Finite Group Databasebeta

← #14770342

Subgroups — #14770342

Order 2816.

1014 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623070C211yesmaximal, characteristic
2M16×Dic22C212yesmaximal, complemented
3#13069609C212yesmaximal, complemented
4#13069607C212yesmaximal, complemented
5#13069603C212yesmaximal, complemented
6#13068608C211yesmaximal, characteristic
7#13068606C211yesmaximal, characteristic
8#13068606C211yesmaximal, characteristic
9#100×Dic11C211yesmaximal, characteristic
10#100×Dic11C211yesmaximal, characteristic
11C4×C11×#100C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×D4×Dic11C2211yescharacteristic
14C2×D4×Dic11C2211yescharacteristic
15C2×#66977C412yes—
16C22×Dic11⋊C4C412yes—
17#10623070—22no—
18#10623070—22no—
19#10623070—22no—
20#10623070—22no—
21C2×#66943C2211yescharacteristic
22C2×#66941C2211yescharacteristic
23C2×#66931C412yes—
24C2×#66931C412yes—
25C2×#66923C2211yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27C2×C11×#100C2211yescharacteristic
28C2×C11×#100C2211yescharacteristic
29C4×C11×M16C2212yes—
30C2×#66897C2211yescharacteristic
31C2×#66897C2211yescharacteristic
32#10622731C2212yes—
33#10622731C2212yes—
34M16×Dic11C2212yes—
35M16×Dic11C2212yes—
36#10622537C2212yes—
37#10622314—22no—
38#10622314—22no—
39#10622292—22no—
40C8×Dic22—22no—
41C11×#343C2212yes—
42#10622192C2212yes—
43#10622192C2212yes—
44#10622192C2212yes—
45#10622192C2212yes—
46#10622168C2212yes—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11C2×C412yes—
49C23×Dic11C2×C412yes—
50C23×Dic11C2×C412yes—
51C22×Dic22C2×C412yes—
52C22×Dic22C2×C411yescharacteristic
53C2×C11×M16C2312yes—
54C2×C11×M16C2312yes—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C22⋊C4C2×C412yes—
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11C2×C412yes—
61C2×C22⋊Dic11C2×C412yes—
62D4×Dic11—22no—
63D4×Dic11—22no—
64D4×Dic11—22no—
65D4×Dic11—22no—
66C2×C4⋊Dic11C2×C412yes—
67C2×C4⋊Dic11C2×C411yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70#66977—24no—
71#66977—24no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4C2×C412yes—
77C2×Dic11⋊C4C2×C412yes—
78C2×Dic11⋊C4C2×C412yes—
79C2×Dic11⋊C4C2×C412yes—
80C2×Dic11⋊C4C2×C411yescharacteristic
81C2×Dic11⋊C4C2×C411yescharacteristic
82C2×C4×Dic11C2311yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C2×#4318C2312yes—
85C2×#4318C2312yes—
86#66943—22no—
87#66943—22no—
88#66941—22no—
89#66941—22no—
90#66931—24no—
91#66931—24no—
92#66931—24no—
93#66931—24no—
94#66923—22no—
95#66923—22no—
96C4×Dic22D412yes—
97C4×Dic22D412yes—
98C4×Dic22D412yes—
99C4×Dic22D412yes—
100C11×#100—22no—
101C11×#100Q814yescomplemented
102C11×#97—22no—
103C4×C8×C11—22no—
104#66897—22no—
105#66897—22no—
106#66879—22no—
107#66879—22no—
108Dic11⋊C8—22no—
109Dic11⋊C8—22no—
110Dic11⋊C8—22no—
111Dic11⋊C8—22no—
112C8×Dic11—22no—
113C8×Dic11—22no—
114C4⋊(C11⋊C8)—22no—
115C4⋊(C11⋊C8)—22no—
116#22515—111nomaximal, Sylow
117C24×C11C22×C412yes—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11C2×Q812yes—
121C2×D4×C11#4112yes—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—82no—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—44no—
134C22×Dic11—82no—
135C22×Dic11C22×C411yescharacteristic
136C22×Dic11C22×C412yes—
137C22×Dic11C22×C412yes—
138C22×Dic11C22×C411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C2×Dic22—24no—
142C2×Dic22—42no—
143C2×Dic22—82no—
144C2×Dic22C22⋊C412yes—
145C2×Dic22C22⋊C412yes—
146C11×M16—22no—
147C11×M16—22no—
148C11×M16—22no—
149C11×M16C2×Q814yes—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C11×C4⋊C4—22no—
153C11×C22⋊C4—24no—
154C42×C11C2×D412yes—
155C42×C11C2×D412yes—
156C22⋊Dic11—24no—
157C22⋊Dic11—24no—
158C4⋊Dic11—24no—
159C4⋊Dic11—22no—
160C4⋊Dic11—22no—
161C4⋊Dic11C22⋊C412yes—
