Finite Group Databasebeta

← #11803921

Subgroups — #11803921

Order 1152.

1141 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63893C211yesmaximal, characteristic
2#10592627C211yesmaximal, characteristic, complemented
3C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
4C3×#4933C211yesmaximal, characteristic, complemented
5#10591379C211yesmaximal, characteristic
6#10591372C211yesmaximal, characteristic
7#10591369C211yesmaximal, characteristic
8D3×C3⋊#95C211yesmaximal, characteristic
9#10591331C211yesmaximal, characteristic, complemented
10#10591272C211yesmaximal, characteristic, complemented
11#10591271C211yesmaximal, characteristic, complemented
12#10591237C211yesmaximal, characteristic
13#10591236C211yesmaximal, characteristic, complemented
14#10591234C211yesmaximal, characteristic, complemented
15#10591191C211yesmaximal, characteristic, complemented
16#75300—31nomaximal
17#73447—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×#627C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C2×C32×C42C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39#63893C418yescomplemented
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
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×#897—31no—
55C2×#878—31no—
56C3×#387—31no—
57C3×C4×C22⋊C4—31no—
58C4×#217—31no—
59C2×C3⋊#95—31no—
60#4989—31no—
61#4980—31no—
62#4972—31no—
63#4950—31no—
64#4946—31no—
65#4942—31no—
66C4×(C2×D3)⋊C4D311yescharacteristic
67#4933—31no—
68#4933D311yescharacteristic, complemented
69#4929—31no—
70#4928—31no—
71#4928—31no—
72#4928—61no—
73#4668—31no—
74#4667—31no—
75#4666—31no—
76D3×#95—31no—
77#4655—31no—
78#4654—31no—
79#4654—31no—
80#4653—31no—
81#4647—31no—
82#4646—31no—
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
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C2×C3×C4×D3—41no—
101C2×C3×C4×D3—41no—
102C2×C3×C4×D3Q814yescomplemented
103C2×#627—41no—
104C2×#627—41no—
105C2×#627C2×C414yescomplemented
106C2×D3×Dic3—22no—
107C2×D3×Dic3—41no—
108C2×D3×Dic3—41no—
109C2×D3×Dic3—41no—
110C2×D3×Dic3—41no—
111C2×D3×Dic3C2×C414yes—
112C32×C42—41no—
113C4⋊(C3⋊Dic3)—41no—
114C4⋊(C3⋊Dic3)C2×C414yescomplemented
115#3750—41no—
116#3750—41no—
117C3×(C2×D3)⋊C4—22no—
118C3×(C2×D3)⋊C4C2×C414yes—
119C3×Dic3⋊C4—41no—
120C3×Dic3⋊C4C2×C414yescomplemented
121C3×C4×Dic3—41no—
122#3724—41no—
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3C2×C414yescomplemented
125(C2×D3)⋊Dic3—22no—
126(C2×D3)⋊Dic3C2×C414yes—
127Dic32—41no—
128Dic32—41no—
129#2329—91noSylow
130C23×C3×C4—31no—
131C23×Dic3—31no—
132C23×Dic3—31no—
133C22×C4×D3—31no—
134C22×C4×D3—31no—
135C22×C4×D3C2×D311yescharacteristic
136C22×Dic6—31no—
137C22×Dic6—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C42—21no—
143C2×C3×C42—31no—
144C2×C3×C42C2×D311yescharacteristic
145C2×C3×C42C2×D311yescharacteristic
146C2×#217—31no—
147C2×#217—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4C2×D311yescharacteristic
151C2×(C2×D3)⋊C4C2×D311yescharacteristic
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—31no—
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—61no—
159C2×C4⋊Dic3—61no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—61no—
169C2×Dic3⋊C4—61no—
170C2×Dic3⋊C4C2×D311yescharacteristic
171C2×Dic3⋊C4C2×D311yescharacteristic
