Finite Group Databasebeta

← #30598388

Subgroups — #30598388

Order 15616.

998 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 998 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461683C211yesmaximal, characteristic, complemented
2#21461328C212yesmaximal, complemented
3#21461144C212yesmaximal, complemented
4#21461058C211yesmaximal, characteristic, complemented
5C2×#16840412C211yesmaximal, characteristic
6#16840779C2212yes—
7#16840765C2212yes—
8C2×#14519837—21no—
9#16840642—21no—
10#16840621—24no—
11D4⋊#92420—24no—
12#16840606—21no—
13#16840605—21no—
14C22×#11758224—21no—
15#16840412—24no—
16#16840412—24no—
17C2×#14519776C2211yescharacteristic
18C2×#14519759—21no—
19C2×#14519758—21no—
20C2×#14519754—21no—
21C2×#14519748C411yescharacteristic
22C2×D4×Dic61C2211yescharacteristic
23C2×C4×C22⋊D61C2211yescharacteristic
24C22×C4⋊Dic61C411yescharacteristic
25C2×C4⋊C4×D61C411yescharacteristic
26C2×#121×C61C411yescharacteristic
27C2×#11758217—22no—
28#14519844—22no—
29#14519844—22no—
30C4⋊#92420—22no—
31#14519837—42no—
32C22⋊#92420—22no—
33C4×#92420—22no—
34C2×#11758224—28no—
35C2×#11758224—44no—
36C2×#11758224—42no—
37C2×#11758224—42no—
38C22×Dic122—21no—
39C22×C22⋊D61—21no—
40C22×C22⋊D61D411yescharacteristic
41C23×Dic61—21no—
42C23×Dic61—21no—
43C22×C4×D61—21no—
44C22×C4×D61C2×C411yescharacteristic
45#14519776—22no—
46#14519776D414yes—
47#14519759—28no—
48#14519758—28no—
49#14519754—28no—
50#14519748—22no—
51#14519748—22no—
52D4×Dic61—22no—
53D4×Dic61D414yes—
54C4×C22⋊D61—22no—
55C4×C22⋊D61—22no—
56C2×C4⋊Dic61—21no—
57C2×C4⋊Dic61—22no—
58C2×C4⋊Dic61—22no—
59C2×C4⋊Dic61C2×C411yescharacteristic
60C2×C4⋊Dic61C2×C411yescharacteristic
61C2×#11758196—21no—
62C2×#11758196—21no—
63C2×#11758196D411yescharacteristic
64C4⋊C4×D61—22no—
65C4⋊C4×D61—22no—
66C2×C22⋊Dic61—21no—
67C2×C22⋊Dic61—21no—
68C2×C22⋊Dic61D411yescharacteristic
69C2×#11758198D411yescharacteristic
70C2×C4×Dic61C2311yescharacteristic
71C22×D4×C61—21no—
72C22×D4×C61C2×C411yescharacteristic
73C23×C4×C61C2×C411yescharacteristic
74#121×C61—22no—
75#121×C61—22no—
76C2×C4⋊C4×C61C2×C411yescharacteristic
77C2×C22⋊C4×C61—21no—
78C24×C61—21no—
79C24×C61C22⋊C411yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C2×D4×C61—24no—
82C2×D4×C61—21no—
83C2×D4×C61—42no—
84C2×D4×C61—42no—
85C2×D4×C61—42no—
86C2×D4×C61C22⋊C412yes—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—42no—
91C22×C4×C61C22⋊C411yescharacteristic
92C22×C4×C61C22×C411yescharacteristic
93C2×C22⋊D61—24no—
94C2×C22⋊D61—22no—
95C2×C22⋊D61—22no—
96C2×C22⋊D61—42no—
97C2×C22⋊D61—42no—
98C2×C22⋊D61D812yes—
99C2×C22⋊D61SD1612yes—
100C22×Dic61—24no—
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61—24no—
104C22×Dic61—42no—
105C22×Dic61—42no—
106C22×Dic61—41no—
107C22×Dic61—41no—
108C22×Dic61—42no—
109C22×Dic61C22⋊C411yescharacteristic
110C22×Dic61C2×D411yescharacteristic
111C22×Dic61C2×D411yescharacteristic
112#11758224—416no—
113#11758224—416no—
114C2×C4×D61—24no—
115C2×C4×D61—21no—
116C2×C4×D61—21no—
117C2×C4×D61—42no—
118C2×C4×D61—42no—
119C2×C4×D61—42no—
120C2×Dic122—24no—
121C2×Dic122—41no—
122C2×Dic122—41no—
123C2×Dic122—42no—
124#11758217—42no—
125#11758217—42no—
126C2×#92420—42no—
127C2×#92420—42no—
128C4⋊C4×C61—21no—
129C4⋊C4×C61C22⋊C412yes—
130C22⋊C4×C61—24no—
131C22⋊Dic61—24no—
132C22⋊Dic61—24no—
133C22⋊Dic61—22no—
134#11758198—22no—
135C4⋊Dic61—24no—
136C4⋊Dic61—21no—
137C4⋊Dic61—21no—
138C4⋊Dic61C22⋊C412yes—
