Finite Group Databasebeta

← #11041820

Subgroups — #11041820

Order 768.

1488 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2313C211yesmaximal, characteristic, complemented
2#82175C211yesmaximal, characteristic
3#82162C211yesmaximal, characteristic, complemented
4#75355C211yesmaximal, characteristic, complemented
5#75293C211yesmaximal, characteristic, complemented
6#75245C211yesmaximal, characteristic, complemented
7#75233C211yesmaximal, characteristic, complemented
8#75218C211yesmaximal, characteristic, complemented
9#75195C211yesmaximal, characteristic, complemented
10#75141C211yesmaximal, characteristic, complemented
11#75114C211yesmaximal, characteristic, complemented
12#75081C211yesmaximal, characteristic, complemented
13#75060C211yesmaximal, characteristic, complemented
14#75042C211yesmaximal, characteristic, complemented
15#75040C211yesmaximal, characteristic, complemented
16#75022C211yesmaximal, characteristic, complemented
17#75005C211yesmaximal, characteristic, complemented
18#74953C211yesmaximal, characteristic, complemented
19#74938C211yesmaximal, characteristic, complemented
20#74096C211yesmaximal, characteristic, complemented
21#74094C211yesmaximal, characteristic
22#74083C211yesmaximal, characteristic, complemented
23#74081C211yesmaximal, characteristic
24#73979C211yesmaximal, characteristic, complemented
25#73963C211yesmaximal, characteristic
26#73932C211yesmaximal, characteristic
27#73918C211yesmaximal, characteristic, complemented
28#73556C211yesmaximal, characteristic
29#73524C211yesmaximal, characteristic, complemented
30#73479C211yesmaximal, characteristic
31C4×#879C211yesmaximal, characteristic, complemented
32#38339—31nomaximal, Sylow
33C22×C3×C4⋊C4C2211yescharacteristic
34C2×#924C2211yescharacteristic
35C2×#898C2211yescharacteristic
36C2×#887C2211yescharacteristic
37C2×#883C2211yescharacteristic
38C2×#879C2211yescharacteristic
39C3×#387C2211yescharacteristic
40C3×#387C2211yescharacteristic
41C3×#387C2211yescharacteristic
42C3×#387C2211yescharacteristic
43C3×#387C2211yescharacteristic
44C3×#387C2211yescharacteristic
45C3×#387C2211yescharacteristic
46C3×#387C2211yescharacteristic
47C3×#381C2211yescharacteristic
48C3×#381C2211yescharacteristic
49C3×#380C2211yescharacteristic
50C3×#380C2211yescharacteristic
51C3×C4×C22⋊C4C2211yescharacteristic
52C3×C4×C22⋊C4C2211yescharacteristic
53#5213C2211yescharacteristic
54#5213C2211yescharacteristic
55#5213C2211yescharacteristic
56#5212C2211yescharacteristic
57#5210C2211yescharacteristic
58#5210C2211yescharacteristic
59#5210C2211yescharacteristic
60C4×#217C2211yescharacteristic
61C4×#217C2211yescharacteristic
62C4×#217C2211yescharacteristic
63C4×#217C2211yescharacteristic
64#4994C2211yescharacteristic
65#4994C2211yescharacteristic
66#4992C2211yescharacteristic
67#4992C2211yescharacteristic
68#4990C2211yescharacteristic
69#4990C2211yescharacteristic
70#4989C2211yescharacteristic
71#4986C2211yescharacteristic
72#4985C2211yescharacteristic
73#4985C2211yescharacteristic
74#4984C2211yescharacteristic
75#4982C2211yescharacteristic
76#4982C2211yescharacteristic
77#4980C2211yescharacteristic
78#4980C2211yescharacteristic
79#4980C2211yescharacteristic
80#4979C2211yescharacteristic
81#4978C2211yescharacteristic
82#4978C2211yescharacteristic
83#4978C2211yescharacteristic
84#4977C2211yescharacteristic
85#4976C2211yescharacteristic
86#4976C2211yescharacteristic
87#4976C2211yescharacteristic
88#4976C2211yescharacteristic
89Dic3×C4⋊C4C2211yescharacteristic
90Dic3×C4⋊C4C2211yescharacteristic
91#4973C2211yescharacteristic
92#4972C2211yescharacteristic
93#4972C2211yescharacteristic
94#4961C2211yescharacteristic
95#4959C2211yescharacteristic
96#4957C2211yescharacteristic
97#4953C2211yescharacteristic
98#4952C2211yescharacteristic
