Finite Group Databasebeta

← #11805440

Subgroups — #11805440

Order 1152.

1765 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#63952C212yesmaximal
4C2×#63900C211yesmaximal, characteristic, complemented
5C3×#5212C211yesmaximal, characteristic, complemented
6#10591693C212yesmaximal, complemented
7#10591378C212yesmaximal, complemented
8#10591359C211yesmaximal, characteristic, complemented
9#10591325C211yesmaximal, characteristic, complemented
10#10591274C211yesmaximal, characteristic, complemented
11#10591264C212yesmaximal, complemented
12C4⋊C4×#67—31nomaximal
13#74010—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C23×C3×Dic3C2212yes—
18C22×#624C2212yes—
19C2×#3757C2211yescharacteristic
20C4×#638C418yescomplemented
21C2×#3752C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×#217C2212yes—
25C2×C3×C4⋊Dic3—24no—
26C2×C3×C4⋊Dic3C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×#3724C2212yes—
32C2×#3724C2212yes—
33C2×#3724C2212yes—
34C2×#3722C2212yes—
35C2×Dic32C2212yes—
36#63952—28no—
37#63900—24no—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40#63579C2212yes—
41C22×C3×C4⋊C4—31no—
42C2×C4×#67—31no—
43C2×C4×#67—31no—
44C2×C4×#67—32no—
45C2×C4×#67—61no—
46C22×C4⋊Dic3D311yescharacteristic, complemented
47C2×D3×C4⋊C4—31no—
48C2×D3×C4⋊C4—31no—
49C2×#67⋊C4—32no—
50C3×#380—31no—
51#5212D311yescharacteristic, complemented
52#5210—32no—
53#4989—32no—
54#4987—31no—
55#4987—31no—
56#4976—32no—
57#4975—31no—
58#4975—31no—
59Dic3×C4⋊C4—31no—
60Dic3×C4⋊C4—31no—
61#4946—32no—
62#4668—32no—
63#4647—32no—
64C24×C32C2311yescharacteristic
65C23×C3⋊D3C2311yescharacteristic
66C22×C32×C4—22no—
67C22×C32×C4—22no—
68C22×C32×C4C2×C414yescomplemented
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C2×#638C2×C414yes—
72C2×#638D414yes—
73C2×#638Q814yes—
74C22×C3⋊Dic3C2311yescharacteristic
75C22×C3⋊Dic3C2311yescharacteristic
76C22×C3⋊Dic3C2311yescharacteristic
77C2×C4×C3⋊D3—22no—
78C2×C4×C3⋊D3—22no—
79C2×C4×C3⋊D3C2×C414yescomplemented
80C22×C3×Dic3—24no—
81C22×C3×Dic3—24no—
82C22×C3×Dic3—42no—
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2312yes—
87C2×#624—24no—
88C2×#624—24no—
89C2×#624—42no—
90#3757C2×C414yescomplemented
91#3752C2×C414yescomplemented
92#3750C2×C414yescomplemented
93C4×C3⋊Dic3C2×C414yescomplemented
94C3×#217—24no—
95C3×C4⋊Dic3—22no—
96C3×C4⋊Dic3—22no—
97C3×C4⋊Dic3—22no—
98C3×C4⋊Dic3—24no—
99C3×C4⋊Dic3D414yescomplemented
100#3724—24no—
101#3724—24no—
102#3724—42no—
103#3722—24no—
104Dic32—24no—
105D4×C4⋊C4—91noSylow
106C23×C3×C4—21no—
107C23×C3×C4—32no—
108C23×C3×C4C2×D311yescharacteristic
109C23×C3×C4C2×D311yescharacteristic
110C22×#67—31no—
111C22×#67—31no—
112C22×#67—61no—
113C23×Dic3C2×D312yes—
114C22×C4×D3—31no—
115C22×C4×D3—31no—
116C22×C4×D3—32no—
117C22×C4×D3—32no—
118C22×C4×D3—61no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C4⋊C4—32no—
124C2×C3×C4⋊C4—64no—
125C2×C3×C22⋊C4—32no—
126C2×#217—31no—
127C2×#217—31no—
128C2×#217—61no—
129C2×#217C2×D312yes—
130C4×#67—38no—
131C4×#67—38no—
132C4×#67—68no—
133C4×#67—68no—
134C2×(C2×D3)⋊C4—31no—
