Finite Group Databasebeta

← #11805805

Subgroups — #11805805

Order 1152.

1271 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#67⋊C4C211yesmaximal, characteristic
2#10592650C211yesmaximal, characteristic, complemented
3C3×#4951C211yesmaximal, characteristic, complemented
4#10591721C211yesmaximal, characteristic
5#10591721C211yesmaximal, characteristic
6Dic3×#217C211yesmaximal, characteristic, complemented
7#10591696C211yesmaximal, characteristic, complemented
8#10591368C211yesmaximal, characteristic, complemented
9Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10D3×C3⋊#95C211yesmaximal, characteristic, complemented
11#10591313C211yesmaximal, characteristic, complemented
12#10591272C211yesmaximal, characteristic, complemented
13#10591262C211yesmaximal, characteristic, complemented
14#10591223C211yesmaximal, characteristic, complemented
15#10591222C211yesmaximal, characteristic, complemented
16#82336—31nomaximal
17#75835—31nomaximal
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C3×#67⋊C4C418yescomplemented
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44#63579C2211yescharacteristic
45#63579C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C3×C4×D4—31no—
55C2×#67⋊C4D311yescharacteristic
56C3×#388—31no—
57#5220—31no—
58#5220—31no—
59#5212—31no—
60#5211—31no—
61C4×#217—31no—
62C2×C3⋊#95—31no—
63#4987—31no—
64#4980—31no—
65#4980—31no—
66#4978—31no—
67#4956—31no—
68#4956—31no—
69#4951—31no—
70#4951—31no—
71#4951—61no—
72#4951D311yescharacteristic, complemented
73#4943—31no—
74Dic3×C22⋊C4—31no—
75Dic3×C22⋊C4—31no—
76Dic3×C22⋊C4—31no—
77C4×(C2×D3)⋊C4—31no—
78#4937—31no—
79#4932—31no—
80#4932—31no—
81#4666—31no—
82D3×#95—31no—
83#4655—31no—
84#4651—31no—
85C24×C32C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C2×C3×#67—22no—
94C2×C3×#67—22no—
95C2×C3×#67C2×C414yes—
96C22×C3×Dic3—41no—
97C22×C3×Dic3—41no—
98C22×C3×Dic3C2×C414yescomplemented
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×D3C2×C414yes—
109C2×D3×Dic3—22no—
110C2×D3×Dic3—22no—
111C2×D3×Dic3—22no—
112C2×D3×Dic3—22no—
113C2×D3×Dic3—41no—
114C2×D3×Dic3—41no—
115C32×C22⋊C4C2×C414yescomplemented
116#3757—22no—
117#3757—41no—
118C4⋊(C3⋊Dic3)—41no—
119C4×C3⋊Dic3—22no—
120C3×#217—22no—
121C3×#217—41no—
122C3×(C2×D3)⋊C4C2×C414yes—
123C3×C4⋊Dic3—41no—
124C3×Dic3⋊C4C2×C414yescomplemented
125C3×C4×Dic3—22no—
126C3×C4×Dic3C2×C414yescomplemented
127(C2×D3)⋊Dic3—22no—
128(C2×D3)⋊Dic3—22no—
129Dic32—41no—
130Dic32—41no—
131#2353—91noSylow
132C22×C3×D4—31no—
133C23×C3×C4—31no—
134C23×C3×C4—31no—
135C22×#67C2×D311yescharacteristic
136C23×Dic3—31no—
137C23×Dic3—31no—
138C23×Dic3C2×D311yescharacteristic
139C22×C4×D3—31no—
140C22×C4×D3—31no—
141C22×C4×D3C2×D311yescharacteristic
142C3×C4×D4—38no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4C2×D311yescharacteristic
150C2×C3×C22⋊C4C2×D311yescharacteristic
151C2×C3×C42—31no—
152C2×C3×C42—31no—
153C2×#217—31no—
154C2×#217—31no—
155C2×#217—31no—
156C2×#217—31no—
157C2×#217—31no—
158C2×#217—31no—
159C2×#217—61no—
160C2×#217—61no—
161C2×#217C2×D311yescharacteristic
162C2×#217C2×D311yescharacteristic
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4C2×D311yescharacteristic
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3—61no—
169C2×C4⋊Dic3C2×D311yescharacteristic
170C2×Dic3⋊C4C2×D311yescharacteristic
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—61no—
178C2×C4×Dic3C2×D311yescharacteristic
179C2×C4×Dic3C2×D311yescharacteristic
180#67⋊C4Dic318yescomplemented
181C3×#95—31no—
182C3×#95—31no—
183C3⋊#95—31no—
184C3⋊#95—31no—
185C3⋊#95—31no—
186C3⋊#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
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—61no—
208C3⋊#95—61no—
