Finite Group Databasebeta

← #10800218

Subgroups — #10800218

Order 768.

1164 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85836C211yesmaximal, characteristic
2C4×D3×M16C211yesmaximal, characteristic, complemented
3#73413C211yesmaximal, characteristic, complemented
4C3×#1759C211yesmaximal, characteristic, complemented
5#71643C211yesmaximal, characteristic, complemented
6#70381C212yesmaximal, complemented
7#70358C212yesmaximal, complemented
8#69866C211yesmaximal, characteristic, complemented
9#69430C211yesmaximal, characteristic, complemented
10#68755C212yesmaximal, complemented
11#68730C212yesmaximal, complemented
12#21383—31nomaximal, Sylow
13C3×C4×#41C2211yescharacteristic
14#5832C2211yescharacteristic
15#5828C2211yescharacteristic
16C2×D3×M16C2212yes—
17#5580C411yescharacteristic, complemented
18#5580C411yescharacteristic, complemented
19#5578C411yescharacteristic, complemented
20#5578C411yescharacteristic, complemented
21#5557C411yescharacteristic, complemented
22#5557C411yescharacteristic, complemented
23#5548C411yescharacteristic, complemented
24#5548C411yescharacteristic, complemented
25#5547—21no—
26#5547—21no—
27#5538—21no—
28#5538—21no—
29#5528—21no—
30#5528—21no—
31#5524C2211yescharacteristic
32#5517C2211yescharacteristic
33C4×#235—21no—
34C4×#235—21no—
35C4×#235C2211yescharacteristic
36C2×C42×D3C2211yescharacteristic
37C2×C3×#104C2212yes—
38C3×C4×M16C2211yescharacteristic
39C3×#376C2211yescharacteristic
40C2×#837C2212yes—
41C2×#825C2212yes—
42Dic3×M16C2212yes—
43C4×(C2×D3)⋊C4C2212yes—
44#4932C2211yescharacteristic
45C4×Dic3⋊C4C2212yes—
46C2×#805C2212yes—
47C4×#208C2211yescharacteristic
48#4707—21no—
49D3×#97—21no—
50C4×ΓL(1,𝔽25)—21no—
51C4×D3×C8—21no—
52#4667—21no—
53#4664—21no—
54#4651—21no—
55#4650—21no—
56C3×#339C2212yes—
57#4555C2212yes—
58#4532C2212yes—
59#4523C2212yes—
60#3444—31no—
61C2×C4×M16—31no—
62#2283—31no—
63#1986—32no—
64#1980—32no—
65#1871—32no—
66#1871—32no—
67#1759—31no—
68#1759—31no—
69#1759—31no—
70#1759D311yescharacteristic, complemented
71C2×C3×#41C2311yescharacteristic
72C2×#235—21no—
73C2×#235—21no—
74C2×#235C2311yescharacteristic
75C22×C4×D3D411yescharacteristic
76C22×C4×D3D411yescharacteristic
77C22×C4×D3C2311yescharacteristic
78C2×C3×M16C2312yes—
79C3×C4×Q8C2×C411yescharacteristic
80C3×C4×Q8C2×C411yescharacteristic
81C3×C4×D4—21no—
82C3×C4×D4—21no—
83C3×C4×D4C2×C411yescharacteristic
84C3×C4×D4C2×C411yescharacteristic
85C3×#117—21no—
86C3×#117C2311yescharacteristic
87C2×C3×C42—21no—
88C2×C3×C42C2312yes—
89C2×C3×C42C2311yescharacteristic
90#947C2×C411yescharacteristic
91#946C2×C411yescharacteristic
92#946C2×C411yescharacteristic
93#944C2×C411yescharacteristic
94#940C2×C411yescharacteristic
95#939—21no—
96#939—21no—
97#938C2×C411yescharacteristic
98#938C2×C411yescharacteristic
99#937—21no—
100#936C2×C411yescharacteristic