135C2×(C2×D3)⋊C4—31no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—61no—
139C2×C4⋊Dic3—24no—
140C2×C4⋊Dic3C2×D312yes—
141C2×C4⋊Dic3C2×D311yescharacteristic
142C2×C4⋊Dic3C2×D311yescharacteristic
143C2×C4⋊Dic3C2×D311yescharacteristic
144C2×C4⋊Dic3C2×D311yescharacteristic
145C2×Dic3⋊C4—31no—
146C2×Dic3⋊C4—31no—
147C2×Dic3⋊C4—32no—
148C2×Dic3⋊C4—32no—
149C2×Dic3⋊C4—32no—
150C2×Dic3⋊C4—32no—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—32no—
153C2×Dic3⋊C4—61no—
154C2×C4×Dic3—31no—
155C2×C4×Dic3—31no—
156C2×C4×Dic3—32no—
157C2×C4×Dic3—32no—
158C2×C4×Dic3—61no—
159D3×C4⋊C4—64no—
160D3×C4⋊C4—64no—
161#67⋊C4—68no—
162C3×#95—32no—
163C3⋊#95—32no—
164C3⋊#95—32no—
165C3⋊#95—32no—
166C3⋊#95—32no—
167C3⋊#95C2×D312yes—
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—21no—
172C23×C32C22×C412yes—
173C23×C32C2×D412yes—
174C23×C32C2×Q812yes—
175C23×C32C2411yescharacteristic
176C22×C3⋊D3—21no—
177C22×C3⋊D3—21no—
178C22×C3⋊D3—21no—
179C22×C3⋊D3—21no—
180C22×C3⋊D3C22×C412yes—
181C22×C3⋊D3C2×D412yes—
182C22×C3⋊D3C2×Q812yes—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—28no—
186C2×C32×C4C22×C412yes—
187C2×C32×C4C22×C412yes—
188C2×C32×C4C2×D412yes—
189C2×C32×C4#4112yes—
190#638C4⋊C4116yescomplemented
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3C22×C412yes—
196C2×C3⋊Dic3C22×C412yes—
197C2×C3⋊Dic3C22×C412yes—
198C2×C3⋊Dic3C2×D412yes—
199C2×C3⋊Dic3C2×Q812yes—
200C4×C3⋊D3—28no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
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—48no—
213C2×C3×Dic3C2×D414yes—
214#624—48no—
215C2×C4×D4—92no—
216C2×C4×D4—91no—
217C22×C4⋊C4—31no—
218C22×C4⋊C4—91no—
219#389—92no—
220#385—92no—
221#385—92no—
222#384—91no—
223#380—31no—
224#380—91no—
225C4×C4⋊C4—91no—
226C24×C3—21no—
227C24×C3C22×D311yescharacteristic
228C24×C3C22×D311yescharacteristic
229C23×D3—31no—
230C23×D3—31no—
231C23×D3—61no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—24no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—32no—
240C22×C3×C4—32no—
241C22×C3×C4—32no—
242C22×C3×C4—32no—
243C22×C3×C4—42no—
244C22×C3×C4—42no—
245C22×C3×C4—64no—
246C22×C3×C4—64no—
247C22×C3×C4—122no—
248C22×C3×C4C4×D314yescomplemented
249C22×C3×C4C4×D314yescomplemented
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C2×#67—34no—
255C2×#67—34no—
256C2×#67—34no—
257C2×#67—34no—
258C2×#67—34no—
259C2×#67—34no—
260C2×#67—64no—
261C2×#67—64no—
262C2×#67—64no—
263C22×Dic3—24no—
264C22×Dic3—24no—
265C22×Dic3—31no—
266C22×Dic3—31no—
267C22×Dic3—31no—
268C22×Dic3—31no—
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—42no—
272C22×Dic3—61no—
273C22×Dic3—61no—
274C22×Dic3—61no—
275C22×Dic3C22×D312yes—
276C22×Dic3C22×D312yes—
277C22×Dic3C22×D312yes—
278C22×Dic3C22×D312yes—
279C2×C4×D3—34no—
280C2×C4×D3—34no—
281C2×C4×D3—64no—
282C2×C4×D3—62no—
283C2×C4×D3—62no—
284C2×C4×D3—62no—
285C2×C4×D3—62no—
286C2×C4×D3—64no—
287C2×C4×D3—64no—
288C2×C4×D3—64no—
289C2×C4×D3—64no—
290C2×C4×D3—122no—
291C2×C4×D3—122no—
292C2×C4×D3—122no—
293C2×C4×D3—122no—
294C3×C4⋊C4—34no—
295C3×C4⋊C4—64no—
296C3×C4⋊C4—62no—
297C3×C4⋊C4—62no—