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C23×C32—21no—
212C23×C32—21no—
213C23×C32—21no—
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32C22×C412yes—
218C23×C32C2411yescharacteristic
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3C22×C412yes—
224C22×C3×D3#4112yes—
225C22×C3×D3#4112yes—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4C22×C412yes—
231C2×C32×C4C22×C412yes—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3#4112yes—
244C3×#67—28no—
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—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—44no—
263C2×C3×Dic3C22×C412yes—
264C2×C3×Dic3C22×C412yes—
265C2×C3×Dic3C22×C412yes—
266C2×C3×Dic3#4112yes—
267C3×C4×D3—44no—
268D3×Dic3—44no—
269D3×Dic3—44no—
270C2×C4×D4—31no—
271#388—31no—
272#388—91no—
273#387—91no—
274#387—91no—
275#386—91no—
276#386—91no—
277#383—91no—
278#381—91no—
279#380—91no—
280C4×C22⋊C4—91no—
281C4×C22⋊C4—91no—
282C4×C22⋊C4—91no—
283#376—91no—
284C2×#95—91no—
285C24×C3—21no—
286C24×C3—31no—
287C24×C3C22×D311yescharacteristic
288C24×C3C22×D311yescharacteristic
289C23×D3C22×D311yescharacteristic
290C2×C3×D4—34no—
291C2×C3×D4—62no—
292C2×C3×D4—62no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—34no—
300C22×C3×C4—34no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—121no—
305C22×C3×C4—121no—
306C22×C3×C4—121no—
307C22×C3×C4—121no—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C2×#67—22no—
313C2×#67—22no—
314C2×#67C2×Dic314yes—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—41no—
324C22×Dic3—41no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329C22×Dic3—62no—
330C22×Dic3—62no—
331C22×Dic3—62no—
332C22×Dic3—62no—
333C22×Dic3—121no—
334C22×Dic3—121no—
335C22×Dic3C2×Dic314yescomplemented
336C22×Dic3C22×D311yescharacteristic
337C22×Dic3C22×D311yescharacteristic
338C22×Dic3C22×D311yescharacteristic
339C22×Dic3C22×D311yescharacteristic
340C22×Dic3C22×D311yescharacteristic
341C22×Dic3C22×D311yescharacteristic
342C22×Dic3C22×D311yescharacteristic
343C2×C4×D3—41no—
344C2×C4×D3—41no—
345C2×C4×D3—62no—
346C2×C4×D3—62no—
347C2×C4×D3—62no—
348C2×C4×D3—62no—
349C2×C4×D3—121no—
350C2×C4×D3—121no—
351C2×C4×D3C2×Dic314yes—
352C3×C4⋊C4—34no—
353C3×C4⋊C4—121no—
354C3×C22⋊C4—24no—
355C3×C22⋊C4—34no—
356C3×C22⋊C4—62no—
357C3×C22⋊C4—121no—
358C3×C22⋊C4C4×D314yescomplemented
359C3×C22⋊C4C2×Dic314yescomplemented
360C3×C42—34no—
361C3×C42—62no—
362#217—22no—
363#217—41no—
364#217—62no—
365#217—62no—
366#217—62no—
367#217—62no—
368#217—122no—
369#217—121no—
370#217—121no—
371#217—122no—
372(C2×D3)⋊C4—62no—
373(C2×D3)⋊C4—62no—
374(C2×D3)⋊C4C2×Dic314yes—
375C4⋊Dic3—41no—
376C4⋊Dic3—121no—
377C4⋊Dic3—121no—
378C4⋊Dic3—122no—
379Dic3⋊C4C2×Dic314yescomplemented
380C4×Dic3—22no—
381C4×Dic3—62no—
382C4×Dic3—62no—
383C4×Dic3—122no—
384C4×Dic3—121no—
385C4×Dic3—121no—
386C4×Dic3—121no—
387C4×Dic3—121no—
388C4×Dic3C2×Dic314yescomplemented
389C22×C32—22no—
390C22×C32—22no—
391C22×C32—22no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32—41no—
395C22×C32—41no—
396C22×C32C23×C411yescharacteristic
397C22×C32C2×#4111yescharacteristic
398C22×C32C2×#4111yescharacteristic
399C22×C32C2×#4111yescharacteristic
400C22×C32C2×#4111yescharacteristic
401C22×C32H(5,𝔽2)11yescharacteristic
402C22×C32H(5,𝔽2)11yescharacteristic
403C2×C3×D3—22no—
404C2×C3×D3—22no—
405C2×C3×D3—22no—
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3—22no—
409C2×C3×D3#11714yes—
410C32×C4—22no—
411C32×C4—22no—
412C3⋊Dic3—22no—
413C3⋊Dic3—41no—
414C3⋊Dic3—41no—
415C3⋊Dic3—41no—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C22×D4—31no—
424C23×C4—31no—
425C23×C4—31no—
426C23×C4—91no—
427C23×C4—91no—
