Finite Group Databasebeta

← C2×#21423638 #28571339

Subgroups — C2×#21423638 #28571339

Order 15104.

702 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837750C211yesmaximal, characteristic
2C2×#16837602C211yesmaximal, characteristic
3C2×#16837533C211yesmaximal, characteristic, complemented
4#21423638C218yesmaximal, direct product factor
5C2×#16837154C211yesmaximal, characteristic, complemented
6C2×#16837151C211yesmaximal, characteristic, complemented
7C2×#16837145C211yesmaximal, characteristic
8C2×C59×#477C211yesmaximal, characteristic, complemented
9C22×#11745671—21no—
10C2×#14273724C2211yescharacteristic
11#16837750—22no—
12#16837750C2214yes—
13#16837602—22no—
14#16837602C2214yes—
15#16837533—22no—
16#16837533C2214yescomplemented
17C2×C4⋊(C59⋊C8)—21no—
18C2×C4⋊(C59⋊C8)C2211yescharacteristic
19C2×C4⋊(C59⋊C8)C2211yescharacteristic
20C2×#14273647—21no—
21C2×#14273647—21no—
22C2×#14273647—21no—
23C2×#14273638—21no—
24C2×C4×C59⋊C8C2211yescharacteristic
25#16837154C2214yescomplemented
26#16837151C2214yescomplemented
27#16837145C2214yes—
28C2×C4⋊Q8×C59C2211yescharacteristic
29C2×C4×Q8×C59C2211yescharacteristic
30C59×#477—22no—
31C59×#477C2214yescomplemented
32C2×#107×C59—21no—
33C2×C4⋊C8×C59C2211yescharacteristic
34C2×#103×C59—21no—
35C22×D236—21no—
36C22×D236—21no—
37C22×D236—21no—
38C2×#11745671—24no—
39C2×#11745671—44no—
40C22×C59⋊C8—21no—
41C22×C59⋊C8—21no—
42C22×C59⋊C8D411yescharacteristic
43C22×C59⋊C8D411yescharacteristic
44#14273724—21no—
45#14273724—21no—
46#14273724—21no—
47#14273724C2312yes—
48C4⋊(C59⋊C8)—21no—
49C4⋊(C59⋊C8)—21no—
50C4⋊(C59⋊C8)—24no—
51C4⋊(C59⋊C8)C2312yes—
52C4⋊(C59⋊C8)C2312yes—
53#14273647—24no—
54#14273647—24no—
55#14273647—24no—
56#14273638—24no—
57C4×C59⋊C8D412yes—
58C4×C59⋊C8C2312yes—
59C22×Q8×C59—21no—
60C22×Q8×C59D411yescharacteristic
61C22×C8×C59—21no—
62C4⋊Q8×C59—21no—
63C4⋊Q8×C59—21no—
64C4⋊Q8×C59—21no—
65C4⋊Q8×C59C2312yes—
66C4×Q8×C59—21no—
67C4×Q8×C59—21no—
68C4×Q8×C59D412yes—
69C4×Q8×C59C2312yes—
70C2×C4⋊C4×C59—21no—
71C2×C4⋊C4×C59—21no—
72C2×C4⋊C4×C59—21no—
73C2×C4⋊C4×C59D411yescharacteristic
74C2×C42×C59—21no—
75C2×C42×C59C2311yescharacteristic
76#107×C59—24no—
77C4⋊C8×C59—21no—
78C4⋊C8×C59C2312yes—
79#103×C59—24no—
80C23×D59—41no—
81C2×Q8×C59—21no—
82C2×Q8×C59—22no—
83C2×Q8×C59—22no—
84C2×Q8×C59—22no—
85C2×Q8×C59—41no—
86C2×Q8×C59—82no—
87C2×Q8×C59C2×D412yes—
88C22×C4×C59—21no—
89C22×C4×C59—21no—
90C22×C4×C59—41no—
91C22×C4×C59C2×D411yescharacteristic
92C22×C4×C59C2×D411yescharacteristic
93C22×C4×C59#4111yescharacteristic
94C2×D236—22no—
95C2×D236—22no—
96C2×D236—22no—
97C2×D236—42no—
98C2×D236—42no—
99C2×D236—42no—
100C2×D236—42no—
101C2×D236—41no—
102C2×D236—41no—
103C2×D236—41no—
104C2×D236—82no—
105C2×C8×C59—22no—
106C2×C8×C59—42no—
107C4⋊C4×C59—22no—
108C4⋊C4×C59—21no—
109C4⋊C4×C59—22no—
110C4⋊C4×C59—22no—
111C4⋊C4×C59—22no—
112C4⋊C4×C59—41no—
113C4⋊C4×C59—41no—
114C4⋊C4×C59C2×D412yes—
115C42×C59—22no—
116C42×C59—22no—
117C42×C59C2×D411yescharacteristic
118C42×C59C2×D411yescharacteristic
119C42×C59#4111yescharacteristic
120C42×C59C2411yescharacteristic
121#11745671—48no—
