Finite Group Databasebeta

← #14672123

Subgroups — #14672123

Order 2816.

448 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078257C211yesmaximal, characteristic
2#13070311C211yesmaximal, characteristic, complemented
3#13070307C211yesmaximal, characteristic
4#13070265C211yesmaximal, characteristic
5#13068664C211yesmaximal, characteristic, complemented
6#13068418C211yesmaximal, characteristic, complemented
7C11×#2123C211yesmaximal, characteristic, complemented
8C11×#536C2211yescharacteristic
9#10623361C2211yescharacteristic
10C2×#67001C2211yescharacteristic
11C22×#4325C411yescharacteristic, complemented
12C11×#413C2211yescharacteristic
13C11×#410C2211yescharacteristic
14#10622850C2211yescharacteristic
15#10622850C2211yescharacteristic
16#10622838C411yescharacteristic, complemented
17C2×#66886—21no—
18#10622662—21no—
19#10622662—21no—
20#10622661—21no—
21#10622661—21no—
22#10622614C411yescharacteristic, complemented
23#10622611C411yescharacteristic, complemented
24#10622610—21no—
25C11×#352—22no—
26C11⋊#338—21no—
27#10622186—22no—
28#10622171—21no—
29#10622115—22no—
30#10622109—22no—
31C2×C11×#41C2311yescharacteristic
32C22×Q8×C11C2×C411yescharacteristic
33C22×D44C2×C411yescharacteristic
34C2×C11×M16—21no—
35C11×C4⋊Q8—21no—
36C11×#124—21no—
37C11×#123—21no—
38C11×#123—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×#117—21no—
42C11×#117C2×C411yescharacteristic
43#67001—41no—
44#67001—41no—
45#67000—21no—
46C2×#4325—21no—
47C2×#4325—21no—
48C2×#4325—41no—
49C2×#4325—41no—
50#66993—21no—
51#66990—21no—
52#66990—21no—
53#66983—21no—
54#66983—21no—
55#66979C2×C411yescharacteristic
56C2×#4318—21no—
57C2×#4318—21no—
58C2×#4318C2×C411yescharacteristic
59C2×#4318D411yescharacteristic
60C2×#4318D411yescharacteristic
61C22×C11⋊C8C2×C411yescharacteristic
62C22×C11⋊C8D411yescharacteristic
63C22×C11⋊C8D411yescharacteristic
64C11×#101—21no—
65C11×#100—21no—
66C11×#99—21no—
67C11×#99D412yes—
68#66900—21no—
69#66900D412yes—
70#66899—21no—
71#66899—21no—
72#66897—21no—
73#66897—21no—
74#66886—41no—
75#66886—41no—
76#66873—21no—
77#66873—21no—
78#66872—21no—
79#66871—21no—
80#66867—41no—
81C4×C11⋊C8—41no—
82#13232—111nomaximal, Sylow
83C23×D11—21no—
84C11×#41—41no—
85C11×#41—41no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×Q8×C11C2×D411yescharacteristic
91C2×D4×C11C2×D411yescharacteristic
92C2×D4×C11#4111yescharacteristic
93C2×D4×C11#4111yescharacteristic
94C22×C4×C11—21no—
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C2×C22⋊D11—41no—
99C2×C22⋊D11—41no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—41no—
103C2×D44—41no—
104C11×M16—41no—
105C11×M16—41no—
106C2×C8×C11—41no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—21no—
112C11×C22⋊C4—22no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C42×C11—21no—
116C42×C11—41no—
117C22⋊Dic11—21no—
118#4325—42no—
119#4325—41no—
120#4325—41no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123C4⋊Dic11—21no—
124C4×Dic11—21no—
125#4318—22no—
126#4318—41no—
127#4318—41no—
128#4318—41no—
129#4318—41no—
130#4318—41no—
131#4318—41no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8—21no—
136C2×C11⋊C8—21no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—41no—
139C2×C11⋊C8—41no—
140C2×C11⋊C8C22⋊C411yescharacteristic
141C2×C11⋊C8C22⋊C411yescharacteristic
142C2×C11⋊C8C22⋊C411yescharacteristic
143C2×C11⋊C8C22⋊C411yescharacteristic
144#3057—111no—
145#2135—111no—
146#2134—111no—
147#2123D1111yescharacteristic, complemented
148#2122—111no—
149#1813—111no—
150#1757—111no—
151C23×C11C4×D411yescharacteristic
152C23×C11#12111yescharacteristic
153C23×C11#12411yescharacteristic
154C22×D11—41no—
155C22×D11—81no—
156C22×D11—161no—
157Q8×C11—41no—
158Q8×C11—41no—
159Q8×C11—41no—
160Q8×C11—81no—
161D4×C11—41no—
162D4×C11—41no—
163D4×C11—41no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—81no—
174C2×C4×C11C2×C22⋊C411yescharacteristic
175C2×C4×C11C4×D411yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12711yescharacteristic
178C22⋊D11—161no—
179C22⋊D11—161no—
180C2×Dic11—41no—
181D44—41no—
182D44—41no—
183D44—81no—
184C8×C11—81no—
185C11⋊C8—21no—
186C11⋊C8—21no—
187C11⋊C8—21no—
188C11⋊C8—42no—
189C11⋊C8—81no—
190C11⋊C8#9911yescharacteristic
191C11⋊C8#9911yescharacteristic
192C22×SD16—111no—
193C2×#131—111no—
194#536C2×D1111yescharacteristic
195#535—111no—
196#468—221no—
197#468—221no—
198#465—221no—
199#465—221no—
200C2×#108—221no—
201#427—111no—
202#419—111no—
