Finite Group Databasebeta

← #11807777

Subgroups — #11807777

Order 1152.

1269 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63912C211yesmaximal, characteristic
2#10592686C211yesmaximal, characteristic, complemented
3C3×#4990C211yesmaximal, characteristic, complemented
4C3×#4989C211yesmaximal, characteristic, complemented
5#10591384C211yesmaximal, characteristic, complemented
6#10591383C211yesmaximal, characteristic, complemented
7#10591382C211yesmaximal, characteristic, complemented
8#10591381C211yesmaximal, characteristic, complemented
9#10591379C211yesmaximal, characteristic, complemented
10#10591364C211yesmaximal, characteristic, complemented
11#10591363C211yesmaximal, characteristic, complemented
12#10591316C211yesmaximal, characteristic, complemented
13#10591249C211yesmaximal, characteristic, complemented
14#10591219C211yesmaximal, characteristic, complemented
15#10591193C211yesmaximal, characteristic, complemented
16#75490—31nomaximal
17#74401—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43#63912C418yescomplemented
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#884—31no—
55C2×#884—31no—
56C3×#388—31no—
57C3×#385—31no—
58#5213—31no—
59#5213—31no—
60#4990D311yescharacteristic, complemented
61#4989D311yescharacteristic, complemented
62#4988—31no—
63#4987—31no—
64#4987—31no—
65#4987—61no—
66#4978—31no—
67#4958—31no—
68#4958—31no—
69#4957—31no—
70#4957—31no—
71#4956—31no—
72#4956—31no—
73#4951—31no—
74#4950—31no—
75#4939—31no—
76#4933—31no—
77#4670—31no—
78#4668—31no—
79#4665—31no—
80#4665—31no—
81#4664—31no—
82#4664—31no—
83#4655—31no—
84#4652—31no—
85C23×C3⋊D3C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×C4×C3⋊D3—41no—
95C2×C4×C3⋊D3—41no—
96C2×C4×C3⋊D3C2×C414yescomplemented
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C2×C3×C4×D3—41no—
104C2×C3×C4×D3—41no—
105C2×C3×C4×D3—41no—
106C2×#626—41no—
107C2×#626—41no—
108C2×#626—41no—
109C2×#626—41no—
110C2×#626C2×C414yescomplemented
111C2×#626C2×C414yescomplemented
112C2×#625—41no—
113C2×#625—41no—
114C2×#625C2×C414yes—
115C2×D3×Dic3—41no—
116C2×D3×Dic3—41no—
117C2×D3×Dic3—41no—
118C32×C4⋊C4—41no—
119#3752—41no—
120#3752—41no—
121C4⋊(C3⋊Dic3)—41no—
122C3×(C2×D3)⋊C4—41no—
123C3×(C2×D3)⋊C4—41no—
124C3×(C2×D3)⋊C4—41no—
125C3×(C2×D3)⋊C4C2×C414yescomplemented
126C3×(C2×D3)⋊C4C2×C414yescomplemented
127C3×Dic3⋊C4—41no—
128C3×C4×Dic3—41no—
129#3724C2×C414yescomplemented
130Dic3⋊Dic3—41no—
131#3722—41no—
132#3722—41no—
133(C2×D3)⋊Dic3—41no—
134(C2×D3)⋊Dic3—41no—
135(C2×D3)⋊Dic3—41no—
136Dic32—41no—
137#2377—91noSylow
138C23×C3×C4—31no—
139C22×#67—31no—
140C22×#67—31no—
141C22×#67—31no—
142C22×#67—31no—
143C23×Dic3—31no—
144C22×D12—31no—
145C22×D12—31no—
146C22×C4×D3—31no—
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—61no—
150C22×C4×D3C2×D311yescharacteristic
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4C2×D311yescharacteristic
154C2×C3×C4⋊C4C2×D311yescharacteristic
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C42—31no—
161C2×#217—31no—
162C2×#217—31no—
163C2×#217—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—61no—
