Finite Group Databasebeta

← #11872815

Subgroups — #11872815

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595349C211yesmaximal, characteristic, complemented
2#10595215C211yesmaximal, characteristic
3SD16×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#5169C211yesmaximal, characteristic
5C3×#5162C211yesmaximal, characteristic, complemented
6#10591572C211yesmaximal, characteristic, complemented
7#10591564C211yesmaximal, characteristic, complemented
8#10591558C211yesmaximal, characteristic, complemented
9#10591458C211yesmaximal, characteristic
10#10591446C211yesmaximal, characteristic, complemented
11#10591411C211yesmaximal, characteristic, complemented
12#10590772C211yesmaximal, characteristic, complemented
13#10590742C211yesmaximal, characteristic, complemented
14#10590711C211yesmaximal, characteristic, complemented
15#10590698C211yesmaximal, characteristic, complemented
16#80413—31nomaximal
17#80137—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic, complemented
21D4×C3⋊Dic3C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#944C2211yescharacteristic, complemented
24C2×C3×#215C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27#67⋊Dic3—21no—
28Dic3×#67—21no—
29D3×#217—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63898C2211yescharacteristic
32Dic3×D12C2211yescharacteristic
33#63870—21no—
34#63869C2211yescharacteristic, complemented
35#63862—21no—
36#63861—21no—
37#63856C2211yescharacteristic
38#63855C2211yescharacteristic
39#63845—21no—
40#63843C2211yescharacteristic, complemented
41#63841C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43#63662C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63644C2211yescharacteristic, complemented
46C8×C3⋊Dic3C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#5798—31no—
62#5731—31no—
63#5625—31no—
64#5545—31no—
65C3×#461—31no—
66C3×#450—31no—
67#5218—31no—
68#5169—31no—
69#5169D311yescharacteristic
70#5164—31no—
71#5164—31no—
72#5162—31no—
73#5162D311yescharacteristic, complemented
74Dic3×SD16—31no—
75Dic3×SD16—31no—
76Dic3×SD16—61no—
77#5083—31no—
78#5045—31no—
79#5009—31no—
80#4847—31no—
81#4840—31no—
82#4817—31no—
83#4815—31no—
84#4814—31no—
85#4788—31no—
86#4766—31no—
87#4763—31no—
88#4758—31no—
89#4757—31no—
90#4723—31no—
91#4720—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×D3×D4—22no—
99C3×D3×D4—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105C32×SD16—22no—
106C2×C32×C8C2311yescharacteristic
107#3757—21no—
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4×C3⋊Dic3—21no—
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#217—21no—
115C3×#215—22no—
116C3×#214—22no—
117C3×(C2×D3)⋊C4—21no—
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126#3724—21no—
127#3724—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3D411yescharacteristic
137(C2×D3)⋊Dic3D411yescharacteristic
138Dic32—21no—
139Dic32—21no—
140#3715—22no—
141#3123—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C2×C3×SD16—21no—
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C2×C3×SD16C2×D311yescharacteristic
148C2×C3×SD16C2×D311yescharacteristic
149C3×C4⋊Q8—31no—
150C3×C22⋊Q8—31no—
151C3×C4×D4—31no—
152C2×#217—61no—
153C2×#217—61no—
154#946—31no—
155#946C2×D311yescharacteristic
156Q8×Dic3—31no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159Q8×Dic3—61no—
160#944C2×D311yescharacteristic, complemented
161C2×#215—31no—
162C2×#215C2×D311yescharacteristic
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—61no—
168D4×Dic3—61no—
169D4×Dic3—61no—
170D4×Dic3C2×D311yescharacteristic
171C2×#214—31no—
172C2×#214C2×D311yescharacteristic
