Finite Group Databasebeta

← #29835518

Subgroups — #29835518

Order 15616.

474 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456356C211yesmaximal, characteristic
2#21456352C211yesmaximal, characteristic
3#21448105C211yesmaximal, characteristic, complemented
4#21448104C211yesmaximal, characteristic, complemented
5#21448103C211yesmaximal, characteristic, complemented
6#21448097C211yesmaximal, characteristic, complemented
7#21448095C211yesmaximal, characteristic, complemented
8#21448093C211yesmaximal, characteristic, complemented
9#21448092C211yesmaximal, characteristic, complemented
10#21447606C211yesmaximal, characteristic
11#21447604C211yesmaximal, characteristic
12#21447602C211yesmaximal, characteristic
13#366×D61C211yesmaximal, characteristic
14#21447417C211yesmaximal, characteristic
15C61×#2255C211yesmaximal, characteristic, complemented
16#16840392—21no—
17#16840389—21no—
18C2×#14519716C2211yescharacteristic
19C2×C16×D61C2211yescharacteristic
20#16840172—21no—
21#16840170—21no—
22#16840169—21no—
23#16840168—21no—
24#16840167C2211yescharacteristic
25#16840166C2211yescharacteristic
26#16840166C2211yescharacteristic
27#16840164C2211yescharacteristic
28#16840163C2211yescharacteristic
29#16840163C2211yescharacteristic
30#16839803—21no—
31#16839801—21no—
32#16839799C2211yescharacteristic
33#16839799C2211yescharacteristic
34#107×D61C2211yescharacteristic
35#107×D61C2211yescharacteristic
36#16839716C2211yescharacteristic
37#16839590C2211yescharacteristic
38#16839590C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839588C2211yescharacteristic
43#16839587C2211yescharacteristic
44#16839587C2211yescharacteristic
45#16839587C2211yescharacteristic
46#16839587C2211yescharacteristic
47#16839587C2211yescharacteristic
48#16839587C2211yescharacteristic
49#16839537C2211yescharacteristic
50C4×#11758185C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#500C2211yescharacteristic
53C61×#499C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#367C2211yescharacteristic
56C61×#366C2211yescharacteristic
57C61×#366C2211yescharacteristic
58C61×#346C2211yescharacteristic
59C2×#11758189D411yescharacteristic
60C2×C8×D61C2311yescharacteristic
61#14519777—21no—
62#14519776—21no—
63#14519776—21no—
64#14519776—41no—
65#14519775—41no—
66#14519769—21no—
67#14519768—21no—
68#14519768—21no—
69#14519767—41no—
70#14519767—41no—
71#14519757—41no—
72#14519755—41no—
73#14519755—41no—
74#14519753—41no—
75#14519735—21no—
76#14519735—21no—
77#14519734D411yescharacteristic
78C4⋊C4×D61—21no—
79C4⋊C4×D61—21no—
80#14519716Q814yescomplemented
81C2×#11758185C2311yescharacteristic
82C2×#11758185C2311yescharacteristic
83C16×D61Q814yescomplemented
84#14519711—21no—
85#14519711C2311yescharacteristic
86#14519711C2311yescharacteristic
87#14519711C2311yescharacteristic
88#14519711C2311yescharacteristic
89#14519710—21no—
90#14519710—21no—
91#14519710—21no—
92#14519710—21no—
93#14519709—21no—
94#14519708—21no—
95#14519708—21no—
96#14519708—21no—
97#14519708—21no—
98#14519688D411yescharacteristic
99#14519687D411yescharacteristic
100C8×Dic61C2311yescharacteristic
101C4⋊Q8×C61—21no—
102#125×C61—21no—
103C2×C16×C61C2311yescharacteristic
104C2×C16×C61C2311yescharacteristic
105#107×C61—21no—
106#107×C61C2311yescharacteristic
107#107×C61C2311yescharacteristic
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#106×C61—21no—
111C4×C8×C61C2311yescharacteristic
112C2×Q8×C61—41no—
113C2×C4×D61—41no—
114C2×C4×D61—41no—