99#4952C2211yescharacteristic
100#4952C2211yescharacteristic
101#4951C2211yescharacteristic
102#4951C2211yescharacteristic
103#4949C2211yescharacteristic
104#4947C2211yescharacteristic
105#4945C2211yescharacteristic
106#4945C2211yescharacteristic
107#4944C2211yescharacteristic
108#4940C2211yescharacteristic
109#4940C2211yescharacteristic
110#4940C2211yescharacteristic
111C4×(C2×D3)⋊C4C2211yescharacteristic
112#4936C2211yescharacteristic
113C4×C4⋊Dic3C2211yescharacteristic
114C4×C4⋊Dic3C2211yescharacteristic
115#4933C2211yescharacteristic
116#4933C2211yescharacteristic
117#4933C2211yescharacteristic
118#4933C2211yescharacteristic
119#4933C2211yescharacteristic
120C4×Dic3⋊C4C2211yescharacteristic
121C4×Dic3⋊C4C2211yescharacteristic
122C42×Dic3C2211yescharacteristic
123#4929C2211yescharacteristic
124#4675C2211yescharacteristic
125#4675C2211yescharacteristic
126#4673C2211yescharacteristic
127#4673C2211yescharacteristic
128#4670C2211yescharacteristic
129#4670C2211yescharacteristic
130#4670C2211yescharacteristic
131#4670C2211yescharacteristic
132#4669C2211yescharacteristic
133#4669C2211yescharacteristic
134#4669C2211yescharacteristic
135#4669C2211yescharacteristic
136#4668C2211yescharacteristic
137#4667C2211yescharacteristic
138#4667C2211yescharacteristic
139#4666C2211yescharacteristic
140C3⋊#401C2211yescharacteristic
141C3⋊#401C2211yescharacteristic
142C3⋊#401C2211yescharacteristic
143C3⋊#401C2211yescharacteristic
144#4661C2211yescharacteristic
145#4660C2211yescharacteristic
146#4660C2211yescharacteristic
147#4660C2211yescharacteristic
148#4659C2211yescharacteristic
149#4658C2211yescharacteristic
150#4658C2211yescharacteristic
151#4657C2211yescharacteristic
152#4657C2211yescharacteristic
153#4657C2211yescharacteristic
154#4657C2211yescharacteristic
155#4657C2211yescharacteristic
156#4656C2211yescharacteristic
157#4656C2211yescharacteristic
158#4655C2211yescharacteristic
159#4655C2211yescharacteristic
160#4655C2211yescharacteristic
161#4654C2211yescharacteristic
162#4654C2211yescharacteristic
163#4654C2211yescharacteristic
164#4653C2211yescharacteristic
165#4653C2211yescharacteristic
166#4653C2211yescharacteristic
167#4653C2211yescharacteristic
168#4653C2211yescharacteristic
169#4653C2211yescharacteristic
170#4653C2211yescharacteristic
171#4652C2211yescharacteristic
172#4652C2211yescharacteristic
173#4652C2211yescharacteristic
174#4652C2211yescharacteristic
175#4651C2211yescharacteristic
176#4650C2211yescharacteristic
177#4650C2211yescharacteristic
178#4649C2211yescharacteristic
179#4649C2211yescharacteristic
180#4648C2211yescharacteristic
181#4648C2211yescharacteristic
182#4647C2211yescharacteristic
183#4647C2211yescharacteristic
184#4646C2211yescharacteristic
185#4646C2211yescharacteristic
186#4646C2211yescharacteristic
187#4646C2211yescharacteristic
188#2865—31no—
189#2789—31no—
190#2776—31no—
191#2772—31no—
192#2759—31no—
193#2742—31no—
194#2698—31no—
195#2695—31no—
196#2687—31no—
197#2655—31no—
198#2653—31no—
199#2590—31no—
200#2574—31no—
201#2531—31no—
202#2530—31no—
203#2528—31no—
204#2527—31no—
205#2520—31no—
206#2520—31no—
207#2517—31no—
208#2516—31no—
209#2494—31no—
210#2494—31no—
211#2481—31no—
212#2469—31no—
213#2374—31no—
214#2360—31no—
215#2334—31no—
216#2313D311yescharacteristic, complemented
217C4×#126—31no—
218#2295—31no—
219C23×C3×C4C2311yescharacteristic
220C23×C3×C4C2311yescharacteristic
221C23×C3×C4C2311yescharacteristic
222C22×#67C2311yescharacteristic
223C22×C4×D3C2311yescharacteristic
224C22×Dic6C2311yescharacteristic
225C22×Dic6C2311yescharacteristic
226C2×C3×C4⋊C4—24no—
227C2×C3×C4⋊C4C2311yescharacteristic
228C2×C3×C4⋊C4C2311yescharacteristic
229C2×C3×C4⋊C4C2311yescharacteristic
230C2×C3×C4⋊C4C2311yescharacteristic
231C2×C3×C4⋊C4C2311yescharacteristic
