Finite Group Databasebeta

← #10800211

Subgroups — #10800211

Order 768.

1256 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85836C211yesmaximal, characteristic
2C4×D3×M16C211yesmaximal, characteristic, complemented
3C4×#872C211yesmaximal, characteristic, complemented
4C3×C4×#104C211yesmaximal, characteristic, complemented
5C4×#837C211yesmaximal, characteristic, complemented
6#70381C212yesmaximal, complemented
7#70358C212yesmaximal, complemented
8C4×#825C211yesmaximal, characteristic, complemented
9C4×#805C211yesmaximal, characteristic, complemented
10#68755C212yesmaximal, complemented
11#68730C212yesmaximal, complemented
12#21382—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×#872—21no—
37C2×C42×D3C2211yescharacteristic
38C2×C3×#104C2212yes—
39C3×C4×M16C2211yescharacteristic
40C3×C43C2211yescharacteristic
41C2×#837C2212yes—
42C2×#825C2212yes—
43Dic3×M16C2212yes—
44C4×(C2×D3)⋊C4—21no—
45C4×(C2×D3)⋊C4C2212yes—
46#4932—21no—
47C4×Dic3⋊C4—21no—
48C4×Dic3⋊C4C2212yes—
49C42×Dic3C2211yescharacteristic
50C2×#805C2212yes—
51C4×#208C2211yescharacteristic
52#4707—21no—
53D3×#97—21no—
54C4×ΓL(1,𝔽25)—21no—
55C4×D3×C8—21no—
56C3×#339C2212yes—
57#4555C2212yes—
58#4532C2212yes—
59#4523C2212yes—
60#3444—31no—
61C2×C4×M16—31no—
62C4×#117—31no—
63#1986—32no—
64#1980—32no—
65#1871—32no—
66#1871—32no—
67C4×#104—31no—
68C4×#104—31no—
69C4×#104—31no—
70C4×#104D311yescharacteristic, 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×C42—21no—
89C2×C3×C42—21no—
90C2×C3×C42C2312yes—
91C2×C3×C42C2311yescharacteristic
92#947C2×C411yescharacteristic
93#946C2×C411yescharacteristic
94#946C2×C411yescharacteristic
95#944C2×C411yescharacteristic
96#940C2×C411yescharacteristic
97#939—21no—
98#939—21no—
99#938C2×C411yescharacteristic
100#938C2×C411yescharacteristic
101#937—21no—
102#936C2×C411yescharacteristic
103#935—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—
112C4×#67—21no—
113C4×#67—21no—
114C2×(C2×D3)⋊C4—22no—
115#926—21no—
116#926—21no—
117#926C2311yescharacteristic
118C2×Dic3⋊C4—22no—
119C2×C4×Dic3—21no—
120C2×C4×Dic3—21no—
121C2×C4×Dic3D411yescharacteristic
122C2×C4×Dic3D411yescharacteristic
123C2×C4×Dic3C2312yes—
124C2×C4×Dic3C2311yescharacteristic
125C2×#208C2312yes—
126D3×M16—24no—
127D3×M16—24no—
128C2×ΓL(1,𝔽25)—22no—
129C2×D3×C8—22no—
130#898—21no—
131#898—21no—
132#897C2×C411yescharacteristic
133#897C2×C411yescharacteristic
134#896—21no—
135#896—21no—
136#895C2×C411yescharacteristic
137#895C2×C411yescharacteristic
138#894—21no—
139#894—21no—
140#890C2×C411yescharacteristic
141#890C2×C411yescharacteristic
142#889—21no—
143#889—21no—
144#888C2×C411yescharacteristic
145#888C2×C411yescharacteristic
146#886—21no—
147#885—21no—
148#885—21no—
149#884—21no—
150#884—21no—
151#883—21no—
152#883—21no—
153#882—21no—
154#879—21no—
155#879—21no—
156#878—21no—
157#878—21no—
158C4×D12—21no—
159C4×D12—21no—
160C4×D12—21no—
161C4×D12—21no—
162C4×D12C2×C411yescharacteristic
163C4×D12C2×C411yescharacteristic
164#872—28no—
165#872—21no—
166#872—21no—
167#872—21no—
168#872—21no—
169#872—21no—
170C42×D3—21no—
171C42×D3C2×C411yescharacteristic
172C42×D3C2×C411yescharacteristic
173C42×D3C2×C411yescharacteristic
174C42×D3C2×C411yescharacteristic
175C42×D3D411yescharacteristic
