Finite Group Databasebeta

← #11803927

Subgroups — #11803927

Order 1152.

1221 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63865C211yesmaximal, characteristic
2C3⋊D3×#95C211yesmaximal, characteristic
3C3×#4655C211yesmaximal, characteristic, complemented
4C3×#4647C211yesmaximal, characteristic, complemented
5#10591333C211yesmaximal, characteristic, complemented
6#10591325C211yesmaximal, characteristic
7#10591290C211yesmaximal, characteristic
8#10591290C211yesmaximal, characteristic
9C4×#3722C211yesmaximal, characteristic
10#10591265C211yesmaximal, characteristic, complemented
11#10591262C211yesmaximal, characteristic, complemented
12#10591260C211yesmaximal, characteristic
13#10591255C211yesmaximal, characteristic, complemented
14#10591235C211yesmaximal, characteristic, complemented
15#10591191C211yesmaximal, characteristic, complemented
16#76199—31nomaximal
17#75299—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×#3724C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×#3722C2211yescharacteristic
34C2×#3722C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39#63865C418yescomplemented
40C32×#95C2211yescharacteristic
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
54C2×#896—31no—
55C2×#896—31no—
56C3×#389—31no—
57C3×#387—31no—
58#4989—31no—
59#4989—31no—
60#4987—31no—
61#4987—31no—
62#4984—31no—
63#4980—31no—
64#4978—31no—
65#4978—31no—
66#4976—31no—
67#4973—31no—
68C4×(C2×D3)⋊C4—31no—
69C4×(C2×D3)⋊C4—31no—
70#4933—31no—
71#4929—31no—
72#4668—31no—
73#4668—31no—
74#4666—31no—
75#4666—31no—
76D3×#95—31no—
77D3×#95—31no—
78D3×#95—61no—
79#4655—31no—
80#4655D311yescharacteristic, complemented
81#4652—31no—
82#4647D311yescharacteristic, complemented
83#4646—31no—
84#4646—31no—
85C23×C3⋊D3C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C2×C4×C3⋊D3—22no—
93C2×C4×C3⋊D3—41no—
94C2×C4×C3⋊D3—41no—
95C2×C4×C3⋊D3—41no—
96C2×C4×C3⋊D3—41no—
97C2×C4×C3⋊D3—41no—
98C2×C4×C3⋊D3—41no—
99C2×C4×C3⋊D3C2×C414yes—
100C2×C4×C3⋊D3Q814yescomplemented
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C2×#627—41no—
110C2×#627—41no—
111C2×#627C2×C414yescomplemented
112C3×C4⋊Dic3—41no—
113C3×C4⋊Dic3—41no—
114C3×Dic3⋊C4—41no—
115C3×Dic3⋊C4—41no—
116C3×Dic3⋊C4C2×C414yescomplemented
117C3×Dic3⋊C4C2×C414yescomplemented
118C3×C4×Dic3—41no—
119C3×C4×Dic3—41no—
120#3724C2×C414yescomplemented
121Dic3⋊Dic3—41no—
122Dic3⋊Dic3—41no—
123#3722—22no—
124#3722—22no—
125#3722C2×C414yes—
126#3722C2×C414yes—
127Dic32—41no—
128Dic32—41no—
129#2329—91noSylow
130C22×C4×D3—31no—
131C22×C4×D3—31no—
132C22×C4×D3—31no—
133C22×C4×D3—31no—
134C22×C4×D3—31no—
135C22×C4×D3—31no—
136C22×C4×D3—61no—
137C22×C4×D3—61no—
138C22×C4×D3—61no—
139C22×Dic6—31no—
140C22×Dic6—31no—
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×C4⋊C4—31no—
147C2×C3×C42—31no—
148C2×C3×C42—31no—
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×C4⋊Dic3—31no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3C2×D311yescharacteristic
160C2×C4⋊Dic3C2×D311yescharacteristic
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4C2×D311yescharacteristic
166C2×Dic3⋊C4C2×D311yescharacteristic
167C2×Dic3⋊C4C2×D311yescharacteristic
168C2×Dic3⋊C4C2×D311yescharacteristic
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3C2×D311yescharacteristic
174C2×C4×Dic3C2×D311yescharacteristic
175#896—38no—
176#896—38no—
177C3×#95—21no—
178C3×#95—31no—
179C3×#95—31no—