101#935—21no—
102C4×#67—21no—
103C4×#67—21no—
104C4×#67—21no—
105C4×#67—21no—
106C4×#67—21no—
107C4×#67—21no—
108C4×#67—21no—
109C4×#67—21no—
110C4×#67—21no—
111C4×#67—21no—
112C2×(C2×D3)⋊C4—22no—
113#926—21no—
114#926—21no—
115#926C2311yescharacteristic
116C2×Dic3⋊C4—22no—
117C2×C4×Dic3D411yescharacteristic
118C2×C4×Dic3D411yescharacteristic
119C2×C4×Dic3C2312yes—
120C2×C4×Dic3C2311yescharacteristic
121C2×#208C2312yes—
122D3×M16—24no—
123D3×M16—24no—
124C2×ΓL(1,𝔽25)—22no—
125C2×D3×C8—22no—
126#898—21no—
127#898—21no—
128#897C2×C411yescharacteristic
129#897C2×C411yescharacteristic
130#896—21no—
131#896—21no—
132#895C2×C411yescharacteristic
133#895C2×C411yescharacteristic
134#894—21no—
135#894—21no—
136#890C2×C411yescharacteristic
137#890C2×C411yescharacteristic
138#889—21no—
139#889—21no—
140#888C2×C411yescharacteristic
141#888C2×C411yescharacteristic
142#886—21no—
143#885—21no—
144#885—21no—
145#884—21no—
146#884—21no—
147#883—21no—
148#883—21no—
149#882—21no—
150#879—21no—
151#879—21no—
152#878—21no—
153#878—21no—
154C4×D12—21no—
155C4×D12—21no—
156C4×D12—21no—
157C4×D12—21no—
158C4×D12C2×C411yescharacteristic
159C4×D12C2×C411yescharacteristic
160#872—21no—
161#872—21no—
162#872—21no—
163#872—21no—
164#872—21no—
165C42×D3—21no—
166C42×D3C2×C411yescharacteristic
167C42×D3C2×C411yescharacteristic
168C42×D3C2×C411yescharacteristic
169C42×D3C2×C411yescharacteristic
170C42×D3D411yescharacteristic
171C42×D3D411yescharacteristic
172C42×D3D411yescharacteristic
173C42×D3D411yescharacteristic
174C4×Dic6—21no—
175C4×Dic6—21no—
176C4×Dic6—21no—
177C4×Dic6—21no—
178C4×Dic6C2×C411yescharacteristic
179C4×Dic6C2×C411yescharacteristic
180C3×#104—24no—
181C3×#97—21no—
182C3×C4×C8—21no—
183C3×#95—21no—
184C3×#95—21no—
185#837—24no—
186C3⋊#95—21no—
187C3⋊#95—21no—
188C3⋊#95—22no—
189C3⋊#95—22no—
190#825—24no—
191#815—22no—
192C8×Dic3—22no—
193#805—24no—
194#803—21no—
195C4×C3⋊C8—21no—
196C22×M16—32no—
197#533—31no—
198#533—31no—
199#533—31no—
200#532—31no—
201#532—31no—
202#532—31no—
203#529—31no—
204#529—31no—
205#529—31no—
206#529—31no—
207#529—61no—
208#529—61no—
209#529—61no—
210#529—61no—
211#525—31no—
212#525—31no—
213#525—61no—
214#525—61no—
215C4×#41—31no—
216C4×#41—61no—
217C4×#41—61no—
218C4×#41C2×D311yescharacteristic
219C22×C42—31no—
220C2×#104—32no—
221C2×#104—32no—
222C2×#104—32no—
223C2×#104C2×D312yes—
224C4×M16—32no—
225C4×M16—31no—
226C4×M16—61no—
227C4×M16—61no—
228C4×M16C2×D311yescharacteristic
229C2×#97—61no—
230C2×C4×C8—61no—
231#383—61no—
232#382—61no—
233#381—61no—
234#380—61no—
235C4×C4⋊C4—32no—
236C4×C22⋊C4—32no—
237#376—31no—
238#376C2×D311yescharacteristic
239#339—32no—
240#339—32no—
241#339—32no—
242#339C2×D312yes—
243C23×D3C2×D411yescharacteristic
244C3×#41—22no—
245C3×#41—22no—
246C2×C3×Q8C22×C411yescharacteristic
247C2×C3×D4—21no—
