Finite Group Databasebeta

← #11884001

Subgroups — #11884001

Order 1152.

1159 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63796C211yesmaximal, characteristic, complemented
2C2×#63794C211yesmaximal, characteristic, complemented
3#10594621C211yesmaximal, characteristic, complemented
4#10594329C211yesmaximal, characteristic, complemented
5#10592582C211yesmaximal, characteristic, complemented
6C3×#4889C211yesmaximal, characteristic, complemented
7C3×#4886C211yesmaximal, characteristic, complemented
8#10590881C211yesmaximal, characteristic, complemented
9#10590736C211yesmaximal, characteristic, complemented
10#10590615C211yesmaximal, characteristic, complemented
11#10590606C211yesmaximal, characteristic, complemented
12#10590598C211yesmaximal, characteristic, complemented
13#10590596C211yesmaximal, characteristic, complemented
14#10590549C211yesmaximal, characteristic, complemented
15#10590534C211yesmaximal, characteristic, complemented
16#80834—31nomaximal
17#79794—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×D3×D12—21no—
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22C2×#3797C2211yescharacteristic, complemented
23C2×#3745C2211yescharacteristic, complemented
24C2×C8×C3⋊D3C2211yescharacteristic, complemented
25#64104C2211yescharacteristic
26#64104C2211yescharacteristic, complemented
27C2×C3×#204C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic, complemented
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
30C3×#897C2211yescharacteristic, complemented
31C3×#895C2211yescharacteristic
32C3×#893C2211yescharacteristic
33C3×#887C2211yescharacteristic, complemented
34#63923—21no—
35#63922—21no—
36#63911C2211yescharacteristic
37#63910—21no—
38#63906—21no—
39C4×#626C2211yescharacteristic
40#63895—21no—
41#63894—21no—
42#63864C2211yescharacteristic, complemented
43#63852—21no—
44C2×#3717C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic, complemented
50#63796—24no—
51#63794—24no—
52C32×#107C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic
59C3×#809C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×D3×SD16—31no—
65C2×D3×SD16—31no—
66C2×#908—31no—
67#5633—31no—
68#5609—31no—
69#5576—31no—
70D4×D12—31no—
71C3×#468—31no—
72C3×#440—31no—
73#5176—31no—
74#5127—31no—
75#5046—31no—
76#5037—31no—
77#5027—31no—
78#5016—31no—
79#4889D311yescharacteristic, complemented
80#4886D311yescharacteristic, complemented
81#4883—31no—
82#4883—31no—
83#4883—61no—
84#4819—31no—
85#4810—31no—
86#4806—31no—
87#4806—31no—
88#4776—31no—
89#4773—31no—
90#4773—31no—
91#4762—31no—
92#4712—31no—
93#4706—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626D411yescharacteristic
114C2×#625—21no—
115C2×#624—21no—
116C2×#624—21no—
117#3802—22no—
118#3802—41no—
119D3×D12—22no—
120D3×D12—44no—
121D3×D12—41no—
122#3799—22no—
123#3799—41no—
124#3797—22no—
125#3797—41no—
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128C32×C4⋊C4C2311yescharacteristic
129#3752—21no—
130#3752—21no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132#3745—22no—
133C8×C3⋊D3—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3—21no—
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×#204—22no—
144C3×#204D414yescomplemented
145C3×ΓL(1,𝔽25)—22no—
146Dic3⋊Dic3D411yescharacteristic
147#3722—21no—
148#3722—21no—
149#3722D411yescharacteristic
150(C2×D3)⋊Dic3D411yescharacteristic
151#3717—22no—
152#3717—41no—
153#3715—22no—
154#3715—22no—
155#3714—22no—
156#3714—41no—
157#3265—91noSylow