122C2×C59⋊C8—22no—
123C2×C59⋊C8—22no—
124C2×C59⋊C8—22no—
125C2×C59⋊C8—22no—
126C2×C59⋊C8—42no—
127C2×C59⋊C8—42no—
128C2×C59⋊C8C2×D412yes—
129C2×C59⋊C8C2×D412yes—
130C23×C59#12111yescharacteristic
131C22×D59—42no—
132C22×D59—82no—
133C22×D59—82no—
134C22×D59—82no—
135Q8×C59—22no—
136Q8×C59—22no—
137Q8×C59—42no—
138Q8×C59—82no—
139Q8×C59—82no—
140C2×C4×C59—22no—
141C2×C4×C59—22no—
142C2×C4×C59—22no—
143C2×C4×C59—42no—
144C2×C4×C59—42no—
145C2×C4×C59—42no—
146C2×C4×C59—82no—
147C2×C4×C59#12111yescharacteristic
148C2×C4×C59#12111yescharacteristic
149C2×C4×C59#12111yescharacteristic
150C2×C4×C59#13512yes—
151C2×C4×C59AGL(1,ℤ/8)12yes—
152C2×C4×C59#13712yes—
153C2×C4×C59#13712yes—
154C2×C4×C59C22×D411yescharacteristic
155C2×C4×C59C22×D411yescharacteristic
156C2×C4×C59C2×#4111yescharacteristic
157D236—42no—
158D236—42no—
159D236—42no—
160D236—42no—
161D236—82no—
162D236—82no—
163D236—82no—
164D236—82no—
165C8×C59—42no—
166C59⋊C8—22no—
167C59⋊C8—22no—
168C59⋊C8—42no—
169C59⋊C8—42no—
170C2×#1698—591nomaximal, Sylow
171C22×C59#46412yes—
172C22×C59#46812yes—
173C22×C59#47212yes—
174C22×C59C2×#12111yescharacteristic
175C2×D59—82no—
176C2×D59—82no—
177C2×D59—82no—
178C2×D59—164no—
179C4×C59—21no—
180C4×C59—21no—
181C4×C59—42no—
182C4×C59—42no—
183C4×C59—82no—
184C4×C59#46412yes—
185C4×C59#46812yes—
186C4×C59C2×#13511yescharacteristic
187C4×C59C2×AGL(1,ℤ/8)11yescharacteristic
188C4×C59C2×#13711yescharacteristic
189C4×C59C2×#13711yescharacteristic
190C2×#486—591no—
191C2×#477D5911yescharacteristic, complemented
192C2×#460—591no—
193C2×#446—591no—
194#1698—598no—
195C2×#335—591no—
196C2×#333—591no—
197C2×#331—591no—
198C2×C59#169814yescomplemented
199C2×C59C2×#46411yescharacteristic
200C2×C59C2×#46811yescharacteristic
201C2×C59C2×#47211yescharacteristic
202D59—162no—
203C22×SD16—1181no—
204C2×C4⋊Q8C2×D5911yescharacteristic
205C2×#127—591no—
206C2×C4×Q8C2×D5911yescharacteristic
207#486—594no—
208#486—1182no—
209#477—22no—
210#477C2×D5914yescomplemented
211#460—594no—
212#460—1182no—
213#446—594no—
214#446—1182no—
215C2×#107—21no—
216C2×C4⋊C8—591no—
217C2×C4⋊C8—591no—
218C2×C4⋊C8—1181no—
219C2×C4⋊C8C2×D5911yescharacteristic
220C2×#103—21no—
221C2×#102—1181no—
222C2×#102—1181no—
223C2×#102—1181no—
224C2×#97—1181no—
225C2×C4×C8—591no—
226#335—594no—
227#333—594no—
228#331—594no—
229C59C2×#169811yescharacteristic, complemented, Sylow
230C22×Q8—21no—
231C22×Q8C22⋊D5911yescharacteristic
232C22×D4—1181no—
233C22×D4—1181no—
234C22×D4—1181no—
235C2×SD16—1184no—
236C2×SD16—2364no—
237C22×C8—21no—
238C22×C8—591no—
239C22×C8—591no—
240C22×C8—1181no—
241C22×C8—1181no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8C22×D5912yes—
246#127—592no—
247#127—1181no—
248#127—1181no—
249#127—1181no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8C22⋊D5912yes—
253C4×Q8C22×D5912yes—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4C22⋊D5911yescharacteristic
258C2×C42—21no—
259C2×C42C22×D5911yescharacteristic
260#107—24no—
261C4⋊C8—21no—
262C4⋊C8—592no—
263C4⋊C8—592no—
264C4⋊C8—1184no—
265C4⋊C8—1181no—
266C4⋊C8—1181no—
267C4⋊C8C22×D5912yes—
268#103—24no—
