Finite Group Databasebeta

← #11807779

Subgroups — #11807779

Order 1152.

1247 conjugacy classes of subgroups.

The subgroup lattice has 951 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#884C211yesmaximal, characteristic
2#10592650C211yesmaximal, characteristic, complemented
3C3×#4950C211yesmaximal, characteristic, complemented
4#10591721C211yesmaximal, characteristic, complemented
5#10591710C211yesmaximal, characteristic, complemented
6#10591710C211yesmaximal, characteristic, complemented
7#10591707C211yesmaximal, characteristic, complemented
8#10591379C211yesmaximal, characteristic, complemented
9#10591376C211yesmaximal, characteristic, complemented
10#10591323C211yesmaximal, characteristic, complemented
11#10591313C211yesmaximal, characteristic, complemented
12#10591307C211yesmaximal, characteristic, complemented
13#10591294C211yesmaximal, characteristic, complemented
14#10591262C211yesmaximal, characteristic, complemented
15#10591192C211yesmaximal, characteristic, complemented
16#82639—31nomaximal
17#74401—31nomaximal
18C22×C3×#67C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C3×#884C418yescomplemented
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C3×#121—31no—
55C2×#884D311yescharacteristic
56C3×#385—31no—
57#5221—31no—
58#5221—31no—
59#5220—31no—
60#5220—31no—
61#5220—31no—
62#5220—31no—
63#5213—31no—
64#5213—31no—
65#5212—31no—
66#5211—31no—
67#4990—31no—
68#4988—31no—
69#4987—31no—
70#4980—31no—
71#4980—31no—
72#4978—31no—
73#4957—31no—
74#4956—31no—
75#4951—31no—
76#4951—31no—
77#4951—31no—
78#4951—61no—
79#4950—31no—
80#4950D311yescharacteristic, complemented
81#4668—31no—
82#4665—31no—
83#4664—31no—
84#4652—31no—
85C24×C32C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×C3×#67—41no—
95C2×C3×#67—41no—
96C2×C3×#67—41no—
97C2×C3×#67—41no—
98C2×C3×#67C2×C414yes—
99C2×C3×#67C2×C414yescomplemented
100C22×C3×Dic3—41no—
101C22×C3×Dic3—41no—
102C22×C3×Dic3—41no—
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C2×C3×D12—41no—
110C2×C3×D12—41no—
111C2×C3×D12C2×C414yescomplemented
112C2×C3×C4×D3—41no—
113C2×C3×C4×D3—41no—
114C2×C3×C4×D3C2×C414yescomplemented
115C2×D3×Dic3—41no—
116C2×D3×Dic3—41no—
117C2×D3×Dic3—41no—
118C32×C22⋊C4C2×C414yescomplemented
119#3757—41no—
120#3757—41no—
121C4⋊(C3⋊Dic3)—41no—
122C4×C3⋊Dic3—41no—
123C3×#217—41no—
124C3×(C2×D3)⋊C4C2×C414yescomplemented
125C3×C4⋊Dic3—41no—
126C3×C4⋊Dic3—41no—
127C3×Dic3⋊C4C2×C414yescomplemented
128Dic3⋊Dic3—41no—
129(C2×D3)⋊Dic3—41no—
130(C2×D3)⋊Dic3—41no—
131(C2×D3)⋊Dic3—41no—
132(C2×D3)⋊Dic3—41no—
133(C2×D3)⋊Dic3—41no—
134(C2×D3)⋊Dic3—41no—
135(C2×D3)⋊Dic3—41no—
136Dic32—41no—
137#2377—91noSylow
138C22×C3×D4—31no—
139C22×C3×D4—31no—
140C22×C3×D4—31no—
141C23×C3×C4—31no—
142C23×C3×C4—31no—
143C22×#67C2×D311yescharacteristic
144C22×#67C2×D311yescharacteristic
145C23×Dic3—31no—
146C23×Dic3C2×D311yescharacteristic
147C22×D12C2×D311yescharacteristic
148C22×C4×D3—31no—
149C22×C4×D3C2×D311yescharacteristic
150C3×#121—38no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4—31no—
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4C2×D311yescharacteristic
