Finite Group Databasebeta

← #13148489

Subgroups — #13148489

Order 1728.

1123 conjugacy classes of subgroups.

The subgroup lattice has 835 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88671C211yesmaximal, characteristic
2#11721737C211yesmaximal, characteristic, complemented
3#64090⋊C3C211yesmaximal, characteristic, complemented
4#64086⋊C3C211yesmaximal, characteristic, complemented
5#11721315C211yesmaximal, characteristic, complemented
6C2×#88448C211yesmaximal, characteristic, complemented
7#11721293C211yesmaximal, characteristic, complemented
8C4×#6200C211yesmaximal, characteristic, complemented
9#11721147C211yesmaximal, characteristic, complemented
10#11721123C211yesmaximal, characteristic, complemented
11#11721121C211yesmaximal, characteristic, complemented
12#11721119C211yesmaximal, characteristic, complemented
13C4×#6196C211yesmaximal, characteristic, complemented
14#11721077C211yesmaximal, characteristic, complemented
15#11721076C211yesmaximal, characteristic, complemented
16#10594051—31nomaximal
17#10594049—31nomaximal
18C2×#6235C2211yescharacteristic
19C22×#1084C2211yescharacteristic
20C2×C4×#272C2211yescharacteristic
21C2×#638⋊C3C2211yescharacteristic
22C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
23C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
24C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
25C2×#6200C2211yescharacteristic
26C2×#6199C2211yescharacteristic
27C2×#6199C2211yescharacteristic
28#88671C418yescomplemented
29C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
30C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
31C2×#6196C2211yescharacteristic
32C22⋊C4×H(3,𝔽3)C2211yescharacteristic
33#88542C2211yescharacteristic
34#88540C2211yescharacteristic
35C4×#1084C2211yescharacteristic
36#3757⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38#3750⋊C3C2211yescharacteristic
39#3750⋊C3C2211yescharacteristic
40#3750⋊C3C2211yescharacteristic
41C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
42C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
43C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
44#88451C2211yescharacteristic
45#88450C2211yescharacteristic
46#88449C2211yescharacteristic
47#88448C2211yescharacteristic
48#88448C2211yescharacteristic
49#88448C2211yescharacteristic
50#88448C2211yescharacteristic
51#88448C2211yescharacteristic
52#88447C2211yescharacteristic
53#88447C2211yescharacteristic
54C2×#3805—31no—
55C2×#3804—31no—
56#64090D311yescharacteristic, complemented
57#64086D311yescharacteristic, complemented
58C3×#67⋊C4—31no—
59C3×#67⋊C4—31no—
60C3×#67⋊C4—31no—
61C3×#67⋊C4—61no—
62C3×#877—31no—
63#67⋊Dic3—31no—
64Dic3×#67—31no—
65Dic3×#67—31no—
66C2×#3724—31no—
67C2×Dic3⋊Dic3—31no—
68#63952—31no—
69C4×#627—31no—
70C4×#627—31no—
71C4×#626—31no—
72#63902—31no—
73C4×#625—31no—
74#63883—31no—
75#63880—31no—
76#63878—31no—
77#63877—31no—
78#63877—31no—
79D3×Dic3⋊C4—31no—
80D3×Dic3⋊C4—31no—
81D3×Dic3⋊C4—31no—
