Finite Group Databasebeta

← C2×#22626327 #34030256

Subgroups — C2×#22626327 #34030256

Order 18688.

734 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×#64408C211yesmaximal, characteristic, complemented
2C2×D8×#64408C211yesmaximal, characteristic
3#22626327C218yesmaximal, direct product factor
4C2×#17989513C211yesmaximal, characteristic, complemented
5C2×#17989500C211yesmaximal, characteristic, complemented
6C2×#17989499C211yesmaximal, characteristic
7C2×#17989474C211yesmaximal, characteristic, complemented
8C2×SD32×D73C211yesmaximal, characteristic
9C2×Q8×#64408—21no—
10C2×D4×#64408—21no—
11C2×#14556664C2211yescharacteristic
12Q16×#64408—22no—
13Q16×#64408C2214yescomplemented
14D8×#64408—22no—
15D8×#64408C2214yes—
16C2×#14556660C2211yescharacteristic
17C2×#14556660C2211yescharacteristic
18C2×#14556654—21no—
19C2×#14556653—21no—
20C2×C8×#64408C2211yescharacteristic
21#17989513C2214yescomplemented
22#17989500C2214yescomplemented
23#17989499C2214yes—
24#17989474C2214yescomplemented
25C2×Q16×D73C2211yescharacteristic
26C2×D8×D73C2211yescharacteristic
27C2×#14556536C411yescharacteristic, complemented
28C2×#14556535C411yescharacteristic, complemented
29C2×#14556534C411yescharacteristic, complemented
30SD32×D73C414yescomplemented
31SD32×D73C2214yes—
32C2×C16×D73C2211yescharacteristic
33C2×SD32×C73C411yescharacteristic, complemented
34C23×#64408—41no—
35C2×#11924036D411yescharacteristic
36Q8×#64408—24no—
37Q8×#64408—42no—
38D4×#64408—24no—
39D4×#64408—42no—
40C2×C4⋊#64408—21no—
41C2×C4⋊#64408—21no—
42C2×C4⋊#64408—41no—
43C2×C22⋊#64408—41no—
44C2×C4×#64408—41no—
45C2×C4×#64408D411yescharacteristic
46#14556664—21no—
47#14556664C2312yes—
48C2×#11924031—21no—
49#14556660—21no—
50#14556660—21no—
51#14556660C2312yes—
52#14556660C2312yes—
53#14556654—24no—
54#14556653—24no—
55C8×#64408D412yes—
56C8×#64408C2312yes—
57C2×Q8×D73—21no—
58C2×D4×D73—21no—
59C2×Dic292C2×C411yescharacteristic, complemented
60C2×#11924018—21no—
61Q16×D73—21no—
62Q16×D73—21no—
63Q16×D73C2×C412yescomplemented
64Q16×D73C2312yes—
65C2×D584C2×C411yescharacteristic
66C2×#11924013—21no—
67D8×D73—21no—
68D8×D73—21no—
69D8×D73C2×C412yes—
70D8×D73C2312yes—
71C2×C8×D73C2311yescharacteristic
72#14556536C2×C414yescomplemented
73#14556535C2×C414yescomplemented
74#14556534C2×C414yescomplemented
75C2×#11924003C2×C411yescharacteristic, complemented
76C16×D73C2×C412yescomplemented
77C16×D73C2312yes—
78C2×Q16×C73C2×C411yescharacteristic, complemented
79C2×D8×C73C2×C411yescharacteristic
80SD32×C73C2×C414yescomplemented
81C2×C16×C73C2×C411yescharacteristic, complemented
82C22×#64408—41no—
83C22×#64408—41no—
84C22×#64408—44no—
85C22×#64408—84no—
86C22×#64408D811yescharacteristic
