Finite Group Databasebeta

← #11793117

Subgroups — #11793117

Order 1152.

567 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595049C211yesmaximal, characteristic, complemented
2#10592705C211yesmaximal, characteristic
3#10591113C211yesmaximal, characteristic
4C2×#63570C211yesmaximal, characteristic
5C3×#4532C211yesmaximal, characteristic, complemented
6C3×#4531C211yesmaximal, characteristic, complemented
7#10589171C211yesmaximal, characteristic, complemented
8#68779—31nomaximal
9#68714—31nomaximal
10C2×#3828C2211yescharacteristic
11C32×#117C2211yescharacteristic
12#64135C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63964—22no—
18#63918—21no—
19C4×#627—22no—
20#63869—21no—
21#63633—22no—
22#63570—21no—
23#63570—21no—
24#63570—22no—
25#5517—31no—
26#5470—31no—
27#5139—31no—
28C2×#825—31no—
29#5006—31no—
30#5006—31no—
31#5006—61no—
32#5005—31no—
33C2×#805—31no—
34C3×#339—31no—
35C3×H(3,ℤ/4)—31no—
36#4559—31no—
37#4556—31no—
38#4532D311yescharacteristic, complemented
39#4531D311yescharacteristic, complemented
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×C4⋊C4—21no—
52C32×C22⋊C4—21no—
53C32×C42—21no—
54#3757D412yes—
55C4⋊(C3⋊Dic3)—21no—
56C4×C3⋊Dic3—21no—
57C3×#217—21no—
58C3×C4⋊Dic3—21no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3D411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×C4×Dic3D412yes—
63C3×#208—21no—
64C3×#208—21no—
65C3×#208—21no—
66C3×#208—21no—
67C2×C3×C3⋊C8—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—31no—
77C2×C3×M16—31no—
78C3×#117—21no—
79C3×#117—31no—
80C3×#117C2×D311yescharacteristic
81C3×#117C2×D311yescharacteristic
82C2×C3×C42—31no—
83#926—31no—
84#926—31no—
85#926—61no—
86#926C2×D311yescharacteristic
87#924—62no—
88C2×C4×Dic3C2×D311yescharacteristic
89C2×#208C2×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—61no—
99#825—61no—
100#825—62no—
101#806—62no—
102#806—62no—
103#806—64no—
104#805—61no—
105#805—61no—
106#805—62no—
107C23×C32C2×D411yescharacteristic
108C22×C3⋊D3—21no—
109C2×C32×C4—41no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×Q811yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116#638—41no—
117#638—41no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—22no—
120C4⋊(C3⋊D3)—21no—
121C4⋊(C3⋊D3)—21no—
122C4×C3⋊D3—41no—
123C4×C3⋊D3—41no—
124#634—21no—
125#634—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—42no—
130#627—44no—
131C3×C3⋊C8—41no—
132C3×C3⋊C8—41no—
133#533—91no—
134#421—91no—
135C2×#104—91no—
136#410—91no—
137#344—91no—
138#339—31no—
139H(3,ℤ/4)—31no—
140C22×C3×C4—21no—
141C22×C3×C4—61no—
142C22×C3×C4C22×D311yescharacteristic
143C22×C3×C4C22×D311yescharacteristic
144C2×#67—62no—
145C2×#67—61no—
146C2×#67—61no—
147C22×Dic3—21no—
148#235—61no—
149#235—61no—
150#235—61no—
151#235—61no—
152#235—61no—
153#235—61no—
154#235—61no—
155#235—61no—
156#235—121no—
157#235—121no—
158#235—121no—
159#235—121no—
160C2×D12—31no—
161C2×D12—31no—
162C2×D12—61no—
