Finite Group Databasebeta

← #13072049

Subgroups — #13072049

Order 1408.

788 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66992C211yesmaximal, characteristic, complemented
2C2×#66991C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4C2×#66937C211yesmaximal, characteristic, complemented
5C2×#66937C211yesmaximal, characteristic, complemented
6C2×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
7C11×#394C211yesmaximal, characteristic, complemented
8#10622607C211yesmaximal, characteristic, complemented
9#10622574C211yesmaximal, characteristic, complemented
10#10622570C211yesmaximal, characteristic, complemented
11#10622569C211yesmaximal, characteristic, complemented
12#10622561C211yesmaximal, characteristic, complemented
13#10622555C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622260C211yesmaximal, 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×C4×D11C2211yescharacteristic
25C22×C4×D11C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic
34#66992—24no—
35#66991—24no—
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×C4⋊Dic11C2211yescharacteristic
42C2×C4⋊Dic11C2211yescharacteristic
43C2×Dic11⋊C4C2211yescharacteristic
44C2×Dic11⋊C4C2211yescharacteristic
45C2×Dic11⋊C4C2211yescharacteristic
46C2×Dic11⋊C4C2211yescharacteristic
47C2×Dic11⋊C4C2211yescharacteristic
48C2×C4×Dic11C2211yescharacteristic
49C4⋊C4×D11—24no—
50#66937—24no—
51#66937—24no—
52(C22⋊D11)⋊C4—24no—
53C11×#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
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⋊D11D414yescomplemented
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—22no—
93C2×C4×D11—22no—
94C2×C4×D11—22no—
95C2×C4×D11—22no—
96C2×C4×D11—22no—
97C2×C4×D11—22no—
98C2×C4×D11—22no—
99C2×C4×D11—41no—
100C2×C4×D11—41no—
101C2×C4×D11D414yescomplemented
102C11×C4⋊C4—22no—
103C11×C22⋊C4—22no—
104C11×C22⋊C4—22no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—41no—
107C22⋊Dic11—22no—
108C22⋊Dic11—22no—
109C22⋊Dic11—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—41no—
115C4⋊Dic11—22no—
116C4⋊Dic11—22no—
117Dic11⋊C4—22no—
118Dic11⋊C4—22no—
119Dic11⋊C4—22no—
120Dic11⋊C4—22no—
121Dic11⋊C4D414yescomplemented
122C4×Dic11—22no—
123#2416—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×C11C2×D412yes—
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×D11C2×D412yes—
151C22×D11C2×D412yes—
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×C11—21no—
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—21no—
186C2×Dic11—44no—
187C2×Dic11C2×D412yes—
188C2×Dic11C2×D412yes—
189C2×Dic11C2×D412yes—
190C2×Dic11C2×D412yes—
191C2×Dic11#4112yes—
192D44—44no—
193C4×D11—28no—
194C4×D11—44no—
195C4×D11—44no—
196C2×#121—111no—
197C2×#121—111no—
198C2×#121—111no—
199C2×#121—111no—
200C2×C4×D4—111no—
201C22×C4⋊C4—111no—
202#396—111no—
203#396—111no—
204#394—111no—
205#394D1111yescharacteristic, complemented
206#390—111no—
207#389—111no—
208#386—111no—
209#386—111no—
210#380—111no—
211C22×C11—22no—
212C22×C11—22no—
213C22×C11—22no—
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×C11—41no—
225C22×C11C22×D411yescharacteristic
226C22×C11C22×D411yescharacteristic
227C22×C11C22×D411yescharacteristic
228C22×C11C2×#4111yescharacteristic
229C22×C11C2×#4111yescharacteristic
230C22×C11H(5,𝔽2)11yescharacteristic
231C22×C112−1+411yescharacteristic
232C2×D11—22no—
233C2×D11—22no—
234C2×D11—22no—
235C2×D11—22no—
236C2×D11—22no—
237C2×D11—22no—
238C2×D11—41no—
239C2×D11—41no—
240C2×D11—41no—
241C2×D11—41no—
242C2×D11—41no—
243C2×D11—41no—
244C2×D11—41no—
245C2×D11#12114yescomplemented
246C4×C11—22no—
247C4×C11—22no—
248C4×C11—41no—
249C4×C11—41no—
250C4×C11—41no—
251Dic11—22no—
252Dic11—22no—
253Dic11—41no—
254Dic11—41no—
255Dic11—41no—
256Dic11#12114yescomplemented
257C22×D4—111no—
258C22×D4—111no—
259C22×D4—111no—
260C22×D4—111no—
261C22×D4—111no—
262C22×D4C2×D1111yescharacteristic
263C23×C4—111no—
264C23×C4—111no—
265C23×C4—111no—
266C23×C4—111no—
267#121—224no—
268#121—224no—
269#121—224no—
270#121—224no—
271C4×D4—224no—
272C2×C4⋊C4—111no—
273C2×C4⋊C4—111no—
274C2×C4⋊C4—111no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—111no—
277C2×C4⋊C4—111no—
278C2×C4⋊C4—111no—
279C2×C4⋊C4—224no—
