4⋊Dic3—31no—
166C3×C4⋊Dic3—31no—
167C3×Dic3⋊C4—31no—
168C3×Dic3⋊C4—31no—
169C3×C4×Dic3—31no—
170C3×C4×Dic3—31no—
171#3724—31no—
172#3724—31no—
173#3724—31no—
174Dic3⋊Dic3—31no—
175Dic3⋊Dic3—31no—
176Dic3⋊Dic3—31no—
177Dic3⋊Dic3—31no—
178Dic3⋊Dic3—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)#4112yes—
194C22×H(3,𝔽3)C2411yescharacteristic
195C2×#272—21no—
196C2×#272—21no—
197C2×#272—21no—
198C2×#272—21no—
199C2×#272—21no—
200C2×#272—44no—
201C2×#272#4112yes—
202C2×(C3⋊D3)⋊C3—21no—
203C2×(C3⋊D3)⋊C3—21no—
204C2×(C3⋊D3)⋊C3—21no—
205C4×H(3,𝔽3)—21no—
206C4×H(3,𝔽3)—21no—
207#1084—21no—
208#1084—21no—
209(C3⋊Dic3)⋊C3—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×#123—91no—
217C3×#117—91no—
218C2×C3×C22⋊C4—91no—
219#953—91no—
220C2×#217—91no—
221#937—91no—
222D4×Dic3—91no—
223#929—31no—
224#929—91no—
225C4×#67—91no—
226C2×(C2×D3)⋊C4—31no—
227C2×(C2×D3)⋊C4—31no—
228C2×(C2×D3)⋊C4—61no—
229#926—31no—
230#926—91no—
231#924—91no—
232#898—91no—
233#898—91no—
234#898—91no—
235#897—91no—
236#896—91no—
237#894—91no—
238#894—91no—
239#892—91no—
240#886—91no—
241#886—91no—
242#885—91no—
243#885—91no—
244#883—91no—
245#883—91no—
246#882—91no—
247#67⋊C4—91no—
248#67⋊C4—91no—
249#67⋊C4—91no—
250D3×C22⋊C4—91no—
251D3×C22⋊C4—91no—
252#879—91no—
253#879—91no—
254#878—91no—
255#878—91no—
256#878—91no—
257#877—91no—
258#876—91no—
259#875—91no—
260C4×D12—91no—
261#872—91no—
262C23×C32—21no—
263C23×C32C22×D311yescharacteristic
264C23×C32C22×D311yescharacteristic
265C22×C3⋊D3C22×D311yescharacteristic
266C22×C3×D3—31no—
267C22×C3×D3—31no—
268C22×C3×D3—31no—
269C22×C3×D3—31no—
270C22×C3×D3—31no—
271C22×C3×D3—61no—
272C22×C3×D3—61no—
273C22×C3×D3—62no—
274C22×C3×D3—62no—
275C22×C3×D3—64no—
276C22×C3×D3—62no—
277C22×C3×D3—62no—
278C22×C3×D3—122no—
279C22×C3×D3—121no—
280C22×C3×D3—121no—
281C22×C3×D3—122no—
282C2×C32×C4—22no—
283C2×C32×C4—22no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—42no—
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291#638—22no—
292C2×C3⋊Dic3C22×D311yescharacteristic
293C2×C3⋊Dic3C22×D311yescharacteristic
294C2×C3⋊Dic3C22×D311yescharacteristic
295C2×C3⋊Dic3C22×D311yescharacteristic
296C2×C3⋊Dic3C22×D311yescharacteristic
297C2×C3⋊Dic3C22×D311yescharacteristic
298C2×C3⋊Dic3C22×D311yescharacteristic
299C3×#67—62no—
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—61no—
312C2×C3×Dic3—61no—
313C2×C3×Dic3—121no—
314C2×C3×Dic3—121no—
315C2×C3×Dic3—122no—
316#627—121no—
317#627—121no—
318#626—62no—
319#626—121no—
320#625—62no—
321#625—121no—
322#624—121no—
323D3×Dic3—62no—
324D3×Dic3—62no—
325D3×Dic3—121no—
326D3×Dic3—121no—
327D3×Dic3—121no—
328#551—271noSylow
329C2×H(3,𝔽3)—22no—
330C2×H(3,𝔽3)C2×#4111yescharacteristic
331C2×H(3,𝔽3)C2×#4111yescharacteristic
332C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
333#272—22no—
334#272—41no—
335(C3⋊D3)⋊C3—41no—
336C24×C3—91no—
337C23×D3—31no—
338C23×D3—31no—
339C23×D3—61no—
340C2×C3×D4—91no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—61no—
344C22×C3×C4—91no—
345C22×C3×C4D3211yescharacteristic
346C2×#67—31no—
347C2×#67—91no—
348C2×#67—91no—
349C2×#67—91no—
350C2×#67—91no—
351C2×#67—91no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—61no—
355C22×Dic3—91no—
356C22×Dic3—91no—
357C22×Dic3—91no—
358C2×D12—91no—
359C2×D12—91no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3—91no—
