Finite Group Databasebeta

← #11804855

Subgroups — #11804855

Order 1152.

1985 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3C2×#63898C211yesmaximal, characteristic, complemented
4C4×#3752C211yesmaximal, characteristic, complemented
5C3×#4929C211yesmaximal, characteristic, complemented
6#10591382C212yesmaximal, complemented
7#10591364C212yesmaximal, complemented
8#10591362C212yesmaximal, complemented
9D3×C3⋊#95C212yesmaximal, complemented
10#10591325C211yesmaximal, characteristic, complemented
11#10591221C211yesmaximal, characteristic, complemented
12#82330—31nomaximal
13#76613—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×C3×Dic6C2211yescharacteristic
18C22×#626C2212yes—
19C22×D3×Dic3C2212yes—
20C22×D3×Dic3C2212yes—
21C2×#3796—24no—
22C2×#3796—24no—
23C2×#3796C418yescomplemented
24C2×C32×C42C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C3×C4×D12—24no—
32C2×#3722C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34#63898—24no—
35#63658C2211yescharacteristic
36#63658C2211yescharacteristic
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40#63579C2212yes—
41#63579C2212yes—
42C22×#239—31no—
43C22×#237—31no—
44C2×C3×C4×D4—31no—
45C2×D4×Dic3—31no—
46C2×#893—31no—
47C2×C4×D12D311yescharacteristic, complemented
48C3×#391—31no—
49#5229—31no—
50#5213—32no—
51C2×C3⋊#95—32no—
52#4987—31no—
53#4987—31no—
54#4973—31no—
55#4958—32no—
56#4943—32no—
57C4×(C2×D3)⋊C4—31no—
58C4×(C2×D3)⋊C4—31no—
59C4×(C2×D3)⋊C4—61no—
60#4929D311yescharacteristic, complemented
61#4665—32no—
62#4665—32no—
63#4664—32no—
64D3×#95—32no—
65C23×C3⋊D3C2311yescharacteristic
66C23×C3×D3C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3C2×C414yescomplemented
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C2×C3×D12C2×C414yes—
80C2×C3×D12D414yes—
81C2×C3×D12D414yes—
82C2×C3×C4×D3—24no—
83C2×C3×C4×D3—24no—
84C2×C3×C4×D3—42no—
85C2×C3×Dic6—22no—
86C2×C3×Dic6—22no—
87C2×C3×Dic6C2×C414yescomplemented
88C2×#626—24no—
89C2×#626—24no—
90C2×#626C2×C418yescomplemented
91C2×D3×Dic3—24no—
92C2×D3×Dic3—24no—
93C2×D3×Dic3—24no—
94C2×D3×Dic3—24no—
95C2×D3×Dic3—42no—
96C2×D3×Dic3C2×C418yescomplemented
97#3796—232no—
98C32×C42—22no—
99#3752—22no—
100#3752—22no—
101C4×C3⋊Dic3—22no—
102C3×(C2×D3)⋊C4—24no—
103C3×C4⋊Dic3—22no—
104C3×C4⋊Dic3—22no—
105#3722—42no—
106(C2×D3)⋊Dic3—24no—
107#2339—91noSylow
108C22×C3×Q8—31no—
109C22×C3×D4—31no—
110C23×C3×C4—32no—
111C22×#67—32no—
112C23×Dic3—32no—
113C23×Dic3—32no—
114C2×#239—38no—
115C2×#239—64no—
116C2×#239—64no—
117C2×#237—38no—
118C2×#237—64no—
119C2×#237—64no—
120C22×D12—32no—
121C22×D12C2×D311yescharacteristic
122C22×C4×D3—32no—
123C22×C4×D3—31no—
124C22×C4×D3—31no—
125C22×C4×D3—32no—
126C22×C4×D3—61no—
127C22×C4×D3C2×D312yes—
128C22×Dic6C2×D311yescharacteristic
129C3×C4×D4—64no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C22⋊C4—32no—
133C2×C3×C42—21no—
134C2×C3×C42C2×D311yescharacteristic
135C2×C3×C42C2×D311yescharacteristic
136C2×#217—32no—
137D4×Dic3—64no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—31no—