158C2×C3×C22⋊C4C2×D311yescharacteristic
159C2×#217—31no—
160C2×#217—31no—
161C2×#217—31no—
162C2×#217—31no—
163C2×#217—31no—
164C2×#217—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—61no—
171C2×#217—61no—
172C2×#217C2×D311yescharacteristic
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—31no—
180C2×(C2×D3)⋊C4C2×D311yescharacteristic
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—61no—
185C2×C4⋊Dic3C2×D311yescharacteristic
186C2×C4⋊Dic3C2×D311yescharacteristic
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4C2×D311yescharacteristic
189C2×C4×Dic3—31no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—61no—
194#884Dic318yescomplemented
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—31no—
212C3⋊#95—31no—
213C3⋊#95—61no—
214C3⋊#95—61no—
215C3⋊#95C2×D311yescharacteristic
216C3⋊#95C2×D311yescharacteristic
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32—21no—
221C23×C32—21no—
222C23×C32—21no—
223C23×C32C22×C412yes—
224C23×C32C2411yescharacteristic
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×C4C22×C412yes—
244C2×C32×C4C22×C412yes—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
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⋊Dic3—21no—
257C3×#67—44no—
258C3×#67—44no—
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×Dic3—21no—
275C2×C3×Dic3—44no—
276C2×C3×Dic3C22×C412yes—
277C2×C3×Dic3C22×C412yes—
278C3×D12—44no—
279C3×C4×D3—44no—
280D3×Dic3—44no—
281C2×#121—31no—
282#390—91no—
283#390—91no—
284#388—91no—
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—21no—
297C24×C3—31no—
298C24×C3—31no—
299C24×C3C22×D311yescharacteristic
300C24×C3C22×D311yescharacteristic
301C23×D3C22×D311yescharacteristic
302C23×D3C22×D311yescharacteristic
303C2×C3×D4—34no—
304C2×C3×D4—34no—
305C2×C3×D4—34no—
306C2×C3×D4—121no—
307C2×C3×D4—121no—
308C2×C3×D4—121no—
309C2×C3×D4—121no—
310C2×C3×D4—121no—
311C2×C3×D4—121no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—34no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—121no—
322C22×C3×C4—121no—
323C22×C3×C4—121no—
324C22×C3×C4—121no—
325C22×C3×C4—121no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C2×#67—41no—
331C2×#67—41no—
332C2×#67—41no—
333C2×#67—41no—
334C2×#67C2×Dic314yes—
335C2×#67C2×Dic314yescomplemented
336C22×Dic3—31no—
337C22×Dic3—31no—
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—41no—
345C22×Dic3—41no—
346C22×Dic3—41no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351C22×Dic3—121no—
352C22×Dic3—121no—
353C22×Dic3—121no—
354C22×Dic3C22×D311yescharacteristic
355C22×Dic3C22×D311yescharacteristic
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C2×D12—41no—
361C2×D12—41no—
362C2×D12C2×Dic314yescomplemented
363C2×C4×D3—41no—
364C2×C4×D3—41no—
365C2×C4×D3—121no—
366C2×C4×D3—121no—
367C2×C4×D3—121no—
368C2×C4×D3C2×Dic314yescomplemented
369C3×C4⋊C4—34no—
370C3×C4⋊C4—121no—
371C3×C4⋊C4—121no—
372C3×C22⋊C4—24no—
373C3×C22⋊C4—34no—
374C3×C22⋊C4—121no—
375C3×C22⋊C4C4×D314yescomplemented
376C3×C22⋊C4C2×Dic314yescomplemented
377#217—41no—
378#217—121no—
379#217—121no—
380#217—121no—
381#217—121no—
382#217—121no—