176C2×(C2×D3)⋊C4—61no—
177C2×(C2×D3)⋊C4C2×D311yescharacteristic
178C2×(C2×D3)⋊C4C2×D311yescharacteristic
179C2×(C2×D3)⋊C4C2×D311yescharacteristic
180C2×(C2×D3)⋊C4C2×D311yescharacteristic
181C2×(C2×D3)⋊C4C2×D311yescharacteristic
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—61no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4C2×D311yescharacteristic
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3C2×D311yescharacteristic
193#884—38no—
194#884—38no—
195C3×#95—31no—
196C3×#95—31no—
197C3×#95—31no—
198C3×#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—61no—
212C3⋊#95—61no—
213C3⋊#95C2×D311yescharacteristic
214C3⋊#95C2×D311yescharacteristic
215C3⋊#95C2×D311yescharacteristic
216C3⋊#95C2×D311yescharacteristic
217C23×C32C2411yescharacteristic
218C22×C3⋊D3—21no—
219C22×C3⋊D3—21no—
220C22×C3⋊D3—21no—
221C22×C3⋊D3—21no—
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3C22×C412yes—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3C22×C412yes—
238C22×C3×D3C22×C412yes—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C22×C412yes—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3C22×C412yes—
257C4×C3⋊D3—44no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3C22×C412yes—
275C2×C3×Dic3C22×C412yes—
276C3×C4×D3—44no—
277#626—44no—
278#626—44no—
279#625—44no—
280D3×Dic3—44no—
281C2×#121—91no—
282#390—91no—
283#390—91no—
284#388—31no—
285#388—91no—
286#387—91no—
287#387—91no—
288#386—91no—
289#386—91no—
290#386—91no—
291#386—91no—
292#385—31no—
293#385—91no—
294#381—91no—
295#380—91no—
296C24×C3—31no—
297C24×C3—31no—
298C23×D3—31no—
299C23×D3—31no—
300C23×D3—61no—
301C23×D3C22×D311yescharacteristic
302C23×D3C22×D311yescharacteristic
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—121no—
313C22×C3×C4—121no—
314C22×C3×C4—121no—
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C2×#67—34no—
322C2×#67—34no—
323C2×#67—34no—
324C2×#67—34no—
325C2×#67—121no—
326C2×#67—121no—
327C2×#67—121no—
328C2×#67—121no—
329C2×#67—121no—
330C2×#67—121no—
331C2×#67—121no—
332C2×#67—121no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C22×Dic3—31no—
337C22×Dic3—31no—
338C22×Dic3—31no—
339C22×Dic3—61no—
340C22×Dic3—61no—
341C22×Dic3—61no—
342C22×Dic3—121no—
343C22×Dic3—121no—
344C22×Dic3—121no—
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C22×Dic3C22×D311yescharacteristic
349C22×Dic3C22×D311yescharacteristic
350C22×Dic3C22×D311yescharacteristic
351C2×D12—34no—
352C2×D12—34no—
353C2×D12—121no—
354C2×D12—121no—
355C2×D12—121no—
356C2×D12—121no—
357C2×C4×D3—34no—
358C2×C4×D3—34no—
359C2×C4×D3—41no—
360C2×C4×D3—41no—
361C2×C4×D3—41no—
362C2×C4×D3—64no—
363C2×C4×D3—121no—
364C2×C4×D3—121no—
365C2×C4×D3—121no—
366C2×C4×D3—121no—
367C2×C4×D3—121no—
368C2×C4×D3—121no—
369C2×C4×D3—121no—
370C2×C4×D3—122no—
371C2×C4×D3—122no—
372C3×C4⋊C4—41no—
373C3×C4⋊C4—41no—
374C3×C4⋊C4—42no—
375C3×C4⋊C4—121no—
376C3×C22⋊C4—34no—
377C3×C22⋊C4—34no—
378C3×C22⋊C4—121no—
379C3×C22⋊C4—121no—
380C3×C22⋊C4—121no—
381C3×C42—121no—
382#217—121no—
383#217—121no—
384#217—121no—
385(C2×D3)⋊C4—41no—
386(C2×D3)⋊C4—41no—
387(C2×D3)⋊C4—41no—
