Finite Group Databasebeta

← C2×#22611820 #33239415

Subgroups — C2×#22611820 #33239415

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×#17988710C211yesmaximal, characteristic
3#22611820C218yesmaximal, direct product factor
4C2×#17988409C211yesmaximal, characteristic, complemented
5C2×#17988403C211yesmaximal, characteristic, complemented
6C2×#17988396C211yesmaximal, characteristic
7C2×#17988365C211yesmaximal, characteristic, complemented
8C2×#441×C73C211yesmaximal, characteristic, complemented
9C2×#14556613C2211yescharacteristic
10C2×#14556597—21no—
11#17989028C414yescomplemented
12#17989028C2214yes—
13C2×#14556537C412yescomplemented
14C2×#14556534C412yescomplemented
15C2×#14556531C2211yescharacteristic
16C2×#14556531C2211yescharacteristic
17#17988710—22no—
18#17988710C2214yes—
19C2×#14556527C2211yescharacteristic
20C2×#14556519—21no—
21#17988409C2214yescomplemented
22#17988403C2214yescomplemented
23#17988396C2214yes—
24#17988365C2214yescomplemented
25C22×Q16×C73C2211yescharacteristic
26C2×C4×Q8×C73—21no—
27#441×C73—22no—
28#441×C73C2214yescomplemented
29C2×#106×C73C2211yescharacteristic
30C2×#103×C73—21no—
31C2×#97×C73C2211yescharacteristic
32C2×#11924028—21no—
33#14556613—21no—
34#14556613—21no—
35#14556613C2×C412yes—
36#14556613C2312yes—
37C2×Dic292C2×C411yescharacteristic
38C2×#11924017—21no—
39C2×D584C2×C411yescharacteristic
40#14556597—24no—
41#14556597—42no—
42C2×#11924012—21no—
43C2×#11924011—41no—
44C2×C8×D73—41no—
45#14556537C2×C418yescomplemented
46#14556534C2×C418yescomplemented
47#14556531—21no—
48#14556531C2×C412yes—
49#14556531C2312yes—
50#14556531C2312yes—
51C2×#11924003—21no—
52C2×#11924003C2×C412yes—
53#14556527—21no—
54#14556527C2312yes—
55#14556519—24no—
56C22×Q8×C73—21no—
57C2×Q16×C73—21no—
58C2×Q16×C73—21no—
59C2×Q16×C73—21no—
60C2×Q16×C73C2×C412yes—
61C2×Q16×C73C2×C412yes—
62C2×Q16×C73C2312yes—
63C22×C8×C73D411yescharacteristic
64C22×C8×C73C2311yescharacteristic
65C4×Q8×C73—24no—
66C4×Q8×C73—42no—
67C2×C4⋊C4×C73—21no—
68C2×C4⋊C4×C73—41no—
69C2×C42×C73—41no—
70C2×C42×C73D411yescharacteristic
71#106×C73—21no—
72#106×C73C2312yes—
73#103×C73—24no—
74#97×C73D412yes—
75#97×C73C2312yes—
76#11924028—22no—
77#11924028—22no—
78#11924028—41no—
79#11924028—41no—
80C2×Dic146—21no—
81C2×D292—21no—
82C2×C22⋊D73—41no—
83C2×C4×D73—41no—
84Dic292—21no—
85Dic292C22×C412yes—
86#11924017—22no—
87#11924017—22no—
88D584—21no—
89D584C22×C412yes—
90#11924012—22no—
91#11924012—41no—
92#11924011—44no—
93C2×#10596831—41no—
94C8×D73—44no—
95#11924003—22no—
96#11924003C22×C414yes—
97C2×Q8×C73—22no—
98C2×Q8×C73—22no—
99C2×Q8×C73—22no—
100C2×Q8×C73—41no—
101C2×Q8×C73—41no—
102C2×Q8×C73—41no—
103C22×C4×C73—21no—
104C22×C4×C73—41no—
105C22×C4×C73—41no—
106C22×C4×C73C2×D411yescharacteristic
107Q16×C73—22no—
108Q16×C73—22no—
109Q16×C73—22no—
110Q16×C73C22×C414yes—
