Finite Group Databasebeta

← #11819090

Subgroups — #11819090

Order 1152.

1117 conjugacy classes of subgroups.

The subgroup lattice has 829 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#944C211yesmaximal, characteristic, complemented
2C2×#63895C211yesmaximal, characteristic
3#10592930C211yesmaximal, characteristic
4C3×#5229C211yesmaximal, characteristic, complemented
5#10591367C211yesmaximal, characteristic
6#10591341C211yesmaximal, characteristic, complemented
7#10591310C211yesmaximal, characteristic
8#10591289C211yesmaximal, characteristic
9#10591261C211yesmaximal, characteristic, complemented
10#10591258C211yesmaximal, characteristic
11Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
12#10591235C211yesmaximal, characteristic, complemented
13#10591233C211yesmaximal, characteristic
14#10591225C211yesmaximal, characteristic, complemented
15#10591191C211yesmaximal, characteristic, complemented
16#83258—31nomaximal
17#76517—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C3×#944—24no—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40#63895—24no—
41#63658C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
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×#896—31no—
59C3×#391—31no—
60#5231—31no—
61#5231—31no—
62#5231—31no—
63#5231—61no—
64#5229—31no—
65#5229D311yescharacteristic, complemented
66#4990—31no—
67#4990—31no—
68#4987—31no—
69#4986—31no—
70#4986—31no—
71#4985—31no—
72Dic3×C4⋊C4—31no—
73#4973—31no—
74#4940—31no—
75C4×(C2×D3)⋊C4—31no—
76C4×Dic3⋊C4—31no—
77#4929—31no—
78#4673—31no—
79#4669—31no—
80#4667—31no—
81#4666—31no—
82#4658—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×#624—22no—
111C2×#624—22no—
112C2×#624—22no—
113#3752—22no—
114#3752—22no—
115#3752—41no—
116C3×C4⋊Dic3—22no—
117C3×Dic3⋊C4—22no—
118C3×Dic3⋊C4—22no—
119C3×Dic3⋊C4—22no—
120C3×Dic3⋊C4D414yes—
121C3×C4×Dic3—22no—
122C3×C4×Dic3—41no—
123Dic3⋊Dic3—22no—
124Dic3⋊Dic3—22no—
125#3722—22no—
126#3722—41no—
127#3722Q814yescomplemented
128Dic32—22no—
129Dic32—41no—
130#2492—91noSylow
131C22×C3×Q8—21no—
132C22×C3×Q8—31no—
133C22×C3×Q8C2×D311yescharacteristic
134C22×C3×Q8C2×D311yescharacteristic
135C22×C4×D3—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×C4⋊C4—31no—
146C2×C3×C42—31no—
147C2×C3×C42—31no—
148#944—24no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—61no—
162C2×(C2×D3)⋊C4—61no—
163C2×(C2×D3)⋊C4—61no—
164C2×C4⋊Dic3—31no—
165C2×C4⋊Dic3—31no—
166C2×C4⋊Dic3C2×D311yescharacteristic
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4C2×D311yescharacteristic
170C2×Dic3⋊C4C2×D311yescharacteristic
171C2×Dic3⋊C4C2×D311yescharacteristic
172C2×Dic3⋊C4C2×D311yescharacteristic
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3C2×D311yescharacteristic
178C2×C4×Dic3C2×D311yescharacteristic
179#897—64no—
180#896—64no—
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⋊#95C2×D311yescharacteristic
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×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×Dic3—21no—
257C2×C3×Dic3C2×D412yes—
258C2×C3×Dic3C2×D412yes—
259C2×C3×Dic3C2×Q812yes—
260C2×C3×Dic3C2×Q812yes—
261C2×C3×Dic3#4112yes—
262C2×C3×Dic3#4112yes—
263C3×Dic6—44no—
264#627—44no—
265#624—44no—
266C2×C4⋊Q8—31no—
267C2×C22⋊Q8—91no—
268#400—91no—
269#400—91no—
270#393—91no—
271#393—91no—
272#391—31no—
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—
281C23×D3—31no—
282C23×D3—31no—
283C23×D3—61no—
284C2×C3×Q8—22no—
285C2×C3×Q8—22no—
286C2×C3×Q8—22no—
287C2×C3×Q8—22no—
288C2×C3×Q8—42no—
289C2×C3×Q8—42no—
290C2×C3×Q8—41no—
291C2×C3×Q8—41no—
292C2×C3×Q8—42no—
293C2×C3×Q8—62no—
294C2×C3×Q8—62no—
295C2×C3×Q8—121no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
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×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
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×Dic3C22×D311yescharacteristic
323C22×Dic3C22×D311yescharacteristic
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C2×C4×D3—62no—