162C4⋊Dic11C22⋊C412yes—
163Dic11⋊C4—22no—
164Dic11⋊C4—22no—
165Dic11⋊C4—22no—
166Dic11⋊C4—22no—
167Dic11⋊C4—24no—
168Dic11⋊C4—22no—
169Dic11⋊C4—22no—
170Dic11⋊C4C22⋊C411yescharacteristic
171Dic11⋊C4C22⋊C411yescharacteristic
172Dic11⋊C4C22⋊C411yescharacteristic
173Dic11⋊C4C22⋊C411yescharacteristic
174Dic11⋊C4C22⋊C412yes—
175Dic11⋊C4C22⋊C412yes—
176C4×Dic11C2×D412yes—
177C4×Dic11C2×D412yes—
178C4×Dic11C2×D412yes—
179C4×Dic11C2×D412yes—
180#4318—22no—
181#4318—22no—
182#4318—22no—
183#4318—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×#554—111no—
187Q8×M16—112no—
188#1998—112no—
189#1998—112no—
190#1997—112no—
191#1800—111no—
192#1800—111no—
193#1800—111no—
194C4×#100—111no—
195C4×#100—111no—
196C4×#100D1111yescharacteristic
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11C4×Q814yes—
202C23×C11C23×C411yescharacteristic
203D4×C11—24no—
204D4×C11—24no—
205C2×C4×C11—22no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—82no—
210C2×C4×C11—82no—
211C2×C4×C11C2×C22⋊C411yescharacteristic
212C2×C4×C11C2×C22⋊C411yescharacteristic
213C2×C4×C11C2×C22⋊C412yes—
214C2×C4×C11C22×D412yes—
215C2×C4×C11C22×Q811yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C112−1+412yes—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—44no—
225C2×Dic11—44no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—82no—
229C2×Dic11—82no—
230C2×Dic11C2×C22⋊C411yescharacteristic
231C2×Dic11C2×C22⋊C411yescharacteristic
232C2×Dic11C2×C22⋊C411yescharacteristic
233C2×Dic11C2×C22⋊C412yes—
234C2×Dic11C2×C22⋊C412yes—
235C2×Dic11C2×C22⋊C411yescharacteristic
236Dic22—24no—
237Dic22—42no—
238Dic22—84no—
239C8×C11—24no—
240C8×C11—42no—
241C11⋊C8—42no—
242C11⋊C8—42no—
243#554—222no—
244#554—222no—
245#554—222no—
246#554—222no—
247C2×C4⋊Q8—111no—
248C2×#125—111no—
249C2×#125—111no—
250C2×C22⋊Q8—112no—
251C2×C22⋊Q8—112no—
252C2×C22⋊Q8—112no—
253C2×C4×Q8—111no—
254C2×C4×D4—111no—
255C2×C4×D4—111no—
256C2×C4×D4C2×D1111yescharacteristic
257C22×C4⋊C4—112no—
258#446—222no—
259#446—222no—
260#446—222no—
261C8×Q8—222no—
262#423—112no—
263#423—112no—
264#423—112no—
265C2×#100—111no—
266C2×#100—111no—
267C2×#100C2×D1111yescharacteristic
268C2×#100C2×D1111yescharacteristic
269C4×M16—112no—
270C4×M16—112no—
271C4×M16C2×D1112yes—
272#343—112no—
273#343—112no—
274#343—112no—
275#343—112no—
276#343—112no—
277#343C2×D1112yes—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—24no—
281C22×C11—44no—
282C22×C11—44no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11C22×C22⋊C411yescharacteristic
286C22×C11C2×C4×Q811yescharacteristic
287C22×C11#51911yescharacteristic
288C4×C11—22no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—42no—
292C4×C11#54812yes—
293C4×C11D4×Q812yes—
294Dic11—22no—
295Dic11—21no—
296Dic11—22no—
297Dic11—21no—
298Dic11—21no—
299Dic11—42no—
300Dic11—42no—
301Dic11#41312yes—
302C22×Q8—111no—
303C22×Q8—112no—
304C22×D4C22×D1111yescharacteristic
305C23×C4—112no—
306C23×C4—112no—
307C23×C4C4×D1112yes—
308C2×M16—112no—
309C2×M16—112no—
310C2×M16C22×D1112yes—
311C2×M16C22×D1112yes—
312C4⋊Q8—222no—
313C4⋊Q8—222no—
314#125—222no—
315#125—222no—
316#125—222no—
317#125—222no—
318C22⋊Q8—224no—
319C22⋊Q8—224no—
320C22⋊Q8—224no—
321C22⋊Q8—224no—
322C22⋊Q8—224no—
323C22⋊Q8—224no—
324C4×Q8—112no—
325C4×Q8—112no—
326C4×Q8—112no—
327C4×Q8—112no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4—222no—
331C4×D4—222no—
332C4×D4—222no—
333C4×D4—222no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—111no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4—112no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—112no—
340C2×C4⋊C4—112no—
341C2×C4⋊C4—112no—
342C2×C4⋊C4—111no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4C22×D1111yescharacteristic
