Finite Group Databasebeta

← #10800528

Subgroups — #10800528

Order 768.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5791C211yesmaximal, characteristic
2C3×#2280C211yesmaximal, characteristic, complemented
3C2×C4×#217C211yesmaximal, characteristic, complemented
4#69529C212yesmaximal, complemented
5#69528C212yesmaximal, complemented
6#69496C214yesmaximal, complemented
7C4×#806C214yesmaximal, complemented
8#21420—31nomaximal, Sylow
9C24×C3×C4C2211yescharacteristic
10C22×#235C411yescharacteristic, complemented
11C2×C3×#117—21no—
12C2×#953C2212yes—
13C22×#217C2212yes—
14#5791—21no—
15#5791—21no—
16#5791—21no—
17#5791—21no—
18#5791—21no—
19#5791—21no—
20#5791—21no—
21#5791—21no—
22C2×#930C411yescharacteristic, complemented
23C2×#930C2211yescharacteristic
24C2×#929C412yescomplemented
25C2×C4×#67C412yescomplemented
26C2×C4×#67C2212yes—
27C2×#926C411yescharacteristic, complemented
28C2×#924C411yescharacteristic, complemented
29C2×#924C2211yescharacteristic
30C22×C4×Dic3—21no—
31C3×#381—21no—
32C3×#380—21no—
33C3×#380C2212yes—
34C3×#379C2212yes—
35C3×C4×C22⋊C4—21no—
36C3×C4×C22⋊C4C2212yes—
37C4×#217—21no—
38C4×#217—21no—
39C4×#217C2212yes—
40C4×#217C2212yes—
41C2×C3⋊#95—21no—
42C2×#806C2218yes—
43#4527C2218yes—
44C2×#525—31no—
45#2280D311yescharacteristic, complemented
46C2×C4×C22⋊C4—31no—
47#1996—32no—
48#1964—32no—
49#1898—34no—
50C4×#99—34no—
51C25×C3C2311yescharacteristic
52C23×C3×C4—44no—
53C23×C3×C4C2×C411yescharacteristic
54C23×C3×C4C2×C411yescharacteristic
55C23×C3×C4C2×C411yescharacteristic
56C23×C3×C4C2×C411yescharacteristic
57C23×C3×C4D411yescharacteristic
58C23×C3×C4D411yescharacteristic
59C23×C3×C4D411yescharacteristic
60C23×C3×C4D411yescharacteristic
61C23×C3×C4D411yescharacteristic
62C23×C3×C4D411yescharacteristic
63C23×C3×C4D411yescharacteristic
64C23×C3×C4D411yescharacteristic
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2311yescharacteristic
67C22×#67C2×C412yes—
68C22×#67C2×C412yes—
69C22×#67C2312yes—
70C23×Dic3—22no—
71C2×#235—21no—
72C2×#235—21no—
73C2×#235—21no—
74C2×#235—21no—
75C2×#235—44no—
76C22×D12C2×C411yescharacteristic, complemented
77C22×C4×D3C2×C412yescomplemented
78C22×Dic6C2×C411yescharacteristic, complemented
79C3×#117—44no—
80C2×C3×C4⋊C4—22no—
81C2×C3×C22⋊C4—22no—
82C2×C3×C22⋊C4—22no—
83C2×C3×C22⋊C4C2314yes—
84C2×C3×C42—22no—
85#953—22no—
86#953—22no—
87#953—22no—
88#953—22no—
89C2×#217—22no—
90C2×#217—28no—
91C2×#217C2×C412yes—
92C2×#217C2×C412yes—
93C2×#217C2312yes—
94C2×#217C2314yes—
95#930—21no—
96#930—21no—
97#930—21no—
98#930—21no—
99#930—21no—
100#930—21no—
101#930—21no—
102#930—21no—
103#929—22no—
104#929—22no—
105#929—22no—
106#929—22no—
107C4×#67—22no—
108C4×#67—22no—
109C4×#67—22no—
110C4×#67—22no—
111C4×#67—22no—
112C4×#67—22no—
113C4×#67—22no—
114C4×#67—22no—
115C2×(C2×D3)⋊C4C2×C412yescomplemented
116C2×(C2×D3)⋊C4C2×C412yescomplemented
117#926—21no—
118#926—21no—
119#926—21no—
120#926—21no—
121C2×C4⋊Dic3C2×C411yescharacteristic, complemented
122C2×C4⋊Dic3C2×C411yescharacteristic, complemented
123#924—21no—
124#924—21no—
125#924—21no—
126#924—21no—