248C2×C3×D4C22×C411yescharacteristic
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—22no—
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2411yescharacteristic
256C2×#67—21no—
257C2×#67—21no—
258C2×#67—21no—
259C2×#67—21no—
260C2×#67—21no—
261C22×Dic3—22no—
262C22×Dic3C2×D411yescharacteristic
263C22×Dic3C2×D411yescharacteristic
264C22×Dic3C2×D411yescharacteristic
265#235—22no—
266#235—22no—
267#235—44no—
268#235—44no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12C22×C411yescharacteristic
272C2×C4×D3—22no—
273C2×C4×D3—22no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—42no—
278C2×C4×D3—42no—
279C2×C4×D3C22⋊C411yescharacteristic
280C2×C4×D3C22⋊C411yescharacteristic
281C2×C4×D3C22⋊C411yescharacteristic
282C2×C4×D3C22⋊C411yescharacteristic
283C2×C4×D3C22⋊C411yescharacteristic
284C2×C4×D3C22⋊C411yescharacteristic
285C2×C4×D3C22⋊C411yescharacteristic
286C2×C4×D3C22⋊C411yescharacteristic
287C2×C4×D3C22×C411yescharacteristic
288C2×C4×D3C22×C411yescharacteristic
289C2×C4×D3C2×D411yescharacteristic
290C2×C4×D3C2×D411yescharacteristic
291C2×Dic6—21no—
292C2×Dic6—21no—
293C2×Dic6C22×C411yescharacteristic
294C3×M16—22no—
295C3×M16#4114yescomplemented
296C2×C3×C8—22no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4C22×C411yescharacteristic
300C3×C4⋊C4C22×C411yescharacteristic
301C3×C22⋊C4—21no—
302C3×C22⋊C4—21no—
303C3×C22⋊C4—21no—
304C3×C42—21no—
305C3×C42—21no—
306C3×C42—21no—
307C3×C42—22no—
308C3×C42—22no—
309C3×C42C22×C411yescharacteristic
310C3×C42C22×C411yescharacteristic
311C3×C42C2×D411yescharacteristic
312C3×C42C2×D411yescharacteristic
313#217—21no—
314#217—21no—
315#217—21no—
316#217—21no—
317#217—21no—
318(C2×D3)⋊C4—21no—
319(C2×D3)⋊C4—21no—
320(C2×D3)⋊C4—21no—
321(C2×D3)⋊C4—21no—
322(C2×D3)⋊C4—21no—
323(C2×D3)⋊C4—21no—
324(C2×D3)⋊C4—21no—
325(C2×D3)⋊C4—21no—
326(C2×D3)⋊C4—21no—
327(C2×D3)⋊C4—21no—
328(C2×D3)⋊C4—44no—
329C4⋊Dic3—21no—
330C4⋊Dic3—21no—
331C4⋊Dic3—21no—
332C4⋊Dic3—21no—
333C4⋊Dic3C22×C411yescharacteristic
334C4⋊Dic3C22×C411yescharacteristic
335Dic3⋊C4—21no—
336Dic3⋊C4—21no—
337Dic3⋊C4—21no—
338Dic3⋊C4—21no—
339Dic3⋊C4—21no—
340Dic3⋊C4—21no—
341Dic3⋊C4—21no—
342Dic3⋊C4—21no—
343Dic3⋊C4—21no—
344Dic3⋊C4—21no—
345Dic3⋊C4—44no—
346C4×Dic3—21no—
347C4×Dic3—21no—
348C4×Dic3—21no—
349C4×Dic3—22no—
350C4×Dic3—22no—
351C4×Dic3C22⋊C411yescharacteristic
352C4×Dic3C22⋊C411yescharacteristic
353C4×Dic3C22⋊C411yescharacteristic
354C4×Dic3C22⋊C411yescharacteristic
355C4×Dic3C22⋊C411yescharacteristic
356C4×Dic3C22⋊C411yescharacteristic
357C4×Dic3C22⋊C411yescharacteristic
358C4×Dic3C22⋊C411yescharacteristic
359C4×Dic3C22×C411yescharacteristic
360C4×Dic3C22×C411yescharacteristic
361C4×Dic3C2×D411yescharacteristic
362C4×Dic3C2×D411yescharacteristic
363#208—22no—
364#208#4114yescomplemented
365C2×C3⋊C8—22no—
366ΓL(1,𝔽25)—28no—
367D3×C8—28no—
368C2×#41—31no—