298C3×C4⋊C4—62no—
299C3×C22⋊C4—64no—
300#217—24no—
301#217—34no—
302#217—34no—
303#217—64no—
304(C2×D3)⋊C4—34no—
305(C2×D3)⋊C4—34no—
306(C2×D3)⋊C4—64no—
307(C2×D3)⋊C4—64no—
308(C2×D3)⋊C4—64no—
309C4⋊Dic3—22no—
310C4⋊Dic3—22no—
311C4⋊Dic3—22no—
312C4⋊Dic3—24no—
313C4⋊Dic3#6714yescomplemented
314Dic3⋊C4—34no—
315Dic3⋊C4—34no—
316Dic3⋊C4—64no—
317Dic3⋊C4—64no—
318Dic3⋊C4—64no—
319Dic3⋊C4—64no—
320Dic3⋊C4—64no—
321Dic3⋊C4—122no—
322Dic3⋊C4—122no—
323C4×Dic3—34no—
324C4×Dic3—34no—
325C4×Dic3—64no—
326C4×Dic3—64no—
327C4×Dic3—64no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—22no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32C2×C4⋊C414yescomplemented
335C22×C32C23×C411yescharacteristic
336C22×C32C22×D411yescharacteristic
337C22×C32C22×D411yescharacteristic
338C22×C32C22×Q811yescharacteristic
339C22×C32C2×#4111yescharacteristic
340C22×C32H(5,𝔽2)11yescharacteristic
341C22×C322−1+411yescharacteristic
342C2×C3⋊D3—22no—
343C2×C3⋊D3—22no—
344C2×C3⋊D3—22no—
345C2×C3⋊D3—22no—
346C2×C3⋊D3—22no—
347C2×C3⋊D3—22no—
348C2×C3⋊D3C2×C4⋊C414yescomplemented
349C32×C4—22no—
350C32×C4C4×D414yescomplemented
351C3⋊Dic3—22no—
352C3⋊Dic3—22no—
353C3⋊Dic3C2×C4⋊C414yescomplemented
354C3×Dic3—24no—
355C3×Dic3—42no—
356C3×Dic3—42no—
357C3×Dic3—42no—
358C22×D4—91no—
359C23×C4—32no—
360C23×C4—92no—
361C23×C4—91no—
362C23×C4D3211yescharacteristic
363C4×D4—98no—
364C4×D4—188no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—64no—
371C2×C4⋊C4—91no—
372C2×C4⋊C4—92no—
373C2×C4⋊C4—92no—
374C2×C4⋊C4—92no—
375C2×C4⋊C4—184no—
376C2×C22⋊C4—32no—
377C2×C22⋊C4—91no—
378C2×C22⋊C4—91no—
379C2×C22⋊C4—92no—
380C2×C42—91no—
381C2×C42—92no—
382#95—32no—
383#95—92no—
384#95—92no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3C2×C4×D312yes—
402C23×C3C2×C4×D312yes—
403C23×C3D3×D412yes—
404C23×C3D3×D412yes—
405C23×C3D3×Q812yes—
406C23×C3D3×Q812yes—
407C23×C3C23×D311yescharacteristic
408C23×C3C23×D311yescharacteristic
409C22×D3—32no—
410C22×D3—32no—
411C22×D3—32no—
412C22×D3—32no—
413C22×D3—32no—
414C22×D3—32no—
415C22×D3—62no—
416C22×D3—62no—
417C22×D3—62no—
418C22×D3—61no—
419C22×D3—61no—
420C22×D3—61no—
421C22×D3—61no—
422C22×D3—61no—
423C22×D3—61no—
424C22×D3—61no—
425C22×D3—61no—
426C22×D3—121no—
427C22×D3—121no—
428C22×D3—121no—
429C22×D3—121no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—28no—
435C2×C3×C4—28no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—34no—
441C2×C3×C4—48no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—62no—
445C2×C3×C4—62no—
446C2×C3×C4—62no—
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×C4×D312yes—
459C2×C3×C4C2×C4×D312yes—
460C2×C3×C4#23512yes—
461C2×C3×C4D3×D412yes—
462C2×C3×C4#23712yes—
463C2×C3×C4C2×#6712yes—
464#67—316no—
465#67—316no—
466#67—616no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—32no—
479C2×Dic3—32no—
480C2×Dic3—32no—
481C2×Dic3—32no—
482C2×Dic3—32no—
483C2×Dic3—32no—
484C2×Dic3—32no—
485C2×Dic3—32no—
486C2×Dic3—32no—
487C2×Dic3—32no—
488C2×Dic3—48no—
489C2×Dic3—62no—
490C2×Dic3—62no—
491C2×Dic3—62no—
492C2×Dic3—62no—