176C42×D3D411yescharacteristic
177C42×D3D411yescharacteristic
178C42×D3D411yescharacteristic
179C4×Dic6—21no—
180C4×Dic6—21no—
181C4×Dic6—21no—
182C4×Dic6—21no—
183C4×Dic6C2×C411yescharacteristic
184C4×Dic6C2×C411yescharacteristic
185C3×#104—24no—
186C3×#97—21no—
187C3×C4×C8—21no—
188#837—24no—
189C3⋊#95—22no—
190C3⋊#95—22no—
191#825—24no—
192#815—22no—
193C8×Dic3—22no—
194#805—24no—
195#803—21no—
196C4×C3⋊C8—21no—
197C22×M16—32no—
198#533—31no—
199#533—31no—
200#533—31no—
201#532—31no—
202#532—31no—
203#532—31no—
204#529—31no—
205#529—31no—
206#529—31no—
207#529—31no—
208#529—61no—
209#529—61no—
210#529—61no—
211#529—61no—
212#525—31no—
213#525—31no—
214#525—61no—
215#525—61no—
216C4×#41—31no—
217C4×#41—61no—
218C4×#41—61no—
219C4×#41C2×D311yescharacteristic
220C2×#117—61no—
221C22×C42—31no—
222C2×#104—32no—
223C2×#104—32no—
224C2×#104—32no—
225C2×#104C2×D312yes—
226C4×M16—32no—
227C4×M16—31no—
228C4×M16—61no—
229C4×M16—61no—
230C4×M16C2×D311yescharacteristic
231C2×#97—61no—
232C2×C4×C8—61no—
233C4×C4⋊C4—32no—
234C4×C4⋊C4—61no—
235C4×C22⋊C4—32no—
236C4×C22⋊C4—61no—
237#376—61no—
238C43—31no—
239C43C2×D311yescharacteristic
240#339—32no—
241#339—32no—
242#339—32no—
243#339C2×D312yes—
244C23×D3C2×D411yescharacteristic
245C3×#41—22no—
246C3×#41—22no—
247C2×C3×Q8C22×C411yescharacteristic
248C2×C3×D4—21no—
249C2×C3×D4C22×C411yescharacteristic
250C22×C3×C4—22no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2411yescharacteristic
257C2×#67—21no—
258C2×#67—21no—
259C2×#67—21no—
260C2×#67—21no—
261C2×#67—21no—
262C22×Dic3—22no—
263C22×Dic3C2×D411yescharacteristic
264C22×Dic3C2×D411yescharacteristic
265C22×Dic3C2×D411yescharacteristic
266#235—22no—
267#235—22no—
268#235—44no—
269#235—44no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12C22×C411yescharacteristic
273C2×C4×D3—22no—
274C2×C4×D3—22no—
275C2×C4×D3—24no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—42no—
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×D3C22×C411yescharacteristic
290C2×C4×D3C2×D411yescharacteristic
291C2×C4×D3C2×D411yescharacteristic
292C2×Dic6—21no—
293C2×Dic6—21no—
294C2×Dic6C22×C411yescharacteristic
295C3×M16—22no—
296C3×M16#4114yescomplemented
297C2×C3×C8—22no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4C22×C411yescharacteristic
301C3×C4⋊C4C22×C411yescharacteristic
302C3×C22⋊C4—21no—
303C3×C22⋊C4—21no—
304C3×C22⋊C4—21no—
305C3×C42—24no—
306C3×C42—21no—
307C3×C42—21no—
308C3×C42—21no—
309C3×C42—22no—
310C3×C42—22no—
311C3×C42—42no—
312C3×C42C22×C411yescharacteristic
313C3×C42C22×C411yescharacteristic
314C3×C42C2×D411yescharacteristic
315C3×C42C2×D411yescharacteristic
316#217—21no—
317#217—21no—
318#217—21no—
319#217—21no—
320#217—21no—
321(C2×D3)⋊C4—28no—
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—21no—
329(C2×D3)⋊C4—21no—
330(C2×D3)⋊C4—21no—
331(C2×D3)⋊C4—21no—
332C4⋊Dic3—21no—
333C4⋊Dic3—21no—
334C4⋊Dic3—21no—
335C4⋊Dic3—21no—
336C4⋊Dic3C22×C411yescharacteristic
337C4⋊Dic3C22×C411yescharacteristic
338Dic3⋊C4—28no—
339Dic3⋊C4—21no—
340Dic3⋊C4—21no—
341Dic3⋊C4—21no—
342Dic3⋊C4—21no—
343Dic3⋊C4—21no—
344Dic3⋊C4—21no—
345Dic3⋊C4—21no—
346Dic3⋊C4—21no—
347Dic3⋊C4—21no—
348Dic3⋊C4—21no—
349C4×Dic3—24no—
350C4×Dic3—21no—
351C4×Dic3—21no—
352C4×Dic3—21no—
