Finite Group Databasebeta

← #11884333

Subgroups — #11884333

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64128C211yesmaximal, characteristic, complemented
2#10595431C211yesmaximal, characteristic, complemented
3#10595341C211yesmaximal, characteristic, complemented
4C2×#63794C211yesmaximal, characteristic, complemented
5C3×#5190C211yesmaximal, characteristic, complemented
6C3×#5189C211yesmaximal, characteristic, complemented
7#10591657C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591602C211yesmaximal, characteristic, complemented
10#10591593C211yesmaximal, characteristic, complemented
11#10591568C211yesmaximal, characteristic, complemented
12#10591565C211yesmaximal, characteristic, complemented
13#10590843C211yesmaximal, characteristic, complemented
14#10590768C211yesmaximal, characteristic, complemented
15#10590736C211yesmaximal, characteristic, complemented
16#81882—31nomaximal
17#80921—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×#3832C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C2×C32×Q16C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24C2×#3755C2211yescharacteristic, complemented
25#64128—24no—
26C2×#3745C2211yescharacteristic
27C2×C8×C3⋊D3C2211yescharacteristic, complemented
28C3×#947C2211yescharacteristic
29C3×#946C2211yescharacteristic
30C3×#946C2211yescharacteristic
31C3×#944C2211yescharacteristic, complemented
32C2×C3×#216C2211yescharacteristic, complemented
33C2×C3×#215C2211yescharacteristic
34C2×C3×#204C2211yescharacteristic
35C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
36#63923—21no—
37#63921—21no—
38#63916C2211yescharacteristic
39#63910—21no—
40#63910—21no—
41C4×#626C2211yescharacteristic
42#63897—21no—
43#63894C2211yescharacteristic
44#63894C2211yescharacteristic, complemented
45#63883—21no—
46#63871C2211yescharacteristic, complemented
47#63853—21no—
48#63853—21no—
49C2×#3717C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51#63794—24no—
52C3×#835C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#817C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61#63557C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
63C2×#919—31no—
64C2×#919—31no—
65C2×#919—61no—
66C2×#914—31no—
67C2×#908—31no—
68#5726—31no—
69#5676—31no—
70#5631—31no—
71#5630—31no—
72C3×#497—31no—
73C3×#470—31no—
74#5190D311yescharacteristic, complemented
75#5189D311yescharacteristic, complemented
76#5187—31no—
77#5187—31no—
78#5172—31no—
79#5171—31no—
80#5169—31no—
81#5127—31no—
82#5083—31no—
83#5057—31no—
84#5047—31no—
85#5046—31no—
86#4869—31no—
87#4864—31no—
88#4819—31no—
89#4818—31no—
90#4810—31no—
91#4808—31no—
92#4711—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97#3832—22no—
98#3832—22no—
99#3832—41no—
100#3832—41no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3—21no—
107C2×C4×C3⋊D3C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626D411yescharacteristic
115C2×#624—21no—
116C2×#624—21no—
117C2×#624—21no—
118D3×D12—22no—
119D3×D12—41no—
120#3799—22no—
121#3799—41no—
122C32×Q16—22no—
123C2×C32×C8C2311yescharacteristic
124#3755—22no—
125#3755—22no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3745D414yescomplemented
128C8×C3⋊D3—22no—
129C3×#216—41no—
130C3×#215—41no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×C4×Dic3C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C3×#204—22no—
145C3×ΓL(1,𝔽25)—22no—
146Dic3⋊Dic3—21no—
