Finite Group Databasebeta

← #11787106

Subgroups — #11787106

Order 1152.

577 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594776C211yesmaximal, characteristic
2#10592801C211yesmaximal, characteristic, complemented
3C3×#5110C211yesmaximal, characteristic
4C3×#5102C211yesmaximal, characteristic, complemented
5#10591231C211yesmaximal, characteristic
6#10589171C211yesmaximal, characteristic, complemented
7#10589170C211yesmaximal, characteristic, complemented
8#70546—31nomaximal
9#70002—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63815—22no—
18#63814—22no—
19D3×#208—22no—
20#63641—22no—
21C3×(C2×D3)⋊C8—22no—
22C3×Dic3⋊C8—22no—
23#63580C414yes—
24#5819—31no—
25#5745—31no—
26C3×#424—31no—
27C3×#408—31no—
28#5240—31no—
29#5110D311yescharacteristic
30#5102—31no—
31#5102—31no—
32#5102—61no—
33#5102D311yescharacteristic, complemented
34#5006—31no—
35#4559—31no—
36#4559—31no—
37#4556—31no—
38#4533—31no—
39C22×C32×C4C2311yescharacteristic
40C2×C3×#67C2×C412yes—
41C3×#235—21no—
42C3×#235—21no—
43C3×#235—21no—
44C3×#235—21no—
45C2×C3×D12Q811yescharacteristic
46C2×C3×C4×D3D412yes—
47C2×C3×Dic6Q811yescharacteristic
48C2×C32×C8—21no—
49C2×C32×C8—21no—
50C2×C32×C8—21no—
51#3757C2×C412yes—
52C4⋊(C3⋊Dic3)—21no—
53C4×C3⋊Dic3—21no—
54#3748—21no—
55#3748—21no—
56C2×C3⋊(C3⋊C8)D412yes—
57C3×#217C2×C412yes—
58C3×C4⋊Dic3—21no—
59C3×C4×Dic3—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C3×#208—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8D412yes—
66#3711—24no—
67D3×C3⋊C8—24no—
68#1868—91noSylow
69C2×C3×#41—31no—
70C2×#235C2×D311yescharacteristic
71C2×C3×M16—31no—
72C2×C3×M16—31no—
73C22×C3×C8—21no—
74C22×C3×C8C2×D311yescharacteristic
75C22×C3×C8C2×D311yescharacteristic
76C3×#117—31no—
77#948—62no—
78#948—62no—
79#926—31no—
80#926—31no—
81#926—61no—
82#926C2×D311yescharacteristic
83C2×#208—31no—
84C2×#208—31no—
85C2×#208—61no—
86C2×#208—62no—
87C2×#208C2×D311yescharacteristic
88C2×#208C2×D311yescharacteristic
89#907—62no—
90D3×M16—62no—
91#901—62no—
92C3×C4⋊C8—62no—
93C3×C22⋊C8—62no—
94#834—34no—
95(C2×D3)⋊C8—22no—
96Dic3⋊C8—22no—
97Dic3⋊C8—62no—
98Dic3⋊C8—62no—
99Dic3⋊C8—64no—
100#806—34no—
101C23×C32C22×C411yescharacteristic
102C22×C3×D3C4⋊C412yes—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×Q811yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C3⋊Dic3—22no—
110C3×#67—22no—
111C3×#67—22no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3C4⋊C412yes—
114C3×D12—21no—
115C3×D12—21no—
116C3×C4×D3—22no—
117C3×C4×D3—22no—
118C3×Dic6—21no—
119C3×Dic6—21no—
120C32×C8—41no—
121C3⋊(C3⋊C8)—22no—
122C3×C3⋊C8—22no—
123C3×C3⋊C8—41no—
124#568—91no—
125#424—31no—
126#424—91no—
127#410—91no—
128#408—31no—
129#344—91no—
130#344—91no—
131C3×#41—61no—
132C3×#41—61no—
133C3×#41—61no—
134C3×#41—61no—
135C2×C3×Q8—31no—
136C2×C3×D4—32no—
137C2×C3×D4—31no—
138C22×C3×C4—21no—
139C22×C3×C4—32no—