269#102—1184no—
270#102—1184no—
271#102—1184no—
272#97—1184no—
273C4×C8—592no—
274C4×C8—592no—
275C24—2361no—
276C2×Q8—21no—
277C2×Q8—22no—
278C2×Q8—22no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—82no—
282C2×Q8C2×C22⋊D5912yes—
283C2×D4—1182no—
284C2×D4—1182no—
285C2×D4—1182no—
286C2×D4—4722no—
287C2×D4—2361no—
288C2×D4—2361no—
289C2×D4—2361no—
290C2×D4—2362no—
291C2×D4—2362no—
292C2×D4—2362no—
293C2×D4—2362no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—41no—
297C22×C4D4×D5911yescharacteristic
298C22×C4#1174568711yescharacteristic
299C22×C4C2×C22⋊D5911yescharacteristic
300SD16—2368no—
301C2×C8—22no—
302C2×C8—42no—
303C2×C8—592no—
304C2×C8—592no—
305C2×C8—1182no—
306C2×C8—1182no—
307C2×C8—1182no—
308C2×C8—1182no—
309C2×C8—2362no—
310C2×C8—2362no—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4C2×C22⋊D5912yes—
319C42—22no—
320C42—22no—
321C42D4×D5911yescharacteristic
322C42#1174568711yescharacteristic
323C42C2×C22⋊D5911yescharacteristic
324C42C23×D5911yescharacteristic
325C23—4722no—
326C23—4722no—
327C23—4722no—
328C23—2362no—
329C23#1427369911yescharacteristic
330Q8—22no—
331Q8—22no—
332Q8—42no—
333Q8—82no—
334Q8—82no—
335D4—4722no—
336D4—4722no—
337D4—4722no—
338D4—4722no—
339D4—2362no—
340D4—2362no—
341D4—2362no—
342D4—2362no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—82no—
350C2×C4#1427369911yescharacteristic
351C2×C4#1427369911yescharacteristic
352C2×C4#1427369911yescharacteristic
353C2×C4#1427375012yes—
354C2×C4#1427375212yes—
355C2×C4#1427375812yes—
356C2×C4#1427375912yes—
357C2×C4C2×D4×D5911yescharacteristic
358C2×C4C22×C22⋊D5911yescharacteristic
359C2×C4C2×#1174568711yescharacteristic
360C8—42no—
361C8—1182no—
362C8—1182no—
363C8—2362no—
364C8—2362no—
365C22—9444no—
366C22—4722no—
367C22—4722no—
368C22—4722no—
369C22#1683762612yes—
370C22#1683765012yes—
371C22#1683767012yes—
372C22C2×#1427369911yescharacteristic
373C4—21no—
374C4—21no—
375C4—42no—
376C4—42no—
377C4—82no—
378C4#1683762612yes—
379C4#1683765012yes—
380C4C2×#1427375011yescharacteristic
381C4C2×#1427375211yescharacteristic
382C4C2×#1427375811yescharacteristic
383C4C2×#1427375911yescharacteristic
384C2—9442no—
385C2#2142363814yesdirect product factor
386C2C2×#1683762611yescharacteristic
387C2C2×#1683765011yescharacteristic
388C2C2×#1683767011yescharacteristic
subgroupG/H
centerC23#14273699
commutator, cosocleC42×C59C24
FrattiniC42C23×D59
FittingC2×C59×#477C2
socleC23×C59#121
prime radicalC2×#14273724C22
hypercenterC2×#477D59
hypocenterC59C2×#1698
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. C2×#16837533C2semidirect
4. #21423638C2direct (N × H)
5. C2×#16837154C2semidirect
6. C2×#16837151C2semidirect
8. C2×C59×#477C2semidirect
16. #16837533C22semidirect
25. #16837154C22semidirect
26. #16837151C22semidirect
31. C59×#477C22semidirect
191. C2×#477D59semidirect
198. C2×C59#1698semidirect
210. #477C2×D59semidirect
229. C59C2×#1698semidirect
385. C2#21423638direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168377502
C2×#168376022
C2×#168375332
#214236382
C2×#168371542
C2×#168371512
C2×#168371452
C2×C59×#4772
C2×#169859