Finite Group Databasebeta

← #30597832

Subgroups — #30597832

Order 15616.

534 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 102 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#21462535C211yesmaximal, characteristic
2#21461554C211yesmaximal, characteristic, complemented
3#21461553C211yesmaximal, characteristic, complemented
4#21461197C211yesmaximal, characteristic
5#21460702C211yesmaximal, characteristic, complemented
6#21460700C211yesmaximal, characteristic, complemented
7#21444309C211yesmaximal, characteristic
8C2×#14519865C411yescharacteristic, complemented
9C22×D61⋊C8C2211yescharacteristic
10#16840792—21no—
11#16840791—21no—
12#16840790—21no—
13#16840789—21no—
14#16840769C411yescharacteristic, complemented
15#16840737C411yescharacteristic, complemented
16#16840733C2211yescharacteristic
17C2×#14519834C2211yescharacteristic
18#16840727C411yescharacteristic, complemented
19C2×C4×#92420—21no—
20C2×C8×#6923—21no—
21C4×C22⋊#6923C2211yescharacteristic
22#16840628—21no—
23(C2×#6923)⋊C8—21no—
24#16840616C412yescomplemented
25#16840614C412yescomplemented
26#16840275C2211yescharacteristic
27C22⋊C8×D61C2211yescharacteristic
28#16839609C2211yescharacteristic
29#16839499C411yescharacteristic, complemented
30#16839497C411yescharacteristic, complemented
31#16839495C411yescharacteristic, complemented
32C61×#328C411yescharacteristic, complemented
33#14519865—42no—
34C2×#11758213—21no—
35C2×#11758213C2×C411yescharacteristic
36C2×#11758213C2×C411yescharacteristic
37C2×D61⋊C8—21no—
38C2×D61⋊C8—42no—
39C2×D61⋊C8C2×C411yescharacteristic
40C2×D61⋊C8C2×C411yescharacteristic
41C2×D61⋊C8D411yescharacteristic
42C2×D61⋊C8D411yescharacteristic
43C22×#92420—21no—
44C22×#92420D411yescharacteristic
45C22×#92420D411yescharacteristic
46C2×C22⋊#6923—21no—
47C2×C4×#6923—21no—
48#14519844—21no—
49C4⋊#92420—21no—
50#14519834—21no—
51#14519834—21no—
52#14519834—21no—
53#14519834—21no—
54#14519834C2×C412yes—
55C22⋊#92420—21no—
56#14519832—21no—
57C4×#92420—21no—
58C4×#92420—42no—
59C8×#6923—42no—
60(C2×#6923)⋊C4C2×C412yes—
61C2×#11758226C2×C411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C2×C8×D61—21no—
64#14519762—21no—
65#14519753C2×C411yescharacteristic
66#14519752C2×C411yescharacteristic
67#14519751C2×C411yescharacteristic
68#14519747—21no—
69#14519739—21no—
70#14519737—21no—
71#14519735C2×C411yescharacteristic
72C2×#11758198—21no—
73C2×C4×Dic61—21no—
74C22⋊#92418C2×C411yescharacteristic
75#14519689—21no—
76#14519684C2×C411yescharacteristic
77C22⋊Q8×C61C2×C411yescharacteristic
78C22⋊C8×C61C2×C411yescharacteristic
79#95×C61C2×C411yescharacteristic
80C23×D61#4111yescharacteristic
81C22×#6923—22no—
82C2×Q8×C61C4211yescharacteristic
83C22×C4×C61—21no—
84C22×C4×C61C22×C411yescharacteristic
85C2×C22⋊D61—21no—
86C22×Dic61—21no—
87C22×Dic61C2×D411yescharacteristic
88#11758226—41no—
89#11758226—41no—
90C2×D244—21no—
91C2×D244—21no—
92C2×D244C4211yescharacteristic
93C2×C4×D61—21no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61C22×C411yescharacteristic
97C2×C4×D61C22×C411yescharacteristic
98C2×C4×D61C2×D411yescharacteristic
99C2×C4×D61#4111yescharacteristic
100C22⋊#6923—22no—
101C22⋊#6923—22no—
102C2×#92420—22no—
103C2×#92420—21no—
104C2×#92420—21no—
105C2×#92420—22no—
106C2×#92420—41no—
107C2×#92420—41no—
108C2×#92420—41no—
109C2×#92420C22⋊C411yescharacteristic
110C2×#92420C22⋊C411yescharacteristic
111C2×#92420C22⋊C411yescharacteristic
112C2×#92420C22⋊C411yescharacteristic
113C4×#6923—41no—