158C2×#239—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—61no—
165C2×#235—31no—
166C22×D12—31no—
167C22×D12—61no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×M16—31no—
171C3×C22⋊Q8—31no—
172C3×#121—31no—
173C3×C4×Q8—31no—
174C3×C4×D4—31no—
175#947—31no—
176C2×#215—31no—
177C2×#215—31no—
178C2×#215—31no—
179C2×#215—31no—
180#940—31no—
181#937—61no—
182C2×#214—31no—
183C2×#214—31no—
184C2×#213—31no—
185C2×#213—31no—
186#930—61no—
187C4×#67—31no—
188#914—64no—
189D3×SD16—64no—
190D3×SD16—64no—
191#908—64no—
192C2×D24—31no—
193C2×D24—31no—
194C2×D24—31no—
195C2×D24—31no—
196C2×D24—61no—
197C2×#204—31no—
198C2×#204—31no—
199C2×#204C2×D311yescharacteristic
200C2×#204C2×D311yescharacteristic, complemented
201C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
202C2×D3×C8—31no—
203C2×D3×C8—31no—
204C2×D3×C8—61no—
205#897—61no—
206#897C2×D311yescharacteristic, complemented
207#896—61no—
208#895—31no—
209#895—31no—
210#895—31no—
211#895—31no—
212#895—61no—
213#895—61no—
214#895—61no—
215#895C2×D311yescharacteristic
216#893—61no—
217#893C2×D311yescharacteristic
218#887C2×D311yescharacteristic, complemented
219#885—61no—
220#884—61no—
221#884—61no—
222#882—61no—
223#882—61no—
224#882—61no—
225#875—31no—
226#875—61no—
227#874—31no—
228C4×D12—31no—
229C4×D12—61no—
230C3×#107—21no—
231C3×#107C2×D311yescharacteristic, complemented
232C3×#107C2×D311yescharacteristic, complemented
233C3×#103—31no—
234C3×#103—31no—
235C3×#102—31no—
236C3×#102—31no—
237C3×#97—31no—
238#830—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242#815C2×D311yescharacteristic, complemented
243Dic3⋊C8—31no—
244#810C2×D311yescharacteristic, complemented
245#810C2×D311yescharacteristic, complemented
246#809—31no—
247#809—31no—
248#809—31no—
249#809—31no—
250#809—61no—
251#809—61no—
252#809C2×D311yescharacteristic
253#809C2×D311yescharacteristic, complemented
254C4⋊(C3⋊C8)—31no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3C2×D411yescharacteristic
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C2×D32—81no—
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)—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—42no—
276C4⋊(C3⋊D3)—42no—
277C4×C3⋊D3—21no—
278C4×C3⋊D3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—42no—
288C3×D12C2×D412yes—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—42no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6C2×D412yescomplemented
296#627—42no—
297#626—22no—
298#626—42no—
299#626—42no—
300#626—42no—
301#626—81no—
302#625—42no—
303#624—42no—
304#624—42no—
305C32×C8C2×D412yescomplemented
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
313#496—91no—
314#468—31no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—31no—
323#435—91no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C2×C3×Q8—31no—
329C2×C3×Q8—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C22×C3×C4—31no—
334C22×C3×C4—61no—
335C2×#67—31no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342#239—62no—
343#239—121no—
344D3×Q8—62no—
345D3×Q8—62no—
346D3×Q8—121no—
347D3×Q8—121no—
348D3×D4—62no—
349D3×D4—62no—
350D3×D4—62no—
351D3×D4—121no—
352D3×D4—124no—
353D3×D4—121no—
354D3×D4—121no—
355#235—62no—
356#235—121no—
357C2×D12—21no—
358C2×D12—31no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—62no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—121no—
375C2×D12—121no—
376C2×D12—121no—
377C2×D12—124no—
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—21no—
381C2×C4×D3—31no—
382C2×C4×D3—31no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3C22×D311yescharacteristic
