Finite Group Databasebeta

← #11860504

Subgroups — #11860504

Order 1152.

1181 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596016C211yesmaximal, characteristic, complemented
2C2×#63937C211yesmaximal, characteristic
3#10593889C211yesmaximal, characteristic, complemented
4C3×#5018C211yesmaximal, characteristic, complemented
5C3×C4×#213C211yesmaximal, characteristic, complemented
6#10591445C211yesmaximal, characteristic, complemented
7#10591436C211yesmaximal, characteristic, complemented
8#10591416C211yesmaximal, characteristic, complemented
9#10590611C211yesmaximal, characteristic, complemented
10#10590582C211yesmaximal, characteristic, complemented
11#10590484C211yesmaximal, characteristic, complemented
12#10590459C211yesmaximal, characteristic, complemented
13C4×#3717C211yesmaximal, characteristic, complemented
14#10590346C211yesmaximal, characteristic, complemented
15#10590321C211yesmaximal, characteristic, complemented
16#79775—31nomaximal
17#79587—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22C4×#638—21no—
23C2×#3752—21no—
24#64102C2211yescharacteristic
25#64101C2211yescharacteristic
26#64090—21no—
27C22⋊C4×C3⋊D3—21no—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29#64081C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic, complemented
33C3×C4×Dic6C2211yescharacteristic, complemented
34#63937C418yescomplemented
35#63904—21no—
36#63900C2211yescharacteristic
37#63898C2211yescharacteristic, complemented
38#63880—21no—
39#63877—21no—
40D3×Dic3⋊C4—21no—
41#63843C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#810C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#803C2211yescharacteristic, complemented
53C3×C4×C3⋊C8C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61#63553C2211yescharacteristic, complemented
62C2×#914—31no—
63C2×#911—31no—
64#5574—31no—
65#5546—31no—
66#5545—31no—
67#5545—31no—
68#5545—61no—
69C3×#440—31no—
70C3×C4×D8—31no—
71Dic3×SD16—31no—
72#5152—31no—
73C4×#215—31no—
74#5018D311yescharacteristic, complemented
75#5014—31no—
76C4×#213D311yescharacteristic, complemented
77#4889—31no—
78#4881—31no—
79#4881—31no—
80#4872—31no—
81#4817—31no—
82#4804—31no—
83#4785—31no—
84#4772—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4758—31no—
88#4756—31no—
89#4711—31no—
90#4708—31no—
91C4×#204—31no—
92#4689—31no—
93C23×C3⋊D3—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×#638—21no—
97C22×C3⋊Dic3—21no—
98D4×C3⋊D3—22no—
99D4×C3⋊D3C2×C414yescomplemented
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3796—22no—
112#3796C2×C414yescomplemented
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115C32×C42C2311yescharacteristic
116#3757—21no—
117#3752—21no—
118#3752—21no—
119#3752—21no—
120#3752D411yescharacteristic
121#3752D411yescharacteristic
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123#3750D411yescharacteristic
124#3750D411yescharacteristic
125C4×C3⋊Dic3—21no—
126C4×C3⋊Dic3C2311yescharacteristic
127C3×#214C2×C414yescomplemented
128C3×#213C2×C414yescomplemented
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3724—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3717C2×C414yescomplemented
143#3714C2×C414yescomplemented
144#3712C2×C414yescomplemented
145#3710—22no—
146#2946—91noSylow
147C2×#239—31no—
148C2×#237—31no—
149C2×D3×D4—31no—
150C2×D3×D4—31no—
151C2×D3×D4—61no—
152C2×C3×SD16—31no—
153C2×C3×D8—31no—
154C3×C4×Q8—31no—
155C3×C4×D4—21no—
