Finite Group Databasebeta

← #14908370

Subgroups — #14908370

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×#10622808C211yesmaximal, characteristic, complemented
2#13081719C211yesmaximal, characteristic, complemented
3C2×#10622756C211yesmaximal, characteristic, complemented
4#13070744C214yesmaximal, complemented
5#13070739C214yesmaximal, complemented
6#13070410C211yesmaximal, characteristic, complemented
7#13070365C211yesmaximal, characteristic, complemented
8C2×#10622134C211yesmaximal, characteristic, complemented
9C11×#3067C211yesmaximal, characteristic
10C11×#575—21no—
11C2×C11×#135C2211yescharacteristic
12C2×C11×#131C2211yescharacteristic
13C2×#67004—21no—
14C22×Dic44C2211yescharacteristic
15C11×#473C2212yes—
16C11×#472C2212yes—
17C11×#471—22no—
18C2×C11×#108C2211yescharacteristic
19C11×#413—21no—
20#10622808—22no—
21#10622808—22no—
22C2×#66893C2212yescomplemented
23C2×#66891C2212yescomplemented
24#10622756—22no—
25#10622756C2214yes—
26#10622753—22no—
27#10622753C2214yes—
28C2×#66888—21no—
29C2×#66883C2211yescharacteristic
30C2×#66876—22no—
31C2×#66876C2211yescharacteristic
32C2×#66876C2211yescharacteristic
33#10622203C2212yescomplemented
34#10622201C2212yescomplemented
35#10622134C2214yescomplemented
36#10622131C2214yescomplemented
37C2×C11×#41—21no—
38C2×C11×#41D411yescharacteristic
39C22×Dic22—21no—
40C11×#137—22no—
41C11×#137—41no—
42C11×AGL(1,ℤ/8)—22no—
43C11×AGL(1,ℤ/8)—41no—
44C11×#135—21no—
45C11×#135—21no—
46C11×#135—21no—
47C11×#135—21no—
48C11×#135—42no—
49C2×C11×Q16C2311yescharacteristic
50C2×C11×SD16—21no—
51C2×C11×D8C2311yescharacteristic
52C11×#131—21no—
53C11×#131—21no—
54C11×#131D412yes—
55C11×#131C2312yes—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16D411yescharacteristic
59C22×C8×C11—21no—
60C22×C8×C11C2311yescharacteristic
61#67004—24no—
62#67004—42no—
63C2×#4326—41no—
64C2×#4324—41no—
65C2×#4318—21no—
66C2×Dic44—21no—
67C2×Dic44—21no—
68C2×Dic44—21no—
69C2×Dic44—21no—
70C2×Dic44—21no—
71C2×Dic44C2312yes—
72C11×#108—21no—
73C11×#108C2312yes—
74C11×#101—22no—
75C11×#100—22no—
76#66893—24no—
77#66891—24no—
78#66888—24no—
79#66883—21no—
80#66883C2312yes—
81#66876—21no—
82#66876—24no—
83#66876D412yes—
84#66876D412yes—
85#66876C2312yes—
86C2×C11⋊C16—21no—
87C2×C11⋊C16—24no—
88C2×C11⋊C16C2312yes—
89#33619—111nomaximal, Sylow
90C11×#41—21no—
91C11×#41—21no—
92C11×#41—41no—
93C11×#41—41no—
94C11×#41—41no—
95C11×#41—41no—
96C11×#41D812yes—
97C11×#41C2×D412yes—
98C2×Q8×C11—21no—
99C2×Q8×C11D811yescharacteristic
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—41no—
103C2×D4×C11D811yescharacteristic
104C22×C4×C11—21no—
105C22×C4×C11—41no—
106C22×C4×C11C2×D411yescharacteristic
107C22×Dic11—41no—
108C2×Dic22—22no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C2×Dic22—41no—
112C2×Dic22—41no—
113C2×Dic22—41no—
114C11×Q16—21no—
115C11×Q16—21no—
116C11×Q16—42no—
117C11×SD16—41no—
118C11×SD16—41no—
119C11×SD16—42no—
120C11×SD16—42no—
121C11×D8—21no—
122C11×D8—21no—
123C11×D8—42no—
124C11×M16—22no—
125C11×M16—22no—
126C11×M16—21no—
127C11×M16—22no—
128C11×M16—41no—
129C11×M16C2×D412yes—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—21no—
133C2×C8×C11—41no—
