Finite Group Databasebeta

← #13073553

Subgroups — #13073553

Order 1408.

760 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66992C211yesmaximal, characteristic, complemented
2C2×#66949C211yesmaximal, characteristic, complemented
3C2×#66938C211yesmaximal, characteristic, complemented
4C2×#66937C211yesmaximal, characteristic, complemented
5C2×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
6C2×#66931C211yesmaximal, characteristic, complemented
7C11×#390C211yesmaximal, characteristic, complemented
8#10622836C211yesmaximal, characteristic, complemented
9#10622605C211yesmaximal, characteristic, complemented
10#10622573C211yesmaximal, characteristic, complemented
11#10622570C211yesmaximal, characteristic, complemented
12#10622570C211yesmaximal, characteristic, complemented
13#10622562C211yesmaximal, characteristic, complemented
14#10622552C211yesmaximal, characteristic, complemented
15C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C23×Dic11C2211yescharacteristic
22C22×D44C2211yescharacteristic
23C22×C4×D11C2211yescharacteristic
24C22×Dic22C2211yescharacteristic
25C2×C11×C4⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C42×C11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic
34#66992—24no—
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×C4⋊Dic11C2211yescharacteristic
43C2×Dic11⋊C4C2211yescharacteristic
44C2×Dic11⋊C4C2211yescharacteristic
45C2×Dic11⋊C4C2211yescharacteristic
46C2×Dic11⋊C4C2211yescharacteristic
47C2×Dic11⋊C4C2211yescharacteristic
48C2×C4×Dic11C2211yescharacteristic
49C2×C4×Dic11C2211yescharacteristic
50#66949—24no—
51#66938—24no—
52#66937—24no—
53(C22⋊D11)⋊C4—24no—
54#66931—24no—
55C11⋊#95C2211yescharacteristic
56C11⋊#95C2211yescharacteristic
57C24×C11C2311yescharacteristic
58C24×C11C2311yescharacteristic
59C23×D11C2311yescharacteristic
60C23×D11C2311yescharacteristic
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—41no—
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C2×C22⋊D11—22no—
70C2×C22⋊D11—22no—
71C2×C22⋊D11—22no—
72C2×C22⋊D11—22no—
73C2×C22⋊D11—22no—
74C2×C22⋊D11—22no—
75C2×C22⋊D11—22no—
76C2×C22⋊D11—22no—
77C2×C22⋊D11—22no—
78C2×C22⋊D11—22no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—41no—
81C22×Dic11—22no—
82C22×Dic11—22no—
83C22×Dic11—22no—
84C22×Dic11C2311yescharacteristic
85C22×Dic11C2311yescharacteristic
86C22×Dic11C2311yescharacteristic
87C22×Dic11C2311yescharacteristic
88C22×Dic11C2311yescharacteristic
89C22×Dic11C2311yescharacteristic
90C2×D44—22no—
91C2×D44—22no—
92C2×D44—41no—
93C2×C4×D11—22no—
94C2×C4×D11—22no—
95C2×C4×D11—22no—
96C2×Dic22—22no—
97C2×Dic22—22no—
98C2×Dic22—22no—
99C11×C4⋊C4—22no—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—22no—
103C11×C22⋊C4—22no—
104C42×C11—41no—
105C22⋊Dic11—22no—
106C22⋊Dic11—22no—
107C22⋊Dic11—22no—
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—22no—
110(C2×D11)⋊C4—22no—
111(C2×D11)⋊C4—22no—
112(C2×D11)⋊C4—22no—
113(C2×D11)⋊C4—22no—
114(C2×D11)⋊C4—22no—
115C4⋊Dic11—22no—
116Dic11⋊C4—22no—
117Dic11⋊C4—22no—
118Dic11⋊C4—22no—
119Dic11⋊C4D414yescomplemented
120Dic11⋊C4D414yescomplemented
121C4×Dic11—41no—
122C4×Dic11D414yescomplemented
123#2540—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11#4112yes—
138C23×C11C2411yescharacteristic
139C22×D11—21no—
140C22×D11—21no—