232C2×C3×C4⋊C4C2311yescharacteristic
233C2×C3×C4⋊C4C2311yescharacteristic
234C2×C3×C4⋊C4C2311yescharacteristic
235C2×C3×C22⋊C4C2311yescharacteristic
236C2×C3×C22⋊C4C2311yescharacteristic
237C2×C3×C22⋊C4C2311yescharacteristic
238C2×C3×C22⋊C4C2311yescharacteristic
239C2×C3×C42C2311yescharacteristic
240C2×C3×C42C2311yescharacteristic
241C2×C3×C42C2311yescharacteristic
242C2×C3×C42C2311yescharacteristic
243C2×#217C2311yescharacteristic
244C2×#217C2311yescharacteristic
245C2×#217C2311yescharacteristic
246C2×#217C2311yescharacteristic
247C2×#217C2311yescharacteristic
248C2×#217C2311yescharacteristic
249C2×#217C2311yescharacteristic
250C2×(C2×D3)⋊C4C2311yescharacteristic
251C2×(C2×D3)⋊C4C2311yescharacteristic
252C2×(C2×D3)⋊C4C2311yescharacteristic
253C2×(C2×D3)⋊C4C2311yescharacteristic
254C2×(C2×D3)⋊C4C2311yescharacteristic
255C2×(C2×D3)⋊C4C2311yescharacteristic
256C2×(C2×D3)⋊C4C2311yescharacteristic
257C2×(C2×D3)⋊C4C2311yescharacteristic
258C2×(C2×D3)⋊C4C2311yescharacteristic
259C2×(C2×D3)⋊C4C2311yescharacteristic
260C2×(C2×D3)⋊C4C2311yescharacteristic
261C2×(C2×D3)⋊C4C2311yescharacteristic
262C2×(C2×D3)⋊C4C2311yescharacteristic
263C2×C4⋊Dic3C2311yescharacteristic
264C2×C4⋊Dic3C2311yescharacteristic
265C2×C4⋊Dic3C2311yescharacteristic
266C2×C4⋊Dic3C2311yescharacteristic
267C2×C4⋊Dic3C2311yescharacteristic
268C2×C4⋊Dic3C2311yescharacteristic
269C2×C4⋊Dic3C2311yescharacteristic
270C2×C4⋊Dic3C2311yescharacteristic
271C2×C4⋊Dic3C2311yescharacteristic
272C2×C4⋊Dic3C2311yescharacteristic
273#924—24no—
274C2×Dic3⋊C4C2311yescharacteristic
275C2×Dic3⋊C4C2311yescharacteristic
276C2×Dic3⋊C4C2311yescharacteristic
277C2×Dic3⋊C4C2311yescharacteristic
278C2×Dic3⋊C4C2311yescharacteristic
279C2×Dic3⋊C4C2311yescharacteristic
280C2×Dic3⋊C4C2311yescharacteristic
281C2×Dic3⋊C4C2311yescharacteristic
282C2×Dic3⋊C4C2311yescharacteristic
283C2×Dic3⋊C4C2311yescharacteristic
284C2×Dic3⋊C4C2311yescharacteristic
285C2×Dic3⋊C4C2311yescharacteristic
286C2×Dic3⋊C4C2311yescharacteristic
287C2×Dic3⋊C4C2311yescharacteristic
288C2×Dic3⋊C4C2311yescharacteristic
289C2×Dic3⋊C4C2311yescharacteristic
290C2×Dic3⋊C4C2311yescharacteristic
291C2×Dic3⋊C4C2311yescharacteristic
292C2×Dic3⋊C4C2311yescharacteristic
293C2×Dic3⋊C4C2311yescharacteristic
294C2×Dic3⋊C4C2311yescharacteristic
295C2×C4×Dic3C2311yescharacteristic
296C2×C4×Dic3C2311yescharacteristic
297C2×C4×Dic3C2311yescharacteristic
298C2×C4×Dic3C2311yescharacteristic
299C2×C4×Dic3C2311yescharacteristic
300C2×C4×Dic3C2311yescharacteristic
301C2×C4×Dic3C2311yescharacteristic
302C2×C4×Dic3C2311yescharacteristic
303C2×C4×Dic3C2311yescharacteristic
304C2×C4×Dic3C2311yescharacteristic
305C2×C4×Dic3C2311yescharacteristic
306C2×C4×Dic3C2311yescharacteristic
307C2×C4×Dic3C2311yescharacteristic
308C2×C4×Dic3C2311yescharacteristic
309C2×C4×Dic3C2311yescharacteristic
310#898—24no—
311#887—24no—
312#883—24no—
313#879—24no—
314C3×#95C2311yescharacteristic
315C3×#95C2311yescharacteristic
316C3×#95C2311yescharacteristic
317C3×#95C2311yescharacteristic
318C3×#95C2311yescharacteristic
319C3×#95C2311yescharacteristic
320C3×#95C2311yescharacteristic
321C3×#95C2311yescharacteristic
322C3×#95C2311yescharacteristic
323C3×#95C2311yescharacteristic
324C3×#95C2311yescharacteristic
325C3×#95C2311yescharacteristic
326C3×#95C2311yescharacteristic
327C3×#95C2311yescharacteristic
328C3×#95C2311yescharacteristic
329C3×#95C2311yescharacteristic
330C3⋊#95C2311yescharacteristic
331C3⋊#95C2311yescharacteristic
332C3⋊#95C2311yescharacteristic
333C3⋊#95C2311yescharacteristic
334C3⋊#95C2311yescharacteristic
335C3⋊#95C2311yescharacteristic
336C3⋊#95C2311yescharacteristic
337C3⋊#95C2311yescharacteristic
338C3⋊#95C2311yescharacteristic
339C3⋊#95C2311yescharacteristic
340C3⋊#95C2311yescharacteristic
341C3⋊#95C2311yescharacteristic