388(C2×D3)⋊C4—121no—
389(C2×D3)⋊C4—121no—
390(C2×D3)⋊C4—121no—
391(C2×D3)⋊C4—121no—
392(C2×D3)⋊C4—121no—
393(C2×D3)⋊C4—121no—
394(C2×D3)⋊C4—121no—
395(C2×D3)⋊C4—121no—
396(C2×D3)⋊C4—121no—
397(C2×D3)⋊C4—121no—
398(C2×D3)⋊C4—121no—
399(C2×D3)⋊C4—122no—
400(C2×D3)⋊C4—122no—
401(C2×D3)⋊C4C4×D314yescomplemented
402(C2×D3)⋊C4C4×D314yescomplemented
403C4⋊Dic3—121no—
404C4⋊Dic3—121no—
405C4⋊Dic3—121no—
406C4⋊Dic3—122no—
407Dic3⋊C4—34no—
408Dic3⋊C4—34no—
409Dic3⋊C4—41no—
410Dic3⋊C4—121no—
411C4×Dic3—41no—
412C4×Dic3—121no—
413C4×Dic3—121no—
414C22×C32C23×C411yescharacteristic
415C22×C32H(5,𝔽2)11yescharacteristic
416C22×C32H(5,𝔽2)11yescharacteristic
417C22×C32H(5,𝔽2)11yescharacteristic
418C22×C32H(5,𝔽2)11yescharacteristic
419C22×C32H(5,𝔽2)11yescharacteristic
420C22×C322−1+411yescharacteristic
421C2×C3⋊D3—22no—
422C2×C3⋊D3—22no—
423C2×C3⋊D3—22no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—22no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C32×C4—22no—
443C32×C4—41no—
444C32×C4—41no—
445C3⋊Dic3—22no—
446C3⋊Dic3—41no—
447C3⋊Dic3—41no—
448C3×Dic3—22no—
449C3×Dic3—22no—
450C3×Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C22×D4—91no—
455C22×D4—91no—
456C22×D4—91no—
457C23×C4—31no—
458C23×C4—91no—
459C23×C4—91no—
460#121—98no—
461C2×C4⋊C4—31no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—91no—
465C2×C4⋊C4D3211yescharacteristic
466C2×C22⋊C4—31no—
467C2×C22⋊C4—31no—
468C2×C22⋊C4—31no—
469C2×C22⋊C4—31no—
470C2×C22⋊C4—31no—
471C2×C22⋊C4—91no—
472C2×C22⋊C4—91no—
473C2×C22⋊C4—91no—
474C2×C22⋊C4—91no—
475C2×C22⋊C4—91no—
476C2×C22⋊C4—91no—
477C2×C22⋊C4—91no—
478C2×C42—31no—
479C2×C42—91no—
480#95—31no—
481#95—31no—
482#95—31no—
483#95—31no—
484#95—91no—
485#95—91no—
486#95—91no—
487#95—91no—
488#95—91no—
489#95—91no—
490C23×C3—21no—
491C23×C3—32no—
492C23×C3—32no—
493C23×C3—61no—
494C23×C3—61no—
495C23×C3—61no—
496C23×C3—61no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—61no—
500C23×C3—61no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3C23×D311yescharacteristic
506C23×C3C23×D311yescharacteristic
507C22×D3—21no—
508C22×D3—21no—
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—21no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—32no—
520C22×D3—32no—
521C22×D3—62no—
522C22×D3—62no—
523C22×D3—62no—
524C22×D3—61no—
525C22×D3—61no—
526C22×D3—61no—
527C22×D3—61no—
528C22×D3—61no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—61no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—121no—
537C22×D3—121no—
538C22×D3—121no—
539C22×D3—121no—
540C22×D3C2×C4×D312yes—
541C22×D3C2×C4×D312yes—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—22no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—124no—
586C2×C3×C4C2×C4×D312yes—
587C2×C3×C4C2×C4×D312yes—
588#67—124no—
589#67—124no—
590#67—124no—
591#67—124no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—32no—
609C2×Dic3—32no—
610C2×Dic3—62no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—121no—
628C2×Dic3—121no—
629C2×Dic3—121no—
630C2×Dic3—121no—
631C2×Dic3—121no—
632C2×Dic3—121no—
633C2×Dic3—121no—
634C2×Dic3—121no—
635C2×Dic3—124no—
636C2×Dic3C2×C4×D312yes—
