Finite Group Databasebeta

← #11807773

Subgroups — #11807773

Order 1152.

1295 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63910C211yesmaximal, characteristic
2#10592364C211yesmaximal, characteristic, complemented
3C3×#4668C211yesmaximal, characteristic, complemented
4C3×#4652C211yesmaximal, characteristic, complemented
5#10591387C211yesmaximal, characteristic, complemented
6#10591384C211yesmaximal, characteristic, complemented
7#10591382C211yesmaximal, characteristic, complemented
8#10591382C211yesmaximal, characteristic, complemented
9#10591371C211yesmaximal, characteristic, complemented
10#10591367C211yesmaximal, characteristic, complemented
11#10591320C211yesmaximal, characteristic, complemented
12#10591305C211yesmaximal, characteristic, complemented
13#10591290C211yesmaximal, characteristic, complemented
14#10591262C211yesmaximal, characteristic, complemented
15#10591258C211yesmaximal, characteristic, complemented
16#75313—31nomaximal
17#74401—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43#63910C418yescomplemented
44C32×#95C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#895—31no—
55C2×#884—31no—
56C3×#387—31no—
57C3×#385—31no—
58#5213—31no—
59#5213—31no—
60#4990—31no—
61#4989—31no—
62#4988—31no—
63#4988—31no—
64#4987—31no—
65#4980—31no—
66#4978—31no—
67#4957—31no—
68#4956—31no—
69#4951—31no—
70#4940—31no—
71#4939—31no—
72#4669—31no—
73#4668—31no—
74#4668D311yescharacteristic, complemented
75#4667—31no—
76#4665—31no—
77#4665—31no—
78#4665—31no—
79#4665—31no—
80#4665—31no—
81#4665—61no—
82#4664—31no—
83#4664—31no—
84#4652D311yescharacteristic, complemented
85C23×C3⋊D3C2311yescharacteristic
86C23×C3⋊D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C2×C4⋊(C3⋊D3)—41no—
94C2×C4⋊(C3⋊D3)—41no—
95C2×C4⋊(C3⋊D3)C2×C414yescomplemented
96C2×C4×C3⋊D3—41no—
97C2×C4×C3⋊D3—41no—
98C2×C4×C3⋊D3—41no—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C2×C3×C4×D3—41no—
107C2×C3×C4×D3—41no—
108C2×C3×C4×D3—41no—
109C2×#626—41no—
110C2×#626—41no—
111C2×#626—41no—
112C2×#626—41no—
113C2×#626C2×C414yes—
114C2×#626C2×C414yescomplemented
115C2×#624—41no—
116C2×#624—41no—
117C2×#624C2×C414yescomplemented
118#3752—41no—
119#3752—41no—
120#3752—41no—
121C3×(C2×D3)⋊C4—41no—
122C3×(C2×D3)⋊C4C2×C414yescomplemented
123C3×C4⋊Dic3—41no—
124C3×Dic3⋊C4—41no—
125C3×Dic3⋊C4—41no—
126C3×Dic3⋊C4C2×C414yescomplemented
127C3×C4×Dic3—41no—
128Dic3⋊Dic3—41no—
129#3722—41no—
130#3722—41no—
131#3722—41no—
132#3722—41no—
133#3722C2×C414yescomplemented
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×D12—31no—
142C22×D12—31no—
143C22×D12—31no—
144C22×D12—31no—
145C22×D12—61no—
146C22×C4×D3—31no—
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—31no—
150C22×C4×D3—61no—
151C22×C4×D3C2×D311yescharacteristic
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4—31no—
154C2×C3×C4⋊C4—31no—
155C2×C3×C4⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C42—31no—
159C2×#217—31no—
160C2×#217—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—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—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—61no—
180C2×(C2×D3)⋊C4—61no—
181C2×(C2×D3)⋊C4—61no—
182C2×(C2×D3)⋊C4C2×D311yescharacteristic
183C2×(C2×D3)⋊C4C2×D311yescharacteristic
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3C2×D311yescharacteristic
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4C2×D311yescharacteristic
188C2×Dic3⋊C4C2×D311yescharacteristic
189C2×Dic3⋊C4C2×D311yescharacteristic
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3C2×D311yescharacteristic
193#895—38no—
194#884—38no—
195C3×#95—21no—
196C3×#95—31no—
197C3×#95—31no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95C2×D311yescharacteristic
201C3×#95C2×D311yescharacteristic
