Finite Group Databasebeta

← #29596925

Subgroups — #29596925

Order 15616.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458921C211yesmaximal, characteristic, complemented
2C2×#16839882C211yesmaximal, characteristic
3#21447448C211yesmaximal, characteristic, complemented
4#21447447C211yesmaximal, characteristic, complemented
5#21443902C211yesmaximal, characteristic, complemented
6#21443898C211yesmaximal, characteristic, complemented
7C61×#2115C211yesmaximal, characteristic, complemented
8C2×#14519797C411yescharacteristic
9C2×#14519783C2211yescharacteristic
10#16840180—22no—
11#16840178—22no—
12C2×#14519717C2211yescharacteristic
13C2×#14519717C2211yescharacteristic
14M32×D61—22no—
15#16839882—22no—
16#16839882—22no—
17C2×#14519712C411yescharacteristic
18C2×#14519704C411yescharacteristic
19C2×#14519703C411yescharacteristic
20C2×#14519687C2211yescharacteristic
21#16839547—22no—
22#16839546—22no—
23C2×#131×C61C2211yescharacteristic
24C2×M32×C61C2211yescharacteristic
25C2×M32×C61C2211yescharacteristic
26C61×#349—22no—
27C2×#11758222C2×C411yescharacteristic
28#14519797—22no—
29#14519797—22no—
30C2×#11758202C811yescharacteristic
31C2×#11758200C811yescharacteristic
32C2×#11758201C811yescharacteristic
33C2×#11758199C811yescharacteristic
34#14519783—21no—
35#14519783—21no—
36#14519783D412yes—
37#14519783D412yes—
38C2×#11758194C2×C411yescharacteristic
39C2×#11758189—21no—
40C22×#92418C2×C411yescharacteristic
41C2×C8×D61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43#14519717—21no—
44#14519717—21no—
45#14519717—21no—
46#14519717—21no—
47#14519716—24no—
48C2×#11758185—21no—
49C2×#11758185D412yes—
50C16×D61—24no—
51#14519712—22no—
52#14519704—22no—
53#14519703—22no—
54#14519687—21no—
55#14519687—21no—
56C2×#41×C61C2×C411yescharacteristic
57#131×C61—21no—
58#131×C61—21no—
59#131×C61—21no—
60#131×C61—21no—
61C2×M16×C61—21no—
62C2×M16×C61C2×C411yescharacteristic
63C22×C8×C61—21no—
64C22×C8×C61C2311yescharacteristic
65M32×C61—21no—
66M32×C61—21no—
67M32×C61—21no—
68M32×C61D412yes—
69C2×C16×C61—21no—
70C2×C16×C61—21no—
71#41×C61—21no—
72#41×C61—21no—
73#41×C61—21no—
74#41×C61—21no—
75C2×Q8×C61C2×C811yescharacteristic
76C2×D4×C61—21no—
77C2×D4×C61C2×C811yescharacteristic
78C22×C4×C61—21no—
79C22×C4×C61C22×C411yescharacteristic
80C2×C22⋊D61—21no—
81C22×Dic61—21no—
82#11758222—21no—
83#11758222—21no—
84#11758222C22⋊C412yes—
85#11758222M1612yes—
86C2×D244C2×C811yescharacteristic
87C2×C4×D61—21no—
88C2×Dic122C2×C811yescharacteristic
89M16×C61—21no—
90M16×C61—21no—
91M16×C61—41no—
92M16×C61—41no—
93C2×C8×C61—21no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61C2×D411yescharacteristic
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61C2×D411yescharacteristic
99C2×C8×C61C2×D411yescharacteristic
100C2×C8×C61#4111yescharacteristic
101C2×C8×C61#4111yescharacteristic
102#11758202—22no—
103#11758201—22no—
104#11758200—22no—
105#11758199—22no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108#11758194—21no—
109#11758194C22⋊C412yes—
110C2×#92418—21no—
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418C2×C811yescharacteristic
114C2×#92418C2×C811yescharacteristic
115#11758189—22no—
116#11758189—22no—
117C8×D61—22no—
118C8×D61—22no—
119C16×C61—22no—
120C16×C61—41no—
121#11758185—22no—
122#11758185—41no—
123C23×C61—21no—
124C23×C61#13111yescharacteristic
125C22×D61—21no—
126Q8×C61—21no—
127Q8×C61—21no—
128D4×C61—21no—
129D4×C61—21no—
130D4×C61—41no—
131D4×C61—41no—
132C2×C4×C61—21no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61C2×C22⋊C411yescharacteristic
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61C22×C811yescharacteristic
139C2×C4×C61C2×M1611yescharacteristic
140C2×C4×C61#13111yescharacteristic
141C22⋊D61—22no—
142C22⋊D61—22no—
143C2×Dic61—21no—
144C2×Dic61—41no—
145C2×Dic61—81no—
146D244—21no—
147D244C22⋊C812yes—
148C4×D61—22no—
149C4×D61—22no—
150Dic122—21no—
151Dic122C22⋊C812yes—
152C8×C61—41no—
153C8×C61#12011yescharacteristic
154C8×C61#12111yescharacteristic
155C8×C61#12111yescharacteristic
156C8×C61#12311yescharacteristic
157#92418—22no—
158#92418—21no—
159#92418—21no—
160#12986—611nomaximal, Sylow
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—81no—
164C22×C61#40811yescharacteristic
165C22×C61C8×D411yescharacteristic
166C22×C61#43511yescharacteristic
167C2×D61—22no—
168C2×D61—81no—
169C4×C61—41no—
170C4×C61#38611yescharacteristic
171C4×C61C2×C22⋊C811yescharacteristic
