Finite Group Databasebeta

← #11808857

Subgroups — #11808857

Order 1152.

1105 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2C2×C4×#627C211yesmaximal, characteristic
3C4×#3750C211yesmaximal, characteristic
4C3×C4×Dic3⋊C4C211yesmaximal, characteristic
5#10591346C211yesmaximal, characteristic
6#10591344C211yesmaximal, characteristic
7#10591342C211yesmaximal, characteristic
8#10591339C211yesmaximal, characteristic
9#10591338C211yesmaximal, characteristic
10C4×#3724C211yesmaximal, characteristic
11C4×Dic3⋊Dic3C211yesmaximal, characteristic
12#10591222C211yesmaximal, characteristic
13#10591200C211yesmaximal, characteristic
14#10591198C211yesmaximal, characteristic
15#10591195C211yesmaximal, characteristic
16#82467—31nomaximal
17#73669—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C22×#627C2211yescharacteristic
20C2×C32×C42C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
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×C3×C4×Dic3C2211yescharacteristic
34C3×C4×Dic6—24no—
35C2×#3724C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C4×#627—24no—
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×C3×C4×Q8—31no—
56C2×C4×Dic6—31no—
57C2×C4×Dic6—31no—
58C2×C4×Dic6D311yescharacteristic
59C3×C4×C4⋊C4—31no—
60#5230—31no—
61#5230—31no—
62#4983—31no—
63#4983—31no—
64#4982—31no—
65#4982—31no—
66#4981—31no—
67#4981—31no—
68#4979—31no—
69#4979—31no—
70#4979—31no—
71#4979—31no—
72C4×C4⋊Dic3—31no—
73#4932—31no—
74#4932—31no—
75C4×Dic3⋊C4—31no—
76C4×Dic3⋊C4—31no—
77C4×Dic3⋊C4—31no—
78C4×Dic3⋊C4—31no—
79C4×Dic3⋊C4—31no—
80C4×Dic3⋊C4—61no—
81C4×Dic3⋊C4D311yescharacteristic
82#4657—31no—
83#4657—31no—
84#4656—31no—
85#4656—31no—
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
100C22×C3×Dic3C2311yescharacteristic
101C2×C3×Dic6—22no—
102C2×C3×Dic6—22no—
103C2×C3×Dic6—22no—
104C2×#627—22no—
105C2×#627—22no—
106C2×#627—22no—
107C32×C42—22no—
108#3750—22no—
109#3750—22no—
110C4×C3⋊Dic3—22no—
111C4×C3⋊Dic3Q814yescomplemented
112C3×C4⋊Dic3—22no—
113C3×Dic3⋊C4—22no—
114C3×Dic3⋊C4—22no—
115C3×Dic3⋊C4—22no—
116C3×Dic3⋊C4—22no—
117C3×C4×Dic3—22no—
118C3×C4×Dic3—22no—
119C3×C4×Dic3D414yes—
120C3×C4×Dic3Q814yescomplemented
121#3724—22no—
122#3724—22no—
123#3724—22no—
124Dic3⋊Dic3—22no—
125Dic3⋊Dic3—22no—
126Dic3⋊Dic3—22no—
127Dic3⋊Dic3—22no—
128#2399—91noSylow
129C22×C3×Q8—31no—
130C22×Dic6—31no—
131C22×Dic6—31no—
132C22×Dic6C2×D311yescharacteristic
133C3×C4×Q8—64no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C42—21no—
140C2×C3×C42—31no—
141C2×C3×C42—31no—
142C2×C3×C42—31no—
143C2×C3×C42—31no—
144C2×C3×C42C2×D311yescharacteristic
145C2×C3×C42C2×D311yescharacteristic
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—31no—
149C2×C4⋊Dic3—31no—
150C2×C4⋊Dic3C2×D311yescharacteristic
151C2×Dic3⋊C4—31no—
152C2×Dic3⋊C4—31no—
153C2×Dic3⋊C4—31no—
154C2×Dic3⋊C4—31no—
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—61no—
166C2×Dic3⋊C4—61no—
167C2×Dic3⋊C4C2×D311yescharacteristic
168C2×Dic3⋊C4C2×D311yescharacteristic
169C2×Dic3⋊C4C2×D311yescharacteristic
170C2×Dic3⋊C4C2×D311yescharacteristic
