Finite Group Databasebeta

← C2×#22626337 #34030287

Subgroups — C2×#22626337 #34030287

Order 18688.

646 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989634C211yesmaximal, characteristic
2C2×#17989627C211yesmaximal, characteristic, complemented
3#22626337C218yesmaximal, direct product factor
4C2×#17989511C211yesmaximal, characteristic, complemented
5C2×#17989506C211yesmaximal, characteristic, complemented
6C2×#17989503C211yesmaximal, characteristic
7C2×#17989478C211yesmaximal, characteristic, complemented
8C2×#17989026C211yesmaximal, characteristic
9C2×#14556678—21no—
10C2×Q8×#64408—21no—
11C2×#14556666C2211yescharacteristic
12#17989634—22no—
13#17989634C2214yes—
14#17989627—22no—
15#17989627C2214yescomplemented
16C2×#14556661C2211yescharacteristic
17C2×#14556659C2211yescharacteristic
18C2×#14556655—21no—
19C2×#14556654—21no—
20C2×#14556645C2211yescharacteristic
21#17989511C2214yescomplemented
22#17989506C2214yescomplemented
23#17989503C2214yes—
24#17989478C2214yescomplemented
25C2×#14556610C2211yescharacteristic
26C2×Q16×D73C2211yescharacteristic
27#17989026C414yescomplemented
28#17989026C2214yes—
29C2×Dic584C411yescharacteristic, complemented
30C2×#14556537C411yescharacteristic, complemented
31C2×#14556535C411yescharacteristic, complemented
32C2×#14556530C2211yescharacteristic
33C2×SD32×C73C411yescharacteristic, complemented
34#14556678—24no—
35#14556678—42no—
36C2×#11924038—21no—
37C2×#11924037—41no—
38C2×#11924036D411yescharacteristic
39C22×#10596833—41no—
40Q8×#64408—24no—
41Q8×#64408—42no—
42C2×C4⋊#64408—21no—
43C2×C4⋊#64408—41no—
44C2×C4×#64408—41no—
45C2×C4×#64408D411yescharacteristic
46#14556666—21no—
47#14556666C2312yes—
48C2×#11924031—21no—
49#14556661—21no—
50#14556661C2312yes—
51#14556659—21no—
52#14556659C2312yes—
53#14556655—24no—
54#14556654—24no—
55#14556645D412yes—
56#14556645C2312yes—
57C2×#11924027—21no—
58C2×Q8×D73—21no—
59#14556610—21no—
60#14556610—21no—
61#14556610C2×C412yes—
62#14556610C2312yes—
63C2×Dic292C2×C411yescharacteristic
64C2×Dic292C2×C411yescharacteristic
65C2×#11924018—21no—
66Q16×D73—21no—
67Q16×D73—21no—
68Q16×D73C2×C412yes—
69Q16×D73C2312yes—
70C2×#11924016—21no—
71C2×C8×D73C2311yescharacteristic
72Dic584C2×C414yescomplemented
73#14556537C2×C414yescomplemented
74#14556535C2×C414yescomplemented
75#14556530C2×C412yes—
76#14556530C2312yes—
77C2×#11924003C2×C411yescharacteristic
78C2×Q16×C73C2×C411yescharacteristic
79C2×D8×C73C2×C411yescharacteristic
80SD32×C73C2×C414yescomplemented
81C2×C16×C73C2×C411yescharacteristic
82C22×#64408—21no—
83C22×#64408—41no—
84#11924038—22no—
85#11924038—41no—
86#11924037—44no—
87#11924036—21no—
88#11924036C2×D412yes—
89C2×#10596833—21no—
90C2×#10596833—44no—
91C2×#10596833—41no—
92C4⋊#64408—22no—
93C4⋊#64408—44no—
94C4⋊#64408—41no—
95C4×#64408—21no—
96C4×#64408—44no—
97C4×#64408C2×D412yes—
98#11924031—22no—
99#11924027—22no—
100#11924027—22no—
101#11924027—41no—
102#11924027—41no—
103C2×Dic146—21no—
104C2×Dic146—21no—
105C2×Dic146—41no—
106Q8×D73—22no—
107Q8×D73—22no—
108Q8×D73—41no—
109Q8×D73—41no—
110C2×C22⋊D73—41no—
111C22×Dic73—41no—
112C2×C4×D73—41no—
113C2×C4×D73C2×D411yescharacteristic