389C2×Dic6—61no—
390C2×Dic6—61no—
391C2×Dic6C22×D311yescharacteristic
392C2×Dic6C22×D311yescharacteristic
393C3×SD16—34no—
394C3×SD16—62no—
395C3×M16—62no—
396C2×C3×C8—21no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C22×D311yescharacteristic
401C3×C4⋊C4—21no—
402C3×C4⋊C4—21no—
403C3×C4⋊C4—61no—
404C3×C4⋊C4—61no—
405C3×C4⋊C4C22×D311yescharacteristic
406C3×C4⋊C4C22×D311yescharacteristic
407C3×C4⋊C4C22×D311yescharacteristic
408C3×C4⋊C4C22×D311yescharacteristic
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C42—31no—
413C3×C42—61no—
414#217—31no—
415#215—62no—
416#215—62no—
417#215—62no—
418#215—121no—
419#214—62no—
420#214—62no—
421#213—62no—
422#213—121no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—31no—
427(C2×D3)⋊C4—31no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—61no—
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—
437(C2×D3)⋊C4—121no—
438(C2×D3)⋊C4—121no—
439C4⋊Dic3—21no—
440C4⋊Dic3—31no—
441Dic3⋊C4—21no—
442Dic3⋊C4—31no—
443C4×Dic3—21no—
444C4×Dic3C22×D311yescharacteristic
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450D24—62no—
451D24—62no—
452D24—62no—
453D24—122no—
454D24—121no—
455#204—22no—
456#204—62no—
457#204—121no—
458#204D1214yescomplemented
459ΓL(1,𝔽25)—22no—
460D3×C8—62no—
461D3×C8—62no—
462D3×C8—122no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
473C2×C3×D3—22no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482D32—84no—
483D32—84no—
484C32×C4—41no—
485C32×C4—41no—
486C32×C4C22×D411yescharacteristic
487C32×C4H(5,𝔽2)11yescharacteristic
488C3⋊Dic3—21no—
489C3×Dic3—21no—
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—41no—
494C2×#41—91no—
495C22×Q8—91no—
496C22×D4—91no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—31no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—184no—
507C2×D8—91no—
508C2×D8—91no—
509C2×D8—91no—
510C2×M16—31no—
511C22×C8—91no—
512#127—91no—
513#124—91no—
514#124—181no—
515C22⋊Q8—31no—
516C22⋊Q8—181no—
517#121—31no—
518#121—91no—
519#121—91no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—31no—
525C4×D4—31no—
526C4×D4—91no—
527C4×D4—181no—
528#107D3211yescharacteristic, complemented
529C4⋊C8—91no—
530#103—31no—
531#103—31no—
532#102—31no—
533#102—31no—
534#102—91no—
535#102—91no—
536C22⋊C8—91no—
537C22⋊C8—91no—
538#97—31no—
539C23×C3—31no—
540C23×C3—61no—
541C23×C3—61no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—31no—
545C22×D3—31no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—121no—
552C22×D3—121no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3—241no—
565C22×D3D3×D411yescharacteristic
566C3×Q8—32no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×Q8—61no—
570C3×D4—32no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—61no—
574C3×D4—122no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—31no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—122no—
590C2×C3×C4C23×D311yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592#67—62no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—122no—
598#67—241no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—31no—
602C2×Dic3—31no—
603C2×Dic3—61no—
604C2×Dic3D3×D411yescharacteristic
605C2×Dic3D3×D411yescharacteristic
606C2×Dic3D3×D411yescharacteristic
607D12—21no—
608D12—21no—
609D12—21no—
610D12—42no—
611D12—62no—
612D12—61no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—61no—
617D12—61no—
618D12—61no—
619D12—61no—
620D12—121no—
621D12—121no—
622D12—121no—