342C3⋊#95C2311yescharacteristic
343C3⋊#95C2311yescharacteristic
344C3⋊#95C2311yescharacteristic
345C3⋊#95C2311yescharacteristic
346C3⋊#95C2311yescharacteristic
347C3⋊#95C2311yescharacteristic
348C3⋊#95C2311yescharacteristic
349C3⋊#95C2311yescharacteristic
350C3⋊#95C2311yescharacteristic
351C3⋊#95C2311yescharacteristic
352C3⋊#95C2311yescharacteristic
353C3⋊#95C2311yescharacteristic
354C3⋊#95C2311yescharacteristic
355C3⋊#95C2311yescharacteristic
356C3⋊#95C2311yescharacteristic
357C3⋊#95C2311yescharacteristic
358C3⋊#95C2311yescharacteristic
359C3⋊#95C2311yescharacteristic
360C3⋊#95C2311yescharacteristic
361C3⋊#95C2311yescharacteristic
362C3⋊#95C2311yescharacteristic
363C3⋊#95C2311yescharacteristic
364C3⋊#95C2311yescharacteristic
365C3⋊#95C2311yescharacteristic
366C3⋊#95C2311yescharacteristic
367C3⋊#95C2311yescharacteristic
368C3⋊#95C2311yescharacteristic
369C3⋊#95C2311yescharacteristic
370C3⋊#95C2311yescharacteristic
371C3⋊#95C2311yescharacteristic
372C3⋊#95C2311yescharacteristic
373C3⋊#95C2311yescharacteristic
374C3⋊#95C2311yescharacteristic
375C3⋊#95C2311yescharacteristic
376C3⋊#95C2311yescharacteristic
377C3⋊#95C2311yescharacteristic
378C3⋊#95C2311yescharacteristic
379C3⋊#95C2311yescharacteristic
380C2×#126—31no—
381C2×#126—31no—
382C2×#123—31no—
383C2×C22⋊Q8—31no—
384C2×C4×Q8—31no—
385C22×C4⋊C4C2×D311yescharacteristic
386#401—31no—
387#401—31no—
388#401—31no—
389#401—31no—
390#400—31no—
391#400—31no—
392#400—31no—
393#400—31no—
394#400—31no—
395#400—31no—
396#400—31no—
397#400—31no—
398#400—31no—
399#399—31no—
400#398—31no—
401#398—31no—
402#398—31no—
403#398—31no—
404#398—31no—
405#398—31no—
406#398—31no—
407#398—31no—
408#397—31no—
409#397—31no—
410#397—31no—
411#397—31no—
412#397—31no—
413#397—31no—
414#397—31no—
415#397—31no—
416#396—31no—
417#396—31no—
418#395—31no—
419#395—31no—
420#395—31no—
421#394—31no—
422#394—31no—
423#393—31no—
424#393—31no—
425#393—31no—
426#391—31no—
427#391—31no—
428#391—31no—
429#391—31no—
430#391—31no—
431#391—31no—
432#390—31no—
433#389—31no—
434#389—31no—
435#389—31no—
436#389—31no—
437#389—31no—
438#389—31no—
439#389—31no—
440#389—31no—
441#389—31no—
442#388—31no—
443#388—31no—
444#388—31no—
445#388—31no—
446#388—31no—
447#388—31no—
448#388—31no—
449#388—31no—
450#388—31no—
451#388—31no—
452#388—31no—
453#388—31no—
454#388—31no—
455#388—31no—
456#388—31no—
457#388—31no—
458#388—31no—
459#388—31no—
460#387—31no—
461#387—31no—
462#387—31no—
463#387—31no—
464#387—31no—
465#387—31no—
466#387—31no—
467#387—31no—
468#387—31no—
469#387—31no—
470#387—31no—
471#387—31no—
472#387—31no—
473#387—31no—
474#387—31no—
475#387—31no—
476#387—31no—
477#387—31no—
478#387—31no—
479#387—31no—
480#387—31no—
481#387—31no—
482#387—31no—
483#387—31no—
484#387—31no—
485#387—31no—
486#387—31no—
487#387—31no—
488#387C2×D311yescharacteristic
489#387C2×D311yescharacteristic
490#387C2×D311yescharacteristic
491#387C2×D311yescharacteristic
492#387C2×D311yescharacteristic
493#387C2×D311yescharacteristic
494#387C2×D311yescharacteristic
495#387C2×D311yescharacteristic
496#386—31no—
497#386—31no—
498#386—31no—
499#385—31no—
500#385—31no—
501#385—31no—
502#385—31no—
503#385—31no—
504#383—31no—
505#382—31no—
506#382—31no—
507#382—31no—
508#382—31no—
509#381C2×D311yescharacteristic
510#381C2×D311yescharacteristic
511#380—31no—
512#380—31no—
513#380—31no—
514#380C2×D311yescharacteristic
515#380C2×D311yescharacteristic
516C4×C4⋊C4—31no—
517C4×C4⋊C4—31no—
518C4×C4⋊C4—31no—
519C4×C4⋊C4—31no—
520C4×C4⋊C4—31no—
521C4×C4⋊C4—31no—
522C4×C4⋊C4—31no—
523C4×C4⋊C4—31no—
524C4×C22⋊C4—31no—
525C4×C22⋊C4—31no—
526C4×C22⋊C4—31no—
527C4×C22⋊C4—31no—
528C4×C22⋊C4—31no—
529C4×C22⋊C4—31no—
530C4×C22⋊C4C2×D311yescharacteristic
531C4×C22⋊C4C2×D311yescharacteristic
532#376—31no—
533#376—31no—