115C2×C4×D61C2×D411yescharacteristic
116C2×Dic122—41no—
117C2×Dic122—41no—
118C2×Dic122—41no—
119C2×C8×C61C2×D411yescharacteristic
120C2×C8×C61C2411yescharacteristic
121C4⋊C4×C61—21no—
122C4⋊C4×C61—21no—
123C4⋊C4×C61—21no—
124C4⋊C4×C61—21no—
125C4⋊C4×C61—41no—
126C4⋊C4×C61—41no—
127C4⋊C4×C61—41no—
128C42×C61C2×D411yescharacteristic
129#11758198—41no—
130#11758198—41no—
131#11758198D811yescharacteristic
132#11758198D811yescharacteristic
133C4⋊Dic61—21no—
134C4⋊Dic61—21no—
135C4⋊Dic61—21no—
136C4⋊Dic61—21no—
137C4⋊Dic61—41no—
138C4⋊Dic61—41no—
139C4⋊Dic61—41no—
140#11758196—41no—
141#11758196—41no—
142#11758196—41no—
143#11758196—41no—
144#11758196—41no—
145#11758196—41no—
146#11758196—41no—
147#11758196—41no—
148#11758196D811yescharacteristic
149#11758196D811yescharacteristic
150C4×Dic61—41no—
151C4×Dic61—41no—
152C4×Dic61C2×D411yescharacteristic
153C2×#92418C2×D411yescharacteristic
154C2×#92418C2×D411yescharacteristic
155#11758189Q1614yes—
156C8×D61C2×Q812yes—
157C8×D61C2×Q812yes—
158C16×C61C2×Q812yes—
159C16×C61C2×Q812yes—
160#11758185C2×Q812yes—
161#11758185C2×Q812yes—
162C22×D61C2×D811yescharacteristic
163Q8×C61—161no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61C2×D811yescharacteristic
169C2×C4×C61C2×D811yescharacteristic
170C2×C4×C61C22×D411yescharacteristic
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61C2×D811yescharacteristic
176C2×Dic61C2×D811yescharacteristic
177C2×Dic61C2×D811yescharacteristic
178C4×D61—161no—
179C4×D61—161no—
180C4×D61C4⋊Q812yes—
181C4×D61C2×Q1612yes—
182Dic122—161no—
183Dic122—161no—
184Dic122—161no—
185C8×C61C2×Q1612yes—
186C8×C61C22×Q811yescharacteristic
187C8×C61C22×Q811yescharacteristic
188#92418C4⋊Q812yes—
189#92418C2×Q1612yes—
190#33729—611nomaximal, Sylow
191C22×C61C22×D811yescharacteristic
192C2×D61—21no—
193C2×D61—21no—
194C2×D61#50012yes—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—81no—
198C4×C61—81no—
199C4×C61—81no—
200C4×C61—81no—
201C4×C61C2×C4⋊Q811yescharacteristic
202C4×C61C22×Q1611yescharacteristic
203Dic61—21no—
204Dic61—21no—
205Dic61—81no—
206Dic61—81no—
207Dic61—81no—
208Dic61—81no—
209Dic61#50012yes—
210#3164—611no—
211#3164—611no—
212#2255—611no—
213#2255—611no—
214#2255—611no—
215#2255D6111yescharacteristic, complemented
216#2253—611no—
217#2253—611no—
218#2252—611no—
219#2252—611no—
220#2159—611no—
221#2159—611no—
222#2158—611no—
223C2×#366—611no—
224#2108—611no—
225C2×C61C2×#50011yescharacteristic
226C2×C61#341511yescharacteristic
227C2×C61#341711yescharacteristic
228D61—22no—
229#544—1221no—
230#544—1221no—
231C2×M32—611no—
232C22×C16—611no—
233#501—1221no—
234#501—1221no—
235#501—1221no—
236#501—1221no—
237#500—611no—
238#500—611no—
239#500—611no—
240#500C2×D6111yescharacteristic
241#499—611no—
242#499—611no—
243#499—611no—
244#499C2×D6111yescharacteristic
245#428—1221no—
246#428—1221no—
247#427—611no—
248#427—611no—
249C2×#107—611no—
250C2×#107—611no—
251#405—611no—
252#367—611no—
253#367—611no—
254#367—611no—
255#367—611no—
256#367C2×D6111yescharacteristic
257#367C2×D6111yescharacteristic
258#366—611no—
259#366—611no—
260#366—611no—
261#366—611no—
262#366—611no—
263#366—611no—
264#366—611no—
265#366—611no—
266#366C2×D6111yescharacteristic
267#366C2×D6111yescharacteristic
268#346—611no—
269#346C2×D6111yescharacteristic
270C4×C16—611no—
271C4×C16—611no—
272C61#3372911yescharacteristic, complemented, Sylow
273C2×M16—611no—
274C22×C8—611no—
275C4⋊Q8—21no—
276C4⋊Q8—1221no—
277C4⋊Q8—1221no—
278C4⋊Q8—1221no—