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—31no—
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⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3—21no—
229C22×C3⋊D3—21no—
230C22×C3⋊D3C22×C412yes—
231C22×C3⋊D3C22×C412yes—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
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—
254C4⋊(C3⋊D3)—44no—
255C4×C3⋊D3—44no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
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—
276C2×C3×Dic3C22×C412yes—
277C3×C4×D3—44no—
278#626—44no—
279#626—44no—
280#624—44no—
281C2×#121—91no—
282#390—91no—
283#390—91no—
284#388—91no—
285#388—91no—
286#387—31no—
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—
297C23×D3—31no—
298C23×D3—31no—
299C23×D3—31no—
300C23×D3—31no—
301C23×D3—61no—
302C23×D3—61no—
303C23×D3C22×D311yescharacteristic
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—121no—
315C22×C3×C4—121no—
316C22×C3×C4—121no—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C2×#67—34no—
324C2×#67—34no—
325C2×#67—121no—
326C2×#67—121no—
327C2×#67—121no—
328C2×#67—121no—
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3C22×D311yescharacteristic
336C22×Dic3C22×D311yescharacteristic
337C22×Dic3C22×D311yescharacteristic
338C22×Dic3C22×D311yescharacteristic
339C22×Dic3C22×D311yescharacteristic
340C22×Dic3C22×D311yescharacteristic
341C22×Dic3C22×D311yescharacteristic
342C2×D12—34no—
343C2×D12—34no—
344C2×D12—34no—
345C2×D12—34no—
346C2×D12—64no—
347C2×D12—121no—
348C2×D12—121no—
349C2×D12—121no—
350C2×D12—121no—
351C2×D12—122no—
352C2×D12—122no—
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—121no—
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—121no—
371C2×C4×D3—121no—
372C2×C4×D3—122no—
373C2×C4×D3—122no—
374C2×C4×D3—122no—
375C3×C4⋊C4—34no—
376C3×C4⋊C4—121no—
377C3×C4⋊C4—121no—
378C3×C4⋊C4—121no—
379C3×C22⋊C4—34no—
380C3×C22⋊C4—121no—
381C3×C42—121no—
382#217—121no—
383#217—121no—
384(C2×D3)⋊C4—34no—
385(C2×D3)⋊C4—34no—
386(C2×D3)⋊C4—41no—
387(C2×D3)⋊C4—121no—
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—121no—
400(C2×D3)⋊C4—121no—
401(C2×D3)⋊C4—122no—
402(C2×D3)⋊C4—121no—
403(C2×D3)⋊C4—121no—
404(C2×D3)⋊C4—122no—
405(C2×D3)⋊C4—122no—
406(C2×D3)⋊C4C4×D314yescomplemented
407C4⋊Dic3—41no—
408C4⋊Dic3—121no—
409Dic3⋊C4—41no—
410Dic3⋊C4—41no—
411Dic3⋊C4—121no—
412Dic3⋊C4C4×D314yescomplemented
413C4×Dic3—41no—
414C4×Dic3—121no—
415C4×Dic3—121no—
416C22×C32C23×C411yescharacteristic
417C22×C32H(5,𝔽2)11yescharacteristic
418C22×C32H(5,𝔽2)11yescharacteristic
419C22×C32H(5,𝔽2)11yescharacteristic
420C22×C32H(5,𝔽2)11yescharacteristic
421C22×C32H(5,𝔽2)11yescharacteristic
422C22×C322−1+411yescharacteristic
423C2×C3⋊D3—22no—
424C2×C3⋊D3—22no—
425C2×C3⋊D3—22no—
426C2×C3⋊D3—22no—
427C2×C3⋊D3—22no—
428C2×C3⋊D3—22no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3—41no—
432C2×C3⋊D3—41no—
433C2×C3⋊D3—41no—
434C2×C3⋊D3—41no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3×D3—22no—
438C2×C3×D3—22no—
439C2×C3×D3—22no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C32×C4—22no—
445C32×C4—41no—
446C32×C4—41no—
447C3⋊Dic3—41no—
448C3⋊Dic3—41no—
449C3×Dic3—22no—
450C3×Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C22×D4—91no—
457C22×D4—91no—
458C22×D4—91no—
459C23×C4—31no—
460C23×C4—91no—
461C23×C4—91no—
462#121—98no—
463C2×C4⋊C4—31no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—31no—
466C2×C4⋊C4—31no—
467C2×C4⋊C4—91no—
468C2×C22⋊C4—31no—
469C2×C22⋊C4—31no—
470C2×C22⋊C4—91no—
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×C22⋊C4—91no—
479C2×C22⋊C4—91no—
480C2×C42—31no—
481C2×C42—91no—
482#95—31no—
483#95—31no—
484#95—31no—
485#95—31no—
486#95—91no—
487#95—91no—
488#95—91no—
489#95—91no—
490#95—91no—
491#95D3211yescharacteristic
492C23×C3—21no—
