Finite Group Databasebeta

← #30598164

Subgroups — #30598164

Order 15616.

1120 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461674C211yesmaximal, characteristic, complemented
2C4×#14519834C211yesmaximal, characteristic, complemented
3C2×Q8⋊#92420C212yesmaximal, complemented
4C2×#16840610C212yesmaximal, complemented
5C2×C4×#11758226C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×#14519834—21no—
8C2×#14519834—21no—
9C2×C4×#92420C2212yes—
10#16840628—21no—
11#16840628—21no—
12Q8⋊#92420—24no—
13#16840610—24no—
14C22×#11758226C411yescharacteristic
15C4×#11758226—24no—
16C4×#11758226—24no—
17C2×Q8×Dic61C2211yescharacteristic
18C2×C4×D244—21no—
19C2×C4×D244C411yescharacteristic
20C2×#14519739—21no—
21C2×#14519739C2211yescharacteristic
22C2×#14519735—21no—
23C2×#14519735C411yescharacteristic
24C2×C42×D61—21no—
25C2×C42×D61C2211yescharacteristic
26C2×C4×Q8×C61C411yescharacteristic
27C22×#92420—22no—
28C22×#92420—22no—
29C4⋊#92420—22no—
30C4⋊#92420—22no—
31#14519834—24no—
32#14519834—42no—
33C4×#92420—22no—
34C4×#92420—22no—
35C2×#11758226—22no—
36C2×#11758226—22no—
37C2×#11758226—22no—
38C2×#11758226—22no—
39C2×#11758226—22no—
40C2×#11758226C814yescomplemented
41C22×D244—21no—
42C22×D244C2×C411yescharacteristic
43C22×C4×D61—21no—
44C22×C4×D61—21no—
45C22×C4×D61—21no—
46C22×C4×D61C2×C411yescharacteristic
47C22×C4×D61D411yescharacteristic
48C22×C4×D61D411yescharacteristic
49Q8×Dic61—22no—
50Q8×Dic61D414yes—
51C4×D244—28no—
52C4×D244—22no—
53C4×D244—22no—
54#14519739—28no—
55#14519739—22no—
56#14519739D414yes—
57#14519735—28no—
58#14519735—22no—
59#14519735—22no—
60C2×C4⋊Dic61—21no—
61C2×C4⋊Dic61C2×C411yescharacteristic
62C2×#11758198—21no—
63C2×#11758198—21no—
64C2×#11758198—21no—
65C2×C4×Dic61—21no—
66C2×C4×Dic61—21no—
67C2×C4×Dic61D411yescharacteristic
68C2×C4×Dic61D411yescharacteristic
69C2×C4×Dic61C2311yescharacteristic
70C42×D61—28no—
71C42×D61—22no—
72C42×D61—22no—
73C22×Q8×C61C2×C411yescharacteristic
74C4×Q8×C61—22no—
75C4×Q8×C61—22no—
76C2×C4⋊C4×C61—21no—
77C2×C4⋊C4×C61C2×C411yescharacteristic
78C2×C42×C61—21no—
79C2×C42×C61C2×C411yescharacteristic
80C23×D61—21no—
81C23×D61C22⋊C411yescharacteristic
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61C22⋊C412yes—
86C2×Q8×C61C2×C812yes—
87C2×Q8×C61M1612yes—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61C22⋊C411yescharacteristic
91C22×C4×C61C22⋊C411yescharacteristic
92C22×C4×C61C22×C411yescharacteristic
93C22×Dic61—21no—
94C22×Dic61C22⋊C411yescharacteristic
95C22×Dic61C2×D411yescharacteristic
96C22×Dic61C2×D411yescharacteristic
97#11758226—28no—
98#11758226—28no—
99#11758226—28no—
100#11758226—28no—
101C2×D244—24no—
102C2×D244—24no—
103C2×D244—24no—
104C2×D244—21no—
105C2×D244—21no—
106C2×D244—21no—
107C2×D244C22⋊C412yes—
108C2×D244C2×C812yes—
109C2×D244M1612yes—
110C2×C4×D61—24no—
111C2×C4×D61—24no—
112C2×C4×D61—21no—
113C2×C4×D61—21no—
114C2×C4×D61—21no—
115C2×C4×D61—21no—
116C2×C4×D61—24no—
117C2×C4×D61—24no—