82#63838—31no—
83#63837—31no—
84#63836—31no—
85C23×H(3,𝔽3)C2311yescharacteristic
86C22×#272C2311yescharacteristic
87C22×(C3⋊D3)⋊C3C2311yescharacteristic
88C2×C4×H(3,𝔽3)C2311yescharacteristic
89C2×C4×H(3,𝔽3)C2311yescharacteristic
90#6235C2×C414yescomplemented
91C2×#1084—41no—
92C2×#1084C2311yescharacteristic
93C2×#1084C2311yescharacteristic
94C2×#1084C2311yescharacteristic
95C4×#272—41no—
96#638⋊C3C2×C414yescomplemented
97C2×(C3⋊Dic3)⋊C3—41no—
98C2×(C3⋊Dic3)⋊C3C2×C414yescomplemented
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C4×(C3⋊D3)⋊C3—41no—
107#6200C2×C414yescomplemented
108#6199—41no—
109#6199C2×C414yescomplemented
110((C3⋊D3)⋊C3)⋊C4—41no—
111((C3⋊D3)⋊C3)⋊C4C2×C414yescomplemented
112#6196C2×C414yescomplemented
113#5546—91no—
114#5546—91no—
115#5523—91no—
116C2×#638C2×D311yescharacteristic
117C22×C3⋊Dic3C2×D311yescharacteristic
118C22×C3⋊Dic3C2×D311yescharacteristic
119C2×C4×C3⋊D3C2×D311yescharacteristic
120C2×C3×#67—31no—
121C2×C3×#67—31no—
122C2×C3×#67—31no—
123C2×C3×#67—61no—
124C22×C3×Dic3—31no—
125C22×C3×Dic3—31no—
126C22×C3×Dic3—31no—
127C22×C3×Dic3—31no—
128C22×C3×Dic3—61no—
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—61no—
133C2×#627—31no—
134C2×#627—31no—
135C2×#626—31no—
136C2×#625—31no—
137C2×#624—31no—
138C2×#624—31no—
139#3805—38no—
140#3804—38no—
141C2×D3×Dic3—31no—
142C2×D3×Dic3—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
149C32×C22⋊C4C2×D311yescharacteristic
150#3757C2×D311yescharacteristic
151#3752C2×D311yescharacteristic
152#3750C2×D311yescharacteristic
153#3750C2×D311yescharacteristic
154#3750C2×D311yescharacteristic
155C4×C3⋊Dic3C2×D311yescharacteristic
156C4×C3⋊Dic3C2×D311yescharacteristic
157C4×C3⋊Dic3C2×D311yescharacteristic
158C3×#217—31no—
159C3×(C2×D3)⋊C4—31no—
160C3×(C2×D3)⋊C4—31no—
161C3×(C2×D3)⋊C4—31no—
162C3×(C2×D3)⋊C4—61no—
163C3×Dic3⋊C4—31no—
164C3×Dic3⋊C4—31no—
165C3×Dic3⋊C4—31no—
166C3×Dic3⋊C4—31no—
167C3×Dic3⋊C4—31no—
168C3×Dic3⋊C4—61no—
169C3×C4×Dic3—31no—
170C3×C4×Dic3—31no—
171C3×C4×Dic3—31no—
172C3×C4×Dic3—31no—
173C3×C4×Dic3—31no—
174C3×C4×Dic3—61no—
175#3724—31no—
176#3724—31no—
177#3724—31no—
178#3724—31no—
179#3724—31no—
180Dic3⋊Dic3—31no—
181Dic3⋊Dic3—31no—
182Dic3⋊Dic3—31no—
183Dic3⋊Dic3—31no—
184Dic3⋊Dic3—31no—
185Dic3⋊Dic3—31no—
186Dic3⋊Dic3—31no—
187#3722—31no—
188(C2×D3)⋊Dic3—31no—
189(C2×D3)⋊Dic3—31no—
190(C2×D3)⋊Dic3—31no—
191Dic32—31no—
192Dic32—31no—
193Dic32—31no—
194Dic32—31no—
195C22×H(3,𝔽3)—21no—
196C22×H(3,𝔽3)—21no—
197C22×H(3,𝔽3)C22×C412yes—
198C22×H(3,𝔽3)C2411yescharacteristic
199C2×#272—21no—
200C2×#272—21no—
201C2×#272C22×C412yes—
202C2×(C3⋊D3)⋊C3—21no—
203C2×(C3⋊D3)⋊C3—21no—
204C2×(C3⋊D3)⋊C3C22×C412yes—
205C4×H(3,𝔽3)—21no—
206C4×H(3,𝔽3)—21no—
207#1084—21no—
208#1084—21no—
209#1084C22×C412yes—
210(C3⋊Dic3)⋊C3—21no—
211(C3⋊Dic3)⋊C3—21no—
212(C3⋊Dic3)⋊C3—21no—
213(C3⋊Dic3)⋊C3—21no—
214(C3⋊Dic3)⋊C3C22×C412yes—
215(C3⋊Dic3)⋊C3C22×C412yes—
216(C3⋊Dic3)⋊C3C22×C412yes—
217C2×#237—91no—
218C2×#237—91no—