353C4×Dic3—22no—
354C4×Dic3—22no—
355C4×Dic3—42no—
356C4×Dic3C22⋊C411yescharacteristic
357C4×Dic3C22⋊C411yescharacteristic
358C4×Dic3C22⋊C411yescharacteristic
359C4×Dic3C22⋊C411yescharacteristic
360C4×Dic3C22⋊C411yescharacteristic
361C4×Dic3C22⋊C411yescharacteristic
362C4×Dic3C22⋊C411yescharacteristic
363C4×Dic3C22⋊C411yescharacteristic
364C4×Dic3C22×C411yescharacteristic
365C4×Dic3C22×C411yescharacteristic
366C4×Dic3C2×D411yescharacteristic
367C4×Dic3C2×D411yescharacteristic
368#208—22no—
369#208#4114yescomplemented
370C2×C3⋊C8—22no—
371ΓL(1,𝔽25)—28no—
372D3×C8—28no—
373C2×#41—31no—
374C2×#41—61no—
375C2×#41—61no—
376C2×#41C22×D311yescharacteristic
377C23×C4—31no—
378C23×C4—31no—
379C23×C4—31no—
380C2×M16—32no—
381C2×M16—62no—
382C2×M16—64no—
383C2×M16—64no—
384C2×M16C22×D312yes—
385C22×C8—62no—
386C4⋊Q8—31no—
387C4⋊Q8—31no—
388C4⋊Q8—31no—
389#127—31no—
390#126—61no—
391#126—61no—
392#126—61no—
393#126—61no—
394#125—31no—
395#125—31no—
396#125—61no—
397#125—61no—
398#124—31no—
399#124—31no—
400#124—61no—
401#124—61no—
402#123—61no—
403#123—61no—
404#123—61no—
405#123—61no—
406#123—61no—
407#123—61no—
408C22⋊Q8—31no—
409C22⋊Q8—31no—
410C22⋊Q8—31no—
411C22⋊Q8—31no—
412C22⋊Q8—61no—
413C22⋊Q8—61no—
414C22⋊Q8—61no—
415C22⋊Q8—61no—
416#121—31no—
417#121—31no—
418#121—31no—
419#121—31no—
420#121—61no—
421#121—61no—
422#121—61no—
423#121—61no—
424#120—61no—
425#120—61no—
426C4×Q8—31no—
427C4×Q8—31no—
428C4×Q8—61no—
429C4×Q8—61no—
430C4×Q8—61no—
431C4×Q8—61no—
432C4×Q8C4×D311yescharacteristic
433C4×Q8C4×D311yescharacteristic
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—31no—
437C4×D4—31no—
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×D4—61no—
448C4×D4—61no—
449C4×D4—61no—
450C4×D4—61no—
451C4×D4—61no—
452C4×D4C4×D311yescharacteristic
453C4×D4C4×D311yescharacteristic
454#117—21no—
455#117—31no—
456#117—61no—
457#117—61no—
458#117—61no—
459#117—61no—
460#117—68no—
461#117—61no—
462#117—61no—
463#117—61no—
464#117C22×D311yescharacteristic
465C2×C4⋊C4—62no—
466C2×C22⋊C4—62no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—31no—
471C2×C42—31no—
472C2×C42—31no—
473C2×C42—31no—
474C2×C42—31no—
475C2×C42—31no—
476C2×C42—31no—
477C2×C42—31no—
478C2×C42—31no—
479C2×C42—31no—
480C2×C42—31no—
481C2×C42—32no—
482C2×C42—61no—
483C2×C42—61no—
484C2×C42—61no—
485C2×C42C22×D312yes—
486C2×C42C22×D311yescharacteristic
487#104—24no—
488#104—64no—
489#104—64no—
490#104—64no—
491#97—21no—
492#97—62no—
493#97—61no—
494C4×C8—21no—
495C4×C8—62no—
496C4×C8—61no—
497#95—62no—
498#95—62no—
499C23×C3—21no—
500C23×C3C22×D411yescharacteristic
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—21no—
504C22×D3—41no—
505C22×D3C2×C22⋊C411yescharacteristic
506C22×D3C2×C22⋊C411yescharacteristic
507C3×Q8—21no—
508C3×Q8—21no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—42no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—24no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—42no—
519C2×C3×C4—42no—
520C2×C3×C4—42no—
521C2×C3×C4—42no—
522C2×C3×C4—42no—
523C2×C3×C4C2×C22⋊C411yescharacteristic
524C2×C3×C4C2×C22⋊C411yescharacteristic
525C2×C3×C4C2×C22⋊C411yescharacteristic
526C2×C3×C4C2×C22⋊C411yescharacteristic
527C2×C3×C4C23×C411yescharacteristic