118C2×C4×D61—22no—
119C2×C4×D61—24no—
120C2×C4×D61—22no—
121C2×C4×D61—22no—
122C2×C4×D61—22no—
123C2×C4×D61—21no—
124C2×C4×D61—21no—
125C2×C4×D61—41no—
126C2×C4×D61—42no—
127C2×C4×D61—42no—
128C2×C4×D61—42no—
129C2×C4×D61—41no—
130C2×C4×D61—41no—
131C2×C4×D61C2×C812yes—
132C2×C4×D61M1612yes—
133C2×#92420—24no—
134C2×#92420—42no—
135C2×#92420—42no—
136C2×#92420—42no—
137C2×#92420—42no—
138C2×#92420—42no—
139C4⋊C4×C61—24no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61C22⋊C412yes—
142C42×C61—24no—
143C42×C61—21no—
144C42×C61—21no—
145#11758198—24no—
146#11758198—24no—
147#11758198—24no—
148C4⋊Dic61—21no—
149C4⋊Dic61—24no—
150C4⋊Dic61C22⋊C412yes—
151C4×Dic61—24no—
152C4×Dic61—22no—
153C4×Dic61—24no—
154C4×Dic61—22no—
155C4×Dic61C2×D412yes—
156C4×Dic61C2×D412yes—
157C23×C61C2×C22⋊C411yescharacteristic
158C22×D61—21no—
159C22×D61—22no—
160C22×D61—22no—
161C22×D61—21no—
162C22×D61—22no—
163C22×D61—21no—
164C22×D61—21no—
165C22×D61—21no—
166C22×D61—21no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61C22⋊C812yes—
172Q8×C61—22no—
173Q8×C61—22no—
174Q8×C61—22no—
175Q8×C61C22⋊C814yescomplemented
176C2×C4×C61—22no—
177C2×C4×C61—21no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—21no—
181C2×C4×C61—21no—
182C2×C4×C61—22no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61#10412yes—
188C2×C4×C61C2×C22⋊C411yescharacteristic
189C2×C4×C61C2×C22⋊C411yescharacteristic
190C2×C4×C61C22×C811yescharacteristic
191C2×C4×C61C2×M1611yescharacteristic
192C2×C4×C61C2×M1611yescharacteristic
193C2×C4×C61C2×M1611yescharacteristic
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—21no—
197C2×Dic61—21no—
198C2×Dic61—22no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61C22⋊C812yes—
202C2×Dic61#12012yes—
203C2×Dic61#12012yes—
204C2×Dic61#13512yes—
205C2×Dic61AGL(1,ℤ/8)11yescharacteristic
206C2×Dic61#13711yescharacteristic
207D244—216no—
208D244—22no—
209D244—22no—
210D244—22no—
211D244C22⋊C814yescomplemented
212C4×D61—216no—
213C4×D61—22no—
214C4×D61—22no—
215C4×D61—22no—
216C4×D61—22no—
217C4×D61—44no—
218C4×D61—48no—
219C4×D61—42no—
220C4×D61—44no—
221C4×D61—42no—
222C4×D61—44no—
223#92420—44no—
224#92420—82no—
225#8312—611nomaximal, Sylow
226C22×C61#37911yescharacteristic
227C22×C61C2×C22⋊C811yescharacteristic
228C22×C61#40711yescharacteristic
229C22×C61#41611yescharacteristic
230C22×C61#41711yescharacteristic
231C22×C61C2×#10411yescharacteristic
232C22×C61#42111yescharacteristic
233C2×D61—22no—
234C2×D61—22no—
235C2×D61—22no—
236C2×D61—24no—
237C2×D61—42no—
238C2×D61—42no—
239C2×D61—41no—
240C2×D61—42no—
241C2×D61—41no—
242C2×D61—42no—
243C2×D61—41no—
244C2×D61—42no—
245C2×D61—41no—
246C2×D61—42no—
247C4×C61—24no—
248C4×C61—22no—
249C4×C61—41no—
250C4×C61—42no—
251C4×C61C2×C22⋊C811yescharacteristic
252C4×C61C2×C22⋊C811yescharacteristic
253C4×C61#40711yescharacteristic
254C4×C61#40711yescharacteristic
255Dic61—22no—
256Dic61—22no—
257Dic61—42no—
258Dic61#44912yes—
259Dic61#45212yes—