369C2×#41—61no—
370C2×#41—61no—
371C2×#41C22×D311yescharacteristic
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—31no—
375C2×M16—32no—
376C2×M16—62no—
377C2×M16—64no—
378C2×M16—64no—
379C2×M16C22×D312yes—
380C22×C8—62no—
381C4⋊Q8—31no—
382C4⋊Q8—31no—
383C4⋊Q8—31no—
384#127—31no—
385#126—61no—
386#126—61no—
387#126—61no—
388#126—61no—
389#125—31no—
390#125—31no—
391#125—61no—
392#125—61no—
393#124—31no—
394#124—31no—
395#124—61no—
396#124—61no—
397#123—61no—
398#123—61no—
399#123—61no—
400#123—61no—
401#123—61no—
402#123—61no—
403C22⋊Q8—31no—
404C22⋊Q8—31no—
405C22⋊Q8—31no—
406C22⋊Q8—31no—
407C22⋊Q8—61no—
408C22⋊Q8—61no—
409C22⋊Q8—61no—
410C22⋊Q8—61no—
411#121—31no—
412#121—31no—
413#121—31no—
414#121—31no—
415#121—61no—
416#121—61no—
417#121—61no—
418#121—61no—
419#120—61no—
420#120—61no—
421C4×Q8—31no—
422C4×Q8—31no—
423C4×Q8—61no—
424C4×Q8—61no—
425C4×Q8—61no—
426C4×Q8—61no—
427C4×Q8C4×D311yescharacteristic
428C4×Q8C4×D311yescharacteristic
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—31no—
432C4×D4—31no—
433C4×D4—61no—
434C4×D4—61no—
435C4×D4—61no—
436C4×D4—61no—
437C4×D4—61no—
438C4×D4—61no—
439C4×D4—61no—
440C4×D4—61no—
441C4×D4—61no—
442C4×D4—61no—
443C4×D4—61no—
444C4×D4—61no—
445C4×D4—61no—
446C4×D4—61no—
447C4×D4C4×D311yescharacteristic
448C4×D4C4×D311yescharacteristic
449#117—21no—
450#117—31no—
451#117—61no—
452#117—61no—
453#117—61no—
454#117—61no—
455#117—61no—
456#117—61no—
457#117—61no—
458#117C22×D311yescharacteristic
459C2×C4⋊C4—62no—
460C2×C22⋊C4—62no—
461C2×C42—21no—
462C2×C42—31no—
463C2×C42—31no—
464C2×C42—31no—
465C2×C42—31no—
466C2×C42—31no—
467C2×C42—31no—
468C2×C42—31no—
469C2×C42—31no—
470C2×C42—31no—
471C2×C42—31no—
472C2×C42—31no—
473C2×C42—32no—
474C2×C42—61no—
475C2×C42C22×D312yes—
476C2×C42C22×D311yescharacteristic
477#104—24no—
478#104—64no—
479#104—64no—
480#104—64no—
481#97—21no—
482#97—62no—
483#97—61no—
484C4×C8—21no—
485C4×C8—62no—
486C4×C8—61no—
487#95—21no—
488#95—21no—
489#95—62no—
490#95—62no—
491#95—61no—
492#95—61no—
493C23×C3—21no—
494C23×C3C22×D411yescharacteristic
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—21no—
498C22×D3—41no—
499C22×D3C2×C22⋊C411yescharacteristic
500C22×D3C2×C22⋊C411yescharacteristic
501C3×Q8—21no—
502C3×Q8—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—42no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—42no—
512C2×C3×C4—42no—
513C2×C3×C4—42no—
514C2×C3×C4—42no—
515C2×C3×C4—42no—
516C2×C3×C4—42no—
517C2×C3×C4C2×C22⋊C411yescharacteristic
518C2×C3×C4C2×C22⋊C411yescharacteristic
519C2×C3×C4C2×C22⋊C411yescharacteristic
520C2×C3×C4C2×C22⋊C411yescharacteristic
521C2×C3×C4C23×C411yescharacteristic
522C2×C3×C4C22×D411yescharacteristic
523C2×C3×C4C2×#4112yes—
524C2×C3×C4C2×#4112yes—
525#67—42no—
526#67—42no—
527#67—42no—
528#67—42no—