363C2×C4×D3—91no—
364C2×C4×D3—91no—
365C2×C4×D3—91no—
366C2×Dic6—91no—
367C2×Dic6—91no—
368C2×Dic6—91no—
369C3×C4⋊C4—91no—
370C3×C4⋊C4—91no—
371C3×C4⋊C4—91no—
372C3×C4⋊C4—91no—
373C3×C22⋊C4—91no—
374C3×C22⋊C4—91no—
375C3×C22⋊C4—91no—
376C3×C22⋊C4—91no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4—91no—
381C3×C22⋊C4—91no—
382C3×C42—91no—
383C3×C42—91no—
384#217—31no—
385#217—31no—
386#217—31no—
387#217—91no—
388#217—91no—
389#217—91no—
390#217—91no—
391#217—91no—
392#217—91no—
393#217—91no—
394#217—91no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—31no—
400(C2×D3)⋊C4—31no—
401(C2×D3)⋊C4—31no—
402(C2×D3)⋊C4—31no—
403(C2×D3)⋊C4—31no—
404(C2×D3)⋊C4—31no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
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—
415(C2×D3)⋊C4—91no—
416(C2×D3)⋊C4—91no—
417(C2×D3)⋊C4—91no—
418(C2×D3)⋊C4—91no—
419(C2×D3)⋊C4—91no—
420(C2×D3)⋊C4—91no—
421C4⋊Dic3—31no—
422C4⋊Dic3—31no—
423C4⋊Dic3—91no—
424C4⋊Dic3—91no—
425C4⋊Dic3—91no—
426C4⋊Dic3—91no—
427C4⋊Dic3—91no—
428C4⋊Dic3—91no—
429Dic3⋊C4—31no—
430Dic3⋊C4—31no—
431Dic3⋊C4—91no—
432Dic3⋊C4—91no—
433Dic3⋊C4—91no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4—91no—
441C4×Dic3—31no—
442C4×Dic3—31no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C4×Dic3—91no—
446C4×Dic3—91no—
447C4×Dic3—91no—
448C22×C32—22no—
449C22×C32—22no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32—22no—
456C22×C32#23512yes—
457C22×C32#23712yes—
458C22×C32C23×D311yescharacteristic
459C22×C32C23×D311yescharacteristic
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3×D3—32no—
464C2×C3×D3—32no—
465C2×C3×D3—62no—
466C2×C3×D3—61no—
467C2×C3×D3—61no—
468C2×C3×D3—61no—
469C2×C3×D3—61no—
470C2×C3×D3—62no—
471C2×C3×D3—61no—
472C2×C3×D3—61no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—61no—
477C2×C3×D3—61no—
478C2×C3×D3—61no—
479C2×C3×D3—61no—
480C2×C3×D3—121no—
481C2×C3×D3—121no—
482C2×C3×D3—121no—
483C2×C3×D3—121no—
484C2×C3×D3—124no—
485C2×C3×D3—124no—
486C2×C3×D3—128no—
487C32×C4—21no—
488C32×C4—21no—
489C32×C4—21no—
490C32×C4—21no—
491C32×C4—41no—
492C32×C4—41no—
493C3⋊Dic3—21no—
494C3⋊Dic3—21no—
495C3⋊Dic3—21no—
496C3⋊Dic3—21no—
497C3⋊Dic3—21no—
498C3⋊Dic3—21no—
499C3⋊Dic3—21no—
500C3×Dic3—61no—
501C3×Dic3—61no—
502C3×Dic3—61no—
503C3×Dic3—61no—
504C3×Dic3—61no—
505C3×Dic3—61no—
506C3×Dic3—61no—
507C3×Dic3—61no—
508C3×Dic3—61no—
509C3×Dic3—61no—
510C3×Dic3—61no—
511C3×Dic3—121no—
512C3×Dic3—121no—
513#126—271no—
514#126—271no—
515#124—271no—
516#123—91no—
517#123—271no—
518#123—271no—
519C22⋊Q8—271no—
520C22⋊Q8—271no—
521#120—271no—
522C4×D4—271no—
523C4×D4—271no—
524#117—91no—
525#117—271no—
526C2×C22⋊C4—91no—
527C2×C22⋊C4—271no—
528H(3,𝔽3)#55111yescharacteristic, complemented, Sylow
529C23×C3—31no—
530C23×C3—31no—
531C23×C3—61no—
532C23×C3—91no—
533C23×C3—91no—
534C23×C3—91no—
535C23×C3—182no—
536C23×C3—182no—
537C23×C3—361no—
538C23×C3C2×D3211yescharacteristic
539C22×D3—31no—
540C22×D3—31no—
541C22×D3—31no—
542C22×D3—31no—
543C22×D3—31no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—62no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—62no—
550C22×D3—64no—
551C22×D3—91no—
552C22×D3—122no—
553C22×D3—121no—
554C22×D3—121no—
555C22×D3—122no—
556C3×D4—182no—
557C2×C3×C4—22no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—62no—