219C2×#235—91no—
220C3×C4×D4—91no—
221C3×C4×D4—91no—
222C3×#117—91no—
223D4×Dic3—91no—
224D4×Dic3—91no—
225C4×#67—91no—
226C4×#67—91no—
227C4×#67—91no—
228C4×#67—91no—
229C2×C4⋊Dic3—91no—
230C2×Dic3⋊C4—91no—
231C2×Dic3⋊C4—91no—
232C2×Dic3⋊C4—91no—
233C2×Dic3⋊C4—91no—
234#892—91no—
235#892—91no—
236D3×C4⋊C4—91no—
237D3×C4⋊C4—91no—
238D3×C4⋊C4—91no—
239D3×C4⋊C4—91no—
240#887—91no—
241#887—91no—
242#67⋊C4—31no—
243#67⋊C4—31no—
244#67⋊C4—31no—
245#67⋊C4—61no—
246#67⋊C4—91no—
247#67⋊C4—91no—
248#67⋊C4—91no—
249#67⋊C4—91no—
250#67⋊C4—91no—
251#877—31no—
252#877—91no—
253#877—91no—
254#877—91no—
255C4×D12—91no—
256C4×D12—91no—
257#872—91no—
258#872—91no—
259C4×Dic6—91no—
260C4×Dic6—91no—
261C4×Dic6—91no—
262C4×Dic6—91no—
263C23×C32—21no—
264C23×C32C22×D311yescharacteristic
265C23×C32C22×D311yescharacteristic
266C22×C3⋊D3C22×D311yescharacteristic
267C22×C3×D3—31no—
268C22×C3×D3—31no—
269C22×C3×D3—31no—
270C22×C3×D3—61no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277#638C4×D314yescomplemented
278C2×C3⋊Dic3—41no—
279C2×C3⋊Dic3C4×D314yescomplemented
280C2×C3⋊Dic3C22×D311yescharacteristic
281C2×C3⋊Dic3C22×D311yescharacteristic
282C2×C3⋊Dic3C22×D311yescharacteristic
283C2×C3⋊Dic3C22×D311yescharacteristic
284C2×C3⋊Dic3C22×D311yescharacteristic
285C2×C3⋊Dic3C22×D311yescharacteristic
286C2×C3⋊Dic3C22×D311yescharacteristic
287C4×C3⋊D3—41no—
288C3×#67—34no—
289C3×#67—34no—
290C3×#67—34no—
291C3×#67—64no—
292C2×C3×Dic3—34no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—31no—
298C2×C3×Dic3—31no—
299C2×C3×Dic3—31no—
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—61no—
307C2×C3×Dic3—61no—
308C2×C3×Dic3—61no—
309C2×C3×Dic3—121no—
310C2×C3×Dic3—121no—
311C2×C3×Dic3—121no—
312C2×C3×Dic3—122no—
313C3×C4×D3—121no—
314C3×C4×D3—121no—
315C3×C4×D3—121no—
316C3×C4×D3—122no—
317#627—34no—
318#627—34no—
319#626—34no—
320#625—34no—
321#624—34no—
322#624—121no—
323D3×Dic3—34no—
324D3×Dic3—34no—
325D3×Dic3—34no—
326D3×Dic3—121no—
327D3×Dic3—121no—
328D3×Dic3—121no—
329#520—271noSylow
330C2×H(3,𝔽3)—22no—
331C2×H(3,𝔽3)C23×C411yescharacteristic
332C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
333C2×H(3,𝔽3)2−1+411yescharacteristic
334#272—22no—
335(C3⋊D3)⋊C3—22no—
336C2×C3×D4—91no—
337C2×C3×D4—91no—
338C22×C3×C4—91no—
339C22×C3×C4—91no—
340C22×C3×C4—91no—
341C22×C3×C4—91no—
342C22×C3×C4—91no—
343C2×#67—31no—
344C2×#67—31no—
345C2×#67—31no—
346C2×#67—61no—
347C2×#67—91no—
348C2×#67—91no—
349C2×#67—91no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—61no—
355C22×Dic3—91no—
356C22×Dic3—91no—
357C22×Dic3—91no—
358C22×Dic3—91no—
359C22×Dic3—91no—
360C22×Dic3—91no—
361#237—98no—
362#237—98no—
363#235—98no—
364C2×D12—91no—
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—61no—
369C2×C4×D3—91no—
370C2×C4×D3—91no—
371C2×C4×D3—91no—
372C2×C4×D3—91no—
373C2×C4×D3—91no—
374C2×C4×D3—91no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×Dic6—91no—
379C2×Dic6—91no—
380C2×Dic6—91no—