529#67—42no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—41no—
536C2×Dic3—42no—
537C2×Dic3—42no—
538C2×Dic3—42no—
539C2×Dic3C2×C22⋊C411yescharacteristic
540C2×Dic3C2×C22⋊C411yescharacteristic
541C2×Dic3C2×C22⋊C411yescharacteristic
542C2×Dic3C2×C22⋊C411yescharacteristic
543C2×Dic3C2×C22⋊C411yescharacteristic
544C2×Dic3C2×C22⋊C411yescharacteristic
545D12—21no—
546D12—21no—
547D12—42no—
548D12—42no—
549C4×D3—22no—
550C4×D3—22no—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—22no—
556C4×D3—22no—
557C4×D3—22no—
558C4×D3—22no—
559C4×D3—41no—
560C4×D3—41no—
561C4×D3—41no—
562C4×D3—41no—
563C4×D3—42no—
564C4×D3—42no—
565C4×D3—42no—
566Dic6—21no—
567Dic6—21no—
568Dic6—42no—
569Dic6—42no—
570C3×C8—24no—
571C3⋊C8—24no—
572C24—31no—
573#41—22no—
574#41—22no—
575#41—62no—
576#41—62no—
577#41—124no—
578#41—124no—
579C2×Q8—31no—
580C2×Q8—61no—
581C2×Q8—61no—
582C2×Q8C2×C4×D311yescharacteristic
583C2×D4—21no—
584C2×D4—31no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4C2×C4×D311yescharacteristic
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—62no—
613C22×C4—62no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—62no—
618C22×C4—122no—
619C22×C4—122no—
620C22×C4D3×D411yescharacteristic
621C22×C4D3×D411yescharacteristic
622C22×C4C23×D311yescharacteristic
623M16—22no—
624M16—34no—
625M16—68no—
626M16—62no—
627M16#23514yescomplemented
628C2×C8—22no—
629C2×C8—68no—
630C2×C8—62no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—31no—
634C4⋊C4—31no—
635C4⋊C4—61no—
636C4⋊C4—61no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—124no—
650C4⋊C4C2×C4×D311yescharacteristic
651C4⋊C4C2×C4×D311yescharacteristic
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—61no—
656C22⋊C4—61no—
657C22⋊C4—61no—
658C22⋊C4—61no—
659C22⋊C4—61no—
660C22⋊C4—61no—
661C22⋊C4—61no—
662C22⋊C4—61no—
663C22⋊C4—61no—
664C22⋊C4—61no—
665C22⋊C4—61no—
666C22⋊C4—61no—
667C22⋊C4—61no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—124no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—22no—
675C42—22no—
676C42—31no—
677C42—31no—
678C42—31no—
679C42—31no—
680C42—31no—
681C42—31no—
682C42—31no—
683C42—31no—
684C42—31no—
685C42—31no—
686C42—31no—
687C42—31no—
688C42—61no—
689C42—61no—
690C42—61no—
691C42—62no—
692C42—62no—
693C42C2×C4×D311yescharacteristic
694C42C2×C4×D311yescharacteristic
695C42D3×D411yescharacteristic
696C42D3×D411yescharacteristic
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3C22×C22⋊C411yescharacteristic
703C22×C3#53212yes—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—44no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3#42112yes—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—82no—
722C3×C4C4×#4111yescharacteristic
723C3×C4C4×#4111yescharacteristic
724C3×C4#52512yes—
725Dic3—21no—
726Dic3—21no—
727Dic3—21no—
728Dic3—21no—
729Dic3—21no—
730Dic3—41no—
