Finite Group Databasebeta

← #29834808

Subgroups — #29834808

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839800C211yesmaximal, characteristic, complemented
2#21448024C212yesmaximal, complemented
3#21448019C211yesmaximal, characteristic, complemented
4#21448014C211yesmaximal, characteristic, complemented
5#21448007C212yesmaximal, complemented
6#21448002C211yesmaximal, characteristic, complemented
7#21447997C211yesmaximal, characteristic, complemented
8#21447601C212yesmaximal, complemented
9#21447526C212yesmaximal, complemented
10C2×C22⋊#11758185C211yesmaximal, characteristic, complemented
11C61×#3050C211yesmaximal, characteristic
12C2×#14519736—21no—
13C22×#11758185C2212yes—
14#16839800—21no—
15#16839800—21no—
16#16839800C2212yes—
17#16839800C2212yes—
18C2×#14519711C2211yescharacteristic
19C2×#14519711C2211yescharacteristic
20C2×#14519709—21no—
21#16839589C2212yescomplemented
22#16839589C2212yescomplemented
23#16839587C2212yescomplemented
24#16839587C2212yescomplemented
25#16839566C2212yescomplemented
26#16839566C2212yescomplemented
27#16839563C2212yescomplemented
28#16839563C2212yescomplemented
29C22⋊#11758185C2211yescharacteristic
30C22⋊#11758185C2211yescharacteristic
31C22⋊#11758185C2212yes—
32C2×#135×C61C2211yescharacteristic
33C23×C8×C61C2211yescharacteristic
34C61×#525—21no—
35C61×#467C2211yescharacteristic
36C61×#467C2211yescharacteristic
37C61×#466C2211yescharacteristic
38C61×#466C2211yescharacteristic
39C61×#465—21no—
40C61×#465—21no—
41C61×#427C2211yescharacteristic
42C61×#416—21no—
43#14519736—22no—
44#14519736—22no—
45#14519736—41no—
46#14519736—41no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61—21no—
49C2×C22⋊Dic61—41no—
50C2×C4×Dic61—41no—
51C2×#11758185—24no—
52C2×#11758185C2312yes—
53C2×#11758185C2312yes—
54#14519711—21no—
55#14519711—21no—
56#14519711C2312yes—
57#14519711C2312yes—
58#14519709—22no—
59#14519709—22no—
60C2×#41×C61—21no—
61C23×C4×C61D411yescharacteristic
62#135×C61—24no—
63C2×Q16×C61C2311yescharacteristic
64C2×SD16×C61—21no—
65C2×D8×C61C2311yescharacteristic
66C22×C8×C61—24no—
67C22×C8×C61D411yescharacteristic
68C22×C8×C61D411yescharacteristic
69C22×C8×C61D411yescharacteristic
70C22×C8×C61C2311yescharacteristic
71C22×C8×C61C2311yescharacteristic
72C22×C8×C61C2311yescharacteristic
73#123×C61—41no—
74C22⋊Q8×C61—21no—
75C22⋊Q8×C61—21no—
76#121×C61—21no—
77#121×C61—21no—
78#120×C61—41no—
79C4×D4×C61—41no—
80C4×D4×C61—41no—
81#117×C61—21no—
82#107×C61C2311yescharacteristic
83#107×C61C2311yescharacteristic
84#106×C61—21no—
85#103×C61—21no—
86#103×C61—21no—
87#102×C61—21no—
88#102×C61—21no—
89C24×C61D811yescharacteristic
90#41×C61—42no—
91#41×C61—42no—
92C2×Q8×C61—21no—
93C2×D4×C61—21no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C2×D4×C61—41no—
97C22×C4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61—41no—
100C22×C4×C61D811yescharacteristic
101C22×C4×C61D811yescharacteristic
102C22×C4×C61D811yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×Dic61—41no—
107C22×Dic61—41no—
108Q16×C61—22no—
109SD16×C61—42no—
110D8×C61—22no—
111C2×C8×C61—22no—
112C2×C8×C61—22no—
113C2×C8×C61—22no—
114C2×C8×C61—22no—
115C2×C8×C61—22no—
116C2×C8×C61C2×D411yescharacteristic
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2×D411yescharacteristic
119C2×C8×C61#4114yes—
120C2×C8×C61C2411yescharacteristic
121C4⋊C4×C61—21no—
