Finite Group Databasebeta

← #11793111

Subgroups — #11793111

Order 1152.

565 conjugacy classes of subgroups.

The subgroup lattice has 469 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595049C211yesmaximal, characteristic, complemented
2#10592838C211yesmaximal, characteristic
3#10591232C211yesmaximal, characteristic
4C2×#63570C211yesmaximal, characteristic
5C3×#4556C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#69042—31nomaximal
9#68779—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63964—22no—
18#63918—21no—
19C4×#627—22no—
20#63869—21no—
21#63652—22no—
22#63581—22no—
23#63570—21no—
24#63570—21no—
25#5517—31no—
26#5470—31no—
27#5139—31no—
28#5139—31no—
29#5139—61no—
30C2×#825—31no—
31#5006—31no—
32#5006—31no—
33C2×#805—31no—
34C3×#344—31no—
35C3×#339—31no—
36#4557—31no—
37#4556D311yescharacteristic, complemented
38#4555D311yescharacteristic, complemented
39#4531—31no—
40C22×C32×C4C2311yescharacteristic
41C2×#638—21no—
42#3828—21no—
43#3828—21no—
44#3828—21no—
45#3828—21no—
46C2×C4⋊(C3⋊D3)Q811yescharacteristic, complemented
47C2×C4×C3⋊D3—21no—
48C2×#634Q811yescharacteristic, complemented
49C22×C3×Dic3—21no—
50C2×#627—22no—
51C32×M16—21no—
52C32×M16—21no—
53C2×C32×C8—21no—
54#3757—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4×C3⋊Dic3D412yes—
57C3×#217—21no—
58C3×#217D412yes—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4×Dic3—21no—
62C3×C4×Dic3—21no—
63C3×C4×Dic3—21no—
64C3×C4×Dic3D411yescharacteristic
65C3×C4×Dic3D411yescharacteristic
66C3×#208—21no—
67C3×#208—21no—
68C2×C3×C3⋊C8—21no—
69#3724—22no—
70Dic3⋊Dic3—22no—
71Dic3⋊Dic3—22no—
72#2031—91noSylow
73C2×#235—31no—
74C2×#235—31no—
75C2×#235—61no—
76C2×C3×M16—21no—
77C2×C3×M16—31no—
78C2×C3×M16C2×D311yescharacteristic
79C2×C3×M16C2×D311yescharacteristic
80C3×#117—31no—
81C3×#117—31no—
82C2×C3×C42—31no—
83#926—31no—
84#926—31no—
85#926—61no—
86#926C2×D311yescharacteristic
87#926C2×D311yescharacteristic
88#924—62no—
89C2×C4×Dic3C2×D311yescharacteristic
90C2×#208C2×D311yescharacteristic
91#890—61no—
92#888—61no—
93#878—62no—
94#870—61no—
95#869—61no—
96C4×Dic6—62no—
97C4×Dic6—62no—
98#825—62no—
99#825—62no—
100#825—64no—
101#825—61no—
102#825—61no—
103#806—62no—
104#806—62no—
105#805—61no—
106#805—61no—
107C23×C32C2×D411yescharacteristic
108C22×C3⋊D3—21no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×Q811yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115#638—41no—
116#638—41no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—21no—
119C4⋊(C3⋊D3)—21no—
120C4⋊(C3⋊D3)—21no—
121C4×C3⋊D3—41no—
122C4×C3⋊D3—41no—
123#634—21no—
124#634—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—42no—
129C2×C3×Dic3—41no—
130#627—44no—
131C32×C8—41no—
132C3×C3⋊C8—41no—
133#533—91no—
134#421—91no—
135C2×#104—91no—
136#410—91no—
137#344—31no—
138#339—31no—
139H(3,ℤ/4)—91no—
140C22×C3×C4—21no—
141C22×C3×C4—61no—
142C22×C3×C4C22×D311yescharacteristic
143C22×C3×C4C22×D311yescharacteristic
144C2×#67—61no—
145C2×#67—61no—
146C2×#67—121no—
147C22×Dic3—21no—
148#235—62no—
149#235—62no—
150#235—61no—
151#235—61no—
152#235—61no—
153#235—61no—
154#235—61no—
155#235—61no—
156#235—61no—
157#235—61no—