140C2×(C2×D3)⋊C4—31no—
141C2×(C2×D3)⋊C4—31no—
142C2×(C2×D3)⋊C4—31no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—61no—
146C2×(C2×D3)⋊C4—61no—
147C2×(C2×D3)⋊C4C2×D312yes—
148C2×C4⋊Dic3C2×D311yescharacteristic
149C2×C4⋊Dic3C2×D311yescharacteristic
150C2×C4×Dic3—31no—
151C2×C4×Dic3—31no—
152C2×C4×Dic3—61no—
153#893—64no—
154C4×D12—24no—
155C3×#95—32no—
156C3×#95—32no—
157C3⋊#95—31no—
158C3⋊#95—31no—
159C3⋊#95—31no—
160C3⋊#95—31no—
161C3⋊#95—32no—
162C3⋊#95—32no—
163C3⋊#95—32no—
164C3⋊#95—32no—
165C3⋊#95—32no—
166C3⋊#95—32no—
167C3⋊#95—61no—
168C3⋊#95—61no—
169C3⋊#95C2×D312yes—
170C3⋊#95C2×D312yes—
171C23×C32C2411yescharacteristic
172C22×C3⋊D3—21no—
173C22×C3⋊D3—21no—
174C22×C3⋊D3—21no—
175C22×C3⋊D3—21no—
176C22×C3⋊D3—21no—
177C22×C3⋊D3—21no—
178C22×C3⋊D3C22×C412yes—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3—22no—
182C22×C3×D3—22no—
183C22×C3×D3C22×C414yes—
184C22×C3×D3C2×D414yes—
185C22×C3×D3C2×D414yes—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4C22×C412yes—
192C2×C32×C4C2×D412yes—
193C2×C32×C4C2×D412yes—
194C2×C32×C4#4112yescomplemented
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3C22×C412yes—
203C2×C3⋊Dic3#4112yescomplemented
204C4×C3⋊D3—28no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3C22×C414yes—
214C3×D12C22⋊C4116yescomplemented
215C3×C4×D3—48no—
216C3×Dic6—28no—
217#626—216no—
218D3×Dic3—216no—
219D3×Dic3—48no—
220C22×#41—91no—
221C2×C4×D4—31no—
222C2×C4×D4—91no—
223#391—31no—
224#391—91no—
225#386—92no—
226#386—92no—
227#381—92no—
228#380—91no—
229C4×C22⋊C4—91no—
230C2×#95—92no—
231C24×C3—32no—
232C23×D3—31no—
233C23×D3—31no—
234C23×D3—61no—
235C23×D3C22×D312yes—
236C2×C3×Q8—34no—
237C2×C3×Q8—62no—
238C2×C3×Q8—62no—
239C2×C3×D4—34no—
240C2×C3×D4—34no—
241C2×C3×D4—34no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—32no—
246C22×C3×C4—32no—
247C22×C3×C4—32no—
248C22×C3×C4—64no—
249C22×C3×C4—64no—
250C22×C3×C4—122no—
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C22×C3×C4C22×D311yescharacteristic
257C2×#67—38no—
258C2×#67—64no—
259C2×#67—64no—
260C22×Dic3—31no—
261C22×Dic3—31no—
262C22×Dic3—31no—
263C22×Dic3—31no—
264C22×Dic3—38no—
265C22×Dic3—31no—
266C22×Dic3—31no—
267C22×Dic3—61no—
268C22×Dic3—61no—
269C22×Dic3—61no—
270C22×Dic3—64no—
271C22×Dic3—64no—
272C22×Dic3—64no—
273C22×Dic3—64no—
274C22×Dic3—122no—
275C22×Dic3C22×D312yes—
276C22×Dic3C22×D312yes—
277C22×Dic3C22×D312yes—
278#239—632no—
279#237—632no—
280C2×D12—38no—
281C2×D12—64no—
282C2×D12—64no—
283C2×D12C4×D314yes—
284C2×D12D1214yes—
285C2×D12#6714yes—
286C2×C4×D3—24no—
287C2×C4×D3—24no—
288C2×C4×D3—38no—
289C2×C4×D3—34no—
290C2×C4×D3—34no—
291C2×C4×D3—42no—
292C2×C4×D3—64no—
293C2×C4×D3—64no—
294C2×C4×D3—64no—
295C2×C4×D3—62no—
296C2×C4×D3—62no—
297C2×C4×D3—62no—
298C2×C4×D3—62no—
299C2×C4×D3—64no—
300C2×C4×D3—64no—
301C2×C4×D3—122no—
302C2×C4×D3—122no—
303C2×C4×D3—122no—
304C2×Dic6—22no—
305C2×Dic6—22no—
306C2×Dic6C4×D314yescomplemented
307C3×C4⋊C4—62no—
308C3×C4⋊C4—62no—
309C3×C22⋊C4—64no—
310C3×C42—22no—
311C3×C42—22no—