147Dic3⋊Dic3D411yescharacteristic
148#3722—21no—
149#3722—21no—
150#3722—21no—
151#3722D411yescharacteristic
152(C2×D3)⋊Dic3—21no—
153(C2×D3)⋊Dic3D411yescharacteristic
154#3717—22no—
155#3714—22no—
156#3267—91noSylow
157C2×#239—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#239—31no—
161C2×#239—31no—
162C2×#239—61no—
163C2×#239—61no—
164C2×D3×D4—31no—
165C2×#235—31no—
166C22×D12—31no—
167C2×C3×Q16—21no—
168C2×C3×Q16—31no—
169C2×C3×Q16C2×D311yescharacteristic, complemented
170C2×C3×Q16C2×D311yescharacteristic, complemented
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×M16—31no—
174C3×C4⋊Q8—31no—
175C3×#124—31no—
176C3×C22⋊Q8—31no—
177C3×C22⋊Q8—31no—
178#947C2×D311yescharacteristic
179#946—31no—
180#946C2×D311yescharacteristic
181#946C2×D311yescharacteristic
182#944C2×D311yescharacteristic, complemented
183C2×#216C2×D311yescharacteristic, complemented
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—61no—
190C2×#215—61no—
191C2×#215C2×D311yescharacteristic
192#938—31no—
193C2×#213—31no—
194C4×#67—31no—
195#919—64no—
196#919—64no—
197#919—68no—
198#914—64no—
199#908—64no—
200C2×D24—31no—
201C2×D24—31no—
202C2×D24—31no—
203C2×D24—61no—
204C2×#204—31no—
205C2×#204C2×D311yescharacteristic
206C2×ΓL(1,𝔽25)C2×D311yescharacteristic
207C2×D3×C8—31no—
208C2×D3×C8—31no—
209C2×D3×C8—61no—
210#897—31no—
211#895—31no—
212#895—61no—
213#895—61no—
214#894—61no—
215#894—61no—
216#894—61no—
217#894—61no—
218#893—31no—
219#893—31no—
220D3×C4⋊C4—61no—
221D3×C4⋊C4—61no—
222#884—61no—
223#884—61no—
224#883—61no—
225#883—61no—
226#882—61no—
227#882—61no—
228D3×C22⋊C4—61no—
229D3×C22⋊C4—61no—
230C4×D12—31no—
231C4×D12—31no—
232C4×D12—31no—
233C3×#106—31no—
234C3×#103—31no—
235C3×#103—31no—
236C3×#97—31no—
237#835—31no—
238#835C2×D311yescharacteristic, complemented
239#835C2×D311yescharacteristic, complemented
240#832—31no—
241#830—31no—
242#821—31no—
243#821—31no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—31no—
247#817C2×D311yescharacteristic, complemented
248#815C2×D311yescharacteristic, complemented
249Dic3⋊C8—31no—
250#810—31no—
251#809—31no—
252#809—31no—
253#809—31no—
254C4⋊(C3⋊C8)—31no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3C2×D411yescharacteristic
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×Q8—21no—
266C32×Q8—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3C2×D411yescharacteristic
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—42no—
274C4⋊(C3⋊D3)—42no—
275C4⋊(C3⋊D3)C2×D412yes—
276C4⋊(C3⋊D3)C2×D412yes—
277C4×C3⋊D3—21no—
278C4×C3⋊D3—21no—
279C4×C3⋊D3—42no—
280C4×C3⋊D3—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293#626—41no—
294#626—42no—
295#626—42no—
296#626—81no—
297#624—42no—
298#624—42no—
299#624—81no—
300C32×C8C2×D412yes—
301C3⋊(C3⋊C8)—21no—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C2×AGL(1,ℤ/8)—91no—
305C2×#135—91no—
306#547—91no—
307#546—91no—
308#497—31no—
309#470—31no—
310#465—91no—
311#463—91no—
312#461—91no—
313#452—91no—
314#452—91no—
315#450—91no—
316#449—91no—
317#442—91no—
318#435—91no—
319C23×D3—61no—
320C23×D3—61no—
321C2×C3×Q8—21no—
322C2×C3×Q8—21no—
323C2×C3×Q8—31no—
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—31no—
329C22×C3×C4—31no—
330C2×#67—31no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334#239—62no—
335#239—62no—
336#239—62no—
337#239—62no—
338#239—62no—
339#239—64no—
340#239—64no—
341#239—121no—