383#217—121no—
384#217—121no—
385#217—121no—
386#217—121no—
387#217—121no—
388#217—121no—
389#217—122no—
390#217—122no—
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)⋊C4C2×Dic314yescomplemented
399C4⋊Dic3—41no—
400C4⋊Dic3—41no—
401C4⋊Dic3—121no—
402C4⋊Dic3—121no—
403C4⋊Dic3—121no—
404C4⋊Dic3—122no—
405Dic3⋊C4—121no—
406Dic3⋊C4C2×Dic314yescomplemented
407C4×Dic3—121no—
408C4×Dic3—121no—
409C4×Dic3—121no—
410C4×Dic3—121no—
411C4×Dic3—122no—
412C22×C32—22no—
413C22×C32—22no—
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32C23×C411yescharacteristic
420C22×C32H(5,𝔽2)11yescharacteristic
421C22×C32H(5,𝔽2)11yescharacteristic
422C22×C32H(5,𝔽2)11yescharacteristic
423C22×C32H(5,𝔽2)11yescharacteristic
424C22×C32H(5,𝔽2)11yescharacteristic
425C22×C322−1+411yescharacteristic
426C2×C3×D3—22no—
427C2×C3×D3—22no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C32×C4—22no—
441C32×C4—22no—
442C3⋊Dic3—41no—
443C3⋊Dic3—41no—
444C3⋊Dic3—41no—
445C3⋊Dic3—41no—
446C3×Dic3—22no—
447C3×Dic3—22no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C3×Dic3—41no—
452C22×D4—31no—
453C22×D4—31no—
454C22×D4—31no—
455C23×C4—31no—
456C23×C4—31no—
457C23×C4—91no—
458#121—38no—
459C2×C4⋊C4—31no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—31no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—31no—
465C2×C22⋊C4—31no—
466C2×C22⋊C4—91no—
467C2×C22⋊C4—91no—
468C2×C22⋊C4—91no—
469C2×C22⋊C4—91no—
470C2×C22⋊C4—91no—
471C2×C22⋊C4—91no—
472C2×C22⋊C4—91no—
473C2×C22⋊C4—91no—
474C2×C22⋊C4—91no—
475C2×C22⋊C4D3211yescharacteristic
476C2×C42—91no—
477C2×C42—91no—
478#95—31no—
479#95—31no—
480#95—91no—
481#95—91no—
482#95—91no—
483#95—91no—
484#95—91no—
485#95—91no—
486#95—91no—
487#95—91no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—22no—
502C23×C3—32no—
503C23×C3—32no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—61no—
511C23×C3—61no—
512C23×C3—61no—
513C23×C3—61no—
514C23×C3—61no—
515C23×C3—61no—
516C23×C3—61no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3C2×C4×D312yes—
523C23×C3C22×Dic312yes—
524C23×C3C23×D311yescharacteristic
525C23×C3C23×D311yescharacteristic
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3C22×Dic312yes—
539C22×D3C22×Dic312yes—
540C3×D4—124no—
541C3×D4—124no—
542C3×D4—124no—
543C2×C3×C4—21no—
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—22no—
552C2×C3×C4—22no—
553C2×C3×C4—32no—
554C2×C3×C4—32no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
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—124no—
576C2×C3×C4—124no—
577C2×C3×C4C2×C4×D312yes—
578C2×C3×C4C2×C4×D312yes—
579C2×C3×C4C22×Dic312yes—
580C2×C3×C4C22×Dic312yes—
581#67—44no—
582#67—44no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—44no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
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—121no—
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—121no—
636C2×Dic3—124no—
637C2×Dic3C22×Dic312yes—
638C2×Dic3C22×Dic312yes—
639D12—44no—
640C4×D3—44no—
641C4×D3—124no—
642C2×C32—42no—
643C2×C32#51811yescharacteristic
644C2×C32#51811yescharacteristic
645C2×C32#52011yescharacteristic