428C4×D4—38no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—91no—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—31no—
434C2×C22⋊C4—31no—
435C2×C22⋊C4—91no—
436C2×C22⋊C4—91no—
437C2×C22⋊C4—91no—
438C2×C22⋊C4—91no—
439C2×C22⋊C4D3211yescharacteristic
440C2×C42—31no—
441C2×C42—31no—
442C2×C42—91no—
443C2×C42—91no—
444C2×C42—91no—
445#95—31no—
446#95—31no—
447#95—91no—
448#95—91no—
449#95—91no—
450#95—91no—
451#95—91no—
452#95—91no—
453#95—91no—
454#95—91no—
455#95—91no—
456#95—91no—
457#95—91no—
458#95—91no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—22no—
473C23×C3—32no—
474C23×C3—32no—
475C23×C3—32no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3C2×C4×D312yes—
487C23×C3C22×Dic312yes—
488C23×C3C23×D311yescharacteristic
489C23×C3C23×D311yescharacteristic
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3#23512yes—
495C22×D3#23512yes—
496C22×D3C22×Dic312yes—
497C3×D4—68no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—32no—
509C2×C3×C4—32no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—124no—
534C2×C3×C4—124no—
535C2×C3×C4C2×C4×D312yes—
536C2×C3×C4C2×C4×D312yes—
537C2×C3×C4C22×Dic312yes—
538C2×C3×C4C22×Dic312yes—
539#67—28no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—32no—
558C2×Dic3—32no—
559C2×Dic3—44no—
560C2×Dic3—62no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—62no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—121no—
585C2×Dic3—121no—
586C2×Dic3—121no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—121no—
590C2×Dic3—121no—
591C2×Dic3—121no—
592C2×Dic3—121no—
593C2×Dic3—121no—
594C2×Dic3—124no—
595C2×Dic3—124no—
596C2×Dic3#23712yes—
597C2×Dic3C22×Dic312yes—
598C2×Dic3C22×Dic312yes—
599C2×Dic3C22×Dic312yes—
600C4×D3—44no—
601C4×D3—124no—
602C4×D3—124no—
603C2×C32—42no—
604C2×C32C2×#11711yescharacteristic
605C2×C32C4×#4111yescharacteristic
606C2×C32#51811yescharacteristic
607C2×C32#55111yescharacteristic
608C2×C32#55111yescharacteristic
609C2×C32#55311yescharacteristic
610C2×C32#55311yescharacteristic
611C3×D3—24no—
612C24—31no—
613C24C2×D3211yescharacteristic
614C2×D4—34no—
615C2×D4—62no—
616C2×D4—62no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—34no—
622C22×C4—34no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—91no—
627C22×C4—91no—
628C22×C4—91no—
629C22×C4—91no—
630C22×C4—121no—
631C22×C4—121no—
632C22×C4—121no—
633C22×C4—121no—
634C22×C4—182no—
635C22×C4—182no—
636C22×C4—182no—
637C22×C4—182no—
638C22×C4—361no—
639C22×C4—361no—
640C22×C4C2×D3211yescharacteristic
641C22×C4C2×D3211yescharacteristic
642C4⋊C4—34no—
643C4⋊C4—121no—
644C4⋊C4—361no—
645C22⋊C4—34no—
646C22⋊C4—62no—
647C22⋊C4—121no—
648C22⋊C4—182no—
649C22⋊C4—182no—
650C22⋊C4—182no—
651C22⋊C4—361no—
652C22⋊C4D3×Dic314yescomplemented
653C42—34no—
654C42—62no—
655C42—182no—
656C42—361no—
657C42—361no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—34no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—62no—
684C22×C3—62no—
685C22×C3—62no—
686C22×C3—62no—
687C22×C3—62no—
688C22×C3—62no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3C22×C4×D311yescharacteristic
694C22×C3C2×#23511yescharacteristic
695C22×C3C2×#23511yescharacteristic
696C22×C3C2×#23711yescharacteristic
697C22×C3#100411yescharacteristic
698C22×C3#100411yescharacteristic
699C22×C3#100411yescharacteristic
700C22×C3D3×#4111yescharacteristic
701C22×C3D3×#4111yescharacteristic
702C22×C3D3×#4111yescharacteristic
703C22×C3D3×#4111yescharacteristic
704C22×C3D3×#4111yescharacteristic
705C22×C3#100911yescharacteristic
706C22×C3C23×Dic311yescharacteristic
707C2×D3—22no—
708C2×D3—22no—
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—22no—
713C2×D3#92614yes—
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—42no—
719C3×C4—42no—
720C3×C4—62no—
