Finite Group Databasebeta

← #11819092

Subgroups — #11819092

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#944C211yesmaximal, characteristic, complemented
2C2×#63893C211yesmaximal, characteristic
3#10592928C211yesmaximal, characteristic, complemented
4C3×#5231C211yesmaximal, characteristic
5#10591366C211yesmaximal, characteristic
6Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic
7#10591341C211yesmaximal, characteristic, complemented
8#10591304C211yesmaximal, characteristic
9#10591285C211yesmaximal, characteristic
10#10591283C211yesmaximal, characteristic
11#10591261C211yesmaximal, characteristic, complemented
12#10591241C211yesmaximal, characteristic, complemented
13#10591235C211yesmaximal, characteristic, complemented
14#10591226C211yesmaximal, characteristic, complemented
15#10591191C211yesmaximal, characteristic, complemented
16#83258—31nomaximal
17#76793—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C3×#944—24no—
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
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
45C3×C3⋊#95C2211yescharacteristic
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×#944D311yescharacteristic, complemented
57C2×#897—31no—
58C2×#878—31no—
59C3×#393—31no—
60#5231—31no—
61#5231D311yescharacteristic
62#5229—31no—
63#5229—31no—
64#5229—31no—
65#5229—61no—
66#4990—31no—
67#4990—31no—
68#4987—31no—
69#4986—31no—
70#4986—31no—
71Dic3×C4⋊C4—31no—
72#4973—31no—
73#4947—31no—
74#4945—31no—
75#4944—31no—
76#4942—31no—
77Dic3×C22⋊C4—31no—
78C4×(C2×D3)⋊C4—31no—
79#4929—31no—
80#4659—31no—
81#4658—31no—
82#4649—31no—
83#4646—31no—
84#4646—31no—
85#4646—31no—
86C23×C3×D3C2311yescharacteristic
87C2×C32×Q8—22no—
88C2×C32×Q8—22no—
89C2×C32×Q8—41no—
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C2×C3×Dic6—22no—
105C2×C3×Dic6—22no—
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—
113C4⋊(C3⋊Dic3)—22no—
114C4×C3⋊Dic3—41no—
115C3×(C2×D3)⋊C4—22no—
116C3×(C2×D3)⋊C4—22no—
117C3×(C2×D3)⋊C4—41no—
118C3×Dic3⋊C4—22no—
119C3×Dic3⋊C4—22no—
120C3×Dic3⋊C4—22no—
121C3×Dic3⋊C4D414yes—
122C3×C4×Dic3—22no—
123Dic3⋊Dic3—22no—
124Dic3⋊Dic3—22no—
125(C2×D3)⋊Dic3—22no—
126(C2×D3)⋊Dic3—41no—
127(C2×D3)⋊Dic3Q814yescomplemented
128Dic32—22no—
129Dic32—41no—
130#2492—91noSylow
131C22×C3×Q8—21no—
132C22×C3×Q8—31no—
133C22×C3×Q8C2×D311yescharacteristic
134C22×C3×Q8C2×D311yescharacteristic
135C23×Dic3—31no—
136C22×C4×D3—31no—
137C22×Dic6—31no—
138C22×Dic6—31no—
139C22×Dic6C2×D311yescharacteristic
140C3×C4⋊Q8—64no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C42—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—31no—
152#944—24no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4C2×D311yescharacteristic
157C2×(C2×D3)⋊C4C2×D311yescharacteristic
158C2×(C2×D3)⋊C4C2×D311yescharacteristic
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—61no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4C2×D311yescharacteristic
167C2×Dic3⋊C4C2×D311yescharacteristic
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×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—61no—
177C2×C4×Dic3C2×D311yescharacteristic
178#897—64no—
179#878—64no—