342#239—121no—
343#239—121no—
344#239—121no—
345#239—121no—
346#239—122no—
347#239—122no—
348D3×D4—62no—
349D3×D4—121no—
350#235—62no—
351#235—121no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—31no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—62no—
360C2×D12—61no—
361C2×D12—61no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—61no—
367C2×D12—121no—
368C2×D12—121no—
369C2×D12—121no—
370C2×D12C22×D311yescharacteristic
371C2×C4×D3—31no—
372C2×C4×D3—31no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—121no—
385C2×C4×D3—121no—
386C2×C4×D3C22×D311yescharacteristic
387C2×Dic6C22×D311yescharacteristic
388C3×Q16—24no—
389C3×Q16—22no—
390C3×Q16—22no—
391C3×Q16—121no—
392C3×SD16—62no—
393C3×SD16—121no—
394C3×M16—62no—
395C2×C3×C8—21no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C3×C4⋊C4—31no—
401C3×C4⋊C4—31no—
402C3×C4⋊C4—61no—
403C3×C4⋊C4—61no—
404C3×C4⋊C4—61no—
405C3×C4⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C42—31no—
411#217—31no—
412#217—61no—
413#216—41no—
414#215—41no—
415#215—62no—
416#215—62no—
417#215—62no—
418#215—62no—
419#215—62no—
420#215—64no—
421#215—64no—
422#213—62no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—31no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437C4⋊Dic3—31no—
438C4⋊Dic3—61no—
439C4⋊Dic3C22×D311yescharacteristic
440C4⋊Dic3C22×D311yescharacteristic
441Dic3⋊C4—21no—
442Dic3⋊C4—21no—
443Dic3⋊C4—21no—
444Dic3⋊C4—21no—
445Dic3⋊C4—31no—
446Dic3⋊C4—61no—
447C4×Dic3C22×D311yescharacteristic
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8C22×D311yescharacteristic
452C2×C3⋊C8C22×D311yescharacteristic
453D24—34no—
454D24—34no—
455D24—64no—
456D24—62no—
457#204—22no—
458#204—62no—
459ΓL(1,𝔽25)—22no—
460D3×C8—64no—
461D3×C8—62no—
462D3×C8—62no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—21no—
465C2×C3⋊D3—22no—
466C2×C3⋊D3—22no—
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479D32—84no—
480C32×C4—41no—
481C32×C4—41no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3⋊Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C3×Dic3—41no—
491C2×#41—91no—
492C2×#41—91no—
493C2×#41—91no—
494C22×D4—91no—
495AGL(1,ℤ/8)—184no—
496#135—184no—
497C2×Q16—31no—
498C2×Q16D3211yescharacteristic, complemented
499C2×SD16—31no—
500C2×SD16—31no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×D8—91no—
505C2×D8—91no—
506C2×M16—31no—
507C22×C8—91no—
508C4⋊Q8—31no—
509#124—31no—
510#123—181no—
511#123—181no—
512#123—181no—
513C22⋊Q8—31no—
514C22⋊Q8—31no—
515C22⋊Q8—91no—
516#121—91no—
517#121—181no—
518#121—181no—
519#120—181no—
520C4×D4—91no—
521C4×D4—91no—
522C4×D4—91no—
523C2×C4⋊C4—181no—
524C2×C22⋊C4—181no—
525#106—31no—
526C4⋊C8—91no—
527#103—31no—
528#103—31no—
529#103—91no—
530#102—91no—
531#102—91no—
532#102—91no—
533C22⋊C8—91no—
534C22⋊C8—91no—
535#97—31no—
536C23×C3—31no—
537C23×C3—61no—
538C22×D3—21no—
539C22×D3—31no—
540C22×D3—31no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—121no—
547C22×D3—121no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—241no—
553C22×D3—241no—
554C22×D3D3×D411yescharacteristic
555C3×Q8—22no—
556C3×Q8—22no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—21no—
560C3×Q8—21no—
561C3×Q8—21no—
562C3×Q8—21no—
563C3×Q8—21no—
564C3×Q8—21no—
565C3×Q8—41no—
566C3×Q8—41no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×D4—61no—
570C3×D4—61no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4C23×D311yescharacteristic