646C2×C32#56011yescharacteristic
647C2×C32#56011yescharacteristic
648C2×C32#56211yescharacteristic
649C2×C32#56211yescharacteristic
650C3×D3—42no—
651C3×D3—42no—
652C24—31no—
653C24—31no—
654C24C2×D3211yescharacteristic
655C2×D4—34no—
656C2×D4—34no—
657C2×D4—34no—
658C2×D4—121no—
659C2×D4—121no—
660C2×D4—121no—
661C2×D4—121no—
662C2×D4—121no—
663C2×D4—121no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—34no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—91no—
672C22×C4—91no—
673C22×C4—91no—
674C22×C4—91no—
675C22×C4—121no—
676C22×C4—121no—
677C22×C4—121no—
678C22×C4—121no—
679C22×C4—121no—
680C22×C4—361no—
681C22×C4—361no—
682C22×C4—361no—
683C22×C4C2×D3211yescharacteristic
684C22×C4C2×D3211yescharacteristic
685C4⋊C4—34no—
686C4⋊C4—121no—
687C4⋊C4—121no—
688C4⋊C4—361no—
689C4⋊C4—361no—
690C22⋊C4—34no—
691C22⋊C4—121no—
692C22⋊C4—361no—
693C22⋊C4—361no—
694C22⋊C4—361no—
695C22⋊C4—361no—
696C22⋊C4—361no—
697C22⋊C4—361no—
698C22⋊C4—361no—
699C22⋊C4—361no—
700C22⋊C4—361no—
701C22⋊C4D3×Dic314yescomplemented
702C42—361no—
703C42—361no—
704C22×C3—22no—
705C22×C3—22no—
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—22no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—62no—
729C22×C3—62no—
730C22×C3—62no—
731C22×C3—62no—
732C22×C3—62no—
733C22×C3—62no—
734C22×C3—81no—
735C22×C3—81no—
736C22×C3—81no—
737C22×C3—81no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3C22×C4×D311yescharacteristic
747C22×C3#100411yescharacteristic
748C22×C3#100411yescharacteristic
749C22×C3#100411yescharacteristic
750C22×C3#100411yescharacteristic
751C22×C3#100411yescharacteristic
752C22×C3#100411yescharacteristic
753C22×C3#100411yescharacteristic
754C22×C3#100711yescharacteristic
755C22×C3#100911yescharacteristic
756C22×C3#100911yescharacteristic
757C22×C3#100911yescharacteristic
758C22×C3#101011yescharacteristic
759C22×C3C23×Dic311yescharacteristic
760C2×D3—22no—
761C2×D3—22no—
762C2×D3—22no—
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—22no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C3×C4—22no—
775C3×C4—22no—
776C3×C4—22no—
777C3×C4—22no—
778C3×C4—42no—
779C3×C4—42no—
780C3×C4—62no—
781C3×C4—62no—
782C3×C4—121no—
783C3×C4—121no—
784C3×C4—121no—
785C3×C4—121no—
786Dic3—22no—
787Dic3—22no—
788Dic3—41no—
789Dic3—41no—
790Dic3—41no—
791Dic3—41no—
792Dic3—122no—
793Dic3—122no—
794Dic3—121no—
795Dic3—121no—
796Dic3—121no—
797Dic3—121no—
798Dic3—121no—
799Dic3—121no—
800Dic3—121no—
801Dic3—121no—
802Dic3—241no—
803Dic3—241no—
804C32#237711yescharacteristic, complemented, Sylow
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—32no—
812C23—32no—
813C23—61no—
814C23—61no—
815C23—61no—
816C23—61no—
817C23—61no—
818C23—61no—
819C23—61no—
820C23—61no—
821C23—61no—
822C23—61no—
823C23—61no—
824C23—61no—
825C23C2×D3×Dic312yes—
826C23C22×D3211yescharacteristic
827D4—124no—
828D4—124no—
829D4—124no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—32no—
835C2×C4—32no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
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—124no—
853C2×C4—124no—
854C2×C4—181no—
855C2×C4—181no—
856C2×C4—181no—
