Finite Group Databasebeta

← #11889141

Subgroups — #11889141

Order 1152.

960 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595379C211yesmaximal, characteristic, complemented
2#10595293C211yesmaximal, characteristic
3#10592873C211yesmaximal, characteristic, complemented
4C3×#5169C211yesmaximal, characteristic, complemented
5C3×#5163C211yesmaximal, characteristic, complemented
6#10591652C211yesmaximal, characteristic, complemented
7#10591634C211yesmaximal, characteristic, complemented
8#10591566C211yesmaximal, characteristic, complemented
9#10591477C211yesmaximal, characteristic, complemented
10#10591425C211yesmaximal, characteristic, complemented
11D3×#832C211yesmaximal, characteristic, complemented
12#10590941C211yesmaximal, characteristic, complemented
13#10590907C211yesmaximal, characteristic, complemented
14#10590767C211yesmaximal, characteristic, complemented
15#10590680C211yesmaximal, characteristic, complemented
16#80397—31nomaximal
17#80160—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic, complemented
22#64155C2211yescharacteristic, complemented
23#64147C2211yescharacteristic
24C2×#3743C2211yescharacteristic, complemented
25C3×#946C2211yescharacteristic, complemented
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic, complemented
29C3×#940C2211yescharacteristic
30#63983—21no—
31#63976—21no—
32#63970—21no—
33#63908C2211yescharacteristic
34C4×#626C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63890—21no—
37D3×C4⋊Dic3C2211yescharacteristic, complemented
38#63877—21no—
39#63869C2211yescharacteristic, complemented
40#63868—21no—
41#63849C2211yescharacteristic, complemented
42#63846—21no—
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63659C2211yescharacteristic, complemented
46#63645C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61D4×#67—31no—
62#5717—31no—
63#5642—31no—
64#5581—31no—
65C3×#460—31no—
66C3×#450—31no—
67C2×#832—31no—
68#5174—31no—
69#5174—31no—
70#5174—61no—
71#5171—31no—
72#5169—31no—
73#5169—31no—
74#5169D311yescharacteristic, complemented
75#5164—31no—
76#5163D311yescharacteristic, complemented
77#5071—31no—
78#5048—31no—
79#5026—31no—
80#4847—31no—
81#4836—31no—
82#4784—31no—
83#4779—31no—
84#4774—31no—
85#4770—31no—
86#4770—31no—
87D3×#102—31no—
88#4766—31no—
89#4764—31no—
90#4736—31no—
91#4730—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106D3×#67—44no—
107C2×#626D411yescharacteristic
108C2×#625—21no—
109C2×#625—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112#3802—22no—
113#3802—41no—
114C32×SD16—41no—
115C2×C32×C8C2311yescharacteristic
116#3757—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122#3743—41no—
123C3×#215—22no—
124C3×#215—41no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3D411yescharacteristic
138#3722—21no—
139#3722D411yescharacteristic
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3D411yescharacteristic
143Dic32—21no—
144D3×C3⋊C8—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×D3×D4C2×D311yescharacteristic
152C2×C3×SD16—21no—
153C2×C3×SD16—31no—
154C2×C3×SD16—31no—
155C2×C3×SD16C2×D311yescharacteristic, complemented
156C2×C3×SD16C2×D311yescharacteristic, complemented
157C3×#127—31no—
158C3×C22⋊Q8—31no—
159C3×C4×Q8—31no—
160#953—61no—
161#946—31no—
162#946—31no—
163#946—61no—
164#946C2×D311yescharacteristic, complemented
165Q8×Dic3C2×D311yescharacteristic, complemented
166C2×#215C2×D311yescharacteristic
167C2×#215C2×D311yescharacteristic, complemented
168#940C2×D311yescharacteristic
169#939—61no—
170#938—31no—
171#938—31no—
172#938—31no—
173#938—61no—
174#938—61no—
175#937—61no—
176#937—61no—
177#937—61no—
178D4×Dic3—31no—
179#930—31no—
180C4×#67—31no—
181C2×C4⋊Dic3—31no—
182C22×C3⋊C8—31no—
183C2×ΓL(1,𝔽25)—31no—
184C2×ΓL(1,𝔽25)—31no—
185C2×ΓL(1,𝔽25)—61no—
186C2×D3×C8—31no—
187#898—61no—
188#894—61no—
