Finite Group Databasebeta

← C2×#10589113 #11796087

Subgroups — C2×#10589113 #11796087

Order 1152.

581 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64110C211yesmaximal, characteristic
2C2×C3×#812C211yesmaximal, characteristic, complemented
3C22×C3×C3⋊C16C211yesmaximal, characteristic, complemented
4#10589113C214yesmaximal, direct product factor
5C2×#4515—31nomaximal
6C2×#4508—31nomaximal
7C2×#3828C411yescharacteristic
8C22×C32×C8C2211yescharacteristic
9C2×#3748C411yescharacteristic
10#64110—21no—
11#64110—21no—
12#64110C412yes—
13#64110C2212yes—
14C2×#3743—21no—
15C2×C8×C3⋊D3—21no—
16C3×#812—21no—
17C3×#812C2212yescomplemented
18C2×C3×C3⋊C16—21no—
19C2×C3×C3⋊C16—21no—
20C2×C3×C3⋊C16—21no—
21C2×C3×C3⋊C16C2212yescomplemented
22C2×#901—31no—
23C2×#901—31no—
24C2×#901—61no—
25C2×C3×M32—31no—
26C22×C3×C16—31no—
27C2×#812D311yescharacteristic, complemented
28C22×C3⋊C16D311yescharacteristic, complemented
29#4515—34no—
30#4508—34no—
31C22×C32×C4C2×C411yescharacteristic
32C2×#638—21no—
33#3828—21no—
34#3828—21no—
35#3828C812yes—
36#3828C2×C412yes—
37C2×C4⋊(C3⋊D3)C811yescharacteristic
38C2×C4×C3⋊D3—21no—
39C2×#634C811yescharacteristic
40C2×C32×C8C2×C411yescharacteristic
41C2×C32×C8D411yescharacteristic
42C2×C32×C8D411yescharacteristic
43C2×C32×C8D411yescharacteristic
44C2×C32×C8D411yescharacteristic
45C2×C32×C8C2311yescharacteristic
46#3748—21no—
47#3748C2×C412yes—
48C2×C3⋊(C3⋊C8)—21no—
49#3743—22no—
50#3743—22no—
51C8×C3⋊D3—22no—
52C8×C3⋊D3—22no—
53C3×C3⋊C16—22no—
54C3×C3⋊C16—22no—
55C2×#350—91noSylow
56C2×#235—31no—
57C2×#235—31no—
58C2×#235—61no—
59C22×C3×C8—21no—
60C22×C3×C8C2×D311yescharacteristic
61C22×C3×C8C2×D311yescharacteristic
62C2×#208—31no—
63C2×#208—31no—
64C2×#208—61no—
65#901—32no—
66#901—32no—
67#901—32no—
68#901—32no—
69#901—62no—
70#901—62no—
71#901—62no—
72#901—62no—
73#901—61no—
74#901—61no—
75#901—61no—
76#901—61no—
77C2×ΓL(1,𝔽25)—62no—
78C2×ΓL(1,𝔽25)—61no—
79C2×ΓL(1,𝔽25)—61no—
80C2×D3×C8—62no—
81C2×D3×C8—61no—
82C2×D3×C8—61no—
83C3×M32—32no—
84C3×M32—61no—
85C2×C3×C16—32no—
86C2×C3×C16—61no—
87C2×C3×C16—61no—
88C2×C3×C16—61no—
89#812—21no—
90#812C2×D312yescomplemented
91C2×C3⋊C16—21no—
92C2×C3⋊C16—21no—
93C2×C3⋊C16—21no—
94C2×C3⋊C16C2×D312yescomplemented
95C23×C32M1611yescharacteristic
96C22×C3⋊D3—21no—
97C2×C32×C4C22⋊C411yescharacteristic
98C2×C32×C4C22⋊C411yescharacteristic
99C2×C32×C4C2×C811yescharacteristic
100C2×C32×C4C2×C811yescharacteristic
101C2×C32×C4M1611yescharacteristic
102C2×C32×C4C22×C411yescharacteristic
103#638—22no—
104#638—22no—
105C2×C3⋊Dic3—21no—
106C4⋊(C3⋊D3)—21no—
107C4⋊(C3⋊D3)C2×C812yes—
108C4×C3⋊D3—22no—
109C4×C3⋊D3—22no—
110#634—21no—
111#634C2×C812yes—
112C32×C8C22⋊C411yescharacteristic
113C32×C8C22⋊C411yescharacteristic
114C32×C8C2×D411yescharacteristic
115C32×C8C2×D411yescharacteristic
116C3⋊(C3⋊C8)—22no—
117C2×#131—91no—
118C2×M32—31no—
119C22×C16—31no—
120#350—94no—
121C22×C3×C4—21no—
122C22×C3×C4C4×D311yescharacteristic
123C22×C3×C4C4×D311yescharacteristic
124C2×#67—62no—
125C2×#67—61no—
126C2×#67—61no—
127#235—32no—
128#235—32no—
129#235—32no—
130#235—32no—
131#235—62no—
132#235—62no—
133#235—62no—
134#235—62no—
135#235—61no—
136#235—61no—
137#235—61no—
138#235—61no—
139C2×D12—31no—
140C2×D12—31no—
141C2×D12—61no—
142C2×C4×D3—62no—
143C2×C4×D3—61no—