280C2×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
289C2×C22⋊C4C2×D1111yescharacteristic
290C2×C22⋊C4C2×D1111yescharacteristic
291C2×C22⋊C4C2×D1111yescharacteristic
292C2×C22⋊C4C2×D1111yescharacteristic
293C2×C42—111no—
294#95—111no—
295#95—111no—
296#95—111no—
297#95C2×D1111yescharacteristic
298C2×C11—42no—
299C2×C11—81no—
300C2×C11C2×#12111yescharacteristic
301C2×C11C2×#12111yescharacteristic
302C2×C11#53711yescharacteristic
303C2×C11D4211yescharacteristic
304C2×C11#54711yescharacteristic
305C2×C11#54811yescharacteristic
306C2×C11#55311yescharacteristic
307D11—24no—
308D11—81no—
309C24—111no—
310C24—111no—
311C24C22×D1111yescharacteristic
312C24C22×D1111yescharacteristic
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—41no—
316C2×D4—114no—
317C2×D4—222no—
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—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—111no—
334C22×C4—114no—
335C22×C4—111no—
336C22×C4—111no—
337C22×C4—111no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—222no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—441no—
348C22×C4—441no—
349C22×C4C22×D1111yescharacteristic
350C22×C4C22×D1111yescharacteristic
351C22×C4C22×D1111yescharacteristic
352C22×C4C22×D1111yescharacteristic
353C22×C4C22×D1111yescharacteristic
354C4⋊C4—22no—
355C4⋊C4—114no—
356C4⋊C4—222no—
357C4⋊C4—222no—
358C4⋊C4—222no—
359C4⋊C4—222no—
360C4⋊C4—222no—
361C4⋊C4—222no—
362C22⋊C4—22no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—41no—
366C22⋊C4—222no—
367C22⋊C4—222no—
368C22⋊C4—222no—
369C22⋊C4—222no—
370C22⋊C4—222no—
371C22⋊C4—222no—
372C22⋊C4—222no—
373C22⋊C4—441no—
374C42—222no—
375C11#241611yescharacteristic, complemented, Sylow
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—21no—
389C23—112no—
390C23—112no—
391C23—112no—
392C23—221no—
393C23—221no—
394C23—221no—
395C23—221no—
396C23—221no—
397C23—221no—
398C23—221no—
399C23—221no—
400C23—221no—
401C23—221no—
402C23—221no—
403C23D4×D1112yes—
404C23C23×D1111yescharacteristic
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—21no—
424C2×C4—112no—
425C2×C4—112no—
426C2×C4—112no—
427C2×C4—112no—
428C2×C4—112no—
429C2×C4—228no—
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—221no—
442C2×C4—221no—
443C2×C4—444no—
444C2×C4—444no—
445C2×C4—444no—
446C2×C4D4×D1112yes—
447C2×C4D4×D1112yes—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—114no—
463C22—222no—
464C22—222no—
465C22—222no—
466C22—222no—
467C22—222no—
468C22—222no—
469C22—441no—
470C22—441no—
471C22—441no—
472C22—441no—
473C22—441no—
474C22—441no—
475C22—441no—
476C22C2×D4×D1111yescharacteristic
477C22C2×D4×D1111yescharacteristic
478C22C2×D4×D1111yescharacteristic
479C22#6703711yescharacteristic
480C22#41×D1111yescharacteristic
481C22#41×D1111yescharacteristic
482C22#6704311yescharacteristic
483C4—22no—
484C4—22no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—114no—
489C4—222no—
490C4—222no—
491C4—441no—
492C4—441no—
493C4—441no—
494C2—42no—
495C2—81no—
496C2—224no—
497C2—881no—
498C2#1062312111yescharacteristic
499C2D11×#12111yescharacteristic
500C2D11×#12111yescharacteristic
501C2#1062313911yescharacteristic
502C2#1062318611yescharacteristic
503C2#1062319211yescharacteristic
504C2#1062320811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
hypercenter#394D11
hypocenterC11#2416
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#66992C2semidirect
2. C2×#66991C2semidirect
3. C2×C4⋊C4×D11C2semidirect
4. C2×#66937C2semidirect
5. C2×#66937C2semidirect
6. C2×(C22⋊D11)⋊C4C2semidirect
7. C11×#394C2semidirect
8. #10622607C2semidirect
9. #10622574C2semidirect
10. #10622570C2semidirect
11. #10622569C2semidirect
12. #10622561C2semidirect
13. #10622555C2semidirect
14. #10622278C2semidirect
15. #10622260C2semidirect
80. C2×C22⋊D11D4semidirect
101. C2×C4×D11D4semidirect
121. Dic11⋊C4D4semidirect
205. #394D11semidirect
245. C2×D11#121semidirect
256. Dic11#121semidirect
375. C11#2416semidirect

Maximal subgroups

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

subgroupindex
C2×#669922
C2×#669912
C2×C4⋊C4×D112
C2×#669372
C2×(C22⋊D11)⋊C42
C11×#3942
#106226072
#106225742
#106225702
#106225692
#106225612
#106225552
#106222782
#106222602
#241611