563C2×C3×C4—62no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—91no—
567C2×C3×C4—91no—
568C2×C3×C4—91no—
569C2×C3×C4—91no—
570C2×C3×C4—91no—
571C2×C3×C4—91no—
572C2×C3×C4—91no—
573C2×C3×C4—91no—
574C2×C3×C4—91no—
575C2×C3×C4—122no—
576C2×C3×C4—361no—
577C2×C3×C4C2×D3211yescharacteristic
578C2×C3×C4C2×D3211yescharacteristic
579#67—62no—
580#67—182no—
581#67—182no—
582#67—182no—
583#67—361no—
584#67—361no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—91no—
599C2×Dic3—91no—
600C2×Dic3—91no—
601C2×Dic3—91no—
602C2×Dic3—91no—
603C2×Dic3—91no—
604C2×Dic3—91no—
605C2×Dic3—121no—
606C2×Dic3—121no—
607C2×Dic3—122no—
608C2×Dic3—182no—
609C2×Dic3—361no—
610C2×Dic3—361no—
611D12—182no—
612D12—361no—
613C4×D3—182no—
614C4×D3—182no—
615C4×D3—361no—
616C4×D3—361no—
617C4×D3—361no—
618C4×D3—361no—
619Dic6—361no—
620Dic6—361no—
621Dic6—361no—
622C2×C32—24no—
623C2×C32—22no—
624C2×C32—22no—
625C2×C32—21no—
626C2×C32—21no—
627C2×C32—21no—
628C2×C32C2×#23511yescharacteristic
629C2×C32C2×#23711yescharacteristic
630C2×C32D3×#4111yescharacteristic
631C2×C32D3×#4111yescharacteristic
632C2×C32#100911yescharacteristic
633C2×C32#100911yescharacteristic
634C3⋊D3—41no—
635C3×D3—62no—
636C3×D3—62no—
637C3×D3—122no—
638C3×D3—122no—
639C3×D3—121no—
640C3×D3—121no—
641C3×D3—121no—
642C24—91no—
643C2×Q8—271no—
644C2×D4—91no—
645C2×D4—271no—
646C2×D4—271no—
647C22×C4—91no—
648C22×C4—271no—
649C22×C4—271no—
650C22×C4—271no—
651C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
652C4⋊C4—91no—
653C4⋊C4—91no—
654C4⋊C4—91no—
655C4⋊C4—91no—
656C4⋊C4—271no—
657C4⋊C4—271no—
658C4⋊C4—271no—
659C4⋊C4—271no—
660C22⋊C4—91no—
661C22⋊C4—91no—
662C22⋊C4—91no—
663C22⋊C4—91no—
664C22⋊C4—91no—
665C22⋊C4—91no—
666C22⋊C4—91no—
667C22⋊C4—91no—
668C22⋊C4—91no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C22⋊C4—271no—
672C22⋊C4—271no—
673C22⋊C4—271no—
674C42—91no—
675C42—91no—
676C42—271no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—31no—
680C22×C3—31no—
681C22×C3—32no—
682C22×C3—32no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—62no—
688C22×C3—62no—
689C22×C3—61no—
690C22×C3—62no—
691C22×C3—92no—
692C22×C3—181no—
693C22×C3—181no—
694C22×C3—181no—
695C22×C3—181no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3—181no—
699C22×C3—181no—
700C22×C3—364no—
701C22×C3#380412yes—
702C22×C3C22×D3211yescharacteristic
703C2×D3—32no—
704C2×D3—32no—
705C2×D3—62no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—61no—
713C2×D3—61no—
714C2×D3—61no—
715C2×D3—61no—
716C2×D3—62no—
717C2×D3—61no—
718C2×D3—61no—
719C2×D3—61no—
720C2×D3—121no—
721C2×D3—121no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—124no—
725C2×D3—124no—
726C2×D3—128no—
727C2×D3—181no—
728C2×D3—181no—
729C2×D3—181no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—61no—
733C3×C4—61no—
734C3×C4—61no—
735C3×C4—61no—
736C3×C4—121no—
737C3×C4—121no—
738C3×C4—181no—
739C3×C4—181no—
740C3×C4—181no—
741C3×C4—181no—
742C3×C4—181no—
743C3×C4—181no—
744C3×C4—181no—
745C3×C4—181no—
746C3×C4—181no—
747Dic3—61no—
748Dic3—61no—
749Dic3—61no—
750Dic3—61no—
751Dic3—61no—
752Dic3—61no—
753Dic3—61no—
754Dic3—61no—
755Dic3—61no—
756Dic3—61no—
757Dic3—61no—
758Dic3—121no—
759Dic3—121no—
760Dic3—181no—
761Dic3—181no—
762Dic3—181no—
763Dic3—181no—
764Dic3—181no—
765Dic3—181no—
766Dic3—181no—
