Finite Group Databasebeta

← C2×#22611819 #33239414

Subgroups — C2×#22611819 #33239414

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×#17989027C211yesmaximal, characteristic
2C2×#17988709C211yesmaximal, characteristic
3C2×#17988693C211yesmaximal, characteristic, complemented
4#22611819C218yesmaximal, direct product factor
5C2×#17988409C211yesmaximal, characteristic, complemented
6C2×#17988404C211yesmaximal, characteristic, complemented
7C2×#17988364C211yesmaximal, characteristic, complemented
8C2×#360×C73C211yesmaximal, characteristic
9C22×Dic292C2211yescharacteristic
10C2×#14556598—21no—
11C2×#14556556—21no—
12#17989027C414yescomplemented
13#17989027C2214yes—
14C2×#14556537C412yescomplemented
15C2×#14556535C412yescomplemented
16C2×#14556531C2211yescharacteristic
17#17988709—22no—
18#17988709C2214yes—
19#17988693—22no—
20#17988693C2214yescomplemented
21C2×#14556527C2211yescharacteristic
22C2×#14556518—21no—
23C2×#14556514—21no—
24C2×#14556501C2211yescharacteristic
25#17988409C2214yescomplemented
26#17988404C2214yescomplemented
27#17988364C2214yescomplemented
28C2×#135×C73C2211yescharacteristic
29C2×M32×C73C2211yescharacteristic
30C2×#106×C73C2211yescharacteristic
31#360×C73C2214yes—
32C22×Dic146—21no—
33C2×Dic292—21no—
34C2×Dic292—21no—
35C2×Dic292—21no—
36C2×Dic292C2×C412yes—
37C2×Dic292C2×C412yes—
38C2×Dic292C2312yes—
39#14556598—24no—
40#14556598—42no—
41C2×#11924012—21no—
42C2×#11924012—41no—
43C22×#10596831—41no—
44C22×#10596831D411yescharacteristic
45#14556556—24no—
46#14556556—42no—
47C2×#11924007—41no—
48C2×C4×Dic73—41no—
49C2×C4×Dic73D411yescharacteristic
50#14556537C2×C418yescomplemented
51#14556535C2×C418yescomplemented
52#14556531C2×C412yes—
53#14556531C2312yes—
54C2×#11924003C2×C412yes—
55#14556527—21no—
56#14556527C2312yes—
57#14556518—24no—
58#14556514—24no—
59#14556501D412yes—
60#14556501C2312yes—
61C2×#41×C73—21no—
62#135×C73—21no—
63#135×C73—21no—
64#135×C73C2×C412yes—
65#135×C73C2312yes—
66C2×Q16×C73C2×C411yescharacteristic
67C2×SD16×C73—21no—
68C2×D8×C73C2×C411yescharacteristic
69C22×C8×C73C2311yescharacteristic
70C2×C4⋊C4×C73—21no—
71M32×C73—21no—
72M32×C73C2312yes—
73C2×C16×C73—21no—
74#106×C73—21no—
75#106×C73C2312yes—
76C2×Dic146—22no—
77C2×Dic146—22no—
78C2×Dic146—22no—
79C2×Dic146—41no—
80C2×Dic146—41no—
81C2×Dic146—41no—
82C22×Dic73—21no—
83C22×Dic73—41no—
84Dic292—22no—
85Dic292—22no—
86Dic292—22no—
87Dic292C22×C414yes—
88#11924012—22no—
89#11924012—44no—
90#11924012—41no—
91C2×#10596831—21no—
92C2×#10596831—21no—
93C2×#10596831—44no—
94C2×#10596831—41no—
95C2×#10596831C2×D412yes—
96#11924007—44no—
97C4×Dic73—21no—
98C4×Dic73—44no—
99C4×Dic73C2×D412yes—
100#11924003C22×C414yes—
101#41×C73—22no—
102#41×C73—22no—
103#41×C73—41no—
104#41×C73—41no—
105C2×Q8×C73—21no—
106C2×D4×C73—21no—
107C2×D4×C73—41no—
108C22×C4×C73—41no—
109C22×C4×C73—41no—
110C22×C4×C73C2×D411yescharacteristic
111Q16×C73—21no—
112Q16×C73C22×C412yes—
113SD16×C73—22no—
114SD16×C73—22no—
115D8×C73—21no—
116D8×C73C22×C412yes—
117C2×C8×C73C22×C411yescharacteristic
118C2×C8×C73C22×C411yescharacteristic
119C2×C8×C73C2×D411yescharacteristic
120C2×C8×C73#4111yescharacteristic
121C2×C8×C73#4111yescharacteristic
122C2×C8×C73C2411yescharacteristic
123C4⋊C4×C73—22no—
124C4⋊C4×C73—41no—
125C16×C73—22no—
126C23×C73—41no—
127C23×C73AGL(1,ℤ/8)11yescharacteristic
128Q8×C73—22no—
129Q8×C73—41no—
130D4×C73—22no—
131D4×C73—42no—
132D4×C73—42no—
133D4×C73—41no—
134C2×C4×C73—41no—
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
145C2×Dic73—22no—
146C2×Dic73—42no—
147C2×Dic73—42no—
148C2×Dic73—42no—
149C2×Dic73—42no—
150Dic146—24no—
151Dic146—42no—
152Dic146—42no—
153Dic146—42no—
154C8×C73C4×D411yescharacteristic
155C8×C73C4×D411yescharacteristic
156C8×C73C23×C411yescharacteristic
157C8×C73C2×#4111yescharacteristic
158#10596831—22no—
159#10596831—42no—
160C22×C73—22no—
161C22×C73—42no—
162C22×C73—82no—
163C22×C73#44211yescharacteristic
164C22×C73#44211yescharacteristic
165C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
166C4×C73—42no—
167C4×C73—82no—
168C4×C73#44211yescharacteristic
169C4×C73#44211yescharacteristic
170C4×C73C2×C4×D411yescharacteristic
171C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