731Dic3—41no—
732Dic3—41no—
733Dic3—82no—
734Dic3#42112yes—
735C23—21no—
736C23—31no—
737C23—31no—
738C23—62no—
739C23—62no—
740C23—61no—
741C23—121no—
742C23C2×D3×D411yescharacteristic
743Q8—21no—
744Q8—21no—
745Q8—61no—
746Q8—61no—
747Q8—122no—
748Q8—122no—
749D4—21no—
750D4—21no—
751D4—42no—
752D4—61no—
753D4—61no—
754D4—122no—
755D4—122no—
756D4—122no—
757D4—122no—
758D4—122no—
759D4—122no—
760D4—122no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—31no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—31no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—122no—
798C2×C4—122no—
799C2×C4—121no—
800C2×C4—122no—
801C2×C4—122no—
802C2×C4—122no—
803C2×C4—122no—
804C2×C4D3×C22⋊C411yescharacteristic
805C2×C4D3×C22⋊C411yescharacteristic
806C2×C4D3×C22⋊C411yescharacteristic
807C2×C4D3×C22⋊C411yescharacteristic
808C2×C4C22×C4×D311yescharacteristic
809C2×C4C2×#23512yes—
810C2×C4C2×D3×D411yescharacteristic
811C2×C4D3×#4112yes—
812C8—24no—
813C8—64no—
814C2×C3—22no—
815C2×C3—81no—
816C2×C3#229711yescharacteristic
817C2×C3C2×#42111yescharacteristic
818C2×C3C2×#42111yescharacteristic
819D3—22no—
820D3—41no—
821D3—81no—
822C22—21no—
823C22—21no—
824C22—32no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—61no—
829C22—61no—
830C22—61no—
831C22—61no—
832C22—61no—
833C22—124no—
834C22—121no—
835C22—121no—
836C22—121no—
837C22C2×D3×C22⋊C411yescharacteristic
838C22#554812yes—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—32no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—61no—
848C4—61no—
849C4—61no—
850C4—61no—
851C4—61no—
852C4—82no—
853C4—121no—
854C4—121no—
855C4—121no—
856C4—242no—
857C4C4×#23511yescharacteristic
858C4#552211yescharacteristic
859C4#554712yes—
860C3#2138311yescharacteristic, complemented, Sylow
861C2—22no—
862C2—62no—
863C2—81no—
864C2—121no—
865C2—241no—
866C2#7356311yescharacteristic
867C2D3×#42111yescharacteristic
868C2D3×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1759C2
socleC22×C3C22×C22⋊C4
prime radical#85836C2
cosocleC22×C3×C4C24
hypercenter#1759D3
hypocenterC3#21383
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. C4×D3×M16C2semidirect
3. #73413C2semidirect
4. C3×#1759C2semidirect
5. #71643C2semidirect
6. #70381C2semidirect
7. #70358C2semidirect
8. #69866C2semidirect
9. #69430C2semidirect
10. #68755C2semidirect
11. #68730C2semidirect
17. #5580C4semidirect
18. #5580C4semidirect
19. #5578C4semidirect
20. #5578C4semidirect
21. #5557C4semidirect
22. #5557C4semidirect
23. #5548C4semidirect
24. #5548C4semidirect
70. #1759D3semidirect
295. C3×M16#41semidirect
364. #208#41semidirect
627. M16#235semidirect
860. C3#21383semidirect

Maximal subgroups

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

subgroupindex
#858362
C4×D3×M162
#734132
C3×#17592
#716432
#703812
#703582
#698662
#694302
#687552
#687302
#213833