Finite Group Databasebeta

← #30601970

Subgroups — #30601970

Order 15616.

552 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 90 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#21462008C211yesmaximal, characteristic, complemented
2#21461959C211yesmaximal, characteristic
3#21461696C211yesmaximal, characteristic, complemented
4#21461555C211yesmaximal, characteristic, complemented
5#21461259C211yesmaximal, characteristic, complemented
6#21461256C211yesmaximal, characteristic
7C2×#16839994C211yesmaximal, characteristic
8C2×#14519846—21no—
9C2×#14519836—22no—
10D61⋊(C22⋊C8)C2211yescharacteristic
11C2×#14519831—21no—
12#16840704C2211yescharacteristic
13#16840704C2211yescharacteristic
14C4×C22⋊#6923C2211yescharacteristic
15#16840640—22no—
16#16840636—21no—
17(C2×#6923)⋊C8—21no—
18#16840616—22no—
19#16840614—22no—
20C22×#11758201C411yescharacteristic, complemented
21C22×C8×D61C2211yescharacteristic
22C2×#14519753C2211yescharacteristic
23C2×#14519752C2211yescharacteristic
24#16839994—21no—
25#16839994—21no—
26#16839994—21no—
27#16839994—21no—
28C2×#14519708C411yescharacteristic, complemented
29C2×#14519699C411yescharacteristic, complemented
30C2×#103×C61C411yescharacteristic, complemented
31C2×D61⋊C8—21no—
32C2×C4⋊#6923—21no—
33C2×C4⋊#6923—21no—
34C2×C22⋊#6923—21no—
35C2×C22⋊#6923—21no—
36C2×C22⋊#6923D412yes—
37C2×C4×#6923—21no—
38#14519846—42no—
39#14519836—44no—
40#14519834D412yes—
41C22⋊#92420—21no—
42#14519831—42no—
43(C2×#6923)⋊C4—21no—
44(C2×#6923)⋊C4—21no—
45(C2×#6923)⋊C4—21no—
46C22×D244—21no—
47C22×D244C2×C411yescharacteristic
48C22×C4×D61C2311yescharacteristic
49C2×#11758201—21no—
50C2×#11758201—21no—
51C2×#11758201—42no—
52C22×#92418C2×C411yescharacteristic
53C2×C8×D61—42no—
54C2×C8×D61D411yescharacteristic
55C2×C8×D61D411yescharacteristic
56C2×C8×D61D411yescharacteristic
57C2×C8×D61D411yescharacteristic
58#14519753—21no—
59#14519753—21no—
60#14519753—21no—
61#14519753—21no—
62#14519752—21no—
63#14519752—21no—
64#14519752—21no—
65#14519752—21no—
66C2×C4⋊Dic61C2×C411yescharacteristic
67C2×#11758196—21no—
68C2×#11758198—21no—
69C2×#11758198—21no—
70#14519708—21no—
71#14519708—21no—
72#14519699—21no—
73#14519699—21no—
74C22×Q8×C61C2×C411yescharacteristic
75C22×C8×C61C2×C411yescharacteristic
76C2×C4⋊C4×C61C2×C411yescharacteristic
77#103×C61—21no—
78#103×C61—21no—
79C23×D61—21no—
80C23×D61C2×D411yescharacteristic
81C22×#6923—22no—
82C22×#6923—41no—
83C22×#6923—41no—
84C2×Q8×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61—41no—
87C2×Q8×C61—41no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61C22×C411yescharacteristic
91C22×Dic61—21no—
92C22×Dic61#4111yescharacteristic
93C2×D244—21no—
94C2×D244—21no—
95C2×D244—41no—
96C2×D244—41no—
97C2×D244—41no—
98C2×D244—41no—
99C2×D244—42no—
100C2×D244—42no—
101C2×C4×D61—41no—
102C2×C4×D61—41no—
103C2×C4×D61C2×D411yescharacteristic
104C2×C4×D61C2×D411yescharacteristic
105C2×C4×D61C2×D411yescharacteristic
106C2×C4×D61#4111yescharacteristic
107C22⋊#6923—22no—
108C22⋊#6923—22no—
109C22⋊#6923—42no—
110C22⋊#6923—42no—
111C2×#92420—22no—
112C4⋊#6923—41no—
113C4⋊#6923—41no—
114C4⋊#6923—41no—
115C4⋊#6923—41no—
116C4×#6923—41no—
117C4×#6923—41no—
118D61⋊C8—41no—
119D61⋊C8—41no—
120C2×C8×C61—41no—
121C2×C8×C61C22⋊C411yescharacteristic
122C2×C8×C61C22⋊C411yescharacteristic
123C4⋊C4×C61—21no—
124C4⋊C4×C61—21no—
125#11758201—42no—
126#11758201—42no—
127#11758198—41no—
