Finite Group Databasebeta

← C2×#13070695 #14908157

Subgroups — C2×#13070695 #14908157

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622808C211yesmaximal, characteristic
2C2×#10622794C211yesmaximal, characteristic, complemented
3C2×#10622809C211yesmaximal, characteristic
4#13070695C218yesmaximal, direct product factor
5C2×#10622149C211yesmaximal, characteristic, complemented
6C2×#10622155C211yesmaximal, characteristic, complemented
7C2×#10622203C211yesmaximal, characteristic, complemented
8C2×C11×#510C211yesmaximal, characteristic
9C2×C11×#135C2211yescharacteristic
10C22×C11×Q16C2211yescharacteristic
11C2×#67001—21no—
12C2×#66997—21no—
13C22×#4326—21no—
14C22×Dic44C2211yescharacteristic
15C11×#510—22no—
16C11×#510C2214yes—
17C2×C11×Q32—21no—
18C2×C11×SD32—21no—
19C2×C11×M32C2211yescharacteristic
20C2×#66901—21no—
21#10622809—22no—
22#10622809C2214yes—
23#10622808—22no—
24#10622808C2214yes—
25#10622794—22no—
26#10622794C2214yescomplemented
27C2×#66893—21no—
28C2×#66891—21no—
29C2×#66883C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C2×#66876C2211yescharacteristic
32#10622203C2214yescomplemented
33#10622155C2214yescomplemented
34#10622149C2214yescomplemented
35C2×C11×#41—21no—
36C22×Q8×C11—21no—
37C22×Dic22—21no—
38C11×#135—21no—
39C11×#135—21no—
40C11×#135D412yes—
41C11×#135C2312yes—
42C2×C11×Q16—21no—
43C2×C11×Q16—21no—
44C2×C11×Q16—21no—
45C2×C11×Q16—21no—
46C2×C11×Q16—21no—
47C2×C11×Q16D411yescharacteristic
48C2×C11×Q16C2312yes—
49C2×C11×SD16—21no—
50C2×C11×D8D411yescharacteristic
51C22×C8×C11C2311yescharacteristic
52#67001—24no—
53#67001—42no—
54#66997—24no—
55#66997—42no—
56C2×#4326—24no—
57C2×#4326—41no—
58C2×#4326—41no—
59C2×#4326—42no—
60C2×Dic11⋊C4—42no—
61C2×C4×Dic11D411yescharacteristic
62C2×#4318—21no—
63C2×#4318—41no—
64C22×C11⋊C8—41no—
65C22×C11⋊C8D411yescharacteristic
66C2×Dic44—21no—
67C2×Dic44—21no—
68C2×Dic44—21no—
69C2×Dic44—21no—
70C2×Dic44—21no—
71C2×Dic44C2312yes—
72C11×Q32—24no—
73C11×SD32—24no—
74C11×M32—21no—
75C11×M32C2312yes—
76C2×C11×C16—21no—
77#66901—24no—
78#66893—24no—
79#66891—24no—
80#66883—21no—
81#66883C2312yes—
82C8×Dic11D412yes—
83C8×Dic11C2312yes—
84#66876—21no—
85#66876C2312yes—
86C2×C11⋊C16—21no—
87C2×#2214—111nomaximal, Sylow
88C11×#41—22no—
89C11×#41—22no—
90C11×#41—41no—
91C11×#41—41no—
92C2×Q8×C11—21no—
93C2×Q8×C11—22no—
94C2×Q8×C11—41no—
95C2×Q8×C11—41no—
96C2×Q8×C11—41no—
97C2×Q8×C11—41no—
98C2×Q8×C11—41no—
99C2×D4×C11—21no—
100C2×D4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C22×Dic11—21no—
105C22×Dic11—41no—
106C2×Dic22—22no—
107C2×Dic22—41no—
108C2×Dic22—41no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C2×Dic22—41no—
112C11×Q16—21no—
113C11×Q16—22no—
114C11×Q16—22no—
115C11×Q16—41no—
116C11×Q16—41no—
117C11×Q16C2×D412yes—
118C11×SD16—22no—
119C11×SD16—22no—
120C11×D8—21no—
121C11×D8C2×D412yes—
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11#4111yescharacteristic
126C2×C8×C11#4111yescharacteristic
127C2×C8×C11C2411yescharacteristic
128#4326—44no—
129#4326—44no—
130Dic11⋊C4—48no—
131C4×Dic11—21no—
132C4×Dic11C2×D412yes—
