Finite Group Databasebeta

← #15879472

Subgroups — #15879472

Order 3328.

1114 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719248C211yesmaximal, characteristic
2#13117711C212yesmaximal, complemented
3#13115821C212yesmaximal, complemented
4#13115819C214yesmaximal, complemented
5#13114824C211yesmaximal, characteristic
6#13114822C212yesmaximal
7#99×Dic13C212yesmaximal
8C4×C13×#99C211yesmaximal, characteristic
9C2×C4×D4×C13C2211yescharacteristic
10C2×D4×Dic13C2212yes—
11C22×C4⋊Dic13C411yescharacteristic, complemented
12C22×C4⋊Dic13C2211yescharacteristic
13C2×#88178C411yescharacteristic, complemented
14C2×#88178C2211yescharacteristic
15#11719248—24no—
16#11719248—22no—
17#11719248—22no—
18C2×#88144C412yescomplemented
19C2×#88132C412yescomplemented
20C2×#88132C2212yes—
21C2×#88123C411yescharacteristic, complemented
22C2×C4×Dic26C411yescharacteristic, complemented
23C2×C13×#99C2211yescharacteristic
24C2×C13×#99C2211yescharacteristic
25C4×C13×C22⋊C4C2212yes—
26C2×#88074C2212yes—
27#11718873C2212yes—
28#11718603C2214yes—
29C22⋊C4×Dic13C2214yes—
30C4×C4⋊Dic13—22no—
31#11718589—22no—
32#11718315—24no—
33C13×#342C2212yes—
34#11718119C2214yes—
35#11718119C2214yes—
36#11718118C2212yes—
37C22×D4×C13C2311yescharacteristic
38C23×C4×C13C2×C411yescharacteristic
39C23×C4×C13C2311yescharacteristic
40C23×Dic13C2×C412yes—
41C23×Dic13C2312yes—
42C22×Dic26C2×C411yescharacteristic
43C22×Dic26C2×C412yes—
44C4×D4×C13—22no—
45C4×D4×C13—22no—
46C2×C13×C4⋊C4C2×C411yescharacteristic
47C2×C13×C22⋊C4C2×C411yescharacteristic
48C2×C13×C22⋊C4C2312yes—
49C2×C13×C22⋊C4C2311yescharacteristic
50C2×C13×C22⋊C4C2312yes—
51C2×C42×C13—22no—
52C2×C42×C13C2×C411yescharacteristic
53C2×C22⋊Dic13C2×C412yes—
54C2×C22⋊Dic13C2314yes—
55C2×C22⋊Dic13C2312yes—
56D4×Dic13—24no—
57D4×Dic13—24no—
58C2×C4⋊Dic13—22no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13—21no—
61C2×C4⋊Dic13—22no—
62C2×C4⋊Dic13C2×C412yes—
63C2×C4⋊Dic13C2×C411yescharacteristic
64C2×C4⋊Dic13C2×C412yes—
65C2×C4⋊Dic13C2×C411yescharacteristic
66C2×C4⋊Dic13C2×C411yescharacteristic
67C2×C4⋊Dic13C2×C412yes—
68C2×C4⋊Dic13D414yes—
69C2×C4⋊Dic13D412yes—
70C2×C4⋊Dic13D412yes—
71#88178—22no—
72#88178—22no—
73#88178—22no—
74#88178—22no—
75C2×#6101—24no—
76C2×#6101C2×C412yes—
77C2×#6101C2×C412yes—
78C2×#6101C2×C412yes—
79C2×C4×Dic13—24no—
80C2×C4×Dic13C2×C412yes—
81#88144—24no—
82#88144—24no—
83#88132—24no—
84#88132—24no—
85#88132—24no—
86#88132—24no—
87#88123—22no—
88#88123—22no—
89C4×Dic26—22no—
90C4×Dic26—21no—
91C4×Dic26—21no—
92C13×#99—22no—
93C13×#99Q814yescomplemented
94C13×#95—22no—
95#88074—24no—
96#88071—22no—
97#88071—24no—
98#88071—24no—
99#22513—131nomaximal, Sylow
100C24×C13C22×C411yescharacteristic
101C24×C13C2411yescharacteristic
102C2×D4×C13—22no—
103C2×D4×C13—22no—
104C2×D4×C13C2×Q812yes—
105C2×D4×C13#4112yes—
106C22×C4×C13—22no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—22no—