180C3×#95—31no—
181C3×#95—31no—
182C3×#95C2×D311yescharacteristic
183C3×#95C2×D311yescharacteristic
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—61no—
203C3⋊#95—61no—
204C3⋊#95—61no—
205C3⋊#95C2×D311yescharacteristic
206C3⋊#95C2×D311yescharacteristic
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C23×C32C2411yescharacteristic
210C22×C3⋊D3—21no—
211C22×C3⋊D3—21no—
212C22×C3⋊D3—21no—
213C22×C3⋊D3—21no—
214C22×C3⋊D3C22×C412yes—
215C22×C3⋊D3C2×Q812yes—
216C22×C3⋊D3#4112yes—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4C22×C412yes—
225C2×C32×C4C2×Q812yes—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3C22×C412yes—
234C2×C3⋊Dic3C2×Q812yes—
235C4×C3⋊D3—44no—
236C4×C3⋊D3—44no—
237C4×C3⋊D3—44no—
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×Dic3—21no—
258C2×C3×Dic3C22×C412yes—
259C2×C3×Dic3C22×C412yes—
260C2×C3×Dic3C22×C412yes—
261C2×C3×Dic3C22×C412yes—
262#627—44no—
263C2×C22⋊Q8—91no—
264#391—91no—
265#391—91no—
266#389—31no—
267#389—91no—
268#387—31no—
269#387—91no—
270#387—91no—
271#387—91no—
272#385—91no—
273#385—91no—
274#380—91no—
275C4×C22⋊C4—91no—
276C4×C22⋊C4—91no—
277C2×#95—91no—
278C23×D3—31no—
279C23×D3—31no—
280C23×D3—61no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×Dic3—31no—
299C22×Dic3—31no—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C2×C4×D3—34no—
316C2×C4×D3—34no—
317C2×C4×D3—34no—
318C2×C4×D3—34no—
319C2×C4×D3—64no—
320C2×C4×D3—64no—
321C2×C4×D3—62no—
322C2×C4×D3—62no—
323C2×C4×D3—64no—
324C2×C4×D3—121no—
325C2×C4×D3—121no—
326C2×C4×D3—121no—
327C2×C4×D3—121no—
328C2×C4×D3—121no—
329C2×C4×D3—121no—
330C2×C4×D3—121no—
331C2×C4×D3—121no—
332C2×C4×D3—121no—
333C2×C4×D3—121no—
334C2×C4×D3—121no—
335C2×C4×D3—121no—
336C2×C4×D3—122no—
337C2×C4×D3—122no—
338C2×C4×D3—122no—
339C2×C4×D3—122no—
340C2×C4×D3—122no—
341C2×C4×D3—122no—
342C2×Dic6—34no—
343C2×Dic6—34no—
344C2×Dic6—121no—
345C2×Dic6—121no—
346C2×Dic6—121no—
347C2×Dic6—121no—
348C3×C4⋊C4—34no—
349C3×C4⋊C4—34no—
350C3×C4⋊C4—121no—
351C3×C4⋊C4—121no—
352C3×C4⋊C4—121no—
353C3×C4⋊C4—121no—
354C3×C42—121no—
355C3×C42—121no—
356(C2×D3)⋊C4—34no—
357(C2×D3)⋊C4—34no—
358(C2×D3)⋊C4—34no—
359(C2×D3)⋊C4—34no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—62no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364C4⋊Dic3—41no—
365C4⋊Dic3—41no—
366C4⋊Dic3—121no—
367C4⋊Dic3—121no—
368Dic3⋊C4—34no—
369Dic3⋊C4—34no—
370Dic3⋊C4—41no—
371Dic3⋊C4—41no—
372Dic3⋊C4—121no—
373Dic3⋊C4—121no—
374Dic3⋊C4C4×D314yescomplemented
375Dic3⋊C4C4×D314yescomplemented
376C4×Dic3—41no—
377C4×Dic3—41no—
378C4×Dic3—121no—
379C4×Dic3—121no—
380C4×Dic3—121no—
381C4×Dic3—121no—
382C22×C32C23×C411yescharacteristic
383C22×C32C22×Q811yescharacteristic
384C22×C32C2×#4111yescharacteristic
385C22×C32H(5,𝔽2)11yescharacteristic
386C22×C32H(5,𝔽2)11yescharacteristic
387C22×C32H(5,𝔽2)11yescharacteristic
388C22×C322−1+411yescharacteristic
389C2×C3⋊D3—22no—
390C2×C3⋊D3—22no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3—22no—
393C2×C3⋊D3—22no—
394C2×C3⋊D3—22no—
395C2×C3⋊D3C4×Q814yes—
396C32×C4—22no—
397C32×C4—22no—
398C32×C4—41no—
399C3⋊Dic3—22no—
400C3⋊Dic3—22no—
401C3⋊Dic3—41no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—22no—
405C3×Dic3—22no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C22×Q8—91no—
411C23×C4—91no—
412C23×C4—91no—
413C23×C4—91no—
414C22⋊Q8—98no—
415C2×C4⋊C4—31no—
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×C4⋊C4—91no—
