Finite Group Databasebeta

← #14908368

Subgroups — #14908368

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
1C2×#10622522C211yesmaximal, characteristic, complemented
2#13078336C211yesmaximal, characteristic
3C2×#10622756C211yesmaximal, characteristic, complemented
4#13070746C214yesmaximal, complemented
5#13070741C214yesmaximal, complemented
6#13070411C211yesmaximal, characteristic, complemented
7#13070366C211yesmaximal, characteristic, complemented
8C2×#10622155C211yesmaximal, characteristic, complemented
9C11×#3407C211yesmaximal, characteristic, complemented
10C2×C11×#131C2211yescharacteristic
11C2×#67004—21no—
12#10623353—21no—
13C22×Dic44C2211yescharacteristic
14C2×#66957C2211yescharacteristic
15C11×#504—22no—
16C11×#504C2214yes—
17C2×C11×M32—22no—
18C2×C11×M32C2211yescharacteristic
19C2×C11×M32C2211yescharacteristic
20#10622756—22no—
21#10622756C2214yes—
22#10622756C2212yes—
23#10622755C2212yes—
24#10622754—22no—
25C2×#66888—21no—
26#10622745—21no—
27C2×#66883C2211yescharacteristic
28C2×#66883C2211yescharacteristic
29#10622522—22no—
30#10622522—22no—
31C2×Dic88C2212yescomplemented
32C2×#66864C2212yescomplemented
33#10622155C2214yescomplemented
34#10622155C2212yescomplemented
35#10622154C2212yescomplemented
36#10622144C2214yescomplemented
37C2×C11×#41D411yescharacteristic
38C2×#4339—21no—
39C22×Dic22—21no—
40C11×#131—21no—
41C11×#131—21no—
42C11×#131D412yes—
43C11×#131C2312yes—
44C2×C11×M16—21no—
45C2×C11×M16D411yescharacteristic
46C22×C8×C11—21no—
47C22×C8×C11C2311yescharacteristic
48#67004—22no—
49#67004—24no—
50#67004—42no—
51#67003—42no—
52#67002—22no—
53C2×#4326—41no—
54#66995—41no—
55C2×#4324—41no—
56#66985—41no—
57C2×#4318—21no—
58C2×#4318—21no—
59C2×Dic44—21no—
60C2×Dic44—21no—
61C2×Dic44—21no—
62C2×Dic44—21no—
63C2×Dic44—21no—
64C2×Dic44C2311yescharacteristic
65C2×Dic44C2312yes—
66#66957—21no—
67#66957—21no—
68#66957—21no—
69#66957—21no—
70C2×D88C2311yescharacteristic
71C2×#4314—21no—
72C11×M32—21no—
73C11×M32—24no—
74C11×M32D412yes—
75C11×M32D412yes—
76C11×M32C2312yes—
77C2×C11×C16—21no—
78C2×C11×C16—24no—
79C2×C11×C16C2312yes—
80#66888—22no—
81#66888—24no—
82#66887—22no—
83#66883—21no—
84#66883—21no—
85#66883C2312yes—
86#66883C2312yes—
87Dic88—24no—
88#66864—24no—
89#33619—111nomaximal, Sylow
90C11×#41—21no—
91C11×#41—21no—
92C11×#41D812yes—
93C11×#41C2×D412yes—
94C2×Q8×C11D811yescharacteristic
95C2×D4×C11—21no—
96C2×D4×C11D811yescharacteristic
97C22×C4×C11—21no—
98C22×C4×C11C2×D411yescharacteristic
99C2×C22⋊D11—41no—
100C22×Dic11—41no—
101#4339—41no—
102#4339—41no—
103#4339—41no—
104#4339—41no—
105C2×D44—21no—
106C2×C4×D11—41no—
107C2×Dic22—21no—
108C2×Dic22—22no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C2×Dic22—41no—
112C2×Dic22—41no—
113C2×Dic22—41no—
114C11×M16—22no—
115C11×M16—22no—
116C11×M16—21no—
117C11×M16C2×D412yes—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—21no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11#4111yescharacteristic
125C2×C8×C11#4111yescharacteristic
126C2×C8×C11C2411yescharacteristic
127#4326—42no—
128#4326—44no—
129#4325—42no—
130#4324—42no—
