Finite Group Databasebeta

← #10972993

Subgroups — #10972993

Order 768.

2534 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#41C211yesmaximal, characteristic, complemented
2C2×#5833C211yesmaximal, characteristic
3#84087C211yesmaximal, characteristic, complemented
4#82494C212yesmaximal, complemented
5#82493C212yesmaximal, complemented
6#82406C212yesmaximal, complemented
7#82405C212yesmaximal, complemented
8#82357C214yesmaximal, complemented
9#82356C214yesmaximal, complemented
10#82288C212yesmaximal, complemented
11#82270C211yesmaximal, characteristic, complemented
12#82263C212yesmaximal, complemented
13#82234C211yesmaximal, characteristic, complemented
14#82080C212yesmaximal, complemented
15#82075C212yesmaximal, complemented
16#82070C211yesmaximal, characteristic, complemented
17C2×#4928C211yesmaximal, characteristic, complemented
18#35255—31nomaximal, Sylow
19C22×C3×#41C2211yescharacteristic
20C22×#235C2211yescharacteristic
21C3×C4×#41—28no—
22C2×C3×C4×Q8C2211yescharacteristic
23C2×C3×C4×Q8C2211yescharacteristic
24C2×C3×C4×D4C2212yes—
25C2×C3×C4×D4C2212yes—
26C2×C3×C4×D4C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×#117C2211yescharacteristic
29C2×C3×#117C2212yes—
30C22×C3×C42C2211yescharacteristic
31C22×C3×C42C2212yes—
32#5833—28no—
33C2×#946C2212yes—
34C2×#939C2214yes—
35C2×#938C2212yes—
36C2×#930C2212yes—
37C2×#929C2214yes—
38C2×#926C2211yescharacteristic
39C22×C4⋊Dic3C2211yescharacteristic
40C22×C4⋊Dic3C2211yescharacteristic
41C2×#924C2212yes—
42C22×Dic3⋊C4C2212yes—
43#5229C2212yes—
44#5221C2212yes—
45#5220C2214yes—
46#5213C2212yes—
47#5213C2212yes—
48#5213C2214yes—
49#5212C2212yes—
50#5212C2212yes—
51#5211C2214yes—
52#5210C2214yes—
53C2×C3⋊#95C2212yes—
54#4993C2214yes—
55#4992C2214yes—
56#4987C2212yes—
57#4987C2212yes—
58#4985C2214yes—
59#4983C2214yes—
60#4977C2212yes—
61#4975C2212yes—
62#4959C2214yes—
63#4959C2214yes—
64#4958C2214yes—
65#4952C2214yes—
66#4952C2214yes—
67#4946C2214yes—
68#4940C2214yes—
69#4940C2214yes—
70#4939C2212yes—
71#4939C2211yescharacteristic
72#4939C2211yescharacteristic
73C4×(C2×D3)⋊C4C2212yes—
74C4×(C2×D3)⋊C4C2212yes—
75#4933C2214yes—
76#4933C2214yes—
77#4929C2211yescharacteristic
78#4929C2212yes—
79#4929C2211yescharacteristic
80#4928C2212yes—
81#4928C2212yes—
82#4928C2212yes—
83#4928C2212yes—
84#4928C2212yes—
85#4928C2212yes—
86C2×#537—31no—
87C2×C4×#41D311yescharacteristic, complemented
88#2855—32no—
89#2854—32no—
90#2625—32no—
91#2624—32no—
92#2444—34no—
93#2443—34no—
94#2423—32no—
95#2422—32no—
96#2421—32no—
97#2420—32no—
98#2317—31no—
99#2311—31no—
100#2311—31no—
101#2297—31no—
102C2×#389—31no—
103C2×C3×#41—24no—
104C2×C3×#41—24no—
105C2×C3×#41D418yes—
106C22×C3×Q8C2311yescharacteristic
107C22×C3×D4C2312yes—
108C22×C3×D4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2312yes—
111C23×C3×C4C2312yes—
112C23×C3×C4C2311yescharacteristic
113C23×C3×C4C2312yes—
114C23×C3×C4C2311yescharacteristic
115C22×#67C2312yes—
116C22×#67C2314yes—
117C23×Dic3C2312yes—
118C23×Dic3C2312yes—
119C2×#235—24no—
120C2×#235—24no—
121C2×#235—24no—
122C22×D12C2311yescharacteristic
123C22×C4×D3C2312yes—
124C22×Dic6C2311yescharacteristic
125C3×C4×Q8—24no—
126C3×C4×Q8—24no—
127C3×C4×D4—24no—
128C3×C4×D4—24no—
129C3×C4×D4—28no—
130C3×C4×D4—28no—