110C22×C4×C13—42no—
111C22×C4×C13—42no—
112C22×C4×C13C22×C411yescharacteristic
113C22×C4×C13C22×C411yescharacteristic
114C22×C4×C13C22×C411yescharacteristic
115C22×C4×C13C22×C411yescharacteristic
116C22×C4×C13C22×C411yescharacteristic
117C22×C4×C13C2×D412yes—
118C22×C4×C13C2×D412yes—
119C22×Dic13—22no—
120C22×Dic13—22no—
121C22×Dic13—24no—
122C22×Dic13—82no—
123C22×Dic13—82no—
124C22×Dic13C22×C412yes—
125C22×Dic13C22×C412yes—
126C22×Dic13C22×C412yes—
127C22×Dic13C22×C412yes—
128C22×Dic13C2×D414yes—
129C22×Dic13C2×D414yes—
130C2×Dic26—21no—
131C2×Dic26—21no—
132C2×Dic26—24no—
133C2×Dic26—42no—
134C2×Dic26—82no—
135C13×C4⋊C4—22no—
136C13×C22⋊C4—22no—
137C13×C22⋊C4—22no—
138C13×C22⋊C4—22no—
139C13×C22⋊C4—22no—
140C13×C22⋊C4—22no—
141C13×C22⋊C4C2×Q814yes—
142C42×C13—21no—
143C42×C13—21no—
144C42×C13—44no—
145C22⋊Dic13—24no—
146C22⋊Dic13—24no—
147C22⋊Dic13—24no—
148C22⋊Dic13—24no—
149C4⋊Dic13—21no—
150C4⋊Dic13—21no—
151C4⋊Dic13—24no—
152C4⋊Dic13—22no—
153C4⋊Dic13—22no—
154C4⋊Dic13—44no—
155C4⋊Dic13C22⋊C412yes—
156C4⋊Dic13C22⋊C411yescharacteristic
157C4⋊Dic13C22⋊C411yescharacteristic
158C4⋊Dic13C22⋊C412yes—
159C4⋊Dic13C22⋊C412yes—
160C4⋊Dic13C22⋊C414yes—
161C4⋊Dic13C22⋊C414yes—
162#6101—24no—
163#6101—22no—
164#6101—22no—
165#6101—24no—
166#6101—84no—
167C4×Dic13—22no—
168C4×Dic13—22no—
169C4×Dic13—84no—
170C2×#554—131no—
171#2345—132no—
172#1996—132no—
173#1996—134no—
174#1799—132no—
175#1799—131no—
176C4×#99—132no—
177C4×#99D1311yescharacteristic
178C23×C13—21no—
179C23×C13—21no—
180C23×C13—41no—
181C23×C13—41no—
182C23×C13—41no—
183C23×C13—41no—
184C23×C13C4×Q812yes—
185C23×C13C23×C411yescharacteristic
186C23×C13C22×D412yes—
187C23×C13C22×Q811yescharacteristic
188C23×C13C2×#4111yescharacteristic
189C23×C132−1+412yes—
190D4×C13—24no—
191D4×C13—24no—
192C2×C4×C13—21no—
193C2×C4×C13—21no—
194C2×C4×C13—24no—
195C2×C4×C13—22no—
196C2×C4×C13—21no—
197C2×C4×C13—21no—
198C2×C4×C13—24no—
199C2×C4×C13—41no—
200C2×C4×C13—42no—
201C2×C4×C13—42no—
202C2×C4×C13—42no—
203C2×C4×C13—42no—
204C2×C4×C13—42no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13—42no—
210C2×C4×C13C2×C22⋊C412yes—
211C2×C4×C13C2×C22⋊C411yescharacteristic
212C2×C4×C13C2×C22⋊C411yescharacteristic
213C2×C4×C13C4×Q812yes—
214C2×Dic13—22no—
215C2×Dic13—22no—
216C2×Dic13—44no—
217C2×Dic13—44no—
218C2×Dic13—42no—
219C2×Dic13—42no—
220C2×Dic13—42no—
221C2×Dic13—42no—
222C2×Dic13—44no—
223C2×Dic13—44no—
224C2×Dic13—44no—
225C2×Dic13—82no—
226C2×Dic13—82no—
227C2×Dic13C2×C22⋊C412yes—
228C2×Dic13C2×C22⋊C412yes—
229C2×Dic13C2×C22⋊C414yes—
230Dic26—42no—
231Dic26—42no—
232Dic26—84no—
233#554—262no—
234#554—264no—
235#554—262no—
236C2×C4⋊Q8—131no—
237C2×#125—132no—
238C2×C22⋊Q8—131no—
239C2×C22⋊Q8—131no—
240C2×C22⋊Q8—132no—
241C2×C22⋊Q8—132no—
242C2×C4×Q8—131no—
243C2×C4×D4—132no—
244C2×C4×D4C2×D1311yescharacteristic
245C22×C4⋊C4—131no—
