Finite Group Databasebeta

← #11786656

Subgroups — #11786656

Order 1152.

555 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594776C211yesmaximal, characteristic
2#10592824C211yesmaximal, characteristic, complemented
3C3×#5132C211yesmaximal, characteristic
4#10591141C211yesmaximal, characteristic, complemented
5#10591070C211yesmaximal, characteristic
6C3×#4558C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70135—31nomaximal
9#68945—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63815—22no—
18#63814—22no—
19D3×#208—22no—
20#63646—22no—
21C3×#824C412yes—
22C3×#823C412yes—
23#63577—22no—
24(C2×D3)⋊(C3⋊C8)—22no—
25#5819—31no—
26#5745—31no—
27C3×#413—31no—
28#5234—31no—
29#5132D311yescharacteristic
30#5125—31no—
31#5125—31no—
32#5125—31no—
33#5125—61no—
34#5124—31no—
35#5110—31no—
36C3×#341—31no—
37#4558—31no—
38#4558D311yescharacteristic, complemented
39#4552—31no—
40C22×C32×C4C2311yescharacteristic
41C2×C3×#67Q812yes—
42C3×#235—21no—
43C3×#235—21no—
44C3×#235—21no—
45C3×#235—21no—
46C2×C3×D12C2×C411yescharacteristic
47C2×C3×C4×D3D412yes—
48C2×C3×Dic6C2×C411yescharacteristic
49C32×M16—21no—
50C32×M16C2×C412yes—
51C2×C32×C8—21no—
52#3748—21no—
53#3748—21no—
54#3748—21no—
55#3748D412yes—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208C2×C412yes—
61C3×#208D412yes—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#3711—24no—
68D3×C3⋊C8—24no—
69#1858—91noSylow
70C2×C3×#41—31no—
71C2×#235C2×D311yescharacteristic
72C2×C3×M16—21no—
73C2×C3×M16—31no—
74C2×C3×M16—31no—
75C2×C3×M16C2×D311yescharacteristic
76C2×C3×M16C2×D311yescharacteristic
77C22×C3×C8—31no—
78#948—62no—
79#948—62no—
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—31no—
83C2×#208—31no—
84C2×#208—61no—
85C2×#208—61no—
86C2×#208—62no—
87C2×#208C2×D311yescharacteristic
88C2×#208C2×D311yescharacteristic
89C22×C3⋊C8C2×D311yescharacteristic
90#907—62no—
91D3×M16—62no—
92#901—62no—
93C3×#101—32no—
94C3×#100—32no—
95#830—62no—
96#824Dic312yes—
97#823Dic312yes—
98#822—62no—
99(C2×D3)⋊C8—62no—
100#819—62no—
101#819—62no—
102#819—64no—
103#819—62no—
104C23×C32C2×Q811yescharacteristic
105C22×C3×D3C4⋊C412yes—
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C3×#67—22no—
113C3×#67—22no—
114C2×C3×Dic3C4⋊C412yes—
115C3×D12—21no—
116C3×D12—21no—
117C3×C4×D3—22no—
118C3×C4×D3—22no—
119C3×Dic6—21no—
120C3×Dic6—21no—
121C32×C8—22no—
122C3⋊(C3⋊C8)—22no—
123C3⋊(C3⋊C8)—41no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—41no—
127#568—91no—
128#430—91no—
129#430—91no—
130#413—31no—
131#408—91no—
132#341—31no—
133#341—91no—
134C3×#41—61no—
135C3×#41—61no—
136C3×#41—61no—
137C3×#41—61no—
138C2×C3×Q8—31no—
139C2×C3×D4—32no—
140C2×C3×D4—31no—
141C22×C3×C4—21no—
142C22×C3×C4—32no—
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C2×#67Dic612yes—
146#235—21no—
147#235—21no—
148#235—21no—
149#235—21no—
150C2×D12C2×Dic311yescharacteristic
151C2×C4×D3D1212yes—
152C2×Dic6C2×Dic311yescharacteristic
153C3×M16—22no—
154C3×M16—21no—
155C3×M16—21no—
156C3×M16—22no—
157C3×M16—32no—
158C3×M16—32no—
159C3×M16—61no—
160C3×M16—61no—
161C3×M16C4×D312yes—
162C3×M16C2×Dic312yes—
163C2×C3×C8—22no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C2×C3×C8—61no—
171#208—21no—
172#208—21no—
173#208—32no—
174#208—32no—
175#208—62no—
176#208—64no—
177#208—61no—
178#208—61no—
179#208—62no—
180#208—61no—
181#208—61no—
182#208—61no—
183#208—61no—
184#208—121no—
185#208—121no—
186#208D1212yes—
187#208C2×Dic312yes—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—64no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—121no—
199C2×C3⋊C8—121no—
200ΓL(1,𝔽25)—64no—
201D3×C8—64no—
202C22×C32—41no—
203C22×C32C2×C4⋊C411yescharacteristic
204C22×C32C22⋊Q811yescharacteristic
205C22×C32C22⋊Q811yescharacteristic
206C2×C3×D3—22no—
207C2×C3×D3—42no—
208C32×C4C4×D411yescharacteristic
209C32×C4C4×D411yescharacteristic
210C32×C4#12011yescharacteristic
211C32×C4#12311yescharacteristic
212C3×Dic3—22no—
213C2×#41—31no—
214#131—182no—
215#131—182no—
216C2×M16—31no—
217C2×M16—31no—
218C2×M16—91no—
219C2×M16—91no—
220C2×M16—182no—