131C3×#117—28no—
132C3×#117—24no—
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C4⋊C4C2312yes—
136C2×C3×C4⋊C4C2312yes—
137C2×C3×C22⋊C4C2312yes—
138C2×C3×C22⋊C4C2312yes—
139C2×C3×C22⋊C4C2312yes—
140C2×C3×C42—28no—
141C2×C3×C42—24no—
142C2×C3×C42C2311yescharacteristic
143C2×C3×C42C2312yes—
144C2×C3×C42C2311yescharacteristic
145C2×C3×C42C2311yescharacteristic
146C2×C3×C42C2311yescharacteristic
147C2×C3×C42C2312yes—
148C2×C3×C42C2312yes—
149C2×#217C2312yes—
150C2×#217C2314yes—
151C2×#217C2314yes—
152C2×#217C2314yes—
153#946—28no—
154#939—216no—
155#938—28no—
156#930—28no—
157#929—48no—
158C2×(C2×D3)⋊C4C2312yes—
159C2×(C2×D3)⋊C4C2312yes—
160C2×(C2×D3)⋊C4C2314yes—
161C2×(C2×D3)⋊C4C2312yes—
162C2×(C2×D3)⋊C4C2312yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×(C2×D3)⋊C4C2314yes—
165#926—24no—
166C2×C4⋊Dic3—24no—
167C2×C4⋊Dic3—24no—
168C2×C4⋊Dic3C2312yes—
169C2×C4⋊Dic3C2312yes—
170C2×C4⋊Dic3C2311yescharacteristic
171C2×C4⋊Dic3C2311yescharacteristic
172C2×C4⋊Dic3C2312yes—
173C2×C4⋊Dic3C2312yes—
174#924—28no—
175C2×Dic3⋊C4—44no—
176C2×Dic3⋊C4C2314yes—
177C2×Dic3⋊C4C2314yes—
178C2×Dic3⋊C4C2314yes—
179C2×Dic3⋊C4C2314yes—
180C2×Dic3⋊C4C2314yes—
181C2×C4×Dic3C2312yes—
182C3⋊#95C2314yes—
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2312yes—
187C3⋊#95C2312yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2312yes—
191C3⋊#95C2312yes—
192C3⋊#95C2314yes—
193C3⋊#95C2314yes—
194C22×#41—31no—
195C22×#41C2×D311yescharacteristic
196#537—68no—
197C2×#123—34no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—32no—
200C2×#121—32no—
201C2×#121—34no—
202C2×#121—32no—
203C4×#41—28no—
204C2×C4×Q8C2×D311yescharacteristic
205C2×C4×Q8C2×D311yescharacteristic
206C2×C4×D4C2×D311yescharacteristic
207C2×C4×D4C2×D311yescharacteristic
208C2×C4×D4C2×D312yes—
209C2×C4×D4C2×D312yes—
210C2×#117—31no—
211C2×#117C2×D311yescharacteristic
212C2×#117C2×D312yes—
213C22×C4⋊C4—31no—
214C22×C4⋊C4—31no—
215C22×C4⋊C4—32no—
216C22×C42C2×D312yes—
217C22×C42C2×D311yescharacteristic
218#400—34no—
219#399—34no—
220#398—34no—
221#397—34no—
222#397—34no—
223#397—34no—
224#394—34no—
225#394—34no—
226#391—32no—
227#391—32no—
228#391—31no—
229#391—31no—
230#390—32no—
231#390—32no—
232#390—31no—
233#390—31no—
234#389—32no—
235#389—32no—
236#389—32no—
237#389—32no—
238#389—32no—
239#389—32no—
240#388—34no—
241#388—34no—
242#387—34no—
243#387—34no—
244#386—34no—
245#386—34no—
246#386—32no—
247#386—32no—
248#386—34no—
249#385—34no—
250#385—34no—
251#384—32no—
252#382—32no—
253#381—34no—
254#380—32no—
255#380—32no—
256#380—32no—
257#380—32no—
258C4×C22⋊C4—32no—
259C4×C22⋊C4—32no—
260C2×#95—32no—
261C24×C3C2412yes—
262C24×C3C2411yescharacteristic
263C23×D3C2412yes—
264C3×#41—232no—
265C2×C3×Q8—22no—
266C2×C3×Q8—22no—
267C2×C3×Q8C2×D414yes—
268C2×C3×D4—24no—
269C2×C3×D4—24no—
270C2×C3×D4—22no—
271C2×C3×D4—22no—
272C2×C3×D4C2×D414yes—
273C2×C3×D4C2×D418yes—
274C22×C3×C4—24no—
275C22×C3×C4—24no—
276C22×C3×C4—24no—
277C22×C3×C4—24no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—24no—
282C22×C3×C4—22no—
283C22×C3×C4—24no—
284C22×C3×C4—42no—
285C22×C3×C4—41no—
286C22×C3×C4—41no—
287C22×C3×C4—42no—
288C22×C3×C4C2×D418yes—
289C22×C3×C4C2×D414yes—
290C22×C3×C4#4114yes—
291C22×C3×C4#4114yes—