721C3×C4—62no—
722C3×C4—62no—
723C3×C4—62no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4—121no—
727Dic3—22no—
728Dic3—22no—
729Dic3—22no—
730Dic3—22no—
731Dic3—41no—
732Dic3—41no—
733Dic3—41no—
734Dic3—62no—
735Dic3—62no—
736Dic3—122no—
737Dic3—122no—
738Dic3—121no—
739Dic3—121no—
740Dic3—121no—
741Dic3—121no—
742Dic3—121no—
743Dic3—121no—
744Dic3—241no—
745Dic3—241no—
746C32#235311yescharacteristic, complemented, Sylow
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—32no—
754C23—32no—
755C23—32no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23C2×D3×Dic312yes—
761C23C22×D3211yescharacteristic
762D4—68no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—32no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—32no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—92no—
789C2×C4—124no—
790C2×C4—124no—
791C2×C4—181no—
792C2×C4—181no—
793C2×C4—181no—
794C2×C4—181no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4—181no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4—181no—
801C2×C4—181no—
802C2×C4—364no—
803C2×C4—364no—
804C2×C4C2×D3×Dic312yes—
805C2×C4C2×D3×Dic312yes—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—42no—
814C2×C3—42no—
815C2×C3—64no—
816C2×C3—82no—
817C2×C3D3×#11711yescharacteristic
818C2×C3C4×#23711yescharacteristic
819C2×C3#554011yescharacteristic
820C2×C3#554011yescharacteristic
821C2×C3#554511yescharacteristic
822C2×C3#555611yescharacteristic
823C2×C3#555611yescharacteristic
824C2×C3#561411yescharacteristic
825C2×C3#565811yescharacteristic
826C2×C3#567911yescharacteristic
827C2×C3#570911yescharacteristic
828C2×C3C2×#92611yescharacteristic
829C2×C3#579811yescharacteristic
830C2×C3Dic3×#4111yescharacteristic
831D3—24no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—34no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—62no—
841C22—62no—
842C22—62no—
843C22—62no—
844C22—62no—
845C22—62no—
846C22D3×#23511yescharacteristic
847C22D3×#23511yescharacteristic
848C22D3×#23711yescharacteristic
849C22#6431211yescharacteristic
850C22#6431311yescharacteristic
851C22#6431411yescharacteristic
852C22C22×D3×Dic311yescharacteristic
853C4—22no—
854C4—22no—
855C4—62no—
856C4—62no—
857C4—62no—
858C4—62no—
859C4—121no—
860C4—121no—
861C4—121no—
862C4—182no—
863C4—361no—
864C4—361no—
865C4—361no—
866C3—21no—
867C3#7583511yescharacteristic, complemented
868C3#8233611yescharacteristic, complemented
869C2—42no—
870C2—64no—
871C2#1059409711yescharacteristic
872C2#1059419811yescharacteristic
873C2#1059429911yescharacteristic
874C2#1059430011yescharacteristic
875C2D3×#92611yescharacteristic
876C2Dic3×#23711yescharacteristic
877C2#1059521511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2353
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×#4951C2semidirect
6. Dic3×#217C2semidirect
7. #10591696C2semidirect
8. #10591368C2semidirect
9. Dic3×(C2×D3)⋊C4C2semidirect
10. D3×C3⋊#95C2semidirect
11. #10591313C2semidirect
12. #10591272C2semidirect
13. #10591262C2semidirect
14. #10591223C2semidirect
15. #10591222C2semidirect
35. C3×#67⋊C4C4semidirect
72. #4951D3semidirect
98. C22×C3×Dic3C2×C4semidirect
115. C32×C22⋊C4C2×C4semidirect
124. C3×Dic3⋊C4C2×C4semidirect
126. C3×C4×Dic3C2×C4semidirect
180. #67⋊C4Dic3semidirect
335. C22×Dic3C2×Dic3semidirect
358. C3×C22⋊C4C4×D3semidirect
359. C3×C22⋊C4C2×Dic3semidirect
379. Dic3⋊C4C2×Dic3semidirect
388. C4×Dic3C2×Dic3semidirect
652. C22⋊C4D3×Dic3semidirect
746. C32#2353semidirect
867. C3#75835semidirect
868. C3#82336semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#67⋊C42
#105926502
C3×#49512
#105917212
Dic3×#2172
#105916962
#105913682
Dic3×(C2×D3)⋊C42
D3×C3⋊#952
#105913132
#105912722
#105912622
#105912232
#105912222
#823363
#758353