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—61no—
176C2×C4×Dic3—61no—
177C2×C4×Dic3C2×D311yescharacteristic
178C2×C4×Dic3C2×D311yescharacteristic
179C2×C4×Dic3C2×D311yescharacteristic
180C2×C4×Dic3C2×D311yescharacteristic
181C4×Dic6—24no—
182C4×Dic6—64no—
183C4×Dic6—64no—
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—31no—
206C3⋊#95—61no—
207C3⋊#95—61no—
208C3⋊#95C2×D311yescharacteristic
209C3⋊#95C2×D311yescharacteristic
210C23×C32C2411yescharacteristic
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4C2×D412yes—
217C2×C32×C4C2×Q812yes—
218C2×C32×C4C2×Q812yes—
219C2×C32×C4#4112yes—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3C2×Q812yes—
230C2×C3⋊Dic3C2×Q812yes—
231C2×C3⋊Dic3#4112yes—
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×Dic3C2×D412yes—
251C2×C3×Dic3C2×D412yes—
252C2×C3×Dic3C2×Q812yes—
253C2×C3×Dic3C2×Q812yes—
254C2×C3×Dic3#4112yes—
255C2×C3×Dic3#4112yes—
256C3×Dic6—28no—
257#627—28no—
258C2×C4×Q8—31no—
259C2×C4×Q8—91no—
260#398—91no—
261#398—91no—
262#398—91no—
263#398—91no—
264#395—91no—
265#395—91no—
266#395—91no—
267#395—91no—
268C4×C4⋊C4—31no—
269C4×C4⋊C4—91no—
270C4×C4⋊C4—91no—
271C4×C4⋊C4—91no—
272#376—91no—
273C2×C3×Q8—62no—
274C2×C3×Q8—62no—
275C2×C3×Q8—62no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D311yescharacteristic
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—31no—
299C22×Dic3—31no—
300C22×Dic3—31no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305C22×Dic3C22×D311yescharacteristic
306C22×Dic3C22×D311yescharacteristic
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312C22×Dic3C22×D311yescharacteristic
313C2×Dic6—22no—
314C2×Dic6—22no—
315C2×Dic6—22no—
316C2×Dic6—62no—
317C2×Dic6—62no—
318C2×Dic6—62no—
319C2×Dic6—62no—
320C2×Dic6—62no—
321C2×Dic6—62no—
322C3×C4⋊C4—62no—
323C3×C4⋊C4—62no—
324C3×C4⋊C4—62no—
325C3×C4⋊C4—62no—
326C3×C4⋊C4—62no—
327C3×C42—22no—
328C3×C42—22no—
329C3×C42—34no—
330C3×C42—34no—
331C3×C42—42no—
332C3×C42—62no—
333C3×C42—62no—
334C4⋊Dic3—22no—
335C4⋊Dic3—62no—
336C4⋊Dic3—62no—
337C4⋊Dic3—62no—
338C4⋊Dic3—62no—
339Dic3⋊C4—22no—
340Dic3⋊C4—22no—
341Dic3⋊C4—22no—
342Dic3⋊C4—22no—
343Dic3⋊C4—62no—
344Dic3⋊C4—62no—
345Dic3⋊C4—62no—
346Dic3⋊C4—62no—
347Dic3⋊C4—62no—
348Dic3⋊C4—62no—
349Dic3⋊C4—62no—
350Dic3⋊C4—62no—
351Dic3⋊C4—64no—
352Dic3⋊C4—64no—
353Dic3⋊C4—62no—
354Dic3⋊C4—62no—
355Dic3⋊C4—62no—
356Dic3⋊C4—62no—
357Dic3⋊C4—62no—
358Dic3⋊C4—62no—
359C4×Dic3—22no—
360C4×Dic3—22no—
361C4×Dic3—34no—
362C4×Dic3—34no—
363C4×Dic3—64no—
364C4×Dic3—62no—
365C4×Dic3—62no—
366C4×Dic3—122no—
367C4×Dic3Dic614yescomplemented
368C4×Dic3#6714yes—
369C22×C32C22×D411yescharacteristic
370C22×C32C22×Q811yescharacteristic
371C22×C32C22×Q811yescharacteristic
372C22×C32C2×#4111yescharacteristic
373C22×C32C2×#4111yescharacteristic
374C22×C32C2×#4111yescharacteristic
375C22×C32C2×#4111yescharacteristic
376C32×C4—22no—
377C32×C4—41no—
378C32×C4C4⋊Q814yes—
379C3⋊Dic3—22no—
380C3⋊Dic3—22no—
381C3⋊Dic3—22no—
382C3⋊Dic3—41no—
383C3×Dic3—22no—
384C3×Dic3—22no—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—22no—