203#418—111no—
204#413—111no—
205#413—111no—
206#413C2×D1111yescharacteristic
207#410C2×D1111yescharacteristic
208#405—221no—
209#356—222no—
210#355—222no—
211#352—22no—
212AΣL(1,𝔽16)—222no—
213#344—221no—
214#338—221no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11#39011yescharacteristic
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—162no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—81no—
230C4×C11—82no—
231C4×C11—81no—
232C4×C11C2×#9911yescharacteristic
233C4×C11#41011yescharacteristic
234Dic11—81no—
235C2×#41C22×D1111yescharacteristic
236C22×Q8C4×D1111yescharacteristic
237C22×D4—111no—
238C2×SD16—221no—
239C2×SD16—221no—
240C2×SD16—441no—
241C2×SD16—441no—
242#131—441no—
243#131—441no—
244C2×M16—21no—
245C2×M16—111no—
246C2×M16—111no—
247C2×M16—111no—
248C2×M16—221no—
249C2×M16—221no—
250C22×C8—111no—
251C22×C8—111no—
252C22×C8—111no—
253C4⋊Q8—21no—
254#127—221no—
255#124—21no—
256#124—221no—
257#123—21no—
258#123—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261#121—221no—
262#121—221no—
263#120—221no—
264#120—221no—
265#117—21no—
266#117—111no—
267#117C4×D1111yescharacteristic
268#108—441no—
269#108—441no—
270#107—221no—
271#106—221no—
272#103—221no—
273#103—221no—
274#102—221no—
275#102—221no—
276#101—21no—
277#101—112no—
278#101—221no—
279#100—21no—
280#100—221no—
281#100—221no—
282#99—21no—
283#99C22⋊D1112yes—
284#97—441no—
285C4×C8—441no—
286C2×C11—21no—
287C2×C11—41no—
288C2×C11—41no—
289C2×C11—41no—
290C2×C11#196411yescharacteristic
291D11—161no—
292C24—221no—
293#41—41no—
294#41—41no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8D4×D1111yescharacteristic
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—441no—
303C2×D4—441no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4#433911yescharacteristic
307C2×D4#434111yescharacteristic
308C2×D4C2×C22⋊D1111yescharacteristic
309C22×C4—21no—
310C22×C4C2×C4×D1111yescharacteristic
311C22×C4D4×D1111yescharacteristic
312C22×C4D4×D1111yescharacteristic
313SD16—441no—
314SD16—441no—
315SD16—442no—
316M16—41no—
317M16—41no—
318M16—222no—
319M16—441no—
320M16—441no—
321M16—441no—
322M16—441no—
323M16—441no—
324M16—441no—
325C2×C8—41no—
326C2×C8—111no—
327C2×C8—111no—
328C2×C8—111no—
329C2×C8—111no—
330C2×C8—221no—
331C2×C8—221no—
332C2×C8—221no—
333C2×C8—221no—
334C2×C8—221no—
335C2×C8—221no—
336C2×C8—441no—
337C2×C8—441no—
338C4⋊C4—21no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—221no—
343C22⋊C4—21no—
344C22⋊C4—22no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—221no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C42—21no—
351C42—41no—
352C42—221no—
353C11#1323211yescharacteristic, complemented, Sylow
354C23—441no—
355C23—881no—
356C23—1761no—
357C23#6693811yescharacteristic
358C23C4×C22⋊D1111yescharacteristic
359C23#6699211yescharacteristic
360Q8—41no—
361Q8—41no—
362Q8—41no—
363Q8—81no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—441no—
368D4—441no—
369D4—881no—
370D4—1761no—
371D4—1761no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—441no—
383C2×C4C22⋊C4×D1111yescharacteristic
384C2×C4(C22⋊D11)⋊C411yescharacteristic
385C2×C4#6693711yescharacteristic
386C2×C4#6699311yescharacteristic
387C8—81no—
388C8—111no—
389C8—111no—
390C8—221no—
391C8—221no—
392C8—221no—
393C8—442no—
394C8—881no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—881no—
402C22—881no—
403C22—881no—
404C22—1762no—
405C22#1062257011yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—81no—
410C4—82no—
411C4—81no—
412C4—881no—
413C4#1062235311yescharacteristic
414C4D11×#9911yescharacteristic
415C2—21no—
416C2—41no—
417C2—41no—
418C2—41no—
419C2—1761no—
420C2#1306945011yescharacteristic
subgroupG/H
centerC2#13069450
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#2123C2
socleC2×C11#1964
prime radical#10623361C22
cosocleC2×C11×#41C23
hypercenter#2123D11
hypocenterC11#13232
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2123

Complements

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

NH ≅ G/Ntype
2. #13070311C2semidirect
5. #13068664C2semidirect
6. #13068418C2semidirect
7. C11×#2123C2semidirect
11. C22×#4325C4semidirect
16. #10622838C4semidirect
22. #10622614C4semidirect
23. #10622611C4semidirect
147. #2123D11semidirect
353. C11#13232semidirect

Maximal subgroups

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

subgroupindex
#130782572
#130703112
#130703072
#130702652
#130686642
#130684182
C11×#21232
#1323211