189#892—31no—
190#892—31no—
191D3×C4⋊C4—31no—
192#890—31no—
193#890—61no—
194#889—61no—
195#886—61no—
196#877—61no—
197#876—61no—
198C4×D12—31no—
199C4×D12—31no—
200#872—61no—
201#870—31no—
202C3×C4⋊C8—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C22⋊C8—31no—
208#835—31no—
209#835—31no—
210#835—61no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—31no—
217#832—61no—
218#832C2×D311yescharacteristic, complemented
219#832C2×D311yescharacteristic, complemented
220#821—31no—
221#821—31no—
222#821C2×D311yescharacteristic
223#821C2×D311yescharacteristic, complemented
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8C2×D311yescharacteristic, complemented
227#818—31no—
228#818—31no—
229#818—31no—
230#818—61no—
231#817—31no—
232#815—31no—
233Dic3⋊C8C2×D311yescharacteristic, complemented
234#809—31no—
235#809—31no—
236#808—31no—
237#807—31no—
238#803—31no—
239C23×C32—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—81no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C32×Q8—21no—
251C32×Q8—21no—
252C32×D4—21no—
253C32×D4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C2411yescharacteristic
256#638—42no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C4×C3⋊D3—21no—
261C4×C3⋊D3—21no—
262C3×#67—42no—
263C3×#67—42no—
264C3×#67—81no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12#4112yes—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276#626—22no—
277#625—42no—
278#625—42no—
279D3×Dic3—42no—
280D3×Dic3—42no—
281C32×C8—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—91no—
287#490—91no—
288#482—91no—
289#480—91no—
290#478—91no—
291#468—91no—
292#465—91no—
293#460—31no—
294#450—31no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C24×C3—61no—
301C23×D3—21no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×Q8—21no—
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×D4—21no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—61no—
311C2×C3×D4—61no—
312C2×C3×D4—61no—
313C2×C3×D4—62no—
314C2×C3×D4—121no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C22×C3×C4—31no—
318C2×#67—21no—
319C2×#67—21no—
320C2×#67—21no—
321C2×#67—31no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—121no—
329C2×#67—124no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332D3×D4—22no—
333D3×D4—41no—
334D3×D4—62no—
335D3×D4—62no—
336D3×D4—121no—
337D3×D4—121no—
338D3×D4—124no—
339C2×D12—31no—
340C2×D12C22×D311yescharacteristic
341C2×D12C22×D311yescharacteristic
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3C22×D311yescharacteristic
348C3×SD16—41no—
349C3×SD16—41no—
350C3×SD16—42no—
351C3×SD16—62no—
352C3×SD16—121no—
353C2×C3×C8—21no—
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—31no—
364C3×C42—61no—
365#217—31no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—121no—
371#215—22no—
372#215—41no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—121no—
384C4⋊Dic3—21no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—31no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—121no—
405C4×Dic3—21no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3C22×D311yescharacteristic
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8—121no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415ΓL(1,𝔽25)—121no—
416ΓL(1,𝔽25)—121no—
417ΓL(1,𝔽25)—122no—
418D3×C8—121no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—22no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—84no—
435C2×C3×D3AGL(1,ℤ/8)12yes—
436D32—84no—
437C32×C4—41no—
438C32×C4C2×#4111yescharacteristic
439C32×C4H(5,𝔽2)11yescharacteristic
440C3⋊Dic3—21no—
441C3⋊Dic3—41no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C22×D4—31no—
449C22×D4—91no—
450C22×D4—181no—
451C2×SD16—31no—
452C2×SD16—31no—
453C2×SD16D3211yescharacteristic, complemented
454C2×M16—91no—
455C22×C8—91no—
456#127—31no—
457#126—181no—
458#125—91no—