122C4⋊C4×C61—21no—
123C4⋊C4×C61—41no—
124C4⋊C4×C61—41no—
125C22⋊C4×C61—41no—
126C22⋊C4×C61—41no—
127C22⋊C4×C61—41no—
128C22⋊C4×C61—41no—
129C22⋊C4×C61—41no—
130C42×C61—41no—
131C22⋊Dic61—42no—
132C22⋊Dic61—42no—
133C4⋊Dic61—22no—
134C4⋊Dic61—22no—
135C4⋊Dic61—41no—
136C4⋊Dic61—41no—
137C4×Dic61—42no—
138C4×Dic61—42no—
139#11758185—22no—
140#11758185—22no—
141C23×C61—22no—
142C23×C61—22no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61C2×D811yescharacteristic
146C23×C61C2×D811yescharacteristic
147C23×C61C2×D811yescharacteristic
148Q8×C61—41no—
149Q8×C61—41no—
150D4×C61—41no—
151D4×C61—41no—
152D4×C61—82no—
153D4×C61—82no—
154D4×C61—82no—
155C2×C4×C61—22no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—22no—
161C2×C4×C61—22no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—82no—
166C2×C4×C61#12312yes—
167C2×C4×C61C2×D811yescharacteristic
168C2×C4×C61C2×D811yescharacteristic
169C2×C4×C61C2×D811yescharacteristic
170C2×C4×C61#13712yes—
171C2×C4×C61C22×D411yescharacteristic
172C2×Dic61—42no—
173C2×Dic61—42no—
174C2×Dic61—82no—
175C2×Dic61—82no—
176C8×C61—21no—
177C8×C61—21no—
178C8×C61#12312yes—
179C8×C61C2×#4112yes—
180#33645—611nomaximal, Sylow
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—44no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61#48012yes—
193C22×C61#50812yes—
194C22×C61C22×D811yescharacteristic
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—81no—
198C4×C61—81no—
199C4×C61—81no—
200C4×C61#48012yes—
201C4×C61C2×#12311yescharacteristic
202C4×C61C2×#13711yescharacteristic
203Dic61—82no—
204Dic61—82no—
205#3050D6111yescharacteristic
206C2×#427—611no—
207#2237—612no—
208#2236—611no—
209#2235—611no—
210#2234—612no—
211#2233—611no—
212#2232—611no—
213#2158—612no—
214#2138—612no—
215C2×C22⋊C16—611no—
216C2×C61—22no—
217C2×C61—22no—
218C2×C61—41no—
219C2×C61—161no—
220C2×C61C2×#48011yescharacteristic
221C2×C61C2×#50811yescharacteristic
222C2×C61#341411yescharacteristic
223C2×#135C2×D6111yescharacteristic
224C23×C8C2×D6111yescharacteristic
225#525—21no—
226C2×#117—1221no—
227C22×C16—612no—
228#467C2×D6111yescharacteristic
229#467C2×D6111yescharacteristic
230#466C2×D6111yescharacteristic
231#466C2×D6111yescharacteristic
232#465—21no—
233#465—21no—
234#427—612no—
235#427—612no—
236#427—1221no—
237#427—1221no—
238#427C2×D6111yescharacteristic
239C2×#107—611no—
240C2×#107—611no—
241C2×#106—1221no—
242#416—21no—
243#367—612no—
244#367—612no—
245#366—612no—
246#366—612no—
247#358—612no—
248#358—612no—
249#357—612no—
250#357—612no—
251C22⋊C16—611no—
252C22⋊C16—611no—
253C22⋊C16—612no—
254C61#3364511yescharacteristic, complemented, Sylow
255C2×#41—21no—
256C23×C4C22⋊D6111yescharacteristic
257#135—24no—
258C2×Q16C22×D6111yescharacteristic
259C2×SD16—21no—
260C2×D8C22×D6111yescharacteristic
261C22×C8—24no—
262C22×C8C22⋊D6111yescharacteristic
263C22×C8C22⋊D6111yescharacteristic
264C22×C8C22⋊D6111yescharacteristic
265C22×C8C22×D6111yescharacteristic
266C22×C8C22×D6111yescharacteristic
267C22×C8C22×D6111yescharacteristic
268#123—41no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271#121—21no—
272#121—21no—
273#120—41no—
274C4×D4—41no—
275C4×D4—41no—
276#117—21no—
277#117—1222no—
278#117—1222no—
279#117—2441no—
280#117—2441no—
281C2×C4⋊C4—1221no—
282C2×C4⋊C4—1221no—
283C2×C22⋊C4—2441no—
284C2×C42—2441no—
285C2×C16—612no—
