Finite Group Databasebeta

← #11819114

Subgroups — #11819114

Order 1152.

1083 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#888C211yesmaximal, characteristic, complemented
2C2×#63893C211yesmaximal, characteristic
3#10592685C211yesmaximal, characteristic, complemented
4C3×#4990C211yesmaximal, characteristic
5#10591366C211yesmaximal, characteristic
6Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic
7#10591343C211yesmaximal, characteristic, complemented
8#10591307C211yesmaximal, characteristic
9#10591304C211yesmaximal, characteristic
10#10591304C211yesmaximal, characteristic
11#10591261C211yesmaximal, characteristic, complemented
12Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
13#10591235C211yesmaximal, characteristic, complemented
14#10591220C211yesmaximal, characteristic, complemented
15#10591191C211yesmaximal, characteristic, complemented
16#83258—31nomaximal
17#75547—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×#888—24no—
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40#63893—24no—
41#63658C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×C3×C4⋊Q8—31no—
56C2×#897—31no—
57C2×#888D311yescharacteristic, complemented
58C2×#878—31no—
59C3×#388—31no—
60#5231—31no—
61#5231—31no—
62#5229—31no—
63#5229—31no—
64#4990—31no—
65#4990D311yescharacteristic
66#4987—31no—
67#4986—31no—
68#4986—31no—
69#4986—31no—
70#4986—61no—
71Dic3×C4⋊C4—31no—
72#4973—31no—
73#4951—31no—
74#4947—31no—
75#4947—31no—
76#4942—31no—
77Dic3×C22⋊C4—31no—
78C4×(C2×D3)⋊C4—31no—
79C4×Dic3⋊C4—31no—
80#4929—31no—
81#4929—31no—
82#4660—31no—
83#4646—31no—
84#4646—31no—
85#4646—31no—
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C2×C3×Dic6—22no—
102C2×C3×Dic6—22no—
103C2×C3×Dic6—22no—
104C2×C3×Dic6—22no—
105C2×C3×Dic6—41no—
106C2×C3×Dic6—41no—
107C2×#627—22no—
108C2×#627—22no—
109C2×#627—22no—
110C2×D3×Dic3—22no—
111C2×D3×Dic3—22no—
112C2×D3×Dic3—22no—
113C32×C4⋊C4—22no—
114C4⋊(C3⋊Dic3)—22no—
115C3×(C2×D3)⋊C4—22no—
116C3×(C2×D3)⋊C4—41no—
117C3×(C2×D3)⋊C4Q814yescomplemented
118C3×C4⋊Dic3—22no—
119C3×Dic3⋊C4—22no—
120C3×Dic3⋊C4D414yes—
121C3×C4×Dic3—22no—
122C3×C4×Dic3—41no—
123Dic3⋊Dic3—22no—
124Dic3⋊Dic3—22no—
125(C2×D3)⋊Dic3—22no—
126(C2×D3)⋊Dic3—22no—
127(C2×D3)⋊Dic3—41no—
128Dic32—22no—
129Dic32—41no—
130#2492—91noSylow
131C22×C3×Q8—31no—
132C22×C3×Q8—31no—
133C23×Dic3—31no—
134C22×C4×D3—31no—
135C22×Dic6—31no—
136C22×Dic6—31no—
137C22×Dic6C2×D311yescharacteristic
138C22×Dic6C2×D311yescharacteristic
139C3×C4⋊Q8—64no—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4C2×D311yescharacteristic
145C2×C3×C4⋊C4C2×D311yescharacteristic
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C42—31no—
150C2×C3×C42—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×#217—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4C2×D311yescharacteristic
158C2×(C2×D3)⋊C4C2×D311yescharacteristic
159C2×(C2×D3)⋊C4C2×D311yescharacteristic
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—31no—
164C2×C4⋊Dic3—61no—
165C2×C4⋊Dic3C2×D311yescharacteristic
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4C2×D311yescharacteristic
169C2×Dic3⋊C4C2×D311yescharacteristic
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3C2×D311yescharacteristic