87C22×#64408D811yescharacteristic
88#11924036—21no—
89#11924036C2×D412yes—
90C2×#10596833—21no—
91C4⋊#64408—22no—
92C4⋊#64408—22no—
93C4⋊#64408—44no—
94C4⋊#64408—41no—
95C4⋊#64408—41no—
96C22⋊#64408—44no—
97C4×#64408—44no—
98C4×#64408D812yes—
99C4×#64408C2×D412yes—
100#11924031—22no—
101C23×D73—41no—
102C2×Dic146—21no—
103C2×Dic146—41no—
104Q8×D73—22no—
105Q8×D73—22no—
106Q8×D73—41no—
107Q8×D73—41no—
108C2×D292—21no—
109C2×C22⋊D73—41no—
110D4×D73—22no—
111D4×D73—22no—
112D4×D73—41no—
113D4×D73—41no—
114C2×C4×D73—41no—
115C2×C4×D73C2×D411yescharacteristic
116Dic292—21no—
117Dic292C22×C412yescomplemented
118#11924018—22no—
119#11924018—22no—
120D584—21no—
121D584C22×C412yes—
122#11924013—22no—
123#11924013—22no—
124C2×#10596831#4111yescharacteristic
125C8×D73C22×C411yescharacteristic
126C8×D73C2×D411yescharacteristic
127C8×D73#4111yescharacteristic
128C8×D73C2411yescharacteristic
129#11924003C22×C412yescomplemented
130C2×Q8×C73—21no—
131C2×D4×C73—21no—
132Q16×C73—21no—
133Q16×C73C22×C412yescomplemented
134D8×C73—21no—
135D8×C73C22×C412yes—
136C2×C8×C73C22×C411yescharacteristic
137C16×C73C22×C412yescomplemented
138C23×C73—41no—
139C22×D73—41no—
140C22×D73—42no—
141C22×D73—42no—
142C22×D73—82no—
143C22×D73—82no—
144C22×D73C2×D811yescharacteristic
145C2×#64408—22no—
146C2×#64408—22no—
147C2×#64408—42no—
148C2×#64408—42no—
149C2×#64408—88no—
150C2×#64408—82no—
151C2×#64408—82no—
152C2×#64408C2×D812yes—
153C2×#64408C2×D812yes—
154Q8×C73—22no—
155Q8×C73—41no—
156D4×C73—22no—
157D4×C73—41no—
158C2×C4×C73—41no—
159C2×C4×C73C4×D411yescharacteristic
160C22⋊D73—42no—
161C22⋊D73—42no—
162C2×Dic73—41no—
163C2×Dic73#13511yescharacteristic
164D292—22no—
165D292—41no—
166C4×D73—42no—
167C4×D73—42no—
168C4×D73C4×D411yescharacteristic
169C4×D73C2×D811yescharacteristic
170C4×D73#13511yescharacteristic
171C4×D73C22×D411yescharacteristic
172Dic146—22no—
173Dic146—41no—
174Dic146—42no—
175Dic146—42no—
176#10596833—22no—
177C8×C73C4×D411yescharacteristic
178C8×C73C23×C411yescharacteristic
179#10596831C4×D411yescharacteristic
180#10596831C2×#4111yescharacteristic
181C22×C73—42no—
182C22×C73—82no—
183C22×C73C4×D811yescharacteristic
184C2×D73—42no—
185C2×D73—82no—
186C2×D73—82no—
187C2×D73—82no—
188C2×D73—84no—
189C2×D73C4×D811yescharacteristic
190C2×D73#50912yes—
191C2×D73#51012yes—
192C2×D73C22×D811yescharacteristic
193#64408—22no—
194#64408—22no—
195#64408—82no—
196#64408—82no—
197C4×C73—42no—
198C4×C73C4×D811yescharacteristic
199C4×C73C2×C4×D411yescharacteristic
200Dic73—42no—
201Dic73C4×D811yescharacteristic
202Dic73C2×#13511yescharacteristic
203C2×#2175—731nomaximal, Sylow
204C2×C73—82no—
205C2×C73#217512yescomplemented
206C2×C73C2×C4×D811yescharacteristic
207D73—82no—