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3C2×D311yescharacteristic
177#897—38no—
178#878—38no—
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—61no—
202C3⋊#95—61no—
203C3⋊#95C2×D311yescharacteristic
204C3⋊#95C2×D311yescharacteristic
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⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3C22×C412yes—
237C2×C3⋊Dic3C22×C412yes—
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×Dic3C22×C412yes—
256C2×C3×Dic3C22×C412yes—
257C2×C3×Dic3C22×C412yes—
258C2×C3×Dic3C2×Q812yes—
259C3×C4×D3—44no—
260#627—44no—
261D3×Dic3—44no—
262D3×Dic3—44no—
263C2×C22⋊Q8—91no—
264#391—91no—
265#391—91no—
266#389—91no—
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—31no—
276C4×C22⋊C4—91no—
277C2×#95—91no—
278C24×C3—31no—
279C23×D3C22×D311yescharacteristic
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—34no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—121no—
292C22×C3×C4—121no—
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×Dic3—31no—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—34no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—62no—
313C22×Dic3—121no—
314C22×Dic3—121no—
315C22×Dic3—121no—
316C22×Dic3—121no—
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D311yescharacteristic
321C22×Dic3C22×D311yescharacteristic
322C22×Dic3C22×D311yescharacteristic
323C22×Dic3C22×D311yescharacteristic
324C2×C4×D3—34no—
325C2×C4×D3—41no—
326C2×C4×D3—41no—
327C2×C4×D3—62no—
328C2×C4×D3—121no—
329C2×C4×D3—121no—
330C2×C4×D3—121no—
331C2×C4×D3—121no—
332C2×C4×D3Dic614yescomplemented
333C2×Dic6—34no—
334C2×Dic6—34no—
335C2×Dic6—121no—
336C2×Dic6—121no—
337C2×Dic6—121no—
338C2×Dic6—121no—
339C3×C4⋊C4—34no—
340C3×C4⋊C4—121no—
341C3×C22⋊C4—34no—
342C3×C22⋊C4—62no—
343C3×C42—41no—
344C3×C42—41no—
345C3×C42—42no—
346C3×C42—121no—
347#217—34no—
348#217—62no—
349(C2×D3)⋊C4—22no—
350(C2×D3)⋊C4—34no—
351(C2×D3)⋊C4—62no—
352(C2×D3)⋊C4C4×D314yes—
353C4⋊Dic3—34no—
354C4⋊Dic3—34no—
355C4⋊Dic3—34no—
356C4⋊Dic3—64no—
357C4⋊Dic3—121no—
358C4⋊Dic3—121no—
359C4⋊Dic3—121no—
360C4⋊Dic3—122no—
361Dic3⋊C4—34no—
362Dic3⋊C4—41no—
363Dic3⋊C4—121no—
364Dic3⋊C4—121no—
365Dic3⋊C4—121no—
366Dic3⋊C4—121no—
367Dic3⋊C4—121no—
368Dic3⋊C4—121no—
369Dic3⋊C4—121no—
370Dic3⋊C4—122no—
371Dic3⋊C4—122no—
372Dic3⋊C4C4×D314yescomplemented
373C4×Dic3—41no—
374C4×Dic3—121no—
375C4×Dic3—121no—
376C4×Dic3—121no—
377C4×Dic3—121no—
378C22×C32C23×C411yescharacteristic
379C22×C32C22×Q811yescharacteristic
380C22×C32C2×#4111yescharacteristic
381C22×C32H(5,𝔽2)11yescharacteristic
382C22×C32H(5,𝔽2)11yescharacteristic
383C22×C32H(5,𝔽2)11yescharacteristic
384C22×C322−1+411yescharacteristic
385C2×C3×D3—22no—
386C2×C3×D3—22no—
387C2×C3×D3—22no—
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3C4×Q814yes—
392C32×C4—22no—
393C32×C4—22no—
394C32×C4—41no—
395C3⋊Dic3—22no—
396C3⋊Dic3—22no—
397C3⋊Dic3—41no—
398C3⋊Dic3—41no—
399C3×Dic3—22no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C22×Q8—91no—
407C23×C4—31no—
408C23×C4—91no—
409C23×C4—91no—
410C22⋊Q8—98no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—91no—
414C2×C4⋊C4—91no—
415C2×C4⋊C4—91no—
416C2×C4⋊C4—91no—
417C2×C4⋊C4—91no—
418C2×C4⋊C4—91no—
419C2×C4⋊C4—91no—
420C2×C22⋊C4—31no—
421C2×C22⋊C4—31no—
422C2×C22⋊C4—91no—
423C2×C22⋊C4—91no—