173C4×#67—61no—
174C2×(C2×D3)⋊C4—61no—
175#926—31no—
176#926—31no—
177#924—31no—
178#898—61no—
179#898—61no—
180#893—31no—
181#892—31no—
182#890—31no—
183#890—61no—
184#889—61no—
185#889—61no—
186#889—61no—
187#887—31no—
188#67⋊C4—61no—
189D3×C22⋊C4—61no—
190#879—61no—
191#879—61no—
192C4×D12—31no—
193#872—31no—
194#870—31no—
195C3×C4⋊C8—31no—
196C3×#103—31no—
197C3×#103—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×C22⋊C8—31no—
201#835—31no—
202#835—31no—
203#835—31no—
204#835—61no—
205#835C2×D311yescharacteristic, complemented
206#832—31no—
207#832—31no—
208#832—31no—
209#832—61no—
210#832C2×D311yescharacteristic
211#830—31no—
212#821—31no—
213#821C2×D311yescharacteristic
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8C2×D311yescharacteristic
216#818—31no—
217#818—31no—
218#817—31no—
219#817—31no—
220#817—61no—
221#816—31no—
222#816C2×D311yescharacteristic, complemented
223#815—31no—
224#815—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8C2×D311yescharacteristic, complemented
227C8×Dic3—31no—
228C8×Dic3—31no—
229C8×Dic3—61no—
230#808—31no—
231#808—31no—
232#807—31no—
233#807—31no—
234C4⋊(C3⋊C8)—31no—
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3—24no—
238C22×C3×D3—81no—
239C22×C3×D3—81no—
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×D4—21no—
244C32×D4#4112yes—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—81no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252C3×#67—24no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—81no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12#4112yes—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266D3×Dic3—81no—
267D3×Dic3—81no—
268C32×C8—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—91no—
273#518—91no—
274#485—91no—
275#485—91no—
276#478—91no—
277#478—91no—
278#461—31no—
279#461—91no—
280#450—31no—
281#450—91no—
282#440—91no—
283#440—91no—
284C4×SD16—91no—
285C4×SD16—91no—
286#433—91no—
287C24×C3—61no—
288C23×D3—21no—
289C2×C3×Q8—21no—
290C2×C3×Q8—31no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C2×C3×D4—62no—
297C2×C3×D4—62no—
298C2×C3×D4C22×D311yescharacteristic
299C2×C3×D4C22×D311yescharacteristic
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C2×#67—21no—
303C22×Dic3—21no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3—121no—
309D3×D4—22no—
310D3×D4—22no—
311C2×D12C22×D311yescharacteristic
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3C22×D311yescharacteristic
315C2×Dic6C22×D311yescharacteristic
316C3×SD16—24no—
317C3×SD16—22no—
318C3×SD16—22no—
319C3×SD16—62no—
320C3×SD16—62no—
321C2×C3×C8—21no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C2×C3×C8C22×D311yescharacteristic
325C2×C3×C8C22×D311yescharacteristic
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C22⋊C4—61no—
332C3×C22⋊C4—61no—
333C3×C42—31no—
334#217—21no—
335#217—31no—
336#217—31no—
337#217—61no—
338#217—61no—
339#217—61no—
340#217—61no—
341#217—61no—
342#217—61no—
343#217—121no—
344#215—22no—
345#215—62no—
346#214—22no—
347#214—62no—
348(C2×D3)⋊C4—21no—
349(C2×D3)⋊C4—31no—
350(C2×D3)⋊C4—31no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355C4⋊Dic3—31no—
356C4⋊Dic3—31no—
357C4⋊Dic3—31no—
358C4⋊Dic3—31no—
359C4⋊Dic3—31no—
360C4⋊Dic3—31no—
361C4⋊Dic3—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—121no—
368C4⋊Dic3C22×D311yescharacteristic
369C4⋊Dic3C22×D311yescharacteristic
370Dic3⋊C4—21no—
371Dic3⋊C4—21no—
372Dic3⋊C4—21no—
373Dic3⋊C4—31no—
374Dic3⋊C4—31no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381C4×Dic3—31no—
382C4×Dic3—31no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—121no—