292C22×C3×C4C2411yescharacteristic
293C22×C3×C4C2412yes—
294C22×C3×C4C2411yescharacteristic
295C22×C3×C4C2412yes—
296C22×C3×C4C2412yes—
297C22×C3×C4C2411yescharacteristic
298C22×C3×C4C2411yescharacteristic
299C22×C3×C4C2411yescharacteristic
300C22×C3×C4C2411yescharacteristic
301C2×#67—24no—
302C2×#67—24no—
303C2×#67—24no—
304C2×#67—28no—
305C2×#67—44no—
306C2×#67—44no—
307C22×Dic3—24no—
308C22×Dic3—24no—
309C22×Dic3—42no—
310C22×Dic3—42no—
311C22×Dic3—42no—
312C22×Dic3—42no—
313C22×Dic3C2412yes—
314C22×Dic3C2412yes—
315C22×Dic3C2412yes—
316C22×Dic3C2414yes—
317C22×Dic3C2414yes—
318#235—416no—
319C2×D12—22no—
320C2×D12—22no—
321C2×D12—22no—
322C2×C4×D3—24no—
323C2×C4×D3—24no—
324C2×C4×D3—24no—
325C2×Dic6—22no—
326C2×Dic6—22no—
327C2×Dic6—22no—
328C3×C4⋊C4—24no—
329C3×C4⋊C4—24no—
330C3×C4⋊C4—22no—
331C3×C4⋊C4—22no—
332C3×C22⋊C4—24no—
333C3×C22⋊C4—24no—
334C3×C22⋊C4—24no—
335C3×C42—22no—
336C3×C42—24no—
337C3×C42—22no—
338C3×C42—24no—
339C3×C42—24no—
340C3×C42—22no—
341C3×C42—22no—
342#217—28no—
343#217—24no—
344#217—44no—
345#217—44no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—24no—
348(C2×D3)⋊C4—24no—
349(C2×D3)⋊C4—42no—
350(C2×D3)⋊C4—42no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353C4⋊Dic3—24no—
354C4⋊Dic3—24no—
355C4⋊Dic3—24no—
356C4⋊Dic3—24no—
357C4⋊Dic3—22no—
358C4⋊Dic3—22no—
359Dic3⋊C4—28no—
360Dic3⋊C4—28no—
361Dic3⋊C4—44no—
362Dic3⋊C4—44no—
363Dic3⋊C4—44no—
364C4×Dic3—24no—
365C2×#41—24no—
366C2×#41—24no—
367C2×#41—64no—
368C2×#41—64no—
369C2×#41—64no—
370C2×#41#6718yes—
371C22×Q8—31no—
372C22×Q8C22×D311yescharacteristic
373C22×D4—32no—
374C22×D4—34no—
375C22×D4—31no—
376C22×D4C22×D312yes—
377C22×D4C22×D311yescharacteristic
378C23×C4—32no—
379C23×C4—32no—
380C23×C4—32no—
381C23×C4C22×D311yescharacteristic
382C23×C4C22×D312yes—
383C23×C4C22×D311yescharacteristic
384C23×C4C22×D312yes—
385C23×C4C22×D312yes—
386C23×C4C22×D311yescharacteristic
387#123—128no—
388C22⋊Q8—68no—
389C22⋊Q8—68no—
390#121—68no—
391#121—616no—
392#121—68no—
393C4×Q8—24no—
394C4×Q8—24no—
395C4×D4—24no—
396C4×D4—24no—
397C4×D4—28no—
398C4×D4—28no—
399#117—28no—
400#117—24no—
401#117—64no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—32no—
404C2×C4⋊C4—34no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—32no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4—31no—
409C2×C4⋊C4—34no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4—34no—
412C2×C4⋊C4—34no—
413C2×C4⋊C4—64no—
414C2×C4⋊C4—64no—
415C2×C4⋊C4—124no—
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C4⋊C4C22×D312yes—
419C2×C4⋊C4C22×D312yes—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—32no—
429C2×C22⋊C4—32no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4C22×D312yes—
432C2×C22⋊C4C22×D312yes—
433C2×C22⋊C4C22×D312yes—
434C2×C42—28no—
435C2×C42—24no—
436C2×C42—32no—
437C2×C42C22×D312yes—
438C2×C42C22×D311yescharacteristic
439C2×C42C22×D311yescharacteristic
440C2×C42C22×D311yescharacteristic
441C2×C42C22×D312yes—
442C2×C42C22×D312yes—
443C2×C42C22×D311yescharacteristic
444#95—34no—
445#95—34no—
446#95—32no—
447#95—32no—
448#95—32no—
449#95—32no—
450#95—34no—
451#95—34no—
452#95—34no—
453#95—34no—
454#95—34no—
455#95—34no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3C22×D414yes—
467C23×C3C22×D412yes—