331C2×C4×D3—62no—
332C2×C4×D3—62no—
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×C4⋊C4—62no—
350C3×C42—62no—
351C3×C42—121no—
352(C2×D3)⋊C4—34no—
353(C2×D3)⋊C4—34no—
354(C2×D3)⋊C4—62no—
355(C2×D3)⋊C4—62no—
356(C2×D3)⋊C4—62no—
357(C2×D3)⋊C4—62no—
358(C2×D3)⋊C4—62no—
359(C2×D3)⋊C4—62no—
360(C2×D3)⋊C4—122no—
361(C2×D3)⋊C4—122no—
362(C2×D3)⋊C4—121no—
363(C2×D3)⋊C4—121no—
364(C2×D3)⋊C4—121no—
365(C2×D3)⋊C4—121no—
366(C2×D3)⋊C4—122no—
367C4⋊Dic3—22no—
368C4⋊Dic3—62no—
369C4⋊Dic3—62no—
370Dic3⋊C4—22no—
371Dic3⋊C4—22no—
372Dic3⋊C4—22no—
373Dic3⋊C4—62no—
374Dic3⋊C4—62no—
375Dic3⋊C4#6714yes—
376C4×Dic3—22no—
377C4×Dic3—41no—
378C4×Dic3—62no—
379C4×Dic3—62no—
380C4×Dic3—121no—
381C4×Dic3—121no—
382C22×C32C22×D411yescharacteristic
383C22×C32C22×Q811yescharacteristic
384C22×C32C2×#4111yescharacteristic
385C22×C32C2×#4111yescharacteristic
386C22×C32C2×#4111yescharacteristic
387C22×C32H(5,𝔽2)11yescharacteristic
388C22×C322−1+411yescharacteristic
389C2×C3⋊D3—22no—
390C2×C3⋊D3—22no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3—41no—
393C2×C3⋊D3—41no—
394C2×C3⋊D3—41no—
395C2×C3⋊D3—41no—
396C32×C4—22no—
397C32×C4—22no—
398C32×C4—41no—
399C3⋊Dic3—41no—
400C3⋊Dic3—41no—
401C3⋊Dic3—41no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—22no—
405C3×Dic3—41no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3#12414yes—
410C22×Q8—31no—
411C22×Q8—91no—
412C22×Q8D3211yescharacteristic
413C23×C4—91no—
414C4⋊Q8—64no—
415C22⋊Q8—184no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4—31no—
421C2×C4⋊C4—91no—
422C2×C4⋊C4—91no—
423C2×C22⋊C4—91no—
424C2×C22⋊C4—91no—
425C2×C22⋊C4—91no—
426C2×C22⋊C4—91no—
427C2×C22⋊C4—91no—
428C2×C22⋊C4—91no—
429C2×C42—31no—
430C2×C42—31no—
431C2×C42—91no—
432C2×C42—91no—
433#95—31no—
434#95—31no—
435#95—31no—
436#95—31no—
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—
446#95—91no—
447C23×C3—21no—
448C23×C3C23×D311yescharacteristic
449C23×C3C23×D311yescharacteristic
450C22×D3—32no—
451C22×D3—32no—
452C22×D3—62no—
453C22×D3—61no—
454C22×D3—61no—
455C22×D3—61no—
456C22×D3—61no—
457C22×D3—61no—
458C22×D3—61no—
459C22×D3—61no—
460C22×D3—61no—
461C22×D3—61no—
462C22×D3—61no—
463C22×D3—61no—
464C22×D3—61no—
465C22×D3—121no—
466C22×D3—121no—
467C22×D3—121no—
468C22×D3—121no—
469C22×D3—121no—
470C22×D3—121no—
471C3×Q8—44no—
472C3×Q8—44no—
473C3×Q8—48no—
474C3×Q8—124no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—22no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—32no—
495C2×C3×C4—32no—
496C2×C3×C4—32no—
497C2×C3×C4—32no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
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×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
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#23512yes—
523C2×C3×C4D3×D412yes—
524C2×C3×C4#23712yes—
525C2×C3×C4C2×#6712yes—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
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—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3—121no—
568C2×Dic3—121no—
569C2×Dic3—121no—
570C2×Dic3—121no—
571C2×Dic3D3×Q812yes—
572C2×Dic3D3×Q812yes—
573C2×Dic3#23912yes—
574C2×Dic3#23912yes—
575C2×Dic3C2×#6712yes—
576C2×Dic3C2×#6712yes—
577C4×D3—124no—
578C4×D3—124no—
579Dic6—44no—
580Dic6—124no—
581Dic6—124no—
582C2×C32C2×#12411yescharacteristic
583C2×C32#53311yescharacteristic
584C2×C32#54211yescharacteristic
585C2×C32#54611yescharacteristic
586C2×C32D4×Q811yescharacteristic
587C2×C32#55411yescharacteristic
588C2×C32#55611yescharacteristic
589C3⋊D3—42no—
590C24—91no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—41no—
594C2×Q8—62no—
595C2×Q8—62no—
596C2×Q8—121no—
597C2×Q8—182no—
598C2×Q8—182no—
599C2×Q8—182no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—91no—
609C22×C4—91no—
610C22×C4—91no—
611C22×C4—182no—
612C22×C4—182no—
613C22×C4—182no—
614C22×C4C2×D3211yescharacteristic
615C22×C4C2×D3211yescharacteristic
616C22×C4C2×D3211yescharacteristic