172Dic73—42no—
173Dic73—44no—
174C2×#2180—731nomaximal, Sylow
175C2×C73—21no—
176C2×C73—21no—
177C2×C73—82no—
178C2×C73#218012yescomplemented
179C2×C73C2×#44211yescharacteristic
180C2×#510—731no—
181C2×#444—731no—
182C2×#441—731no—
183#2180—738no—
184C2×#365—731no—
185C2×#362—731no—
186C2×#360D7311yescharacteristic
187C2×#347—731no—
188C73C2×#218011yescharacteristic, complemented, Sylow
189C2×#135C2×D7311yescharacteristic
190C22×Q16—731no—
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×#108—731no—
204C2×#106C2×D7311yescharacteristic
205C2×#104—1461no—
206C2×#103—1461no—
207C2×#97—731no—
208#365—734no—
209#362—734no—
210#360C2×D7314yes—
211#347—734no—
212C2×#41—21no—
213C22×Q8—1461no—
214#135—21no—
215#135—21no—
216#135C4×D7312yes—
217#135C22×D7312yes—
218C2×Q16—732no—
219C2×Q16—732no—
220C2×Q16—732no—
221C2×Q16—1461no—
222C2×Q16—1461no—
223C2×Q16—1461no—
224C2×Q16C4×D7311yescharacteristic
225C2×SD16—21no—
226C2×D8C4×D7311yescharacteristic
227#131—2922no—
228#131—1464no—
229C2×M16—2921no—
230C2×M16—1461no—
231C22×C8—2921no—
232C22×C8—731no—
233C22×C8C22×D7311yescharacteristic
234C4×Q8—2922no—
235C4×Q8—1464no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—2921no—
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—732no—
249#108—1461no—
250#106—21no—
251#106C22×D7312yes—
252#104—1464no—
253#103—1464no—
254#97—732no—
255#97—732no—
256#41—22no—
257#41—22no—
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×Q8—2921no—
262C2×Q8—2921no—
263C2×Q8—2921no—
264C2×Q8—1462no—
265C2×Q8—1462no—
266C2×Q8—1462no—
267C2×D4—21no—
268C2×D4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—2921no—
272C22×C4—1461no—
273C22×C4D4×D7311yescharacteristic
274Q16—21no—
275Q16—734no—
276Q16—1462no—
277Q16—1462no—
278Q16—1462no—
279Q16C2×C4×D7312yes—
280SD16—22no—
281SD16—22no—
282D8—21no—
283D8C2×C4×D7312yes—
284M16—2921no—
285M16—2924no—
286M16—1462no—
287C2×C8—2921no—
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—22no—
299C4⋊C4—41no—
300C4⋊C4—2924no—
301C42—2924no—
302C42—732no—
303C42—1461no—
304C16—22no—
305C16—734no—
306C23—41no—
307C23#1455661511yescharacteristic
308Q8—22no—
309Q8—41no—
310Q8—2922no—
311Q8—2922no—
312Q8—2922no—
313Q8—1464no—
314D4—22no—
315D4—42no—
316D4—42no—
317D4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—82no—
323C2×C4—2922no—
324C2×C4—2922no—
325C2×C4—2922no—
326C2×C4—2922no—
327C2×C4—1462no—
328C2×C4#1455655111yescharacteristic
329C2×C4#1455655111yescharacteristic
330C2×C4#1455661511yescharacteristic
331C2×C4#1455661811yescharacteristic
332C2×C4#1455661811yescharacteristic
333C2×C4C2×D4×D7311yescharacteristic
334C8—2922no—
335C8—1462no—
336C8#1455655111yescharacteristic
337C8#1455655111yescharacteristic
338C8C22×C4×D7311yescharacteristic
339C8C2×#1192402711yescharacteristic
340C22—22no—
341C22—42no—
342C22—82no—
343C22#1798869611yescharacteristic
344C22#1798869611yescharacteristic
345C22C2×#1455661511yescharacteristic
346C4—42no—
347C4—82no—
348C4—2922no—
349C4—2924no—
350C4#1798869611yescharacteristic
351C4#1798869611yescharacteristic
352C4C2×#1455655111yescharacteristic
353C4C2×#1455661811yescharacteristic
354C2—21no—
355C2—21no—
356C2—82no—
357C2#2261181912yesdirect product factor
358C2C2×#1798869611yescharacteristic
subgroupG/H
centerC22#17988696
commutatorC8×C73C23×C4
FrattiniC2×C8C23×D73
FittingC2×#360×C73C2
socleC22×C73#442
prime radicalC2×#135×C73C22
cosocleC2×C8×C73C24
hypercenterC2×#360D73
hypocenterC73C2×#2180
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

Complements

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

NH ≅ G/Ntype
3. C2×#17988693C2semidirect
4. #22611819C2direct (N × H)
5. C2×#17988409C2semidirect
6. C2×#17988404C2semidirect
7. C2×#17988364C2semidirect
12. #17989027C4semidirect
14. C2×#14556537C4semidirect
15. C2×#14556535C4semidirect
20. #17988693C22semidirect
25. #17988409C22semidirect
26. #17988404C22semidirect
27. #17988364C22semidirect
50. #14556537C2×C4semidirect
51. #14556535C2×C4semidirect
178. C2×C73#2180semidirect
188. C73C2×#2180semidirect
357. C2#22611819direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179890272
C2×#179887092
C2×#179886932
#226118192
C2×#179884092
C2×#179884042
C2×#179883642
C2×#360×C732
C2×#218073