Finite Group Databasebeta

← C2×#22611825 #33239420

Subgroups — C2×#22611825 #33239420

Order 18688.

646 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989028C211yesmaximal, characteristic
2C2×#17988708C211yesmaximal, characteristic
3C2×#17988694C211yesmaximal, characteristic, complemented
4#22611825C218yesmaximal, direct product factor
5C2×#17988411C211yesmaximal, characteristic, complemented
6C2×#17988398C211yesmaximal, characteristic
7C2×#17988364C211yesmaximal, characteristic, complemented
8C2×#362×C73C211yesmaximal, characteristic, complemented
9C2×#14556613C2211yescharacteristic
10C2×#14556599—21no—
11C2×Q8×Dic73—21no—
12#17989028C414yescomplemented
13#17989028C2214yes—
14C2×#14556537C412yescomplemented
15C2×#14556534C412yescomplemented
16C2×#14556531C2211yescharacteristic
17#17988708—22no—
18#17988708C2214yes—
19#17988694—22no—
20#17988694C2214yescomplemented
21C2×#14556523C2211yescharacteristic
22C2×#14556517—21no—
23C2×#14556515—21no—
24C2×#14556501C2211yescharacteristic
25#17988411C2214yescomplemented
26#17988398C2214yes—
27#17988364C2214yescomplemented
28C22×Q16×C73C2211yescharacteristic
29C2×M32×C73C2211yescharacteristic
30C2×#108×C73C2211yescharacteristic
31#362×C73C2214yescomplemented
32C2×#11924028—21no—
33#14556613—21no—
34#14556613—21no—
35#14556613C2×C412yes—
36#14556613C2312yes—
37C2×Dic292C2×C411yescharacteristic
38C2×#11924017—21no—
39C2×D584C2×C411yescharacteristic
40#14556599—24no—
41#14556599—42no—
42C2×#11924011—41no—
43C22×#10596831D411yescharacteristic
44C2×C8×D73—41no—
45Q8×Dic73—24no—
46Q8×Dic73—42no—
47C2×C4⋊Dic73—21no—
48C2×C4⋊Dic73—41no—
49C2×C4×Dic73—41no—
50C2×C4×Dic73D411yescharacteristic
51#14556537C2×C418yescomplemented
52#14556534C2×C418yescomplemented
53#14556531C2×C412yes—
54#14556531C2312yes—
55C2×#11924003C2×C412yes—
56#14556523—21no—
57#14556523C2312yes—
58#14556517—24no—
59#14556515—24no—
60#14556501D412yes—
61#14556501C2312yes—
62C22×Q8×C73—21no—
63C2×Q16×C73—21no—
64C2×Q16×C73—21no—
65C2×Q16×C73—21no—
66C2×Q16×C73C2×C412yes—
67C2×Q16×C73C2×C412yes—
68C2×Q16×C73C2312yes—
69C2×M16×C73—21no—
70C22×C8×C73C2311yescharacteristic
71M32×C73—21no—
72M32×C73C2312yes—
73C2×C16×C73—21no—
74#108×C73—21no—
75#108×C73C2312yes—
76#11924028—22no—
77#11924028—22no—
78#11924028—41no—
79#11924028—41no—
80C2×Dic146—21no—
81C2×D292—21no—
82C2×C22⋊D73—41no—
83C22×Dic73—21no—
84C22×Dic73—41no—
85C2×C4×D73—41no—
86Dic292—21no—
87Dic292C22×C412yes—
88#11924017—22no—
89#11924017—22no—
90D584—21no—
91D584C22×C412yes—
92#11924011—44no—
93C2×#10596831—21no—
94C2×#10596831—21no—
95C2×#10596831C2×D412yes—
96C8×D73—44no—
97C4⋊Dic73—22no—
98C4⋊Dic73—44no—
99C4⋊Dic73—41no—
100C4×Dic73—21no—
101C4×Dic73—44no—
102C4×Dic73C2×D412yes—
103#11924003C22×C414yes—
104C2×Q8×C73—22no—
105C2×Q8×C73—22no—
106C2×Q8×C73—22no—
107C2×Q8×C73—41no—
108C2×Q8×C73—41no—
109C2×Q8×C73—41no—
110C22×C4×C73—41no—
111C22×C4×C73C2×D411yescharacteristic
112Q16×C73—22no—
113Q16×C73—22no—
114Q16×C73—22no—
115Q16×C73C22×C414yes—
116M16×C73—22no—