286C2×C16—612no—
287C2×C16—1224no—
288#107—612no—
289#107—612no—
290#107—1221no—
291#107—1221no—
292#107C22×D6111yescharacteristic
293#107C22×D6111yescharacteristic
294#106—21no—
295#106—1222no—
296#106—1222no—
297#103—21no—
298#103—21no—
299#102—21no—
300#102—21no—
301C24#1175819911yescharacteristic
302#41—42no—
303#41—42no—
304C2×Q8—21no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—41no—
312C22×C4—2441no—
313C22×C4—2441no—
314C22×C4#1175819911yescharacteristic
315C22×C4#1175819911yescharacteristic
316C22×C4#1175819911yescharacteristic
317C22×C4C2×C22⋊D6111yescharacteristic
318C22×C4C2×C22⋊D6111yescharacteristic
319C22×C4C2×C22⋊D6111yescharacteristic
320Q16—22no—
321SD16—42no—
322D8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8#1175822414yes—
329C2×C8C2×C22⋊D6111yescharacteristic
330C2×C8C2×C22⋊D6111yescharacteristic
331C2×C8C2×C22⋊D6111yescharacteristic
332C2×C8C23×D6111yescharacteristic
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—1222no—
338C4⋊C4—1222no—
339C4⋊C4—2441no—
340C4⋊C4—2441no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—2442no—
347C22⋊C4—2442no—
348C42—41no—
349C42—2442no—
350C42—2442no—
351C16—1222no—
352C16—1222no—
353C23—22no—
354C23—22no—
355C23—41no—
356C23—41no—
357C23C2×#1175819911yescharacteristic
358C23C2×#1175819911yescharacteristic
359C23C2×#1175819911yescharacteristic
360Q8—41no—
361Q8—41no—
362D4—41no—
363D4—41no—
364D4—82no—
365D4—82no—
366D4—82no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—82no—
378C2×C4—4882no—
379C2×C4—4882no—
380C2×C4—2442no—
381C2×C4—2442no—
382C2×C4#1451975812yes—
383C2×C4C2×#1175819911yescharacteristic
384C2×C4C2×#1175819911yescharacteristic
385C2×C4C2×#1175819911yescharacteristic
386C2×C4#1451980712yes—
387C2×C4C22×C22⋊D6111yescharacteristic
388C8—21no—
389C8—21no—
390C8#1451975812yes—
391C8C2×#1175822412yes—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—44no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22#1684007312yes—
404C22#1684019212yes—
405C22C22×#1175819911yescharacteristic
406C4—21no—
407C4—21no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—4882no—
412C4—4882no—
413C4#1684007312yes—
414C4C2×#1451975811yescharacteristic
415C4C2×#1451980711yescharacteristic
416C2—22no—
417C2—22no—
418C2—41no—
419C2—161no—
420C2C2×#1684007311yescharacteristic
421C2C2×#1684019211yescharacteristic
422C2#2145895311yescharacteristic
subgroupG/H
centerC2×C4C2×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
Fitting, prime radicalC61×#3050C2
socleC22×C61C22×D8
hypercenter#3050D61
hypocenterC61#33645
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C2×#16839800C2semidirect
2. #21448024C2semidirect
3. #21448019C2semidirect
4. #21448014C2semidirect
5. #21448007C2semidirect
6. #21448002C2semidirect
7. #21447997C2semidirect
8. #21447601C2semidirect
9. #21447526C2semidirect
10. C2×C22⋊#11758185C2semidirect
21. #16839589C22semidirect
22. #16839589C22semidirect
23. #16839587C22semidirect
24. #16839587C22semidirect
25. #16839566C22semidirect
26. #16839566C22semidirect
27. #16839563C22semidirect
28. #16839563C22semidirect
254. C61#33645semidirect

Maximal subgroups

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

subgroupindex
C2×#168398002
#214480242
#214480192
#214480142
#214480072
#214480022
#214479972
#214476012
#214475262
C2×C22⋊#117581852
C61×#30502
#3364561