587C2×C3×C4C23×D311yescharacteristic
588#67—121no—
589#67—122no—
590#67—122no—
591#67—241no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—61no—
598C2×Dic3D3×D411yescharacteristic
599C2×Dic3D3×D411yescharacteristic
600C2×Dic3D3×D411yescharacteristic
601D12—21no—
602D12—21no—
603D12—32no—
604D12—32no—
605D12—32no—
606D12—32no—
607D12—62no—
608D12—62no—
609D12—61no—
610D12—61no—
611D12—61no—
612D12—61no—
613D12—121no—
614D12—121no—
615D12—122no—
616D12—122no—
617D12—122no—
618D12—122no—
619D12—124no—
620D12—124no—
621D12—121no—
622D12—122no—
623D12—122no—
624D12—241no—
625C4×D3—21no—
626C4×D3—21no—
627C4×D3—62no—
628C4×D3—62no—
629C4×D3—61no—
630C4×D3—61no—
631C4×D3—61no—
632C4×D3—61no—
633C4×D3—122no—
634C4×D3—122no—
635C4×D3—122no—
636C4×D3—122no—
637C4×D3—122no—
638C4×D3—122no—
639C4×D3—122no—
640C4×D3—122no—
641C4×D3—124no—
642C4×D3—124no—
643C4×D3—241no—
644C4×D3—241no—
645Dic6—21no—
646Dic6—21no—
647C3×C8—22no—
648C3×C8—61no—
649C3×C8—61no—
650C3×C8D3×D412yes—
651C3×C8D3×D412yes—
652C3⋊C8—21no—
653C3⋊C8—21no—
654C3⋊C8—62no—
655C3⋊C8—61no—
656C3⋊C8—61no—
657C2×C32D4211yescharacteristic
658C2×C32#57511yescharacteristic
659C2×C32#57711yescharacteristic
660C3⋊D3—41no—
661C3⋊D3—42no—
662C3⋊D3—42no—
663C3×D3—41no—
664C3×D3—81no—
665C24—181no—
666#41—182no—
667#41—182no—
668#41—182no—
669#41—361no—
670#41—361no—
671#41—361no—
672C2×Q8—31no—
673C2×Q8C2×D3211yescharacteristic
674C2×Q8C2×D3211yescharacteristic
675C2×D4—31no—
676C2×D4—91no—
677C2×D4—91no—
678C2×D4—91no—
679C2×D4—181no—
680C2×D4—181no—
681C2×D4—181no—
682C2×D4—182no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—361no—
686C22×C4—31no—
687C22×C4—91no—
688C22×C4—181no—
689C22×C4—181no—
690C22×C4—181no—
691C22×C4—181no—
692C22×C4—181no—
693Q16—22no—
694Q16—121no—
695SD16—62no—
696SD16—121no—
697SD16—182no—
698SD16—182no—
699SD16—182no—
700D8—94no—
701D8—182no—
702M16—62no—
703C2×C8—31no—
704C2×C8—31no—
705C2×C8—91no—
706C2×C8—182no—
707C2×C8C2×D3211yescharacteristic
708C4⋊C4—31no—
709C4⋊C4—31no—
710C4⋊C4—61no—
711C4⋊C4—61no—
712C4⋊C4—61no—
713C4⋊C4—61no—
714C4⋊C4—91no—
715C4⋊C4—181no—
716C22⋊C4—61no—
717C22⋊C4—61no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—91no—
721C22⋊C4—91no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C42—31no—
727C22×C3—21no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3C2×D3×D411yescharacteristic
735C22×C3C2×D3×D411yescharacteristic
736C2×D3—21no—
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—62no—
743C2×D3—61no—
744C2×D3—62no—
745C2×D3—62no—
746C2×D3—61no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—61no—
751C2×D3—62no—
752C2×D3—62no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—122no—
756C2×D3—122no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—241no—
766C2×D3—241no—
767C2×D3—241no—
768C2×D3—241no—
769C2×D3—244no—
770C2×D3—244no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—42no—
774C3×C4—42no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4—41no—
778C3×C4—41no—
779C3×C4—61no—
780C3×C4—61no—
781C3×C4—61no—
782C3×C4—121no—
783C3×C4—121no—
784C3×C4—121no—
785C3×C4C2×D3×D411yescharacteristic
786C3×C4C2×D3×D411yescharacteristic
787C3×C4#100411yescharacteristic
788C3×C4#100911yescharacteristic
789Dic3—21no—
790Dic3—21no—
791Dic3—21no—
792Dic3—41no—
793Dic3—41no—
794Dic3—41no—
795Dic3—62no—
796Dic3—61no—
797Dic3—61no—