637C2×Dic3C2×C4×D312yes—
638D12—124no—
639D12—124no—
640C4×D3—44no—
641C4×D3—124no—
642C4×D3—124no—
643C4×D3—128no—
644C4×D3—124no—
645C2×C32#51811yescharacteristic
646C2×C32#51811yescharacteristic
647C2×C32#52011yescharacteristic
648C2×C32#56011yescharacteristic
649C2×C32#56011yescharacteristic
650C2×C32#56211yescharacteristic
651C2×C32#56211yescharacteristic
652C3⋊D3—42no—
653C3×D3—42no—
654C3×D3—42no—
655C24—31no—
656C24—31no—
657C24—91no—
658C2×D4—94no—
659C2×D4—94no—
660C2×D4—94no—
661C2×D4—361no—
662C2×D4—361no—
663C2×D4—361no—
664C2×D4—361no—
665C2×D4—361no—
666C2×D4—361no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—91no—
674C22×C4—94no—
675C22×C4—91no—
676C22×C4—91no—
677C22×C4—121no—
678C22×C4—121no—
679C22×C4—121no—
680C22×C4—361no—
681C22×C4—361no—
682C22×C4—361no—
683C22×C4—361no—
684C22×C4—361no—
685C22×C4C2×D3211yescharacteristic
686C22×C4C2×D3211yescharacteristic
687C22×C4C2×D3211yescharacteristic
688C4⋊C4—41no—
689C4⋊C4—94no—
690C4⋊C4—121no—
691C4⋊C4—361no—
692C4⋊C4—361no—
693C22⋊C4—34no—
694C22⋊C4—34no—
695C22⋊C4—121no—
696C22⋊C4—121no—
697C22⋊C4—121no—
698C22⋊C4—361no—
699C22⋊C4—361no—
700C22⋊C4—361no—
701C22⋊C4—361no—
702C22⋊C4—361no—
703C22⋊C4—361no—
704C22⋊C4—361no—
705C42—121no—
706C42—361no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—62no—
715C22×C3—62no—
716C22×C3—62no—
717C22×C3—62no—
718C22×C3—62no—
719C22×C3—62no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3C22×C4×D311yescharacteristic
729C22×C3C22×C4×D311yescharacteristic
730C22×C3#100411yescharacteristic
731C22×C3#100411yescharacteristic
732C22×C3#100411yescharacteristic
733C22×C3#100411yescharacteristic
734C22×C3#100411yescharacteristic
735C22×C3#100711yescharacteristic
736C22×C3#100911yescharacteristic
737C22×C3#100911yescharacteristic
738C22×C3#100911yescharacteristic
739C22×C3#100911yescharacteristic
740C22×C3#100911yescharacteristic
741C22×C3#101011yescharacteristic
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—64no—
757C2×D3—62no—
758C2×D3—62no—
759C2×D3—62no—
760C2×D3—62no—
761C2×D3—62no—
762C2×D3—62no—
763C2×D3—122no—
764C2×D3—122no—
765C2×D3—122no—
766C2×D3—122no—
767C2×D3—122no—
768C2×D3—122no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C3×C4—24no—
778C3×C4—22no—
779C3×C4—22no—
780C3×C4—41no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—41no—
784C3×C4—62no—
785C3×C4—62no—
786C3×C4—81no—
787C3×C4—81no—
788C3×C4—121no—
789C3×C4—121no—
790C3×C4—121no—
791C3×C4—121no—
792Dic3—22no—
793Dic3—22no—
794Dic3—41no—
795Dic3—41no—
796Dic3—41no—
797Dic3—41no—
798Dic3—62no—
799Dic3—62no—
800Dic3—122no—
801Dic3—121no—
802Dic3—121no—
803Dic3—121no—
804Dic3—121no—
805Dic3—241no—
806Dic3—241no—
807C32#237711yescharacteristic, complemented, Sylow
808C23—32no—
809C23—32no—
810C23—61no—
811C23—61no—
812C23—61no—
813C23—61no—
814C23—61no—
815C23—61no—
816C23—61no—
817C23—61no—
818C23—61no—
819C23—61no—
820C23—61no—
821C23—61no—
822C23—92no—
823C23—181no—
824C23—181no—
825C23—181no—
826C23—181no—
827C23—181no—
828C23—181no—
829C23C22×D3211yescharacteristic
830D4—364no—
831D4—364no—
