Finite Group Databasebeta

← C2×#21447762 #29833785

Subgroups — C2×#21447762 #29833785

Order 15616.

1146 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519800C211yesmaximal, characteristic
2C22×#14519723C211yesmaximal, characteristic, complemented
3C22×#14519722C211yesmaximal, characteristic, complemented
4C2×#16840004C211yesmaximal, characteristic, complemented
5#21447762C218yesmaximal, direct product factor
6C2×#16839562C211yesmaximal, characteristic, complemented
7C2×#16839541C211yesmaximal, characteristic, complemented
8C2×C61×#358C211yesmaximal, characteristic, complemented
9C22×#11758226—21no—
10C2×#14519800—24no—
11C2×#14519800—22no—
12C2×#14519800—24no—
13C2×#14519800C2214yes—
14C22×Dic244C2211yescharacteristic
15C22×#11758201—21no—
16C22×D488C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×#14519757—21no—
19C2×#14519723—24no—
20C2×#14519723C2214yescomplemented
21C2×#14519722—24no—
22C2×#14519722C2214yescomplemented
23C22×#11758185C2211yescharacteristic
24#16840004—22no—
25#16840004C2214yescomplemented
26C2×#14519700—21no—
27#16839562C2214yescomplemented
28#16839541C2214yescomplemented
29C22×Q16×C61C2211yescharacteristic
30C22×C16×C61C2211yescharacteristic
31C2×#107×C61C2211yescharacteristic
32C61×#358C2214yescomplemented
33C2×#11758226—28no—
34C2×#11758226—24no—
35C2×#11758226—44no—
36C2×#11758226—42no—
37C22×Dic122—21no—
38C22×D244—21no—
39C22×D244—41no—
40C22×C4×D61—41no—
41C22×C4×D61D411yescharacteristic
42#14519800—216no—
43#14519800—28no—
44#14519800—28no—
45C2×Dic244—22no—
46C2×Dic244—22no—
47C2×Dic244—21no—
48C2×Dic244C2312yes—
49C2×#11758201—28no—
50C2×#11758201—24no—
51C2×D488—21no—
52C2×D488—22no—
53C2×D488D414yes—
54C2×D488C2312yes—
55C22×#92418D411yescharacteristic
56C2×C8×D61—22no—
57C2×C8×D61—22no—
58C2×C8×D61D412yes—
59C2×C8×D61C2312yes—
60#14519757—24no—
61#14519757—42no—
62C2×C4⋊Dic61—41no—
63C2×#11758198—41no—
64#14519723—28no—
65#14519722—28no—
66C2×#11758185—22no—
67C2×#11758185C2312yes—
68#14519700—24no—
69C22×Q8×C61—21no—
70C2×Q16×C61—21no—
71C2×Q16×C61—22no—
72C2×Q16×C61D414yes—
73C2×Q16×C61C2312yes—
74C22×C8×C61C2311yescharacteristic
75C2×C4⋊C4×C61—21no—
76C2×C16×C61—22no—
77C2×C16×C61C2312yes—
78#107×C61—21no—
79#107×C61C2312yes—
80C23×D61—41no—
81C23×D61D811yescharacteristic
82C2×Q8×C61—24no—
83C2×Q8×C61—22no—
84C2×Q8×C61—41no—
85C2×Q8×C61—42no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61C2×D411yescharacteristic
89C22×Dic61—41no—
90C22×Dic61D811yescharacteristic
91#11758226—216no—
92#11758226—48no—
93#11758226—416no—
94C2×D244—24no—
95C2×D244—22no—
96C2×D244—48no—
97C2×D244—44no—
98C2×D244—41no—
99C2×D244—42no—
100C2×C4×D61—22no—
101C2×C4×D61—22no—
102C2×C4×D61—48no—
103C2×C4×D61—44no—
104C2×C4×D61D812yes—
105C2×C4×D61C2×D412yes—
106C2×Dic122—22no—
107C2×Dic122—42no—
108C2×Dic122—42no—
109C2×Dic122—41no—
110Q16×C61—24no—
111Q16×C61—22no—
112Q16×C61C2×D414yes—
113C2×C8×C61C2×D411yescharacteristic
114C2×C8×C61C2×D412yes—
115C2×C8×C61C2×D412yes—
116C2×C8×C61C2411yescharacteristic
117C4⋊C4×C61—22no—
118C4⋊C4×C61—41no—
119#11758201—216no—
120#11758198—44no—
121C4⋊Dic61—44no—
122C2×#92418—22no—
123C2×#92418C2×D412yes—