140C22×C3×C4C22×D311yescharacteristic
141C22×C3×C4C22×D311yescharacteristic
142C2×#67C4×D312yes—
143#235—21no—
144#235—21no—
145#235—21no—
146#235—21no—
147C2×D12Dic611yescharacteristic
148C2×C4×D3#6712yes—
149C2×Dic6Dic611yescharacteristic
150C3×M16—61no—
151C3×M16—61no—
152C3×M16—61no—
153C3×M16—61no—
154C2×C3×C8—22no—
155C2×C3×C8—21no—
156C2×C3×C8—21no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C2×C3×C8—21no—
161C2×C3×C8—32no—
162C2×C3×C8—41no—
163C2×C3×C8—41no—
164C2×C3×C8—61no—
165C3×C4⋊C4—61no—
166C3×C22⋊C4—32no—
167C3×C42—61no—
168#217—32no—
169#217—32no—
170#217—62no—
171#217C4×D312yes—
172C4⋊Dic3—21no—
173C4⋊Dic3—62no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4×Dic3—21no—
177C4×Dic3—62no—
178C4×Dic3—61no—
179C4×Dic3—61no—
180#208—21no—
181#208—21no—
182#208—21no—
183#208—21no—
184#208—64no—
185#208—61no—
186#208—61no—
187#208—61no—
188#208—61no—
189#208—121no—
190#208—121no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—32no—
193C2×C3⋊C8—32no—
194C2×C3⋊C8—62no—
195C2×C3⋊C8—64no—
196C2×C3⋊C8#6712yes—
197ΓL(1,𝔽25)—64no—
198D3×C8—64no—
199C22×C32—41no—
200C22×C32C2×C4⋊C411yescharacteristic
201C22×C32C4×D411yescharacteristic
202C22×C32C4×D411yescharacteristic
203C2×C3×D3—22no—
204C2×C3×D3—42no—
205C32×C4#12011yescharacteristic
206C32×C4C22⋊Q811yescharacteristic
207C32×C4C22⋊Q811yescharacteristic
208C32×C4#12311yescharacteristic
209C3⋊Dic3—42no—
210C3×Dic3—22no—
211C3×Dic3—42no—
212C2×#41—31no—
213#131—182no—
214#131—182no—
215C2×M16—31no—
216C2×M16—31no—
217C2×M16—91no—
218C2×M16—182no—
219C22×C8D3211yescharacteristic
220#117—31no—
221#117—91no—
222C4⋊C8—62no—
223C4⋊C8—182no—
224#99—94no—
225C22⋊C8—62no—
226C23×C3—21no—
227C23×C3—32no—
228C23×C3C2×C4×D311yescharacteristic
229C23×C3C2×C4×D311yescharacteristic
230C22×D3Dic3⋊C412yes—
231C3×Q8—61no—
232C3×Q8—61no—
233C3×D4—62no—
234C3×D4—62no—
235C3×D4—61no—
236C3×D4—61no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—32no—
244C2×C3×C4—62no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4C2×Dic611yescharacteristic
248C2×C3×C4#23511yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4#23711yescharacteristic
254C2×C3×C4#23711yescharacteristic
255C2×C3×C4D3×Q811yescharacteristic
256C2×C3×C4#23911yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258C2×C3×C4C2×#6711yescharacteristic
259#67—22no—
260#67—22no—
261C2×Dic3—22no—
262C2×Dic3—64no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3Dic3⋊C412yes—
266D12—21no—
267D12—21no—
268C4×D3—22no—
269C4×D3—22no—
270Dic6—21no—
271Dic6—21no—
272C3×C8—42no—
273C3×C8—41no—
274C3×C8—41no—
275C3×C8—62no—
276C3×C8—121no—
277C3⋊C8—22no—
278C3⋊C8—41no—
279C3⋊C8—62no—
280C3⋊C8—62no—
281C3⋊C8—122no—
282C2×C32—21no—
283C2×C32—21no—
284C2×C32—21no—
285C2×C32#38511yescharacteristic
286C3×D3—42no—
287#41—61no—
288#41—61no—
289#41—61no—
290#41—61no—
291C2×Q8—31no—
