Finite Group Databasebeta

← #11793865

Subgroups — #11793865

Order 1152.

617 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594795C211yesmaximal, characteristic
2C2×#63652C211yesmaximal, characteristic, complemented
3C3×#5132C211yesmaximal, characteristic, complemented
4#10591120C211yesmaximal, characteristic, complemented
5C2×#63568C211yesmaximal, characteristic, complemented
6#10591078C211yesmaximal, characteristic, complemented
7C3×C3⋊#338C211yesmaximal, characteristic, complemented
8#70144—31nomaximal
9#68719—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63833—21no—
18#63831—21no—
19#63830—21no—
20#63829—22no—
21#63825—21no—
22#63652—21no—
23#63652—21no—
24C3×#824—21no—
25C3×#823—21no—
26#63572—22no—
27#63568—21no—
28#63568—21no—
29#63561—21no—
30#63559—21no—
31#5822—31no—
32#5748—31no—
33C3×#413—31no—
34C2×#837—31no—
35C2×#825—31no—
36C2×#825—31no—
37C2×#825—31no—
38C2×#825—61no—
39#5132—31no—
40#5132—31no—
41#5132D311yescharacteristic, complemented
42#5118—31no—
43#5118—31no—
44C3×#338—31no—
45C3⋊#338D311yescharacteristic, complemented
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C22×C3⋊Dic3—21no—
49#3828—21no—
50#3828—21no—
51#3828—21no—
52#3828—21no—
53C2×C4⋊(C3⋊D3)D411yescharacteristic
54C2×C4×C3⋊D3—21no—
55C2×#634D411yescharacteristic
56C2×C3×#67—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C2×C3×D12D411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6D411yescharacteristic
64C32×M16—21no—
65C32×M16—21no—
66C2×C32×C8—21no—
67C4×C3⋊Dic3—21no—
68C4×C3⋊Dic3D411yescharacteristic
69C4×C3⋊Dic3D411yescharacteristic
70C3×#208—21no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208—21no—
74C3×#208—21no—
75C3×#208—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8D412yes—
79#3719—22no—
80#3717—22no—
81#3716—22no—
82#3714—22no—
83#2050—91noSylow
84C2×C3×#41—31no—
85C2×#235—31no—
86C2×#235—31no—
87C2×#235—61no—
88C2×#235C2×D311yescharacteristic
89C2×C3×M16—21no—
90C2×C3×M16—31no—
91C2×C3×M16—31no—
92C2×C3×M16—31no—
93C2×C3×M16C2×D311yescharacteristic
94C2×C3×M16C2×D311yescharacteristic
95#951—61no—
96#950—62no—
97#949—61no—
98#942—61no—
99#932—61no—
100C2×C4×Dic3—31no—
101C2×C4×Dic3—31no—
102C2×C4×Dic3—61no—
103C2×#208C2×D311yescharacteristic
104C2×#208C2×D311yescharacteristic
105C2×#208C2×D311yescharacteristic
106#909—61no—
107#909—61no—
108#908—61no—
109#908—61no—
110#904—62no—
111C3×#101—61no—
112C3×#100—61no—
113#837—61no—
114#837—61no—
115#825—61no—
116#825—61no—
117#825—61no—
118#825—61no—
119#825—61no—
120#825—61no—
121#825—62no—
122#825—62no—
123#824—21no—
124#824—61no—
125#824—61no—
126#823—21no—
127#823—61no—
128#823—61no—
129Dic3⋊C8—62no—
130Dic3⋊C8—62no—
131C23×C32#4111yescharacteristic
132C22×C3⋊D3—21no—
133C22×C3×D3—21no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C32×C4#4111yescharacteristic
140#638—41no—
141#638—41no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—42no—
146C4⋊(C3⋊D3)—21no—
147C4⋊(C3⋊D3)—21no—
148C4×C3⋊D3—41no—
149C4×C3⋊D3—41no—
150#634—21no—
151#634—21no—
152C3×#67—41no—
153C3×#67—41no—
154C2×C3×Dic3—21no—
155C3×D12—21no—
156C3×D12—21no—
157C3×C4×D3—41no—
158C3×C4×D3—41no—
159C3×Dic6—21no—
160C3×Dic6—21no—
161C32×C8—41no—
162C3×C3⋊C8—22no—
163C3×C3⋊C8—41no—
164C3×C3⋊C8—41no—
165#575—91no—
166#423—91no—
167C2×#104—91no—
168C2×#104—91no—
169#413—31no—
170#413—91no—
171#338—31no—
172C3×#41—61no—
173C3×#41—61no—
174C3×#41—61no—
175C3×#41—61no—
176C2×C3×Q8—31no—
177C2×C3×D4—31no—
178C2×C3×D4—61no—
179C22×C3×C4—21no—