617C4⋊C4—34no—
618C4⋊C4—62no—
619C4⋊C4—62no—
620C4⋊C4—62no—
621C4⋊C4—62no—
622C4⋊C4—182no—
623C4⋊C4—182no—
624C22⋊C4—94no—
625C22⋊C4—182no—
626C22⋊C4—182no—
627C22⋊C4—182no—
628C22⋊C4—361no—
629C22⋊C4—361no—
630C42—62no—
631C42—121no—
632C42—182no—
633C42—361no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3C2×#23511yescharacteristic
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C2×#23711yescharacteristic
644C22×C3#100411yescharacteristic
645C22×C3#100411yescharacteristic
646C22×C3C2×D3×Q811yescharacteristic
647C22×C3C2×D3×Q811yescharacteristic
648C22×C3C2×#23911yescharacteristic
649C22×C3C2×#23911yescharacteristic
650C22×C3#100711yescharacteristic
651C22×C3#100711yescharacteristic
652C22×C3D3×#4111yescharacteristic
653C22×C3D3×#4111yescharacteristic
654C22×C3C22×#6711yescharacteristic
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—62no—
658C2×D3—62no—
659C2×D3—62no—
660C2×D3—62no—
661C2×D3—122no—
662C2×D3—122no—
663C2×D3—122no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—241no—
673C2×D3—241no—
674C2×D3—241no—
675C2×D3—241no—
676C3×C4—22no—
677C3×C4—22no—
678C3×C4—22no—
679C3×C4—22no—
680C3×C4—34no—
681C3×C4—42no—
682C3×C4—42no—
683C3×C4—42no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—62no—
687C3×C4—62no—
688C3×C4—62no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4—121no—
693Dic3—22no—
694Dic3—22no—
695Dic3—22no—
696Dic3—41no—
697Dic3—41no—
698Dic3—41no—
699Dic3—41no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707Dic3—241no—
708Dic3—241no—
709Dic3#94714yes—
710C32#249211yescharacteristic, complemented, Sylow
711C23—92no—
712C23—181no—
713C23—181no—
714C23—181no—
715C23—181no—
716C23—181no—
717C23—181no—
718C23C22×D3211yescharacteristic
719Q8—44no—
720Q8—124no—
721Q8—364no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C4—181no—
758C2×C4—181no—
759C2×C4—181no—
760C2×C4—181no—
761C2×C4—181no—
762C2×C4—364no—
763C2×C4#380412yes—
764C2×C4D3×#6712yes—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3#549011yescharacteristic
773C2×C3#556811yescharacteristic
774C2×C3#557811yescharacteristic
775C2×C3#563611yescharacteristic
776C2×C3#564011yescharacteristic
777C2×C3D3×#12411yescharacteristic
778C2×C3#572711yescharacteristic
779C2×C3#572811yescharacteristic
780C2×C3#573011yescharacteristic
781C2×C3#573211yescharacteristic
782C2×C3#573311yescharacteristic
783C2×C3#580611yescharacteristic
784C2×C3C2×#94711yescharacteristic
785C2×C3Q8×#6711yescharacteristic
786D3—122no—
787D3—122no—
788D3—242no—
789C22—182no—
790C22—182no—
791C22—182no—
792C22—361no—
793C22—361no—
794C22—361no—
795C22—361no—
796C22#6431611yescharacteristic
797C22D32×Q811yescharacteristic
798C22D3×#23911yescharacteristic
799C22D3×#23911yescharacteristic
800C22C2×#380411yescharacteristic
801C22C2×D3×#6711yescharacteristic
802C22#6433011yescharacteristic
803C4—22no—
804C4—22no—
805C4—34no—
806C4—41no—
807C4—62no—
808C4—62no—
809C4—62no—
810C4—121no—
811C4—121no—
812C4—121no—
813C4—121no—
814C4—361no—
815C4—361no—
816C4—361no—
817C3—21no—
818C3#7651711yescharacteristic, complemented
819C3#8325811yescharacteristic, complemented
820C2—362no—
821C2#1059534311yescharacteristic
822C2#1059537211yescharacteristic
823C2#1059537411yescharacteristic
824C2#1059538711yescharacteristic
825C2#1059540311yescharacteristic
826C2D3×#94711yescharacteristic
827C2#1059549311yescharacteristic
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
4. C3×#5229C2semidirect
6. #10591341C2semidirect
9. #10591261C2semidirect
11. Dic3×Dic3⋊C4C2semidirect
12. #10591235C2semidirect
14. #10591225C2semidirect
15. #10591191C2semidirect
56. C2×#944D3semidirect
65. #5229D3semidirect
127. #3722Q8semidirect
710. C32#2492semidirect
818. C3#76517semidirect
819. 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×#638952
#105929302
C3×#52292
#105913672
#105913412
#105913102
#105912892
#105912612
#105912582
Dic3×Dic3⋊C42
#105912352
#105912332
#105912252
#105911912
#832583
#765173