156C3×C4×D4—31no—
157C3×C4×D4C2×D311yescharacteristic
158C3×C4×D4C2×D311yescharacteristic
159Q8×Dic3—31no—
160C2×#215—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—61no—
165C2×#214C2×D311yescharacteristic
166C2×#213—31no—
167C2×#213C2×D311yescharacteristic
168C4×#67—61no—
169C4×#67—61no—
170C4×#67—61no—
171C4×#67—62no—
172C2×(C2×D3)⋊C4—61no—
173C2×(C2×D3)⋊C4—61no—
174C2×(C2×D3)⋊C4—62no—
175C2×Dic3⋊C4—61no—
176#914—38no—
177#911—38no—
178C2×D24—31no—
179C2×#204—31no—
180C2×ΓL(1,𝔽25)—31no—
181C2×ΓL(1,𝔽25)—31no—
182C2×D3×C8—31no—
183C2×D3×C8—31no—
184#893—31no—
185#893—31no—
186#893—31no—
187#893—61no—
188#893—61no—
189#892—31no—
190#892—31no—
191#892—61no—
192D3×C4⋊C4—31no—
193D3×C4⋊C4—31no—
194D3×C4⋊C4—61no—
195#887—31no—
196#67⋊C4—61no—
197#67⋊C4—61no—
198#67⋊C4—61no—
199#67⋊C4—62no—
200D3×C22⋊C4—61no—
201D3×C22⋊C4—61no—
202D3×C22⋊C4—62no—
203#877—61no—
204C4×D12—31no—
205C4×D12—31no—
206C4×D12—61no—
207C4×D12—61no—
208C4×D12C2×D311yescharacteristic, complemented
209#872—31no—
210#872—31no—
211#872—61no—
212#872—61no—
213C4×Dic6C2×D311yescharacteristic, complemented
214C3×#107—31no—
215C3×#107—31no—
216C3×#103—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#97—31no—
221C3×C4×C8—31no—
222#835—31no—
223#832—31no—
224#832C2×D311yescharacteristic
225#832C2×D311yescharacteristic
226#821—31no—
227#821—31no—
228#821—31no—
229#817—31no—
230#817—31no—
231#816—31no—
232#815—31no—
233#815—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#810C2×D311yescharacteristic, complemented
237#809—31no—
238#809—31no—
239#809C2×D311yescharacteristic, complemented
240#808—31no—
241#808—31no—
242#807C2×D311yescharacteristic, complemented
243#807C2×D311yescharacteristic, complemented
244#803C2×D311yescharacteristic, complemented
245C4×C3⋊C8C2×D311yescharacteristic, complemented
246C23×C32—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—24no—
249C22×C3⋊D3—81no—
250C22×C3⋊D3—81no—
251C22×C3⋊D3C2×D411yescharacteristic
252C22×C3×D3—21no—
253C32×D4—21no—
254C32×D4C22×C412yes—
255C2×C32×C4—21no—
256C2×C32×C4—81no—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2411yescharacteristic
260#638—24no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—81no—
263C2×C3⋊Dic3C2×D411yescharacteristic
264C2×C3⋊Dic3C2×D411yescharacteristic
265C2×C3⋊Dic3C2×D411yescharacteristic
266C4⋊(C3⋊D3)—21no—
267C4⋊(C3⋊D3)C22×C412yes—
268C4×C3⋊D3—81no—
269C4×C3⋊D3—81no—
270C4×C3⋊D3C22×C412yes—
271C4×C3⋊D3#4112yes—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C3×D12—21no—
276C3×D12C22×C412yes—
277C3×C4×D3—81no—
278C3×Dic6—21no—
279C3×Dic6C22×C412yes—
280#626—24no—
281#624—81no—
282D3×Dic3—24no—
283D3×Dic3—81no—
284C3×C3⋊C8—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8C22×C412yes—
287C3×C3⋊C8C22×C412yes—
288C2×AGL(1,ℤ/8)—91no—
289#520—91no—
290#518—91no—
291#442—91no—
292#442—91no—
293#440—31no—
294#440—91no—
295C4×SD16—91no—
296C4×SD16—91no—
297C4×D8—31no—
298C4×D8—91no—
299#428—91no—
300#416—91no—
301C2×#102—91no—
302#405—91no—
303C23×D3—61no—
304C23×D3—61no—
305C23×D3—62no—
306C2×C3×Q8—31no—
307C2×C3×D4—21no—
308C2×C3×D4—31no—
309C2×C3×D4C22×D311yescharacteristic
310C2×C3×D4C22×D311yescharacteristic
311C22×C3×C4—22no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—62no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—62no—
324#239—34no—
325#239—62no—
326#237—34no—
327#237—62no—
328D3×D4—34no—
329D3×D4—34no—
330D3×D4—64no—
