Finite Group Databasebeta

← #14803577

Subgroups — #14803577

Order 2816.

732 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078992C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic
3#13077565C211yesmaximal, characteristic, complemented
4#13069973C212yesmaximal, complemented
5#13069876C212yesmaximal, complemented
6#13069518C212yesmaximal, complemented
7#13069455C211yesmaximal, characteristic
8#13069389C211yesmaximal, characteristic, complemented
9#13069277C212yesmaximal, complemented
10C4×#66900C211yesmaximal, characteristic, complemented
11C11×#3078C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C22×#4325C2212yes—
15C2×#66927C2211yescharacteristic
16C11×#479—22no—
17C11×#477—21no—
18C11×#475—21no—
19C11×#428C2212yes—
20C11×#423C2211yescharacteristic
21C11×#419C2212yes—
22C2×#66900C2211yescharacteristic
23C2×#66900C2211yescharacteristic
24C2×#66887C2212yes—
25C2×#66887C2212yes—
26C2×#66886C2212yes—
27#10622701—21no—
28#10622701—21no—
29#10622680—22no—
30#10622640—21no—
31#10622640—22no—
32#10622640—21no—
33#10622637—21no—
34#10622637—22no—
35Q8×C11⋊C8—21no—
36#10622614C2212yes—
37#10622614C2212yes—
38#10622612C2212yes—
39#10622610C2212yes—
40C2×#66873C2212yes—
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43C4×#4318C2211yescharacteristic
44#10622196C2212yes—
45#10622168C2211yescharacteristic
46#10622168C2211yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C22×D44—21no—
49C22×D44—21no—
50C22×D44C2312yes—
51C2×C11×M16C2312yes—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×#125D412yes—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C11×#117C2312yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C2×#4325—24no—
69C2×#4325—22no—
70C2×#4325—22no—
71C2×#4325—42no—
72C2×#4318C2311yescharacteristic
73C2×#4318C2311yescharacteristic
74C2×#4318C2311yescharacteristic
75C2×#4318C2311yescharacteristic
76C22×C11⋊C8C2312yes—
77#66927—21no—
78#66927—21no—
79#66927—21no—
80#66927—21no—
81C11×#107—22no—
82C11×#106—22no—
83C11×C4⋊C8—21no—
84C11×C4⋊C8—21no—
85C11×#103—22no—
86C11×#103—22no—
87#66900—22no—
88#66900—22no—
89#66887—24no—
90#66887—42no—
91#66886—42no—
92#66873—22no—
93#66873—22no—
94#66873—22no—
95#66873—22no—
96#66873—22no—
97#66873—22no—
98C4⋊(C11⋊C8)—22no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)D411yescharacteristic
101C4⋊(C11⋊C8)D412yes—
102C4⋊(C11⋊C8)D411yescharacteristic
103#66867—21no—
104#66867—21no—
105#66867—22no—
106C4×C11⋊C8—21no—
107C4×C11⋊C8—21no—
108C4×C11⋊C8—22no—
109#25315—111nomaximal, Sylow
110C23×D11—22no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11#4112yes—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44—41no—
131C2×D44—41no—
132C2×D44—41no—
133C2×D44—41no—
134C2×D44—82no—
135C2×D44—82no—
136C11×M16—22no—
137C11×M16—22no—
138C2×C8×C11—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4C2×D412yes—
148C11×C4⋊C4C2×D412yes—
149C11×C22⋊C4—22no—
150C42×C11—22no—
151C42×C11—41no—
152C42×C11—41no—
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157#4325—44no—
158#4325—44no—
159#4318—21no—
160#4318—21no—
161#4318—21no—
162#4318—21no—
163#4318—21no—
164#4318—21no—
165#4318—21no—