260C2×C4×#41—611no—
261#1797—611no—
262C4×C22⋊C8—611no—
263C2×Q8⋊C8—612no—
264C2×D4⋊C8—612no—
265C2×C61#147611yescharacteristic
266C2×C61#147711yescharacteristic
267C2×C61#148811yescharacteristic
268C2×C61#148911yescharacteristic
269C2×C61#177911yescharacteristic
270C2×C61#178811yescharacteristic
271C2×C61#178911yescharacteristic
272D61—42no—
273D61—44no—
274C22×#41—611no—
275C4×#41—1224no—
276C4×#41—1224no—
277C2×C4×Q8—611no—
278C2×C4×Q8#692311yescharacteristic
279C2×C4×D4—611no—
280C2×C4×D4—611no—
281C2×C4×D4—1221no—
282C2×C4×D4—1221no—
283C2×#117—611no—
284C2×#117—1221no—
285C22×C42—611no—
286C22×C42—1221no—
287C2×C4⋊C8—612no—
288C2×C22⋊C8—1221no—
289C2×C22⋊C8—1221no—
290C2×C4×C8—612no—
291#336—1221no—
292#336—1221no—
293Q8⋊C8—1224no—
294D4⋊C8—1224no—
295C61#831211yescharacteristic, complemented, Sylow
296C2×#41—614no—
297C2×#41—1222no—
298C2×#41—1222no—
299C2×#41—1222no—
300C2×#41—1222no—
301C2×#41—1222no—
302C22×Q8C2×#692311yescharacteristic
303C22×D4—611no—
304C22×D4—1221no—
305C23×C4—611no—
306C23×C4—611no—
307C23×C4—611no—
308C23×C4—1221no—
309C23×C4—1221no—
310C23×C4—1221no—
311C22×C8—1222no—
312C22×C8—1222no—
313C4×Q8—22no—
314C4×Q8—22no—
315C4×Q8—614no—
316C4×Q8—1222no—
317C4×D4—614no—
318C4×D4—1222no—
319C4×D4—1222no—
320C4×D4—1228no—
321C4×D4—1222no—
322C4×D4—1228no—
323#117—1222no—
324#117—1228no—
325#117—1222no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—611no—
328C2×C4⋊C4—1221no—
329C2×C4⋊C4C2×#692311yescharacteristic
330C2×C22⋊C4—1221no—
331C2×C22⋊C4—1221no—
332C2×C22⋊C4—1221no—
333C2×C42—21no—
334C2×C42—611no—
335C2×C42—611no—
336C2×C42—611no—
337C2×C42—1222no—
338C2×C42—1222no—
339C2×C42—1228no—
340C2×C42—1221no—
341C2×C42—1221no—
342C2×C42C2×#692311yescharacteristic
343C4⋊C8—1222no—
344C4⋊C8—1222no—
345C22⋊C8—1224no—
346C22⋊C8—2442no—
347C4×C8—1222no—
348C4×C8—1222no—
349C24—611no—
350C24—1221no—
351#41—1228no—
352#41—1228no—
353#41—1228no—
354#41—1228no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8D61⋊C812yes—
359C2×Q8#1175821312yes—
360C2×Q8C22⋊#692312yes—
361C2×D4—612no—
362C2×D4—612no—
363C2×D4—612no—
364C2×D4—1224no—
365C2×D4—1224no—
366C2×D4—1224no—
367C2×D4—1221no—
368C2×D4—1221no—
369C2×D4—1221no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—612no—
376C22×C4—612no—
377C22×C4—1224no—
378C22×C4—1221no—
379C22×C4—1224no—
380C22×C4—1222no—
381C22×C4—1222no—
382C22×C4—1222no—
383C22×C4—1221no—
384C22×C4—1224no—
385C22×C4—1224no—
386C22×C4—1224no—
387C22×C4—1221no—
388C22×C4—1221no—
389C22×C4—1221no—
390C22×C4—1221no—
391C22×C4—1221no—
392C22×C4—1222no—
393C22×C4—2441no—
394C22×C4—2442no—
395C22×C4—2442no—
396C22×C4—2441no—
397C22×C4—2441no—
398C22×C4—2442no—
399C22×C4C22⋊#692311yescharacteristic
400C22×C4C22⋊#692311yescharacteristic
401C22×C4C22×#692311yescharacteristic
402C2×C8—1224no—
403C2×C8—2442no—
404C2×C8—2442no—
405C2×C8—2442no—
406C2×C8—2442no—
407C2×C8—2442no—
408C4⋊C4—24no—
409C4⋊C4—21no—
410C4⋊C4—612no—
411C4⋊C4—1224no—
412C4⋊C4—1221no—