331D3×D4—62no—
332D3×D4—62no—
333D3×D4—64no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12C22×D311yescharacteristic
339C2×C4×D3—21no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—62no—
350C2×C4×D3—62no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×Dic6C22×D311yescharacteristic
354C3×SD16—34no—
355C3×D8—34no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C2×C3×C8—31no—
359C2×C3×C8—31no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C22⋊C4—22no—
367C3×C22⋊C4—21no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—61no—
370C3×C42—21no—
371C3×C42—61no—
372C3×C42C22×D311yescharacteristic
373C3×C42C22×D311yescharacteristic
374#217—61no—
375#217—61no—
376#217—61no—
377#217—62no—
378#215—34no—
379#214C4×D314yescomplemented
380#213—34no—
381#213C4×D314yescomplemented
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—31no—
384(C2×D3)⋊C4—31no—
385(C2×D3)⋊C4—31no—
386(C2×D3)⋊C4—31no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—62no—
395(C2×D3)⋊C4—62no—
396(C2×D3)⋊C4—62no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399C4⋊Dic3—31no—
400C4⋊Dic3—31no—
401C4⋊Dic3—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3C22×D311yescharacteristic
404C4⋊Dic3C22×D311yescharacteristic
405Dic3⋊C4—21no—
406Dic3⋊C4—31no—
407Dic3⋊C4—31no—
408Dic3⋊C4—31no—
409Dic3⋊C4—31no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415C4×Dic3—21no—
416C4×Dic3—31no—
417C4×Dic3—31no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—62no—
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428D24—34no—
429#204—34no—
430ΓL(1,𝔽25)—34no—
431ΓL(1,𝔽25)—34no—
432D3×C8—62no—
433D3×C8—62no—
434C22×C32—22no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32C22×D411yescharacteristic
438C2×C3⋊D3—22no—
439C2×C3⋊D3—21no—
440C2×C3⋊D3—21no—
441C2×C3⋊D3—41no—
442C2×C3⋊D3—41no—
443C2×C3⋊D3—84no—
444C2×C3⋊D3C4×D412yes—
445C2×C3×D3—22no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C32×C4—21no—
449C32×C4—21no—
450C32×C4—41no—
451C32×C4C23×C411yescharacteristic
452C32×C4C2×#4111yescharacteristic
453C3⋊Dic3—21no—
454C3⋊Dic3—21no—
455C3⋊Dic3—41no—
456C3⋊Dic3C4×D412yes—
457C3×Dic3—22no—
458C3×Dic3—41no—
459C3×Dic3—41no—
460C2×#41—91no—
461C22×D4—91no—
462AGL(1,ℤ/8)—98no—
463C2×SD16—31no—
464C2×SD16—91no—
465C2×D8—31no—
466C2×D8—91no—
467C2×M16—91no—
468C22×C8—91no—
469C4×Q8—31no—
470C4×Q8—91no—
471C4×D4—31no—
472C4×D4—91no—
473C4×D4—91no—
474C4×D4—91no—
475C4×D4—91no—
476C4×D4—181no—
477C4×D4—181no—
478C4×D4—181no—
479C4×D4—181no—
480C4×D4D3211yescharacteristic
481#117—91no—
482#117—91no—
483#117—181no—
484C2×C4⋊C4—91no—
485C2×C4⋊C4—181no—
486C2×C22⋊C4—181no—
487C2×C22⋊C4—181no—
488#107—31no—
489#107—31no—
490#106—91no—
491#106—91no—
492#103—31no—
493#103—91no—
494#102—31no—
495#102—31no—
496#102—31no—
497#102—91no—
498#102—91no—
499#102—91no—
500#97—31no—
501#97—91no—
502C4×C8—31no—
503C4×C8—91no—
504C23×C3—22no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—61no—
508C22×D3—21no—
509C22×D3—31no—
510C22×D3—31no—
511C22×D3—61no—
512C22×D3—64no—
513C22×D3—64no—
514C22×D3—62no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—68no—
518C22×D3—241no—
519C22×D3—241no—
520C22×D3—241no—
521C22×D3—241no—
522C22×D3—242no—
523C22×D3—242no—
524C3×Q8—32no—
525C3×Q8—61no—
526C3×D4—22no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—22no—
530C3×D4—32no—
531C3×D4—61no—
532C3×D4C2×C4×D312yes—
533C3×D4C2×C4×D312yes—