246C22×C4⋊C4—131no—
247C2×#99—132no—
248C2×#99C2×D1311yescharacteristic
249C2×#99C2×D1311yescharacteristic
250#389—262no—
251#387—264no—
252#380—132no—
253#380—134no—
254C4×C4⋊C4—262no—
255C4×C22⋊C4—134no—
256C4×C22⋊C4C2×D1312yes—
257#342—132no—
258#342—134no—
259#342—134no—
260#342C2×D1312yes—
261C22×C13—22no—
262C22×C13—21no—
263C22×C13—22no—
264C22×C13—21no—
265C22×C13—22no—
266C22×C13—41no—
267C22×C13—41no—
268C22×C13—42no—
269C22×C13—42no—
270C22×C13—42no—
271C22×C13—41no—
272C22×C13—41no—
273C22×C13C22×C22⋊C411yescharacteristic
274C22×C13C2×C4×Q811yescharacteristic
275C22×C13#51911yescharacteristic
276C22×C13#54812yes—
277C22×C13D4×Q812yes—
278C4×C13—22no—
279C4×C13—21no—
280C4×C13—22no—
281C4×C13—44no—
282C4×C13—41no—
283C4×C13—41no—
284C4×C13—82no—
285C4×C13#41012yes—
286Dic13—24no—
287Dic13—22no—
288Dic13—22no—
289Dic13—42no—
290Dic13—42no—
291Dic13—84no—
292C22×Q8—131no—
293C22×Q8—132no—
294C22×D4C22×D1311yescharacteristic
295C23×C4—132no—
296C23×C4—132no—
297C23×C4C4×D1311yescharacteristic
298C23×C4C22×D1311yescharacteristic
299C4⋊Q8—262no—
300C4⋊Q8—262no—
301#125—264no—
302#125—264no—
303C22⋊Q8—264no—
304C22⋊Q8—264no—
305C22⋊Q8—264no—
306C22⋊Q8—264no—
307C22⋊Q8—262no—
308C22⋊Q8—262no—
309C22⋊Q8—262no—
310C22⋊Q8—262no—
311C4×Q8—262no—
312C4×Q8—261no—
313C4×Q8—261no—
314C4×D4—22no—
315C4×D4—22no—
316C4×D4—264no—
317C4×D4—264no—
318C2×C4⋊C4—131no—
319C2×C4⋊C4—132no—
320C2×C4⋊C4—131no—
321C2×C4⋊C4—132no—
322C2×C4⋊C4—134no—
323C2×C4⋊C4—132no—
324C2×C4⋊C4—132no—
325C2×C4⋊C4—131no—
326C2×C4⋊C4—132no—
327C2×C4⋊C4—132no—
328C2×C4⋊C4—132no—
329C2×C4⋊C4—132no—
330C2×C4⋊C4—262no—
331C2×C4⋊C4—261no—
332C2×C4⋊C4—261no—
333C2×C4⋊C4—262no—
334C2×C4⋊C4—264no—
335C2×C4⋊C4C4×D1311yescharacteristic
336C2×C22⋊C4—132no—
337C2×C22⋊C4—132no—
338C2×C22⋊C4—134no—
339C2×C22⋊C4C4×D1311yescharacteristic
340C2×C22⋊C4C22×D1312yes—
341C2×C22⋊C4C22×D1311yescharacteristic
342C2×C22⋊C4C22×D1312yes—
343C2×C42—22no—
344C2×C42—132no—
345C2×C42—264no—
346C2×C42C4×D1311yescharacteristic
347#99—22no—
348#99—264no—
349#99Dic2614yescomplemented
350#95—22no—
351#95—264no—
352#95—264no—
353#95—262no—
354C2×C13—22no—
355C2×C13—22no—
356C2×C13—21no—
357C2×C13—21no—
358C2×C13—42no—
359C2×C13Q8×C22⋊C411yescharacteristic
360C2×C13C2×#41011yescharacteristic
361C2×C13#288311yescharacteristic
362C24C2×C4×D1311yescharacteristic
363C24C23×D1311yescharacteristic
364C2×Q8—264no—
365C2×Q8—261no—
366C2×Q8—261no—
367C2×Q8—522no—
368C2×Q8—1042no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4C2×Dic2612yes—
372C2×D4#612712yes—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—132no—
380C22×C4—132no—
381C22×C4—134no—
382C22×C4—134no—
383C22×C4—132no—
384C22×C4—132no—
385C22×C4—262no—
386C22×C4—262no—
387C22×C4—264no—
388C22×C4—1042no—
389C22×C4—1042no—
390C22×C4C2×C4×D1311yescharacteristic
391C22×C4C2×C4×D1311yescharacteristic
392C22×C4C2×C4×D1311yescharacteristic