172C4×C61C8×D411yescharacteristic
173C4×C61#43511yescharacteristic
174Dic61—22no—
175Dic61—81no—
176#3407—611no—
177C2×#444—611no—
178#2117—611no—
179#2117—611no—
180#2115D6111yescharacteristic, complemented
181#1377—611no—
182#1375—611no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—81no—
187C2×C61#186911yescharacteristic
188D61—42no—
189C2×#135—611no—
190C2×#131—611no—
191C2×#131C2×D6111yescharacteristic
192#504—1222no—
193#504—1222no—
194C2×M32—611no—
195C2×M32—611no—
196C2×M32—1222no—
197C2×M32C2×D6111yescharacteristic
198C2×M32C2×D6111yescharacteristic
199#444—1222no—
200#444—1222no—
201C2×#108—611no—
202C2×#104—611no—
203C2×#104—611no—
204C2×#97—611no—
205#350—1222no—
206#350—1222no—
207#349—22no—
208C61#1298611yescharacteristic, complemented, Sylow
209C2×#41—611no—
210C2×#41C4×D6111yescharacteristic
211#135—1222no—
212#135—1222no—
213C2×Q16—611no—
214C2×SD16—611no—
215C2×SD16—611no—
216C2×D8—611no—
217#131—21no—
218#131—21no—
219#131—21no—
220#131—21no—
221#131—612no—
222#131—612no—
223#131—1221no—
224#131—1221no—
225C2×M16—21no—
226C2×M16—611no—
227C2×M16—1221no—
228C2×M16C4×D6111yescharacteristic
229C22×C8—21no—
230C22×C8—611no—
231C22×C8—1221no—
232C22×C8C22×D6111yescharacteristic
233C2×C42—611no—
234M32—21no—
235M32—21no—
236M32—21no—
237M32—1224no—
238M32—1221no—
239M32—1221no—
240M32—1221no—
241M32—1221no—
242M32C22⋊D6112yes—
243C2×C16—21no—
244C2×C16—21no—
245C2×C16—612no—
246C2×C16—1224no—
247C2×C16—1221no—
248#108—1222no—
249#104—1222no—
250#104—1222no—
251#97—1221no—
252#97—1221no—
253#41—21no—
254#41—21no—
255#41—21no—
256#41—21no—
257#41—612no—
258#41—612no—
259#41—1221no—
260#41—1221no—
261C2×Q8—611no—
262C2×Q8C8×D6111yescharacteristic
263C2×D4—21no—
264C2×D4—611no—
265C2×D4—1221no—
266C2×D4C8×D6111yescharacteristic
267C22×C4—21no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4C2×C4×D6111yescharacteristic
271Q16—1222no—
272SD16—1222no—
273SD16—1222no—
274D8—1222no—
275M16—21no—
276M16—21no—
277M16—41no—
278M16—41no—
279M16—612no—
280M16—1221no—
281M16—1222no—
282M16—1222no—
283C2×C8—21no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—1221no—
291C2×C8—1222no—
292C2×C8—1222no—
293C2×C8#1175822211yescharacteristic
294C2×C8D4×D6111yescharacteristic
295C2×C8D4×D6111yescharacteristic
296C2×C8D4×D6111yescharacteristic
297C2×C8#1175822411yescharacteristic
298C2×C8C2×C22⋊D6111yescharacteristic
299C42—1221no—
300C42—1221no—
301C16—22no—
302C16—41no—
303C16—1222no—
304C16—2441no—
305C23—21no—
306C23—1221no—
307C23#1451978311yescharacteristic
308Q8—21no—
309Q8—21no—
310Q8—612no—
311Q8—1221no—
312D4—21no—
313D4—21no—
314D4—41no—
315D4—41no—
316D4—612no—
317D4—1222no—
318D4—1222no—
319D4—1221no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—1221no—
324C2×C4—1222no—
325C2×C4—1222no—
326C2×C4—4881no—
327C2×C4—2441no—
328C2×C4C22⋊C4×D6111yescharacteristic
329C2×C4#1451973711yescharacteristic
330C2×C4C4×C22⋊D6111yescharacteristic
331C2×C4C2×C8×D6111yescharacteristic
332C2×C4M16×D6111yescharacteristic
333C2×C4#1451978511yescharacteristic
334C8—41no—
335C8—1221no—
336C8—1221no—
337C8—1222no—
338C8#1451974511yescharacteristic
339C8#1451974811yescharacteristic
340C8#1451975011yescharacteristic
341C8#1451975911yescharacteristic
342C22—41no—
343C22—41no—
344C22—81no—
345C22—1222no—
346C22—4881no—
347C22#1683972711yescharacteristic
348C22C8×C22⋊D6111yescharacteristic
349C22#1683983611yescharacteristic
350C4—41no—
351C4—1222no—
352C4—4881no—
353C4#1683963811yescharacteristic
354C4C22⋊C8×D6111yescharacteristic
355C4#1683982511yescharacteristic
356C4#1683983111yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—81no—
361C2—2442no—
362C2#2144610811yescharacteristic
subgroupG/H
centerC4#16839638
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#2115C2
socleC2×C61#1869
prime radicalC2×#14519797C4
cosocleC22×C8×C61C23
hypercenter#2115D61
hypocenterC61#12986
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2115

Complements

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

NH ≅ G/Ntype
1. #21458921C2semidirect
3. #21447448C2semidirect
4. #21447447C2semidirect
5. #21443902C2semidirect
6. #21443898C2semidirect
7. C61×#2115C2semidirect
180. #2115D61semidirect
208. C61#12986semidirect

Maximal subgroups

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

subgroupindex
#214589212
C2×#168398822
#214474482
#214474472
#214439022
#214438982
C61×#21152
#1298661