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⋊#95C2×D311yescharacteristic
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—
220C32×Q8—44no—
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×C4—21no—
228C2×C32×C4C2×D412yes—
229C2×C32×C4#4112yes—
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⋊Dic3C2×Q812yes—
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×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D412yes—
259C2×C3×Dic3C2×D412yes—
260C2×C3×Dic3C2×Q812yes—
261C2×C3×Dic3#4112yes—
262C2×C3×Dic3#4112yes—
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—31no—
271#393—91no—
272#391—91no—
273#391—91no—
274#391—91no—
275#391—91no—
276#388—91no—
277#388—91no—
278#380—91no—
279C4×C4⋊C4—91no—
280C4×C22⋊C4—91no—
281C24×C3—31no—
282C23×D3C22×D311yescharacteristic
283C2×C3×Q8—24no—
284C2×C3×Q8—22no—
285C2×C3×Q8—22no—
286C2×C3×Q8—22no—
287C2×C3×Q8—22no—
288C2×C3×Q8—42no—
289C2×C3×Q8—41no—
290C2×C3×Q8—41no—
291C2×C3×Q8—42no—
292C2×C3×Q8—62no—
293C2×C3×Q8—62no—
294C2×C3×Q8—121no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×Dic3—31no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—62no—
324C22×Dic3—62no—
325C22×Dic3—62no—
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C2×C4×D3—62no—
334C2×C4×D3—62no—
335C2×C4×D3—62no—
336C2×Dic6—22no—
337C2×Dic6—22no—
338C2×Dic6—41no—
339C2×Dic6—62no—
340C2×Dic6—62no—
341C2×Dic6—62no—
342C2×Dic6—62no—
343C2×Dic6—62no—
344C2×Dic6—62no—
345C3×C4⋊C4—34no—
346C3×C4⋊C4—62no—
347C3×C4⋊C4—62no—
348C3×C4⋊C4—62no—
349C3×C22⋊C4—62no—
350C3×C22⋊C4—62no—
351C3×C22⋊C4—121no—
352C3×C42—62no—
353#217—34no—
354#217—62no—
355#217—121no—
356(C2×D3)⋊C4—22no—
357(C2×D3)⋊C4—22no—
358(C2×D3)⋊C4—34no—
359(C2×D3)⋊C4—41no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—121no—
362C4⋊Dic3—62no—
363C4⋊Dic3—62no—
364C4⋊Dic3—62no—
365C4⋊Dic3—62no—
366C4⋊Dic3—122no—
367Dic3⋊C4—22no—
368Dic3⋊C4—22no—
369Dic3⋊C4—22no—
370Dic3⋊C4—62no—
371Dic3⋊C4—62no—
372Dic3⋊C4#6714yes—
373C4×Dic3—22no—
374C4×Dic3—62no—
375C4×Dic3—62no—
376C4×Dic3—121no—
377C4×Dic3—121no—
378C4×Dic3—121no—
379C4×Dic3—121no—
380C4×Dic3—122no—
381C22×C32C22×D411yescharacteristic
382C22×C32C22×Q811yescharacteristic
383C22×C32C2×#4111yescharacteristic
384C22×C32C2×#4111yescharacteristic
385C22×C32C2×#4111yescharacteristic
386C22×C32H(5,𝔽2)11yescharacteristic
387C22×C322−1+411yescharacteristic
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—41no—
392C2×C3×D3—41no—
393C2×C3×D3—41no—
394C2×C3×D3—41no—
395C32×C4—22no—
396C32×C4—22no—
397C32×C4—41no—
398C3⋊Dic3—22no—
399C3⋊Dic3—41no—
400C3⋊Dic3—41no—
401C3⋊Dic3—41no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3#12414yes—
409C22×Q8—31no—
410C22×Q8—91no—
411C22×Q8D3211yescharacteristic
412C23×C4—91no—
413C4⋊Q8—64no—
414C22⋊Q8—184no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—91no—
420C2×C4⋊C4—91no—
421C2×C4⋊C4—91no—
422C2×C22⋊C4—31no—
423C2×C22⋊C4—31no—
424C2×C22⋊C4—31no—
425C2×C22⋊C4—91no—
426C2×C22⋊C4—91no—
427C2×C22⋊C4—91no—
428C2×C42—31no—
429C2×C42—91no—
430C2×C42—91no—
431C2×C42—91no—
432#95—31no—
433#95—31no—
434#95—31no—
435#95—91no—
436#95—91no—
437#95—91no—
438#95—91no—
439#95—91no—
440#95—91no—
441#95—91no—
442#95—91no—