131#4324—44no—
132#4323—42no—
133#4318—22no—
134#4318—22no—
135#4318—41no—
136#4318—41no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8—41no—
139Dic44—22no—
140Dic44—21no—
141Dic44—21no—
142Dic44—22no—
143Dic44—41no—
144Dic44—41no—
145D88—21no—
146D88—21no—
147#4314—41no—
148#4314—41no—
149C11×C16—22no—
150C11×C16C2×D414yes—
151C2×#510—111no—
152#3407D1111yescharacteristic, complemented
153#3067—111no—
154C2×#473—111no—
155#2223—114no—
156#2222—114no—
157#2161—111no—
158#2148—111no—
159C2×#362—111no—
160C23×C11—21no—
161C23×C11#13511yescharacteristic
162C22×D11—41no—
163Q8×C11—21no—
164Q8×C11C2×D812yes—
165D4×C11—22no—
166D4×C11—22no—
167D4×C11—21no—
168D4×C11C2×D812yes—
169C2×C4×C11—21no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11#13511yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C22⋊D11—81no—
179C22⋊D11—81no—
180C2×Dic11—42no—
181C2×Dic11—41no—
182C2×Dic11—81no—
183C2×Dic11—81no—
184D44—41no—
185D44—41no—
186C4×D11—81no—
187C4×D11—81no—
188Dic22—41no—
189Dic22—42no—
190Dic22—42no—
191Dic22—41no—
192Dic22—81no—
193Dic22—81no—
194C8×C11—22no—
195C8×C11#12111yescharacteristic
196C8×C11#12111yescharacteristic
197C8×C11C22×D411yescharacteristic
198C8×C11C2×#4111yescharacteristic
199C11⋊C8—42no—
200C11⋊C8—42no—
201#575—221no—
202C2×#137—221no—
203C2×#135—111no—
204C22×Q16—111no—
205C2×#131C2×D1111yescharacteristic
206#510—222no—
207#510—222no—
208C2×Q32—112no—
209C2×SD32—112no—
210#504—22no—
211#504C2×D1114yes—
212C2×M32—22no—
213C2×M32C2×D1111yescharacteristic
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—22no—
229C22×C11—41no—
230C22×C11—81no—
231C22×C11#46611yescharacteristic
232C22×C11#46611yescharacteristic
233C22×C11C2×#13511yescharacteristic
234C2×D11—81no—
235C2×D11—161no—
236C4×C11—22no—
237C4×C11#46611yescharacteristic
238C4×C11#46611yescharacteristic
239C4×C11C2×#12111yescharacteristic
240C4×C11C22×D811yescharacteristic
241Dic11—82no—
242Dic11—81no—
243C2×#41—221no—
244C2×#41D4411yescharacteristic
245C22×Q8—221no—
246#137—224no—
247#137—222no—
248#137—442no—
249#137—441no—
250AGL(1,ℤ/8)—222no—
251AGL(1,ℤ/8)—441no—
252#135—221no—
253#135—221no—
254#135—221no—
255#135—221no—
256#135—442no—
257C2×Q16—112no—
258C2×Q16—111no—
259C2×Q16—221no—
260C2×Q16—221no—
261C2×Q16—221no—
262C2×Q16—221no—
263C2×Q16—221no—
264C2×Q16—441no—
265C2×SD16—221no—
266C2×SD16—441no—
267C2×D8—111no—
268#131—21no—
269#131—21no—
270#131D4412yes—
271#131C22×D1112yes—
272C2×M16—21no—
273C2×M16—221no—
274C2×M16—221no—
275C2×M16D4411yescharacteristic
276C22×C8—21no—
277C22×C8C22×D1111yescharacteristic
278Q32—224no—
279SD32—224no—
280M32—21no—
281M32—24no—
282M32C22⋊D1112yes—
283M32C22⋊D1112yes—
284M32C22×D1112yes—
285C2×C16—21no—
286C2×C16—24no—
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—42no—
299C2×C11C2×#46611yescharacteristic
300D11—161no—
301#41—21no—
302#41—21no—
303#41—441no—
304#41—441no—
305#41—441no—
306#41—441no—
307#41D8812yes—
308#41C2×D4412yes—
309C2×Q8—221no—
310C2×Q8—222no—
311C2×Q8—441no—
312C2×Q8—441no—
313C2×Q8—441no—
314C2×Q8—441no—
315C2×Q8—441no—
316C2×Q8D8811yescharacteristic