117M16×C73—41no—
118C2×C8×C73—41no—
119C2×C8×C73C22×C411yescharacteristic
120C2×C8×C73C22×C411yescharacteristic
121C2×C8×C73C2×D411yescharacteristic
122C2×C8×C73#4111yescharacteristic
123C2×C8×C73#4111yescharacteristic
124C2×C8×C73C2411yescharacteristic
125C16×C73—22no—
126C23×C73AGL(1,ℤ/8)11yescharacteristic
127C22×D73—41no—
128Q8×C73—24no—
129Q8×C73—42no—
130Q8×C73—42no—
131Q8×C73—42no—
132C2×C4×C73—42no—
133C2×C4×C73—42no—
134C2×C4×C73—42no—
135C2×C4×C73C4×D411yescharacteristic
136C2×C4×C73C4×D411yescharacteristic
137C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C73C22×D411yescharacteristic
141C22⋊D73—42no—
142C22⋊D73—42no—
143C2×Dic73—22no—
144C2×Dic73—42no—
145C2×Dic73—41no—
146C2×Dic73—42no—
147C2×Dic73—82no—
148D292—22no—
149D292—41no—
150C4×D73—42no—
151C4×D73—42no—
152Dic146—22no—
153Dic146—41no—
154C8×C73—42no—
155C8×C73C4×D411yescharacteristic
156C8×C73C4×D411yescharacteristic
157C8×C73C23×C411yescharacteristic
158C8×C73C2×#4111yescharacteristic
159#10596831—22no—
160C22×C73—22no—
161C22×C73#44211yescharacteristic
162C22×C73#44211yescharacteristic
163C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
164C2×D73—42no—
165C2×D73—82no—
166C4×C73—44no—
167C4×C73#44211yescharacteristic
168C4×C73#44211yescharacteristic
169C4×C73C2×C4×D411yescharacteristic
170C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
171Dic73—42no—
172Dic73—42no—
173Dic73—82no—
174C2×#2180—731nomaximal, Sylow
175C2×C73—21no—
176C2×C73—21no—
177C2×C73#218012yescomplemented
178C2×C73C2×#44211yescharacteristic
179D73—82no—
180C2×#510—731no—
181C2×#444—731no—
182C2×#441—731no—
183#2180—738no—
184C2×#365—731no—
185C2×#362D7311yescharacteristic, complemented
186C2×#360—731no—
187C2×#347—731no—
188C73C2×#218011yescharacteristic, complemented, Sylow
189C2×#135—731no—
190C22×Q16C2×D7311yescharacteristic
191C2×#131—1461no—
192C2×C4×Q8—1461no—
193#510—734no—
194#510—734no—
195C2×Q32—732no—
196C2×SD32—732no—
197C2×M32—731no—
198C2×M32C2×D7311yescharacteristic
199#444—734no—
200#444—1462no—
201#441—734no—
202#441—1462no—
203C2×#108C2×D7311yescharacteristic
204C2×#106—731no—
205C2×#104—1461no—
206C2×#103—1461no—
207C2×#97—731no—
208#365—734no—
209#362C2×D7314yescomplemented
210#360—734no—
211#347—734no—
212C2×#41—1461no—
213C22×Q8—21no—
214#135—732no—
215#135—732no—
216#135—1461no—
217#135—1461no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16—731no—
222C2×Q16C4×D7312yes—
223C2×Q16C4×D7312yes—
224C2×Q16C22×D7312yes—
225C2×SD16—1461no—
226C2×D8—731no—
227#131—2922no—
228#131—1464no—
229C2×M16—21no—
230C2×M16—2921no—
231C22×C8—2921no—
232C22×C8—731no—
233C22×C8C22×D7311yescharacteristic
234C4×Q8—2922no—
235C4×Q8—1464no—
236C2×C4⋊C4—2921no—
237C2×C4⋊C4—1461no—
238C2×C42—2921no—
239C2×C42—731no—
240Q32—738no—
241SD32—738no—
242M32—21no—
243M32—732no—
244M32—732no—
245M32C22×D7312yes—
246C2×C16—21no—
247C2×C16—732no—
248#108—21no—
249#108C22×D7312yes—
250#106—732no—
251#106—1461no—
252#104—1464no—
253#103—1464no—
254#97—732no—
255#97—732no—
256#41—2921no—