158#235—121no—
159#235—121no—
160C2×D12—31no—
161C2×D12—31no—
162C2×D12—61no—
163C2×C4×D3—61no—
164C2×C4×D3—61no—
165C2×C4×D3—121no—
166C2×Dic6—31no—
167C2×Dic6—31no—
168C2×Dic6—61no—
169C2×Dic6—62no—
170C2×Dic6—62no—
171C3×M16—22no—
172C3×M16—21no—
173C3×M16—21no—
174C3×M16—21no—
175C3×M16—21no—
176C3×M16—41no—
177C3×M16—61no—
178C3×M16—61no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—41no—
182C2×C3×C8—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C22⋊C4—32no—
186C3×C22⋊C4—61no—
187C3×C42—31no—
188C3×C42—31no—
189C3×C42—61no—
190C3×C42—61no—
191C3×C42—61no—
192#217—21no—
193#217—61no—
194#217—61no—
195#217—121no—
196#217D1212yes—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3—62no—
200C4⋊Dic3—62no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—121no—
204Dic3⋊C4—62no—
205Dic3⋊C4—62no—
206Dic3⋊C4—62no—
207Dic3⋊C4—62no—
208C4×Dic3—21no—
209C4×Dic3—21no—
210C4×Dic3—21no—
211C4×Dic3—32no—
212C4×Dic3—32no—
213C4×Dic3—62no—
214C4×Dic3D1211yescharacteristic
215C4×Dic3D1211yescharacteristic
216#208—21no—
217#208—21no—
218C2×C3⋊C8—21no—
219C22×C32—41no—
220C22×C32#12011yescharacteristic
221C22×C32C22⋊Q811yescharacteristic
222C22×C32#12411yescharacteristic
223C2×C3⋊D3—41no—
224C2×C3⋊D3—81no—
225C32×C4C22⋊Q811yescharacteristic
226C32×C4C22⋊Q811yescharacteristic
227C32×C4#12411yescharacteristic
228C32×C4#12411yescharacteristic
229C3⋊Dic3—41no—
230C3⋊Dic3—42no—
231C3×Dic3—22no—
232C3×Dic3—42no—
233C3×Dic3—41no—
234C3×Dic3—81no—
235C2×#41—91no—
236C2×M16—31no—
237C2×M16D3211yescharacteristic
238C4⋊Q8—181no—
239#125—181no—
240C22⋊Q8—182no—
241C4×Q8—182no—
242#117—31no—
243#117—31no—
244#117—91no—
245C2×C42—31no—
246#104—181no—
247#104—181no—
248#104—182no—
249#99—182no—
250C23×C3—21no—
251C23×C3C2×D1211yescharacteristic
252C23×C3D3×D411yescharacteristic
253C22×D3—61no—
254C22×D3—61no—
255C22×D3—121no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—62no—
265C2×C3×C4—122no—
266C2×C3×C4—121no—
267C2×C3×C4C2×D1211yescharacteristic
268C2×C3×C4#23511yescharacteristic
269C2×C3×C4#23511yescharacteristic
270C2×C3×C4#23511yescharacteristic
271C2×C3×C4#23511yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4#23711yescharacteristic
276C2×C3×C4#23711yescharacteristic
277C2×C3×C4D3×Q811yescharacteristic
278C2×C3×C4D3×Q811yescharacteristic
279#67—122no—
280#67—122no—
281#67—121no—
282#67—121no—
283#67—121no—
284#67—121no—
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—22no—
288C2×Dic3—42no—
289C2×Dic3—41no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—121no—
295C2×Dic3—122no—
296D12—62no—
297D12—61no—
298D12—61no—
299D12—61no—
300D12—61no—
301D12—121no—
302C4×D3—122no—
303C4×D3—122no—
304C4×D3—121no—
305C4×D3—121no—
306C4×D3—121no—
307C4×D3—121no—
308Dic6—62no—
309Dic6—61no—
310Dic6—61no—
311Dic6—61no—
312Dic6—61no—
313Dic6—121no—
314Dic6—124no—
315Dic6—124no—
316C3×C8—42no—
317C3×C8—41no—
318C3×C8—41no—
319C3×C8—121no—
320C3⋊C8—41no—
321C2×C32—21no—
322C2×C32—21no—
323C2×C32—21no—
324C2×C32#39311yescharacteristic
325C3⋊D3—81no—
326#41—181no—
327#41—181no—
328#41—181no—
329#41—181no—
330C2×Q8—91no—
331C2×Q8—182no—
332C2×D4—91no—
333C2×D4—181no—
334C22×C4—61no—
335C22×C4—181no—