424C2×C42—31no—
425C2×C42—91no—
426C2×C42—91no—
427C2×C42D3211yescharacteristic
428#95—31no—
429#95—31no—
430#95—31no—
431#95—31no—
432#95—31no—
433#95—31no—
434#95—91no—
435#95—91no—
436#95—91no—
437#95—91no—
438#95—91no—
439#95—91no—
440#95—91no—
441#95—91no—
442C23×C3—21no—
443C23×C3—32no—
444C23×C3—32no—
445C23×C3—32no—
446C23×C3—61no—
447C23×C3—61no—
448C23×C3—61no—
449C23×C3—61no—
450C23×C3C23×D311yescharacteristic
451C23×C3C23×D311yescharacteristic
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3C2×Dic612yes—
457C22×D3C2×C4×D312yes—
458C22×D3#23512yes—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—21no—
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—22no—
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—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
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—124no—
504C2×C3×C4C2×Dic612yes—
505C2×C3×C4C2×C4×D312yes—
506C2×C3×C4C2×C4×D312yes—
507C2×C3×C4D3×Q812yes—
508C2×Dic3—21no—
509C2×Dic3—21no—
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—32no—
526C2×Dic3—32no—
527C2×Dic3—32no—
528C2×Dic3—32no—
529C2×Dic3—62no—
530C2×Dic3—62no—
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—61no—
550C2×Dic3—61no—
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×Dic3—124no—
563C2×Dic3C2×Dic612yes—
564C2×Dic3C2×C4×D312yes—
565C2×Dic3C2×C4×D312yes—
566C2×Dic3C2×C4×D312yes—
567C4×D3—44no—
568C4×D3—124no—
569C4×D3—124no—
570Dic6—124no—
571Dic6—124no—
572C2×C32C2×C4×Q811yescharacteristic
573C2×C32#51811yescharacteristic
574C2×C32#52011yescharacteristic
575C2×C32#53811yescharacteristic
576C2×C32#53911yescharacteristic
577C2×C32#54311yescharacteristic
578C2×C32#54411yescharacteristic
579C3×D3—24no—
580C24—31no—
581C2×Q8—94no—
582C2×Q8—361no—
583C2×Q8—361no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—34no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—94no—
593C22×C4—91no—
594C22×C4—91no—
595C22×C4—91no—
596C22×C4—91no—
597C22×C4—121no—
598C22×C4—121no—
599C22×C4—182no—
600C22×C4—361no—
601C22×C4—361no—
602C22×C4—361no—
603C22×C4—361no—
604C22×C4C2×D3211yescharacteristic
605C22×C4C2×D3211yescharacteristic
606C22×C4C2×D3211yescharacteristic
607C4⋊C4—34no—
608C4⋊C4—94no—
609C4⋊C4—94no—
610C4⋊C4—121no—
611C4⋊C4—361no—
612C4⋊C4—361no—
613C4⋊C4—361no—
614C4⋊C4—361no—
615C4⋊C4—361no—
616C22⋊C4—34no—
617C22⋊C4—62no—
618C22⋊C4—94no—
619C22⋊C4—182no—
620C42—41no—
621C42—121no—
622C42—361no—
623C42—361no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—34no—
632C22×C3—62no—
633C22×C3—62no—
634C22×C3—62no—
635C22×C3—62no—
636C22×C3—62no—
637C22×C3—62no—
638C22×C3C22×Dic611yescharacteristic
639C22×C3C22×C4×D311yescharacteristic
640C22×C3C22×C4×D311yescharacteristic
641C22×C3C2×#23511yescharacteristic
642C22×C3#100411yescharacteristic
643C22×C3#100411yescharacteristic
644C22×C3#100411yescharacteristic
645C22×C3C2×D3×Q811yescharacteristic
646C22×C3D3×#4111yescharacteristic
647C22×C3#100911yescharacteristic
648C22×C3#100911yescharacteristic
649C22×C3#100911yescharacteristic
650C22×C3#101011yescharacteristic
651C22×C3#101011yescharacteristic
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—22no—
655C2×D3—22no—
656C2×D3—22no—
657C2×D3—22no—
658C2×D3C4×Dic614yes—
659C3×C4—24no—
660C3×C4—22no—
661C3×C4—22no—
