Finite Group Databasebeta

← #14654331

Subgroups — #14654331

Order 2816.

804 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C2×#10622841C211yesmaximal, characteristic
2#13074732C211yesmaximal, characteristic
3C2×#10622105C211yesmaximal, characteristic
4C2×#10622176C211yesmaximal, characteristic
5#13066887C211yesmaximal, characteristic
6#13066458C211yesmaximal, characteristic
7C2×C11×#451C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C22×C11×Q16—21no—
10C2×C11×C22⋊Q8C2211yescharacteristic
11C22×#4326—21no—
12C2×#66977C2211yescharacteristic
13C11×#451—22no—
14C11×#451—22no—
15C2×C11×#103—21no—
16C2×C11×C22⋊C8C2211yescharacteristic
17#10622842—21no—
18#10622841—22no—
19#10622841—22no—
20C2×#66899—21no—
21C2×C11⋊#95—22no—
22C2×C11⋊#95C2211yescharacteristic
23C2×C11⋊#95C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25#10622596—21no—
26#10622593—21no—
27#10622592—21no—
28#10622555—22no—
29#10622176—22no—
30#10622105—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11—21no—
34C22×Q8×C11—21no—
35C22×Q8×C11—21no—
36C22×Q8×C11—44no—
37C22×Q8×C11D412yes—
38C22×Q8×C11D411yescharacteristic
39C23×C4×C11—21no—
40C23×C4×C11C2311yescharacteristic
41C23×Dic11—21no—
42C23×Dic11D412yes—
43C22×Dic22D411yescharacteristic
44C2×C11×Q16—24no—
45C2×C11×Q16—44no—
46C22×C8×C11—21no—
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8—21no—
49C11×C22⋊Q8—21no—
50C11×C22⋊Q8—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C22⋊C4—21no—
54C2×C22⋊Dic11—21no—
55C2×#4326—24no—
56C2×#4326—44no—
57C2×C4⋊Dic11D411yescharacteristic
58#66977—21no—
59#66977—21no—
60#66977—21no—
61#66977—21no—
62C2×Dic11⋊C4—21no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C22×C11⋊C8—21no—
66C11×#103—24no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8D412yes—
69#66899—24no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C11⋊#95—21no—
73C11⋊#95—21no—
74C11⋊#95—21no—
75C11⋊#95—21no—
76C11⋊#95—44no—
77C22⋊(C11⋊C8)—21no—
78C22⋊(C11⋊C8)D412yes—
79#9967—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C2×Q8×C11—24no—
82C2×Q8×C11—24no—
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—44no—
88C2×Q8×C11—42no—
89C2×Q8×C11—42no—
90C2×Q8×C11—44no—
91C2×Q8×C11—42no—
92C2×Q8×C11—44no—
93C2×Q8×C11—44no—
94C2×Q8×C11—41no—
95C2×Q8×C11—41no—
96C22×C4×C11—24no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—22no—
115C22×Dic11—42no—
116C22×Dic11—42no—
117C22×Dic11—42no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C22×Dic11—42no—
121C22×Dic11Q1614yescomplemented
122C2×Dic22—21no—
123C2×Dic22—21no—
124C2×Dic22—42no—
125C11×Q16—48no—
126C2×C8×C11—22no—
127C2×C8×C11—42no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C22⋊Dic11—41no—
135C22⋊Dic11—41no—
136#4326—48no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139Dic11⋊C4—41no—
140Dic11⋊C4—41no—
141Dic11⋊C4—82no—
142Dic11⋊C4—82no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—42no—
145C2×#451—111no—
146C2×#451D1111yescharacteristic
147#2659—111no—
148C2×#328—111no—
149C2×#328—111no—
150#1446—111no—
151#1280—111no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—22no—
155C23×C11#12011yescharacteristic
156C23×C11#12111yescharacteristic
157C23×C11#12711yescharacteristic
158C23×C11C2×Q1612yes—
159C23×C11#13712yes—
160Q8×C11—24no—
161Q8×C11—24no—
162Q8×C11—42no—
163Q8×C11—42no—
164Q8×C11—44no—
165Q8×C11—44no—
166Q8×C11—42no—
167Q8×C11—81no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—24no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—44no—
177C2×C4×C11—42no—
178C2×C4×C11—44no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12011yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×Dic11—24no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—44no—
192C2×Dic11—44no—
193C2×Dic11—42no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—82no—
200C2×Dic11—82no—
201C2×Dic11—81no—
202C2×Dic11—81no—
203Dic22—42no—
204Dic22—81no—
205C8×C11—42no—
206C11⋊C8—42no—
207C23×Q8C2×D1111yescharacteristic
208C22×Q16—21no—
209C22×Q16—221no—
210C2×C22⋊Q8—111no—
211C2×C22⋊Q8C2×D1111yescharacteristic
212#451—22no—
213#451—22no—
214#451—222no—
215#451—222no—
216C2×#103—21no—
217C2×#103—221no—
218C2×C22⋊C8—111no—
219C2×C22⋊C8C2×D1111yescharacteristic
220#398—221no—
221#398—221no—
222#395—221no—
223#395—221no—
224#380—222no—
225C2×#95—111no—
226C2×#95—111no—
227C2×#95—222no—
228#328—222no—
229#328—222no—
230C22×C11—22no—
231C22×C11—22no—
232C22×C11—22no—