336C22×C4C2×D3211yescharacteristic
337M16—21no—
338M16—21no—
339M16—61no—
340M16—61no—
341C2×C8—21no—
342C2×C8—61no—
343C4⋊C4—61no—
344C4⋊C4—61no—
345C4⋊C4—182no—
346C4⋊C4—182no—
347C4⋊C4—182no—
348C4⋊C4—181no—
349C22⋊C4—32no—
350C22⋊C4—61no—
351C22⋊C4—181no—
352C42—31no—
353C42—31no—
354C42—61no—
355C42—61no—
356C42—61no—
357C42—92no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—81no—
364C22×C3#87511yescharacteristic
365C22×C3#88211yescharacteristic
366C22×C3#88211yescharacteristic
367C22×C3#88511yescharacteristic
368C22×C3#89611yescharacteristic
369C22×C3#89711yescharacteristic
370C2×D3—122no—
371C2×D3—121no—
372C2×D3—121no—
373C2×D3—242no—
374C2×D3—241no—
375C2×D3—241no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—62no—
381C3×C4—122no—
382C3×C4—121no—
383C3×C4—241no—
384C3×C4#87511yescharacteristic
385C3×C4#88511yescharacteristic
386C3×C4#88511yescharacteristic
387C3×C4#88511yescharacteristic
388C3×C4#89611yescharacteristic
389C3×C4#89611yescharacteristic
390C3×C4#89611yescharacteristic
391C3×C4#89711yescharacteristic
392Dic3—22no—
393Dic3—42no—
394Dic3—41no—
395Dic3—81no—
396Dic3—122no—
397Dic3—122no—
398Dic3—122no—
399Dic3—121no—
400Dic3—121no—
401Dic3—242no—
402C32#203111yescharacteristic, complemented, Sylow
403C23—181no—
404C23D3×D1211yescharacteristic
405Q8—181no—
406Q8—181no—
407Q8—364no—
408D4—181no—
409D4—181no—
410D4—361no—
411D4—361no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—62no—
415C2×C4—122no—
416C2×C4—121no—
417C2×C4—181no—
418C2×C4—182no—
419C2×C4—361no—
420C2×C4—361no—
421C2×C4#379711yescharacteristic
422C2×C4#379811yescharacteristic
423C2×C4D3×D1211yescharacteristic
424C2×C4#380411yescharacteristic
425C2×C4#380411yescharacteristic
426C2×C4#381111yescharacteristic
427C8—41no—
428C8—121no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—41no—
437C2×C3—41no—
438C2×C3—41no—
439C2×C3#467311yescharacteristic
440C2×C3#467311yescharacteristic
441D3—242no—
442D3—241no—
443D3—241no—
444C22—41no—
445C22—361no—
446C22—721no—
447C22#6385211yescharacteristic
448C22#6389511yescharacteristic
449C22#6392311yescharacteristic
450C4—62no—
451C4—121no—
452C4—122no—
453C4—241no—
454C4—362no—
455C4—361no—
456C4#6385211yescharacteristic
457C4#6386511yescharacteristic
458C4#6389511yescharacteristic
459C4#6395311yescharacteristic
460C3—21no—
461C3#6877911yescharacteristic, complemented
462C3#6904211yescharacteristic, complemented
463C2—21no—
464C2—21no—
465C2—21no—
466C2—721no—
467C2#1059120511yescharacteristic
subgroupG/H
centerC4#63953
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#393
prime radicalC2×#3828C22
hypercenterC2×M16D32
hypocenterC32#2031
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
1. #10595049C2semidirect
5. C3×#4556C2semidirect
6. C3×#4555C2semidirect
7. #10589158C2semidirect
37. #4556D3semidirect
38. #4555D3semidirect
46. C2×C4⋊(C3⋊D3)Q8semidirect
48. C2×#634Q8semidirect
402. C32#2031semidirect
461. C3#68779semidirect
462. C3#69042semidirect

Maximal subgroups

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

subgroupindex
#105950492
#105928382
#105912322
C2×#635702
C3×#45562
C3×#45552
#105891582
#690423
#687793