163C2×C4×D3—62no—
164C2×C4×D3—61no—
165C2×C4×D3—61no—
166C2×Dic6—31no—
167C2×Dic6—31no—
168C2×Dic6—61no—
169C2×Dic6—62no—
170C2×Dic6—62no—
171C3×M16—61no—
172C3×M16—61no—
173C3×M16—61no—
174C3×M16—61no—
175C2×C3×C8—61no—
176C2×C3×C8—61no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—41no—
180C3×C4⋊C4—61no—
181C3×C22⋊C4—22no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—61no—
185C3×C42—21no—
186C3×C42—21no—
187C3×C42—32no—
188C3×C42—31no—
189C3×C42—31no—
190C3×C42—41no—
191C3×C42—61no—
192#217—21no—
193#217—32no—
194#217—32no—
195#217—62no—
196C4⋊Dic3—21no—
197C4⋊Dic3—62no—
198C4⋊Dic3—62no—
199C4⋊Dic3—61no—
200C4⋊Dic3—61no—
201C4⋊Dic3—121no—
202Dic3⋊C4—62no—
203Dic3⋊C4—62no—
204Dic3⋊C4—62no—
205Dic3⋊C4—62no—
206C4×Dic3—21no—
207C4×Dic3—61no—
208C4×Dic3—61no—
209C4×Dic3—121no—
210C4×Dic3D1212yes—
211C4×Dic3D1211yescharacteristic
212C4×Dic3D1211yescharacteristic
213#208—21no—
214#208—21no—
215#208—21no—
216#208—21no—
217C2×C3⋊C8—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×C4—81no—
226C32×C4C22⋊Q811yescharacteristic
227C32×C4C22⋊Q811yescharacteristic
228C32×C4#12411yescharacteristic
229C32×C4#12411yescharacteristic
230C3⋊Dic3—41no—
231C3⋊Dic3—42no—
232C3×Dic3—22no—
233C3×Dic3—42no—
234C3×Dic3—41no—
235C2×#41—91no—
236C2×M16—31no—
237C2×M16—31no—
238C4⋊Q8—181no—
239#125—181no—
240C22⋊Q8—182no—
241C4×Q8—182no—
242#117—31no—
243#117—91no—
244#117D3211yescharacteristic
245C2×C42—31no—
246#104—181no—
247#104—181no—
248#104—182no—
249#99—182no—
250C23×C3—21no—
251C23×C3D3×D411yescharacteristic
252C23×C3D3×D411yescharacteristic
253C22×D3—62no—
254C22×D3—61no—
255C22×D3—61no—
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—42no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—62no—
268C2×C3×C4—122no—
269C2×C3×C4C2×D1211yescharacteristic
270C2×C3×C4C2×D1211yescharacteristic
271C2×C3×C4#23511yescharacteristic
272C2×C3×C4#23511yescharacteristic
273C2×C3×C4#23511yescharacteristic
274C2×C3×C4#23511yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4#23711yescharacteristic
278C2×C3×C4#23711yescharacteristic
279C2×C3×C4D3×Q811yescharacteristic
280C2×C3×C4D3×Q811yescharacteristic
281#67—122no—
282#67—122no—
283#67—121no—
284#67—121no—
285#67—121no—
286#67—121no—
287C2×Dic3—21no—
288C2×Dic3—21no—
289C2×Dic3—22no—
290C2×Dic3—42no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—122no—
297D12—61no—
298D12—61no—
299D12—61no—
300D12—61no—
301D12—121no—
302D12—121no—
303C4×D3—122no—
304C4×D3—122no—
305C4×D3—121no—
306C4×D3—121no—
307C4×D3—121no—
308C4×D3—121no—
309Dic6—61no—
310Dic6—61no—
311Dic6—61no—
312Dic6—61no—
313Dic6—121no—
314Dic6—121no—
315Dic6—124no—
316Dic6—124no—
317C3×C8—121no—
318C3×C8—121no—
319C3⋊C8—41no—
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—61no—
338M16—61no—
339M16—61no—
340M16—61no—
341C2×C8—61no—
342C2×C8—61no—
343C4⋊C4—21no—
344C4⋊C4—61no—
345C4⋊C4—182no—
346C4⋊C4—182no—
347C4⋊C4—182no—
348C4⋊C4—181no—
349C22⋊C4—21no—