127#924—21no—
128#924—21no—
129#924—21no—
130#924—21no—
131C2×Dic3⋊C4C2×C412yescomplemented
132C2×Dic3⋊C4C2×C412yescomplemented
133C2×C4×Dic3—22no—
134C2×C4×Dic3—22no—
135C2×C4×Dic3—44no—
136C2×C4×Dic3C2×C412yescomplemented
137C3×#95—22no—
138C3×#95—22no—
139C3⋊#95—22no—
140C3⋊#95—22no—
141#806—216no—
142C22×#41—31no—
143C24×C4C2×D311yescharacteristic
144#525—61no—
145#525—61no—
146#525—61no—
147#525—61no—
148#525—61no—
149#525—61no—
150#525—61no—
151#525—61no—
152C2×#123—32no—
153C2×C22⋊Q8—31no—
154C2×C22⋊Q8—31no—
155C2×#121—31no—
156C2×#121—31no—
157C2×#120—32no—
158C2×C4×D4—32no—
159C2×C4×D4—32no—
160C2×#117—21no—
161C2×#117—31no—
162C22×C22⋊C4—32no—
163C22×C42—61no—
164C2×#99—38no—
165#381—21no—
166#380—21no—
167#380C2×D312yes—
168#379C2×D312yes—
169C4×C22⋊C4—21no—
170C4×C22⋊C4—32no—
171C4×C22⋊C4—32no—
172C4×C22⋊C4—61no—
173C4×C22⋊C4—61no—
174C4×C22⋊C4C2×D312yes—
175C2×#95—61no—
176#342—38no—
177C24×C3—24no—
178C24×C3—42no—
179C24×C3—42no—
180C24×C3C22×C411yescharacteristic
181C24×C3C22×C411yescharacteristic
182C24×C3C2×D411yescharacteristic
183C24×C3C2×D411yescharacteristic
184C24×C3C2×D411yescharacteristic
185C24×C3C2×D411yescharacteristic
186C24×C3C2411yescharacteristic
187C23×D3C22×C412yes—
188C22×C3×C4—24no—
189C22×C3×C4—24no—
190C22×C3×C4—24no—
191C22×C3×C4—24no—
192C22×C3×C4—42no—
193C22×C3×C4—42no—
194C22×C3×C4—42no—
195C22×C3×C4—42no—
196C22×C3×C4—42no—
197C22×C3×C4—42no—
198C22×C3×C4—42no—
199C22×C3×C4—42no—
200C22×C3×C4—42no—
201C22×C3×C4—42no—
202C22×C3×C4—42no—
203C22×C3×C4C22⋊C411yescharacteristic
204C22×C3×C4C22⋊C411yescharacteristic
205C22×C3×C4C22⋊C411yescharacteristic
206C22×C3×C4C22⋊C411yescharacteristic
207C22×C3×C4C22⋊C411yescharacteristic
208C22×C3×C4C22⋊C411yescharacteristic
209C22×C3×C4C22⋊C411yescharacteristic
210C22×C3×C4C22⋊C411yescharacteristic
211C22×C3×C4C22⋊C411yescharacteristic
212C22×C3×C4C22⋊C411yescharacteristic
213C22×C3×C4C22⋊C411yescharacteristic
214C22×C3×C4C22⋊C411yescharacteristic
215C22×C3×C4C22⋊C411yescharacteristic
216C22×C3×C4C22⋊C411yescharacteristic
217C22×C3×C4C22⋊C411yescharacteristic
218C22×C3×C4C22⋊C411yescharacteristic
219C22×C3×C4C22×C411yescharacteristic
220C22×C3×C4C22×C411yescharacteristic
221C22×C3×C4C22×C411yescharacteristic
222C22×C3×C4C22×C411yescharacteristic
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2×D411yescharacteristic
227C22×C3×C4C2×D411yescharacteristic
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2×D411yescharacteristic
231C2×#67—22no—
232C2×#67—22no—
233C2×#67—22no—
234C2×#67—22no—
235C2×#67—22no—
236C2×#67—22no—
237C2×#67—28no—
238C2×#67—44no—
239C2×#67—44no—
240C22×Dic3—28no—
241C22×Dic3—24no—
242C22×Dic3—44no—
243C22×Dic3—44no—
244C22×Dic3C22×C412yes—
245C22×Dic3C22×C412yes—
246C22×Dic3C22×C412yes—
247#235—44no—
248#235—44no—
249#235—44no—
250#235—44no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—42no—
254C2×C4×D3—22no—
255C2×C4×D3—22no—
256C2×C4×D3—44no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—42no—
260C3×C4⋊C4—44no—
261C3×C22⋊C4—28no—
262C3×C22⋊C4—44no—
263C3×C22⋊C4—44no—
264C3×C42—44no—
265#217—28no—