381C3×C4⋊C4—91no—
382C3×C4⋊C4—91no—
383C3×C4⋊C4—91no—
384C3×C4⋊C4—91no—
385C3×C22⋊C4—31no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—61no—
388C3×C22⋊C4—91no—
389C3×C22⋊C4—91no—
390C3×C22⋊C4—91no—
391C3×C22⋊C4D3211yescharacteristic
392C3×C42—91no—
393C3×C42—91no—
394C3×C42—91no—
395C3×C42—91no—
396#217—31no—
397#217—91no—
398#217—91no—
399#217—91no—
400(C2×D3)⋊C4—31no—
401(C2×D3)⋊C4—31no—
402(C2×D3)⋊C4—31no—
403(C2×D3)⋊C4—61no—
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—
409C4⋊Dic3—91no—
410C4⋊Dic3—91no—
411C4⋊Dic3—91no—
412C4⋊Dic3—91no—
413C4⋊Dic3—91no—
414C4⋊Dic3—91no—
415Dic3⋊C4—31no—
416Dic3⋊C4—31no—
417Dic3⋊C4—31no—
418Dic3⋊C4—31no—
419Dic3⋊C4—31no—
420Dic3⋊C4—61no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
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—
436C4×Dic3—31no—
437C4×Dic3—31no—
438C4×Dic3—31no—
439C4×Dic3—31no—
440C4×Dic3—31no—
441C4×Dic3—61no—
442C4×Dic3—91no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C4×Dic3—91no—
446C4×Dic3—91no—
447C4×Dic3—91no—
448C4×Dic3—91no—
449C4×Dic3—91no—
450C4×Dic3—91no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—22no—
457C22×C32—41no—
458C22×C32—41no—
459C22×C32C2×C4×D312yes—
460C22×C32C2×C4×D312yes—
461C22×C32C23×D311yescharacteristic
462C22×C32C23×D311yescharacteristic
463C2×C3⋊D3—21no—
464C2×C3⋊D3—21no—
465C2×C3⋊D3C2×C4×D312yes—
466C2×C3×D3—32no—
467C2×C3×D3—32no—
468C2×C3×D3—32no—
469C2×C3×D3—62no—
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—
478C32×C4—21no—
479C32×C4—21no—
480C32×C4—21no—
481C32×C4—21no—
482C32×C4—41no—
483C32×C4—41no—
484C3⋊Dic3—21no—
485C3⋊Dic3—21no—
486C3⋊Dic3—21no—
487C3⋊Dic3—21no—
488C3⋊Dic3C2×C4×D312yes—
489C3⋊Dic3C2×C4×D312yes—
490C3⋊Dic3C2×C4×D312yes—
491C3×Dic3—32no—
492C3×Dic3—32no—
493C3×Dic3—32no—
494C3×Dic3—32no—
495C3×Dic3—32no—
496C3×Dic3—62no—
497C3×Dic3—62no—
498C3×Dic3—61no—
499C3×Dic3—61no—
500C3×Dic3—61no—
501C3×Dic3—61no—
502C3×Dic3—61no—
503C3×Dic3—61no—
504C3×Dic3—61no—
505C3×Dic3—61no—
506C3×Dic3—121no—
507C2×#41—271no—
508C4×Q8—271no—
509C4×Q8—271no—
510C4×D4—91no—
511C4×D4—91no—
512C4×D4—271no—
513C4×D4—271no—
514C4×D4—271no—
515C4×D4—271no—
516#117—91no—
517#117—271no—
518#117—271no—
519C2×C4⋊C4—271no—
520C2×C4⋊C4—271no—
521C2×C4⋊C4—271no—
522H(3,𝔽3)#52011yescharacteristic, complemented, Sylow
523C23×C3—31no—
524C23×C3—31no—
525C23×C3—61no—
526C23×C3—91no—
527C23×C3—91no—
528C23×C3C2×D3211yescharacteristic
529C22×D3—31no—
530C22×D3—31no—
531C22×D3—31no—
532C22×D3—61no—
533C22×D3—91no—
534C3×D4—94no—
535C3×D4—94no—
536C2×C3×C4—31no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—91no—
543C2×C3×C4—91no—
544C2×C3×C4—91no—
545C2×C3×C4—94no—
546C2×C3×C4—91no—
547C2×C3×C4—91no—
548C2×C3×C4—91no—
549C2×C3×C4—91no—
550C2×C3×C4—91no—
551C2×C3×C4—91no—
552C2×C3×C4—91no—
553C2×C3×C4—361no—
554C2×C3×C4—361no—
555C2×C3×C4—361no—
556C2×C3×C4—361no—
557C2×C3×C4C2×D3211yescharacteristic
558C2×C3×C4C2×D3211yescharacteristic
559#67—34no—
560#67—34no—
