Finite Group Databasebeta

← #11808727

Subgroups — #11808727

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63837C211yesmaximal, characteristic, complemented
2C2×#63836C211yesmaximal, characteristic
3#10592692C211yesmaximal, characteristic
4C3×#4983C211yesmaximal, characteristic, complemented
5C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
6#10591347C211yesmaximal, characteristic
7#10591340C211yesmaximal, characteristic, complemented
8#10591338C211yesmaximal, characteristic, complemented
9#10591311C211yesmaximal, characteristic
10#10591243C211yesmaximal, characteristic, complemented
11Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
12#10591233C211yesmaximal, characteristic
13#10591233C211yesmaximal, characteristic
14#10591210C211yesmaximal, characteristic, complemented
15#10591205C211yesmaximal, characteristic
16#77739—31nomaximal
17#73778—31nomaximal
18C22×#627C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43#63837—24no—
44#63836—24no—
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#892—31no—
56C2×#887—31no—
57C2×#872—31no—
58C2×C4×Dic6—31no—
59C3×#398—31no—
60C3×C4×C4⋊C4—31no—
61#4994—31no—
62#4994—31no—
63#4994—31no—
64#4993—31no—
65#4993—31no—
66#4993—61no—
67#4983D311yescharacteristic, complemented
68#4982—31no—
69#4979—31no—
70Dic3×C4⋊C4—31no—
71Dic3×C4⋊C4D311yescharacteristic, complemented
72C4×(C2×D3)⋊C4—31no—
73C4×(C2×D3)⋊C4—31no—
74C4×Dic3⋊C4—31no—
75C4×Dic3⋊C4—31no—
76#4676—31no—
77#4673—31no—
78#4673—31no—
79#4666—31no—
80#4666—31no—
81#4660—31no—
82#4658—31no—
83#4657—31no—
84#4656—31no—
85#4649—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×#627—22no—
102C2×#627—22no—
103C2×#627—22no—
104C2×#624—22no—
105C2×#624—22no—
106C2×#624Q814yescomplemented
107C32×C4⋊C4—22no—
108#3752—22no—
109#3752—22no—
110#3752—22no—
111#3750—22no—
112#3750—22no—
113C3×C4⋊Dic3—22no—
114C3×Dic3⋊C4—22no—
115C3×Dic3⋊C4—22no—
116C3×Dic3⋊C4—22no—
117C3×C4×Dic3—22no—
118C3×C4×Dic3—22no—
119C3×C4×Dic3—22no—
120#3724—22no—
121Dic3⋊Dic3—22no—
122Dic3⋊Dic3—22no—
123Dic3⋊Dic3—22no—
124#3722—22no—
125#3722—22no—
126#3722—22no—
127Dic32—22no—
128Dic32—22no—
129Dic32D414yes—
130#2396—91noSylow
131C22×C4×D3—31no—
132C22×C4×D3—31no—
133C22×Dic6—31no—
134C22×Dic6—31no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4C2×D311yescharacteristic
141C2×C3×C4⋊C4C2×D311yescharacteristic
142C2×C3×C42—31no—
143C2×C3×C42—31no—
144C2×C3×C42—31no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—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×(C2×D3)⋊C4—61no—
158C2×(C2×D3)⋊C4—61no—
159C2×(C2×D3)⋊C4—61no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3C2×D311yescharacteristic
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4—31no—
173C2×Dic3⋊C4—61no—
174C2×Dic3⋊C4—61no—
175C2×Dic3⋊C4C2×D311yescharacteristic
176C2×Dic3⋊C4C2×D311yescharacteristic
177C2×Dic3⋊C4C2×D311yescharacteristic
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3—31no—
183C2×C4×Dic3—31no—
184C2×C4×Dic3C2×D311yescharacteristic
185C2×C4×Dic3C2×D311yescharacteristic
186C2×C4×Dic3C2×D311yescharacteristic
187#892—64no—
188#887—64no—
189#872—64no—
190C4×Dic6—64no—