623D12—121no—
624D12—122no—
625D12—122no—
626D12—122no—
627D12—122no—
628D12—122no—
629D12—122no—
630D12—122no—
631D12—242no—
632D12—242no—
633D12—241no—
634D12C2×D1212yes—
635C4×D3—21no—
636C4×D3—21no—
637C4×D3—42no—
638C4×D3—61no—
639C4×D3—61no—
640C4×D3—61no—
641C4×D3—61no—
642C4×D3—121no—
643C4×D3—121no—
644C4×D3—122no—
645C4×D3—122no—
646C4×D3—122no—
647C4×D3—122no—
648Dic6—21no—
649Dic6—21no—
650Dic6—21no—
651Dic6—122no—
652Dic6—122no—
653Dic6C2×D1212yescomplemented
654C3×C8—22no—
655C3×C8—61no—
656C3×C8—61no—
657C3×C8C2×D1212yescomplemented
658C3×C8D3×D412yescomplemented
659C3⋊C8—21no—
660C3⋊C8—21no—
661C3⋊C8—61no—
662C3⋊C8—61no—
663C3⋊C8—121no—
664C2×C32D4211yescharacteristic
665C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
666C2×C32#57711yescharacteristic
667C3⋊D3—22no—
668C3⋊D3—81no—
669C3⋊D3—81no—
670C3×D3—41no—
671C3×D3—42no—
672C3×D3—81no—
673C24—181no—
674C24—181no—
675#41—182no—
676#41—361no—
677C2×Q8—31no—
678C2×Q8—31no—
679C2×Q8—181no—
680C2×Q8—182no—
681C2×Q8—361no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—61no—
685C2×D4—91no—
686C2×D4—91no—
687C2×D4—91no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—182no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—182no—
697C2×D4—361no—
698C2×D4—364no—
699C2×D4—361no—
700C22×C4—31no—
701C22×C4—61no—
702C22×C4—91no—
703C22×C4—181no—
704C22×C4—181no—
705SD16—34no—
706SD16—62no—
707SD16—182no—
708SD16—182no—
709SD16—182no—
710SD16—361no—
711D8—182no—
712D8—182no—
713D8—361no—
714M16—62no—
715C2×C8—31no—
716C2×C8—31no—
717C2×C8—91no—
718C2×C8—182no—
719C2×C8C2×D3211yescharacteristic
720C4⋊C4—61no—
721C4⋊C4—61no—
722C4⋊C4—91no—
723C4⋊C4C2×D3211yescharacteristic
724C4⋊C4C2×D3211yescharacteristic
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—61no—
728C22⋊C4—91no—
729C22⋊C4—91no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C22⋊C4—181no—
734C42—31no—
735C42—61no—
736C22×C3—21no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—61no—
740C22×C3—62no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3C2×D3×D411yescharacteristic
747C22×C3C2×D3×D411yescharacteristic
748C2×D3—21no—
749C2×D3—21no—
750C2×D3—22no—
751C2×D3—21no—
752C2×D3—32no—
753C2×D3—32no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—62no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—241no—
779C2×D3—241no—
780C2×D3—241no—
781C2×D3—241no—
782C2×D3—241no—
783C2×D3—241no—
784C2×D3—244no—
785C2×D3—244no—
786C2×D3—244no—
787C2×D3—244no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—41no—
794C3×C4—61no—
795C3×C4—61no—
796C3×C4—61no—
797C3×C4—62no—
798C3×C4—81no—
799C3×C4—81no—
800C3×C4—121no—
801C3×C4C22×D1211yescharacteristic
802C3×C4C2×D3×D411yescharacteristic
803C3×C4#100911yescharacteristic
804C3×C4#100911yescharacteristic
805Dic3—21no—
806Dic3—21no—
807Dic3—22no—
808Dic3—21no—
809Dic3—41no—
810Dic3—61no—
811Dic3—61no—
812Dic3—121no—
813C32#326511yescharacteristic, complemented, Sylow
814C23—31no—
815C23—61no—
816C23—61no—
817C23—91no—
818C23—181no—
819C23—181no—
820C23—362no—
821C23—362no—
822C23—362no—
823C23—362no—
824C23—721no—
825C23—721no—
826Q8—32no—
827Q8—61no—
828Q8—61no—
829Q8—61no—
830Q8—362no—
831D4—32no—
832D4—61no—
833D4—61no—
834D4—61no—
835D4—122no—
836D4—182no—
837D4—181no—
838D4—181no—
839D4—181no—
840D4—181no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—362no—
845D4—362no—
846D4—362no—
847D4—721no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—31no—
851C2×C4—31no—
852C2×C4—31no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—91no—