144C2×C4×D3—61no—
145C2×Dic6—31no—
146C2×Dic6—31no—
147C2×Dic6—61no—
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—21no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8C4×D311yescharacteristic
155C2×C3×C8C4×D311yescharacteristic
156C2×C3×C8D1211yescharacteristic
157C2×C3×C8D1211yescharacteristic
158C2×C3×C8D1211yescharacteristic
159C2×C3×C8D1211yescharacteristic
160C2×C3×C8#6711yescharacteristic
161C2×C3×C8#6711yescharacteristic
162C2×C3×C8#6711yescharacteristic
163C2×C3×C8#6711yescharacteristic
164C2×C3×C8C22×D311yescharacteristic
165C2×C3×C8C22×D311yescharacteristic
166#208—32no—
167#208—32no—
168#208—62no—
169#208—62no—
170#208—61no—
171#208—61no—
172C2×C3⋊C8—62no—
173C2×C3⋊C8—61no—
174C2×C3⋊C8—61no—
175ΓL(1,𝔽25)—64no—
176ΓL(1,𝔽25)—64no—
177ΓL(1,𝔽25)—62no—
178ΓL(1,𝔽25)—62no—
179ΓL(1,𝔽25)—62no—
180ΓL(1,𝔽25)—62no—
181D3×C8—64no—
182D3×C8—64no—
183D3×C8—62no—
184D3×C8—62no—
185D3×C8—62no—
186D3×C8—62no—
187C3×C16—62no—
188C3×C16—62no—
189C3⋊C16—22no—
190C3⋊C16—22no—
191C22×C32—22no—
192C22×C32C22⋊C811yescharacteristic
193C22×C32C22⋊C811yescharacteristic
194C22×C32C2×M1611yescharacteristic
195C2×C3⋊D3—22no—
196C2×C3⋊D3—42no—
197C32×C4C22⋊C811yescharacteristic
198C32×C4C22⋊C811yescharacteristic
199C32×C4C2×C22⋊C411yescharacteristic
200C32×C4C22×C811yescharacteristic
201C3⋊Dic3—22no—
202C2×#41—91no—
203#131—92no—
204#131—92no—
205#131—181no—
206#131—181no—
207C2×M16—91no—
208C2×M16—181no—
209C22×C8—181no—
210C22×C8D3211yescharacteristic
211M32—32no—
212M32—61no—
213C2×C16—32no—
214C2×C16—61no—
215C2×C16—61no—
216C2×C16—61no—
217C23×C3—21no—
218C23×C3ΓL(1,𝔽25)11yescharacteristic
219C23×C3ΓL(1,𝔽25)11yescharacteristic
220C22×D3—62no—
221C22×D3—61no—
222C22×D3—61no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4D3×C811yescharacteristic
230C2×C3×C4D3×C811yescharacteristic
231C2×C3×C4D3×C811yescharacteristic
232C2×C3×C4D3×C811yescharacteristic
233C2×C3×C4ΓL(1,𝔽25)11yescharacteristic
234C2×C3×C4ΓL(1,𝔽25)11yescharacteristic
235C2×C3×C4(C2×D3)⋊C411yescharacteristic
236C2×C3×C4(C2×D3)⋊C411yescharacteristic
237C2×C3×C4(C2×D3)⋊C411yescharacteristic
238C2×C3×C4(C2×D3)⋊C411yescharacteristic
239C2×C3×C4C2×C4×D311yescharacteristic
240C2×C3×C4C2×C4×D311yescharacteristic
241#67—64no—
242#67—64no—
243#67—62no—
244#67—62no—
245#67—62no—
246#67—62no—
247C2×Dic3—62no—
248C2×Dic3—61no—
249C2×Dic3—61no—
250D12—32no—
251D12—32no—
252D12—62no—
253D12—62no—
254D12—61no—
255D12—61no—
256C4×D3—64no—
257C4×D3—64no—
258C4×D3—62no—
259C4×D3—62no—
260C4×D3—62no—
261C4×D3—62no—
262Dic6—32no—
263Dic6—32no—
264Dic6—62no—
265Dic6—62no—
266Dic6—61no—
267Dic6—61no—
268C3×C8—21no—
269C3×C8—21no—
270C3×C8—21no—
271C3×C8—21no—
272C3×C8(C2×D3)⋊C411yescharacteristic
273C3×C8(C2×D3)⋊C411yescharacteristic
274C3×C8(C2×D3)⋊C411yescharacteristic
275C3×C8(C2×D3)⋊C411yescharacteristic
276C3×C8C2×D1211yescharacteristic
277C3×C8C2×D1211yescharacteristic
278C3×C8C2×#6711yescharacteristic
279C3×C8C2×#6711yescharacteristic
280C3⋊C8—64no—
281C3⋊C8—62no—
282C3⋊C8—62no—
283C2×C32—21no—
284C2×C32—21no—
285C2×C32#35012yescomplemented
286C2×C32C2×C22⋊C811yescharacteristic
287C3⋊D3—42no—
288#41—92no—
289#41—92no—
290#41—181no—
291#41—181no—
292C2×Q8—91no—
293C2×D4—91no—
294C2×D4—181no—
295C22×C4—181no—
296C22×C4#62411yescharacteristic
297M16—92no—