459#125—181no—
460#123—181no—
461C22⋊Q8—31no—
462C22⋊Q8—91no—
463#121—91no—
464#121—91no—
465#121—181no—
466#120—181no—
467#120—181no—
468C4×Q8—31no—
469C4×D4—91no—
470C4×D4—91no—
471#117—91no—
472#117—181no—
473C2×C4⋊C4—91no—
474#107—91no—
475#107—91no—
476#106—91no—
477C4⋊C8—31no—
478#103—91no—
479#102—31no—
480#102—31no—
481#102—31no—
482#102—31no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488C22⋊C8—31no—
489C22⋊C8—91no—
490#97—91no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—31no—
494C23×C3—41no—
495C23×C3—61no—
496C23×C3—61no—
497C23×C3—122no—
498C23×C3—122no—
499C23×C3—241no—
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—31no—
503C22×D3—31no—
504C22×D3—42no—
505C22×D3—42no—
506C22×D3—61no—
507C22×D3—81no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—241no—
513C22×D3—241no—
514C22×D3D3×D411yescharacteristic
515C3×Q8—21no—
516C3×Q8—21no—
517C3×Q8—21no—
518C3×Q8—21no—
519C3×Q8—41no—
520C3×Q8—41no—
521C3×D4—21no—
522C3×D4—21no—
523C3×D4—21no—
524C3×D4—21no—
525C3×D4—32no—
526C3×D4—41no—
527C3×D4—41no—
528C3×D4—61no—
529C3×D4—61no—
530C3×D4—61no—
531C3×D4—122no—
532C3×D4—122no—
533C3×D4—241no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
540C2×C3×C4—41no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4C23×D311yescharacteristic
546C2×C3×C4C23×D311yescharacteristic
547#67—42no—
548#67—42no—
549#67—62no—
550#67—81no—
551#67—122no—
552#67—122no—
553#67—122no—
554#67—122no—
555#67—122no—
556#67—122no—
557#67—242no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—121no—
568C2×Dic3—121no—
569C2×Dic3—122no—
570C2×Dic3—122no—
571C2×Dic3D3×D411yescharacteristic
572C2×Dic3D3×D411yescharacteristic
573C2×Dic3D3×D411yescharacteristic
574D12—21no—
575D12—21no—
576D12—21no—
577D12—62no—
578D12#23712yes—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—61no—
582C4×D3—61no—
583C4×D3—61no—
584C4×D3—61no—
585C4×D3—121no—
586C4×D3—121no—
587C4×D3—122no—
588C4×D3—122no—
589C3×C8—22no—
590C3×C8—21no—
591C3×C8—21no—
592C3×C8—61no—
593C3×C8—61no—
594C3⋊C8—21no—
595C3⋊C8—21no—
596C3⋊C8—61no—
597C3⋊C8—61no—
598C3⋊C8—121no—
599C2×C32—81no—
600C2×C32#54611yescharacteristic
601C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
602C2×C32#57711yescharacteristic
603C3⋊D3—41no—
604C3×D3—22no—
605C3×D3—42no—
606C3×D3—81no—
607C24—61no—
608C24—181no—
609C2×Q8C2×D3211yescharacteristic
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—61no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—62no—
616C2×D4—91no—
617C2×D4—121no—
618C2×D4—181no—
619C2×D4—182no—
620C2×D4—181no—
621C2×D4—181no—
622C2×D4—361no—
623C2×D4—364no—
624C2×D4C2×D3211yescharacteristic
625C22×C4—31no—
626C22×C4—91no—
627C22×C4—181no—
628C22×C4—181no—
629SD16—41no—
630SD16—62no—
631SD16—121no—
632M16—361no—
633C2×C8—31no—
634C2×C8—31no—
635C2×C8—91no—
636C2×C8—361no—
637C2×C8C2×D3211yescharacteristic
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—91no—
643C4⋊C4—91no—
644C4⋊C4—91no—
645C4⋊C4—181no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C22⋊C4—61no—
650C22⋊C4—91no—
651C22⋊C4—91no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C42—31no—
658C42—61no—
659C42—181no—
660C22×C3—21no—
661C22×C3—32no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—62no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—244no—
680C22×C3C2×D3×D411yescharacteristic
681C22×C3C2×D3×D411yescharacteristic
682C2×D3—21no—
683C2×D3—21no—
684C2×D3—22no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—84no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—244no—
701C2×D3—244no—
702C2×D3#91412yes—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—61no—
708C3×C4—61no—
709C3×C4—61no—
710C3×C4—81no—
711C3×C4—121no—
712C3×C4—121no—
713C3×C4C2×#23711yescharacteristic
714C3×C4#100411yescharacteristic
715C3×C4#100411yescharacteristic