180C22×C3×C4—61no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C2×#67—21no—
184C2×#67—61no—
185C2×#67—61no—
186C2×#67—121no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—121no—
190#235—21no—
191#235—21no—
192#235—21no—
193#235—21no—
194#235—62no—
195#235—62no—
196#235—61no—
197#235—61no—
198#235—61no—
199#235—61no—
200#235—61no—
201#235—61no—
202#235—61no—
203#235—61no—
204#235—121no—
205#235—121no—
206C2×D12—31no—
207C2×D12—31no—
208C2×D12—61no—
209C2×D12#6711yescharacteristic
210C2×C4×D3—21no—
211C2×C4×D3—61no—
212C2×C4×D3—61no—
213C2×C4×D3—121no—
214C2×Dic6—31no—
215C2×Dic6—31no—
216C2×Dic6—61no—
217C2×Dic6#6711yescharacteristic
218C3×M16—22no—
219C3×M16—21no—
220C3×M16—21no—
221C3×M16—21no—
222C3×M16—21no—
223C3×M16—41no—
224C3×M16—61no—
225C3×M16—61no—
226C3×M16—61no—
227C3×M16—61no—
228C3×M16—61no—
229C3×M16—61no—
230C2×C3×C8—21no—
231C2×C3×C8—21no—
232C2×C3×C8—32no—
233C2×C3×C8—41no—
234C2×C3×C8—61no—
235C2×C3×C8—61no—
236#216—62no—
237#215—62no—
238#214—62no—
239#213—62no—
240C4×Dic3—31no—
241C4×Dic3—31no—
242C4×Dic3—31no—
243C4×Dic3—31no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—121no—
249#208—21no—
250#208—21no—
251#208—21no—
252#208—21no—
253#208—21no—
254#208—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8D1212yes—
258Dic12—62no—
259D24—62no—
260#204—62no—
261#204—62no—
262C22×C32—41no—
263C22×C32#12111yescharacteristic
264C22×C32#12311yescharacteristic
265C22×C32#12311yescharacteristic
266C2×C3⋊D3—41no—
267C2×C3⋊D3—81no—
268C2×C3×D3—41no—
269C2×C3×D3—81no—
270C32×C4#12011yescharacteristic
271C32×C4#12111yescharacteristic
272C32×C4#12111yescharacteristic
273C32×C4#12411yescharacteristic
274C3⋊Dic3—22no—
275C3⋊Dic3—41no—
276C3⋊Dic3—41no—
277C3×Dic3—41no—
278C2×#41—31no—
279C2×#41—91no—
280#137—181no—
281#137—181no—
282AGL(1,ℤ/8)—181no—
283AGL(1,ℤ/8)—181no—
284#135—182no—
285C2×M16—31no—
286C2×M16—31no—
287C2×M16—31no—
288C2×M16D3211yescharacteristic
289C2×C42—91no—
290C4⋊C8—182no—
291#104—181no—
292#104—181no—
293#104—181no—
294#104—181no—
295#101—61no—
296#101—181no—
297#100—61no—
298#100—181no—
299C23×C3—21no—
300C23×C3—61no—
301C23×C3#23511yescharacteristic
302C23×C3#23911yescharacteristic
303C22×D3—21no—
304C22×D3—61no—
305C22×D3—61no—
306C22×D3—121no—
307C3×Q8—61no—
308C3×Q8—61no—
309C3×D4—61no—
310C3×D4—61no—
311C3×D4—121no—
312C3×D4—121no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—61no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4C2×D1211yescharacteristic
323C2×C3×C4#23511yescharacteristic
324C2×C3×C4#23511yescharacteristic
325C2×C3×C4#23511yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4#23711yescharacteristic
333C2×C3×C4C2×#6711yescharacteristic
334#67—41no—
335#67—41no—
336#67—122no—
337#67—122no—
338#67—121no—
339#67—121no—
340#67—121no—
341#67—121no—
342C2×Dic3—21no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C2×Dic3—122no—
353C2×Dic3—122no—
354C2×Dic3—124no—
355D12—21no—
356D12—21no—
357D12—62no—
358D12—61no—
359D12—61no—
360D12—61no—
361D12—61no—
362D12—121no—
363C4×D3—41no—
364C4×D3—41no—
365C4×D3—122no—
366C4×D3—122no—
367C4×D3—121no—
368C4×D3—121no—
369C4×D3—121no—
370C4×D3—121no—
371Dic6—21no—
372Dic6—21no—
373Dic6—62no—
374Dic6—61no—
375Dic6—61no—
376Dic6—61no—
377Dic6—61no—
378Dic6—121no—
379C3×C8—42no—
380C3×C8—41no—
381C3×C8—41no—
382C3×C8—62no—
383C3×C8—121no—
384C3×C8—121no—
385C3⋊C8—22no—
386C3⋊C8—41no—
387C3⋊C8—41no—
388C2×C32—21no—
389C2×C32—21no—
390C2×C32—21no—
391C2×C32#39411yescharacteristic
392C3⋊D3—81no—
393C3×D3—81no—
394#41—61no—