493C2×Dic3—62no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—121no—
503C2×Dic3—121no—
504C2×Dic3—121no—
505C2×Dic3—121no—
506C2×Dic3C2×#6714yes—
507C4×D3—68no—
508C4×D3—68no—
509C4×D3—128no—
510C4×D3—128no—
511C4×D3—128no—
512C2×C32—24no—
513C2×C32C22×C4⋊C411yescharacteristic
514C2×C32C2×C4×D411yescharacteristic
515C2×C32#52011yescharacteristic
516C2×C32D4211yescharacteristic
517C2×C32#54711yescharacteristic
518C2×C32D4×Q811yescharacteristic
519C2×C32#55411yescharacteristic
520C3⋊D3—24no—
521C24—91no—
522C24C2×D3211yescharacteristic
523C2×D4—94no—
524C2×D4—94no—
525C2×D4—94no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—32no—
529C22×C4—32no—
530C22×C4—32no—
531C22×C4—32no—
532C22×C4—64no—
533C22×C4—64no—
534C22×C4—91no—
535C22×C4—91no—
536C22×C4—91no—
537C22×C4—94no—
538C22×C4—122no—
539C22×C4—184no—
540C22×C4—184no—
541C22×C4—182no—
542C22×C4—182no—
543C22×C4—362no—
544C22×C4#62414yescomplemented
545C22×C4C2×D3211yescharacteristic
546C22×C4C2×D3211yescharacteristic
547C4⋊C4—34no—
548C4⋊C4—64no—
549C4⋊C4—62no—
550C4⋊C4—62no—
551C4⋊C4—62no—
552C4⋊C4—94no—
553C4⋊C4—184no—
554C4⋊C4—184no—
555C4⋊C4—362no—
556C22⋊C4—64no—
557C22⋊C4—94no—
558C22⋊C4—94no—
559C22⋊C4—184no—
560C42—94no—
561C42—184no—
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—24no—
582C22×C3—42no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—42no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3D3×C4⋊C414yescomplemented
589C22×C3D3×C4⋊C414yescomplemented
590C22×C3C22×C4×D311yescharacteristic
591C22×C3C22×C4×D311yescharacteristic
592C22×C3C2×#23511yescharacteristic
593C22×C3C2×D3×D411yescharacteristic
594C22×C3C2×D3×D411yescharacteristic
595C22×C3C2×D3×D411yescharacteristic
596C22×C3C2×#23711yescharacteristic
597C22×C3#100411yescharacteristic
598C22×C3C2×D3×Q811yescharacteristic
599C22×C3C2×D3×Q811yescharacteristic
600C22×C3#100711yescharacteristic
601C22×C3#100911yescharacteristic
602C22×C3#101011yescharacteristic
603C22×C3C22×#6711yescharacteristic
604C2×D3—34no—
605C2×D3—34no—
606C2×D3—64no—
607C2×D3—62no—
608C2×D3—62no—
609C2×D3—62no—
610C2×D3—62no—
611C2×D3—62no—
612C2×D3—62no—
613C2×D3—62no—
614C2×D3—62no—
615C2×D3—62no—
616C2×D3—62no—
617C2×D3—62no—
618C2×D3—62no—
619C2×D3—122no—
620C2×D3—122no—
621C2×D3—122no—
622C2×D3—122no—
623C2×D3—122no—
624C2×D3—122no—
625C3×C4—22no—
626C3×C4—22no—
627C3×C4—24no—
628C3×C4—42no—
629C3×C4—64no—
630C3×C4—122no—
631C3×C4—122no—
632C3×C4—122no—
633C3×C4#67⋊C414yescomplemented
634C3×C4C4×#6714yescomplemented
635Dic3—24no—
636Dic3—34no—
637Dic3—34no—
638Dic3—42no—
639Dic3—42no—
640Dic3—42no—
641Dic3—64no—
642Dic3—62no—
643Dic3—62no—
644Dic3—62no—
645Dic3—62no—
646Dic3—122no—
647Dic3—122no—
648C32D4×C4⋊C411yescharacteristic, complemented, Sylow
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—92no—
654C23—92no—
655C23—92no—
656C23—181no—
657C23—181no—
658C23—181no—
659C23—181no—
660C23#379712yes—
661C23#380212yes—
662C23C2×#62412yes—
663C23C22×D3211yescharacteristic
664D4—916no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—28no—
668C2×C4—34no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—92no—
