Finite Group Databasebeta

← C2×#22626331 #34030270

Subgroups — C2×#22626331 #34030270

Order 18688.

662 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989631C211yesmaximal, characteristic, complemented
2C2×#17989629C211yesmaximal, characteristic, complemented
3#22626331C218yesmaximal, direct product factor
4C2×#17989516C211yesmaximal, characteristic, complemented
5C2×#17989502C211yesmaximal, characteristic, complemented
6C2×#17989501C211yesmaximal, characteristic, complemented
7C2×C16×#64408C211yesmaximal, characteristic, complemented
8C2×#17989018C211yesmaximal, characteristic
9C2×#14556679—21no—
10C2×#14556678—21no—
11C2×#14556664C2211yescharacteristic
12#17989631—22no—
13#17989631C2214yescomplemented
14#17989629—22no—
15#17989629C2214yescomplemented
16C2×#14556662C2211yescharacteristic
17C2×#14556662C2211yescharacteristic
18C2×#14556656—21no—
19C2×#14556655—21no—
20C2×C8×#64408C2211yescharacteristic
21#17989516C2214yescomplemented
22#17989502C2214yescomplemented
23#17989501C2214yescomplemented
24C16×#64408C2214yescomplemented
25C2×#14556614C2211yescharacteristic
26C2×#14556610C2211yescharacteristic
27#17989018C414yescomplemented
28#17989018C2214yes—
29C2×#14556537C411yescharacteristic, complemented
30C2×#14556536C411yescharacteristic, complemented
31C2×#14556532C411yescharacteristic, complemented
32C2×C16×D73C2211yescharacteristic
33C2×SD32×C73C411yescharacteristic, complemented
34#14556679—24no—
35#14556679—42no—
36#14556678—24no—
37#14556678—42no—
38C2×#11924038—21no—
39C2×#11924038—21no—
40C2×#11924038—41no—
41C2×#11924037—41no—
42C2×#11924036—41no—
43C2×#11924036D411yescharacteristic
44C22×#10596833—41no—
45C2×C4×#64408D411yescharacteristic
46#14556664—21no—
47#14556664C2312yes—
48C2×#11924031—21no—
49#14556662—21no—
50#14556662—21no—
51#14556662C2312yes—
52#14556662C2312yes—
53#14556656—24no—
54#14556655—24no—
55C8×#64408D412yes—
56C8×#64408C2312yes—
57C2×#11924029—21no—
58C2×#11924027—21no—
59#14556614—21no—
60#14556614—21no—
61#14556614C2×C412yes—
62#14556614C2312yes—
63#14556610—21no—
64#14556610—21no—
65#14556610C2×C412yes—
66#14556610C2312yes—
67C2×Dic292C2×C411yescharacteristic
68C2×#11924016—21no—
69C2×#11924015—21no—
70C2×D584C2×C411yescharacteristic
71C2×C8×D73C2311yescharacteristic
72#14556537C2×C414yescomplemented
73#14556536C2×C414yescomplemented
74#14556532C2×C414yescomplemented
75C2×#11924003C2×C411yescharacteristic
76C16×D73C2×C412yes—
77C16×D73C2312yes—
78C2×Q16×C73C2×C411yescharacteristic
79C2×D8×C73C2×C411yescharacteristic
80SD32×C73C2×C414yescomplemented
81C2×C16×C73C2×C411yescharacteristic
82C22×#64408—21no—
83#11924038—22no—
84#11924038—22no—
85#11924038—41no—
86#11924038—41no—
87#11924038—44no—
88#11924037—44no—
89#11924036—44no—
90#11924036D812yes—
91#11924036C2×D412yes—
92C2×#10596833—41no—
93C2×#10596833—41no—
94C2×#10596833—44no—
95C2×#10596833D811yescharacteristic
96C2×#10596833D811yescharacteristic
97C4×#64408—21no—
98C4×#64408C2×D412yes—
99#11924031—22no—
100#11924029—22no—
101#11924029—22no—
102#11924029—41no—
103#11924029—41no—
104#11924027—22no—
105#11924027—22no—
106#11924027—41no—
107#11924027—41no—
108C2×Dic146—21no—
109C2×D292—21no—
110C2×D292—41no—
111C2×C22⋊D73—41no—
112C22×Dic73—41no—
113C2×C4×D73—41no—
114C2×C4×D73C2×D411yescharacteristic