391C4×Dic3C22×D311yescharacteristic
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8C22×D311yescharacteristic
396C2×C3⋊C8C22×D311yescharacteristic
397C22×C32—22no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32C22×D411yescharacteristic
401C2×C3×D3—21no—
402C2×C3×D3—22no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—84no—
408C32×C4—41no—
409C32×C4C2×#4111yescharacteristic
410C32×C4C2×#4111yescharacteristic
411C3⋊Dic3—21no—
412C3⋊Dic3—21no—
413C3⋊Dic3—41no—
414C3⋊Dic3—41no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C22×D4—31no—
422C2×SD16—31no—
423C2×SD16—31no—
424C2×SD16—91no—
425C2×SD16D3211yescharacteristic
426C4⋊Q8—31no—
427#126—181no—
428#126—181no—
429#125—91no—
430#125—181no—
431#125—181no—
432C22⋊Q8—31no—
433C22⋊Q8—91no—
434C4×Q8—91no—
435C4×Q8—91no—
436C4×D4—31no—
437C4×D4—91no—
438C4×D4—91no—
439C4×D4—91no—
440C4×D4—181no—
441C4×D4—181no—
442#117—91no—
443#117—91no—
444C2×C22⋊C4—181no—
445C2×C22⋊C4—181no—
446#107—91no—
447#107—91no—
448#106—91no—
449#106—91no—
450C4⋊C8—31no—
451C4⋊C8—91no—
452#103—31no—
453#103—31no—
454#103—91no—
455#103—91no—
456#102—31no—
457#102—31no—
458#102—91no—
459#102—91no—
460C22⋊C8—31no—
461C22⋊C8—91no—
462#97—91no—
463C4×C8—91no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—31no—
467C23×C3—41no—
468C23×C3—64no—
469C23×C3—61no—
470C23×C3—241no—
471C23×C3—241no—
472C22×D3—21no—
473C22×D3—24no—
474C22×D3—81no—
475C22×D3—81no—
476C22×D3D3×D411yescharacteristic
477C3×Q8—22no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—41no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—22no—
488C3×D4—32no—
489C3×D4—41no—
490C3×D4—64no—
491C3×D4—61no—
492C3×D4#23712yes—
493C3×D4#23712yes—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—41no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—241no—
507C2×C3×C4C23×D311yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509#67—24no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—81no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—241no—
527C2×Dic3—241no—
528C2×Dic3—241no—
529C2×Dic3—241no—
530C2×Dic3—242no—
531C2×Dic3D3×D411yescharacteristic
532C2×Dic3D3×D411yescharacteristic
533C2×Dic3D3×D411yescharacteristic
534D12—21no—
535D12#23712yes—
536C4×D3—21no—
537C4×D3—21no—
538C4×D3—241no—
539C4×D3—241no—
540Dic6—21no—
541Dic6—21no—
542C3×C8—22no—
543C3×C8—21no—
544C3×C8—21no—
545C3×C8—61no—
546C3×C8—61no—
547C3⋊C8—21no—
548C3⋊C8—21no—
549C3⋊C8—61no—
550C3⋊C8—61no—
551C3⋊C8—121no—
552C2×C32—42no—
553C2×C32#52511yescharacteristic
554C2×C32#57711yescharacteristic
555C2×C32#57711yescharacteristic
556C3×D3—41no—
557C3×D3—42no—
558C24—61no—
559C2×Q8—31no—
560C2×Q8C2×D3211yescharacteristic
561C2×D4—31no—
562C2×D4—61no—
563C2×D4—62no—
564C2×D4—62no—
565C2×D4C2×D3211yescharacteristic
566C22×C4—31no—
567C22×C4—61no—
568C22×C4—181no—
569C22×C4—181no—
570C22×C4—181no—
571SD16—22no—
572SD16—62no—
573SD16—62no—
574SD16—182no—
575C2×C8—31no—
576C2×C8—31no—
577C2×C8—91no—
578C2×C8C2×D3211yescharacteristic
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—91no—
585C4⋊C4—91no—
586C4⋊C4—91no—
587C4⋊C4—91no—
588C4⋊C4—181no—
589C4⋊C4—181no—
590C4⋊C4—181no—
591C4⋊C4—181no—
592C4⋊C4—181no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—91no—
596C22⋊C4—91no—
597C22⋊C4—181no—
598C22⋊C4—181no—
599C22⋊C4—181no—
600C22⋊C4—181no—
601C22⋊C4—181no—
602C42—31no—
603C42—91no—
604C42—181no—
605C42—181no—
606C42—181no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—21no—
610C22×C3—42no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—62no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—121no—