128#11758198—41no—
129#11758198—41no—
130#11758198—41no—
131C4⋊Dic61—21no—
132C4⋊Dic61—21no—
133#11758196—41no—
134#11758196—41no—
135C2×#92418—22no—
136C2×#92418C22⋊C411yescharacteristic
137C2×#92418C22⋊C411yescharacteristic
138C8×D61—22no—
139C8×D61—22no—
140C8×D61—41no—
141C8×D61—41no—
142C23×C61C4×D411yescharacteristic
143C22×D61—41no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61—42no—
147C22×D61—81no—
148C22×D61—81no—
149C22×D61#12111yescharacteristic
150C22×D61#12711yescharacteristic
151C22×D61AGL(1,ℤ/8)12yes—
152C22×D61#13712yes—
153C2×#6923—42no—
154C2×#6923—42no—
155C2×#6923—42no—
156C2×#6923—81no—
157C2×#6923—81no—
158C2×#6923—81no—
159C2×#6923—81no—
160C2×#6923—81no—
161C2×#6923—81no—
162Q8×C61—41no—
163Q8×C61—41no—
164Q8×C61—81no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—42no—
170C2×C4×C61—81no—
171C2×C4×C61C2×C22⋊C411yescharacteristic
172C2×C4×C61C4×D411yescharacteristic
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—81no—
176C2×Dic61#12111yescharacteristic
177C2×Dic61#12411yescharacteristic
178D244—41no—
179D244—41no—
180D244—81no—
181D244—82no—
182D244—81no—
183D244—81no—
184C4×D61—21no—
185C4×D61—21no—
186C4×D61—21no—
187C4×D61—21no—
188C4×D61—41no—
189C4×D61—41no—
190#92420—42no—
191C8×C61—21no—
192C8×C61—21no—
193#92418—21no—
194#92418#9912yescomplemented
195#9786—611nomaximal, Sylow
196C22×C61—21no—
197C22×C61—21no—
198C22×C61#39011yescharacteristic
199C22×C61#44012yes—
200C2×D61—21no—
201C2×D61—21no—
202C2×D61—21no—
203C2×D61—21no—
204C2×D61—42no—
205C2×D61—42no—
206C2×D61—81no—
207C2×D61—81no—
208C2×D61—81no—
209C2×D61—162no—
210C2×D61#46812yes—
211C2×D61#49611yescharacteristic
212C2×D61#49711yescharacteristic
213#6923—82no—
214#6923—161no—
215#6923—161no—
216C4×C61—21no—
217C4×C61—81no—
218C4×C61—81no—
219C4×C61C2×#9911yescharacteristic
220C4×C61#41011yescharacteristic
221Dic61—21no—
222Dic61—21no—
223Dic61—81no—
224C2×#465—611no—
225#1996—611no—
226#1964—611no—
227#1808—611no—
228#1752—611no—
229#1520—611no—
230#1519—611no—
231C2×C61—22no—
232C2×C61#196411yescharacteristic
233C2×C61#197311yescharacteristic
234C2×C61#197611yescharacteristic
235D61—22no—
236D61—21no—
237D61—21no—
238D61—161no—
239C22×SD16—611no—
240C23×C8—611no—
241C2×C22⋊Q8—611no—
242C2×#121—611no—
243#465—1221no—
244#465—1221no—
245#465—1221no—
246#465—1221no—
247C2×#107—1221no—
248C2×#106—611no—
249C2×#103#692311yescharacteristic, complemented
250C2×#102—611no—
251C2×#99—1222no—
252C2×C22⋊C8—611no—
253C2×#97—1221no—
254#380—611no—
255#380—611no—
256C4×C22⋊C4—611no—
257#342—1222no—
258#340—1221no—
259#336—1221no—
260#328—1222no—
261#327—1222no—
262C61#978611yescharacteristic, complemented, Sylow
263C22×Q8C2×#692311yescharacteristic
264C22×D4—611no—
265C22×D4—1221no—
266C23×C4—611no—
267C2×SD16—1221no—
268C2×SD16—1221no—
269C2×SD16—2442no—
270C22×C8—611no—
271C22×C8—611no—
272C22×C8—611no—
273C22×C8—611no—
274C22×C8—611no—
275C22×C8—1221no—
276C22×C8—2442no—
277C22×C8C2×#692311yescharacteristic
278C22⋊Q8—1221no—
279C22⋊Q8—1221no—
280C22⋊Q8—1221no—
281C22⋊Q8—1221no—
282#121—1221no—
283#121—1221no—
284#121—1221no—
285#121—1221no—
286C2×C4⋊C4—611no—
287C2×C4⋊C4—1221no—
288C2×C4⋊C4—1221no—
289C2×C4⋊C4—1221no—
290C2×C4⋊C4C2×#692311yescharacteristic
291C2×C22⋊C4—612no—
292C2×C22⋊C4—1221no—
293C2×C22⋊C4—1221no—
294C2×C22⋊C4—1221no—
295C2×C22⋊C4—1221no—
296C2×C42—1221no—
297#107—2442no—
298#106—1221no—