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—21no—
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11#4112yes—
153D4×C11—44no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11C2×D412yes—
167C2×C4×C11C2×D412yes—
168C2×C4×C11C2×D412yes—
169C22⋊D11—28no—
170C22⋊D11—44no—
171C22⋊D11—44no—
172C22⋊D11—44no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—44no—
186C2×Dic11C2×D412yes—
187C2×Dic11C2×D412yes—
188C2×Dic11C2×D412yes—
189C2×Dic11C2×D412yes—
190C2×Dic11C2×D412yes—
191C2×Dic11C2×D412yes—
192D44—44no—
193C4×D11—44no—
194Dic22—44no—
195C2×#124—111no—
196C2×C22⋊Q8—111no—
197C2×C22⋊Q8—111no—
198C2×#121—111no—
199C2×#121—111no—
200C2×C4×D4—111no—
201#399—111no—
202#399—111no—
203#392—111no—
204#392—111no—
205#390—111no—
206#390—111no—
207#390—111no—
208#390D1111yescharacteristic, complemented
209C4×C4⋊C4—111no—
210C22×C11—22no—
211C22×C11—22no—
212C22×C11—22no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11C22×D411yescharacteristic
225C22×C11C22×D411yescharacteristic
226C22×C11C22×D411yescharacteristic
227C22×C11C2×#4111yescharacteristic
228C22×C11C2×#4111yescharacteristic
229C22×C11H(5,𝔽2)11yescharacteristic
230C22×C112−1+411yescharacteristic
231C2×D11—22no—
232C2×D11—22no—
233C2×D11—22no—
234C2×D11—41no—
235C2×D11—41no—
236C2×D11—41no—
237C2×D11—41no—
238C2×D11—41no—
239C2×D11—41no—
240C2×D11—41no—
241C2×D11—41no—
242C2×D11—41no—
243C2×D11—41no—
244C2×D11—41no—
245C4×C11—22no—
246C4×C11—22no—
247C4×C11—22no—
248C4×C11—41no—
249C4×C11—41no—
250Dic11—22no—
251Dic11—22no—
252Dic11—22no—
253Dic11—41no—
254Dic11—41no—
255Dic11#12714yes—
256C22×Q8—111no—
257C22×D4—111no—
258C22×D4—111no—
259C22×D4—111no—
260C22×D4—111no—
261C22×D4—111no—
262C22×D4C2×D1111yescharacteristic
263C23×C4—111no—
264C23×C4—111no—
265#124—224no—
266C22⋊Q8—224no—
267C22⋊Q8—224no—
268#121—224no—
269#121—224no—
270C4×D4—224no—
271C2×C4⋊C4—111no—
272C2×C4⋊C4—111no—
273C2×C4⋊C4—111no—
274C2×C4⋊C4—111no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—111no—
277C2×C4⋊C4C2×D1111yescharacteristic
278C2×C22⋊C4—111no—
279C2×C22⋊C4—111no—
280C2×C22⋊C4—111no—
281C2×C22⋊C4—111no—
282C2×C22⋊C4—111no—
283C2×C22⋊C4—111no—
284C2×C22⋊C4—111no—
285C2×C22⋊C4—111no—
286C2×C22⋊C4—111no—
287C2×C22⋊C4—111no—
288C2×C22⋊C4C2×D1111yescharacteristic
289C2×C22⋊C4C2×D1111yescharacteristic
290C2×C22⋊C4C2×D1111yescharacteristic
291C2×C22⋊C4C2×D1111yescharacteristic
292C2×C42—111no—
293C2×C42—111no—
294C2×C42C2×D1111yescharacteristic
295#95—111no—
296#95—111no—
297C2×C11—42no—
298C2×C11—81no—
299C2×C11#52511yescharacteristic
300C2×C11C2×#12711yescharacteristic
301C2×C11#53711yescharacteristic
302C2×C11#54611yescharacteristic
303C2×C11#54611yescharacteristic
304C2×C11#54811yescharacteristic
305C2×C11#54811yescharacteristic
306D11—42no—
307D11—81no—
308C24—111no—
309C24—111no—
310C24C22×D1111yescharacteristic
311C24C22×D1111yescharacteristic
312C2×Q8—222no—
313C2×Q8—222no—
314C2×Q8—222no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—41no—
318C2×D4—222no—
319C2×D4—222no—
320C2×D4—222no—
321C2×D4—222no—
322C2×D4—222no—
323C2×D4—222no—
324C2×D4—222no—
325C2×D4—222no—
326C2×D4—222no—
327C2×D4—222no—
328C2×D4—222no—
329C2×D4—222no—
330C2×D4—441no—
331C2×D4—441no—
332C2×D4—441no—
333C22×C4—111no—
334C22×C4—111no—
335C22×C4—111no—
336C22×C4—111no—
337C22×C4—111no—