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—42no—
665C3×C4—42no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—62no—
669C3×C4—62no—
670C3×C4—62no—
671C3×C4—62no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4—121no—
675Dic3—22no—
676Dic3—22no—
677Dic3—22no—
678Dic3—22no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3—62no—
683Dic3—62no—
684Dic3—62no—
685Dic3—62no—
686Dic3—122no—
687Dic3—122no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—241no—
693Dic3—241no—
694C32#232911yescharacteristic, complemented, Sylow
695C23—32no—
696C23—32no—
697C23—32no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23C22×D3211yescharacteristic
703Q8—364no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—32no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
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—92no—
733C2×C4—92no—
734C2×C4—124no—
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—364no—
746C2×C4—364no—
747C2×C4D3×Dic612yes—
748C2×C4C4×D3212yes—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—64no—
757C2×C3C2×C4×Dic611yescharacteristic
758C2×C3#548311yescharacteristic
759C2×C3#551911yescharacteristic
760C2×C3#552111yescharacteristic
761C2×C3#554511yescharacteristic
762C2×C3#554611yescharacteristic
763C2×C3#554611yescharacteristic
764C2×C3#556011yescharacteristic
765C2×C3#556411yescharacteristic
766C2×C3C4×D3×Q811yescharacteristic
767C2×C3#563411yescharacteristic
768C2×C3#565711yescharacteristic
769C2×C3#568911yescharacteristic
770C2×C3#570711yescharacteristic
771D3—24no—
772C22—34no—
773C22—62no—
774C22—62no—
775C22—62no—
776C22—62no—
777C22—62no—
778C22—62no—
779C22C2×D3×Dic611yescharacteristic
780C22#6429811yescharacteristic
781C22C2×C4×D3211yescharacteristic
782C22D3×#23511yescharacteristic
783C22#6430711yescharacteristic
784C22#6430811yescharacteristic
785C22#6433011yescharacteristic
786C4—22no—
787C4—22no—
788C4—41no—
789C4—62no—
790C4—62no—
791C4—62no—
792C4—62no—
793C4—121no—
794C4—121no—
795C4—121no—
796C4—182no—
797C4—182no—
798C4—361no—
799C4—361no—
800C3—21no—
801C3#7344711yescharacteristic, complemented
802C3#7530011yescharacteristic, complemented
803C2—64no—
804C2C4×D3×Dic611yescharacteristic
805C2#1059391411yescharacteristic
806C2#1059395911yescharacteristic
807C2#1059399411yescharacteristic
808C2#1059487611yescharacteristic
809C2#1059497111yescharacteristic
810C2#1059508511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2329
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592627C2semidirect
4. C3×#4933C2semidirect
9. #10591331C2semidirect
10. #10591272C2semidirect
11. #10591271C2semidirect
13. #10591236C2semidirect
14. #10591234C2semidirect
15. #10591191C2semidirect
39. #63893C4semidirect
68. #4933D3semidirect
102. C2×C3×C4×D3Q8semidirect
105. C2×#627C2×C4semidirect
114. C4⋊(C3⋊Dic3)C2×C4semidirect
120. C3×Dic3⋊C4C2×C4semidirect
124. Dic3⋊Dic3C2×C4semidirect
332. C2×C4×D3Dic6semidirect
372. Dic3⋊C4C4×D3semidirect
694. C32#2329semidirect
801. C3#73447semidirect
802. C3#75300semidirect

Maximal subgroups

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

subgroupindex
C2×#638932
#105926272
C3×C4×(C2×D3)⋊C42
C3×#49332
#105913792
#105913722
#105913692
D3×C3⋊#952
#105913312
#105912722
#105912712
#105912372
#105912362
#105912342
#105911912
#753003
#734473