133#4318—22no—
134#4318—44no—
135#4318—41no—
136C2×C11⋊C8—44no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8D811yescharacteristic
139C2×C11⋊C8D811yescharacteristic
140C2×C11⋊C8D812yes—
141C2×C11⋊C8C2×D412yes—
142Dic44—22no—
143Dic44—22no—
144Dic44—41no—
145Dic44—41no—
146C11×C16—22no—
147C11⋊C16—22no—
148C2×#510—111no—
149C2×#510D1111yescharacteristic
150C2×#494—111no—
151C2×#443—111no—
152#2214—118no—
153C2×#364—111no—
154C2×#362—111no—
155C2×#362—111no—
156C23×C11—41no—
157C23×C11AGL(1,ℤ/8)11yescharacteristic
158Q8×C11—22no—
159Q8×C11—41no—
160Q8×C11—42no—
161Q8×C11—42no—
162Q8×C11—81no—
163Q8×C11—81no—
164D4×C11—22no—
165D4×C11—42no—
166D4×C11—42no—
167D4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11C2×D811yescharacteristic
177C2×C4×C11C2×D811yescharacteristic
178C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C2×Dic11—24no—
181C2×Dic11—22no—
182C2×Dic11—42no—
183C2×Dic11—81no—
184C2×Dic11—81no—
185Dic22—42no—
186Dic22—42no—
187Dic22—81no—
188Dic22—81no—
189C8×C11#12111yescharacteristic
190C8×C11#12111yescharacteristic
191C8×C11C22×D411yescharacteristic
192C8×C11C2×#4111yescharacteristic
193C11⋊C8—42no—
194C11⋊C8C2×D812yes—
195C11⋊C8C2×D812yes—
196C2×#135C2×D1111yescharacteristic
197C22×Q16—111no—
198C22×Q16—221no—
199C22×Q16C2×D1111yescharacteristic
200C2×#131—221no—
201C2×C4⋊Q8—221no—
202#510—22no—
203#510—114no—
204#510—222no—
205#510C2×D1114yes—
206C2×Q32—21no—
207C2×Q32—221no—
208C2×SD32—21no—
209C2×SD32—221no—
210C2×M32—111no—
211C2×M32C2×D1111yescharacteristic
212#494—114no—
213#494—222no—
214#443—114no—
215#443—222no—
216C2×#108—111no—
217C2×#104—221no—
218C2×C4×C8—111no—
219#364—114no—
220#362—114no—
221#362—114no—
222C22×C11—22no—
223C22×C11—42no—
224C22×C11—82no—
225C22×C11#45911yescharacteristic
226C22×C11#45911yescharacteristic
227C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
228C4×C11—42no—
229C4×C11—82no—
230C4×C11#45911yescharacteristic
231C4×C11#45911yescharacteristic
232C4×C11C2×#12111yescharacteristic
233C4×C11C22×D811yescharacteristic
234Dic11—24no—
235Dic11—82no—
236C2×#41—21no—
237C22×Q8—21no—
238C22×Q8—221no—
239#135—21no—
240#135—21no—
241#135C22⋊D1112yes—
242#135C22×D1112yes—
243C2×Q16—21no—
244C2×Q16—21no—
245C2×Q16—21no—
246C2×Q16—21no—
247C2×Q16—21no—
248C2×Q16—112no—
249C2×Q16—224no—
250C2×Q16—221no—
251C2×Q16—221no—
252C2×Q16—221no—
253C2×Q16—221no—
254C2×Q16—221no—
255C2×Q16—441no—
256C2×Q16—441no—
257C2×Q16—442no—
258C2×Q16C22⋊D1111yescharacteristic
259C2×Q16C22×D1112yes—
260C2×SD16—21no—
261C2×D8C22⋊D1111yescharacteristic
262#131—224no—
263#131—442no—
264C2×M16—221no—
265C2×M16—441no—
266C22×C8—111no—
267C22×C8—441no—
268C22×C8C22×D1111yescharacteristic
269C4⋊Q8—224no—
270C4⋊Q8—442no—
271C2×C4⋊C4—442no—
272C2×C42—111no—
273Q32—24no—
274Q32—224no—
275SD32—24no—
276SD32—224no—
277M32—21no—
278M32—112no—
279M32—221no—
280M32C22×D1112yes—
281C2×C16—21no—
282C2×C16—221no—
283#108—112no—
284#108—221no—
285#104—224no—
286C4×C8—112no—
287C4×C8—112no—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—82no—
291C2×C11#221412yescomplemented