534C43—31no—
535C24×C3C2411yescharacteristic
536C23×D3C2411yescharacteristic
537C22×C3×C4—22no—
538C22×C3×C4—22no—
539C22×C3×C4—22no—
540C22×C3×C4—22no—
541C22×C3×C4—41no—
542C22×C3×C4—41no—
543C22×C3×C4—41no—
544C22×C3×C4—41no—
545C22×C3×C4—41no—
546C22×C3×C4C2411yescharacteristic
547C22×C3×C4C2411yescharacteristic
548C22×C3×C4C2411yescharacteristic
549C22×C3×C4C2411yescharacteristic
550C22×C3×C4C2411yescharacteristic
551C22×C3×C4C2411yescharacteristic
552C22×C3×C4C2411yescharacteristic
553C22×C3×C4C2411yescharacteristic
554C22×C3×C4C2411yescharacteristic
555C22×C3×C4C2411yescharacteristic
556C22×C3×C4C2411yescharacteristic
557C22×C3×C4C2411yescharacteristic
558C22×C3×C4C2411yescharacteristic
559C22×C3×C4C2411yescharacteristic
560C2×#67—22no—
561C2×#67—41no—
562C2×#67—41no—
563C22×Dic3C2411yescharacteristic
564C22×Dic3C2411yescharacteristic
565C22×Dic3C2411yescharacteristic
566C22×Dic3C2411yescharacteristic
567C22×Dic3C2411yescharacteristic
568C22×Dic3C2411yescharacteristic
569C22×Dic3C2411yescharacteristic
570C22×Dic3C2411yescharacteristic
571C22×Dic3C2411yescharacteristic
572C22×Dic3C2411yescharacteristic
573C22×Dic3C2411yescharacteristic
574C22×Dic3C2411yescharacteristic
575C22×Dic3C2411yescharacteristic
576C22×Dic3C2411yescharacteristic
577C22×Dic3C2411yescharacteristic
578C2×C4×D3—22no—
579C2×C4×D3—41no—
580C2×C4×D3—41no—
581C2×Dic6—22no—
582C2×Dic6—22no—
583C2×Dic6—41no—
584C2×Dic6—41no—
585C2×Dic6—41no—
586C2×Dic6—41no—
587C3×C4⋊C4—22no—
588C3×C4⋊C4—22no—
589C3×C4⋊C4—22no—
590C3×C4⋊C4—41no—
591C3×C4⋊C4—41no—
592C3×C4⋊C4—41no—
593C3×C4⋊C4—41no—
594C3×C4⋊C4#4114yes—
595C3×C22⋊C4—22no—
596C3×C22⋊C4—22no—
597C3×C22⋊C4—41no—
598C3×C22⋊C4—41no—
599C3×C42—41no—
600C3×C42—41no—
601C3×C42—41no—
602C3×C42—41no—
603#217—22no—
604#217—22no—
605#217—22no—
606#217—41no—
607#217—41no—
608#217—41no—
609#217#4114yes—
610(C2×D3)⋊C4—22no—
611(C2×D3)⋊C4—22no—
612(C2×D3)⋊C4—22no—
613(C2×D3)⋊C4—22no—
614(C2×D3)⋊C4—22no—
615(C2×D3)⋊C4—41no—
616(C2×D3)⋊C4—41no—
617(C2×D3)⋊C4—41no—
618(C2×D3)⋊C4—41no—
619(C2×D3)⋊C4—41no—
620(C2×D3)⋊C4—41no—
621(C2×D3)⋊C4—41no—
622(C2×D3)⋊C4—41no—
623C4⋊Dic3—22no—
624C4⋊Dic3—22no—
625C4⋊Dic3—22no—
626C4⋊Dic3—22no—
627C4⋊Dic3—22no—
628C4⋊Dic3—22no—
629C4⋊Dic3—41no—
630C4⋊Dic3—41no—
631C4⋊Dic3—41no—
632C4⋊Dic3—41no—
633Dic3⋊C4—22no—
634Dic3⋊C4—22no—
635Dic3⋊C4—22no—
636Dic3⋊C4—22no—
637Dic3⋊C4—22no—
638Dic3⋊C4—22no—
639Dic3⋊C4—22no—
640Dic3⋊C4—22no—
641Dic3⋊C4—41no—
642Dic3⋊C4—41no—
643Dic3⋊C4—41no—
644Dic3⋊C4—41no—
645Dic3⋊C4—41no—
646Dic3⋊C4—41no—
647Dic3⋊C4—41no—
648Dic3⋊C4—41no—
649Dic3⋊C4—41no—
650Dic3⋊C4—41no—
651Dic3⋊C4—41no—
652Dic3⋊C4—41no—
653Dic3⋊C4—41no—
654C4×Dic3—22no—
655C4×Dic3—22no—
656C4×Dic3—22no—
657C4×Dic3—22no—
658C4×Dic3—22no—
659C4×Dic3—22no—
660C4×Dic3—41no—
661C4×Dic3—41no—
662C4×Dic3—41no—
663C4×Dic3—41no—
664C4×Dic3—41no—
665C4×Dic3—41no—
666C4×Dic3—41no—
667C4×Dic3—41no—
668C4×Dic3—41no—
669C22×Q8—31no—
670C22×Q8—31no—
671C22×D4—31no—
672C23×C4—31no—
673C23×C4C22×D311yescharacteristic
674C23×C4C22×D311yescharacteristic
675C23×C4C22×D311yescharacteristic
676#126—64no—
677#126—64no—
678#123—64no—
679C22⋊Q8—64no—
680C4×Q8—64no—
681C2×C4⋊C4—24no—
682C2×C4⋊C4—31no—
683C2×C4⋊C4—31no—
684C2×C4⋊C4—31no—
685C2×C4⋊C4—31no—
686C2×C4⋊C4—31no—
687C2×C4⋊C4—31no—
688C2×C4⋊C4—31no—
689C2×C4⋊C4—31no—
690C2×C4⋊C4—31no—
691C2×C4⋊C4—31no—
692C2×C4⋊C4—31no—
693C2×C4⋊C4—31no—
694C2×C4⋊C4—31no—
695C2×C4⋊C4—31no—
696C2×C4⋊C4—31no—
697C2×C4⋊C4—31no—
698C2×C4⋊C4—31no—
699C2×C4⋊C4—31no—
700C2×C4⋊C4—31no—
701C2×C4⋊C4—31no—
702C2×C4⋊C4—31no—
703C2×C4⋊C4—31no—
704C2×C4⋊C4—31no—
705C2×C4⋊C4—31no—
706C2×C4⋊C4—31no—
707C2×C4⋊C4—31no—
708C2×C4⋊C4—31no—
709C2×C4⋊C4—31no—
710C2×C4⋊C4—31no—
711C2×C4⋊C4—31no—
712C2×C4⋊C4—31no—
713C2×C4⋊C4C22×D311yescharacteristic