111C2×C8×C73—21no—
112C2×C8×C73—21no—
113C2×C8×C73C22×C411yescharacteristic
114C2×C8×C73C22×C411yescharacteristic
115C2×C8×C73C2×D412yes—
116C2×C8×C73C2×D411yescharacteristic
117C2×C8×C73#4111yescharacteristic
118C2×C8×C73#4111yescharacteristic
119C2×C8×C73C2411yescharacteristic
120C4⋊C4×C73—22no—
121C4⋊C4×C73—44no—
122C4⋊C4×C73—41no—
123C42×C73—21no—
124C42×C73—44no—
125C42×C73C2×D412yes—
126C23×C73AGL(1,ℤ/8)11yescharacteristic
127C22×D73—41no—
128Q8×C73—24no—
129Q8×C73—42no—
130Q8×C73—42no—
131Q8×C73—42no—
132C2×C4×C73—22no—
133C2×C4×C73—42no—
134C2×C4×C73—42no—
135C2×C4×C73—42no—
136C2×C4×C73—42no—
137C2×C4×C73—42no—
138C2×C4×C73—82no—
139C2×C4×C73C4×D411yescharacteristic
140C2×C4×C73C4×D411yescharacteristic
141C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C73C22×D411yescharacteristic
145C22⋊D73—42no—
146C22⋊D73—42no—
147C2×Dic73—41no—
148D292—22no—
149D292—41no—
150C4×D73—42no—
151C4×D73—42no—
152Dic146—22no—
153Dic146—41no—
154C8×C73—22no—
155C8×C73C4×D411yescharacteristic
156C8×C73C4×D411yescharacteristic
157C8×C73C23×C411yescharacteristic
158C8×C73C2×#4111yescharacteristic
159#10596831—42no—
160C22×C73—22no—
161C22×C73#44211yescharacteristic
162C22×C73#44211yescharacteristic
163C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
164C2×D73—42no—
165C2×D73—82no—
166C4×C73—42no—
167C4×C73—44no—
168C4×C73—82no—
169C4×C73#44211yescharacteristic
170C4×C73#44211yescharacteristic
171C4×C73C2×C4×D411yescharacteristic
172C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
173Dic73—42no—
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×#441D7311yescharacteristic, complemented
183#2180—738no—
184C2×#365—731no—
185C2×#362—731no—
186C2×#360—731no—
187C2×#347—731no—
188C73C2×#218011yescharacteristic, complemented, Sylow
189C2×#135—731no—
190C22×Q16C2×D7311yescharacteristic
191C2×#131—1461no—
192C2×C4×Q8—21no—
193#510—734no—
194#510—734no—
195C2×Q32—732no—
196C2×SD32—732no—
197C2×M32—731no—
198C2×M32—731no—
199#444—734no—
200#444—1462no—
201#441—22no—
202#441C2×D7314yescomplemented
203C2×#108—731no—
204C2×#106C2×D7311yescharacteristic
205C2×#104—1461no—
206C2×#103—21no—
207C2×#97C2×D7311yescharacteristic
208#365—734no—
209#362—734no—
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—2921no—
230C2×M16—1461no—
231C22×C8—2921no—
232C22×C8C22⋊D7311yescharacteristic
233C22×C8C22×D7311yescharacteristic
234C4×Q8—24no—
235C4×Q8—42no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—41no—
238C2×C42—41no—
239C2×C42C22⋊D7311yescharacteristic
240Q32—738no—
241SD32—738no—
242M32—732no—
243M32—732no—
244M32—732no—
245M32—1461no—
246C2×C16—732no—
247C2×C16—1461no—
248#108—732no—
249#108—1461no—
250#106—21no—
251#106C22×D7312yes—
252#104—1464no—
253#103—24no—
254#97C22⋊D7312yes—
255#97C22×D7312yes—
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—21no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—2921no—