139C4⋊Dic61C22⋊C412yes—
140#11758196—24no—
141#11758196—24no—
142#11758196—22no—
143C4×Dic61C2×D412yes—
144C4×Dic61C2×D412yes—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61—22no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61—42no—
151C23×C61—42no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61#10212yes—
155C23×C61C2×C22⋊C411yescharacteristic
156C22×D61—21no—
157C22×D61—21no—
158C22×D61—41no—
159C22×D61—41no—
160C22×D61#10212yes—
161D4×C61—24no—
162D4×C61—42no—
163D4×C61—48no—
164C2×C4×C61—22no—
165C2×C4×C61—22no—
166C2×C4×C61—21no—
167C2×C4×C61—42no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—42no—
171C2×C4×C61—41no—
172C2×C4×C61C2×C22⋊C411yescharacteristic
173C2×C4×C61C2×C22⋊C411yescharacteristic
174C22⋊D61—24no—
175C22⋊D61—24no—
176C22⋊D61—48no—
177C2×Dic61—21no—
178C2×Dic61—22no—
179C2×Dic61—22no—
180C2×Dic61—41no—
181C2×Dic61—48no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—44no—
187C2×Dic61—44no—
188C2×Dic61—41no—
189C2×Dic61#12012yes—
190C2×Dic61#12012yes—
191C2×Dic61C2×D811yescharacteristic
192C2×Dic61C2×SD1611yescharacteristic
193C2×Dic61AGL(1,ℤ/8)12yes—
194C4×D61—42no—
195C4×D61—48no—
196C4×D61—42no—
197Dic122—44no—
198Dic122—44no—
199#92420—82no—
200#92420—82no—
201#8387—611nomaximal, Sylow
202C22×C61—21no—
203C22×C61—21no—
204C22×C61—22no—
205C22×C61—42no—
206C22×C61—42no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61—42no—
210C22×C61—42no—
211C22×C61—42no—
212C22×C61—82no—
213C22×C61—82no—
214C22×C61#37911yescharacteristic
215C22×C61C2×#10211yescharacteristic
216C22×C61#41811yescharacteristic
217C2×D61—22no—
218C2×D61—42no—
219C2×D61—41no—
220C2×D61—41no—
221C2×D61—42no—
222C4×C61—21no—
223C4×C61—41no—
224C4×C61—42no—
225C4×C61#41312yes—
226Dic61—22no—
227Dic61—41no—
228Dic61—42no—
229Dic61—42no—
230Dic61#44712yes—
231Dic61#45012yes—
232C2×#547—611no—
233#1800—611no—
234#1546—612no—
235#1486—612no—
236#1460—611no—
237C2×C61—21no—
238C2×C61—21no—
239C2×C61—42no—
240C2×C61—82no—
241C2×C61#178511yescharacteristic
242C2×C61#178611yescharacteristic
243C2×C61#179611yescharacteristic
244D61—42no—
245C22×#41—1221no—
246#547—1224no—
247#547—1224no—
248C2×C4⋊Q8—611no—
249C2×#123—1221no—
250C2×#123—1221no—
251C2×C22⋊Q8—1221no—
252C2×#121—611no—
253C2×#121#692311yescharacteristic
254C2×C4×D4—611no—
255C2×C4×D4—611no—
256C22×C4⋊C4—611no—
257C22×C4⋊C4—611no—
258#431—612no—
259#423—612no—
260C2×#100—1221no—
261#343—1221no—
262#332—1224no—
263D4⋊C8—1224no—
264#323—1221no—
265#323—1221no—
266C61#838711yescharacteristic, complemented, Sylow
267C2×#41—1228no—
268C2×#41—2442no—
269C2×#41—2442no—
270C2×#41—2444no—
271C22×Q8—1221no—
272C22×D4—21no—
273C22×D4—611no—
274C22×D4—1221no—
275C22×D4C2×#692311yescharacteristic
276C23×C4—611no—
277C23×C4—1221no—
278C23×C4—1221no—
279C23×C4—1221no—
280C23×C4C2×#692311yescharacteristic
281C2×M16—1222no—
282C4⋊Q8—614no—
283C4⋊Q8—1222no—
284#123—1228no—
285#123—1228no—
286C22⋊Q8—1228no—
287#121—22no—
288#121—22no—
289#121—1222no—
290#121—1222no—
291C4×D4—614no—
292C4×D4—1222no—
293C4×D4—1222no—
294C4×D4—1222no—
295C2×C4⋊C4—611no—
296C2×C4⋊C4—611no—
297C2×C4⋊C4—611no—
298C2×C4⋊C4—1222no—
299C2×C4⋊C4—1222no—
300C2×C4⋊C4—1222no—
301C2×C4⋊C4—1221no—
302C2×C4⋊C4—1221no—
303C2×C4⋊C4—1221no—
304C2×C4⋊C4—1222no—
305C2×C4⋊C4C2×#692311yescharacteristic
306C2×C22⋊C4—21no—
307C2×C22⋊C4—611no—
308C2×C22⋊C4—611no—
309C2×C22⋊C4—1221no—
310C2×C22⋊C4—1221no—
311C2×C42—611no—
