Finite Group Databasebeta

← #14908364

Subgroups — #14908364

Order 2816.

636 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081718C211yesmaximal, characteristic, complemented
2#13078332C211yesmaximal, characteristic
3C2×#10622805C211yesmaximal, characteristic, complemented
4#13070743C214yesmaximal, complemented
5#13070738C214yesmaximal, complemented
6#13070411C211yesmaximal, characteristic, complemented
7#13070365C211yesmaximal, characteristic, complemented
8C2×#10622203C211yesmaximal, characteristic, complemented
9C2×C11×#510C211yesmaximal, characteristic, complemented
10C2×C11×#135C2211yescharacteristic
11C22×C11×Q16C2211yescharacteristic
12#10623353—21no—
13C2×#66995—21no—
14C2×#66954C2211yescharacteristic
15C11×#510—22no—
16C11×#510—22no—
17C2×C11×Q32C2212yescomplemented
18C2×C11×SD32C2212yescomplemented
19C2×C11×M32C2211yescharacteristic
20#10622850—21no—
21C2×#66900—21no—
22#10622805—22no—
23#10622805C2214yes—
24#10622805C2212yes—
25#10622790—22no—
26#10622773C2212yes—
27C2×#66883C2211yescharacteristic
28C2×#66883C2211yescharacteristic
29C2×#66876C2211yescharacteristic
30#10622520—22no—
31D11×M32—22no—
32#10622514C2214yes—
33#10622203C2214yescomplemented
34#10622203C2212yescomplemented
35#10622201C2212yescomplemented
36#10622144C2214yescomplemented
37C2×C11×#41—21no—
38C22×Q8×C11—21no—
39C2×#4339D411yescharacteristic
40C11×#135—21no—
41C11×#135—21no—
42C11×#135—21no—
43C11×#135—21no—
44C2×C11×Q16—21no—
45C2×C11×Q16—21no—
46C2×C11×Q16—21no—
47C2×C11×Q16—21no—
48C2×C11×Q16—21no—
49C2×C11×Q16C2312yes—
50C2×C11×Q16C2311yescharacteristic
51C2×C11×SD16—21no—
52C2×C11×D8C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54#67004—41no—
55#67003—42no—
56#67002—41no—
57C2×#4326—41no—
58#66995—22no—
59#66995—24no—
60#66995—42no—
61C2×#4325—41no—
62#66985—22no—
63C2×#4318—21no—
64C2×#4318—21no—
65C2×#4318D411yescharacteristic
66#66954—21no—
67#66954—21no—
68#66954D412yes—
69#66954C2312yes—
70C2×#4313—21no—
71C2×C8×D11—21no—
72C11×Q32—24no—
73C11×SD32—24no—
74C11×M32D412yes—
75C11×M32D412yes—
76C2×C11×C16C2312yes—
77#66900—22no—
78#66900—24no—
79#66897—22no—
80#66883—21no—
81#66883—21no—
82#66883C2312yes—
83#66883C2312yes—
84#66876—21no—
85#66876C2312yes—
86C2×C11⋊C16—21no—
87#66862—24no—
88C16×D11—24no—
89#33619—111nomaximal, Sylow
90C11×#41—41no—
91C11×#41—41no—
92C11×#41—41no—
93C11×#41—41no—
94C2×Q8×C11—21no—
95C2×Q8×C11—22no—
96C2×Q8×C11—41no—
97C2×Q8×C11—41no—
98C2×Q8×C11—41no—
99C2×Q8×C11—41no—
100C2×Q8×C11—41no—
101C2×D4×C11—21no—
102C2×D4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11C2×D411yescharacteristic
106C2×C22⋊D11—21no—
107#4339—21no—
108#4339—21no—
109#4339D812yes—
110#4339C2×D412yes—
111C2×D44D811yescharacteristic
112C2×C4×D11—21no—
113C2×Dic22D811yescharacteristic
114C11×Q16—22no—
115C11×Q16—21no—
116C11×Q16—22no—
117C11×Q16—21no—
118C11×Q16—41no—
119C11×Q16—41no—
120C11×SD16—41no—
121C11×SD16—41no—
122C11×D8—21no—
123C11×D8—21no—
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11#4111yescharacteristic
128C2×C8×C11#4111yescharacteristic
129C2×C8×C11C2411yescharacteristic
130#4326—44no—
131#4326—42no—
132#4325—44no—
133#4325—42no—
134#4324—42no—