114Dic292—21no—
115Dic292—21no—
116Dic292C22×C412yes—
117Dic292C22×C412yes—
118#11924018—22no—
119#11924018—22no—
120#11924016—22no—
121#11924016—22no—
122C2×#10596831#4111yescharacteristic
123C8×D73C22×C411yescharacteristic
124C8×D73C2×D411yescharacteristic
125C8×D73#4111yescharacteristic
126C8×D73C2411yescharacteristic
127#11924003C22×C412yes—
128C2×Q8×C73—21no—
129C2×D4×C73—21no—
130Q16×C73—21no—
131Q16×C73C22×C412yes—
132D8×C73—21no—
133D8×C73C22×C412yes—
134C2×C8×C73C22×C411yescharacteristic
135C16×C73C22×C412yes—
136C23×C73—41no—
137C22×D73AGL(1,ℤ/8)11yescharacteristic
138C2×#64408—22no—
139C2×#64408—42no—
140C2×#64408—42no—
141C2×#64408—82no—
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—41no—
152C2×Dic73—42no—
153C2×Dic73—42no—
154C2×Dic73AGL(1,ℤ/8)11yescharacteristic
155C4×D73—42no—
156C4×D73—42no—
157C4×D73C4×D411yescharacteristic
158C4×D73AGL(1,ℤ/8)11yescharacteristic
159C4×D73AGL(1,ℤ/8)11yescharacteristic
160C4×D73C22×D411yescharacteristic
161Dic146—22no—
162Dic146—22no—
163Dic146—41no—
164Dic146—41no—
165Dic146—42no—
166Dic146—42no—
167#10596833—22no—
168#10596833—42no—
169C8×C73C4×D411yescharacteristic
170C8×C73C23×C411yescharacteristic
171#10596831C4×D411yescharacteristic
172#10596831C2×#4111yescharacteristic
173C22×C73—42no—
174C22×C73—82no—
175C22×C73#44211yescharacteristic
176C2×D73—22no—
177C2×D73#44211yescharacteristic
178C2×D73C2×AGL(1,ℤ/8)11yescharacteristic
179#64408—42no—
180#64408—82no—
181C4×C73—42no—
182C4×C73#44211yescharacteristic
183C4×C73C2×C4×D411yescharacteristic
184Dic73—42no—
185Dic73—42no—
186Dic73#44211yescharacteristic
187Dic73C2×AGL(1,ℤ/8)11yescharacteristic
188C2×#2180—731nomaximal, Sylow
189C2×C73—82no—
190C2×C73#218012yescomplemented
191C2×C73C2×#44211yescharacteristic
192D73—21no—
193D73—21no—
194C2×#510—731no—
195C2×#444—731no—
196C2×#441—731no—
197#2180—738no—
198C2×#365—731no—
199C2×#362—731no—
200C2×#360—731no—
201C2×#347—731no—
202C73C2×#218011yescharacteristic, complemented, Sylow
203C2×#135—731no—
204C22×Q16—731no—
205C2×#131—1461no—
206C2×C4×Q8—1461no—
207#510—734no—
208#510—734no—
209C2×Q32—731no—
210C2×Q32—731no—
211C2×SD32—731no—
212C2×SD32#6440811yescharacteristic, complemented
213C2×M32—731no—
214C2×M32—731no—
215#444—734no—
216#444—1462no—
217#441—734no—
218#441—1462no—
219C2×#108—731no—
220C2×#106—731no—
221C2×#104—1461no—
222C2×#103—1461no—
223C2×#97—731no—
224#365—734no—
225#362—734no—
226#360—734no—
227#347—734no—
228C2×#41—1461no—
229C22×Q8—1461no—
230#135—732no—
231#135—732no—
232#135—1461no—
233#135—1461no—
234C2×Q16—732no—
235C2×Q16—732no—
236C2×Q16—731no—
237C2×Q16—731no—
238C2×Q16—1461no—
239C2×Q16—1461no—
240C2×Q16—1461no—
241C2×Q16C2×#6440811yescharacteristic
242C2×SD16—1461no—
243C2×D8C2×#6440811yescharacteristic
244#131—2922no—
245#131—1464no—
246C2×M16—2921no—
247C2×M16—1461no—
248C22×C8—2921no—
249C22×C8—731no—
250C22×C8—731no—
251C4×Q8—2922no—
252C4×Q8—1464no—
253C2×C4⋊C4—2921no—
254C2×C4⋊C4—1461no—
255C2×C42—2921no—
256C2×C42—731no—
257Q32—734no—
258Q32—734no—
259SD32—734no—
260SD32C2×#6440814yescomplemented
261M32—732no—
262M32—732no—
263M32—732no—
264M32—1461no—
265C2×C16—731no—