317C2×D4—21no—
318C2×D4—221no—
319C2×D4—441no—
320C2×D4D8811yescharacteristic
321C22×C4—21no—
322C22×C4—441no—
323C22×C4—441no—
324C22×C4C2×D4411yescharacteristic
325Q16—222no—
326Q16—221no—
327Q16—222no—
328Q16—221no—
329Q16—444no—
330Q16—442no—
331Q16—441no—
332Q16—441no—
333SD16—442no—
334SD16—444no—
335SD16—442no—
336SD16—441no—
337SD16—441no—
338D8—221no—
339D8—221no—
340D8—442no—
341M16—21no—
342M16—22no—
343M16—22no—
344M16—222no—
345M16—222no—
346M16—441no—
347M16—441no—
348M16C2×D4412yes—
349C2×C8—21no—
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—441no—
353C2×C8—441no—
354C2×C8C2×D4411yescharacteristic
355C2×C8#433911yescharacteristic
356C2×C8#433911yescharacteristic
357C2×C8C2×C22⋊D1111yescharacteristic
358C2×C8C2×C22⋊D1111yescharacteristic
359C2×C8C23×D1111yescharacteristic
360C16—22no—
361C16C2×C22⋊D1114yes—
362C11#3361911yescharacteristic, complemented, Sylow
363C23—21no—
364C23—441no—
365C23#6695711yescharacteristic
366Q8—21no—
367Q8—442no—
368Q8—441no—
369Q8—441no—
370Q8—442no—
371Q8—881no—
372Q8—881no—
373Q8C2×D8812yes—
374D4—22no—
375D4—22no—
376D4—21no—
377D4—441no—
378D4—441no—
379D4—881no—
380D4—881no—
381D4C2×D8812yes—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—441no—
386C2×C4—442no—
387C2×C4—881no—
388C2×C4—881no—
389C2×C4—881no—
390C2×C4—881no—
391C2×C4C2×D8811yescharacteristic
392C2×C4C2×D8811yescharacteristic
393C2×C4#6695711yescharacteristic
394C2×C4#6698311yescharacteristic
395C2×C4#6698311yescharacteristic
396C2×C4C22×D4411yescharacteristic
397C8—22no—
398C8—442no—
399C8—442no—
400C8#6698311yescharacteristic
401C8#6698311yescharacteristic
402C8C2×#433911yescharacteristic
403C8C22×C22⋊D1111yescharacteristic
404C22—22no—
405C22—41no—
406C22—81no—
407C22—881no—
408C22—1761no—
409C22#1062272811yescharacteristic
410C22#1062272811yescharacteristic
411C22C2×#6695711yescharacteristic
412C4—22no—
413C4—881no—
414C4—882no—
415C4#1062272811yescharacteristic
416C4#1062272811yescharacteristic
417C4C22×D8811yescharacteristic
418C4C2×#6698311yescharacteristic
419C2—21no—
420C2—21no—
421C2—21no—
422C2—42no—
423C2—1761no—
424C2C2×#1062272811yescharacteristic
subgroupG/H
centerC2C2×#10622728
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3407C2
socleC2×C11C2×#466
prime radical#13078336C2
hypercenter#3407D11
hypocenterC11#33619
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3407

Complements

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

NH ≅ G/Ntype
1. C2×#10622522C2semidirect
3. C2×#10622756C2semidirect
4. #13070746C2semidirect
5. #13070741C2semidirect
6. #13070411C2semidirect
7. #13070366C2semidirect
8. C2×#10622155C2semidirect
9. C11×#3407C2semidirect
31. C2×Dic88C22semidirect
32. C2×#66864C22semidirect
33. #10622155C22semidirect
34. #10622155C22semidirect
35. #10622154C22semidirect
36. #10622144C22semidirect
152. #3407D11semidirect
362. C11#33619semidirect

Maximal subgroups

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

subgroupindex
C2×#106225222
#130783362
C2×#106227562
#130707462
#130707412
#130704112
#130703662
C2×#106221552
C11×#34072
#3361911