714C2×C4⋊C4C22×D311yescharacteristic
715C2×C4⋊C4C22×D311yescharacteristic
716C2×C4⋊C4C22×D311yescharacteristic
717C2×C4⋊C4C22×D311yescharacteristic
718C2×C4⋊C4C22×D311yescharacteristic
719C2×C4⋊C4C22×D311yescharacteristic
720C2×C4⋊C4C22×D311yescharacteristic
721C2×C22⋊C4—31no—
722C2×C22⋊C4—31no—
723C2×C22⋊C4—31no—
724C2×C22⋊C4—31no—
725C2×C22⋊C4—31no—
726C2×C22⋊C4—31no—
727C2×C22⋊C4—31no—
728C2×C22⋊C4—31no—
729C2×C22⋊C4—31no—
730C2×C22⋊C4—31no—
731C2×C22⋊C4—31no—
732C2×C22⋊C4—31no—
733C2×C22⋊C4—31no—
734C2×C22⋊C4—31no—
735C2×C22⋊C4—31no—
736C2×C22⋊C4—31no—
737C2×C22⋊C4—31no—
738C2×C22⋊C4—31no—
739C2×C22⋊C4—31no—
740C2×C22⋊C4—31no—
741C2×C22⋊C4C22×D311yescharacteristic
742C2×C22⋊C4C22×D311yescharacteristic
743C2×C22⋊C4C22×D311yescharacteristic
744C2×C22⋊C4C22×D311yescharacteristic
745C2×C42—31no—
746C2×C42—31no—
747C2×C42—31no—
748C2×C42—31no—
749C2×C42—31no—
750C2×C42—31no—
751C2×C42—31no—
752C2×C42—31no—
753C2×C42—31no—
754C2×C42—31no—
755C2×C42—31no—
756C2×C42—31no—
757C2×C42—31no—
758C2×C42—31no—
759C2×C42—31no—
760C2×C42C22×D311yescharacteristic
761C2×C42C22×D311yescharacteristic
762C2×C42C22×D311yescharacteristic
763C2×C42C22×D311yescharacteristic
764#95—31no—
765#95—31no—
766#95—31no—
767#95—31no—
768#95—31no—
769#95—31no—
770#95—31no—
771#95—31no—
772#95—31no—
773#95—31no—
774#95—31no—
775#95—31no—
776#95—31no—
777#95—31no—
778#95—31no—
779#95—31no—
780#95—31no—
781#95—31no—
782#95—31no—
783#95—31no—
784#95—31no—
785#95—31no—
786#95—31no—
787#95—31no—
788#95—31no—
789#95—31no—
790#95—31no—
791#95—31no—
792#95—31no—
793#95—31no—
794#95—31no—
795#95—31no—
796#95—31no—
797#95—31no—
798#95—31no—
799#95—31no—
800#95—31no—
801#95—31no—
802#95—31no—
803#95—31no—
804#95—31no—
805#95—31no—
806#95—31no—
807#95—31no—
808#95—31no—
809#95—31no—
810#95—31no—
811#95—31no—
812#95—31no—
813#95—31no—
814#95C22×D311yescharacteristic
815#95C22×D311yescharacteristic
816#95C22×D311yescharacteristic
817#95C22×D311yescharacteristic
818#95C22×D311yescharacteristic
819#95C22×D311yescharacteristic
820#95C22×D311yescharacteristic
821#95C22×D311yescharacteristic
822#95C22×D311yescharacteristic
823#95C22×D311yescharacteristic
824#95C22×D311yescharacteristic
825#95C22×D311yescharacteristic
826#95C22×D311yescharacteristic
827#95C22×D311yescharacteristic
828#95C22×D311yescharacteristic
829#95C22×D311yescharacteristic
830C23×C3—21no—
831C23×C3—21no—
832C23×C3—21no—
833C23×C3—21no—
834C23×C3—21no—
835C23×C3—21no—
836C23×C3C2×#4112yes—
837C23×C3C2511yescharacteristic
838C22×D3—21no—
839C22×D3—21no—
840C22×D3—21no—
841C22×D3—21no—
842C22×D3—21no—
843C22×D3—21no—
844C22×D3—21no—
845C2×C3×C4—21no—
846C2×C3×C4—21no—
847C2×C3×C4—21no—
848C2×C3×C4—21no—
849C2×C3×C4—21no—
850C2×C3×C4—21no—
851C2×C3×C4—21no—
852C2×C3×C4—21no—
853C2×C3×C4—21no—
854C2×C3×C4—21no—
855C2×C3×C4—21no—
856C2×C3×C4—21no—
857C2×C3×C4—21no—
858C2×C3×C4—21no—
859C2×C3×C4—21no—
860C2×C3×C4—21no—
861C2×C3×C4—21no—
862C2×C3×C4—21no—
863C2×C3×C4—21no—
864C2×C3×C4—21no—
865C2×C3×C4—21no—
866C2×C3×C4—21no—
867C2×C3×C4—21no—
868C2×C3×C4—21no—
869C2×C3×C4—21no—
870C2×C3×C4—21no—
871C2×C3×C4—21no—
872C2×C3×C4—21no—
873C2×C3×C4—21no—
874C2×C3×C4—21no—
875C2×C3×C4—21no—
876C2×C3×C4—21no—
877C2×C3×C4—21no—
878C2×C3×C4—21no—
879C2×C3×C4—21no—
880C2×C3×C4—21no—
881C2×C3×C4—21no—
882C2×C3×C4—21no—
883C2×C3×C4—21no—
884C2×C3×C4—44no—
885C2×C3×C4—82no—
886C2×C3×C4—82no—
887C2×C3×C4C2×#4112yes—
888C2×C3×C4C2×#4112yes—
889C2×C3×C4C2×#4112yes—
890#67—82no—
891C2×Dic3—21no—
892C2×Dic3—21no—
893C2×Dic3—21no—
894C2×Dic3—21no—
895C2×Dic3—21no—
896C2×Dic3—21no—
897C2×Dic3—21no—
898C2×Dic3—21no—
899C2×Dic3—21no—
900C2×Dic3—21no—
901C2×Dic3—21no—
902C2×Dic3—21no—
903C2×Dic3—21no—
904C2×Dic3—21no—
905C2×Dic3—21no—
906C2×Dic3—21no—
907C2×Dic3—21no—
908C2×Dic3—21no—