312C3×C42—42no—
313#217—64no—
314(C2×D3)⋊C4—24no—
315(C2×D3)⋊C4—62no—
316(C2×D3)⋊C4—62no—
317(C2×D3)⋊C4—64no—
318(C2×D3)⋊C4—64no—
319(C2×D3)⋊C4—64no—
320(C2×D3)⋊C4—62no—
321(C2×D3)⋊C4—62no—
322(C2×D3)⋊C4—122no—
323(C2×D3)⋊C4—122no—
324C4⋊Dic3—22no—
325C4⋊Dic3—22no—
326C4×Dic3—62no—
327C4×Dic3—62no—
328C4×Dic3—122no—
329C22×C32C23×C411yescharacteristic
330C22×C32C22×D411yescharacteristic
331C22×C32C22×D411yescharacteristic
332C22×C32C2×#4111yescharacteristic
333C22×C32C2×#4111yescharacteristic
334C22×C32H(5,𝔽2)11yescharacteristic
335C22×C322−1+411yescharacteristic
336C2×C3⋊D3—22no—
337C2×C3⋊D3—22no—
338C2×C3⋊D3—22no—
339C2×C3⋊D3—41no—
340C2×C3⋊D3—41no—
341C2×C3⋊D3—41no—
342C2×C3⋊D3—41no—
343C2×C3×D3—24no—
344C2×C3×D3—24no—
345C2×C3×D3—24no—
346C2×C3×D3—24no—
347C2×C3×D3—24no—
348C2×C3×D3—24no—
349C2×C3×D3C2×C22⋊C418yes—
350C32×C4—22no—
351C32×C4—41no—
352C32×C4C2×C22⋊C414yes—
353C3⋊Dic3—22no—
354C3⋊Dic3—22no—
355C3⋊Dic3—41no—
356C3×Dic3—24no—
357C3×Dic3—42no—
358C3×Dic3—42no—
359C2×#41—98no—
360C2×#41—184no—
361C2×#41—184no—
362C22×Q8—31no—
363C22×D4—31no—
364C22×D4—92no—
365C23×C4—32no—
366C23×C4—92no—
367C23×C4—92no—
368C23×C4—91no—
369C4×D4—64no—
370C4×D4—184no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C22⋊C4—32no—
374C2×C22⋊C4—92no—
375C2×C22⋊C4—91no—
376C2×C22⋊C4—91no—
377C2×C22⋊C4—92no—
378C2×C42—91no—
379C2×C42D3211yescharacteristic
380#95—32no—
381#95—32no—
382#95—92no—
383#95—92no—
384#95—92no—
385#95—91no—
386#95—91no—
387C23×C3—21no—
388C23×C3—34no—
389C23×C3—34no—
390C23×C3—34no—
391C23×C3—62no—
392C23×C3—62no—
393C23×C3—62no—
394C23×C3—62no—
395C23×C3C23×D311yescharacteristic
396C23×C3C23×D311yescharacteristic
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—22no—
400C22×D3—22no—
401C22×D3—32no—
402C22×D3—32no—
403C22×D3—62no—
404C22×D3—62no—
405C22×D3—62no—
406C22×D3—61no—
407C22×D3—61no—
408C22×D3—61no—
409C22×D3—61no—
410C22×D3—61no—
411C22×D3—61no—
412C22×D3—61no—
413C22×D3—61no—
414C22×D3—61no—
415C22×D3—61no—
416C22×D3—61no—
417C22×D3—61no—
418C22×D3—121no—
419C22×D3—121no—
420C22×D3—121no—
421C22×D3—121no—
422C22×D3C2×C4×D314yes—
423C22×D3C2×D1214yes—
424C22×D3C2×#6714yes—
425C3×Q8—68no—
426C3×D4—316no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—34no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—62no—
448C2×C3×C4—62no—
449C2×C3×C4—62no—
450C2×C3×C4—62no—
451C2×C3×C4—62no—
452C2×C3×C4—62no—
453C2×C3×C4—62no—
454C2×C3×C4—62no—
455C2×C3×C4—128no—
456C2×C3×C4C2×C4×D312yes—
457C2×C3×C4C2×C4×D312yes—
458C2×C3×C4C2×D1212yes—
459C2×C3×C4D3×D412yes—
460C2×C3×C4D3×D412yes—
461C2×C3×C4#23712yescomplemented
462C2×C3×C4#23912yescomplemented
463C2×C3×C4C2×#6712yes—
464#67—616no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—32no—
474C2×Dic3—32no—
475C2×Dic3—32no—
476C2×Dic3—32no—
477C2×Dic3—62no—
478C2×Dic3—62no—
479C2×Dic3—616no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—62no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—121no—
496C2×Dic3—121no—
497C2×Dic3—121no—
498C2×Dic3—121no—
499C2×Dic3—121no—