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11#4111yescharacteristic
138C2×C8×C11#4111yescharacteristic
139C2×C8×C11C2411yescharacteristic
140#4326—44no—
141#4324—44no—
142#4318—22no—
143#4318—41no—
144C2×C11⋊C8—41no—
145Dic44—22no—
146Dic44—22no—
147Dic44—41no—
148Dic44—41no—
149C11⋊C16—22no—
150C11⋊C16C2×D414yes—
151C2×#510—111no—
152#3407—111no—
153#3067D1111yescharacteristic
154C2×#473—111no—
155#2223—114no—
156#2222—114no—
157#2161—111no—
158#2148—111no—
159C2×#362—111no—
160C23×C11—21no—
161C23×C11—41no—
162C23×C11#13511yescharacteristic
163Q8×C11—21no—
164Q8×C11—41no—
165Q8×C11—41no—
166Q8×C11C2×D812yes—
167D4×C11—22no—
168D4×C11—22no—
169D4×C11—21no—
170D4×C11—41no—
171D4×C11—41no—
172D4×C11—81no—
173D4×C11—81no—
174D4×C11C2×D812yes—
175C2×C4×C11—21no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11C2×D811yescharacteristic
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11#13511yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×Dic11—42no—
188C2×Dic11—81no—
189C2×Dic11—81no—
190Dic22—42no—
191Dic22—42no—
192Dic22—81no—
193Dic22—81no—
194C8×C11—22no—
195C8×C11—42no—
196C8×C11#12111yescharacteristic
197C8×C11#12111yescharacteristic
198C8×C11C22×D411yescharacteristic
199C8×C11C2×#4111yescharacteristic
200C11⋊C8—42no—
201#575—21no—
202C2×#137—221no—
203C2×#135C2×D1111yescharacteristic
204C22×Q16—111no—
205C2×#131C2×D1111yescharacteristic
206#510—222no—
207#510—222no—
208C2×Q32—112no—
209C2×SD32—112no—
210#504—114no—
211#504—222no—
212C2×M32—111no—
213C2×M32—111no—
214C2×M32—222no—
215#473—114no—
216#473—222no—
217#473C2×D1112yes—
218#472C2×D1112yes—
219#471—22no—
220C2×#108—111no—
221C2×#108C2×D1111yescharacteristic
222#413—21no—
223C2×#101—221no—
224#368—114no—
225#362—112no—
226#362—114no—
227#361—112no—
228C22×C11—22no—
229C22×C11—41no—
230C22×C11—81no—
231C22×C11—81no—
232C22×C11—161no—
233C22×C11#46611yescharacteristic
234C22×C11#46611yescharacteristic
235C22×C11C2×#13511yescharacteristic
236C4×C11—22no—
237C4×C11—81no—
238C4×C11#46611yescharacteristic
239C4×C11#46611yescharacteristic
240C4×C11C2×#12111yescharacteristic
241C4×C11C22×D811yescharacteristic
242Dic11—82no—
243C2×#41—21no—
244C2×#41C22⋊D1111yescharacteristic
245C22×Q8—221no—
246#137—22no—
247#137—41no—
248#137—224no—
249#137—442no—
250AGL(1,ℤ/8)—22no—
251AGL(1,ℤ/8)—41no—
252#135—21no—
253#135—21no—
254#135—21no—
255#135—21no—
256#135—42no—
257C2×Q16—112no—
258C2×Q16—221no—
259C2×Q16—221no—
260C2×Q16—221no—
261C2×Q16—221no—
262C2×Q16—221no—
263C2×Q16—441no—
264C2×Q16C22×D1111yescharacteristic
265C2×SD16—21no—
266C2×SD16—441no—
267C2×D8C22×D1111yescharacteristic
268#131—21no—
269#131—21no—
270#131C22⋊D1112yes—
271#131C22×D1112yes—
272C2×M16—21no—
273C2×M16—21no—
274C2×M16—221no—
275C2×M16C22⋊D1111yescharacteristic
276C22×C8—21no—
277C22×C8C22×D1111yescharacteristic
278Q32—224no—
279SD32—224no—
280M32—112no—
281M32—112no—
282M32—112no—
283M32—224no—
284M32—221no—
285C2×C16—112no—
286C2×C16—224no—
287C2×C16—221no—
288#108—21no—
289#108—112no—
290#108—221no—
291#108C22×D1112yes—
292#101—22no—
293#101—224no—
294#100—22no—
295C2×C11—21no—
296C2×C11—21no—
297C2×C11—21no—
298C2×C11—42no—
299C2×C11—161no—
300C2×C11C2×#46611yescharacteristic
301#41—21no—
302#41—21no—
303#41—41no—