298M16—181no—
299M16—182no—
300M16—182no—
301C2×C8—181no—
302C2×C8—182no—
303C2×C8—182no—
304C2×C8#62411yescharacteristic
305C2×C8#62611yescharacteristic
306C2×C8#62611yescharacteristic
307C2×C8#62611yescharacteristic
308C2×C8#62611yescharacteristic
309C2×C8C2×D3211yescharacteristic
310C16—62no—
311C16—62no—
312C22×C3—22no—
313C22×C3—22no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—42no—
318C22×C3(C2×D3)⋊C811yescharacteristic
319C22×C3(C2×D3)⋊C811yescharacteristic
320C22×C3(C2×D3)⋊C811yescharacteristic
321C22×C3(C2×D3)⋊C811yescharacteristic
322C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
323C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
324C2×D3—64no—
325C2×D3—62no—
326C2×D3—62no—
327C2×D3—124no—
328C2×D3—122no—
329C2×D3—122no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4(C2×D3)⋊C811yescharacteristic
335C3×C4(C2×D3)⋊C811yescharacteristic
336C3×C4(C2×D3)⋊C811yescharacteristic
337C3×C4(C2×D3)⋊C811yescharacteristic
338C3×C4C2×D3×C811yescharacteristic
339C3×C4C2×D3×C811yescharacteristic
340C3×C4C2×(C2×D3)⋊C411yescharacteristic
341C3×C4C2×(C2×D3)⋊C411yescharacteristic
342Dic3—64no—
343Dic3—62no—
344Dic3—62no—
345C32C2×#35011yescharacteristic, complemented, Sylow
346C23—181no—
347C23#371211yescharacteristic
348Q8—92no—
349Q8—181no—
350D4—92no—
351D4—182no—
352D4—182no—
353D4—181no—
354C2×C4—181no—
355C2×C4—182no—
356C2×C4—182no—
357C2×C4#371011yescharacteristic
358C2×C4#371011yescharacteristic
359C2×C4#371211yescharacteristic
360C2×C4#372211yescharacteristic
361C2×C4#372211yescharacteristic
362C2×C4C2×#62411yescharacteristic
363C8—182no—
364C8#372211yescharacteristic
365C8#372211yescharacteristic
366C8C2×#62611yescharacteristic
367C8C2×#62611yescharacteristic
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—22no—
374C2×C3—41no—
375C2×C3—41no—
376C2×C3#450812yescomplemented
377C2×C3#451512yescomplemented
378C2×C3C2×(C2×D3)⋊C811yescharacteristic
379C2×C3C2×(C2×D3)⋊C811yescharacteristic
380D3—124no—
381D3—122no—
382D3—122no—
383C22—22no—
384C22—182no—
385C22—362no—
386C22#6355711yescharacteristic
387C22#6355711yescharacteristic
388C22C2×#371211yescharacteristic
389C4—182no—
390C4#6355711yescharacteristic
391C4#6355711yescharacteristic
392C4C2×#371011yescharacteristic
393C4C2×#372211yescharacteristic
394C3—21no—
395C3C2×#450811yescharacteristic, complemented
396C3C2×#451511yescharacteristic, complemented
397C2—21no—
398C2—21no—
399C2—362no—
400C2#1058911312yesdirect product factor
401C2C2×#6355711yescharacteristic
subgroupG/H
centerC2×C8#626
commutatorC32×C4C22×C8
FrattiniC2×C8C2×D32
FittingC22×C32×C8C22
socleC22×C32C22⋊C8
prime radicalC2×#3828C4
cosocleC2×C32×C8C23
hypercenterC22×C8D32
hypocenterC32C2×#350
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#812C2semidirect
3. C22×C3×C3⋊C16C2semidirect
4. #10589113C2direct (N × H)
17. C3×#812C22semidirect
21. C2×C3×C3⋊C16C22semidirect
27. C2×#812D3semidirect
28. C22×C3⋊C16D3semidirect
90. #812C2×D3semidirect
94. C2×C3⋊C16C2×D3semidirect
285. C2×C32#350semidirect
345. C32C2×#350semidirect
376. C2×C3#4508semidirect
377. C2×C3#4515semidirect
395. C3C2×#4508semidirect
396. C3C2×#4515semidirect
400. C2#10589113direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641102
C2×C3×#8122
C22×C3×C3⋊C162
#105891132
C2×#45153
C2×#45083