493C23×C3—32no—
494C23×C3—61no—
495C23×C3—61no—
496C23×C3—61no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—61no—
500C23×C3C23×D311yescharacteristic
501C23×C3C23×D311yescharacteristic
502C22×D3—21no—
503C22×D3—21no—
504C22×D3—21no—
505C22×D3—21no—
506C22×D3—21no—
507C22×D3—21no—
508C22×D3—32no—
509C22×D3—32no—
510C22×D3—32no—
511C22×D3—32no—
512C22×D3—62no—
513C22×D3—62no—
514C22×D3—62no—
515C22×D3—62no—
516C22×D3—61no—
517C22×D3—61no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—61no—
522C22×D3—61no—
523C22×D3—61no—
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—61no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—121no—
541C22×D3—121no—
542C22×D3—121no—
543C22×D3—121no—
544C22×D3—121no—
545C22×D3—121no—
546C22×D3—121no—
547C22×D3—121no—
548C22×D3—121no—
549C22×D3—121no—
550C22×D3C2×C4×D312yes—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—22no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—22no—
569C2×C3×C4—32no—
570C2×C3×C4—32no—
571C2×C3×C4—32no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
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—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—124no—
598C2×C3×C4C2×C4×D312yes—
599C2×C3×C4C2×C4×D312yes—
600#67—124no—
601#67—124no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—62no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—121no—
634C2×Dic3—121no—
635C2×Dic3—121no—
636C2×Dic3—121no—
637C2×Dic3—121no—
638C2×Dic3C2×C4×D312yes—
639C2×Dic3C2×C4×D312yes—
640C2×Dic3C2×C4×D312yes—
641D12—124no—
642D12—124no—
643D12—128no—
644D12—124no—
645D12—124no—
646C4×D3—44no—
647C4×D3—124no—
648C4×D3—124no—
649C4×D3—128no—
650C4×D3—124no—
651C4×D3—124no—
652C2×C32#51811yescharacteristic
653C2×C32#51811yescharacteristic
654C2×C32#52011yescharacteristic
655C2×C32#56011yescharacteristic
656C2×C32#56011yescharacteristic
657C2×C32#56211yescharacteristic
658C2×C32#56211yescharacteristic
659C3⋊D3—42no—
660C3⋊D3—42no—
661C3×D3—42no—
662C24—31no—
663C24—91no—
664C24—91no—
665C2×D4—94no—
666C2×D4—94no—
667C2×D4—94no—
668C2×D4—361no—
669C2×D4—361no—
670C2×D4—361no—
671C2×D4—361no—
672C2×D4—361no—
673C2×D4—361no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—94no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—121no—
685C22×C4—121no—
686C22×C4—121no—
687C22×C4—361no—
688C22×C4—361no—
689C22×C4—361no—
690C22×C4—361no—
691C22×C4—361no—
692C22×C4C2×D3211yescharacteristic
693C22×C4C2×D3211yescharacteristic
694C22×C4C2×D3211yescharacteristic
695C4⋊C4—34no—
696C4⋊C4—121no—
697C4⋊C4—121no—
698C4⋊C4—121no—
699C4⋊C4—361no—
700C22⋊C4—34no—
701C22⋊C4—94no—
702C22⋊C4—121no—
703C22⋊C4—361no—
704C22⋊C4—361no—
705C22⋊C4—361no—
706C22⋊C4—361no—
707C22⋊C4—361no—
708C22⋊C4—361no—
709C22⋊C4—361no—
710C22⋊C4—361no—
711C22⋊C4—361no—
712C42—121no—
713C42—361no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—62no—
722C22×C3—62no—
723C22×C3—62no—
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#100711yescharacteristic
735C22×C3#100711yescharacteristic
736C22×C3#100911yescharacteristic
737C22×C3#100911yescharacteristic
738C22×C3#100911yescharacteristic
739C22×C3#100911yescharacteristic
740C22×C3#100911yescharacteristic
741C22×C3#100911yescharacteristic
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—64no—
750C2×D3—62no—
751C2×D3—62no—
752C2×D3—62no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—62no—
759C2×D3—62no—
760C2×D3—62no—
761C2×D3—62no—
762C2×D3—122no—
763C2×D3—122no—
764C2×D3—122no—
765C2×D3—122no—
766C2×D3—122no—
767C2×D3—122no—
768C2×D3—122no—
769C2×D3—122no—
770C2×D3—122no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—241no—
788C2×D3—241no—
789C2×D3—241no—
790C2×D3—241no—
791C3×C4—22no—
792C3×C4—22no—
793C3×C4—42no—
794C3×C4—42no—
795C3×C4—41no—