468C23×C3C2×#4112yes—
469C23×C3C2×#4112yes—
470C23×C3C2511yescharacteristic
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—22no—
478C3×Q8—28no—
479C3×D4—216no—
480C3×D4—28no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—216no—
488C2×C3×C4—21no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—21no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—22no—
500C2×C3×C4—44no—
501C2×C3×C4—48no—
502C2×C3×C4—44no—
503C2×C3×C4—48no—
504C2×C3×C4#123116yescomplemented
505C2×C3×C4C22×D414yes—
506C2×C3×C4C22×D412yes—
507C2×C3×C4C22×D412yes—
508C2×C3×C4C2×#4112yes—
509C2×C3×C4C2×#4112yes—
510C2×C3×C4C2×#4112yes—
511C2×C3×C4C2×#4112yes—
512C2×C3×C4H(5,𝔽2)12yes—
513C2×C3×C42−1+412yes—
514#67—48no—
515#67—88no—
516C2×Dic3—22no—
517C2×Dic3—24no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—24no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—24no—
524C2×Dic3—24no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—24no—
529C2×Dic3—22no—
530C2×Dic3—24no—
531C2×Dic3—48no—
532C2×Dic3—84no—
533D12—44no—
534C4×D3—48no—
535Dic6—44no—
536C24—32no—
537C24C23×D312yes—
538C24C23×D311yescharacteristic
539#41—232no—
540#41—1216no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—62no—
544C2×Q8—62no—
545C2×Q8—62no—
546C2×Q8C2×#6714yes—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—64no—
552C2×D4—64no—
553C2×D4—64no—
554C2×D4—68no—
555C2×D4—62no—
556C2×D4—62no—
557C2×D4—62no—
558C2×D4—124no—
559C2×D4—124no—
560C2×D4C2×#6718yes—
561C2×D4C2×#6714yes—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—32no—
573C22×C4—32no—
574C22×C4—32no—
575C22×C4—34no—
576C22×C4—34no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—64no—
582C22×C4—64no—
583C22×C4—64no—
584C22×C4—64no—
585C22×C4—64no—
586C22×C4—122no—
587C22×C4—122no—
588C22×C4—122no—
589C22×C4—122no—
590C22×C4#23514yes—
591C22×C4#23514yes—
592C22×C4C2×#6718yes—
593C22×C4C2×#6714yes—
594C22×C4C23×D311yescharacteristic
595C22×C4C23×D312yes—
596C22×C4C23×D312yes—
597C22×C4C23×D311yescharacteristic
598C22×C4C23×D311yescharacteristic
599C22×C4C23×D311yescharacteristic
600C22×C4C23×D312yes—
601C22×C4C23×D311yescharacteristic
602C22×C4C23×D311yescharacteristic
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—64no—
608C4⋊C4—64no—
609C4⋊C4—62no—
610C4⋊C4—62no—
611C4⋊C4—68no—
612C4⋊C4—64no—
613C4⋊C4—64no—
614C4⋊C4—68no—
615C4⋊C4—124no—
616C4⋊C4—124no—
617C4⋊C4—124no—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—64no—
622C22⋊C4—68no—
623C22⋊C4—64no—
624C22⋊C4—64no—
625C22⋊C4—68no—
626C22⋊C4—124no—
627C22⋊C4—122no—
628C22⋊C4—124no—
629C22⋊C4—122no—
630C22⋊C4—124no—
631C22⋊C4—124no—
632C42—22no—
633C42—24no—
634C42—22no—
635C42—24no—
636C42—24no—
637C42—22no—
638C42—22no—
639C42—64no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—22no—
646C22×C3—24no—
647C22×C3—24no—
648C22×C3—24no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3C2×#12314yes—
654C22×C3C23×D411yescharacteristic
655C22×C3C22×#4111yescharacteristic
656C22×C3C22×#4111yescharacteristic
657C22×C3C2×H(5,𝔽2)11yescharacteristic
658C22×C3C2×2−1+411yescharacteristic
659C22×C3#58511yescharacteristic
660C22×C3#58511yescharacteristic
661C2×D3—42no—
662C2×D3—42no—
663C2×D3—42no—
664C2×D3—42no—
665C2×D3—42no—
666C2×D3—42no—
667C2×D3—42no—