175C2×C4×Dic3C2×D311yescharacteristic
176#897—64no—
177#888—24no—
178#878—64no—
179C3×#95—31no—
180C3×#95—31no—
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—61no—
206C3⋊#95—61no—
207C3⋊#95—61no—
208C3⋊#95—61no—
209C3⋊#95—61no—
210C3⋊#95C2×D311yescharacteristic
211C3⋊#95C2×D311yescharacteristic
212C23×C32C2411yescharacteristic
213C22×C3×D3—21no—
214C22×C3×D3—21no—
215C22×C3×D3—21no—
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3C2×Q812yes—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4C2×D412yes—
228C2×C32×C4C2×Q812yes—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
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—21no—
244C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
257C2×C3×Dic3C2×D412yes—
258C2×C3×Dic3C2×Q812yes—
259C2×C3×Dic3#4112yes—
260C2×C3×Dic3#4112yes—
261C2×C3×Dic3#4112yes—
262C3×Dic6—44no—
263C3×Dic6—44no—
264#627—44no—
265D3×Dic3—44no—
266C2×C4⋊Q8—31no—
267C2×C22⋊Q8—91no—
268#400—91no—
269#400—91no—
270#393—91no—
271#393—91no—
272#391—91no—
273#391—91no—
274#391—91no—
275#391—91no—
276#388—31no—
277#388—91no—
278#380—91no—
279C4×C4⋊C4—91no—
280C4×C22⋊C4—91no—
281C24×C3—31no—
282C23×D3C22×D311yescharacteristic
283C2×C3×Q8—62no—
284C2×C3×Q8—62no—
285C2×C3×Q8—62no—
286C2×C3×Q8—62no—
287C2×C3×Q8—121no—
288C2×C3×Q8—121no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—31no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—62no—
318C22×Dic3—62no—
319C22×Dic3—62no—
320C22×Dic3C22×D311yescharacteristic
321C22×Dic3C22×D311yescharacteristic
322C22×Dic3C22×D311yescharacteristic
323C22×Dic3C22×D311yescharacteristic
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C2×C4×D3—62no—
328C2×C4×D3—62no—
329C2×C4×D3—62no—
330C2×Dic6—22no—
331C2×Dic6—22no—
332C2×Dic6—22no—
333C2×Dic6—22no—
334C2×Dic6—41no—
335C2×Dic6—41no—
336C2×Dic6—62no—
337C2×Dic6—62no—
338C2×Dic6—62no—
339C2×Dic6—62no—
340C2×Dic6—62no—
341C2×Dic6—62no—
342C3×C4⋊C4—22no—
343C3×C4⋊C4—22no—
344C3×C4⋊C4—34no—
345C3×C4⋊C4—42no—
346C3×C4⋊C4—62no—
347C3×C4⋊C4—62no—
348C3×C22⋊C4—34no—
349C3×C22⋊C4—62no—
350C3×C22⋊C4—121no—
351C3×C42—62no—
352C3×C42—121no—
353#217—62no—
354#217—62no—
355#217—121no—
356(C2×D3)⋊C4—22no—
357(C2×D3)⋊C4—41no—
358(C2×D3)⋊C4—62no—
359(C2×D3)⋊C4—62no—
360(C2×D3)⋊C4—121no—
361(C2×D3)⋊C4Dic614yescomplemented
362C4⋊Dic3—22no—
363C4⋊Dic3—62no—
364C4⋊Dic3—62no—
365C4⋊Dic3—62no—
366C4⋊Dic3—62no—
367C4⋊Dic3—122no—
368Dic3⋊C4—22no—
369Dic3⋊C4—62no—
370Dic3⋊C4—62no—
371Dic3⋊C4#6714yes—
372C4×Dic3—22no—
373C4×Dic3—41no—
374C4×Dic3—62no—
375C4×Dic3—62no—
376C4×Dic3—121no—
377C4×Dic3—121no—
378C22×C32C22×D411yescharacteristic
379C22×C32C22×Q811yescharacteristic
380C22×C32C2×#4111yescharacteristic
381C22×C32C2×#4111yescharacteristic
382C22×C32C2×#4111yescharacteristic
383C22×C32H(5,𝔽2)11yescharacteristic
384C22×C322−1+411yescharacteristic
385C2×C3×D3—22no—
386C2×C3×D3—22no—
387C2×C3×D3—22no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C32×C4—22no—
393C32×C4—22no—
394C32×C4—41no—
395C3⋊Dic3—41no—
396C3⋊Dic3—41no—
397C3⋊Dic3—41no—
398C3⋊Dic3—41no—
399C3×Dic3—22no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3#12414yes—
406C22×Q8—31no—