135#4323—42no—
136#4318—21no—
137#4318—22no—
138#4318—22no—
139#4318—41no—
140#4318—41no—
141#4318C2×D412yes—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145#4313—22no—
146#4313—22no—
147C8×D11—22no—
148C8×D11—22no—
149C11×C16C2×D414yes—
150C11⋊C16—22no—
151C2×#510D1111yescharacteristic, complemented
152#3407—111no—
153#3067—111no—
154C2×#473—111no—
155#2223—114no—
156#2222—114no—
157#2161—111no—
158#2148—111no—
159C2×#362—111no—
160C23×C11—41no—
161C23×C11#13511yescharacteristic
162C22×D11—21no—
163Q8×C11—41no—
164Q8×C11—42no—
165Q8×C11—42no—
166Q8×C11—41no—
167Q8×C11—81no—
168Q8×C11—81no—
169D4×C11—41no—
170D4×C11—41no—
171D4×C11—81no—
172D4×C11—81no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11#13511yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C22⋊D11—22no—
186C22⋊D11—22no—
187C2×Dic11—21no—
188D44—21no—
189D44C2×D812yes—
190C4×D11—22no—
191C4×D11—22no—
192Dic22—21no—
193Dic22C2×D812yes—
194C8×C11#12111yescharacteristic
195C8×C11#12111yescharacteristic
196C8×C11C22×D411yescharacteristic
197C8×C11C2×#4111yescharacteristic
198C11⋊C8—22no—
199C11⋊C8—42no—
200C11⋊C8—42no—
201#575—221no—
202C2×#137—221no—
203C2×#135C2×D1111yescharacteristic
204C22×Q16C2×D1111yescharacteristic
205C2×#131—111no—
206#510—22no—
207#510—22no—
208C2×Q32C2×D1112yescomplemented
209C2×SD32C2×D1112yescomplemented
210#504—114no—
211#504—222no—
212C2×M32—111no—
213C2×M32—222no—
214C2×M32C2×D1111yescharacteristic
215#473—112no—
216#473—114no—
217#473—222no—
218#472—112no—
219#471—222no—
220C2×#108—111no—
221C2×#108—111no—
222#413—221no—
223C2×#101—221no—
224#368—114no—
225#362—114no—
226#362—112no—
227#361—112no—
228C22×C11—41no—
229C22×C11—81no—
230C22×C11—161no—
231C22×C11#46611yescharacteristic
232C22×C11#46611yescharacteristic
233C22×C11C2×#13511yescharacteristic
234C2×D11—22no—
235C2×D11—81no—
236C4×C11—81no—
237C4×C11—82no—
238C4×C11#46611yescharacteristic
239C4×C11#46611yescharacteristic
240C4×C11C2×#12111yescharacteristic
241C4×C11C22×D811yescharacteristic
242Dic11—22no—
243C2×#41—21no—
244C2×#41—111no—
245C22×Q8—21no—
246#137—224no—
247#137—222no—
248#137—442no—
249#137—441no—
250AGL(1,ℤ/8)—222no—
251AGL(1,ℤ/8)—441no—
252#135—21no—
253#135—21no—
254#135—21no—
255#135—21no—
256#135—442no—
257C2×Q16—21no—
258C2×Q16—21no—
259C2×Q16—21no—
260C2×Q16—21no—
261C2×Q16—21no—
262C2×Q16—441no—
263C2×Q16C22×D1112yes—
264C2×Q16C22×D1111yescharacteristic
265C2×SD16—21no—
266C2×SD16—441no—
267C2×D8C22×D1111yescharacteristic
268#131—112no—
269#131—112no—
270#131—221no—
271#131—221no—
272C2×M16—111no—
273C2×M16—221no—
274C2×M16—221no—
275C2×M16—221no—
276C22×C8—221no—
277C22×C8C22×D1111yescharacteristic
278Q32—24no—
279SD32—24no—
280M32—112no—
281M32—221no—
282M32—224no—
283M32C22⋊D1112yes—
284M32C22⋊D1112yes—
285C2×C16—221no—
286C2×C16—224no—
287C2×C16C22×D1112yes—
288#108—112no—
289#108—112no—
290#108—221no—
291#108—221no—
292#101—224no—
293#101—222no—
294#100—222no—
295C2×C11—21no—
296C2×C11—21no—
297C2×C11—21no—
298C2×C11—161no—
299C2×C11C2×#46611yescharacteristic
300D11—42no—
301#41—41no—
302#41—41no—
303#41—41no—
304#41—41no—
305#41—112no—
306#41—112no—
307#41—221no—
308#41—221no—
309C2×Q8—21no—