909C2×Dic3—21no—
910C2×Dic3—21no—
911C2×Dic3—21no—
912C2×Dic3—21no—
913C2×Dic3—21no—
914C2×Dic3—21no—
915C2×Dic3—21no—
916C2×Dic3—21no—
917C2×Dic3—21no—
918C2×Dic3—21no—
919C2×Dic3—21no—
920C2×Dic3—21no—
921C2×Dic3—21no—
922C2×Dic3—21no—
923C2×Dic3—21no—
924C2×Dic3—21no—
925C2×Dic3—21no—
926C2×Dic3—21no—
927C2×Dic3—21no—
928C2×Dic3—21no—
929C2×Dic3—21no—
930C2×Dic3—21no—
931C2×Dic3—21no—
932C2×Dic3—21no—
933C2×Dic3C2×#4112yes—
934C2×Dic3C2×#4112yes—
935C2×Dic32−1+412yes—
936C4×D3—82no—
937Dic6—44no—
938Dic6—82no—
939C24—31no—
940C24C23×D311yescharacteristic
941C2×Q8—62no—
942C2×Q8—62no—
943C2×Q8—121no—
944C2×Q8—121no—
945C2×Q8—121no—
946C2×Q8—121no—
947C2×D4—62no—
948C2×D4—121no—
949C2×D4—121no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—22no—
954C22×C4—31no—
955C22×C4—31no—
956C22×C4—31no—
957C22×C4—31no—
958C22×C4—31no—
959C22×C4—31no—
960C22×C4—31no—
961C22×C4—31no—
962C22×C4—31no—
963C22×C4—31no—
964C22×C4—31no—
965C22×C4—31no—
966C22×C4—31no—
967C22×C4—31no—
968C22×C4—31no—
969C22×C4—41no—
970C22×C4—41no—
971C22×C4—41no—
972C22×C4—41no—
973C22×C4—41no—
974C22×C4—62no—
975C22×C4—121no—
976C22×C4—121no—
977C22×C4C23×D311yescharacteristic
978C22×C4C23×D311yescharacteristic
979C22×C4C23×D311yescharacteristic
980C22×C4C23×D311yescharacteristic
981C22×C4C23×D311yescharacteristic
982C22×C4C23×D311yescharacteristic
983C22×C4C23×D311yescharacteristic
984C22×C4C23×D311yescharacteristic
985C22×C4C23×D311yescharacteristic
986C22×C4C23×D311yescharacteristic
987C22×C4C23×D311yescharacteristic
988C22×C4C23×D311yescharacteristic
989C22×C4C23×D311yescharacteristic
990C22×C4C23×D311yescharacteristic
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—22no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—62no—
999C4⋊C4—62no—
1000C4⋊C4—62no—
1001C4⋊C4—62no—
1002C4⋊C4—62no—
1003C4⋊C4—62no—
1004C4⋊C4—62no—
1005C4⋊C4—62no—
1006C4⋊C4—62no—
1007C4⋊C4—62no—
1008C4⋊C4—62no—
1009C4⋊C4—62no—
1010C4⋊C4—62no—
1011C4⋊C4—62no—
1012C4⋊C4—121no—
1013C4⋊C4—121no—
1014C4⋊C4—121no—
1015C4⋊C4—121no—
1016C4⋊C4—121no—
1017C4⋊C4—121no—
1018C4⋊C4—121no—
1019C4⋊C4—121no—
1020C4⋊C4—121no—
1021C4⋊C4—121no—
1022C4⋊C4—121no—
1023C4⋊C4—121no—
1024C4⋊C4—121no—
1025C4⋊C4—121no—
1026C4⋊C4—121no—
1027C4⋊C4—121no—
1028C4⋊C4—121no—
1029C4⋊C4#23514yes—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—34no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—62no—
1036C22⋊C4—62no—
1037C22⋊C4—62no—
1038C22⋊C4—62no—
1039C22⋊C4—62no—
1040C22⋊C4—62no—
1041C22⋊C4—62no—
1042C22⋊C4—62no—
1043C22⋊C4—121no—
1044C22⋊C4—121no—
1045C22⋊C4—121no—
1046C22⋊C4—121no—
1047C22⋊C4—121no—
1048C22⋊C4—121no—
1049C22⋊C4—121no—
1050C22⋊C4—121no—
1051C22⋊C4—121no—
1052C22⋊C4—121no—
1053C22⋊C4—121no—
1054C42—41no—
1055C42—41no—
1056C42—41no—
1057C42—41no—
1058C42—62no—
1059C42—62no—
1060C42—62no—
1061C42—62no—
1062C42—62no—
1063C42—62no—
1064C42—121no—
1065C42—121no—
1066C42—121no—
1067C42—121no—
1068C42—121no—
1069C42—121no—
1070C42—121no—
1071C42—121no—
1072C42—121no—
1073C22×C3—22no—
1074C22×C3—22no—
1075C22×C3—22no—
1076C22×C3—41no—
1077C22×C3—41no—
1078C22×C3—41no—
1079C22×C3—41no—
1080C22×C3C22×#4111yescharacteristic
1081C22×C3C22×#4111yescharacteristic
1082C22×C3C2×2−1+411yescharacteristic
1083C22×C3#58511yescharacteristic
1084C22×C3#58511yescharacteristic
1085C22×C3#58511yescharacteristic
1086C22×C3#58511yescharacteristic
1087C2×D3—41no—
1088C2×D3—41no—
1089C2×D3—41no—
1090C2×D3—41no—
1091C2×D3—41no—
1092C2×D3—41no—
1093C2×D3—41no—
1094C3×C4—22no—
1095C3×C4—22no—
1096C3×C4—22no—
1097C3×C4—41no—
1098C3×C4—41no—
1099C3×C4—41no—
1100C3×C4—41no—
1101C3×C4—41no—
1102C3×C4—41no—
1103C3×C4—41no—
1104C3×C4—41no—
1105C3×C4—41no—
1106C3×C4—41no—
1107C3×C4—41no—
1108Dic3—22no—
1109Dic3—22no—
1110Dic3—22no—
1111Dic3—41no—
1112Dic3—41no—
1113Dic3—41no—