534C2×C3×C4—22no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—81no—
544C2×C3×C4—81no—
545C2×C3×C4—82no—
546C2×C3×C4—241no—
547C2×C3×C4D3×D411yescharacteristic
548C2×C3×C4D3×D411yescharacteristic
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553#67—64no—
554#67—64no—
555#67—64no—
556#67—68no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—31no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—64no—
570C2×Dic3—62no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—241no—
574C2×Dic3—241no—
575C2×Dic3—241no—
576C2×Dic3—242no—
577D12—21no—
578D12—32no—
579D12—32no—
580D12—62no—
581D12—62no—
582D12—64no—
583D12—61no—
584D12—61no—
585D12C2×C4×D312yes—
586C4×D3—32no—
587C4×D3—32no—
588C4×D3—32no—
589C4×D3—32no—
590C4×D3—62no—
591C4×D3—62no—
592C4×D3—64no—
593C4×D3—81no—
594C4×D3—241no—
595C4×D3—241no—
596C4×D3—241no—
597C4×D3—241no—
598C4×D3—241no—
599C4×D3—241no—
600C4×D3—241no—
601C4×D3—242no—
602C4×D3—242no—
603Dic6—21no—
604Dic6C2×C4×D312yes—
605C3×C8—32no—
606C3×C8—32no—
607C3×C8—61no—
608C3×C8—61no—
609C3⋊C8—21no—
610C3⋊C8—21no—
611C3⋊C8C2×C4×D312yes—
612C3⋊C8C2×C4×D312yes—
613C2×C32—42no—
614C2×C32C2×C4×D411yescharacteristic
615C2×C32#57611yescharacteristic
616C2×C32#57711yescharacteristic
617C3⋊D3—22no—
618C3⋊D3—42no—
619C3×D3—42no—
620C24—181no—
621#41—94no—
622#41—182no—
623C2×Q8—31no—
624C2×D4—31no—
625C2×D4—94no—
626C2×D4—91no—
627C2×D4—181no—
628C2×D4—182no—
629C2×D4—181no—
630C2×D4C2×D3211yescharacteristic
631C22×C4—21no—
632C22×C4—61no—
633C22×C4—91no—
634C22×C4—181no—
635C22×C4—181no—
636C22×C4—181no—
637C22×C4—181no—
638C22×C4—181no—
639C22×C4—181no—
640SD16—34no—
641SD16—94no—
642D8—34no—
643D8—94no—
644M16—94no—
645C2×C8—31no—
646C2×C8—31no—
647C2×C8—31no—
648C2×C8—31no—
649C2×C8—182no—
650C4⋊C4—31no—
651C4⋊C4—31no—
652C4⋊C4—61no—
653C4⋊C4—91no—
654C4⋊C4—91no—
655C4⋊C4—91no—
656C4⋊C4—181no—
657C4⋊C4—181no—
658C4⋊C4C2×D3211yescharacteristic
659C22⋊C4—21no—
660C22⋊C4—61no—
661C22⋊C4—91no—
662C22⋊C4—91no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C22⋊C4—181no—
667C22⋊C4—181no—
668C42—61no—
669C42—91no—
670C42—181no—
671C42—181no—
672C42C2×D3211yescharacteristic
673C22×C3—24no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—21no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—62no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3C2×D3×D411yescharacteristic
687C22×C3C2×D3×D411yescharacteristic
688C2×D3—22no—
689C2×D3—32no—
690C2×D3—32no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—62no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—64no—
699C2×D3—62no—
700C2×D3—62no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—122no—
704C2×D3—122no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—244no—
710C2×D3—244no—
711C2×D3—248no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—42no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—62no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4C22×C4×D311yescharacteristic
727C3×C4C22×C4×D311yescharacteristic
728C3×C4D3×#4111yescharacteristic
729C3×C4D3×#4111yescharacteristic
730Dic3—22no—
731Dic3—32no—
732Dic3—32no—
733Dic3—41no—
734Dic3—41no—
735Dic3—62no—
736Dic3—61no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—121no—
741Dic3—121no—
742Dic3—122no—
743Dic3—121no—
744Dic3—121no—
745C32#294611yescharacteristic, complemented, Sylow
746C23—21no—
747C23—61no—
748C23—91no—
749C23—184no—
750C23—181no—
751C23—721no—