668C3×C4—24no—
669C3×C4—22no—
670C3×C4—22no—
671C3×C4—41no—
672C3×C4—42no—
673C3×C4—41no—
674C3×C4—42no—
675C3×C4C2×#12314yes—
676C3×C4C2×#12314yes—
677Dic3—42no—
678Dic3—44no—
679Dic3—44no—
680Dic3—42no—
681Dic3—42no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—62no—
693C23—62no—
694C23—62no—
695C23—62no—
696C23—62no—
697C23—62no—
698C23—62no—
699C23C2×#23512yes—
700C23C2×#23512yes—
701C23C22×#6714yes—
702C23C22×#6712yes—
703C23C24×D311yescharacteristic
704Q8—28no—
705Q8—124no—
706D4—216no—
707D4—28no—
708D4—128no—
709D4—124no—
710D4—248no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—216no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—44no—
731C2×C4—48no—
732C2×C4—44no—
733C2×C4—48no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—64no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—64no—
741C2×C4—64no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—64no—
745C2×C4—62no—
746C2×C4—64no—
747C2×C4—64no—
748C2×C4—62no—
749C2×C4—128no—
750C2×C4—128no—
751C2×C4—244no—
752C2×C4#929116yescomplemented
753C2×C4C2×#23512yes—
754C2×C4C2×#23512yes—
755C2×C4C2×#23512yes—
756C2×C4C2×#23512yes—
757C2×C4#100912yes—
758C2×C4#101012yes—
759C2×C4C22×#6714yes—
760C2×C4C22×#6712yes—
761C2×C4C22×#6712yes—
762C2×C3—24no—
763C2×C3—44no—
764C2×C3C22×#12311yescharacteristic
765C2×C3#346011yescharacteristic
766C2×C3#346111yescharacteristic
767C2×C3#348811yescharacteristic
768C2×C3#348911yescharacteristic
769C2×C3#351111yescharacteristic
770C2×C3#351211yescharacteristic
771D3—82no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—122no—
786C22—122no—
787C22—122no—
788C22—122no—
789C22—122no—
790C22—122no—
791C22—122no—
792C22C2×#92914yes—
793C22C22×#23511yescharacteristic
794C22C22×#23511yescharacteristic
795C22C2×#100911yescharacteristic
796C22C2×#101011yescharacteristic
797C22#596411yescharacteristic
798C22#596411yescharacteristic
799C22C23×#6711yescharacteristic
800C4—24no—
801C4—22no—
802C4—22no—
803C4—41no—
804C4—42no—
805C4—42no—
806C4—41no—
807C4—124no—
808C4—122no—
809C4—122no—
810C4—122no—
811C4—124no—
812C4C2×#92914yes—
813C4C2×#92914yes—
814C3#3525511yescharacteristic, complemented, Sylow
815C2—24no—
816C2—44no—
817C2—242no—
818C2#8582311yescharacteristic
819C2#8583811yescharacteristic
820C2#8585011yescharacteristic
821C2#8585111yescharacteristic
822C2C22×#92911yescharacteristic
823C2#8726411yescharacteristic
824C2#8727511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×C4×#41C2
prime radicalC2×#5833C2
hypercenterC2×C4×#41D3
hypocenterC3#35255
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×#41C2semidirect
3. #84087C2semidirect
4. #82494C2semidirect
5. #82493C2semidirect
6. #82406C2semidirect
7. #82405C2semidirect
8. #82357C2semidirect
9. #82356C2semidirect
10. #82288C2semidirect
11. #82270C2semidirect
12. #82263C2semidirect
13. #82234C2semidirect
14. #82080C2semidirect
15. #82075C2semidirect
16. #82070C2semidirect
17. C2×#4928C2semidirect
87. C2×C4×#41D3semidirect
504. C2×C3×C4#123semidirect
752. C2×C4#929semidirect
814. C3#35255semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#412
C2×#58332
#840872
#824942
#824932
#824062
#824052
#823572
#823562
#822882
#822702
#822632
#822342
#820802
#820752
#820702
C2×#49282
#352553