257#41—2921no—
258#41—1462no—
259#41—1462no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—1461no—
267C2×D4—2921no—
268C2×D4—1461no—
269C22×C4—41no—
270C22×C4—2921no—
271C22×C4—2921no—
272C22×C4—1461no—
273C22×C4D4×D7311yescharacteristic
274Q16—22no—
275Q16—22no—
276Q16—22no—
277Q16—732no—
278Q16—1461no—
279Q16C2×C4×D7314yes—
280SD16—1462no—
281SD16—1462no—
282D8—732no—
283D8—1461no—
284M16—22no—
285M16—41no—
286M16—2924no—
287C2×C8—41no—
288C2×C8—2924no—
289C2×C8—732no—
290C2×C8—1461no—
291C2×C8—1461no—
292C2×C8C2×C4×D7311yescharacteristic
293C2×C8C2×C4×D7311yescharacteristic
294C2×C8D4×D7311yescharacteristic
295C2×C8#1192402711yescharacteristic
296C2×C8#1192402711yescharacteristic
297C2×C8C23×D7311yescharacteristic
298C4⋊C4—2924no—
299C4⋊C4—2921no—
300C4⋊C4—1462no—
301C42—2924no—
302C42—732no—
303C42—1461no—
304C16—22no—
305C16—734no—
306C23—2921no—
307C23#1455661811yescharacteristic
308Q8—24no—
309Q8—42no—
310Q8—42no—
311Q8—42no—
312Q8—2921no—
313Q8—1462no—
314D4—2922no—
315D4—2922no—
316D4—2921no—
317D4—1462no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—2922no—
322C2×C4—2921no—
323C2×C4—2922no—
324C2×C4—2922no—
325C2×C4—2922no—
326C2×C4—5842no—
327C2×C4—1462no—
328C2×C4#1455655111yescharacteristic
329C2×C4#1455655111yescharacteristic
330C2×C4#1455661511yescharacteristic
331C2×C4#1455661511yescharacteristic
332C2×C4#1455661811yescharacteristic
333C2×C4C2×D4×D7311yescharacteristic
334C8—42no—
335C8—1462no—
336C8#1455655111yescharacteristic
337C8#1455655111yescharacteristic
338C8C22×C4×D7311yescharacteristic
339C8C2×#1192402711yescharacteristic
340C22—22no—
341C22—2922no—
342C22—5842no—
343C22#1798869611yescharacteristic
344C22#1798869611yescharacteristic
345C22C2×#1455661811yescharacteristic
346C4—44no—
347C4—2922no—
348C4—2922no—
349C4—5842no—
350C4#1798869611yescharacteristic
351C4#1798869611yescharacteristic
352C4C2×#1455655111yescharacteristic
353C4C2×#1455661511yescharacteristic
354C2—21no—
355C2—21no—
356C2—5842no—
357C2#2261182512yesdirect product factor
358C2C2×#1798869611yescharacteristic
subgroupG/H
centerC22#17988696
commutatorC8×C73C23×C4
FrattiniC2×C8C23×D73
FittingC2×#362×C73C2
socleC22×C73#442
prime radicalC2×#14556613C22
cosocleC2×C8×C73C24
hypercenterC2×#362D73
hypocenterC73C2×#2180
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
3. C2×#17988694C2semidirect
4. #22611825C2direct (N × H)
5. C2×#17988411C2semidirect
7. C2×#17988364C2semidirect
8. C2×#362×C73C2semidirect
12. #17989028C4semidirect
14. C2×#14556537C4semidirect
15. C2×#14556534C4semidirect
20. #17988694C22semidirect
25. #17988411C22semidirect
27. #17988364C22semidirect
31. #362×C73C22semidirect
51. #14556537C2×C4semidirect
52. #14556534C2×C4semidirect
177. C2×C73#2180semidirect
185. C2×#362D73semidirect
188. C73C2×#2180semidirect
209. #362C2×D73semidirect
357. C2#22611825direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179890282
C2×#179887082
C2×#179886942
#226118252
C2×#179884112
C2×#179883982
C2×#179883642
C2×#362×C732
C2×#218073