561#67—34no—
562#67—64no—
563#67—94no—
564#67—94no—
565#67—94no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—34no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—31no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—94no—
584C2×Dic3—91no—
585C2×Dic3—91no—
586C2×Dic3—91no—
587C2×Dic3—91no—
588C2×Dic3—91no—
589C2×Dic3—91no—
590C2×Dic3—91no—
591C2×Dic3—94no—
592C2×Dic3—94no—
593C2×Dic3—121no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3—122no—
597C2×Dic3—361no—
598C2×Dic3—361no—
599C2×Dic3—361no—
600D12—94no—
601C4×D3—94no—
602C4×D3—94no—
603C4×D3—94no—
604C4×D3—94no—
605C4×D3—121no—
606C4×D3—121no—
607C4×D3—121no—
608C4×D3—122no—
609C4×D3—361no—
610C4×D3—361no—
611C4×D3—361no—
612C4×D3—361no—
613C4×D3—361no—
614Dic6—94no—
615Dic6—94no—
616Dic6—94no—
617C2×C32—22no—
618C2×C32—22no—
619C2×C32—21no—
620C2×C32—21no—
621C2×C32—21no—
622C2×C32—42no—
623C2×C32C22×C4×D311yescharacteristic
624C2×C32C22×C4×D311yescharacteristic
625C2×C32#100411yescharacteristic
626C2×C32#100911yescharacteristic
627C2×C32#101011yescharacteristic
628C2×C32#101011yescharacteristic
629C3⋊D3—22no—
630C3×D3—62no—
631C3×D3—62no—
632C3×D3—62no—
633C3×D3—122no—
634#41—278no—
635C2×Q8—271no—
636C2×D4—91no—
637C2×D4—91no—
638C2×D4—271no—
639C22×C4—91no—
640C22×C4—91no—
641C22×C4—91no—
642C22×C4—91no—
643C22×C4—91no—
644C22×C4—271no—
645C22×C4—271no—
646C22×C4—271no—
647C22×C4—271no—
648C4⋊C4—91no—
649C4⋊C4—91no—
650C4⋊C4—91no—
651C4⋊C4—91no—
652C4⋊C4—271no—
653C4⋊C4—271no—
654C4⋊C4—271no—
655C4⋊C4—271no—
656C4⋊C4—271no—
657C4⋊C4—271no—
658C22⋊C4—91no—
659C22⋊C4—91no—
660C22⋊C4—91no—
661C22⋊C4—271no—
662C22⋊C4—271no—
663C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
664C42—91no—
665C42—91no—
666C42—91no—
667C42—91no—
668C42—271no—
669C42—271no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—31no—
673C22×C3—31no—
674C22×C3—32no—
675C22×C3—32no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—61no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—62no—
682C22×C3—92no—
683C22×C3—92no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—181no—
687C22×C3—181no—
688C22×C3—181no—
689C22×C3—181no—
690C22×C3C4×D3212yes—
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—92no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—181no—
706C2×D3—181no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—61no—
710C3×C4—61no—
711C3×C4—61no—
712C3×C4—61no—
713C3×C4—92no—
714C3×C4—92no—
715C3×C4—92no—
716C3×C4—92no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4—181no—
720C3×C4—181no—
721C3×C4—181no—
722C3×C4—181no—
723C3×C4—181no—
724C3×C4—181no—
725Dic3—32no—
726Dic3—32no—
727Dic3—32no—
728Dic3—32no—
729Dic3—32no—
730Dic3—62no—
731Dic3—61no—
732Dic3—61no—
733Dic3—61no—
734Dic3—61no—
735Dic3—62no—
736Dic3—61no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—92no—
741Dic3—92no—
742Dic3—92no—
743Dic3—121no—
744Dic3—181no—
745Dic3—181no—
746Dic3—181no—
747Dic3—181no—
748C32—21no—