124Dic244—22no—
125Dic244—22no—
126Dic244—42no—
127D488—24no—
128D488—22no—
129D488C2×D414yes—
130C8×D61—24no—
131C8×D61—22no—
132C8×D61—22no—
133C16×C61—22no—
134#11758185—22no—
135C23×C61C2×D811yescharacteristic
136C22×D61—22no—
137C22×D61—22no—
138C22×D61—22no—
139C22×D61—42no—
140C22×D61—44no—
141C22×D61—82no—
142C22×D61—82no—
143C22×D61C2×D812yes—
144Q8×C61—24no—
145Q8×C61—42no—
146Q8×C61—44no—
147C2×C4×C61—42no—
148C2×C4×C61—44no—
149C2×C4×C61—42no—
150C2×C4×C61—82no—
151C2×C4×C61#12012yes—
152C2×C4×C61C2×D811yescharacteristic
153C2×C4×C61AGL(1,ℤ/8)12yes—
154C2×C4×C61C22×D411yescharacteristic
155C2×Dic61—22no—
156C2×Dic61—42no—
157C2×Dic61—82no—
158C2×Dic61C2×D812yes—
159D244—24no—
160D244—416no—
161D244—42no—
162D244—44no—
163C4×D61—22no—
164C4×D61—22no—
165C4×D61—24no—
166C4×D61—416no—
167Dic122—42no—
168Dic122—42no—
169Dic122—82no—
170C8×C61#12012yes—
171C8×C61C22×D411yescharacteristic
172C8×C61C22×D411yescharacteristic
173#92418—22no—
174C2×#2189—611nomaximal, Sylow
175C22×C61#44712yes—
176C22×C61#50812yes—
177C22×C61#51012yes—
178C22×C61C22×D811yescharacteristic
179C2×D61—22no—
180C2×D61—22no—
181C2×D61—22no—
182C2×D61—44no—
183C2×D61—44no—
184C2×D61—82no—
185C2×D61—82no—
186C2×D61—88no—
187C4×C61—44no—
188C4×C61—82no—
189C4×C61#44712yes—
190C4×C61C2×#12011yescharacteristic
191C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
192Dic61—22no—
193Dic61—82no—
194C22×#135—611no—
195C22×Q32—611no—
196C22×SD32—611no—
197C2×#467—611no—
198#2189—618no—
199C2×#358D6111yescharacteristic, complemented
200C2×#357—611no—
201C2×C22⋊C16—611no—
202C2×C61#218914yescomplemented
203C2×C61C2×#44711yescharacteristic
204C2×C61C2×#50811yescharacteristic
205C2×C61C2×#51011yescharacteristic
206D61—42no—
207D61—84no—
208C22×#41—1221no—
209C2×#135—614no—
210C2×#135—1222no—
211C2×#135—1224no—
212C2×#135—1224no—
213C22×Q16—611no—
214C22×Q16C2×D6111yescharacteristic
215C22×SD16—1221no—
216C22×D8—611no—
217C23×C8—611no—
218C2×C22⋊Q8—1221no—
219C2×Q32—614no—
220C2×Q32—1224no—
221C2×SD32—614no—
222C2×SD32—1224no—
223C22×C16—611no—
224C22×C16C2×D6111yescharacteristic
225#467—614no—
226#467—1222no—
227C2×#107C2×D6111yescharacteristic
228C2×#103—1221no—
229#358C2×D6114yescomplemented
230#357—614no—
231C22⋊C16—614no—
232C61C2×#218911yescharacteristic, complemented, Sylow
233C2×#41—1224no—
234C2×#41—1228no—
235C2×#41—2442no—
236C2×#41—2444no—
237C22×Q8—21no—
238C22×Q8—1221no—
239C22×D4—1221no—
240C22×D4—2441no—
241C23×C4—611no—
242C23×C4—2441no—
243#135—1228no—
244#135—12216no—
245#135—1228no—
246C2×Q16—22no—
247C2×Q16—21no—
248C2×Q16—612no—
249C2×Q16—1222no—
250C2×Q16—1222no—
251C2×Q16—1221no—
252C2×Q16D24414yes—
253C2×Q16C22×D6112yes—
254C2×SD16—1224no—
255C2×SD16—1228no—
256C2×D8—614no—
257C2×D8—612no—
258C2×D8—1222no—
259C2×D8—1221no—
260C22×C8—611no—
261C22×C8—612no—
262C22×C8—612no—
263C22×C8—1222no—
264C22×C8—1222no—
265C22×C8C22×D6111yescharacteristic
266C22⋊Q8—1224no—
267C22⋊Q8—2442no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—2441no—
270C2×C22⋊C4—2441no—
271Q32—1228no—
272SD32—1228no—
273C2×C16—22no—
274C2×C16—612no—
275C2×C16—1222no—
276C2×C16C22×D6112yes—
277#107—21no—