443#95—91no—
444#95—91no—
445#95—91no—
446C23×C3—21no—
447C23×C3—32no—
448C23×C3—61no—
449C23×C3—61no—
450C23×C3—61no—
451C23×C3—61no—
452C23×C3—61no—
453C23×C3—61no—
454C23×C3C23×D311yescharacteristic
455C23×C3C23×D311yescharacteristic
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3D3×Q812yes—
463C3×Q8—44no—
464C3×Q8—44no—
465C3×Q8—48no—
466C3×Q8—124no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
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—21no—
477C2×C3×C4—22no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—32no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
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×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4D3×D412yes—
512C2×C3×C4#23712yes—
513C2×C3×C4#23712yes—
514C2×C3×C4C2×#6712yes—
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—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—32no—
532C2×Dic3—32no—
533C2×Dic3—62no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—62no—
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—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—121no—
558C2×Dic3—121no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3—124no—
568C2×Dic3D3×Q812yes—
569C2×Dic3#23912yes—
570C2×Dic3#23912yes—
571C2×Dic3C2×#6712yes—
572C2×Dic3C2×#6712yes—
573C4×D3—124no—
574Dic6—44no—
575Dic6—124no—
576Dic6—124no—
577C2×C32C2×#12411yescharacteristic
578C2×C32#53311yescharacteristic
579C2×C32#54211yescharacteristic
580C2×C32#54611yescharacteristic
581C2×C32D4×Q811yescharacteristic
582C2×C32#55411yescharacteristic
583C2×C32#55611yescharacteristic
584C3×D3—42no—
585C24—31no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—41no—
589C2×Q8—62no—
590C2×Q8—62no—
591C2×Q8—121no—
592C2×Q8—182no—
593C2×Q8—182no—
594C2×Q8—182no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—91no—
603C22×C4—91no—
604C22×C4—91no—
605C22×C4—91no—
606C22×C4—182no—
607C22×C4—182no—
608C22×C4—182no—
609C22×C4C2×D3211yescharacteristic
610C22×C4C2×D3211yescharacteristic
611C22×C4C2×D3211yescharacteristic
612C4⋊C4—34no—
613C4⋊C4—62no—
614C4⋊C4—62no—
615C4⋊C4—62no—
616C4⋊C4—182no—
617C4⋊C4—182no—
618C4⋊C4—182no—
619C22⋊C4—62no—
620C22⋊C4—62no—
621C22⋊C4—94no—
622C22⋊C4—121no—
623C22⋊C4—182no—
624C22⋊C4—361no—
625C42—62no—
626C42—182no—
627C42—361no—
628C42—361no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—62no—
637C22×C3—62no—
638C22×C3—62no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3C2×D3×D411yescharacteristic
644C22×C3C2×#23711yescharacteristic
645C22×C3C2×#23711yescharacteristic
646C22×C3#100411yescharacteristic
647C22×C3#100411yescharacteristic
648C22×C3C2×D3×Q811yescharacteristic
649C22×C3C2×D3×Q811yescharacteristic
650C22×C3C2×#23911yescharacteristic
651C22×C3C2×#23911yescharacteristic
652C22×C3#100711yescharacteristic
653C22×C3D3×#4111yescharacteristic
654C22×C3D3×#4111yescharacteristic
655C22×C3#101011yescharacteristic
656C22×C3C22×#6711yescharacteristic
657C2×D3—22no—
658C2×D3—22no—
659C2×D3—22no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C3×C4—24no—
665C3×C4—22no—
666C3×C4—22no—
667C3×C4—22no—
668C3×C4—22no—
669C3×C4—34no—
670C3×C4—42no—