266C2×C16—1461no—
267C2×C16C2×#6440811yescharacteristic
268#108—732no—
269#108—1461no—
270#106—732no—
271#106—1461no—
272#104—1464no—
273#103—1464no—
274#97—732no—
275#97—732no—
276#41—2921no—
277#41—2921no—
278#41—1462no—
279#41—1462no—
280C2×Q8—21no—
281C2×Q8—2921no—
282C2×Q8—2921no—
283C2×Q8—2921no—
284C2×Q8—1462no—
285C2×Q8—1462no—
286C2×Q8—1461no—
287C2×Q8—1461no—
288C2×D4—21no—
289C2×D4—2921no—
290C22×C4—2921no—
291C22×C4—2921no—
292C22×C4—2921no—
293C22×C4—731no—
294C22×C4—1461no—
295Q16—21no—
296Q16—732no—
297Q16—732no—
298Q16—1462no—
299Q16—1462no—
300Q16—1461no—
301Q16—1461no—
302Q16C22×#6440812yes—
303SD16—1462no—
304SD16—1462no—
305D8—21no—
306D8C22×#6440812yes—
307M16—2921no—
308M16—2924no—
309M16—1462no—
310C2×C8—2921no—
311C2×C8—2924no—
312C2×C8—731no—
313C2×C8—731no—
314C2×C8—731no—
315C2×C8—731no—
316C2×C8—731no—
317C2×C8—732no—
318C2×C8—1461no—
319C2×C8—1461no—
320C2×C8C22×#6440811yescharacteristic
321C4⋊C4—2921no—
322C4⋊C4—2924no—
323C4⋊C4—1462no—
324C42—2924no—
325C42—732no—
326C42—1461no—
327C16—732no—
328C16—1462no—
329C16C22×#6440812yes—
330C23—41no—
331C23—731no—
332Q8—22no—
333Q8—41no—
334Q8—2922no—
335Q8—2922no—
336Q8—2921no—
337Q8—2921no—
338Q8—1462no—
339Q8—1462no—
340D4—22no—
341D4—41no—
342D4—2922no—
343D4—2922no—
344C2×C4—41no—
345C2×C4—2922no—
346C2×C4—2922no—
347C2×C4—2922no—
348C2×C4—2921no—
349C2×C4—2921no—
350C2×C4—2922no—
351C2×C4—2922no—
352C2×C4—2922no—
353C2×C4—5842no—
354C2×C4—731no—
355C2×C4—731no—
356C2×C4—731no—
357C2×C4—731no—
358C2×C4—731no—
359C2×C4—1462no—
360C2×C4D4×#6440811yescharacteristic
361C8—2922no—
362C8—731no—
363C8—731no—
364C8—1462no—
365C8D4×#6440811yescharacteristic
366C8C23×#6440811yescharacteristic
367C22—42no—
368C22—82no—
369C22—731no—
370C22—731no—
371C22—1462no—
372C22#1798962811yescharacteristic
373C4—42no—
374C4—2922no—
375C4—2922no—
376C4—2922no—
377C4—5842no—
378C4—731no—
379C4—731no—
380C4#1798962811yescharacteristic
381C4C2×D4×#6440811yescharacteristic
382C2—82no—
383C2—1461no—
384C2—1461no—
385C2#2262633712yesdirect product factor
386C2C2×#1798962811yescharacteristic
subgroupG/H
centerC22#17989628
commutatorC8×C73C23×C4
FrattiniC8C23×#64408
FittingC2×SD32×C73C4
socleC22×C73#442
prime radicalC2×#14556610C22
cosocleC8×D73C24
hypercenterC2×SD32#64408
hypocenterC73C2×#2180
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
2. C2×#17989627C2semidirect
3. #22626337C2direct (N × H)
4. C2×#17989511C2semidirect
5. C2×#17989506C2semidirect
7. C2×#17989478C2semidirect
15. #17989627C22semidirect
21. #17989511C22semidirect
22. #17989506C22semidirect
24. #17989478C22semidirect
27. #17989026C4semidirect
29. C2×Dic584C4semidirect
30. C2×#14556537C4semidirect
31. C2×#14556535C4semidirect
33. C2×SD32×C73C4semidirect
72. Dic584C2×C4semidirect
73. #14556537C2×C4semidirect
74. #14556535C2×C4semidirect
80. SD32×C73C2×C4semidirect
190. C2×C73#2180semidirect
202. C73C2×#2180semidirect
212. C2×SD32#64408semidirect
260. SD32C2×#64408semidirect
385. C2#22626337direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179896342
C2×#179896272
#226263372
C2×#179895112
C2×#179895062
C2×#179895032
C2×#179894782
C2×#179890262
C2×#218073