389C3×Dic3—41no—
390C3×Dic3—41no—
391C22×Q8—31no—
392C22×Q8—91no—
393C4×Q8—64no—
394C4×Q8—184no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—91no—
401C2×C4⋊C4—91no—
402C2×C4⋊C4—91no—
403C2×C4⋊C4—91no—
404C2×C4⋊C4—91no—
405C2×C4⋊C4—91no—
406C2×C4⋊C4—91no—
407C2×C4⋊C4—91no—
408C2×C4⋊C4—91no—
409C2×C42—31no—
410C2×C42—31no—
411C2×C42—31no—
412C2×C42—31no—
413C2×C42—91no—
414C2×C42—91no—
415C2×C42D3211yescharacteristic
416#95—31no—
417#95—31no—
418#95—91no—
419#95—91no—
420#95—91no—
421#95—91no—
422#95—91no—
423#95—91no—
424#95—91no—
425#95—91no—
426#95—91no—
427#95—91no—
428C23×C3—21no—
429C23×C3C23×D311yescharacteristic
430C23×C3C23×D311yescharacteristic
431C3×Q8—68no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—22no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—32no—
448C2×C3×C4—32no—
449C2×C3×C4—32no—
450C2×C3×C4—32no—
451C2×C3×C4—32no—
452C2×C3×C4—32no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—61no—
458C2×C3×C4—61no—
459C2×C3×C4—61no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4C2×Dic612yes—
476C2×C3×C4#23512yes—
477C2×C3×C4#23512yes—
478C2×C3×C4D3×D412yes—
479C2×C3×C4D3×Q812yes—
480C2×C3×C4D3×Q812yes—
481C2×C3×C4D3×Q812yes—
482C2×C3×C4C2×#6712yes—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—32no—
502C2×Dic3—32no—
503C2×Dic3—32no—
504C2×Dic3—32no—
505C2×Dic3—32no—
506C2×Dic3—32no—
507C2×Dic3—62no—
508C2×Dic3—62no—
509C2×Dic3—62no—
510C2×Dic3—62no—
511C2×Dic3—62no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—62no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—121no—
537C2×Dic3C2×Dic612yes—
538C2×Dic3C2×Dic612yes—
539C2×Dic3#23512yes—
540C2×Dic3#23512yes—
541C2×Dic3C2×#6712yes—
542C2×Dic3C2×#6712yes—
543Dic6—28no—
544Dic6—68no—
545Dic6—68no—
546C2×C32#52511yescharacteristic
547C2×C32#52511yescharacteristic
548C2×C32C2×C4⋊Q811yescharacteristic
549C2×C32#53311yescharacteristic
550C2×C32#53311yescharacteristic
551C2×C32#53311yescharacteristic
552C2×C32#53311yescharacteristic
553C2×Q8—62no—
554C2×Q8—62no—
555C2×Q8—62no—
556C2×Q8—182no—
557C2×Q8—182no—
558C2×Q8—182no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—91no—
568C22×C4—91no—
569C22×C4—91no—
570C22×C4—91no—
571C22×C4C2×D3211yescharacteristic
572C22×C4C2×D3211yescharacteristic
573C22×C4C2×D3211yescharacteristic
574C4⋊C4—62no—
575C4⋊C4—62no—
576C4⋊C4—62no—
577C4⋊C4—62no—
578C4⋊C4—62no—
579C4⋊C4—182no—
580C4⋊C4—182no—
581C4⋊C4—182no—
582C4⋊C4—182no—
583C4⋊C4—182no—
584C4⋊C4—182no—
585C4⋊C4—182no—
586C4⋊C4—182no—
587C4⋊C4—182no—
588C42—22no—
589C42—34no—
590C42—34no—
591C42—62no—
592C42—62no—
593C42—94no—
594C42—182no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3C22×Dic611yescharacteristic
603C22×C3C2×#23511yescharacteristic
604C22×C3C2×#23511yescharacteristic
605C22×C3C2×#23511yescharacteristic
606C22×C3C2×#23511yescharacteristic
607C22×C3C2×D3×D411yescharacteristic
608C22×C3C2×D3×Q811yescharacteristic
609C22×C3C2×D3×Q811yescharacteristic
610C22×C3C2×D3×Q811yescharacteristic
611C22×C3D3×#4111yescharacteristic