166#4318#4112yes—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8C2×D412yes—
174C2×C11⋊C8C2×D412yes—
175#3138—111no—
176#3078D1111yescharacteristic, complemented
177C2×#460—111no—
178#2962—111no—
179#2063—112no—
180#2046—112no—
181#1977—112no—
182#1965—111no—
183#1950—111no—
184#1931—112no—
185C4×#101—111no—
186C23×C11C2×#4111yescharacteristic
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—82no—
191C22×D11—82no—
192Q8×C11—22no—
193Q8×C11—22no—
194Q8×C11—41no—
195Q8×C11—41no—
196Q8×C11—42no—
197Q8×C11—81no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—81no—
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11H(5,𝔽2)11yescharacteristic
216C2×C4×C112−1+411yescharacteristic
217D44—42no—
218D44—42no—
219D44—42no—
220D44—42no—
221D44—82no—
222D44—82no—
223D44—82no—
224D44—82no—
225C8×C11—42no—
226C11⋊C8—22no—
227C11⋊C8—22no—
228C11⋊C8—22no—
229C11⋊C8—41no—
230C11⋊C8—41no—
231C11⋊C8—41no—
232C22×SD16—112no—
233#533C2×D1111yescharacteristic
234C2×#127—111no—
235C2×C4×Q8C2×D1111yescharacteristic
236#490—222no—
237#486—221no—
238#486—221no—
239#479—22no—
240#477—21no—
241#475—21no—
242#460—221no—
243#460—222no—
244#460—221no—
245#446—222no—
246#446—221no—
247C8×Q8—221no—
248C2×#108—112no—
249#428C2×D1112yes—
250#424—112no—
251#423C2×D1111yescharacteristic
252C2×C4⋊C8—111no—
253#419C2×D1112yes—
254#418—112no—
255#418—112no—
256C2×#102—112no—
257C2×#101—111no—
258C2×#101—111no—
259C2×#100—112no—
260C2×#100—112no—
261#405—112no—
262C4×M16—111no—
263C4×M16—111no—
264#343—111no—
265#343—111no—
266#341—112no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11C2×#12111yescharacteristic
270C22×C11#52911yescharacteristic
271C22×C11#54211yescharacteristic
272C2×D11—82no—
273C2×D11—82no—
274C2×D11—82no—
275C2×D11—162no—
276C2×D11—162no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—81no—
284C4×C11#47112yes—
285C4×C11#54611yescharacteristic
286C4×C11#54811yescharacteristic
287C4×C11#54811yescharacteristic
288C4×C11#55011yescharacteristic
289C22×Q8C22×D1111yescharacteristic
290C22×D4—112no—
291C22×D4—221no—
292C22×D4—221no—
293C2×SD16—222no—
294C2×SD16—222no—
295C2×SD16—224no—
296C2×SD16—442no—
297C2×M16—111no—
298C2×M16—111no—
299C2×M16—111no—
300C2×M16—111no—
301C2×M16C22×D1112yes—
302C22×C8—112no—
303C4⋊Q8C22⋊D1111yescharacteristic
304C4⋊Q8C22⋊D1111yescharacteristic
305#127—221no—
306#127—221no—
307#127—221no—
308#127—221no—
309#125C22⋊D1112yes—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×Q8—21no—
318#117C22×D1112yes—
319C2×C4⋊C4—21no—
320C2×C4⋊C4C22×D1111yescharacteristic
321C2×C42—21no—
322C2×C42C22×D1111yescharacteristic
323#108—442no—
324#107—22no—
325#106—22no—
326C4⋊C8—21no—
327C4⋊C8—21no—
328C4⋊C8—111no—
329C4⋊C8—111no—
330C4⋊C8—112no—
331C4⋊C8—222no—
332C4⋊C8—222no—
333#103—22no—
334#103—22no—
335#102—222no—
336#102—222no—
337#102—222no—
338#102—222no—
339#102—222no—
340#102—222no—
341#101—222no—
342#101—222no—
343#100—224no—
344#100—442no—
345#97—222no—
346#97—221no—
347#97—221no—
348C4×C8—222no—
349C4×C8—221no—
350C4×C8—221no—
351C2×C11—21no—
352C2×C11—21no—
353C2×C11#242611yescharacteristic
354C2×C11C2×#47111yescharacteristic