292C2×C11C2×#45911yescharacteristic
293#41—22no—
294#41—22no—
295#41—41no—
296#41—41no—
297C2×Q8—21no—
298C2×Q8—22no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—222no—
305C2×Q8—441no—
306C2×Q8—441no—
307C2×Q8—441no—
308C2×Q8—441no—
309C2×Q8—441no—
310C2×D4—21no—
311C2×D4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—221no—
315C22×C4—441no—
316C22×C4D4×D1111yescharacteristic
317Q16—21no—
318Q16—22no—
319Q16—22no—
320Q16—41no—
321Q16—41no—
322Q16—222no—
323Q16—222no—
324Q16—444no—
325Q16—444no—
326Q16—441no—
327Q16—441no—
328Q16C2×C22⋊D1112yes—
329SD16—22no—
330SD16—22no—
331D8—21no—
332D8C2×C22⋊D1112yes—
333M16—222no—
334M16—444no—
335M16—441no—
336C2×C8—111no—
337C2×C8—111no—
338C2×C8—112no—
339C2×C8—112no—
340C2×C8—444no—
341C2×C8—441no—
342C2×C8D4×D1111yescharacteristic
343C2×C8#434111yescharacteristic
344C2×C8#434111yescharacteristic
345C2×C8C2×C22⋊D1111yescharacteristic
346C2×C8C2×C22⋊D1111yescharacteristic
347C2×C8C23×D1111yescharacteristic
348C4⋊C4—448no—
349C42—112no—
350C42—221no—
351C16—22no—
352C16—222no—
353C11C2×#221411yescharacteristic, complemented, Sylow
354C23—41no—
355C23#6696411yescharacteristic
356Q8—22no—
357Q8—41no—
358Q8—42no—
359Q8—42no—
360Q8—81no—
361Q8—81no—
362Q8—442no—
363Q8—442no—
364Q8—881no—
365Q8—881no—
366D4—22no—
367D4—42no—
368D4—42no—
369D4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—224no—
377C2×C4—222no—
378C2×C4—442no—
379C2×C4—881no—
380C2×C4—881no—
381C2×C4D8×D1111yescharacteristic
382C2×C4D8×D1111yescharacteristic
383C2×C4#6696411yescharacteristic
384C2×C4#6699211yescharacteristic
385C2×C4#6699211yescharacteristic
386C2×C4C2×D4×D1111yescharacteristic
387C8—112no—
388C8—112no—
389C8—442no—
390C8#6699211yescharacteristic
391C8#6699211yescharacteristic
392C8C2×#434111yescharacteristic
393C8C22×C22⋊D1111yescharacteristic
394C22—22no—
395C22—42no—
396C22—82no—
397C22#1062276311yescharacteristic
398C22#1062276311yescharacteristic
399C22C2×#6696411yescharacteristic
400C4—42no—
401C4—82no—
402C4—224no—
403C4—882no—
404C4#1062276311yescharacteristic
405C4#1062276311yescharacteristic
406C4C2×D8×D1111yescharacteristic
407C4C2×#6699211yescharacteristic
408C2—21no—
409C2—21no—
410C2—82no—
411C2#1307069512yesdirect product factor
412C2C2×#1062276311yescharacteristic
subgroupG/H
centerC22#10622763
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#510C2
socleC22×C11#459
prime radicalC2×C11×#135C22
hypercenterC2×#510D11
hypocenterC11C2×#2214
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

Complements

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

NH ≅ G/Ntype
2. C2×#10622794C2semidirect
4. #13070695C2direct (N × H)
5. C2×#10622149C2semidirect
6. C2×#10622155C2semidirect
7. C2×#10622203C2semidirect
26. #10622794C22semidirect
32. #10622203C22semidirect
33. #10622155C22semidirect
34. #10622149C22semidirect
291. C2×C11#2214semidirect
353. C11C2×#2214semidirect
411. C2#13070695direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228082
C2×#106227942
C2×#106228092
#130706952
C2×#106221492
C2×#106221552
C2×#106222032
C2×C11×#5102
C2×#221411