612C22×C3D3×#4111yescharacteristic
613C22×C3D3×#4111yescharacteristic
614C22×C3D3×#4111yescharacteristic
615C22×C3C22×#6711yescharacteristic
616C3×C4—22no—
617C3×C4—22no—
618C3×C4—24no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—62no—
624C3×C4—62no—
625C3×C4—62no—
626C3×C4—62no—
627C3×C4—62no—
628C3×C4—62no—
629C3×C4—121no—
630C3×C4—121no—
631C3×C4#88814yes—
632C3×C4#94414yes—
633Dic3—22no—
634Dic3—22no—
635Dic3—22no—
636Dic3—22no—
637Dic3—22no—
638Dic3—22no—
639Dic3—41no—
640Dic3—41no—
641Dic3—64no—
642Dic3—62no—
643Dic3—62no—
644Dic3—62no—
645Dic3—62no—
646Dic3—62no—
647Dic3—62no—
648Dic3—122no—
649Dic3—122no—
650Dic3—122no—
651Dic3—121no—
652Dic3—121no—
653C32#239911yescharacteristic, complemented, Sylow
654C23C22×D3211yescharacteristic
655Q8—68no—
656Q8—188no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—32no—
663C2×C4—32no—
664C2×C4—32no—
665C2×C4—32no—
666C2×C4—32no—
667C2×C4—32no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—92no—
687C2×C4—92no—
688C2×C4—92no—
689C2×C4—181no—
690C2×C4—181no—
691C2×C4—181no—
692C2×C4—181no—
693C2×C4—181no—
694C2×C4—181no—
695C2×C4—181no—
696C2×C4—181no—
697C2×C4—181no—
698C2×C4D3×Dic612yes—
699C2×C4#379712yes—
700C2×C4#379812yes—
701C2×C4D3×#6712yes—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3#547011yescharacteristic
710C2×C3C2×#88811yescharacteristic
711C2×C3#551711yescharacteristic
712C2×C3#554711yescharacteristic
713C2×C3#554711yescharacteristic
714C2×C3#557811yescharacteristic
715C2×C3#557811yescharacteristic
716C2×C3#557811yescharacteristic
717C2×C3#557811yescharacteristic
718C2×C3#557811yescharacteristic
719C2×C3#557811yescharacteristic
720C2×C3#579111yescharacteristic
721C2×C3C2×#94411yescharacteristic
722C2×C3#582811yescharacteristic
723C22C2×D3×Dic611yescharacteristic
724C22C2×#379711yescharacteristic
725C22C2×#379811yescharacteristic
726C22D3×#23511yescharacteristic
727C22D3×#23511yescharacteristic
728C22#6430611yescharacteristic
729C22C2×D3×#6711yescharacteristic
730C4—22no—
731C4—41no—
732C4—62no—
733C4—62no—
734C4—62no—
735C4—62no—
736C4—62no—
737C4—62no—
738C4—121no—
739C4—121no—
740C4—182no—
741C4—182no—
742C4—182no—
743C4—361no—
744C4#6383914yes—
745C3—21no—
746C3#7366911yescharacteristic, complemented
747C3#8246711yescharacteristic, complemented
748C2#1059387311yescharacteristic
749C2#1059388211yescharacteristic
750C2#1059392611yescharacteristic
751C2#1059393511yescharacteristic
752C2C2×#6383911yescharacteristic
753C2#1059500211yescharacteristic
754C2#1059506011yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, prime radical, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#2399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
111. C4×C3⋊Dic3Q8semidirect
120. C3×C4×Dic3Q8semidirect
367. C4×Dic3Dic6semidirect
653. C32#2399semidirect
746. C3#73669semidirect
747. C3#82467semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
C2×C4×#6272
C4×#37502
C3×C4×Dic3⋊C42
#105913462
#105913442
#105913422
#105913392
#105913382
C4×#37242
C4×Dic3⋊Dic32
#105912222
#105912002
#105911982
#105911952
#824673
#736693