114C4×#6923—41no—
115#11758213—42no—
116#11758213—41no—
117#11758213—41no—
118D61⋊C8—22no—
119D61⋊C8—22no—
120D61⋊C8—41no—
121D61⋊C8—41no—
122D61⋊C8—42no—
123C2×C8×C61—21no—
124C4⋊C4×C61—21no—
125C4⋊C4×C61C4211yescharacteristic
126C22⋊C4×C61—21no—
127#11758198—24no—
128#11758198—21no—
129#11758198—21no—
130#11758198—21no—
131#11758198—21no—
132C4⋊Dic61C4211yescharacteristic
133#11758196—21no—
134C4×Dic61—21no—
135C4×Dic61—41no—
136C4×Dic61—41no—
137C2×#92418—21no—
138C8×D61—41no—
139C8×D61—41no—
140C23×C61C4×D411yescharacteristic
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—22no—
144C22×D61—21no—
145C22×D61—41no—
146C22×D61#11711yescharacteristic
147C22×D61C4×D411yescharacteristic
148C2×#6923—24no—
149C2×#6923—42no—
150C2×#6923—42no—
151Q8×C61—41no—
152C2×C4×C61—22no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61C2×C4211yescharacteristic
159C2×C4×C61C4×D411yescharacteristic
160C22⋊D61—41no—
161C22⋊D61—41no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—22no—
165C2×Dic61—21no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61C2×C22⋊C411yescharacteristic
169C2×Dic61C4×D411yescharacteristic
170D244—41no—
171D244—42no—
172D244—42no—
173C4×D61—21no—
174C4×D61—21no—
175C4×D61—21no—
176C4×D61—21no—
177C4×D61—41no—
178C4×D61—41no—
179C4×D61—41no—
180C4×D61—41no—
181#92420—21no—
182#92420—21no—
183#92420—21no—
184#92420—42no—
185#92420—41no—
186#92420—41no—
187#92420#9912yes—
188C8×C61—41no—
189#92418—41no—
190#8238—611nomaximal, Sylow
191C22×C61—21no—
192C22×C61—21no—
193C22×C61C4×C22⋊C411yescharacteristic
194C22×C61#44311yescharacteristic
195C22×C61#44311yescharacteristic
196C2×D61—21no—
197C2×D61—21no—
198C2×D61—21no—
199C2×D61—21no—
200C2×D61—21no—
201C2×D61—42no—
202C2×D61—42no—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—41no—
206C2×D61#44312yes—
207#6923—44no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—42no—
211C4×C61—41no—
212C4×C61—41no—
213Dic61—21no—
214Dic61—42no—
215Dic61—41no—
216Dic61C2×#9911yescharacteristic
217Dic61#41011yescharacteristic
218#2929—611no—
219C8×C22⋊C4—611no—
220C8×C22⋊C4—611no—
221#1501—611no—
222#1501—611no—
223#1298—611no—
224#1297—611no—
225C2×C61—21no—
226C2×C61—21no—
227C2×C61C4×#9911yescharacteristic
228C2×C61#176411yescharacteristic
229C2×C61#176411yescharacteristic
230D61—22no—
231D61—41no—
232D61—81no—
233C2×#131—611no—
234C23×C8—611no—
235#525—611no—
236#435—1221no—
237#435—1221no—
238C8×D4—1221no—
239C8×D4—1221no—
240#424—611no—
241#408—611no—
242#407—611no—
243C2×C22⋊C8—611no—
244C2×C22⋊C8—611no—
245#405—611no—
246C2×C4×C8—1221no—
247C2×C4×C8—1221no—
248C4×C22⋊C4—611no—
249C4×C22⋊C4—611no—
250#336—1221no—
251#336—1221no—
252#328—612no—
253#328—611no—
254#328#692311yescharacteristic, complemented
255#327—612no—
256#327—611no—
257#327—611no—
258C61#823811yescharacteristic, complemented, Sylow
259C2×#41—611no—
260C23×C4—611no—
261#131—2442no—
262C2×M16—611no—
263C2×M16—611no—
264C2×M16—1221no—
265C22×C8—611no—
266C22×C8—611no—
267C22×C8—611no—
268C22×C8—611no—
269C22×C8—611no—
270C22×C8—611no—
271C22×C8—1221no—
272C22×C8—1221no—
273C22×C8—1221no—
274C22×C8—2442no—
275#123—1221no—
276C22⋊Q8—611no—
277C22⋊Q8C2×#692311yescharacteristic
278#121—611no—
279#121—611no—
280#120—1221no—
281C4×D4—1221no—
282C4×D4—1221no—
283#117—611no—
284C2×C22⋊C4—1221no—
285C2×C22⋊C4—1221no—
286C2×C42—1221no—
287C2×C42—1221no—
288C4⋊C8—1221no—
289C4⋊C8—1221no—
290C22⋊C8—612no—
291C22⋊C8—611no—
292C22⋊C8—1221no—
293C22⋊C8—1221no—