716C3×C4D3×#4111yescharacteristic
717Dic3—21no—
718Dic3—21no—
719Dic3—21no—
720Dic3—41no—
721Dic3—41no—
722Dic3—61no—
723Dic3—61no—
724Dic3—121no—
725Dic3—121no—
726Dic3—121no—
727Dic3—121no—
728Dic3—121no—
729Dic3—241no—
730Dic3—241no—
731C32#331011yescharacteristic, complemented, Sylow
732C23—21no—
733C23—31no—
734C23—61no—
735C23—61no—
736C23—91no—
737C23—122no—
738C23—122no—
739C23—241no—
740C23—362no—
741C23—362no—
742C23—721no—
743Q8—21no—
744Q8—21no—
745D4—21no—
746D4—21no—
747D4—32no—
748D4—61no—
749D4—61no—
750D4—61no—
751D4—122no—
752D4—122no—
753D4—182no—
754D4—241no—
755D4—362no—
756D4—362no—
757D4—362no—
758C2×C4—21no—
759C2×C4—31no—
760C2×C4—31no—
761C2×C4—31no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—91no—
767C2×C4—181no—
768C2×C4—181no—
769C2×C4—181no—
770C2×C4—181no—
771C2×C4—362no—
772C2×C4—362no—
773C2×C4C22×D3211yescharacteristic
774C8—21no—
775C8—61no—
776C8—61no—
777C8—181no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—62no—
782C2×C3—81no—
783C2×C3—81no—
784C2×C3—122no—
785C2×C3—161no—
786C2×C3—241no—
787C2×C3#559111yescharacteristic
788C2×C3#561211yescharacteristic
789C2×C3C2×#91411yescharacteristic
790C2×C3#576211yescharacteristic
791C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
792C2×C3#577511yescharacteristic
793D3—22no—
794D3—42no—
795D3—81no—
796D3—121no—
797D3—121no—
798D3—241no—
799C22—32no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—61no—
804C22—61no—
805C22—62no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—121no—
811C22—181no—
812C22—181no—
813C22—181no—
814C22—244no—
815C22—724no—
816C22D32×D411yescharacteristic
817C4—41no—
818C4—61no—
819C4—61no—
820C4—61no—
821C4—121no—
822C4—121no—
823C4—181no—
824C4—361no—
825C4—361no—
826C4D3×#23711yescharacteristic
827C4#6433011yescharacteristic
828C3—21no—
829C3#8016011yescharacteristic, complemented
830C3#8039711yescharacteristic, complemented
831C2—62no—
832C2—81no—
833C2—122no—
834C2—241no—
835C2—361no—
836C2D3×#91411yescharacteristic
837C2#1059474911yescharacteristic
838C2#1059529411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595293C2
hypercenterC2×SD16D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10595379C2semidirect
3. #10592873C2semidirect
4. C3×#5169C2semidirect
5. C3×#5163C2semidirect
6. #10591652C2semidirect
7. #10591634C2semidirect
8. #10591566C2semidirect
9. #10591477C2semidirect
10. #10591425C2semidirect
11. D3×#832C2semidirect
12. #10590941C2semidirect
13. #10590907C2semidirect
14. #10590767C2semidirect
15. #10590680C2semidirect
21. C2×C32×SD16C22semidirect
22. #64155C22semidirect
24. C2×#3743C22semidirect
25. C3×#946C22semidirect
26. C3×Q8×Dic3C22semidirect
28. C2×C3×#215C22semidirect
37. D3×C4⋊Dic3C22semidirect
39. #63869C22semidirect
41. #63849C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63662C22semidirect
45. #63659C22semidirect
46. #63645C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
50. C3×#821C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. #63575C22semidirect
54. #63573C22semidirect
56. #63563C22semidirect
58. #63562C22semidirect
59. #63557C22semidirect
60. #63554C22semidirect
74. #5169D3semidirect
76. #5163D3semidirect
155. C2×C3×SD16C2×D3semidirect
156. C2×C3×SD16C2×D3semidirect
164. #946C2×D3semidirect
165. Q8×Dic3C2×D3semidirect
167. C2×#215C2×D3semidirect
218. #832C2×D3semidirect
219. #832C2×D3semidirect
223. #821C2×D3semidirect
226. (C2×D3)⋊C8C2×D3semidirect
233. Dic3⋊C8C2×D3semidirect
453. C2×SD16D32semidirect
731. C32#3310semidirect
829. C3#80160semidirect
830. C3#80397semidirect

Maximal subgroups

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

subgroupindex
#105953792
#105952932
#105928732
C3×#51692
C3×#51632
#105916522
#105916342
#105915662
#105914772
#105914252
D3×#8322
#105909412
#105909072
#105907672
#105906802
#803973
#801603