266#217—22no—
267#217—22no—
268#217—22no—
269#217—22no—
270#217—22no—
271#217—22no—
272#217—24no—
273#217#4118yescomplemented
274(C2×D3)⋊C4—22no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—22no—
277(C2×D3)⋊C4—22no—
278C4⋊Dic3—21no—
279C4⋊Dic3—21no—
280C4⋊Dic3—21no—
281C4⋊Dic3—21no—
282Dic3⋊C4—22no—
283Dic3⋊C4—22no—
284Dic3⋊C4—22no—
285Dic3⋊C4—22no—
286C4×Dic3—22no—
287C4×Dic3—22no—
288C4×Dic3—44no—
289C4×Dic3—44no—
290C25C22×D311yescharacteristic
291C2×#41—61no—
292C2×#41—61no—
293C2×#41—61no—
294C2×#41—61no—
295C2×#41—124no—
296C22×Q8—31no—
297C22×D4—32no—
298C22×D4—32no—
299C22×D4—32no—
300C22×D4—31no—
301C23×C4—32no—
302C23×C4—44no—
303C23×C4—62no—
304C23×C4C4×D311yescharacteristic
305C23×C4C4×D311yescharacteristic
306C23×C4C4×D311yescharacteristic
307C23×C4C4×D311yescharacteristic
308C23×C4D1211yescharacteristic
309C23×C4D1211yescharacteristic
310C23×C4D1211yescharacteristic
311C23×C4D1211yescharacteristic
312C23×C4#6711yescharacteristic
313C23×C4#6711yescharacteristic
314C23×C4#6711yescharacteristic
315C23×C4#6711yescharacteristic
316C23×C4C22×D311yescharacteristic
317C23×C4C22×D311yescharacteristic
318#123—62no—
319#123—62no—
320#123—62no—
321#123—62no—
322C22⋊Q8—61no—
323C22⋊Q8—61no—
324C22⋊Q8—61no—
325C22⋊Q8—61no—
326C22⋊Q8—61no—
327C22⋊Q8—61no—
328C22⋊Q8—61no—
329C22⋊Q8—61no—
330#121—61no—
331#121—61no—
332#121—61no—
333#121—61no—
334#121—61no—
335#121—61no—
336#121—61no—
337#121—61no—
338#120—62no—
339#120—62no—
340#120—62no—
341#120—62no—
342C4×D4—62no—
343C4×D4—62no—
344C4×D4—62no—
345C4×D4—62no—
346C4×D4—62no—
347C4×D4—62no—
348C4×D4—62no—
349C4×D4—62no—
350#117—44no—
351#117—61no—
352#117—61no—
353#117—61no—
354#117—61no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—32no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—34no—
363C2×C22⋊C4—32no—
364C2×C22⋊C4—32no—
365C2×C22⋊C4—32no—
366C2×C22⋊C4—32no—
367C2×C22⋊C4—32no—
368C2×C22⋊C4—68no—
369C2×C22⋊C4—62no—
370C2×C22⋊C4C22×D314yes—
371C2×C42—22no—
372C2×C42—32no—
373C2×C42—62no—
374C2×C42—62no—
375C2×C42—124no—
376#99—616no—
377#95—22no—
378#95—22no—
379#95—62no—
380#95—62no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—416no—
402C23×C3C2×C22⋊C411yescharacteristic
403C23×C3C2×C22⋊C411yescharacteristic
404C23×C3C2×C22⋊C411yescharacteristic
405C23×C3C2×C22⋊C411yescharacteristic
406C23×C3C23×C411yescharacteristic
407C23×C3C22×D411yescharacteristic
408C23×C3C22×D411yescharacteristic
409C23×C3C2×#4114yes—
410C22×D3—22no—
411C22×D3—24no—
412C22×D3—42no—
413C22×D3—42no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—44no—
442C2×C3×C4—44no—
443C2×C3×C4—44no—
444C2×C3×C4#9914yescomplemented
445C2×C3×C4C2×C22⋊C411yescharacteristic
446C2×C3×C4C2×C22⋊C411yescharacteristic
447C2×C3×C4C2×C22⋊C411yescharacteristic
448C2×C3×C4C2×C22⋊C411yescharacteristic
449C2×C3×C4C2×C22⋊C411yescharacteristic
450C2×C3×C4C2×C22⋊C411yescharacteristic
451C2×C3×C4C2×C22⋊C411yescharacteristic
452C2×C3×C4C2×C22⋊C411yescharacteristic
453#67—44no—
454#67—44no—
455#67—44no—
456#67—44no—
457#67—44no—
458#67—44no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—22no—