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—31no—
206C3⋊#95—61no—
207C3⋊#95C2×D311yescharacteristic
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—
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×C4—21no—
228C2×C32×C4#4112yes—
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⋊Dic3C2×D412yes—
237C2×C3⋊Dic3#4112yes—
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×Dic3C2×D412yes—
256C2×C3×Dic3C2×D412yes—
257C2×C3×Dic3C2×Q812yes—
258C2×C3×Dic3C2×Q812yes—
259C2×C3×Dic3#4112yes—
260C2×C3×Dic3#4112yes—
261C2×C3×Dic3#4112yes—
262#627—28no—
263#624—28no—
264C2×C4×Q8—91no—
265C2×#117—91no—
266#400—91no—
267#399—91no—
268#398—31no—
269#398—91no—
270#396—91no—
271#396—91no—
272#395—91no—
273#393—91no—
274C4×C4⋊C4—31no—
275C4×C4⋊C4—91no—
276C4×C4⋊C4—91no—
277C4×C22⋊C4—91no—
278C4×C22⋊C4—91no—
279C23×D3—31no—
280C23×D3—31no—
281C23×D3—61no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
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×C4—31no—
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—31no—
304C22×Dic3—31no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C2×C4×D3—34no—
317C2×C4×D3—34no—
318C2×C4×D3—62no—
319C2×C4×D3—62no—
320C2×C4×D3—62no—
321C2×C4×D3—62no—
322C2×Dic6—62no—
323C2×Dic6—62no—
324C2×Dic6—62no—
325C2×Dic6—62no—
326C2×Dic6—62no—
327C2×Dic6—62no—
328C3×C4⋊C4—22no—
329C3×C4⋊C4—22no—
330C3×C4⋊C4—42no—
331C3×C4⋊C4—62no—
332C3×C4⋊C4—62no—
333C3×C4⋊C4—62no—
334C3×C4⋊C4—62no—
335C3×C42—62no—
336C3×C42—62no—
337C3×C42—62no—
338(C2×D3)⋊C4—62no—
339(C2×D3)⋊C4—62no—
340(C2×D3)⋊C4—62no—
341(C2×D3)⋊C4—62no—
342(C2×D3)⋊C4—62no—
343(C2×D3)⋊C4—62no—
344(C2×D3)⋊C4—62no—
345(C2×D3)⋊C4—62no—
346(C2×D3)⋊C4—62no—
347(C2×D3)⋊C4—62no—
348(C2×D3)⋊C4—62no—
349(C2×D3)⋊C4—62no—
350(C2×D3)⋊C4—122no—
351(C2×D3)⋊C4—122no—
352(C2×D3)⋊C4—122no—
353C4⋊Dic3—22no—
354C4⋊Dic3—62no—
355C4⋊Dic3—62no—
356C4⋊Dic3—62no—
357Dic3⋊C4—22no—
358Dic3⋊C4—22no—
359Dic3⋊C4—22no—
360Dic3⋊C4—62no—
361Dic3⋊C4—62no—
362Dic3⋊C4—62no—
363Dic3⋊C4—62no—
364Dic3⋊C4—62no—
365Dic3⋊C4—62no—
366Dic3⋊C4—62no—
367Dic3⋊C4—62no—
368Dic3⋊C4—62no—
369Dic3⋊C4—122no—
370Dic3⋊C4—122no—
371C4×Dic3—22no—
372C4×Dic3—22no—
373C4×Dic3—22no—
374C4×Dic3—34no—
375C4×Dic3—34no—
376C4×Dic3—62no—
377C4×Dic3—62no—
378C4×Dic3—62no—
379C4×Dic3—62no—
380C22×C32C22×D411yescharacteristic
381C22×C32C22×Q811yescharacteristic
382C22×C32C2×#4111yescharacteristic
383C22×C32C2×#4111yescharacteristic
384C22×C32C2×#4111yescharacteristic
385C22×C32C2×#4111yescharacteristic
386C22×C32C2×#4111yescharacteristic
387C2×C3⋊D3—22no—
388C2×C3⋊D3—22no—
389C2×C3⋊D3—22no—
390C2×C3⋊D3—41no—
391C2×C3⋊D3—41no—
392C2×C3⋊D3—41no—
393C2×C3⋊D3—41no—
394C32×C4—22no—
395C32×C4—41no—
396C32×C4—41no—
397C3⋊Dic3—22no—
398C3⋊Dic3—22no—
399C3⋊Dic3—41no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C3×Dic3—41no—
407C3×Dic3C22⋊Q814yes—
408C22×Q8—91no—
409C23×C4—91no—
410C4×Q8—184no—
411#117—184no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—31no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—91no—
417C2×C4⋊C4—91no—
418C2×C4⋊C4—91no—
419C2×C4⋊C4—91no—
420C2×C4⋊C4—91no—
421C2×C4⋊C4—91no—
422C2×C4⋊C4D3211yescharacteristic