500C2×Dic3—121no—
501C2×Dic3—128no—
502C2×Dic3C2×C4×D314yes—
503D12—616no—
504D12(C2×D3)⋊C4116yescomplemented
505C4×D3—48no—
506C4×D3—616no—
507C4×D3—68no—
508C4×D3—68no—
509C4×D3—128no—
510C4×D3—128no—
511Dic6—28no—
512C2×C32C22×C22⋊C411yescharacteristic
513C2×C32C4×#4111yescharacteristic
514C2×C32#52011yescharacteristic
515C2×C32#54611yescharacteristic
516C2×C32#54611yescharacteristic
517C2×C32#54711yescharacteristic
518C2×C32#54711yescharacteristic
519C3⋊D3—42no—
520C3×D3—28no—
521C24—32no—
522C24—91no—
523#41—1832no—
524C2×Q8—34no—
525C2×Q8—62no—
526C2×Q8—62no—
527C2×D4—34no—
528C2×D4—34no—
529C2×D4—34no—
530C2×D4—98no—
531C2×D4—184no—
532C2×D4—184no—
533C22×C4—32no—
534C22×C4—32no—
535C22×C4—32no—
536C22×C4—64no—
537C22×C4—64no—
538C22×C4—98no—
539C22×C4—91no—
540C22×C4—91no—
541C22×C4—94no—
542C22×C4—91no—
543C22×C4—122no—
544C22×C4—184no—
545C22×C4—184no—
546C22×C4—184no—
547C22×C4—184no—
548C22×C4—182no—
549C22×C4—182no—
550C22×C4—362no—
551C22×C4C2×D3211yescharacteristic
552C22×C4C2×D3211yescharacteristic
553C22×C4C2×D3211yescharacteristic
554C4⋊C4—62no—
555C4⋊C4—62no—
556C22⋊C4—64no—
557C22⋊C4—182no—
558C22⋊C4—184no—
559C22⋊C4—182no—
560C22⋊C4—362no—
561C42—22no—
562C42—182no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—21no—
570C22×C3—38no—
571C22×C3—64no—
572C22×C3—64no—
573C22×C3—64no—
574C22×C3—64no—
575C22×C3—64no—
576C22×C3—64no—
577C22×C3C22×C4×D311yescharacteristic
578C22×C3C22×C4×D311yescharacteristic
579C22×C3C22×D1211yescharacteristic
580C22×C3C2×D3×D411yescharacteristic
581C22×C3C2×D3×D411yescharacteristic
582C22×C3C2×#23711yescharacteristic
583C22×C3#100411yescharacteristic
584C22×C3C2×#23911yescharacteristic
585C22×C3#100711yescharacteristic
586C22×C3D3×#4111yescharacteristic
587C22×C3D3×#4111yescharacteristic
588C22×C3#100911yescharacteristic
589C22×C3#101011yescharacteristic
590C22×C3C22×#6711yescharacteristic
591C2×D3—24no—
592C2×D3—24no—
593C2×D3—24no—
594C2×D3—24no—
595C2×D3—24no—
596C2×D3—24no—
597C2×D3—64no—
598C2×D3—62no—
599C2×D3—62no—
600C2×D3—62no—
601C2×D3—62no—
602C2×D3—62no—
603C2×D3—62no—
604C2×D3—122no—
605C2×D3—122no—
606C2×D3—122no—
607C2×D3—122no—
608C2×D3—122no—
609C2×D3—122no—
610C2×D3—121no—
611C2×D3—121no—
612C2×D3—121no—
613C2×D3—121no—
614C2×D3—121no—
615C2×D3—121no—
616C2×D3—121no—
617C2×D3—121no—
618C2×D3C2×(C2×D3)⋊C418yes—
619C3×C4—22no—
620C3×C4—22no—
621C3×C4—24no—
622C3×C4—42no—
623C3×C4—42no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—64no—
627C3×C4—122no—
628C3×C4—122no—
629C3×C4D3×C22⋊C414yes—
630C3×C4C2×(C2×D3)⋊C414yes—
631Dic3—24no—
632Dic3—42no—
633Dic3—42no—
634Dic3—62no—
635Dic3—62no—
636Dic3—62no—
637Dic3—62no—
638Dic3—122no—
639Dic3—122no—
640Dic3—122no—
641Dic3—121no—
642Dic3—121no—
643C32#233911yescharacteristic, complemented, Sylow
644C23—34no—
645C23—34no—
646C23—34no—
647C23—62no—
648C23—62no—
649C23—62no—
650C23—62no—
651C23—92no—
652C23—181no—
653C23—181no—
654C23—181no—
655C23—181no—
656C23—181no—
657C23—181no—
658C23C22×D3211yescharacteristic
659Q8—68no—
660D4—316no—