671C3×C4—42no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—62no—
675C3×C4—62no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4—121no—
680Dic3—22no—
681Dic3—22no—
682Dic3—41no—
683Dic3—41no—
684Dic3—41no—
685Dic3—41no—
686Dic3—62no—
687Dic3—62no—
688Dic3—122no—
689Dic3—122no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697Dic3—241no—
698Dic3#94714yes—
699C32#249211yescharacteristic, complemented, Sylow
700C23—32no—
701C23—61no—
702C23—61no—
703C23—61no—
704C23—61no—
705C23—61no—
706C23—61no—
707C23C22×D3211yescharacteristic
708Q8—44no—
709Q8—124no—
710Q8—364no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—32no—
719C2×C4—32no—
720C2×C4—32no—
721C2×C4—32no—
722C2×C4—32no—
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—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—92no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—181no—
743C2×C4—181no—
744C2×C4—181no—
745C2×C4—181no—
746C2×C4—181no—
747C2×C4—181no—
748C2×C4—181no—
749C2×C4—181no—
750C2×C4—181no—
751C2×C4—364no—
752C2×C4#380512yes—
753C2×C4D3×#6712yes—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—122no—
762C2×C3#559111yescharacteristic
763C2×C3#562211yescharacteristic
764C2×C3#563211yescharacteristic
765C2×C3#563611yescharacteristic
766C2×C3#566911yescharacteristic
767C2×C3#567111yescharacteristic
768C2×C3D3×#12411yescharacteristic
769C2×C3#572811yescharacteristic
770C2×C3#573011yescharacteristic
771C2×C3#573211yescharacteristic
772C2×C3#573311yescharacteristic
773C2×C3#580611yescharacteristic
774C2×C3C2×#94711yescharacteristic
775C2×C3Q8×#6711yescharacteristic
776D3—42no—
777C22—62no—
778C22—62no—
779C22—62no—
780C22—121no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22#6431511yescharacteristic
785C22D32×Q811yescharacteristic
786C22D3×#23911yescharacteristic
787C22D3×#23911yescharacteristic
788C22C2×#380511yescharacteristic
789C22C2×D3×#6711yescharacteristic
790C22#6433011yescharacteristic
791C4—22no—
792C4—22no—
793C4—34no—
794C4—41no—
795C4—62no—
796C4—62no—
797C4—121no—
798C4—121no—
799C4—121no—
800C4—121no—
801C4—182no—
802C4—361no—
803C4—361no—
804C4—361no—
805C3—21no—
806C3#7679311yescharacteristic, complemented
807C3#8325811yescharacteristic, complemented
808C2—122no—
809C2#1059536811yescharacteristic
810C2#1059537211yescharacteristic
811C2#1059538311yescharacteristic
812C2#1059538411yescharacteristic
813C2#1059540011yescharacteristic
814C2D3×#94711yescharacteristic
815C2#1059549411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×Q8C22
prime radicalC23×C3×D3C23
hypercenterC22×Q8D32
hypocenterC32#2492
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#944C2semidirect
3. #10592928C2semidirect
7. #10591341C2semidirect
11. #10591261C2semidirect
12. #10591241C2semidirect
13. #10591235C2semidirect
14. #10591226C2semidirect
15. #10591191C2semidirect
56. C2×#944D3semidirect
127. (C2×D3)⋊Dic3Q8semidirect
699. C32#2492semidirect
806. C3#76793semidirect
807. C3#83258semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9442
C2×#638932
#105929282
C3×#52312
#105913662
Dic3×(C2×D3)⋊C42
#105913412
#105913042
#105912852
#105912832
#105912612
#105912412
#105912352
#105912262
#105911912
#832583
#767933