395#41—61no—
396#41—61no—
397#41—61no—
398#41—181no—
399#41—181no—
400#41—181no—
401#41—181no—
402C2×Q8—31no—
403C2×Q8—91no—
404C2×D4—31no—
405C2×D4—61no—
406C2×D4—91no—
407C2×D4—181no—
408C22×C4—61no—
409C22×C4—181no—
410C22×C4—181no—
411C22×C4C2×D3211yescharacteristic
412Q16—182no—
413SD16—182no—
414SD16—182no—
415D8—182no—
416M16—21no—
417M16—21no—
418M16—61no—
419M16—61no—
420M16—61no—
421M16—61no—
422M16—61no—
423M16—61no—
424C2×C8—21no—
425C2×C8—32no—
426C2×C8—61no—
427C2×C8—61no—
428C42—91no—
429C42—91no—
430C42—181no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—42no—
437C22×C3—121no—
438C22×C3—241no—
439C22×C3#88311yescharacteristic
440C22×C3#88411yescharacteristic
441C22×C3#89411yescharacteristic
442C22×C3#89411yescharacteristic
443C22×C3#89511yescharacteristic
444C22×C3#92911yescharacteristic
445C2×D3—41no—
446C2×D3—81no—
447C2×D3—122no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—242no—
451C2×D3—241no—
452C2×D3—241no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—121no—
458C3×C4#87511yescharacteristic
459C3×C4#88211yescharacteristic
460C3×C4#88411yescharacteristic
461C3×C4#88411yescharacteristic
462C3×C4#88411yescharacteristic
463C3×C4#88511yescharacteristic
464C3×C4#93711yescharacteristic
465C3×C4#93911yescharacteristic
466Dic3—41no—
467Dic3—62no—
468Dic3—62no—
469Dic3—122no—
470Dic3—122no—
471Dic3—121no—
472Dic3—121no—
473Dic3—122no—
474Dic3—121no—
475Dic3—121no—
476C32#205011yescharacteristic, complemented, Sylow
477C23—61no—
478C23—181no—
479C23#379911yescharacteristic
480Q8—61no—
481Q8—61no—
482Q8—181no—
483Q8—181no—
484D4—61no—
485D4—61no—
486D4—121no—
487D4—121no—
488D4—181no—
489D4—181no—
490D4—361no—
491D4—361no—
492C2×C4—61no—
493C2×C4—121no—
494C2×C4—121no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—362no—
499C2×C4—361no—
500C2×C4—361no—
501C2×C4#379811yescharacteristic
502C2×C4D3×D1211yescharacteristic
503C2×C4#380211yescharacteristic
504C2×C4#380411yescharacteristic
505C2×C4D3×#6711yescharacteristic
506C2×C4#381111yescharacteristic
507C8—41no—
508C8—62no—
509C8—121no—
510C8—121no—
511C2×C3—22no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—41no—
520C2×C3—41no—
521C2×C3—241no—
522C2×C3#467211yescharacteristic
523C2×C3#495911yescharacteristic
524D3—81no—
525D3—242no—
526D3—241no—
527D3—241no—
528C22—41no—
529C22—121no—
530C22—241no—
531C22—361no—
532C22—721no—
533C22#6385011yescharacteristic
534C22#6385411yescharacteristic
535C22#6391011yescharacteristic
536C4—121no—
537C4—182no—
538C4—361no—
539C4—361no—
540C4#6385211yescharacteristic
541C4#6391211yescharacteristic
542C4#6392211yescharacteristic
543C4#6397111yescharacteristic
544C3—21no—
545C3#6871911yescharacteristic, complemented
546C3#7014411yescharacteristic, complemented
547C2—21no—
548C2—21no—
549C2—21no—
550C2—241no—
551C2—721no—
552C2#1059129211yescharacteristic
subgroupG/H
centerC4#63852
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#394
prime radical#10594795C2
hypercenterC2×M16D32
hypocenterC32#2050
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63652C2semidirect
3. C3×#5132C2semidirect
4. #10591120C2semidirect
5. C2×#63568C2semidirect
6. #10591078C2semidirect
7. C3×C3⋊#338C2semidirect
41. #5132D3semidirect
45. C3⋊#338D3semidirect
476. C32#2050semidirect
545. C3#68719semidirect
546. C3#70144semidirect

Maximal subgroups

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

subgroupindex
#105947952
C2×#636522
C3×#51322
#105911202
C2×#635682
#105910782
C3×C3⋊#3382
#701443
#687193