221C2×M16D3211yescharacteristic
222C22×C8—31no—
223#108—182no—
224#108—182no—
225#101—32no—
226#100—32no—
227C22⋊C8—182no—
228C23×C3—21no—
229C23×C3—32no—
230C23×C3C2×Dic611yescharacteristic
231C23×C3D3×Q811yescharacteristic
232C22×D3C4⋊Dic312yes—
233C3×Q8—61no—
234C3×Q8—61no—
235C3×D4—62no—
236C3×D4—62no—
237C3×D4—61no—
238C3×D4—61no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—32no—
246C2×C3×C4—62no—
247C2×C3×C4—62no—
248C2×C3×C4C2×C4×D311yescharacteristic
249C2×C3×C4C2×D1211yescharacteristic
250C2×C3×C4C2×D1211yescharacteristic
251C2×C3×C4#23511yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4#23711yescharacteristic
257C2×C3×C4#23711yescharacteristic
258C2×C3×C4#23711yescharacteristic
259C2×C3×C4C22×Dic311yescharacteristic
260#67—22no—
261#67—22no—
262C2×Dic3C4⋊Dic312yes—
263D12—21no—
264D12—21no—
265C4×D3—22no—
266C4×D3—22no—
267Dic6—21no—
268Dic6—21no—
269C3×C8—24no—
270C3×C8—22no—
271C3×C8—22no—
272C3×C8—62no—
273C3×C8—62no—
274C3×C8—121no—
275C3⋊C8—22no—
276C3⋊C8—22no—
277C3⋊C8—41no—
278C3⋊C8—62no—
279C3⋊C8—62no—
280C3⋊C8—122no—
281C3⋊C8—122no—
282C3⋊C8—121no—
283C3⋊C8—121no—
284C2×C32—21no—
285C2×C32—21no—
286C2×C32—21no—
287C2×C32#38511yescharacteristic
288C3×D3—42no—
289#41—61no—
290#41—61no—
291#41—61no—
292#41—61no—
293C2×Q8—31no—
294C2×D4—32no—
295C2×D4—31no—
296C22×C4—32no—
297C22×C4C2×D3211yescharacteristic
298M16—21no—
299M16—32no—
300M16—32no—
301M16—61no—
302M16—61no—
303M16—92no—
304M16—184no—
305M16—181no—
306M16—181no—
307M16—181no—
308M16D3×Dic312yes—
309C2×C8—21no—
310C2×C8—61no—
311C2×C8—61no—
312C2×C8—61no—
313C2×C8—61no—
314C2×C8—61no—
315C2×C8—184no—
316C2×C8—181no—
317C2×C8—181no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3—62no—
324C22×C3—81no—
325C22×C3—122no—
326C22×C3#87811yescharacteristic
327C22×C3#87811yescharacteristic
328C22×C3D3×C4⋊C411yescharacteristic
329C22×C3#89611yescharacteristic
330C22×C3#89711yescharacteristic
331C22×C3C2×C4⋊Dic311yescharacteristic
332C2×D3—22no—
333C2×D3—42no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—62no—
339C3×C4C4×D1211yescharacteristic
340C3×C4#67⋊C411yescharacteristic
341C3×C4#88211yescharacteristic
342C3×C4#88211yescharacteristic
343C3×C4#88311yescharacteristic
344C3×C4#88611yescharacteristic
345C3×C4D4×Dic311yescharacteristic
346C3×C4D4×Dic311yescharacteristic
347Dic3—22no—
348C32#185811yescharacteristic, complemented, Sylow
349C23—32no—
350C23D3×Dic611yescharacteristic
351Q8—61no—
352Q8—61no—
353D4—62no—
354D4—62no—
355D4—61no—
356D4—61no—
357C2×C4—32no—
358C2×C4—62no—
359C2×C4—62no—
360C2×C4#379511yescharacteristic
361C2×C4D3×D1211yescharacteristic
362C2×C4D3×D1211yescharacteristic
363C2×C4C2×D3×Dic311yescharacteristic
364C2×C4#380511yescharacteristic
365C2×C4#381111yescharacteristic
366C8—22no—
367C8—62no—
368C8—62no—
369C8—121no—
370C8—182no—
371C8—361no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—41no—
380C2×C3—41no—
381C2×C3—41no—
382C2×C3—122no—
383C2×C3#466811yescharacteristic
384C2×C3#495011yescharacteristic
385D3—42no—
386C22—41no—
387C22—62no—
388C22—122no—
389C22D3×C4⋊Dic311yescharacteristic
390C22#6389311yescharacteristic
391C22#6389611yescharacteristic
392C4—62no—
393C4#6389111yescharacteristic
394C4Dic3×D1211yescharacteristic
395C4#6392311yescharacteristic
396C4#67⋊Dic311yescharacteristic
397C3—21no—
398C3#6894511yescharacteristic, complemented
399C3#7013511yescharacteristic, complemented
400C2—21no—
401C2—21no—
402C2—21no—
403C2—122no—
404C2#1059137911yescharacteristic
subgroupG/H
centerC4#63923
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#385
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1858
LCSG ▷ C2×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. #10592824C2semidirect
4. #10591141C2semidirect
6. C3×#4558C2semidirect
7. #10589166C2semidirect
38. #4558D3semidirect
348. C32#1858semidirect
398. C3#68945semidirect
399. C3#70135semidirect

Maximal subgroups

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

subgroupindex
#105947762
#105928242
C3×#51322
#105911412
#105910702
C3×#45582
#105891662
#701353
#689453