462C2×Dic3—24no—
463C2×Dic3—28no—
464C2×Dic3—44no—
465C2×Dic3—416no—
466C2×Dic3—44no—
467C2×Dic3—42no—
468C2×Dic3—42no—
469D12—42no—
470D12—42no—
471C4×D3—44no—
472C4×D3—44no—
473Dic6—42no—
474Dic6—42no—
475C24—24no—
476C24—32no—
477C24—42no—
478C24—42no—
479C24C2×C4×D311yescharacteristic
480C24C2×C4×D311yescharacteristic
481C24C2×D1211yescharacteristic
482C24C2×D1211yescharacteristic
483C24C2×#6711yescharacteristic
484C24C2×#6711yescharacteristic
485C24C23×D311yescharacteristic
486#41—124no—
487#41—124no—
488#41—124no—
489#41—124no—
490C2×Q8—61no—
491C2×Q8—61no—
492C2×Q8—122no—
493C2×D4—62no—
494C2×D4—62no—
495C2×D4—62no—
496C2×D4—62no—
497C2×D4—62no—
498C2×D4—68no—
499C2×D4—62no—
500C2×D4—61no—
501C2×D4—61no—
502C2×D4—122no—
503C2×D4—124no—
504C2×D4—124no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—32no—
510C22×C4—32no—
511C22×C4—32no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—68no—
524C22×C4—64no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—124no—
528C22×C4—124no—
529C22×C4—124no—
530C22×C4(C2×D3)⋊C411yescharacteristic
531C22×C4(C2×D3)⋊C411yescharacteristic
532C22×C4(C2×D3)⋊C411yescharacteristic
533C22×C4(C2×D3)⋊C411yescharacteristic
534C22×C4(C2×D3)⋊C411yescharacteristic
535C22×C4(C2×D3)⋊C411yescharacteristic
536C22×C4(C2×D3)⋊C411yescharacteristic
537C22×C4(C2×D3)⋊C411yescharacteristic
538C22×C4(C2×D3)⋊C411yescharacteristic
539C22×C4(C2×D3)⋊C411yescharacteristic
540C22×C4(C2×D3)⋊C411yescharacteristic
541C22×C4(C2×D3)⋊C411yescharacteristic
542C22×C4(C2×D3)⋊C411yescharacteristic
543C22×C4(C2×D3)⋊C411yescharacteristic
544C22×C4(C2×D3)⋊C411yescharacteristic
545C22×C4(C2×D3)⋊C411yescharacteristic
546C22×C4C2×C4×D311yescharacteristic
547C22×C4C2×C4×D311yescharacteristic
548C22×C4C2×C4×D311yescharacteristic
549C22×C4C2×C4×D311yescharacteristic
550C22×C4C2×D1211yescharacteristic
551C22×C4C2×D1211yescharacteristic
552C22×C4C2×D1211yescharacteristic
553C22×C4C2×D1211yescharacteristic
554C22×C4C2×#6711yescharacteristic
555C22×C4C2×#6711yescharacteristic
556C22×C4C2×#6711yescharacteristic
557C22×C4C2×#6711yescharacteristic
558C4⋊C4—44no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—62no—
564C4⋊C4—62no—
565C4⋊C4—62no—
566C4⋊C4—62no—
567C22⋊C4—28no—
568C22⋊C4—38no—
569C22⋊C4—44no—
570C22⋊C4—44no—
571C22⋊C4—68no—
572C22⋊C4—62no—
573C22⋊C4—62no—
574C22⋊C4—62no—
575C22⋊C4—62no—
576C22⋊C4—62no—
577C22⋊C4—64no—
578C22⋊C4—62no—
579C22⋊C4—62no—
580C22⋊C4—62no—
581C22⋊C4—62no—
582C22⋊C4—62no—
583C42—44no—
584C42—62no—
585C42—62no—
586C42—124no—
587C42—124no—
588C22×C3—28no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—44no—
606C22×C3—44no—
607C22×C3—44no—
608C22×C3—44no—
609C22×C3—44no—
610C22×C3—44no—
611C22×C3C2×#9912yes—
612C22×C3#41012yes—
613C22×C3C22×C22⋊C411yescharacteristic
614C22×C3C4×#4112yes—
615C22×C3#52512yes—
616C22×C3#53212yes—
617C2×D3—42no—
618C2×D3—42no—
619C2×D3—42no—
620C2×D3—84no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—84no—
628C3×C4C2×#9912yes—
629C3×C4C2×#9912yes—
630Dic3—48no—
631Dic3—42no—
632Dic3—42no—