208D73#217512yescomplemented
209D73C2×#50911yescharacteristic
210D73C2×#51011yescharacteristic
211C22×SD32—731no—
212C2×C4×Q16—731no—
213C2×C4×D8—731no—
214#2175—738no—
215C2×#366—731no—
216C2×#358—731no—
217C2×#357—731no—
218C2×#346—731no—
219C73C2×#217511yescharacteristic, complemented, Sylow
220C22×Q16—731no—
221C22×D8—731no—
222C2×C4×Q8—1461no—
223C2×C4×D4—1461no—
224C2×SD32—731no—
225C2×SD32—731no—
226C2×SD32—734no—
227C2×SD32—734no—
228C2×SD32—731no—
229C2×SD32#6440811yescharacteristic, complemented
230C22×C16—731no—
231C22×C16—731no—
232C4×Q16—734no—
233C4×Q16—1462no—
234C4×D8—734no—
235C4×D8—1462no—
236C2×#107—731no—
237C2×#107—731no—
238C2×#103—1461no—
239C2×#102—1461no—
240C2×C4×C8—731no—
241#366—734no—
242#358—734no—
243#357—734no—
244#346—734no—
245C22×Q8—1461no—
246C22×D4—1461no—
247C23×C4—2921no—
248C2×Q16—732no—
249C2×Q16—732no—
250C2×Q16—731no—
251C2×Q16—1461no—
252C2×Q16—1461no—
253C2×Q16—1461no—
254C2×Q16C2×#6440811yescharacteristic, complemented
255C2×D8—732no—
256C2×D8—732no—
257C2×D8—731no—
258C2×D8—1461no—
259C2×D8—1461no—
260C2×D8—1461no—
261C2×D8C2×#6440811yescharacteristic
262C22×C8—731no—
263C22×C8—731no—
264C4×Q8—2922no—
265C4×Q8—1464no—
266C4×D4—2922no—
267C4×D4—1464no—
268C2×C4⋊C4—2921no—
269C2×C4⋊C4—1461no—
270C2×C4⋊C4—1461no—
271C2×C22⋊C4—2921no—
272C2×C42—2921no—
273C2×C42—731no—
274SD32—734no—
275SD32—734no—
276SD32—734no—
277SD32C2×#6440814yescomplemented
278C2×C16—731no—
279C2×C16—732no—
280C2×C16—732no—
281C2×C16—732no—
282C2×C16—1461no—
283C2×C16—1461no—
284C2×C16C2×#6440811yescharacteristic, complemented
285#107—732no—
286#107—732no—
287#107—1461no—
288#107—1461no—
289#103—1464no—
290#102—1464no—
291C4×C8—732no—
292C4×C8—732no—
293C24—2921no—
294C2×Q8—21no—
295C2×Q8—2921no—
296C2×Q8—2921no—
297C2×Q8—2921no—
298C2×Q8—1462no—
299C2×Q8—1462no—
300C2×Q8—1461no—
301C2×D4—21no—
302C2×D4—2921no—
303C2×D4—2921no—
304C2×D4—2921no—
305C2×D4—1462no—
306C2×D4—1462no—
307C2×D4—1461no—
308C22×C4—2921no—
309C22×C4—2921no—
310C22×C4—2921no—
311C22×C4—2924no—
312C22×C4—5844no—
313C22×C4—731no—
314C22×C4—731no—
315C22×C4—731no—
316Q16—21no—
317Q16—732no—
318Q16—1462no—
319Q16—1462no—
320Q16—1461no—
321Q16C22×#6440812yescomplemented
322D8—21no—
323D8—732no—
324D8—1462no—
325D8—1462no—
326D8—1461no—
327D8C22×#6440812yes—
328C2×C8—731no—
329C2×C8—731no—
330C2×C8—731no—
331C2×C8—731no—
332C2×C8—731no—
333C2×C8—732no—
334C2×C8—1461no—
335C2×C8—1461no—
336C2×C8C22×#6440811yescharacteristic
337C4⋊C4—2924no—
338C4⋊C4—2921no—
339C4⋊C4—2921no—
340C4⋊C4—1462no—
341C4⋊C4—1462no—
342C22⋊C4—2924no—
343C42—2924no—
344C42—732no—
345C42—732no—
346C16—732no—
347C16—1462no—
348C16C22×#6440812yescomplemented
349C23—41no—
350C23—2922no—