413C4⋊C4C22⋊#692312yes—
414C22⋊C4—1224no—
415C22⋊C4—1224no—
416C22⋊C4—1224no—
417C42—24no—
418C42—21no—
419C42—21no—
420C42—612no—
421C42—612no—
422C42—1222no—
423C42—1222no—
424C42—1224no—
425C42—1224no—
426C23—612no—
427C23—1222no—
428C23—1222no—
429C23—1221no—
430C23—1221no—
431C23—1221no—
432C23—1221no—
433C23—1221no—
434C23—1222no—
435C23—1221no—
436C23—2441no—
437C23—2441no—
438C23—2441no—
439C23—2441no—
440C23C2×C22⋊#692311yescharacteristic
441Q8—22no—
442Q8—22no—
443Q8—22no—
444Q8#1451983414yescomplemented
445D4—614no—
446D4—12216no—
447D4—1222no—
448D4—1222no—
449D4—1222no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—612no—
462C2×C4—611no—
463C2×C4—611no—
464C2×C4—612no—
465C2×C4—612no—
466C2×C4—612no—
467C2×C4—12216no—
468C2×C4—1221no—
469C2×C4—1221no—
470C2×C4—1221no—
471C2×C4—1221no—
472C2×C4—1222no—
473C2×C4—1222no—
474C2×C4—1222no—
475C2×C4—1222no—
476C2×C4—1222no—
477C2×C4—2444no—
478C2×C4—2448no—
479C2×C4—2442no—
480C2×C4—2442no—
481C2×C4—2444no—
482C2×C4—2444no—
483C2×C4—2441no—
484C2×C4—2441no—
485C2×C4#1451984212yes—
486C2×C4C2×C22⋊#692311yescharacteristic
487C2×C4C2×C22⋊#692311yescharacteristic
488C2×C4C2×D61⋊C811yescharacteristic
489C2×C4D61⋊M1611yescharacteristic
490C2×C4D61⋊M1611yescharacteristic
491C2×C4C2×#1175821311yescharacteristic
492C8—4882no—
493C8—2444no—
494C22—1222no—
495C22—1222no—
496C22—1224no—
497C22—1222no—
498C22—2442no—
499C22—2442no—
500C22—2441no—
501C22—2442no—
502C22—2441no—
503C22—2442no—
504C22—2441no—
505C22—2442no—
506C22—2441no—
507C22—2442no—
508C22#1684070311yescharacteristic
509C22D61⋊(C22⋊C8)11yescharacteristic
510C22#1684073311yescharacteristic
511C22#1684075211yescharacteristic
512C22#1684075311yescharacteristic
513C22C2×#1451984211yescharacteristic
514C22#1684076111yescharacteristic
515C4—24no—
516C4—22no—
517C4—41no—
518C4—42no—
519C4—612no—
520C4—612no—
521C4—1222no—
522C4—1222no—
523C4—2442no—
524C4D61⋊(C22⋊C8)11yescharacteristic
525C4C2×#1451983411yescharacteristic
526C4#1684073311yescharacteristic
527C4#1684073411yescharacteristic
528C2—2442no—
529C2—2444no—
530C2#2146111311yescharacteristic
531C2#2146111711yescharacteristic
532C2#2146115311yescharacteristic
533C2#2146115711yescharacteristic
534C2#2146164211yescharacteristic
535C2#2146165911yescharacteristic
536C2#2146166211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C4×Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×#11758226C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×Q8#6923
hypocenterC61#8312
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #21461674C2semidirect
2. C4×#14519834C2semidirect
3. C2×Q8⋊#92420C2semidirect
4. C2×#16840610C2semidirect
40. C2×#11758226C8semidirect
175. Q8×C61C22⋊C8semidirect
211. D244C22⋊C8semidirect
295. C61#8312semidirect
444. Q8#14519834semidirect

Maximal subgroups

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

subgroupindex
#214616742
C4×#145198342
C2×Q8⋊#924202
C2×#168406102
C2×C4×#117582262
#831261