279C4⋊Q8—2441no—
280C4⋊Q8—2441no—
281#125—21no—
282#125—1221no—
283#125—1221no—
284#125—1221no—
285#125—2441no—
286#125—2441no—
287C22⋊Q8—2441no—
288C22⋊Q8—2441no—
289C22⋊Q8—2441no—
290C22⋊Q8—2441no—
291#117—611no—
292#117—1221no—
293#117—1221no—
294C2×C4⋊C4—1221no—
295C2×C4⋊C4—1221no—
296M32—614no—
297C2×C16—611no—
298C2×C16—611no—
299C2×C16—614no—
300C2×C16C22×D6111yescharacteristic
301C2×C16C22×D6111yescharacteristic
302#107—21no—
303#107—611no—
304#107—611no—
305#107—611no—
306#107—611no—
307#107—1221no—
308#107—1221no—
309#107—1221no—
310#107—1221no—
311#107—1221no—
312#107C22×D6111yescharacteristic
313#107C22×D6111yescharacteristic
314#107C22×D6111yescharacteristic
315#107C22×D6111yescharacteristic
316#106—21no—
317#106—1221no—
318#106—1221no—
319#106—1221no—
320#106—1221no—
321#106—1221no—
322#97—611no—
323#97—611no—
324C4×C8—611no—
325C4×C8C22×D6111yescharacteristic
326C2×Q8—41no—
327C2×Q8—2441no—
328C2×Q8—2441no—
329C2×Q8—2441no—
330C22×C4—611no—
331C22×C4—2441no—
332C22×C4—2441no—
333M16—614no—
334C2×C8—611no—
335C2×C8—611no—
336C2×C8—612no—
337C2×C8—612no—
338C2×C8D4×D6111yescharacteristic
339C2×C8C23×D6111yescharacteristic
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—611no—
348C4⋊C4—611no—
349C4⋊C4—1221no—
350C4⋊C4—1221no—
351C4⋊C4—1221no—
352C4⋊C4—1221no—
353C4⋊C4—2441no—
354C4⋊C4—2441no—
355C4⋊C4—2441no—
356C4⋊C4—2441no—
357C4⋊C4—2441no—
358C4⋊C4—2441no—
359C4⋊C4—2441no—
360C4⋊C4—2441no—
361C4⋊C4—2441no—
362C4⋊C4—2441no—
363C4⋊C4—2441no—
364C22⋊C4—611no—
365C22⋊C4—611no—
366C22⋊C4—2441no—
367C22⋊C4—2441no—
368C42—611no—
369C42—2441no—
370C42—2441no—
371C42D4×D6111yescharacteristic
372C16—612no—
373C16—612no—
374C16Q8×D6112yes—
375C16Q8×D6112yes—
376C23—611no—
377Q8—161no—
378Q8—9761no—
379Q8—9761no—
380Q8—9761no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—611no—
386C2×C4—612no—
387C2×C4—612no—
388C2×C4—611no—
389C2×C4—611no—
390C2×C4—9761no—
391C2×C4—9761no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4D8×D6111yescharacteristic
397C2×C4D8×D6111yescharacteristic
398C2×C4C2×D4×D6111yescharacteristic
399C8—612no—
400C8—612no—
401C8Q16×D6112yes—
402C8C2×Q8×D6111yescharacteristic
403C8C2×Q8×D6111yescharacteristic
404C22—612no—
405C22—1221no—
406C22—1221no—
407C22C2×D8×D6111yescharacteristic
408C4—21no—
409C4—21no—
410C4—81no—
411C4—81no—
412C4—81no—
413C4—81no—
414C4—612no—
415C4—1221no—
416C4—1221no—
417C4—4881no—
418C4—4881no—
419C4—4881no—
420C4—4881no—
421C4C4⋊Q8×D6111yescharacteristic
422C4C2×Q16×D6111yescharacteristic
423C2—1222no—
424C2#500×D6111yescharacteristic
425C2#2145895911yescharacteristic
426C2#2145897111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2255C2
socleC22×C61C22×D8
prime radicalC22×D61C2×D8
hypercenter#2255D61
hypocenterC61#33729
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2255

Complements

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

NH ≅ G/Ntype
3. #21448105C2semidirect
4. #21448104C2semidirect
5. #21448103C2semidirect
6. #21448097C2semidirect
7. #21448095C2semidirect
8. #21448093C2semidirect
9. #21448092C2semidirect
15. C61×#2255C2semidirect
80. #14519716Q8semidirect
83. C16×D61Q8semidirect
215. #2255D61semidirect
272. C61#33729semidirect

Maximal subgroups

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

subgroupindex
#214563562
#214563522
#214481052
#214481042
#214481032
#214480972
#214480952
#214480932
#214480922
#214476062
#214476042
#214476022
#366×D612
#214474172
C61×#22552
#3372961