1114Dic3—41no—
1115Dic3—41no—
1116Dic3—41no—
1117Dic3—41no—
1118Dic3—41no—
1119Dic3—41no—
1120Dic3—41no—
1121Dic3—41no—
1122Dic3—41no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—61no—
1130C23—61no—
1131C23—61no—
1132C23—61no—
1133C23—61no—
1134C23—61no—
1135C23—61no—
1136C23D3×#4112yes—
1137C23C24×D311yescharacteristic
1138Q8—124no—
1139Q8—242no—
1140D4—242no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—32no—
1181C2×C4—32no—
1182C2×C4—32no—
1183C2×C4—44no—
1184C2×C4—61no—
1185C2×C4—61no—
1186C2×C4—61no—
1187C2×C4—61no—
1188C2×C4—61no—
1189C2×C4—61no—
1190C2×C4—61no—
1191C2×C4—61no—
1192C2×C4—61no—
1193C2×C4—61no—
1194C2×C4—61no—
1195C2×C4—61no—
1196C2×C4—61no—
1197C2×C4—61no—
1198C2×C4—61no—
1199C2×C4—61no—
1200C2×C4—61no—
1201C2×C4—61no—
1202C2×C4—61no—
1203C2×C4—61no—
1204C2×C4—61no—
1205C2×C4—61no—
1206C2×C4—61no—
1207C2×C4—61no—
1208C2×C4—61no—
1209C2×C4—61no—
1210C2×C4—61no—
1211C2×C4—61no—
1212C2×C4—61no—
1213C2×C4—61no—
1214C2×C4—61no—
1215C2×C4—61no—
1216C2×C4—61no—
1217C2×C4—61no—
1218C2×C4—61no—
1219C2×C4—61no—
1220C2×C4—61no—
1221C2×C4—61no—
1222C2×C4—61no—
1223C2×C4—61no—
1224C2×C4—61no—
1225C2×C4—61no—
1226C2×C4—82no—
1227C2×C4—82no—
1228C2×C4—242no—
1229C2×C4C2×#23512yes—
1230C2×C4C2×#23512yes—
1231C2×C4C2×#23512yes—
1232C2×C3—42no—
1233C2×C3#346111yescharacteristic
1234C2×C3#347511yescharacteristic
1235C2×C3#351611yescharacteristic
1236C2×C3#352111yescharacteristic
1237C2×C3#352111yescharacteristic
1238C2×C3#355711yescharacteristic
1239C2×C3#356611yescharacteristic
1240D3—81no—
1241C22—22no—
1242C22—22no—
1243C22—22no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—121no—
1249C22—121no—
1250C22—121no—
1251C22—121no—
1252C22—121no—
1253C22—121no—
1254C22—121no—
1255C22C22×#23511yescharacteristic
1256C22C2×D3×#4111yescharacteristic
1257C22#596411yescharacteristic
1258C22#596611yescharacteristic
1259C22#596611yescharacteristic
1260C22D3×2−1+411yescharacteristic
1261C22#596811yescharacteristic
1262C4—22no—
1263C4—22no—
1264C4—22no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—62no—
1277C4—62no—
1278C4—62no—
1279C4—121no—
1280C4—121no—
1281C4—121no—
1282C4—121no—
1283C4—121no—
1284C4—121no—
1285C4—121no—
1286C4—121no—
1287C4—121no—
1288C4—121no—
1289C4—121no—
1290C4—121no—
1291C3#3833911yescharacteristic, complemented, Sylow
1292C2—42no—
1293C2—241no—
1294C2#8574411yescharacteristic
1295C2#8586511yescharacteristic
1296C2#8588311yescharacteristic
1297C2#8642911yescharacteristic
1298C2#8643311yescharacteristic
1299C2#8644111yescharacteristic
1300C2#8645011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2313C2
prime radicalC22×#67C23
hypercenter#2313D3
hypocenterC3#38339
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2313

Complements

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

NH ≅ G/Ntype
1. C3×#2313C2semidirect
3. #82162C2semidirect
4. #75355C2semidirect
5. #75293C2semidirect
6. #75245C2semidirect
7. #75233C2semidirect
8. #75218C2semidirect
9. #75195C2semidirect
10. #75141C2semidirect
11. #75114C2semidirect
12. #75081C2semidirect
13. #75060C2semidirect
14. #75042C2semidirect
15. #75040C2semidirect
16. #75022C2semidirect
17. #75005C2semidirect
18. #74953C2semidirect
19. #74938C2semidirect
20. #74096C2semidirect
22. #74083C2semidirect
24. #73979C2semidirect
27. #73918C2semidirect
29. #73524C2semidirect
31. C4×#879C2semidirect
216. #2313D3semidirect
1291. C3#38339semidirect

Maximal subgroups

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

subgroupindex
C3×#23132
#821752
#821622
#753552
#752932
#752452
#752332
#752182
#751952
#751412
#751142
#750812
#750602
#750422
#750402
#750222
#750052
#749532
#749382
#740962
#740942
#740832
#740812
#739792
#739632
#739322
#739182
#735562
#735242
#734792
C4×#8792
#383393