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—31no—
432C2×C42—91no—
433C2×C42—91no—
434C2×C42—91no—
435#95—31no—
436#95—31no—
437#95—31no—
438#95—31no—
439#95—31no—
440#95—91no—
441#95—91no—
442#95—91no—
443#95—91no—
444#95—91no—
445C23×C3—21no—
446C23×C3C23×D311yescharacteristic
447C23×C3C23×D311yescharacteristic
448C22×D3—32no—
449C22×D3—32no—
450C22×D3—62no—
451C22×D3—61no—
452C22×D3—61no—
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—121no—
464C22×D3—121no—
465C22×D3—121no—
466C22×D3—121no—
467C22×D3—121no—
468C22×D3—121no—
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—21no—
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—21no—
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—32no—
492C2×C3×C4—32no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
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×C4—61no—
518C2×C3×C4#23512yes—
519C2×C3×C4#23712yes—
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—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—32no—
538C2×Dic3—32no—
539C2×Dic3—32no—
540C2×Dic3—32no—
541C2×Dic3—62no—
542C2×Dic3—62no—
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#23512yes—
565C2×Dic3#23512yes—
566C2×Dic3D3×D412yes—
567C2×Dic3D3×D412yes—
568C2×Dic3D3×Q812yes—
569C2×Dic3D3×Q812yes—
570C2×Dic3#23912yes—
571C4×D3—68no—
572C4×D3—68no—
573Dic6—68no—
574Dic6—68no—
575C2×C32C2×C22⋊Q811yescharacteristic
576C2×C32#52511yescharacteristic
577C2×C32#52911yescharacteristic
578C2×C32#52911yescharacteristic
579C2×C32#53211yescharacteristic
580C2×C32#53311yescharacteristic
581C2×C32#53311yescharacteristic
582C3⋊D3—42no—
583C24—91no—
584C2×Q8—182no—
585C2×Q8—182no—
586C2×Q8—182no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—94no—
596C22×C4—91no—
597C22×C4—91no—
598C22×C4—91no—
599C22×C4—182no—
600C22×C4—182no—
601C22×C4C2×D3211yescharacteristic
602C22×C4C2×D3211yescharacteristic
603C22×C4C2×D3211yescharacteristic
604C4⋊C4—22no—
605C4⋊C4—62no—
606C4⋊C4—62no—
607C4⋊C4—62no—
608C4⋊C4—62no—
609C4⋊C4—182no—
610C4⋊C4—182no—
611C4⋊C4—182no—
612C4⋊C4—182no—
613C4⋊C4—182no—
614C4⋊C4—182no—
615C22⋊C4—182no—
616C22⋊C4—182no—
617C22⋊C4—182no—
618C22⋊C4—182no—
619C22⋊C4—182no—
620C22⋊C4—182no—
621C42—62no—
622C42—62no—
623C42—62no—
624C42—94no—
625C42—182no—
626C42—182no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3C2×#23511yescharacteristic
635C22×C3C2×#23511yescharacteristic
636C22×C3C2×#23511yescharacteristic
637C22×C3C2×D3×D411yescharacteristic
638C22×C3C2×D3×D411yescharacteristic
639C22×C3C2×#23711yescharacteristic
640C22×C3C2×D3×Q811yescharacteristic
641C22×C3C2×D3×Q811yescharacteristic
642C22×C3C2×#23911yescharacteristic
643C22×C3D3×#4111yescharacteristic
644C22×C3D3×#4111yescharacteristic
645C22×C3D3×#4111yescharacteristic
646C22×C3D3×#4111yescharacteristic
647C22×C3D3×#4111yescharacteristic
648C2×D3—62no—
649C2×D3—62no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—62no—
654C2×D3—122no—
655C2×D3—122no—
656C2×D3—122no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—241no—
666C2×D3—241no—
667C2×D3—241no—
668C2×D3—241no—
669C3×C4—22no—
670C3×C4—22no—
671C3×C4—34no—
672C3×C4—42no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—62no—