633Dic3—42no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—416no—
655C23—62no—
656C23—64no—
657C23—122no—
658C23—122no—
659C23C2×(C2×D3)⋊C411yescharacteristic
660C23C2×(C2×D3)⋊C411yescharacteristic
661C23C2×(C2×D3)⋊C411yescharacteristic
662C23C2×(C2×D3)⋊C411yescharacteristic
663C23C22×C4×D311yescharacteristic
664C23C22×D1211yescharacteristic
665C23D3×#4114yes—
666C23C22×#6711yescharacteristic
667Q8—122no—
668Q8—122no—
669D4—122no—
670D4—124no—
671D4—124no—
672D4—124no—
673D4—124no—
674D4—124no—
675D4—124no—
676D4—122no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—64no—
708C2×C4—68no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—124no—
713C2×C4—124no—
714C2×C4—1216no—
715C2×C4—124no—
716C2×C4—124no—
717C2×C4—122no—
718C2×C4—122no—
719C2×C4#80614yescomplemented
720C2×C4C2×(C2×D3)⋊C411yescharacteristic
721C2×C4C2×(C2×D3)⋊C411yescharacteristic
722C2×C4C2×(C2×D3)⋊C411yescharacteristic
723C2×C4C2×(C2×D3)⋊C411yescharacteristic
724C2×C4C2×(C2×D3)⋊C411yescharacteristic
725C2×C4C2×(C2×D3)⋊C411yescharacteristic
726C2×C4C2×(C2×D3)⋊C411yescharacteristic
727C2×C4C2×(C2×D3)⋊C411yescharacteristic
728C2×C3—22no—
729C2×C3—22no—
730C2×C3—22no—
731C2×C3—22no—
732C2×C3—22no—
733C2×C3—41no—
734C2×C3—41no—
735C2×C3#229711yescharacteristic
736C2×C3C22×#9911yescharacteristic
737C2×C3C2×#41011yescharacteristic
738D3—82no—
739C22—28no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—122no—
763C22—122no—
764C22—122no—
765C22—244no—
766C22C2×#80612yes—
767C22#500612yes—
768C22#552212yes—
769C22#552412yes—
770C22C22×(C2×D3)⋊C411yescharacteristic
771C22#583212yes—
772C4—21no—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—84no—
779C4—128no—
780C4—122no—
781C4—122no—
782C4—122no—
783C4C2×#80612yes—
784C4C2×#80612yes—
785C3#2142011yescharacteristic, complemented, Sylow
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—242no—
794C2C22×#80611yescharacteristic
795C2#8222811yescharacteristic
796C2C2×#500611yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D3)⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×#2280C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#5791C2
cosocleC24×C3C24
hypercenter#2280D3
hypocenterC3#21420
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C3×#2280C2semidirect
3. C2×C4×#217C2semidirect
4. #69529C2semidirect
5. #69528C2semidirect
6. #69496C2semidirect
7. C4×#806C2semidirect
10. C22×#235C4semidirect
22. C2×#930C4semidirect
24. C2×#929C4semidirect
25. C2×C4×#67C4semidirect
27. C2×#926C4semidirect
28. C2×#924C4semidirect
45. #2280D3semidirect
76. C22×D12C2×C4semidirect
77. C22×C4×D3C2×C4semidirect
78. C22×Dic6C2×C4semidirect
115. C2×(C2×D3)⋊C4C2×C4semidirect
116. C2×(C2×D3)⋊C4C2×C4semidirect
121. C2×C4⋊Dic3C2×C4semidirect
122. C2×C4⋊Dic3C2×C4semidirect
131. C2×Dic3⋊C4C2×C4semidirect
132. C2×Dic3⋊C4C2×C4semidirect
136. C2×C4×Dic3C2×C4semidirect
273. #217#41semidirect
444. C2×C3×C4#99semidirect
719. C2×C4#806semidirect
785. C3#21420semidirect

Maximal subgroups

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

subgroupindex
C2×#57912
C3×#22802
C2×C4×#2172
#695292
#695282
#694962
C4×#8062
#214203