310C2×Q8—22no—
311C2×Q8—41no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×Q8—111no—
317C2×D4—21no—
318C2×D4—41no—
319C2×D4—111no—
320C2×D4—221no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—221no—
324C22×C4D4×D1111yescharacteristic
325Q16—22no—
326Q16—21no—
327Q16—22no—
328Q16—21no—
329Q16—41no—
330Q16—41no—
331Q16—444no—
332Q16—442no—
333SD16—41no—
334SD16—41no—
335SD16—442no—
336SD16—444no—
337SD16—442no—
338D8—21no—
339D8—21no—
340D8—442no—
341M16—112no—
342M16—221no—
343M16—222no—
344M16—222no—
345M16—222no—
346M16—222no—
347M16—441no—
348M16—441no—
349C2×C8—221no—
350C2×C8—222no—
351C2×C8—222no—
352C2×C8—441no—
353C2×C8—441no—
354C2×C8D4×D1111yescharacteristic
355C2×C8#434111yescharacteristic
356C2×C8#434111yescharacteristic
357C2×C8C2×C22⋊D1111yescharacteristic
358C2×C8C2×C22⋊D1111yescharacteristic
359C2×C8C23×D1111yescharacteristic
360C16—222no—
361C16C2×C22⋊D1114yes—
362C11#3361911yescharacteristic, complemented, Sylow
363C23—41no—
364C23—221no—
365C23#6696511yescharacteristic
366Q8—42no—
367Q8—41no—
368Q8—41no—
369Q8—42no—
370Q8—81no—
371Q8—81no—
372Q8—112no—
373Q8—221no—
374D4—41no—
375D4—41no—
376D4—81no—
377D4—81no—
378D4—112no—
379D4—222no—
380D4—222no—
381D4—221no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—221no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4D8×D1111yescharacteristic
392C2×C4D8×D1111yescharacteristic
393C2×C4#6696511yescharacteristic
394C2×C4#6699111yescharacteristic
395C2×C4#6699111yescharacteristic
396C2×C4C2×D4×D1111yescharacteristic
397C8—222no—
398C8—442no—
399C8—442no—
400C8#6699111yescharacteristic
401C8#6699111yescharacteristic
402C8C2×#434111yescharacteristic
403C8C22×C22⋊D1111yescharacteristic
404C22—41no—
405C22—81no—
406C22—161no—
407C22—222no—
408C22—881no—
409C22#1062277011yescharacteristic
410C22#1062277011yescharacteristic
411C22C2×#6696511yescharacteristic
412C4—81no—
413C4—82no—
414C4—222no—
415C4#1062277011yescharacteristic
416C4#1062277011yescharacteristic
417C4C2×D8×D1111yescharacteristic
418C4C2×#6699111yescharacteristic
419C2—21no—
420C2—21no—
421C2—21no—
422C2—161no—
423C2—442no—
424C2C2×#1062277011yescharacteristic
subgroupG/H
centerC2C2×#10622770
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#510C2
socleC2×C11C2×#466
prime radical#13078332C2
hypercenterC2×#510D11
hypocenterC11#33619
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

Complements

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

NH ≅ G/Ntype
1. #13081718C2semidirect
3. C2×#10622805C2semidirect
4. #13070743C2semidirect
5. #13070738C2semidirect
6. #13070411C2semidirect
7. #13070365C2semidirect
8. C2×#10622203C2semidirect
9. C2×C11×#510C2semidirect
17. C2×C11×Q32C22semidirect
18. C2×C11×SD32C22semidirect
33. #10622203C22semidirect
34. #10622203C22semidirect
35. #10622201C22semidirect
36. #10622144C22semidirect
151. C2×#510D11semidirect
208. C2×Q32C2×D11semidirect
209. C2×SD32C2×D11semidirect
362. C11#33619semidirect

Maximal subgroups

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

subgroupindex
#130817182
#130783322
C2×#106228052
#130707432
#130707382
#130704112
#130703652
C2×#106222032
C2×C11×#5102
#3361911