233C22×C11—22no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11#39211yescharacteristic
239C22×C11#45112yes—
240C22×C11#45511yescharacteristic
241C22×C11#45611yescharacteristic
242C22×C11B(4,𝔽2)12yes—
243C22×C11#46212yes—
244C22×C11#49411yescharacteristic
245C22×C11#49711yescharacteristic
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—44no—
251C4×C11—81no—
252C4×C11—81no—
253Dic11—44no—
254Dic11—82no—
255Dic11—81no—
256Dic11—81no—
257C22×Q8—21no—
258C22×Q8—21no—
259C22×Q8—21no—
260C22×Q8—21no—
261C22×Q8—21no—
262C22×Q8—44no—
263C22×Q8—111no—
264C22×Q8C22⋊D1111yescharacteristic
265C22×Q8C22⋊D1112yes—
266C23×C4—21no—
267C23×C4—112no—
268C23×C4—221no—
269C23×C4C22×D1111yescharacteristic
270C2×Q16—24no—
271C2×Q16—44no—
272C2×Q16—224no—
273C2×Q16—444no—
274C22×C8—21no—
275C22×C8—221no—
276C22⋊Q8—21no—
277C22⋊Q8—21no—
278C22⋊Q8—21no—
279C22⋊Q8—21no—
280C22⋊Q8—221no—
281C22⋊Q8—221no—
282C22⋊Q8—221no—
283C22⋊Q8—221no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4C22⋊D1111yescharacteristic
290C2×C22⋊C4—21no—
291C2×C22⋊C4—221no—
292#103—24no—
293#103—224no—
294C22⋊C8—21no—
295C22⋊C8—112no—
296C22⋊C8—221no—
297C22⋊C8C22⋊D1112yes—
298#95—222no—
299#95—222no—
300#95—221no—
301#95—221no—
302#95—221no—
303#95—221no—
304#95—444no—
305C2×C11—21no—
306C2×C11—22no—
307C2×C11—21no—
308C2×C11#160212yes—
309C2×C11#160512yes—
310C2×C11#200711yescharacteristic
311C2×C11#201611yescharacteristic
312C2×C11#202111yescharacteristic
313C24D4×D1111yescharacteristic
314C2×Q8—24no—
315C2×Q8—24no—
316C2×Q8—22no—
317C2×Q8—21no—
318C2×Q8—22no—
319C2×Q8—21no—
320C2×Q8—44no—
321C2×Q8—42no—
322C2×Q8—42no—
323C2×Q8—44no—
324C2×Q8—42no—
325C2×Q8—44no—
326C2×Q8—44no—
327C2×Q8—41no—
328C2×Q8—41no—
329C2×Q8—221no—
330C2×Q8—221no—
331C2×Q8—442no—
332C22×C4—24no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—114no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—221no—
345C22×C4—221no—
346C22×C4—442no—
347C22×C4—442no—
348C22×C4—442no—
349C22×C4—441no—
350C22×C4—442no—
351C22×C4—441no—
352C22×C4D4×D1111yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4#434111yescharacteristic
355C22×C4C2×C22⋊D1111yescharacteristic
356C22×C4C2×C22⋊D1111yescharacteristic
357C22×C4C2×C22⋊D1111yescharacteristic
358Q16—48no—
359Q16—448no—
360C2×C8—22no—
361C2×C8—42no—
362C2×C8—222no—
363C2×C8—442no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—221no—
369C4⋊C4—221no—
370C4⋊C4—441no—
371C4⋊C4—441no—
372C4⋊C4—882no—
373C4⋊C4—882no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—441no—
377C22⋊C4—441no—
378C11#996711yescharacteristic, complemented, Sylow
379C23—21no—
380C23—21no—
381C23—22no—
382C23Q16×D1112yes—
383C23#6697112yes—
384C23#6699011yescharacteristic
385C23#6699211yescharacteristic
386C23#6699311yescharacteristic
387Q8—24no—
388Q8—24no—
389Q8—42no—
390Q8—42no—
391Q8—44no—
392Q8—44no—
393Q8—42no—
394Q8—81no—
395Q8—442no—
396Q8—881no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—44no—
406C2×C4—42no—
407C2×C4—44no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—224no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—444no—
417C2×C4—444no—
418C2×C4—442no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—442no—
424C2×C4—882no—
425C2×C4—882no—
426C2×C4—881no—
427C2×C4—881no—
428C2×C4#6699011yescharacteristic
429C2×C4#6699111yescharacteristic
430C2×C4#6699211yescharacteristic
431C2×C4#6700611yescharacteristic
432C8—42no—
433C8—442no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22#1062264512yes—
443C22#1062279411yescharacteristic
444C22#1062279512yes—
445C22#1062279912yes—
446C22#1062280311yescharacteristic
447C22#1062281511yescharacteristic
448C22#1062281811yescharacteristic
449C22#1062283611yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—44no—
455C4—81no—
456C4—81no—
457C4—444no—
458C4—882no—
459C4—881no—
460C4—881no—
461C2—21no—
462C2—21no—
463C2—22no—
464C2#1306757112yes—
465C2#1306758812yes—
466C2#1306966111yescharacteristic
467C2#1306971411yescharacteristic
468C2#1306973911yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC2×C11×#451C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenterC2×#451D11
hypocenterC11#9967
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
121. C22×Dic11Q16semidirect
378. C11#9967semidirect

Maximal subgroups

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

subgroupindex
C2×#106228412
#130747322
C2×#106221052
C2×#106221762
#130668872
#130664582
C2×C11×#4512
#996711