681C2×C4—92no—
682C2×C4—92no—
683C2×C4—92no—
684C2×C4—92no—
685C2×C4—128no—
686C2×C4—181no—
687C2×C4—181no—
688C2×C4—181no—
689C2×C4—181no—
690C2×C4—188no—
691C2×C4—368no—
692C2×C4#380412yes—
693C2×C4C2×#62412yes—
694C2×C4C2×#62412yes—
695C2×C4D3×#6712yes—
696C2×C3—24no—
697C2×C3—24no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—44no—
706C2×C3C2×#67⋊C411yescharacteristic
707C2×C3C2×D3×C4⋊C411yescharacteristic
708C2×C3C2×D3×C4⋊C411yescharacteristic
709C2×C3#550411yescharacteristic
710C2×C3#550711yescharacteristic
711C2×C3#551111yescharacteristic
712C2×C3#552311yescharacteristic
713C2×C3#560911yescharacteristic
714C2×C3#561111yescharacteristic
715C2×C3#563211yescharacteristic
716C2×C3#563511yescharacteristic
717C2×C3C2×C4×#6711yescharacteristic
718C2×C3D4×#6711yescharacteristic
719C2×C3Q8×#6711yescharacteristic
720D3—64no—
721D3—64no—
722D3—124no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—94no—
730C22—182no—
731C22—182no—
732C22—182no—
733C22—182no—
734C22—182no—
735C22—182no—
736C22#6390014yescomplemented
737C22#6429711yescharacteristic
738C22C2×#379711yescharacteristic
739C22C2×#380211yescharacteristic
740C22#6430711yescharacteristic
741C22C2×#380411yescharacteristic
742C22C22×#62411yescharacteristic
743C22C2×D3×#6711yescharacteristic
744C4—22no—
745C4—64no—
746C4—94no—
747C4—122no—
748C4—122no—
749C4—122no—
750C4—182no—
751C4—182no—
752C4#6395214yescomplemented
753C3—21no—
754C3#7401011yescharacteristic, complemented
755C3C4⋊C4×#6711yescharacteristic, complemented
756C2—24no—
757C2—184no—
758C2#1059480311yescharacteristic
759C2#1059492811yescharacteristic
760C2C2×#6390011yescharacteristic
761C2#1059499011yescharacteristic
762C2#1059499111yescharacteristic
763C2#1059506911yescharacteristic
764C2C2×#6395211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32D4×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4⋊Dic3C2semidirect
4. C2×#63900C2semidirect
5. C3×#5212C2semidirect
6. #10591693C2semidirect
7. #10591378C2semidirect
8. #10591359C2semidirect
9. #10591325C2semidirect
10. #10591274C2semidirect
11. #10591264C2semidirect
20. C4×#638C4semidirect
46. C22×C4⋊Dic3D3semidirect
51. #5212D3semidirect
68. C22×C32×C4C2×C4semidirect
79. C2×C4×C3⋊D3C2×C4semidirect
90. #3757C2×C4semidirect
91. #3752C2×C4semidirect
92. #3750C2×C4semidirect
93. C4×C3⋊Dic3C2×C4semidirect
99. C3×C4⋊Dic3D4semidirect
190. #638C4⋊C4semidirect
248. C22×C3×C4C4×D3semidirect
249. C22×C3×C4C4×D3semidirect
313. C4⋊Dic3#67semidirect
334. C22×C32C2×C4⋊C4semidirect
348. C2×C3⋊D3C2×C4⋊C4semidirect
350. C32×C4C4×D4semidirect
353. C3⋊Dic3C2×C4⋊C4semidirect
544. C22×C4#624semidirect
588. C22×C3D3×C4⋊C4semidirect
589. C22×C3D3×C4⋊C4semidirect
633. C3×C4#67⋊C4semidirect
634. C3×C4C4×#67semidirect
648. C32D4×C4⋊C4semidirect
736. C22#63900semidirect
752. C4#63952semidirect
754. C3#74010semidirect
755. C3C4⋊C4×#67semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C22×C3×C4⋊Dic32
C2×#639522
C2×#639002
C3×#52122
#105916932
#105913782
#105913592
#105913252
#105912742
#105912642
C4⋊C4×#673
#740103