115Dic292—21no—
116Dic292C22×C412yes—
117#11924016—22no—
118#11924016—22no—
119#11924015—22no—
120#11924015—22no—
121D584—21no—
122D584C22×C412yes—
123C2×#10596831#4111yescharacteristic
124C8×D73C22×C411yescharacteristic
125C8×D73C2×D411yescharacteristic
126C8×D73#4111yescharacteristic
127C8×D73C2411yescharacteristic
128#11924003C22×C412yes—
129C2×Q8×C73—21no—
130C2×D4×C73—21no—
131Q16×C73—21no—
132Q16×C73C22×C412yes—
133D8×C73—21no—
134D8×C73C22×C412yes—
135C2×C8×C73C22×C411yescharacteristic
136C16×C73C22×C412yes—
137C23×C73—41no—
138C22×D73—41no—
139C22×D73#13511yescharacteristic
140C2×#64408—24no—
141C2×#64408—22no—
142Q8×C73—22no—
143Q8×C73—41no—
144D4×C73—22no—
145D4×C73—41no—
146C2×C4×C73—41no—
147C2×C4×C73C4×D411yescharacteristic
148C22⋊D73—42no—
149C22⋊D73—42no—
150C2×Dic73—41no—
151C2×Dic73—42no—
152C2×Dic73—42no—
153C2×Dic73C2×D811yescharacteristic
154D292—22no—
155D292—42no—
156D292—42no—
157D292—41no—
158C4×D73—42no—
159C4×D73—42no—
160C4×D73C4×D411yescharacteristic
161C4×D73C2×D811yescharacteristic
162C4×D73#13511yescharacteristic
163C4×D73C22×D411yescharacteristic
164Dic146—22no—
165Dic146—41no—
166#10596833—42no—
167#10596833—42no—
168#10596833C2×D812yes—
169#10596833C2×D812yes—
170C8×C73C4×D411yescharacteristic
171C8×C73C23×C411yescharacteristic
172#10596831C4×D411yescharacteristic
173#10596831C2×#4111yescharacteristic
174C22×C73—42no—
175C22×C73—82no—
176C22×C73C4×D811yescharacteristic
177C2×D73—22no—
178C2×D73—42no—
179C2×D73—82no—
180C2×D73C4×D811yescharacteristic
181C2×D73C2×#13511yescharacteristic
182#64408—24no—
183C4×C73—42no—
184C4×C73C4×D811yescharacteristic
185C4×C73C2×C4×D411yescharacteristic
186Dic73—42no—
187Dic73C4×D811yescharacteristic
188Dic73C22×D811yescharacteristic
189C2×#2178—731nomaximal, Sylow
190C2×C73—82no—
191C2×C73#217812yescomplemented
192C2×C73C2×C4×D811yescharacteristic
193D73—21no—
194D73—21no—
195D73—82no—
196C2×#508—731no—
197C2×#443—731no—
198C2×#443—731no—
199#2178—738no—
200C2×#368—731no—
201C2×#359—731no—
202C2×#359—731no—
203C2×C4×C16—731no—
204C73C2×#217811yescharacteristic, complemented, Sylow
205C2×#135—731no—
206C2×#135—731no—
207C2×#131—1461no—
208C2×#131—1461no—
209#508—734no—
210#508—734no—
211C2×Q32—731no—
212C2×SD32—731no—
213C2×SD32#6440811yescharacteristic, complemented
214C2×D16—731no—
215C22×C16—731no—
216C22×C16—731no—
217#443—734no—
218#443—734no—
219#443—1462no—
220#443—1462no—
221C2×#108—731no—
222C2×#108—731no—
223C2×#104—1461no—
224C2×#104—1461no—
225C2×C4×C8—731no—
226#368—734no—
227#359—734no—
228#359—734no—
229C4×C16—734no—
230C2×#41—1461no—
231C2×#41—1461no—
232#135—732no—
233#135—732no—
234#135—732no—
235#135—732no—
236#135—1461no—
237#135—1461no—
238#135—1461no—
239#135—1461no—
240C2×Q16—731no—
241C2×Q16C2×#6440811yescharacteristic
242C2×SD16—1461no—
243C2×SD16—1461no—
244C2×D8—731no—
245C2×D8C2×#6440811yescharacteristic
246#131—2922no—
247#131—2922no—
248#131—1464no—
249#131—1464no—
250C2×M16—2921no—
251C2×M16—2921no—
252C2×M16—1461no—
253C2×M16—1461no—
254C22×C8—2921no—
255C22×C8—2921no—
256C22×C8—731no—
257C22×C8—731no—
258C2×C42—731no—
259Q32—734no—
260SD32—734no—
261SD32C2×#6440814yescomplemented
262D16—734no—
263C2×C16—731no—
264C2×C16—732no—
265C2×C16—732no—
266C2×C16—732no—
267C2×C16—1461no—