749C32#552311yescharacteristic, complemented
750C32#554611yescharacteristic, complemented
751C23—91no—
752C23—91no—
753C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
754Q8—274no—
755D4—94no—
756D4—94no—
757D4—274no—
758C2×C4—91no—
759C2×C4—91no—
760C2×C4—91no—
761C2×C4—91no—
762C2×C4—94no—
763C2×C4—91no—
764C2×C4—91no—
765C2×C4—91no—
766C2×C4—91no—
767C2×C4—91no—
768C2×C4—91no—
769C2×C4—274no—
770C2×C4—274no—
771C2×C4—361no—
772C2×C4—361no—
773C2×C4—361no—
774C2×C4—361no—
775C2×C4—1081no—
776C2×C4—1081no—
777C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
778C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
779C2×C3—22no—
780C2×C3—31no—
781C2×C3—31no—
782C2×C3—31no—
783C2×C3—31no—
784C2×C3—31no—
785C2×C3—31no—
786C2×C3—62no—
787C2×C3—62no—
788C2×C3—61no—
789C2×C3—61no—
790C2×C3—61no—
791C2×C3—122no—
792C2×C3—182no—
793C2×C3—182no—
794C2×C3C2×C4×D3211yescharacteristic
795C2×C3#6430911yescharacteristic
796C2×C3#6431411yescharacteristic
797D3—62no—
798D3—62no—
799D3—62no—
800D3—122no—
801D3—182no—
802C22—21no—
803C22—21no—
804C22—92no—
805C22—92no—
806C22—181no—
807C22—181no—
808C22—181no—
809C22—181no—
810C22C4×((C3⋊D3)⋊C3)⋊C212yes—
811C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
812C4—21no—
813C4—21no—
814C4—92no—
815C4—92no—
816C4—92no—
817C4—92no—
818C4—181no—
819C4—181no—
820C4—181no—
821C4—181no—
822C4—181no—
823C4—181no—
824C3—31no—
825C3—31no—
826C3—61no—
827C3#1059404911yescharacteristic
828C2—22no—
829C2—182no—
830C2—182no—
831C2C2×C4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
832C2#1172250211yescharacteristic
833C2#1172250711yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutatorC2×H(3,𝔽3)C23×C4
Frattini, socleC22×C3C22×D32
FittingC22⋊C4×H(3,𝔽3)C22
prime radicalC2×#88671C2
cosocleC22×H(3,𝔽3)C24
hypercenterC22⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#520
LCSG ▷ C2×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. #11721737C2semidirect
3. #64090⋊C3C2semidirect
4. #64086⋊C3C2semidirect
5. #11721315C2semidirect
6. C2×#88448C2semidirect
7. #11721293C2semidirect
8. C4×#6200C2semidirect
9. #11721147C2semidirect
10. #11721123C2semidirect
11. #11721121C2semidirect
12. #11721119C2semidirect
13. C4×#6196C2semidirect
14. #11721077C2semidirect
15. #11721076C2semidirect
28. #88671C4semidirect
56. #64090D3semidirect
57. #64086D3semidirect
90. #6235C2×C4semidirect
96. #638⋊C3C2×C4semidirect
98. C2×(C3⋊Dic3)⋊C3C2×C4semidirect
107. #6200C2×C4semidirect
109. #6199C2×C4semidirect
111. ((C3⋊D3)⋊C3)⋊C4C2×C4semidirect
112. #6196C2×C4semidirect
277. #638C4×D3semidirect
279. C2×C3⋊Dic3C4×D3semidirect
522. H(3,𝔽3)#520semidirect
749. C32#5523semidirect
750. C32#5546semidirect

Maximal subgroups

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

subgroupindex
C2×#886712
#117217372
#64090⋊C32
#64086⋊C32
#117213152
C2×#884482
#117212932
C4×#62002
#117211472
#117211232
#117211212
#117211192
C4×#61962
#117210772
#117210762
#105940513
#105940493