338C22×C4—111no—
339C22×C4—222no—
340C22×C4—222no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—222no—
345C22×C4C22×D1111yescharacteristic
346C22×C4C22×D1111yescharacteristic
347C22×C4C22×D1111yescharacteristic
348C22×C4C22×D1111yescharacteristic
349C22×C4C22×D1111yescharacteristic
350C4⋊C4—22no—
351C4⋊C4—114no—
352C4⋊C4—114no—
353C4⋊C4—222no—
354C4⋊C4—222no—
355C4⋊C4—222no—
356C4⋊C4—222no—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C22⋊C4—22no—
360C22⋊C4—22no—
361C22⋊C4—222no—
362C22⋊C4—222no—
363C22⋊C4—222no—
364C22⋊C4—222no—
365C22⋊C4—222no—
366C22⋊C4—222no—
367C22⋊C4—222no—
368C22⋊C4—222no—
369C22⋊C4—222no—
370C22⋊C4—222no—
371C42—41no—
372C42—114no—
373C42—441no—
374C11#254011yescharacteristic, complemented, Sylow
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—112no—
389C23—221no—
390C23—221no—
391C23—221no—
392C23—221no—
393C23—221no—
394C23—221no—
395C23—221no—
396C23—221no—
397C23—221no—
398C23—221no—
399C23—221no—
400C23—221no—
401C23—221no—
402C23#433912yes—
403C23C23×D1111yescharacteristic
404Q8—444no—
405D4—44no—
406D4—228no—
407D4—444no—
408D4—444no—
409D4—444no—
410D4—444no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—112no—
424C2×C4—112no—
425C2×C4—112no—
426C2×C4—112no—
427C2×C4—112no—
428C2×C4—112no—
429C2×C4—221no—
430C2×C4—221no—
431C2×C4—221no—
432C2×C4—221no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—221no—
440C2×C4—221no—
441C2×C4—444no—
442C2×C4—444no—
443C2×C4D4×D1112yes—
444C2×C4D4×D1112yes—
445C2×C4D4×D1112yes—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—222no—
461C22—222no—
462C22—222no—
463C22—441no—
464C22—441no—
465C22—441no—
466C22—441no—
467C22—441no—
468C22—441no—
469C22—441no—
470C22—441no—
471C22—441no—
472C22—441no—
473C22—441no—
474C22C2×#433911yescharacteristic
475C22C2×D4×D1111yescharacteristic
476C22C2×D4×D1111yescharacteristic
477C22C2×D4×D1111yescharacteristic
478C22#6703711yescharacteristic
479C22#41×D1111yescharacteristic
480C22#6704311yescharacteristic
481C4—22no—
482C4—22no—
483C4—22no—
484C4—41no—
485C4—41no—
486C4—114no—
487C4—222no—
488C4—222no—
489C4—222no—
490C4—441no—
491C4—441no—
492C2—42no—
493C2—81no—
494C2—442no—
495C2—881no—
496C2#1062302111yescharacteristic
497C2#1062307811yescharacteristic
498C2#1062308311yescharacteristic
499C2#1062312811yescharacteristic
500C2#1062314111yescharacteristic
501C2#1062320811yescharacteristic
502C2D11×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
hypercenter#390D11
hypocenterC11#2540
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#66992C2semidirect
2. C2×#66949C2semidirect
3. C2×#66938C2semidirect
4. C2×#66937C2semidirect
5. C2×(C22⋊D11)⋊C4C2semidirect
6. C2×#66931C2semidirect
7. C11×#390C2semidirect
8. #10622836C2semidirect
9. #10622605C2semidirect
10. #10622573C2semidirect
11. #10622570C2semidirect
12. #10622570C2semidirect
13. #10622562C2semidirect
14. #10622552C2semidirect
15. C4×Dic11⋊C4C2semidirect
119. Dic11⋊C4D4semidirect
120. Dic11⋊C4D4semidirect
122. C4×Dic11D4semidirect
208. #390D11semidirect
374. C11#2540semidirect

Maximal subgroups

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

subgroupindex
C2×#669922
C2×#669492
C2×#669382
C2×#669372
C2×(C22⋊D11)⋊C42
C2×#669312
C11×#3902
#106228362
#106226052
#106225732
#106225702
#106225622
#106225522
C4×Dic11⋊C42
#254011