407C22×Q8—31no—
408C22×Q8—91no—
409C23×C4—91no—
410C4⋊Q8—64no—
411C22⋊Q8—184no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—31no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—91no—
416C2×C4⋊C4—91no—
417C2×C4⋊C4—91no—
418C2×C4⋊C4D3211yescharacteristic
419C2×C22⋊C4—31no—
420C2×C22⋊C4—31no—
421C2×C22⋊C4—31no—
422C2×C22⋊C4—91no—
423C2×C22⋊C4—91no—
424C2×C22⋊C4—91no—
425C2×C42—31no—
426C2×C42—31no—
427C2×C42—91no—
428C2×C42—91no—
429#95—31no—
430#95—31no—
431#95—91no—
432#95—91no—
433#95—91no—
434#95—91no—
435#95—91no—
436#95—91no—
437#95—91no—
438#95—91no—
439#95—91no—
440#95—91no—
441#95—91no—
442#95—91no—
443C23×C3—21no—
444C23×C3—32no—
445C23×C3—61no—
446C23×C3—61no—
447C23×C3—61no—
448C23×C3—61no—
449C23×C3—61no—
450C23×C3—61no—
451C23×C3C23×D311yescharacteristic
452C23×C3C23×D311yescharacteristic
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3C2×Dic612yes—
460C3×Q8—124no—
461C3×Q8—124no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—32no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—32no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4C2×Dic612yes—
507C2×C3×C4D3×D412yes—
508C2×C3×C4D3×Q812yes—
509C2×C3×C4C2×#6712yes—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—121no—
550C2×Dic3—121no—
551C2×Dic3—121no—
552C2×Dic3—121no—
553C2×Dic3—121no—
554C2×Dic3—121no—
555C2×Dic3—121no—
556C2×Dic3—121no—
557C2×Dic3—121no—
558C2×Dic3—121no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—124no—
562C2×Dic3C2×Dic612yes—
563C2×Dic3#23712yes—
564C2×Dic3#23912yes—
565C2×Dic3#23912yes—
566C2×Dic3C2×#6712yes—
567C2×Dic3C2×#6712yes—
568C4×D3—124no—
569Dic6—44no—
570Dic6—44no—
571Dic6—124no—
572Dic6—124no—
573C2×C32C2×#12411yescharacteristic
574C2×C32#53311yescharacteristic
575C2×C32#54211yescharacteristic
576C2×C32#54611yescharacteristic
577C2×C32D4×Q811yescharacteristic
578C2×C32#55411yescharacteristic
579C2×C32#55611yescharacteristic
580C3×D3—42no—
581C24—31no—
582C2×Q8—62no—
583C2×Q8—62no—
584C2×Q8—62no—
585C2×Q8—62no—
586C2×Q8—121no—
587C2×Q8—121no—
588C2×Q8—182no—
589C2×Q8—182no—
590C2×Q8—182no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—91no—
599C22×C4—91no—
600C22×C4—91no—
601C22×C4—91no—
602C22×C4—182no—
603C22×C4—182no—
604C22×C4—182no—
605C22×C4C2×D3211yescharacteristic
606C22×C4C2×D3211yescharacteristic
607C22×C4C2×D3211yescharacteristic
608C4⋊C4—22no—
609C4⋊C4—34no—
610C4⋊C4—62no—
611C4⋊C4—62no—
612C4⋊C4—182no—
613C4⋊C4—182no—
614C4⋊C4—182no—
615C22⋊C4—34no—
616C22⋊C4—62no—
617C22⋊C4—121no—
618C22⋊C4—182no—
619C22⋊C4—182no—
620C22⋊C4—361no—
621C42—62no—
622C42—121no—
623C42—182no—
624C42—361no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—62no—
633C22×C3—62no—
634C22×C3—62no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3C22×Dic611yescharacteristic
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C2×#23711yescharacteristic
642C22×C3#100411yescharacteristic
643C22×C3#100411yescharacteristic
644C22×C3C2×D3×Q811yescharacteristic
645C22×C3C2×#23911yescharacteristic
646C22×C3C2×#23911yescharacteristic
647C22×C3#100711yescharacteristic
648C22×C3D3×#4111yescharacteristic
649C22×C3D3×#4111yescharacteristic
650C22×C3D3×#4111yescharacteristic