393C22×C4C2×C4×D1311yescharacteristic
394C22×C4C2×C4×D1311yescharacteristic
395C22×C4D4×D1312yes—
396C22×C4D4×D1312yes—
397C4⋊C4—22no—
398C4⋊C4—132no—
399C4⋊C4—131no—
400C4⋊C4—131no—
401C4⋊C4—134no—
402C4⋊C4—134no—
403C4⋊C4—132no—
404C4⋊C4—132no—
405C4⋊C4—262no—
406C4⋊C4—262no—
407C4⋊C4—264no—
408C4⋊C4—262no—
409C4⋊C4—262no—
410C4⋊C4—264no—
411C4⋊C4—261no—
412C4⋊C4—261no—
413C4⋊C4—264no—
414C4⋊C4—524no—
415C4⋊C4—1044no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—264no—
422C22⋊C4—264no—
423C22⋊C4—264no—
424C22⋊C4—264no—
425C22⋊C4C2×Dic2614yes—
426C42—21no—
427C42—21no—
428C42—44no—
429C42—262no—
430C42—262no—
431C42—1044no—
432C13#2251311yescharacteristic, complemented, Sylow
433C23—21no—
434C23—21no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23C4×Dic2612yes—
440C23C22×Dic2611yescharacteristic
441C23C22×C4×D1311yescharacteristic
442C23C2×#612711yescharacteristic
443C23C2×D4×D1312yes—
444C23#8825712yes—
445Q8—522no—
446Q8—522no—
447Q8—1044no—
448D4—24no—
449D4—24no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—24no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—132no—
469C2×C4—132no—
470C2×C4—134no—
471C2×C4—262no—
472C2×C4—262no—
473C2×C4—524no—
474C2×C4—524no—
475C2×C4—522no—
476C2×C4—522no—
477C2×C4—522no—
478C2×C4—522no—
479C2×C4—524no—
480C2×C4—524no—
481C2×C4—524no—
482C2×C4—1042no—
483C2×C4—1042no—
484C2×C4C4×Dic2612yes—
485C2×C4C22⋊C4×D1311yescharacteristic
486C2×C4C22⋊C4×D1312yes—
487C2×C4C22⋊C4×D1311yescharacteristic
488C22—22no—
489C22—21no—
490C22—22no—
491C22—21no—
492C22—22no—
493C22—41no—
494C22—41no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—41no—
499C22—41no—
500C22C2×C4×Dic2611yescharacteristic
501C22C2×C22⋊C4×D1311yescharacteristic
502C22#1171922111yescharacteristic
503C22D4×Dic2612yes—
504C22#1171925712yes—
505C4—21no—
506C4—22no—
507C4—22no—
508C4—44no—
509C4—41no—
510C4—41no—
511C4—82no—
512C4—262no—
513C4—262no—
514C4—264no—
515C4—522no—
516C4—522no—
517C4—1044no—
518C4#1171840112yes—
519C2—22no—
520C2—22no—
521C2—21no—
522C2—21no—
523C2—42no—
524C2C22⋊C4×Dic2611yescharacteristic
525C2C2×#1171840111yescharacteristic
526C2#1312329511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC4×C13×#99C2
socleC22×C13C22×C22⋊C4
prime radicalC22×D4×C13C23
cosocleC24×C13C24
hypercenterC4×#99D13
hypocenterC13#22513
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #13117711C2semidirect
3. #13115821C2semidirect
4. #13115819C2semidirect
11. C22×C4⋊Dic13C4semidirect
13. C2×#88178C4semidirect
18. C2×#88144C4semidirect
19. C2×#88132C4semidirect
21. C2×#88123C4semidirect
22. C2×C4×Dic26C4semidirect
93. C13×#99Q8semidirect
349. #99Dic26semidirect
432. C13#22513semidirect

Maximal subgroups

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

subgroupindex
C2×#117192482
#131177112
#131158212
#131158192
#131148242
#131148222
#99×Dic132
C4×C13×#992
#2251313