798C32#326711yescharacteristic, complemented, Sylow
799C23—31no—
800C23—61no—
801C23—91no—
802C23—181no—
803C23—181no—
804C23—362no—
805C23—362no—
806C23—721no—
807Q8—21no—
808Q8—21no—
809Q8—21no—
810Q8—21no—
811Q8—61no—
812Q8—61no—
813D4—61no—
814D4—61no—
815D4—92no—
816D4—92no—
817D4—181no—
818D4—181no—
819D4—362no—
820D4—362no—
821D4—361no—
822D4—362no—
823D4—362no—
824D4—721no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—31no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—91no—
836C2×C4—181no—
837C2×C4—181no—
838C2×C4—362no—
839C2×C4—362no—
840C2×C4—362no—
841C2×C4—362no—
842C2×C4—721no—
843C2×C4C22×D3211yescharacteristic
844C8—61no—
845C8—61no—
846C8—181no—
847C8#381112yes—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—121no—
852C2×C3—241no—
853C2×C3#560911yescharacteristic
854C2×C3#571711yescharacteristic
855C2×C3#577711yescharacteristic
856C2×C3#577711yescharacteristic
857C2×C3#577811yescharacteristic
858C2×C3#577811yescharacteristic
859D3—41no—
860D3—81no—
861D3—122no—
862D3—121no—
863D3—122no—
864D3—122no—
865D3—121no—
866D3—122no—
867D3—122no—
868D3—242no—
869D3—242no—
870C22—61no—
871C22—61no—
872C22—61no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22—181no—
877C22—181no—
878C22—181no—
879C22—182no—
880C22—182no—
881C22—361no—
882C22—361no—
883C22—361no—
884C22—361no—
885C22—724no—
886C22D32×D411yescharacteristic
887C4—41no—
888C4—41no—
889C4—61no—
890C4—61no—
891C4—61no—
892C4—121no—
893C4—121no—
894C4—121no—
895C4—181no—
896C4#6431411yescharacteristic
897C4C2×#381111yescharacteristic
898C3—21no—
899C3#8092111yescharacteristic, complemented
900C3#8188211yescharacteristic, complemented
901C2—121no—
902C2—241no—
903C2—361no—
904C2—362no—
905C2—362no—
906C2#1059476211yescharacteristic
907C2#1059476711yescharacteristic
908C2#1059529711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
hypercenterC2×Q16D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#64128C2semidirect
2. #10595431C2semidirect
3. #10595341C2semidirect
4. C2×#63794C2semidirect
5. C3×#5190C2semidirect
6. C3×#5189C2semidirect
7. #10591657C2semidirect
8. #10591651C2semidirect
9. #10591602C2semidirect
10. #10591593C2semidirect
11. #10591568C2semidirect
12. #10591565C2semidirect
13. #10590843C2semidirect
14. #10590768C2semidirect
15. #10590736C2semidirect
19. C2×#3832C22semidirect
22. C2×C32×Q16C22semidirect
24. C2×#3755C22semidirect
27. C2×C8×C3⋊D3C22semidirect
31. C3×#944C22semidirect
32. C2×C3×#216C22semidirect
44. #63894C22semidirect
46. #63871C22semidirect
52. C3×#835C22semidirect
53. C3×#835C22semidirect
54. C3×#817C22semidirect
55. C3×#815C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63565C22semidirect
59. #63564C22semidirect
61. #63557C22semidirect
74. #5190D3semidirect
75. #5189D3semidirect
127. #3745D4semidirect
169. C2×C3×Q16C2×D3semidirect
170. C2×C3×Q16C2×D3semidirect
182. #944C2×D3semidirect
183. C2×#216C2×D3semidirect
238. #835C2×D3semidirect
239. #835C2×D3semidirect
247. #817C2×D3semidirect
248. #815C2×D3semidirect
498. C2×Q16D32semidirect
798. C32#3267semidirect
899. C3#80921semidirect
900. C3#81882semidirect

Maximal subgroups

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

subgroupindex
C2×#641282
#105954312
#105953412
C2×#637942
C3×#51902
C3×#51892
#105916572
#105916512
#105916022
#105915932
#105915682
#105915652
#105908432
#105907682
#105907362
#818823
#809213