294C22⋊C8—1221no—
295C22⋊C8—1221no—
296C22⋊C8—1221no—
297C22⋊C8—1221no—
298C22⋊C8C2×#692311yescharacteristic
299#97—1221no—
300C4×C8—1221no—
301C4×C8—2442no—
302C4×C8—2442no—
303#95—612no—
304#95—611no—
305#95C2×#692311yescharacteristic
306C24—611no—
307#41—2441no—
308#41—2441no—
309C2×Q8C4×#692311yescharacteristic
310C2×D4—611no—
311C2×D4—1221no—
312C2×D4—1221no—
313C2×D4—1221no—
314C22×C4—21no—
315C22×C4—611no—
316C22×C4—611no—
317C22×C4—611no—
318C22×C4—611no—
319C22×C4—611no—
320C22×C4—1221no—
321C22×C4—1222no—
322C22×C4—1221no—
323C22×C4—2441no—
324C22×C4—2441no—
325C22×C4C22×#692311yescharacteristic
326M16—2442no—
327M16—2441no—
328M16—2441no—
329C2×C8—21no—
330C2×C8—611no—
331C2×C8—611no—
332C2×C8—611no—
333C2×C8—611no—
334C2×C8—1222no—
335C2×C8—1222no—
336C2×C8—1222no—
337C2×C8—1221no—
338C2×C8—1222no—
339C2×C8—1221no—
340C2×C8—1221no—
341C2×C8—2441no—
342C2×C8—2441no—
343C2×C8—2442no—
344C2×C8—2441no—
345C2×C8—2441no—
346C2×C8—2441no—
347C2×C8—2441no—
348C2×C8—2441no—
349C4⋊C4—21no—
350C4⋊C4—611no—
351C4⋊C4—1221no—
352C4⋊C4C4×#692311yescharacteristic
353C22⋊C4—21no—
354C22⋊C4—1221no—
355C22⋊C4—1221no—
356C22⋊C4—1221no—
357C22⋊C4—1224no—
358C22⋊C4—1222no—
359C22⋊C4—1222no—
360C22⋊C4—1221no—
361C42—1221no—
362C42—2441no—
363C42—2441no—
364C42—2441no—
365C42—2441no—
366C23—611no—
367C23—611no—
368C23—1222no—
369C23—1221no—
370C23—1221no—
371C23—1221no—
372C23—2441no—
373C23D4×#692311yescharacteristic
374Q8—41no—
375D4—2441no—
376D4—2442no—
377D4—2442no—
378D4—2441no—
379D4—2441no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—611no—
387C2×C4—611no—
388C2×C4—1221no—
389C2×C4—1221no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1222no—
395C2×C4—1224no—
396C2×C4—1221no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2442no—
403C2×C4—2442no—
404C2×C4—2441no—
405C2×C4C2×C4×#692311yescharacteristic
406C2×C4D4×#692311yescharacteristic
407C8—41no—
408C8—612no—
409C8—1221no—
410C8—1221no—
411C8—1221no—
412C8—2441no—
413C8—2441no—
414C8—2441no—
415C8—2442no—
416C22—21no—
417C22—21no—
418C22—612no—
419C22—1221no—
420C22—1221no—
421C22—1221no—
422C22—1221no—
423C22—1221no—
424C22—2442no—
425C22—2442no—
426C22—2441no—
427C22—2441no—
428C22—2441no—
429C22C22⋊C4×#692311yescharacteristic
430C22#1684080511yescharacteristic
431C22#1684080611yescharacteristic
432C4—21no—
433C4—21no—
434C4—42no—
435C4—41no—
436C4—41no—
437C4—611no—
438C4—611no—
439C4—1221no—
440C4—2442no—
441C4—2444no—
442C4—2441no—
443C2—21no—
444C2—21no—
445C2—1222no—
446C2—4881no—
447C2—2441no—
448C2#99×#692311yescharacteristic
449C2#2146159511yescharacteristic
450C2#2146159611yescharacteristic
subgroupG/H
centerC22C22⋊C4×#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#328C4
socleC22×C61C4×C22⋊C4
prime radical#16840275C22
cosocleC22×C4×D61C23
hypercenter#328#6923
hypocenterC61#8238
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #21461554C2semidirect
3. #21461553C2semidirect
5. #21460702C2semidirect
6. #21460700C2semidirect
8. C2×#14519865C4semidirect
14. #16840769C4semidirect
15. #16840737C4semidirect
18. #16840727C4semidirect
24. #16840616C4semidirect
25. #16840614C4semidirect
29. #16839499C4semidirect
30. #16839497C4semidirect
31. #16839495C4semidirect
32. C61×#328C4semidirect
254. #328#6923semidirect
258. C61#8238semidirect

Maximal subgroups

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

subgroupindex
#214625352
#214615542
#214615532
#214611972
#214607022
#214607002
#214443092
#823861