752C23—721no—
753Q8—32no—
754Q8—61no—
755D4—21no—
756D4—32no—
757D4—61no—
758D4—92no—
759D4—184no—
760D4—184no—
761D4—181no—
762D4C4×D3212yes—
763C2×C4—21no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—81no—
768C2×C4—91no—
769C2×C4—92no—
770C2×C4—92no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—184no—
774C2×C4—181no—
775C2×C4—241no—
776C2×C4—721no—
777C2×C4—721no—
778C2×C4—721no—
779C2×C4—721no—
780C2×C4—721no—
781C2×C4#381111yescharacteristic
782C2×C4#381111yescharacteristic
783C2×C4C22×D3211yescharacteristic
784C8—32no—
785C8—32no—
786C8—61no—
787C8—61no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—44no—
792C2×C3—42no—
793C2×C3—42no—
794C2×C3—122no—
795C2×C3C4×D3×D411yescharacteristic
796C2×C3C4×D3×D411yescharacteristic
797C2×C3#575711yescharacteristic
798C2×C3#577011yescharacteristic
799C2×C3#577411yescharacteristic
800C2×C3#577811yescharacteristic
801D3—42no—
802D3—62no—
803D3—62no—
804D3—122no—
805D3—124no—
806D3—122no—
807D3—122no—
808C22—22no—
809C22—41no—
810C22—41no—
811C22—62no—
812C22—92no—
813C22—121no—
814C22—121no—
815C22—181no—
816C22—181no—
817C22—182no—
818C22—361no—
819C22—361no—
820C22—724no—
821C22C2×#381111yescharacteristic
822C4—21no—
823C4—21no—
824C4—41no—
825C4—62no—
826C4—92no—
827C4—121no—
828C4—121no—
829C4—181no—
830C4—181no—
831C4—361no—
832C4C2×C4×D3211yescharacteristic
833C4#6430611yescharacteristic
834C3—21no—
835C3#7958711yescharacteristic, complemented
836C3#7977511yescharacteristic, complemented
837C2—42no—
838C2—122no—
839C2—182no—
840C2—362no—
841C2C4×#381111yescharacteristic
842C2#1059510211yescharacteristic
843C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#63937C2
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32#2946
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596016C2semidirect
3. #10593889C2semidirect
4. C3×#5018C2semidirect
5. C3×C4×#213C2semidirect
6. #10591445C2semidirect
7. #10591436C2semidirect
8. #10591416C2semidirect
9. #10590611C2semidirect
10. #10590582C2semidirect
11. #10590484C2semidirect
12. #10590459C2semidirect
13. C4×#3717C2semidirect
14. #10590346C2semidirect
15. #10590321C2semidirect
32. C3×C4×D12C22semidirect
33. C3×C4×Dic6C22semidirect
34. #63937C4semidirect
37. #63898C22semidirect
41. #63843C22semidirect
48. C3×#810C22semidirect
49. C3×#809C22semidirect
50. C3×#807C22semidirect
51. C3×#807C22semidirect
52. C3×#803C22semidirect
53. C3×C4×C3⋊C8C22semidirect
54. #63573C22semidirect
55. #63573C22semidirect
56. #63566C22semidirect
59. #63563C22semidirect
60. #63555C22semidirect
61. #63553C22semidirect
74. #5018D3semidirect
76. C4×#213D3semidirect
99. D4×C3⋊D3C2×C4semidirect
112. #3796C2×C4semidirect
127. C3×#214C2×C4semidirect
128. C3×#213C2×C4semidirect
142. #3717C2×C4semidirect
143. #3714C2×C4semidirect
144. #3712C2×C4semidirect
208. C4×D12C2×D3semidirect
213. C4×Dic6C2×D3semidirect
236. #810C2×D3semidirect
239. #809C2×D3semidirect
242. #807C2×D3semidirect
243. #807C2×D3semidirect
244. #803C2×D3semidirect
245. C4×C3⋊C8C2×D3semidirect
379. #214C4×D3semidirect
381. #213C4×D3semidirect
745. C32#2946semidirect
835. C3#79587semidirect
836. C3#79775semidirect

Maximal subgroups

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

subgroupindex
#105960162
C2×#639372
#105938892
C3×#50182
C3×C4×#2132
#105914452
#105914362
#105914162
#105906112
#105905822
#105904842
#105904592
C4×#37172
#105903462
#105903212
#797753
#795873