424C2×C22⋊C4—91no—
425C2×C22⋊C4—91no—
426C2×C22⋊C4—91no—
427C2×C22⋊C4—91no—
428C2×C42—31no—
429C2×C42—31no—
430C2×C42—91no—
431C2×C42—91no—
432#95—31no—
433#95—31no—
434#95—31no—
435#95—31no—
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#95D3211yescharacteristic
446C23×C3—21no—
447C23×C3C23×D311yescharacteristic
448C23×C3C23×D311yescharacteristic
449C22×D3—32no—
450C22×D3—32no—
451C22×D3—32no—
452C22×D3—32no—
453C22×D3—32no—
454C22×D3—32no—
455C22×D3—62no—
456C22×D3—62no—
457C22×D3—62no—
458C22×D3—62no—
459C22×D3—62no—
460C22×D3—62no—
461C22×D3—62no—
462C22×D3—61no—
463C22×D3—61no—
464C22×D3—61no—
465C22×D3—61no—
466C22×D3—61no—
467C22×D3—61no—
468C22×D3—61no—
469C22×D3—61no—
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—21no—
478C2×C3×C4—22no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
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—41no—
496C2×C3×C4—41no—
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×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4C2×C4×D312yes—
518C2×C3×C4C2×C4×D312yes—
519C2×C3×C4D3×Q812yes—
520C2×C3×C4D3×Q812yes—
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—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—32no—
542C2×Dic3—32no—
543C2×Dic3—32no—
544C2×Dic3—32no—
545C2×Dic3—62no—
546C2×Dic3—62no—
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—62no—
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×Dic3C2×C4×D312yes—
569C2×Dic3C2×C4×D312yes—
570C2×Dic3C2×C4×D312yes—
571C2×Dic3C2×C4×D312yes—
572C4×D3—124no—
573C4×D3—124no—
574C4×D3—124no—
575C4×D3—124no—
576C4×D3—128no—
577C4×D3—128no—
578C4×D3—128no—
579C4×D3—124no—
580C4×D3—124no—
581Dic6—124no—
582Dic6—124no—
583C2×C32C2×C4×Q811yescharacteristic
584C2×C32#51811yescharacteristic
585C2×C32#52011yescharacteristic
586C2×C32#53811yescharacteristic
587C2×C32#53911yescharacteristic
588C2×C32#54311yescharacteristic
589C2×C32#54411yescharacteristic
590C3⋊D3—24no—
591C24—91no—
592C2×Q8—94no—
593C2×Q8—361no—
594C2×Q8—361no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—91no—
604C22×C4—91no—
605C22×C4—94no—
606C22×C4—94no—
607C22×C4—91no—
608C22×C4—182no—
609C22×C4—361no—
610C22×C4—361no—
611C22×C4—361no—
612C22×C4—361no—
613C22×C4—361no—
614C22×C4—361no—
615C22×C4C2×D3211yescharacteristic
616C22×C4C2×D3211yescharacteristic
617C22×C4C2×D3211yescharacteristic
618C4⋊C4—34no—
619C4⋊C4—34no—
620C4⋊C4—94no—
621C4⋊C4—121no—
622C4⋊C4—121no—
623C4⋊C4—121no—
624C4⋊C4—121no—
625C4⋊C4—361no—
626C4⋊C4—361no—
627C22⋊C4—94no—
628C22⋊C4—94no—
629C22⋊C4—182no—
630C22⋊C4—182no—
631C42—121no—
632C42—121no—
633C42—361no—
634C42—361no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3C22×C4×D311yescharacteristic
643C22×C3C22×C4×D311yescharacteristic
644C22×C3#100411yescharacteristic
645C22×C3#100411yescharacteristic
646C22×C3#100411yescharacteristic
647C22×C3C2×D3×Q811yescharacteristic
648C22×C3C2×D3×Q811yescharacteristic
649C22×C3#100711yescharacteristic
650C22×C3D3×#4111yescharacteristic
651C22×C3D3×#4111yescharacteristic
652C22×C3#100911yescharacteristic
653C22×C3#100911yescharacteristic
654C22×C3#100911yescharacteristic
655C22×C3#101011yescharacteristic
656C2×D3—34no—
657C2×D3—34no—
658C2×D3—64no—
659C2×D3—64no—
660C2×D3—64no—
661C2×D3—64no—
662C2×D3—64no—
663C2×D3—64no—
664C2×D3—64no—
665C2×D3—62no—
666C2×D3—62no—
667C2×D3—62no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—62no—