355C2×C11#306811yescharacteristic
356D11—162no—
357C24—222no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8#434312yes—
366C2×D4—222no—
367C2×D4—222no—
368C2×D4—222no—
369C2×D4—222no—
370C2×D4—222no—
371C2×D4—222no—
372C2×D4—441no—
373C2×D4—441no—
374C2×D4—441no—
375C2×D4—441no—
376C2×D4—882no—
377C2×D4—882no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4#434111yescharacteristic
381C22×C4#434111yescharacteristic
382C22×C4C23×D1111yescharacteristic
383SD16—444no—
384SD16—444no—
385M16—22no—
386M16—22no—
387M16—112no—
388M16—221no—
389M16—221no—
390M16—221no—
391M16—221no—
392M16—221no—
393M16—221no—
394M16—221no—
395C2×C8—22no—
396C2×C8—112no—
397C2×C8—112no—
398C2×C8—221no—
399C2×C8—222no—
400C2×C8—222no—
401C2×C8—221no—
402C2×C8—221no—
403C2×C8—221no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4C2×C22⋊D1112yes—
413C4⋊C4C2×C22⋊D1112yes—
414C22⋊C4—22no—
415C42—22no—
416C42—41no—
417C42—41no—
418C42D4×D1111yescharacteristic
419C42D4×D1111yescharacteristic
420C42C2×C22⋊D1111yescharacteristic
421C42C2×C22⋊D1111yescharacteristic
422C11#2531511yescharacteristic, complemented, Sylow
423C23—442no—
424C23—442no—
425C23—442no—
426C23—882no—
427C23—882no—
428C23C2×#434111yescharacteristic
429Q8—22no—
430Q8—22no—
431Q8—42no—
432Q8—41no—
433Q8—41no—
434Q8—81no—
435D4—442no—
436D4—442no—
437D4—442no—
438D4—442no—
439D4—882no—
440D4—882no—
441D4—882no—
442D4—882no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—81no—
452C2×C4#6699211yescharacteristic
453C2×C4#6699211yescharacteristic
454C2×C4#6699211yescharacteristic
455C2×C4#6699211yescharacteristic
456C2×C4C2×D4×D1111yescharacteristic
457C2×C4C2×#434311yescharacteristic
458C2×C4#6704011yescharacteristic
459C2×C4#41×D1111yescharacteristic
460C2×C4#6704211yescharacteristic
461C2×C4C22×C22⋊D1111yescharacteristic
462C8—42no—
463C8—222no—
464C8—222no—
465C8—222no—
466C8—441no—
467C8—441no—
468C8—441no—
469C22—21no—
470C22—21no—
471C22—882no—
472C22—882no—
473C22—882no—
474C22—1762no—
475C22—1762no—
476C22#1062315511yescharacteristic
477C22#1062317411yescharacteristic
478C22C2×#6699211yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—42no—
484C4—42no—
485C4—81no—
486C4#1062281612yes—
487C4#1062316111yescharacteristic
488C4#1062316411yescharacteristic
489C4#1062334811yescharacteristic
490C4#1062336511yescharacteristic
491C2—21no—
492C2—21no—
493C2—1762no—
494C2#1307218411yescharacteristic
495C2C2×#1062281611yescharacteristic
496C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3078C2
socleC22×C11C2×#121
prime radicalC2×#66927C22
hypercenter#3078D11
hypocenterC11#25315
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
3. #13077565C2semidirect
4. #13069973C2semidirect
5. #13069876C2semidirect
6. #13069518C2semidirect
8. #13069389C2semidirect
9. #13069277C2semidirect
10. C4×#66900C2semidirect
11. C11×#3078C2semidirect
176. #3078D11semidirect
422. C11#25315semidirect

Maximal subgroups

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

subgroupindex
#130789922
C2×#106226402
#130775652
#130699732
#130698762
#130695182
#130694552
#130693892
#130692772
C4×#669002
C11×#30782
#2531511