304#41—41no—
305#41—41no—
306#41—41no—
307#41#432312yes—
308#41C2×C22⋊D1112yes—
309C2×Q8—21no—
310C2×Q8—222no—
311C2×Q8—441no—
312C2×Q8—441no—
313C2×Q8—441no—
314C2×Q8—441no—
315C2×Q8—441no—
316C2×Q8#432311yescharacteristic
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—41no—
320C2×D4#432311yescharacteristic
321C22×C4—21no—
322C22×C4—41no—
323C22×C4—441no—
324C22×C4C2×C22⋊D1111yescharacteristic
325Q16—21no—
326Q16—21no—
327Q16—42no—
328Q16—222no—
329Q16—222no—
330Q16—444no—
331Q16—441no—
332Q16—441no—
333SD16—42no—
334SD16—42no—
335SD16—41no—
336SD16—41no—
337SD16—444no—
338D8—21no—
339D8—21no—
340D8—42no—
341M16—21no—
342M16—22no—
343M16—22no—
344M16—22no—
345M16—41no—
346M16—222no—
347M16—441no—
348M16C2×C22⋊D1112yes—
349C2×C8—21no—
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—41no—
353C2×C8—441no—
354C2×C8D4×D1111yescharacteristic
355C2×C8D4×D1111yescharacteristic
356C2×C8#434111yescharacteristic
357C2×C8#434111yescharacteristic
358C2×C8C2×C22⋊D1111yescharacteristic
359C2×C8C23×D1111yescharacteristic
360C16—114no—
361C16—222no—
362C11#3361911yescharacteristic, complemented, Sylow
363C23—21no—
364C23—41no—
365C23#6700311yescharacteristic
366Q8—21no—
367Q8—41no—
368Q8—41no—
369Q8—442no—
370Q8—442no—
371Q8—881no—
372Q8—881no—
373Q8C2×#432312yes—
374D4—22no—
375D4—22no—
376D4—21no—
377D4—41no—
378D4—41no—
379D4—81no—
380D4—81no—
381D4C2×#432312yes—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—442no—
389C2×C4—881no—
390C2×C4—881no—
391C2×C4C2×#432311yescharacteristic
392C2×C4C2×#432311yescharacteristic
393C2×C4#6699211yescharacteristic
394C2×C4#6699211yescharacteristic
395C2×C4#6700311yescharacteristic
396C2×C4C22×C22⋊D1111yescharacteristic
397C8—22no—
398C8—42no—
399C8—442no—
400C8#6699211yescharacteristic
401C8#6699211yescharacteristic
402C8C2×D4×D1111yescharacteristic
403C8C2×#434111yescharacteristic
404C22—22no—
405C22—41no—
406C22—81no—
407C22—81no—
408C22—161no—
409C22#1062265111yescharacteristic
410C22#1062265111yescharacteristic
411C22C2×#6700311yescharacteristic
412C4—22no—
413C4—81no—
414C4—882no—
415C4#1062265111yescharacteristic
416C4#1062265111yescharacteristic
417C4C22×#432311yescharacteristic
418C4C2×#6699211yescharacteristic
419C2—21no—
420C2—21no—
421C2—21no—
422C2—42no—
423C2—161no—
424C2C2×#1062265111yescharacteristic
subgroupG/H
centerC2C2×#10622651
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3067C2
socleC2×C11C2×#466
hypercenter#3067D11
hypocenterC11#33619
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3067

Complements

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

NH ≅ G/Ntype
1. C2×#10622808C2semidirect
2. #13081719C2semidirect
3. C2×#10622756C2semidirect
4. #13070744C2semidirect
5. #13070739C2semidirect
6. #13070410C2semidirect
7. #13070365C2semidirect
8. C2×#10622134C2semidirect
22. C2×#66893C22semidirect
23. C2×#66891C22semidirect
33. #10622203C22semidirect
34. #10622201C22semidirect
35. #10622134C22semidirect
36. #10622131C22semidirect
362. C11#33619semidirect

Maximal subgroups

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

subgroupindex
C2×#106228082
#130817192
C2×#106227562
#130707442
#130707392
#130704102
#130703652
C2×#106221342
C11×#30672
#3361911