312C4⋊C8—1222no—
313C4⋊C8—1222no—
314C4⋊C8—1222no—
315#100—2442no—
316C22⋊C8—1222no—
317C4×C8—1222no—
318C24—21no—
319C24—611no—
320C24C22⋊#692311yescharacteristic
321#41—24416no—
322#41—24416no—
323C2×Q8—1224no—
324C2×Q8—2441no—
325C2×Q8—2441no—
326C2×Q8—2442no—
327C2×D4—24no—
328C2×D4—21no—
329C2×D4—42no—
330C2×D4—42no—
331C2×D4—42no—
332C2×D4—612no—
333C2×D4—612no—
334C2×D4—1222no—
335C2×D4—1222no—
336C2×D4—1224no—
337C2×D4—2442no—
338C2×D4—2442no—
339C2×D4C22⋊#692312yes—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—42no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—611no—
347C22×C4—1224no—
348C22×C4—1224no—
349C22×C4—1224no—
350C22×C4—1221no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—1221no—
354C22×C4—2442no—
355C22×C4—2442no—
356C22×C4—2442no—
357C22×C4—2441no—
358C22×C4—2441no—
359C22×C4—2442no—
360C22×C4—2442no—
361C22×C4—2442no—
362C22×C4C22⋊#692311yescharacteristic
363C22×C4C22×#692311yescharacteristic
364M16—2442no—
365M16—2442no—
366C2×C8—2442no—
367C2×C8—2442no—
368C4⋊C4—21no—
369C4⋊C4—612no—
370C4⋊C4—612no—
371C4⋊C4—1222no—
372C4⋊C4—1224no—
373C4⋊C4—1224no—
374C4⋊C4—1224no—
375C4⋊C4—1221no—
376C4⋊C4—1221no—
377C4⋊C4C22⋊#692312yes—
378C22⋊C4—24no—
379C22⋊C4—1222no—
380C22⋊C4—1222no—
381C22⋊C4—1224no—
382C22⋊C4—1224no—
383C42—612no—
384C42—612no—
385C23—21no—
386C23—21no—
387C23—22no—
388C23—41no—
389C23—41no—
390C23—42no—
391C23—42no—
392C23—41no—
393C23—41no—
394C23—612no—
395C23—1221no—
396C23—1221no—
397C23—2441no—
398C23—2441no—
399C23#1451983912yes—
400C23C2×C22⋊#692311yescharacteristic
401Q8—2444no—
402Q8—2444no—
403D4—24no—
404D4—42no—
405D4—48no—
406D4—1224no—
407D4—1224no—
408D4—2448no—
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—22no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—611no—
418C2×C4—611no—
419C2×C4—612no—
420C2×C4—612no—
421C2×C4—612no—
422C2×C4—1221no—
423C2×C4—1222no—
424C2×C4—1222no—
425C2×C4—2442no—
426C2×C4—2448no—
427C2×C4—2444no—
428C2×C4—2444no—
429C2×C4—2441no—
430C2×C4—2448no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4—2441no—
434C2×C4—2441no—
435C2×C4—2442no—
436C2×C4—2441no—
437C2×C4C2×C22⋊#692311yescharacteristic
438C2×C4C2×C22⋊#692311yescharacteristic
439C8—4882no—
440C8—4882no—
441C22—21no—
442C22—21no—
443C22—22no—
444C22—42no—
445C22—42no—
446C22—41no—
447C22—41no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—82no—
452C22—82no—
453C22—1222no—
454C22—2442no—
455C22—2442no—
456C22—2441no—
457C22—2441no—
458C22#1684070311yescharacteristic
459C22C2×#1451983911yescharacteristic
460C22#1684075411yescharacteristic
461C4—21no—
462C4—41no—
463C4—42no—
464C4—612no—
465C4—612no—
466C4—1222no—
467C4—2441no—
468C4—2442no—
469C4—2442no—
470C4#1684074912yes—
471C2—21no—
472C2—21no—
473C2—42no—
474C2—82no—
475C2—2442no—
476C2#2146165611yescharacteristic
477C2#2146165711yescharacteristic
478C2#2146167211yescharacteristic
subgroupG/H
centerC22#16840703
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#121×C61C4
socleC22×C61#379
prime radicalC2×#16840412C2
cosocleC2×C4×Dic61C23
hypercenterC2×#121#6923
hypocenterC61#8387
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #21461683C2semidirect
2. #21461328C2semidirect
3. #21461144C2semidirect
4. #21461058C2semidirect
266. C61#8387semidirect

Maximal subgroups

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

subgroupindex
#214616832
#214613282
#214611442
#214610582
C2×#168404122
#838761