299#106—1221no—
300#103—21no—
301#103—21no—
302#102—1221no—
303#102—1221no—
304#99—2444no—
305C22⋊C8—612no—
306C22⋊C8—1221no—
307#97—2442no—
308#95—1221no—
309#95—1221no—
310#95—1221no—
311C24—611no—
312C24—1221no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—41no—
316C2×Q8—41no—
317C2×D4—1221no—
318C2×D4—1221no—
319C2×D4—2441no—
320C2×D4—2441no—
321C2×D4—2442no—
322C2×D4—2441no—
323C2×D4—2441no—
324C2×D4—2442no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—611no—
332C22×C4—1221no—
333C22×C4—1222no—
334C22×C4—2441no—
335C22×C4—2441no—
336C22×C4—2441no—
337C22×C4—2441no—
338C22×C4C22×#692311yescharacteristic
339SD16—2442no—
340SD16—2442no—
341C2×C8—41no—
342C2×C8—611no—
343C2×C8—611no—
344C2×C8—1222no—
345C2×C8—1222no—
346C2×C8—1222no—
347C2×C8—1222no—
348C2×C8—2441no—
349C2×C8—2441no—
350C2×C8—2441no—
351C2×C8—2441no—
352C2×C8C22⋊#692311yescharacteristic
353C2×C8C22⋊#692311yescharacteristic
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—1221no—
357C4⋊C4—1221no—
358C4⋊C4—2441no—
359C4⋊C4—2441no—
360C4⋊C4—2441no—
361C4⋊C4—2441no—
362C4⋊C4—2441no—
363C4⋊C4—2441no—
364C22⋊C4—1222no—
365C22⋊C4—1222no—
366C22⋊C4—2441no—
367C22⋊C4—2441no—
368C22⋊C4—2441no—
369C22⋊C4—2441no—
370C22⋊C4—2442no—
371C22⋊C4—2442no—
372C42—2441no—
373C42—2441no—
374C23—611no—
375C23—611no—
376C23—612no—
377C23—612no—
378C23—4881no—
379C23—4881no—
380C23—2441no—
381C23—2441no—
382C23—2442no—
383C23—2441no—
384C23D4×#692311yescharacteristic
385Q8—41no—
386Q8—41no—
387Q8—81no—
388D4—4881no—
389D4—4881no—
390D4—4882no—
391D4—4881no—
392D4—2441no—
393D4—2441no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—81no—
400C2×C4—611no—
401C2×C4—611no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—4881no—
407C2×C4—4881no—
408C2×C4—4881no—
409C2×C4—4881no—
410C2×C4—4881no—
411C2×C4—4881no—
412C2×C4—4881no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2442no—
417C2×C4—2442no—
418C2×C4—2442no—
419C2×C4—2441no—
420C2×C4C2×C22⋊#692311yescharacteristic
421C2×C4D4×#692311yescharacteristic
422C8—21no—
423C8—21no—
424C8—612no—
425C8—1221no—
426C8—2442no—
427C22—21no—
428C22—21no—
429C22—611no—
430C22—612no—
431C22—611no—
432C22—1221no—
433C22—1221no—
434C22—1221no—
435C22—1221no—
436C22—9762no—
437C22—4881no—
438C22—4881no—
439C22—4881no—
440C22—2442no—
441C22—2442no—
442C22#1684071411yescharacteristic
443C22#1684080112yes—
444C4—21no—
445C4—81no—
446C4—81no—
447C4—1221no—
448C4—1221no—
449C4—9761no—
450C4—9761no—
451C4—4882no—
452C4—4881no—
453C4D61⋊#9911yescharacteristic
454C4#1684074111yescharacteristic
455C2—22no—
456C2—1221no—
457C2—1222no—
458C2—1221no—
459C2—9761no—
460C2#2146196011yescharacteristic
461C2#2146196911yescharacteristic
462C2#2146197811yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#103×C61C4
socleC22×C61#390
prime radicalC2×#14519752C22
cosocleC22×C4×D61C23
hypercenterC2×#103#6923
hypocenterC61#9786
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. #21462008C2semidirect
3. #21461696C2semidirect
4. #21461555C2semidirect
5. #21461259C2semidirect
20. C22×#11758201C4semidirect
28. C2×#14519708C4semidirect
29. C2×#14519699C4semidirect
30. C2×#103×C61C4semidirect
194. #92418#99semidirect
249. C2×#103#6923semidirect
262. C61#9786semidirect

Maximal subgroups

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

subgroupindex
#214620082
#214619592
#214616962
#214615552
#214612592
#214612562
C2×#168399942
#978661