832D4—364no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—32no—
842C2×C4—32no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—92no—
860C2×C4—124no—
861C2×C4—181no—
862C2×C4—181no—
863C2×C4—181no—
864C2×C4—181no—
865C2×C4—181no—
866C2×C4—181no—
867C2×C4—181no—
868C2×C4—181no—
869C2×C4—364no—
870C2×C4—364no—
871C2×C4C4×D3212yes—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—122no—
880C2×C3—122no—
881C2×C3#550411yescharacteristic
882C2×C3#552311yescharacteristic
883C2×C3#554511yescharacteristic
884C2×C3#554511yescharacteristic
885C2×C3#554511yescharacteristic
886C2×C3#554511yescharacteristic
887C2×C3#559511yescharacteristic
888C2×C3#562011yescharacteristic
889C2×C3#564711yescharacteristic
890C2×C3#564711yescharacteristic
891C2×C3#566611yescharacteristic
892C2×C3#566711yescharacteristic
893C2×C3#568411yescharacteristic
894C2×C3#571111yescharacteristic
895D3—42no—
896D3—42no—
897D3—124no—
898D3—122no—
899D3—122no—
900C22—62no—
901C22—62no—
902C22—62no—
903C22—62no—
904C22—62no—
905C22—62no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—121no—
912C22—121no—
913C22—121no—
914C22—182no—
915C22—182no—
916C22—182no—
917C22—361no—
918C22—361no—
919C22—361no—
920C22—361no—
921C22C2×C4×D3211yescharacteristic
922C22#6430811yescharacteristic
923C22#6431311yescharacteristic
924C22#6431411yescharacteristic
925C22#6431511yescharacteristic
926C22#6432011yescharacteristic
927C22#6433011yescharacteristic
928C4—22no—
929C4—41no—
930C4—41no—
931C4—62no—
932C4—62no—
933C4—121no—
934C4—121no—
935C4—121no—
936C4—121no—
937C4—182no—
938C4—361no—
939C4—361no—
940C3—21no—
941C3#7440111yescharacteristic, complemented
942C3#7549011yescharacteristic, complemented
943C2—122no—
944C2—122no—
945C2—362no—
946C2#1059451011yescharacteristic
947C2#1059459011yescharacteristic
948C2#1059460611yescharacteristic
949C2#1059466311yescharacteristic
950C2#1059505811yescharacteristic
951C2#1059525811yescharacteristic
952C2#1059541711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63912C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2377
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10592686C2semidirect
3. C3×#4990C2semidirect
4. C3×#4989C2semidirect
5. #10591384C2semidirect
6. #10591383C2semidirect
7. #10591382C2semidirect
8. #10591381C2semidirect
9. #10591379C2semidirect
10. #10591364C2semidirect
11. #10591363C2semidirect
12. #10591316C2semidirect
13. #10591249C2semidirect
14. #10591219C2semidirect
15. #10591193C2semidirect
43. #63912C4semidirect
60. #4990D3semidirect
61. #4989D3semidirect
96. C2×C4×C3⋊D3C2×C4semidirect
110. C2×#626C2×C4semidirect
111. C2×#626C2×C4semidirect
125. C3×(C2×D3)⋊C4C2×C4semidirect
126. C3×(C2×D3)⋊C4C2×C4semidirect
129. #3724C2×C4semidirect
401. (C2×D3)⋊C4C4×D3semidirect
402. (C2×D3)⋊C4C4×D3semidirect
807. C32#2377semidirect
941. C3#74401semidirect
942. C3#75490semidirect

Maximal subgroups

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

subgroupindex
C2×#639122
#105926862
C3×#49902
C3×#49892
#105913842
#105913832
#105913822
#105913812
#105913792
#105913642
#105913632
#105913162
#105912492
#105912192
#105911932
#754903
#744013