349C2×C22⋊C4—112no—
350C2×C22⋊C4—112no—
351C2×C22⋊C4C4×D1112yes—
352C2×C42—111no—
353C2×C42—111no—
354C2×C42C22×D1111yescharacteristic
355C4⋊C8—222no—
356C4⋊C8—222no—
357C4⋊C8—222no—
358C4⋊C8—222no—
359C4⋊C8—222no—
360C4⋊C8—222no—
361#100—22no—
362#100—222no—
363#100—222no—
364#100Dic2214yescomplemented
365#97—22no—
366#97—222no—
367#97—222no—
368C4×C8—22no—
369C4×C8—222no—
370C4×C8—222no—
371C2×C11—21no—
372C2×C11—21no—
373C2×C11—44no—
374C2×C11Q8×C22⋊C411yescharacteristic
375C2×C11C2×#41311yescharacteristic
376C2×C11#288811yescharacteristic
377C24C2×C4×D1112yes—
378C2×Q8—112no—
379C2×Q8—112no—
380C2×Q8—224no—
381C2×Q8—442no—
382C2×Q8—882no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4C2×Dic2212yes—
386C2×D4#433912yes—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—82no—
390C22×C4—111no—
391C22×C4—111no—
392C22×C4—111no—
393C22×C4—111no—
394C22×C4—112no—
395C22×C4—112no—
396C22×C4—222no—
397C22×C4—222no—
398C22×C4—222no—
399C22×C4—222no—
400C22×C4—444no—
401C22×C4—882no—
402C22×C4C2×C4×D1112yes—
403C22×C4C2×C4×D1111yescharacteristic
404C22×C4C2×C4×D1111yescharacteristic
405C22×C4C23×D1111yescharacteristic
406M16—22no—
407M16—22no—
408M16—22no—
409M16—222no—
410M16—222no—
411M16—222no—
412M16—222no—
413M16C2×Dic2214yes—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—222no—
417C2×C8—222no—
418C4⋊C4—22no—
419C4⋊C4—111no—
420C4⋊C4—111no—
421C4⋊C4—111no—
422C4⋊C4—111no—
423C4⋊C4—112no—
424C4⋊C4—112no—
425C4⋊C4—112no—
426C4⋊C4—112no—
427C4⋊C4—222no—
428C4⋊C4—222no—
429C4⋊C4—222no—
430C4⋊C4—222no—
431C4⋊C4—224no—
432C4⋊C4—222no—
433C4⋊C4—222no—
434C4⋊C4—224no—
435C4⋊C4—222no—
436C4⋊C4—222no—
437C22⋊C4—24no—
438C22⋊C4—224no—
439C22⋊C4—224no—
440C42—112no—
441C42—112no—
442C42—112no—
443C42—112no—
444C42D4×D1112yes—
445C42D4×D1112yes—
446C11#2251511yescharacteristic, complemented, Sylow
447C23—22no—
448C23—22no—
449C23—42no—
450C23—42no—
451C23C4×Dic2214yes—
452C23C22×C4×D1111yescharacteristic
453Q8—224no—
454Q8—442no—
455Q8—884no—
456D4—24no—
457D4—24no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4—111no—
465C2×C4—112no—
466C2×C4—112no—
467C2×C4—111no—
468C2×C4—111no—
469C2×C4—111no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—444no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—444no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—882no—
481C2×C4—882no—
482C2×C4C22⋊C4×D1112yes—
483C2×C4C22⋊C4×D1111yescharacteristic
484C2×C4C22⋊C4×D1111yescharacteristic
485C2×C4C22×Dic2211yescharacteristic
486C2×C4C2×#433911yescharacteristic
487C2×C4C2×D4×D1112yes—
488C2×C4#6704312yes—
489C8—24no—
490C8—42no—
491C8—442no—
492C8—442no—
493C22—21no—
494C22—21no—
495C22—24no—
496C22—44no—
497C22—44no—
498C22—42no—
499C22—42no—
500C22C2×C4×Dic2211yescharacteristic
501C22C2×C22⋊C4×D1111yescharacteristic
502C22#1062304711yescharacteristic
503C4—22no—
504C4—21no—
505C4—21no—
506C4—42no—
507C4—112no—
508C4—221no—
509C4—222no—
510C4—221no—
511C4—221no—
512C4—222no—
513C4—442no—
514C4—442no—
515C4D4×Dic2212yes—
516C4#1062308312yes—
517C2—21no—
518C2—21no—
519C2—44no—
520C2C22⋊C4×Dic2211yescharacteristic
521C2D11×#41311yescharacteristic
522C2#1307709211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#100C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC4×#100D11
hypocenterC11#22515
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
2. M16×Dic22C2semidirect
3. #13069609C2semidirect
4. #13069607C2semidirect
5. #13069603C2semidirect
101. C11×#100Q8semidirect
364. #100Dic22semidirect
446. C11#22515semidirect

Maximal subgroups

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

subgroupindex
C2×#106230702
M16×Dic222
#130696092
#130696072
#130696032
#130686082
#130686062
#100×Dic112
C4×C11×#1002
#2251511