622C22×C3—121no—
623C22×C3—244no—
624C22×C3C2×D3×D411yescharacteristic
625C22×C3C2×D3×D411yescharacteristic
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—22no—
630C2×D3—41no—
631C2×D3—41no—
632C2×D3—84no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—42no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—61no—
639C3×C4—61no—
640C3×C4—61no—
641C3×C4—121no—
642C3×C4—121no—
643C3×C4—121no—
644C3×C4C2×#23711yescharacteristic
645C3×C4C2×#23711yescharacteristic
646C3×C4C2×#23711yescharacteristic
647C3×C4D3×#4111yescharacteristic
648Dic3—21no—
649Dic3—21no—
650Dic3—21no—
651Dic3—41no—
652Dic3—41no—
653Dic3—41no—
654Dic3—62no—
655Dic3—61no—
656Dic3—61no—
657Dic3—61no—
658Dic3—61no—
659Dic3—121no—
660Dic3—121no—
661Dic3—121no—
662Dic3—121no—
663Dic3—121no—
664Dic3—241no—
665Dic3—241no—
666C32#312311yescharacteristic, complemented, Sylow
667C23—21no—
668C23—31no—
669C23—64no—
670C23—61no—
671C23—241no—
672C23—241no—
673Q8—21no—
674Q8—21no—
675Q8—61no—
676Q8—61no—
677D4—21no—
678D4—32no—
679D4—64no—
680D4—61no—
681D4#380512yes—
682C2×C4—21no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—181no—
694C2×C4—181no—
695C2×C4—241no—
696C2×C4—721no—
697C2×C4—721no—
698C2×C4—721no—
699C2×C4C22×D3211yescharacteristic
700C8—21no—
701C8—61no—
702C8—61no—
703C8—181no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—42no—
708C2×C3—42no—
709C2×C3—82no—
710C2×C3—121no—
711C2×C3—122no—
712C2×C3#558611yescharacteristic
713C2×C3#560611yescharacteristic
714C2×C3#576211yescharacteristic
715C2×C3#576211yescharacteristic
716C2×C3#577511yescharacteristic
717C2×C3#577811yescharacteristic
718D3—41no—
719D3—42no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—61no—
724C22—62no—
725C22—61no—
726C22—61no—
727C22—121no—
728C22—121no—
729C22—244no—
730C22D32×D411yescharacteristic
731C4—41no—
732C4—61no—
733C4—61no—
734C4—61no—
735C4—121no—
736C4—121no—
737C4—121no—
738C4—181no—
739C4—181no—
740C4—361no—
741C4—361no—
742C4D3×#23711yescharacteristic
743C4C2×#380511yescharacteristic
744C3—21no—
745C3#8013711yescharacteristic, complemented
746C3#8041311yescharacteristic, complemented
747C2—42no—
748C2—121no—
749C2—122no—
750C2#1059474811yescharacteristic
751C2#1059475411yescharacteristic
752C2#1059513011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC2×SD16D32
hypocenterC32#3123
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. #10595349C2semidirect
3. SD16×C3⋊Dic3C2semidirect
5. C3×#5162C2semidirect
6. #10591572C2semidirect
7. #10591564C2semidirect
8. #10591558C2semidirect
10. #10591446C2semidirect
11. #10591411C2semidirect
12. #10590772C2semidirect
13. #10590742C2semidirect
14. #10590711C2semidirect
15. #10590698C2semidirect
20. Q8×C3⋊Dic3C22semidirect
23. C3×#944C22semidirect
34. #63869C22semidirect
40. #63843C22semidirect
43. #63662C22semidirect
45. #63644C22semidirect
46. C8×C3⋊Dic3C22semidirect
47. C3×#835C22semidirect
51. C3×#816C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. #63575C22semidirect
54. #63575C22semidirect
55. #63574C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
60. #63555C22semidirect
73. #5162D3semidirect
160. #944C2×D3semidirect
205. #835C2×D3semidirect
222. #816C2×D3semidirect
226. Dic3⋊C8C2×D3semidirect
666. C32#3123semidirect
745. C3#80137semidirect
746. C3#80413semidirect

Maximal subgroups

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

subgroupindex
#105953492
#105952152
SD16×C3⋊Dic32
C3×#51692
C3×#51622
#105915722
#105915642
#105915582
#105914582
#105914462
#105914112
#105907722
#105907422
#105907112
#105906982
#804133
#801373