278#107C22×D6112yes—
279#103—1224no—
280C24—611no—
281C24—2441no—
282#41—12216no—
283#41—2448no—
284#41—24416no—
285C2×Q8—22no—
286C2×Q8—24no—
287C2×Q8—41no—
288C2×Q8—42no—
289C2×Q8—1222no—
290C2×Q8—2442no—
291C2×Q8—2442no—
292C2×Q8—2441no—
293C2×D4—1222no—
294C2×D4—1224no—
295C2×D4—2444no—
296C2×D4—2448no—
297C2×D4—2441no—
298C2×D4—2442no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—611no—
302C22×C4—612no—
303C22×C4—612no—
304C22×C4—1222no—
305C22×C4—1222no—
306C22×C4—2444no—
307C22×C4—2448no—
308C22×C4—2441no—
309C22×C4D4×D6111yescharacteristic
310Q16—22no—
311Q16—24no—
312Q16—1222no—
313Q16—1222no—
314Q16—2442no—
315Q16C2×D24414yes—
316SD16—12216no—
317D8—614no—
318D8—1222no—
319D8—1224no—
320C2×C8—612no—
321C2×C8—1222no—
322C2×C8—1222no—
323C2×C8—1222no—
324C2×C8—1224no—
325C2×C8C2×D24412yes—
326C2×C8D4×D6112yes—
327C2×C8D4×D6111yescharacteristic
328C2×C8C23×D6111yescharacteristic
329C4⋊C4—22no—
330C4⋊C4—41no—
331C4⋊C4—2444no—
332C22⋊C4—2444no—
333C16—22no—
334C16—1222no—
335C23—612no—
336C23—1222no—
337C23—1222no—
338C23—1222no—
339C23—4882no—
340C23—4882no—
341C23—2442no—
342C23—2444no—
343C23D8×D6111yescharacteristic
344Q8—24no—
345Q8—42no—
346Q8—44no—
347Q8—4882no—
348Q8—2442no—
349Q8—2442no—
350D4—1224no—
351D4—24416no—
352D4—2442no—
353D4—2444no—
354C2×C4—42no—
355C2×C4—44no—
356C2×C4—42no—
357C2×C4—82no—
358C2×C4—612no—
359C2×C4—1222no—
360C2×C4—1222no—
361C2×C4—1222no—
362C2×C4—1224no—
363C2×C4—4882no—
364C2×C4—24416no—
365C2×C4—2442no—
366C2×C4#1451974712yes—
367C2×C4D8×D6111yescharacteristic
368C2×C4#1451980412yes—
369C2×C4C2×D4×D6111yescharacteristic
370C8—1222no—
371C8#1451974712yes—
372C8C2×D4×D6111yescharacteristic
373C8C22×D24411yescharacteristic
374C22—1222no—
375C22—1222no—
376C22—1222no—
377C22—4882no—
378C22—4888no—
379C22—4882no—
380C22—2444no—
381C22—2444no—
382C22#1683989712yes—
383C22#1684019312yes—
384C22#1684020412yes—
385C22C2×D8×D6111yescharacteristic
386C4—44no—
387C4—82no—
388C4—1222no—
389C4—4882no—
390C4#1683989712yes—
391C4C2×#1451974711yescharacteristic
392C4C2×#1451980411yescharacteristic
393C2—4884no—
394C2—2442no—
395C2#2144776214yesdirect product factor
396C2C2×#1683989711yescharacteristic
397C2C2×#1684019311yescharacteristic
398C2C2×#1684020411yescharacteristic
subgroupG/H
centerC23D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#358C2
socleC23×C61C2×D8
prime radicalC22×#14519800C2
hypercenterC2×#358D61
hypocenterC61C2×#2189
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C22×#14519723C2semidirect
3. C22×#14519722C2semidirect
4. C2×#16840004C2semidirect
5. #21447762C2direct (N × H)
6. C2×#16839562C2semidirect
7. C2×#16839541C2semidirect
8. C2×C61×#358C2semidirect
20. C2×#14519723C22semidirect
22. C2×#14519722C22semidirect
25. #16840004C22semidirect
27. #16839562C22semidirect
28. #16839541C22semidirect
32. C61×#358C22semidirect
199. C2×#358D61semidirect
202. C2×C61#2189semidirect
229. #358C2×D61semidirect
232. C61C2×#2189semidirect
395. C2#21447762direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198002
C22×#145197232
C22×#145197222
C2×#168400042
#214477622
C2×#168395622
C2×#168395412
C2×C61×#3582
C2×#218961