678C3×C4—62no—
679C3×C4—62no—
680C3×C4—62no—
681C3×C4—81no—
682C3×C4—81no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686Dic3—22no—
687Dic3—22no—
688Dic3—22no—
689Dic3—22no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—62no—
694Dic3—62no—
695Dic3—62no—
696Dic3—62no—
697Dic3—122no—
698Dic3—122no—
699Dic3—121no—
700Dic3—121no—
701Dic3—241no—
702Dic3#89614yes—
703C32#239611yescharacteristic, complemented, Sylow
704C23—92no—
705C23—181no—
706C23—181no—
707C23—181no—
708C23—181no—
709C23—181no—
710C23—181no—
711C23C22×D3211yescharacteristic
712Q8—188no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—32no—
722C2×C4—32no—
723C2×C4—32no—
724C2×C4—32no—
725C2×C4—32no—
726C2×C4—32no—
727C2×C4—32no—
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—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—92no—
746C2×C4—92no—
747C2×C4—188no—
748C2×C4—181no—
749C2×C4—181no—
750C2×C4—181no—
751C2×C4—181no—
752C2×C4—181no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4#380412yes—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3#547911yescharacteristic
764C2×C3C2×#89611yescharacteristic
765C2×C3#552811yescharacteristic
766C2×C3#554711yescharacteristic
767C2×C3#554811yescharacteristic
768C2×C3#557811yescharacteristic
769C2×C3#557811yescharacteristic
770C2×C3#559611yescharacteristic
771C2×C3D3×C22⋊Q811yescharacteristic
772C2×C3#562711yescharacteristic
773C2×C3#564911yescharacteristic
774C2×C3#568811yescharacteristic
775C2×C3#569111yescharacteristic
776C2×C3#572811yescharacteristic
777D3—122no—
778D3—122no—
779D3—242no—
780C22—182no—
781C22—182no—
782C22—182no—
783C22—361no—
784C22—361no—
785C22—361no—
786C22—361no—
787C22D3×#23511yescharacteristic
788C22D3×#23511yescharacteristic
789C22D32×D411yescharacteristic
790C22#6431211yescharacteristic
791C22D32×Q811yescharacteristic
792C22D3×#23911yescharacteristic
793C22C2×#380411yescharacteristic
794C4—22no—
795C4—34no—
796C4—41no—
797C4—41no—
798C4—62no—
799C4—62no—
800C4—62no—
801C4—62no—
802C4—121no—
803C4—121no—
804C4—121no—
805C4—182no—
806C4—182no—
807C4—361no—
808C3—21no—
809C3#7377811yescharacteristic, complemented
810C3#7773911yescharacteristic, complemented
811C2—362no—
812C2#1059439811yescharacteristic
813C2#1059442211yescharacteristic
814C2D3×#89611yescharacteristic
815C2#1059462311yescharacteristic
816C2#1059494811yescharacteristic
817C2#1059513111yescharacteristic
818C2#1059537411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2396
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×#63837C2semidirect
4. C3×#4983C2semidirect
5. C3×Dic3×C4⋊C4C2semidirect
7. #10591340C2semidirect
8. #10591338C2semidirect
10. #10591243C2semidirect
11. Dic3×Dic3⋊C4C2semidirect
14. #10591210C2semidirect
67. #4983D3semidirect
71. Dic3×C4⋊C4D3semidirect
106. C2×#624Q8semidirect
703. C32#2396semidirect
809. C3#73778semidirect
810. C3#77739semidirect

Maximal subgroups

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

subgroupindex
C2×#638372
C2×#638362
#105926922
C3×#49832
C3×Dic3×C4⋊C42
#105913472
#105913402
#105913382
#105913112
#105912432
Dic3×Dic3⋊C42
#105912332
#105912102
#105912052
#777393
#737783