672C2×D3—62no—
673C2×D3—62no—
674C2×D3—62no—
675C2×D3—62no—
676C2×D3—62no—
677C3×C4—22no—
678C3×C4—22no—
679C3×C4—22no—
680C3×C4—22no—
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—62no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4—121no—
694Dic3—22no—
695Dic3—22no—
696Dic3—22no—
697Dic3—22no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702Dic3—62no—
703Dic3—62no—
704Dic3—62no—
705Dic3—62no—
706Dic3—122no—
707Dic3—122no—
708Dic3—122no—
709Dic3—121no—
710Dic3—121no—
711C32#232911yescharacteristic, complemented, Sylow
712C23—92no—
713C23—92no—
714C23—92no—
715C23—181no—
716C23—181no—
717C23—181no—
718C23—181no—
719C23C22×D3211yescharacteristic
720Q8—364no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—32no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
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—92no—
753C2×C4—92no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C4—181no—
758C2×C4—181no—
759C2×C4—181no—
760C2×C4—181no—
761C2×C4—364no—
762C2×C4—364no—
763C2×C4—364no—
764C2×C4#379712yes—
765C2×C4C4×D3212yes—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3#550411yescharacteristic
774C2×C3#552311yescharacteristic
775C2×C3#554511yescharacteristic
776C2×C3#554511yescharacteristic
777C2×C3C4×D3×Q811yescharacteristic
778C2×C3C4×D3×Q811yescharacteristic
779C2×C3#561311yescharacteristic
780C2×C3#563411yescharacteristic
781C2×C3#563411yescharacteristic
782C2×C3#566011yescharacteristic
783C2×C3#568911yescharacteristic
784C2×C3#569211yescharacteristic
785C2×C3#570411yescharacteristic
786C2×C3#572911yescharacteristic
787D3—68no—
788D3—64no—
789D3—64no—
790C22—94no—
791C22—182no—
792C22—182no—
793C22—182no—
794C22—182no—
795C22—182no—
796C22—182no—
797C22C2×#379711yescharacteristic
798C22C2×C4×D3211yescharacteristic
799C22#6430611yescharacteristic
800C22#6431411yescharacteristic
801C22#6431411yescharacteristic
802C22#6431411yescharacteristic
803C22#6431511yescharacteristic
804C4—22no—
805C4—22no—
806C4—41no—
807C4—62no—
808C4—62no—
809C4—62no—
810C4—62no—
811C4—121no—
812C4—121no—
813C4—121no—
814C4—121no—
815C4—182no—
816C4—182no—
817C4—361no—
818C3—21no—
819C3#7529911yescharacteristic, complemented
820C3#7619911yescharacteristic, complemented
821C2—184no—
822C2C4×#379711yescharacteristic
823C2#1059418011yescharacteristic
824C2#1059422611yescharacteristic
825C2#1059425611yescharacteristic
826C2#1059432511yescharacteristic
827C2#1059451011yescharacteristic
828C2#1059457211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2329
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C3×#4655C2semidirect
4. C3×#4647C2semidirect
5. #10591333C2semidirect
10. #10591265C2semidirect
11. #10591262C2semidirect
13. #10591255C2semidirect
14. #10591235C2semidirect
15. #10591191C2semidirect
39. #63865C4semidirect
80. #4655D3semidirect
82. #4647D3semidirect
100. C2×C4×C3⋊D3Q8semidirect
111. C2×#627C2×C4semidirect
116. C3×Dic3⋊C4C2×C4semidirect
117. C3×Dic3⋊C4C2×C4semidirect
120. #3724C2×C4semidirect
374. Dic3⋊C4C4×D3semidirect
375. Dic3⋊C4C4×D3semidirect
711. C32#2329semidirect
819. C3#75299semidirect
820. C3#76199semidirect

Maximal subgroups

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

subgroupindex
C2×#638652
C3⋊D3×#952
C3×#46552
C3×#46472
#105913332
#105913252
#105912902
C4×#37222
#105912652
#105912622
#105912602
#105912552
#105912352
#105911912
#761993
#752993