528C2×C3×C4C22×D411yescharacteristic
529C2×C3×C4C2×#4112yes—
530C2×C3×C4C2×#4112yes—
531#67—42no—
532#67—42no—
533#67—42no—
534#67—42no—
535#67—42no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—24no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—41no—
543C2×Dic3—42no—
544C2×Dic3—42no—
545C2×Dic3C2×C22⋊C411yescharacteristic
546C2×Dic3C2×C22⋊C411yescharacteristic
547C2×Dic3C2×C22⋊C411yescharacteristic
548C2×Dic3C2×C22⋊C411yescharacteristic
549C2×Dic3C2×C22⋊C411yescharacteristic
550C2×Dic3C2×C22⋊C411yescharacteristic
551D12—21no—
552D12—21no—
553D12—42no—
554D12—42no—
555C4×D3—22no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—22no—
561C4×D3—22no—
562C4×D3—22no—
563C4×D3—22no—
564C4×D3—22no—
565C4×D3—22no—
566C4×D3—41no—
567C4×D3—41no—
568C4×D3—42no—
569C4×D3—42no—
570C4×D3—42no—
571C4×D3#10414yescomplemented
572Dic6—21no—
573Dic6—21no—
574Dic6—42no—
575Dic6—42no—
576C3×C8—24no—
577C3⋊C8—24no—
578C24—31no—
579#41—22no—
580#41—22no—
581#41—62no—
582#41—62no—
583#41—124no—
584#41—124no—
585C2×Q8—31no—
586C2×Q8—61no—
587C2×Q8—61no—
588C2×Q8C2×C4×D311yescharacteristic
589C2×D4—21no—
590C2×D4—31no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—61no—
598C2×D4C2×C4×D311yescharacteristic
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
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—31no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—64no—
619C22×C4—62no—
620C22×C4—62no—
621C22×C4—62no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—122no—
626C22×C4D3×D411yescharacteristic
627C22×C4D3×D411yescharacteristic
628C22×C4C23×D311yescharacteristic
629M16—22no—
630M16—34no—
631M16—68no—
632M16—62no—
633M16#23514yescomplemented
634C2×C8—22no—
635C2×C8—68no—
636C2×C8—62no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—31no—
640C4⋊C4—31no—
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—61no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—61no—
653C4⋊C4—68no—
654C4⋊C4—61no—
655C4⋊C4—61no—
656C4⋊C4C2×C4×D311yescharacteristic
657C4⋊C4C2×C4×D311yescharacteristic
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
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—68no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C42—24no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—22no—
682C42—22no—
683C42—31no—
684C42—31no—
685C42—31no—
686C42—31no—
687C42—31no—
688C42—31no—
689C42—31no—
690C42—31no—
691C42—31no—
692C42—31no—
693C42—31no—
694C42—31no—
695C42—42no—
696C42—64no—
697C42—61no—
698C42—61no—
699C42—61no—
700C42—62no—
701C42—62no—
702C42—122no—
703C42C2×C4×D311yescharacteristic
704C42C2×C4×D311yescharacteristic
705C42D3×D411yescharacteristic
706C42D3×D411yescharacteristic
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3C22×C22⋊C411yescharacteristic
713C22×C3#53212yes—
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—21no—
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—44no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3C2×#10412yes—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—44no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4C2×#10412yes—
731C3×C4#42112yes—
732C3×C4C4×#4111yescharacteristic
733C3×C4C4×#4111yescharacteristic
734C3×C4#52512yes—
735Dic3—21no—
736Dic3—21no—
737Dic3—21no—