651C22×C3#101011yescharacteristic
652C22×C3C22×#6711yescharacteristic
653C2×D3—22no—
654C2×D3—22no—
655C2×D3—22no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C3×C4—22no—
661C3×C4—22no—
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—34no—
665C3×C4—42no—
666C3×C4—42no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—62no—
670C3×C4—62no—
671C3×C4—62no—
672C3×C4—81no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4—121no—
676Dic3—22no—
677Dic3—22no—
678Dic3—22no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—241no—
691Dic3—241no—
692Dic3—241no—
693Dic3—241no—
694Dic3#94714yes—
695C32#249211yescharacteristic, complemented, Sylow
696C23—32no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23—61no—
703C23C22×D3211yescharacteristic
704Q8—124no—
705Q8—124no—
706Q8—364no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—32no—
715C2×C4—32no—
716C2×C4—32no—
717C2×C4—32no—
718C2×C4—32no—
719C2×C4—32no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—181no—
743C2×C4—181no—
744C2×C4—181no—
745C2×C4—181no—
746C2×C4—181no—
747C2×C4—364no—
748C2×C4D3×Dic612yes—
749C2×C4D3×#6712yes—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—122no—
758C2×C3#551711yescharacteristic
759C2×C3D4×Dic611yescharacteristic
760C2×C3#553911yescharacteristic
761C2×C3#561011yescharacteristic
762C2×C3#566211yescharacteristic
763C2×C3D3×#12411yescharacteristic
764C2×C3#570211yescharacteristic
765C2×C3#572811yescharacteristic
766C2×C3#573011yescharacteristic
767C2×C3#573211yescharacteristic
768C2×C3#573311yescharacteristic
769C2×C3#580611yescharacteristic
770C2×C3C2×#94711yescharacteristic
771C2×C3Q8×#6711yescharacteristic
772D3—42no—
773C22—62no—
774C22—62no—
775C22—62no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22C2×D3×Dic611yescharacteristic
781C22#6429711yescharacteristic
782C22D3×#23711yescharacteristic
783C22#6431311yescharacteristic
784C22D3×#23911yescharacteristic
785C22D3×#23911yescharacteristic
786C22C2×D3×#6711yescharacteristic
787C4—22no—
788C4—22no—
789C4—34no—
790C4—41no—
791C4—62no—
792C4—62no—
793C4—62no—
794C4—121no—
795C4—121no—
796C4—121no—
797C4—361no—
798C4—361no—
799C4—361no—
800C4—361no—
801C3—21no—
802C3#7554711yescharacteristic, complemented
803C3#8325811yescharacteristic, complemented
804C2—122no—
805C2#1059444511yescharacteristic
806C2#1059445011yescharacteristic
807C2#1059445811yescharacteristic
808C2#1059446011yescharacteristic
809C2Dic6×#6711yescharacteristic
810C2#1059515011yescharacteristic
811C2D3×#94711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2492
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#888C2semidirect
3. #10592685C2semidirect
7. #10591343C2semidirect
11. #10591261C2semidirect
12. Dic3×Dic3⋊C4C2semidirect
13. #10591235C2semidirect
14. #10591220C2semidirect
15. #10591191C2semidirect
57. C2×#888D3semidirect
117. C3×(C2×D3)⋊C4Q8semidirect
361. (C2×D3)⋊C4Dic6semidirect
695. C32#2492semidirect
802. C3#75547semidirect
803. C3#83258semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8882
C2×#638932
#105926852
C3×#49902
#105913662
Dic3×(C2×D3)⋊C42
#105913432
#105913072
#105913042
#105912612
Dic3×Dic3⋊C42
#105912352
#105912202
#105911912
#832583
#755473