351C23—2922no—
352C23—2921no—
353C23—5842no—
354C23—5842no—
355C23—731no—
356Q8—22no—
357Q8—41no—
358Q8—2922no—
359Q8—2922no—
360Q8—2921no—
361Q8—1462no—
362D4—22no—
363D4—41no—
364D4—2922no—
365D4—2922no—
366D4—2921no—
367D4—1462no—
368C2×C4—41no—
369C2×C4—2922no—
370C2×C4—2922no—
371C2×C4—2921no—
372C2×C4—2922no—
373C2×C4—2922no—
374C2×C4—5842no—
375C2×C4—5842no—
376C2×C4—5848no—
377C2×C4—731no—
378C2×C4—731no—
379C2×C4—731no—
380C2×C4—731no—
381C2×C4—731no—
382C2×C4—732no—
383C2×C4—732no—
384C2×C4—1462no—
385C2×C4—1462no—
386C2×C4D4×#6440811yescharacteristic
387C8—731no—
388C8—731no—
389C8—1462no—
390C8D4×#6440811yescharacteristic
391C8C23×#6440811yescharacteristic
392C22—42no—
393C22—82no—
394C22—2922no—
395C22—5842no—
396C22—5842no—
397C22—5844no—
398C22—5842no—
399C22—732no—
400C22—732no—
401C22—731no—
402C22—731no—
403C22D8×#6440811yescharacteristic
404C4—42no—
405C4—2922no—
406C4—5842no—
407C4—5842no—
408C4—731no—
409C4—731no—
410C4—1462no—
411C4—1462no—
412C4D8×#6440811yescharacteristic
413C4C2×D4×#6440811yescharacteristic
414C2—82no—
415C2—5842no—
416C2—731no—
417C2—731no—
418C2—732no—
419C2#2262632712yesdirect product factor
420C2C2×D8×#6440811yescharacteristic
subgroupG/H
centerC22D8×#64408
commutatorC8×C73C23×C4
FrattiniC8C23×#64408
FittingC2×SD32×C73C4
socleC22×C73C4×D8
prime radicalC2×D8×D73C22
cosocleC8×D73C24
hypercenterC2×SD32#64408
hypocenterC73C2×#2175
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×Q16×#64408C2semidirect
3. #22626327C2direct (N × H)
4. C2×#17989513C2semidirect
5. C2×#17989500C2semidirect
7. C2×#17989474C2semidirect
13. Q16×#64408C22semidirect
21. #17989513C22semidirect
22. #17989500C22semidirect
24. #17989474C22semidirect
27. C2×#14556536C4semidirect
28. C2×#14556535C4semidirect
29. C2×#14556534C4semidirect
30. SD32×D73C4semidirect
33. C2×SD32×C73C4semidirect
59. C2×Dic292C2×C4semidirect
63. Q16×D73C2×C4semidirect
72. #14556536C2×C4semidirect
73. #14556535C2×C4semidirect
74. #14556534C2×C4semidirect
75. C2×#11924003C2×C4semidirect
76. C16×D73C2×C4semidirect
78. C2×Q16×C73C2×C4semidirect
80. SD32×C73C2×C4semidirect
81. C2×C16×C73C2×C4semidirect
117. Dic292C22×C4semidirect
129. #11924003C22×C4semidirect
133. Q16×C73C22×C4semidirect
137. C16×C73C22×C4semidirect
205. C2×C73#2175semidirect
208. D73#2175semidirect
219. C73C2×#2175semidirect
229. C2×SD32#64408semidirect
254. C2×Q16C2×#64408semidirect
277. SD32C2×#64408semidirect
284. C2×C16C2×#64408semidirect
321. Q16C22×#64408semidirect
348. C16C22×#64408semidirect
419. C2#22626327direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q16×#644082
C2×D8×#644082
#226263272
C2×#179895132
C2×#179895002
C2×#179894992
C2×#179894742
C2×SD32×D732
C2×#217573