738Dic3—21no—
739Dic3—21no—
740Dic3—44no—
741Dic3—41no—
742Dic3—41no—
743Dic3—41no—
744Dic3C2×#10412yes—
745C23—21no—
746C23—31no—
747C23—31no—
748C23—62no—
749C23—62no—
750C23—61no—
751C23—121no—
752C23C2×D3×D411yescharacteristic
753Q8—21no—
754Q8—21no—
755Q8—61no—
756Q8—61no—
757Q8—122no—
758Q8—122no—
759D4—21no—
760D4—21no—
761D4—42no—
762D4—61no—
763D4—61no—
764D4—122no—
765D4—122no—
766D4—122no—
767D4—122no—
768D4—122no—
769D4—122no—
770D4—122no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—31no—
778C2×C4—34no—
779C2×C4—31no—
780C2×C4—31no—
781C2×C4—31no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—62no—
798C2×C4—62no—
799C2×C4—62no—
800C2×C4—62no—
801C2×C4—62no—
802C2×C4—64no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—121no—
807C2×C4—121no—
808C2×C4—121no—
809C2×C4—122no—
810C2×C4—122no—
811C2×C4—122no—
812C2×C4—122no—
813C2×C4—122no—
814C2×C4D3×C22⋊C411yescharacteristic
815C2×C4D3×C22⋊C411yescharacteristic
816C2×C4D3×C22⋊C411yescharacteristic
817C2×C4D3×C22⋊C411yescharacteristic
818C2×C4C22×C4×D311yescharacteristic
819C2×C4C2×#23512yes—
820C2×C4C2×D3×D411yescharacteristic
821C2×C4D3×#4112yes—
822C8—24no—
823C8—64no—
824C2×C3—22no—
825C2×C3—81no—
826C2×C3#229711yescharacteristic
827C2×C3C22×#10411yescharacteristic
828C2×C3C2×#42111yescharacteristic
829D3—22no—
830D3—41no—
831D3—81no—
832C22—21no—
833C22—21no—
834C22—32no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—61no—
839C22—61no—
840C22—61no—
841C22—61no—
842C22—61no—
843C22—124no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22C2×D3×C22⋊C411yescharacteristic
848C22#554812yes—
849C4—21no—
850C4—21no—
851C4—32no—
852C4—44no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—61no—
857C4—61no—
858C4—61no—
859C4—61no—
860C4—61no—
861C4—124no—
862C4—121no—
863C4—121no—
864C4—121no—
865C4D3×#10412yes—
866C4#482112yes—
867C4C4×#23511yescharacteristic
868C4#552211yescharacteristic
869C4#554712yes—
870C3#2138211yescharacteristic, complemented, Sylow
871C2—22no—
872C2—62no—
873C2—81no—
874C2—121no—
875C2—241no—
876C2#7356311yescharacteristic
877C2C2×D3×#10411yescharacteristic
878C2C2×#482111yescharacteristic
subgroupG/H
centerC42D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×C4×#104C2
socleC22×C3C22×C22⋊C4
prime radical#85836C2
cosocleC22×C3×C4C24
hypercenterC4×#104D3
hypocenterC3#21382
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#104

Complements

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

NH ≅ G/Ntype
2. C4×D3×M16C2semidirect
3. C4×#872C2semidirect
4. C3×C4×#104C2semidirect
5. C4×#837C2semidirect
6. #70381C2semidirect
7. #70358C2semidirect
8. C4×#825C2semidirect
9. C4×#805C2semidirect
10. #68755C2semidirect
11. #68730C2semidirect
17. #5580C4semidirect
18. #5580C4semidirect
19. #5578C4semidirect
20. #5578C4semidirect
21. #5557C4semidirect
22. #5557C4semidirect
23. #5548C4semidirect
24. #5548C4semidirect
70. C4×#104D3semidirect
296. C3×M16#41semidirect
369. #208#41semidirect
571. C4×D3#104semidirect
633. M16#235semidirect
870. C3#21382semidirect

Maximal subgroups

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

subgroupindex
#858362
C4×D3×M162
C4×#8722
C3×C4×#1042
C4×#8372
#703812
#703582
C4×#8252
C4×#8052
#687552
#687302
#213823