273C22×C4C2×C22⋊D7311yescharacteristic
274Q16—22no—
275Q16—22no—
276Q16—22no—
277Q16—732no—
278Q16—1461no—
279Q16C2×C4×D7314yes—
280SD16—1462no—
281SD16—1462no—
282D8—732no—
283D8—1461no—
284M16—2924no—
285M16—2921no—
286M16—1462no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—2924no—
290C2×C8—2921no—
291C2×C8C2×C4×D7311yescharacteristic
292C2×C8C2×C4×D7311yescharacteristic
293C2×C8C2×C22⋊D7312yes—
294C2×C8C2×C22⋊D7311yescharacteristic
295C2×C8#1192402811yescharacteristic
296C2×C8#1192402811yescharacteristic
297C2×C8C23×D7311yescharacteristic
298C4⋊C4—22no—
299C4⋊C4—44no—
300C4⋊C4—41no—
301C42—21no—
302C42—44no—
303C42C2×C22⋊D7312yes—
304C16—734no—
305C16—1462no—
306C23—2921no—
307C23#1455661711yescharacteristic
308Q8—24no—
309Q8—42no—
310Q8—42no—
311Q8—42no—
312Q8—2921no—
313Q8—1462no—
314D4—2922no—
315D4—2922no—
316D4—2921no—
317D4—1462no—
318C2×C4—22no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—82no—
325C2×C4—2921no—
326C2×C4—2922no—
327C2×C4—2922no—
328C2×C4C4×C22⋊D7311yescharacteristic
329C2×C4C4×C22⋊D7311yescharacteristic
330C2×C4#1455661611yescharacteristic
331C2×C4#1455661611yescharacteristic
332C2×C4#1455661711yescharacteristic
333C2×C4C22×C22⋊D7311yescharacteristic
334C8—22no—
335C8—2922no—
336C8C4×C22⋊D7311yescharacteristic
337C8C4×C22⋊D7311yescharacteristic
338C8C22×C4×D7311yescharacteristic
339C8C2×#1192402811yescharacteristic
340C22—22no—
341C22—2922no—
342C22—5842no—
343C22#1798869711yescharacteristic
344C22#1798869711yescharacteristic
345C22C2×#1455661711yescharacteristic
346C4—42no—
347C4—44no—
348C4—82no—
349C4—2922no—
350C4#1798869711yescharacteristic
351C4#1798869711yescharacteristic
352C4C2×C4×C22⋊D7311yescharacteristic
353C4C2×#1455661611yescharacteristic
354C2—21no—
355C2—21no—
356C2—5842no—
357C2#2261182012yesdirect product factor
358C2C2×#1798869711yescharacteristic
subgroupG/H
centerC22#17988697
commutatorC8×C73C23×C4
FrattiniC2×C8C23×D73
FittingC2×#441×C73C2
socleC22×C73#442
prime radicalC2×#14556613C22
cosocleC2×C8×C73C24
hypercenterC2×#441D73
hypocenterC73C2×#2180
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. #22611820C2direct (N × H)
4. C2×#17988409C2semidirect
5. C2×#17988403C2semidirect
7. C2×#17988365C2semidirect
8. C2×#441×C73C2semidirect
11. #17989028C4semidirect
13. C2×#14556537C4semidirect
14. C2×#14556534C4semidirect
21. #17988409C22semidirect
22. #17988403C22semidirect
24. #17988365C22semidirect
28. #441×C73C22semidirect
45. #14556537C2×C4semidirect
46. #14556534C2×C4semidirect
177. C2×C73#2180semidirect
182. C2×#441D73semidirect
188. C73C2×#2180semidirect
202. #441C2×D73semidirect
357. C2#22611820direct (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×#179887102
#226118202
C2×#179884092
C2×#179884032
C2×#179883962
C2×#179883652
C2×#441×C732
C2×#218073