292C2×D4—32no—
293C2×D4—31no—
294C22×C4—32no—
295C22×C4C2×D3211yescharacteristic
296M16—61no—
297M16—61no—
298M16—61no—
299M16—61no—
300M16—184no—
301M16—181no—
302M16—181no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—32no—
307C2×C8—61no—
308C2×C8—92no—
309C2×C8—184no—
310C4⋊C4—61no—
311C4⋊C4—181no—
312C22⋊C4—32no—
313C22⋊C4—92no—
314C42—61no—
315C42—181no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—42no—
322C22×C3—62no—
323C22×C3—122no—
324C22×C3#67⋊C411yescharacteristic
325C22×C3#67⋊C411yescharacteristic
326C22×C3D3×C4⋊C411yescharacteristic
327C22×C3#89311yescharacteristic
328C22×C3C2×Dic3⋊C411yescharacteristic
329C22×C3C4×#6711yescharacteristic
330C2×D3—22no—
331C2×D3—42no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—62no—
337C3×C4—122no—
338C3×C4#87811yescharacteristic
339C3×C4#87811yescharacteristic
340C3×C4#89411yescharacteristic
341C3×C4#89611yescharacteristic
342C3×C4#93511yescharacteristic
343C3×C4#93711yescharacteristic
344C3×C4#93711yescharacteristic
345C3×C4#94611yescharacteristic
346Dic3—22no—
347Dic3—42no—
348Dic3—124no—
349Dic3—122no—
350Dic3—122no—
351C32#186811yescharacteristic, complemented, Sylow
352C23—32no—
353C23C4×D3211yescharacteristic
354Q8—61no—
355Q8—61no—
356D4—62no—
357D4—62no—
358D4—61no—
359D4—61no—
360C2×C4—32no—
361C2×C4—62no—
362C2×C4—62no—
363C2×C4—62no—
364C2×C4—182no—
365C2×C4D3×Dic611yescharacteristic
366C2×C4#379511yescharacteristic
367C2×C4#379611yescharacteristic
368C2×C4D3×#6711yescharacteristic
369C2×C4D3×#6711yescharacteristic
370C2×C4#381111yescharacteristic
371C8—41no—
372C8—62no—
373C8—121no—
374C8—182no—
375C2×C3—22no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—41no—
384C2×C3—41no—
385C2×C3—122no—
386C2×C3#494611yescharacteristic
387C2×C3#498911yescharacteristic
388D3—42no—
389C22—41no—
390C22—62no—
391C22—122no—
392C22D3×Dic3⋊C411yescharacteristic
393C22#6387911yescharacteristic
394C22#6388111yescharacteristic
395C4—62no—
396C4—122no—
397C4—362no—
398C4#6388411yescharacteristic
399C4#6388711yescharacteristic
400C4#6389611yescharacteristic
401C4#6398311yescharacteristic
402C3—21no—
403C3#7000211yescharacteristic, complemented
404C3#7054611yescharacteristic, complemented
405C2—21no—
406C2—21no—
407C2—21no—
408C2—122no—
409C2#1059137211yescharacteristic
subgroupG/H
centerC4#63983
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC2×C32#385
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1868
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10592801C2semidirect
4. C3×#5102C2semidirect
6. #10589171C2semidirect
7. #10589170C2semidirect
33. #5102D3semidirect
351. C32#1868semidirect
403. C3#70002semidirect
404. C3#70546semidirect

Maximal subgroups

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

subgroupindex
#105947762
#105928012
C3×#51102
C3×#51022
#105912312
#105891712
#105891702
#705463
#700023