858C2×C4—122no—
859C2×C4—181no—
860C2×C4—181no—
861C2×C4—362no—
862C2×C4—362no—
863C2×C4C22×D3211yescharacteristic
864C8—61no—
865C8—61no—
866C8—181no—
867C8D3×D1212yescomplemented
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—121no—
872C2×C3—122no—
873C2×C3—241no—
874C2×C3D4×D1211yescharacteristic
875C2×C3#560911yescharacteristic
876C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
877C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
878C2×C3#577811yescharacteristic
879C2×C3#577811yescharacteristic
880D3—42no—
881D3—41no—
882D3—62no—
883D3—62no—
884D3—81no—
885D3—122no—
886D3—241no—
887D3—241no—
888D3—241no—
889D3—241no—
890D3—481no—
891D3—481no—
892C22—61no—
893C22—62no—
894C22—61no—
895C22—61no—
896C22—92no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—181no—
903C22—181no—
904C22—361no—
905C22—361no—
906C22—361no—
907C22—361no—
908C22—361no—
909C22—361no—
910C22—724no—
911C22—724no—
912C22D32×D411yescharacteristic
913C4—41no—
914C4—41no—
915C4—61no—
916C4—62no—
917C4—61no—
918C4—61no—
919C4—121no—
920C4—181no—
921C4C2×D3×D1211yescharacteristic
922C4#6432011yescharacteristic
923C3—21no—
924C3#7979411yescharacteristic, complemented
925C3#8083411yescharacteristic, complemented
926C2—121no—
927C2—122no—
928C2—182no—
929C2—241no—
930C2—721no—
931C2—721no—
932C2#1059462111yescharacteristic
933C2#1059472611yescharacteristic
934C2#1059476711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
hypercenter#107D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C2×#63796C2semidirect
2. C2×#63794C2semidirect
3. #10594621C2semidirect
4. #10594329C2semidirect
5. #10592582C2semidirect
6. C3×#4889C2semidirect
7. C3×#4886C2semidirect
8. #10590881C2semidirect
9. #10590736C2semidirect
10. #10590615C2semidirect
11. #10590606C2semidirect
12. #10590598C2semidirect
13. #10590596C2semidirect
14. #10590549C2semidirect
15. #10590534C2semidirect
21. C2×#3799C22semidirect
22. C2×#3797C22semidirect
23. C2×#3745C22semidirect
24. C2×C8×C3⋊D3C22semidirect
26. #64104C22semidirect
28. C2×C3×#204C22semidirect
29. C2×C3×ΓL(1,𝔽25)C22semidirect
30. C3×#897C22semidirect
33. C3×#887C22semidirect
42. #63864C22semidirect
44. C2×#3717C22semidirect
45. C2×#3717C22semidirect
47. C2×#3715C22semidirect
49. C2×#3714C22semidirect
52. C32×#107C22semidirect
53. #63636C22semidirect
54. #63636C22semidirect
55. C3×#815C22semidirect
56. C3×#810C22semidirect
57. C3×#810C22semidirect
59. C3×#809C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63557C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
79. #4889D3semidirect
80. #4886D3semidirect
144. C3×#204D4semidirect
200. C2×#204C2×D3semidirect
201. C2×ΓL(1,𝔽25)C2×D3semidirect
206. #897C2×D3semidirect
218. #887C2×D3semidirect
231. C3×#107C2×D3semidirect
232. C3×#107C2×D3semidirect
242. #815C2×D3semidirect
244. #810C2×D3semidirect
245. #810C2×D3semidirect
253. #809C2×D3semidirect
295. C3×Dic6C2×D4semidirect
305. C32×C8C2×D4semidirect
458. #204D12semidirect
472. C2×C3⋊D3AGL(1,ℤ/8)semidirect
528. #107D32semidirect
653. Dic6C2×D12semidirect
657. C3×C8C2×D12semidirect
658. C3×C8D3×D4semidirect
813. C32#3265semidirect
867. C8D3×D12semidirect
924. C3#79794semidirect
925. C3#80834semidirect

Maximal subgroups

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

subgroupindex
C2×#637962
C2×#637942
#105946212
#105943292
#105925822
C3×#48892
C3×#48862
#105908812
#105907362
#105906152
#105906062
#105905982
#105905962
#105905492
#105905342
#808343
#797943