661D4—1816no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—34no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—92no—
677C2×C4—92no—
678C2×C4—128no—
679C2×C4—1816no—
680C2×C4—181no—
681C2×C4—181no—
682C2×C4—181no—
683C2×C4—181no—
684C2×C4—188no—
685C2×C4—181no—
686C2×C4—181no—
687C2×C4—181no—
688C2×C4—368no—
689C2×C4#379612yescomplemented
690C2×C4C4×D3212yes—
691C2×C4D3×D1212yes—
692C2×C4D3×#6712yes—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—68no—
701C2×C3C2×D3×C22⋊C411yescharacteristic
702C2×C3C4×#23711yescharacteristic
703C2×C3#554611yescharacteristic
704C2×C3#555411yescharacteristic
705C2×C3#555511yescharacteristic
706C2×C3C4×#23911yescharacteristic
707C2×C3#557411yescharacteristic
708C2×C3#563011yescharacteristic
709C2×C3#563111yescharacteristic
710C2×C3#567611yescharacteristic
711C2×C3#572611yescharacteristic
712C2×C3C22×(C2×D3)⋊C411yescharacteristic
713C2×C3#580611yescharacteristic
714C2×C3#582411yescharacteristic
715D3—28no—
716D3—124no—
717D3—122no—
718D3—122no—
719C22—38no—
720C22—64no—
721C22—64no—
722C22—64no—
723C22—64no—
724C22—64no—
725C22—64no—
726C22—182no—
727C22—182no—
728C22—182no—
729C22—361no—
730C22—361no—
731C22—361no—
732C22—361no—
733C22C2×#379611yescharacteristic
734C22#6429711yescharacteristic
735C22C2×C4×D3211yescharacteristic
736C22C2×D3×D1211yescharacteristic
737C22#6430611yescharacteristic
738C22#6430711yescharacteristic
739C22C2×D3×#6711yescharacteristic
740C4—22no—
741C4—41no—
742C4—64no—
743C4—122no—
744C4—122no—
745C4—182no—
746C4—182no—
747C4—361no—
748C4D3×(C2×D3)⋊C414yes—
749C3—21no—
750C3#7661311yescharacteristic, complemented
751C3#8233011yescharacteristic, complemented
752C2—68no—
753C2—362no—
754C2C4×#379611yescharacteristic
755C2#1059388911yescharacteristic
756C2#1059389611yescharacteristic
757C2#1059400511yescharacteristic
758C2#1059488911yescharacteristic
759C2#1059489011yescharacteristic
760C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×#3796C2
hypercenterC2×C42D32
hypocenterC32#2339
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×D12C2semidirect
3. C2×#63898C2semidirect
4. C4×#3752C2semidirect
5. C3×#4929C2semidirect
6. #10591382C2semidirect
7. #10591364C2semidirect
8. #10591362C2semidirect
9. D3×C3⋊#95C2semidirect
10. #10591325C2semidirect
11. #10591221C2semidirect
23. C2×#3796C4semidirect
47. C2×C4×D12D3semidirect
60. #4929D3semidirect
75. C2×C4×C3⋊D3C2×C4semidirect
87. C2×C3×Dic6C2×C4semidirect
90. C2×#626C2×C4semidirect
96. C2×D3×Dic3C2×C4semidirect
194. C2×C32×C4#41semidirect
203. C2×C3⋊Dic3#41semidirect
214. C3×D12C22⋊C4semidirect
306. C2×Dic6C4×D3semidirect
461. C2×C3×C4#237semidirect
462. C2×C3×C4#239semidirect
504. D12(C2×D3)⋊C4semidirect
643. C32#2339semidirect
689. C2×C4#3796semidirect
750. C3#76613semidirect
751. C3#82330semidirect

Maximal subgroups

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

subgroupindex
C22×#37962
C2×C3×C4×D122
C2×#638982
C4×#37522
C3×#49292
#105913822
#105913642
#105913622
D3×C3⋊#952
#105913252
#105912212
#823303
#766133