796C3×C4—41no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—62no—
800C3×C4—62no—
801C3×C4—62no—
802C3×C4—81no—
803C3×C4—121no—
804C3×C4—121no—
805C3×C4—121no—
806C3×C4—121no—
807Dic3—22no—
808Dic3—22no—
809Dic3—22no—
810Dic3—41no—
811Dic3—41no—
812Dic3—41no—
813Dic3—41no—
814Dic3—122no—
815Dic3—121no—
816Dic3—121no—
817Dic3—121no—
818Dic3—121no—
819Dic3—241no—
820C32#237711yescharacteristic, complemented, Sylow
821C23—32no—
822C23—61no—
823C23—61no—
824C23—61no—
825C23—61no—
826C23—61no—
827C23—61no—
828C23—92no—
829C23—92no—
830C23—181no—
831C23—181no—
832C23—181no—
833C23—181no—
834C23—181no—
835C23—181no—
836C23—181no—
837C23—181no—
838C23—181no—
839C23—181no—
840C23—181no—
841C23—181no—
842C23C22×D3211yescharacteristic
843D4—364no—
844D4—364no—
845D4—364no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—124no—
876C2×C4—181no—
877C2×C4—181no—
878C2×C4—181no—
879C2×C4—181no—
880C2×C4—181no—
881C2×C4—181no—
882C2×C4—364no—
883C2×C4—364no—
884C2×C4C4×D3212yes—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—122no—
893C2×C3#550411yescharacteristic
894C2×C3#552111yescharacteristic
895C2×C3#554511yescharacteristic
896C2×C3#554511yescharacteristic
897C2×C3#554511yescharacteristic
898C2×C3#557411yescharacteristic
899C2×C3#559511yescharacteristic
900C2×C3#564711yescharacteristic
901C2×C3#564711yescharacteristic
902C2×C3#564711yescharacteristic
903C2×C3#566611yescharacteristic
904C2×C3#566611yescharacteristic
905C2×C3#570011yescharacteristic
906C2×C3#571111yescharacteristic
907D3—42no—
908D3—124no—
909D3—122no—
910D3—122no—
911D3—122no—
912D3—122no—
913D3—242no—
914C22—62no—
915C22—62no—
916C22—62no—
917C22—121no—
918C22—121no—
919C22—121no—
920C22—121no—
921C22—182no—
922C22—182no—
923C22—182no—
924C22—182no—
925C22—182no—
926C22—182no—
927C22—361no—
928C22—361no—
929C22—361no—
930C22—361no—
931C22—361no—
932C22—361no—
933C22—361no—
934C22—361no—
935C22C2×C4×D3211yescharacteristic
936C22#6430711yescharacteristic
937C22#6430811yescharacteristic
938C22#6431411yescharacteristic
939C22#6431411yescharacteristic
940C22#6431411yescharacteristic
941C22#6431611yescharacteristic
942C4—22no—
943C4—41no—
944C4—41no—
945C4—62no—
946C4—62no—
947C4—62no—
948C4—121no—
949C4—121no—
950C4—121no—
951C4—121no—
952C4—361no—
953C4—361no—
954C3—21no—
955C3#7440111yescharacteristic, complemented
956C3#7531311yescharacteristic, complemented
957C2—122no—
958C2—362no—
959C2—362no—
960C2#1059399411yescharacteristic
961C2#1059423611yescharacteristic
962C2#1059424411yescharacteristic
963C2#1059425611yescharacteristic
964C2#1059432711yescharacteristic
965C2#1059458811yescharacteristic
966C2#1059459311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63910C2
hypercenter#95D32
hypocenterC32#2377
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592364C2semidirect
3. C3×#4668C2semidirect
4. C3×#4652C2semidirect
5. #10591387C2semidirect
6. #10591384C2semidirect
7. #10591382C2semidirect
8. #10591382C2semidirect
9. #10591371C2semidirect
10. #10591367C2semidirect
11. #10591320C2semidirect
12. #10591305C2semidirect
13. #10591290C2semidirect
14. #10591262C2semidirect
15. #10591258C2semidirect
43. #63910C4semidirect
74. #4668D3semidirect
84. #4652D3semidirect
95. C2×C4⋊(C3⋊D3)C2×C4semidirect
114. C2×#626C2×C4semidirect
117. C2×#624C2×C4semidirect
122. C3×(C2×D3)⋊C4C2×C4semidirect
126. C3×Dic3⋊C4C2×C4semidirect
133. #3722C2×C4semidirect
406. (C2×D3)⋊C4C4×D3semidirect
412. Dic3⋊C4C4×D3semidirect
820. C32#2377semidirect
955. C3#74401semidirect
956. C3#75313semidirect

Maximal subgroups

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

subgroupindex
C2×#639102
#105923642
C3×#46682
C3×#46522
#105913872
#105913842
#105913822
#105913712
#105913672
#105913202
#105913052
#105912902
#105912622
#105912582
#753133
#744013