767C32—21no—
768C32#552711yescharacteristic, complemented
769C32#565811yescharacteristic, complemented
770C23—91no—
771C23—91no—
772C23—91no—
773C23—182no—
774C23—182no—
775C23—361no—
776C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
777Q8—1081no—
778D4—182no—
779D4—542no—
780D4—1081no—
781C2×C4—22no—
782C2×C4—91no—
783C2×C4—91no—
784C2×C4—91no—
785C2×C4—91no—
786C2×C4—91no—
787C2×C4—91no—
788C2×C4—91no—
789C2×C4—91no—
790C2×C4—91no—
791C2×C4—361no—
792C2×C4—542no—
793C2×C4—1081no—
794C2×C4—1081no—
795C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
796C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
797C2×C3—22no—
798C2×C3—31no—
799C2×C3—31no—
800C2×C3—31no—
801C2×C3—31no—
802C2×C3—31no—
803C2×C3—31no—
804C2×C3—62no—
805C2×C3—62no—
806C2×C3—64no—
807C2×C3—61no—
808C2×C3—61no—
809C2×C3—61no—
810C2×C3—182no—
811C2×C3—361no—
812C2×C3—361no—
813C2×C3#6430611yescharacteristic
814C2×C3#6430811yescharacteristic
815C2×C3C2×#380411yescharacteristic
816D3—62no—
817D3—62no—
818D3—122no—
819D3—121no—
820D3—121no—
821D3—122no—
822D3—121no—
823D3—361no—
824C22—21no—
825C22—21no—
826C22—92no—
827C22—181no—
828C22—181no—
829C22—181no—
830C22—181no—
831C22—181no—
832C22—181no—
833C22—181no—
834C22—181no—
835C22—364no—
836C22#8867112yes—
837C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
838C4—21no—
839C4—21no—
840C4—181no—
841C4—181no—
842C4—181no—
843C4—181no—
844C4—181no—
845C4—181no—
846C4—181no—
847C4—181no—
848C4—181no—
849C3—31no—
850C3—31no—
851C3—61no—
852C3#1059496611yescharacteristic
853C2—22no—
854C2—182no—
855C2—361no—
856C2—361no—
857C2#1172249111yescharacteristic
858C2#1172249311yescharacteristic
859C2C2×#8867111yescharacteristic
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#11721323C2
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. C2×#88542C2semidirect
2. #64138⋊C3C2semidirect
3. #64135⋊C3C2semidirect
5. #11721320C2semidirect
6. #11721315C2semidirect
7. #11721309C2semidirect
8. #11721150C2semidirect
9. #11721130C2semidirect
10. #11721123C2semidirect
11. #11721103C2semidirect
12. #11721102C2semidirect
13. #11721092C2semidirect
14. #11721088C2semidirect
15. #11721076C2semidirect
26. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
27. C2×#6196C22semidirect
35. #3752⋊C3C22semidirect
36. #3752⋊C3C22semidirect
37. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
38. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
39. #3750⋊C3C22semidirect
40. #3750⋊C3C22semidirect
41. C4×(C3⋊Dic3)⋊C3C22semidirect
42. C4×(C3⋊Dic3)⋊C3C22semidirect
47. #88450C22semidirect
48. #88449C22semidirect
49. #88448C22semidirect
50. #88448C22semidirect
51. #88448C22semidirect
52. #88447C22semidirect
53. #64138D3semidirect
54. #64135D3semidirect
140. #3752C2×D3semidirect
141. #3752C2×D3semidirect
142. C4⋊(C3⋊Dic3)C2×D3semidirect
143. C4⋊(C3⋊Dic3)C2×D3semidirect
144. #3750C2×D3semidirect
145. #3750C2×D3semidirect
146. C4×C3⋊Dic3C2×D3semidirect
147. C4×C3⋊Dic3C2×D3semidirect
528. H(3,𝔽3)#551semidirect
768. C32#5527semidirect
769. C32#5658semidirect

Maximal subgroups

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

subgroupindex
C2×#885422
#64138⋊C32
#64135⋊C32
#117213232
#117213202
#117213152
#117213092
#117211502
#117211302
#117211232
#117211032
#117211022
#117210922
#117210882
#117210762
#105949403
#105949373