350C22⋊C4—61no—
351C22⋊C4—92no—
352C42—21no—
353C42—31no—
354C42—31no—
355C42—32no—
356C42—61no—
357C42—181no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—81no—
364C22×C3#88211yescharacteristic
365C22×C3#88211yescharacteristic
366C22×C3#88511yescharacteristic
367C22×C3#88511yescharacteristic
368C22×C3#89611yescharacteristic
369C22×C3#89611yescharacteristic
370C2×D3—122no—
371C2×D3—121no—
372C2×D3—121no—
373C2×D3—241no—
374C2×D3—241no—
375C2×D3—242no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—62no—
381C3×C4—81no—
382C3×C4—81no—
383C3×C4—82no—
384C3×C4—122no—
385C3×C4—121no—
386C3×C4#87511yescharacteristic
387C3×C4#87511yescharacteristic
388C3×C4#88511yescharacteristic
389C3×C4#88511yescharacteristic
390C3×C4#89611yescharacteristic
391C3×C4#89611yescharacteristic
392C3×C4#89711yescharacteristic
393C3×C4#89711yescharacteristic
394Dic3—22no—
395Dic3—42no—
396Dic3—41no—
397Dic3—122no—
398Dic3—122no—
399Dic3—122no—
400Dic3—121no—
401Dic3—121no—
402Dic3—242no—
403C32#203111yescharacteristic, complemented, Sylow
404C23—181no—
405C23#381111yescharacteristic
406Q8—181no—
407Q8—181no—
408Q8—364no—
409D4—181no—
410D4—181no—
411D4—361no—
412D4—361no—
413C2×C4—41no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—62no—
417C2×C4—122no—
418C2×C4—181no—
419C2×C4—182no—
420C2×C4—361no—
421C2×C4—361no—
422C2×C4#379711yescharacteristic
423C2×C4#379811yescharacteristic
424C2×C4D3×D1211yescharacteristic
425C2×C4D3×D1211yescharacteristic
426C2×C4#380411yescharacteristic
427C2×C4#380411yescharacteristic
428C8—121no—
429C8—121no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—41no—
438C2×C3—41no—
439C2×C3—41no—
440C2×C3#467311yescharacteristic
441C2×C3#467311yescharacteristic
442D3—242no—
443D3—241no—
444D3—241no—
445C22—41no—
446C22—361no—
447C22—721no—
448C22#6386511yescharacteristic
449C22#6392311yescharacteristic
450C22#6395311yescharacteristic
451C4—62no—
452C4—81no—
453C4—121no—
454C4—122no—
455C4—362no—
456C4—361no—
457C4#6385211yescharacteristic
458C4#6385211yescharacteristic
459C4#6389511yescharacteristic
460C4#6389511yescharacteristic
461C3—21no—
462C3#6871411yescharacteristic, complemented
463C3#6877911yescharacteristic, complemented
464C2—21no—
465C2—21no—
466C2—21no—
467C2—721no—
468C2#1059120511yescharacteristic
subgroupG/H
centerC4#63852
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#393
prime radicalC2×#3828C22
hypercenter#117D32
hypocenterC32#2031
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595049C2semidirect
5. C3×#4532C2semidirect
6. C3×#4531C2semidirect
7. #10589171C2semidirect
38. #4532D3semidirect
39. #4531D3semidirect
46. C2×C4⋊(C3⋊D3)Q8semidirect
48. C2×#634Q8semidirect
403. C32#2031semidirect
462. C3#68714semidirect
463. C3#68779semidirect

Maximal subgroups

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

subgroupindex
#105950492
#105927052
#105911132
C2×#635702
C3×#45322
C3×#45312
#105891712
#687793
#687143