857C2×C4—181no—
858C2×C4—181no—
859C2×C4—181no—
860C2×C4—181no—
861C2×C4—181no—
862C2×C4—181no—
863C2×C4—181no—
864C2×C4—181no—
865C2×C4—181no—
866C2×C4—364no—
867C2×C4C2×D3×Dic312yes—
868C2×C4C2×D3×Dic312yes—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—42no—
877C2×C3—42no—
878C2×C3—82no—
879C2×C3—122no—
880C2×C3—122no—
881C2×C3#550411yescharacteristic
882C2×C3#554511yescharacteristic
883C2×C3#554511yescharacteristic
884C2×C3#559511yescharacteristic
885C2×C3#562011yescharacteristic
886C2×C3#562011yescharacteristic
887C2×C3#562111yescharacteristic
888C2×C3#562111yescharacteristic
889C2×C3#564711yescharacteristic
890C2×C3#564711yescharacteristic
891C2×C3#566611yescharacteristic
892C2×C3#579811yescharacteristic
893C2×C3#579811yescharacteristic
894C2×C3#582711yescharacteristic
895D3—42no—
896D3—42no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—62no—
905C22—62no—
906C22—62no—
907C22—62no—
908C22—62no—
909C22—62no—
910C22—121no—
911C22—121no—
912C22—121no—
913C22—121no—
914C22—121no—
915C22—121no—
916C22—121no—
917C22—121no—
918C22#6429711yescharacteristic
919C22#6430711yescharacteristic
920C22#6431311yescharacteristic
921C22#6431311yescharacteristic
922C22#6431411yescharacteristic
923C22#6431411yescharacteristic
924C22C22×D3×Dic311yescharacteristic
925C4—22no—
926C4—22no—
927C4—62no—
928C4—62no—
929C4—121no—
930C4—121no—
931C4—121no—
932C4—121no—
933C4—361no—
934C4—361no—
935C4—361no—
936C4—361no—
937C3—21no—
938C3#7440111yescharacteristic, complemented
939C3#8263911yescharacteristic, complemented
940C2—42no—
941C2—122no—
942C2—122no—
943C2#1059417411yescharacteristic
944C2#1059423411yescharacteristic
945C2#1059424011yescharacteristic
946C2#1059430811yescharacteristic
947C2#1059498611yescharacteristic
948C2#1059521511yescharacteristic
949C2#1059521511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#884C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2377
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592650C2semidirect
3. C3×#4950C2semidirect
4. #10591721C2semidirect
5. #10591710C2semidirect
6. #10591710C2semidirect
7. #10591707C2semidirect
8. #10591379C2semidirect
9. #10591376C2semidirect
10. #10591323C2semidirect
11. #10591313C2semidirect
12. #10591307C2semidirect
13. #10591294C2semidirect
14. #10591262C2semidirect
15. #10591192C2semidirect
34. C3×#884C4semidirect
80. #4950D3semidirect
99. C2×C3×#67C2×C4semidirect
111. C2×C3×D12C2×C4semidirect
114. C2×C3×C4×D3C2×C4semidirect
118. C32×C22⋊C4C2×C4semidirect
124. C3×(C2×D3)⋊C4C2×C4semidirect
127. C3×Dic3⋊C4C2×C4semidirect
194. #884Dic3semidirect
335. C2×#67C2×Dic3semidirect
362. C2×D12C2×Dic3semidirect
368. C2×C4×D3C2×Dic3semidirect
375. C3×C22⋊C4C4×D3semidirect
376. C3×C22⋊C4C2×Dic3semidirect
398. (C2×D3)⋊C4C2×Dic3semidirect
406. Dic3⋊C4C2×Dic3semidirect
701. C22⋊C4D3×Dic3semidirect
804. C32#2377semidirect
938. C3#74401semidirect
939. C3#82639semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8842
#105926502
C3×#49502
#105917212
#105917102
#105917072
#105913792
#105913762
#105913232
#105913132
#105913072
#105912942
#105912622
#105911922
#826393
#744013