268C2×C16—1461no—
269C2×C16C2×#6440811yescharacteristic
270#108—732no—
271#108—732no—
272#108—1461no—
273#108—1461no—
274#104—1464no—
275#104—1464no—
276C4×C8—732no—
277C4×C8—732no—
278#41—2921no—
279#41—2921no—
280#41—2921no—
281#41—2921no—
282#41—1462no—
283#41—1462no—
284#41—1462no—
285#41—1462no—
286C2×Q8—21no—
287C2×Q8—1461no—
288C2×D4—21no—
289C2×D4—2921no—
290C2×D4—2921no—
291C2×D4—1461no—
292C22×C4—2921no—
293C22×C4—2921no—
294C22×C4—731no—
295C22×C4—1461no—
296Q16—21no—
297Q16—732no—
298Q16—1461no—
299Q16C22×#6440812yes—
300SD16—1462no—
301SD16—1462no—
302SD16—1462no—
303SD16—1462no—
304D8—21no—
305D8—732no—
306D8—1461no—
307D8C22×#6440812yes—
308M16—2921no—
309M16—2921no—
310M16—2924no—
311M16—2924no—
312M16—1462no—
313M16—1462no—
314C2×C8—2921no—
315C2×C8—2921no—
316C2×C8—2924no—
317C2×C8—2924no—
318C2×C8—731no—
319C2×C8—731no—
320C2×C8—732no—
321C2×C8—732no—
322C2×C8—731no—
323C2×C8—731no—
324C2×C8—731no—
325C2×C8—731no—
326C2×C8—731no—
327C2×C8C22×#6440811yescharacteristic
328C42—732no—
329C42—1461no—
330C16—732no—
331C16—1462no—
332C16C22×#6440812yes—
333C23—41no—
334C23—2921no—
335C23—731no—
336Q8—22no—
337Q8—41no—
338Q8—2921no—
339Q8—1462no—
340D4—22no—
341D4—41no—
342D4—2922no—
343D4—2922no—
344D4—2922no—
345D4—2922no—
346D4—2921no—
347D4—1462no—
348C2×C4—41no—
349C2×C4—2922no—
350C2×C4—2922no—
351C2×C4—2921no—
352C2×C4—2922no—
353C2×C4—2922no—
354C2×C4—731no—
355C2×C4—731no—
356C2×C4—731no—
357C2×C4—731no—
358C2×C4—731no—
359C2×C4—1462no—
360C2×C4—1464no—
361C2×C4D4×#6440811yescharacteristic
362C8—2922no—
363C8—2922no—
364C8—732no—
365C8—732no—
366C8—731no—
367C8—731no—
368C8D4×#6440811yescharacteristic
369C8C23×#6440811yescharacteristic
370C22—42no—
371C22—82no—
372C22—2922no—
373C22—5842no—
374C22—731no—
375C22—731no—
376C22—1462no—
377C22D8×#6440811yescharacteristic
378C4—42no—
379C4—2922no—
380C4—731no—
381C4—731no—
382C4—1464no—
383C4D8×#6440811yescharacteristic
384C4C2×D4×#6440811yescharacteristic
385C2—82no—
386C2—5842no—
387C2—1461no—
388C2—1461no—
389C2#2262633112yesdirect product factor
390C2C2×D8×#6440811yescharacteristic
subgroupG/H
centerC22D8×#64408
commutatorC8×C73C23×C4
FrattiniC8C23×#64408
FittingC2×SD32×C73C4
socleC22×C73C4×D8
prime radicalC2×#17989018C2
cosocleC8×D73C24
hypercenterC2×SD32#64408
hypocenterC73C2×#2178
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#17989631C2semidirect
2. C2×#17989629C2semidirect
3. #22626331C2direct (N × H)
4. C2×#17989516C2semidirect
5. C2×#17989502C2semidirect
6. C2×#17989501C2semidirect
7. C2×C16×#64408C2semidirect
13. #17989631C22semidirect
15. #17989629C22semidirect
21. #17989516C22semidirect
22. #17989502C22semidirect
23. #17989501C22semidirect
24. C16×#64408C22semidirect
27. #17989018C4semidirect
29. C2×#14556537C4semidirect
30. C2×#14556536C4semidirect
31. C2×#14556532C4semidirect
33. C2×SD32×C73C4semidirect
72. #14556537C2×C4semidirect
73. #14556536C2×C4semidirect
74. #14556532C2×C4semidirect
80. SD32×C73C2×C4semidirect
191. C2×C73#2178semidirect
204. C73C2×#2178semidirect
213. C2×SD32#64408semidirect
261. SD32C2×#64408semidirect
389. C2#22626331direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179896312
C2×#179896292
#226263312
C2×#179895162
C2×#179895022
C2×#179895012
C2×C16×#644082
C2×#179890182
C2×#217873