Finite Group Databasebeta

← #29597434

Subgroups — #29597434

Order 15616.

456 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455539C211yesmaximal, characteristic
2C2×#16839573C211yesmaximal, characteristic, complemented
3#21447548C211yesmaximal, characteristic, complemented
4#21445878C211yesmaximal, characteristic, complemented
5#21443931C211yesmaximal, characteristic, complemented
6#21443918C211yesmaximal, characteristic, complemented
7C61×#3407C211yesmaximal, characteristic, complemented
8#16840560—21no—
9C2×#14519799C2211yescharacteristic
10#16840037C412yescomplemented
11#16840032C412yescomplemented
12#16840025—22no—
13C2×#14519713C2211yescharacteristic
14C2×#14519713C2211yescharacteristic
15C2×#14519709C2211yescharacteristic
16#16839763—21no—
17#16839744—21no—
18#16839573—22no—
19#16839570—22no—
20#16839530—21no—
21C2×#131×C61C2211yescharacteristic
22C61×#504—22no—
23C61×#504—22no—
24C2×M32×C61—22no—
25C2×M32×C61C2211yescharacteristic
26C2×M32×C61C2211yescharacteristic
27C2×#11758222—21no—
28#14519808—41no—
29#14519807—22no—
30#14519803—41no—
31#14519802—22no—
32#14519799—21no—
33#14519799—21no—
34#14519799—21no—
35#14519799—21no—
36#14519797—42no—
37C2×Dic244C2×C411yescharacteristic
38C2×#11758190—21no—
39C2×D488C2×C411yescharacteristic
40C2×#11758194—21no—
41C2×#11758194—21no—
42C2×C4⋊Dic61—21no—
43#14519713—21no—
44#14519713—21no—
45#14519713—21no—
46#14519713C2×C412yes—
47#14519709—21no—
48#14519709—21no—
49#14519701—41no—
50#14519698—41no—
51#14519695—22no—
52#14519693—22no—
53C2×#41×C61D411yescharacteristic
54#131×C61—21no—
55#131×C61—21no—
56#131×C61C2×C412yes—
57#131×C61D412yes—
58C2×M16×C61—21no—
59C2×M16×C61D411yescharacteristic
60C22×C8×C61—21no—
61C22×C8×C61C2311yescharacteristic
62M32×C61—24no—
63M32×C61—21no—
64M32×C61—21no—
65M32×C61—21no—
66M32×C61D412yes—
67C2×C16×C61—24no—
68C2×C16×C61—21no—
69C2×C16×C61D412yes—
70#41×C61—21no—
71#41×C61—21no—
72#41×C61C22⋊C412yes—
73#41×C61SD1612yes—
74C2×Q8×C61D811yescharacteristic
75C2×D4×C61—21no—
76C2×D4×C61D811yescharacteristic
77C22×C4×C61—21no—
78C22×C4×C61C2×D411yescharacteristic
79C2×C22⋊D61—41no—
80C22×Dic61—41no—
81#11758222—41no—
82#11758222—41no—
83#11758222—41no—
84#11758222—41no—
85C2×D244—21no—
86C2×C4×D61—41no—
87C2×Dic122—21no—
88M16×C61—21no—
89M16×C61—22no—
90M16×C61—22no—
91M16×C61C22⋊C412yes—
92C2×C8×C61—21no—
93C2×C8×C61—22no—
94C2×C8×C61—22no—
95C2×C8×C61C22×C411yescharacteristic
96C2×C8×C61C2×D411yescharacteristic
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61C2×D411yescharacteristic
99C2×C8×C61#4111yescharacteristic
100C2×C8×C61#4111yescharacteristic
101#11758202—42no—
102#11758201—42no—
103#11758200—42no—
104#11758199—42no—
105C4⋊Dic61—41no—
106C4⋊Dic61—41no—
107#11758194—22no—
108#11758194—41no—
109#11758194—41no—
110#11758194—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113Dic244—21no—
114Dic244—21no—
115D488—21no—
116D488—21no—
117#11758190—41no—
118#11758190—41no—
119C16×C61—22no—
120C16×C61—22no—
121C23×C61—21no—
122C23×C61#13511yescharacteristic
123C22×D61—41no—
124Q8×C61—21no—
125Q8×C61#10212yes—
126D4×C61—22no—
127D4×C61—22no—
128D4×C61—21no—
129D4×C61#10212yes—
130C2×C4×C61—21no—
131C2×C4×C61—22no—
132C2×C4×C61—22no—
133C2×C4×C61C2×C22⋊C411yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61C2×D811yescharacteristic
137C2×C4×C61C2×SD1611yescharacteristic
138C2×C4×C61#13511yescharacteristic
139C22⋊D61—81no—
140C22⋊D61—81no—
141C2×Dic61—41no—
142C2×Dic61—81no—
143C2×Dic61—161no—
144D244—41no—
145D244—41no—
146C4×D61—81no—
147C4×D61—81no—
148Dic122—41no—
149Dic122—41no—
150C8×C61—22no—
151C8×C61C4×D411yescharacteristic
152C8×C61C4×D411yescharacteristic
153C8×C61#12011yescharacteristic
154C8×C61#12311yescharacteristic
155#92418—42no—
156#92418—81no—
157#13070—611nomaximal, Sylow
158C22×C61—22no—
159C22×C61—41no—
160C22×C61—81no—
161C22×C61#41611yescharacteristic
162C22×C61#46511yescharacteristic
163C22×C61#46611yescharacteristic
164C2×D61—81no—
165C2×D61—161no—
166C4×C61—22no—
167C4×C61#38611yescharacteristic
168C4×C61C2×#10211yescharacteristic
169C4×C61#46511yescharacteristic
170C4×C61#46611yescharacteristic
171Dic61—81no—
172Dic61—161no—
173#3407D6111yescharacteristic, complemented
174#3067—611no—
175C2×#360—611no—
176#2143—611no—
177#1815—611no—
178#1388—611no—
179#1383—611no—
180C2×C61—21no—
181C2×C61—21no—
182C2×C61—21no—
183C2×C61—42no—
184C2×C61#189311yescharacteristic
185D61—161no—
186#575—1221no—
187C2×#135—611no—
188C2×#131C2×D6111yescharacteristic
189#504—22no—
190#504—22no—
191C2×M32—22no—
192C2×M32C2×D6111yescharacteristic
193C2×M32C2×D6111yescharacteristic
194#473—612no—
195#472—612no—
196#471—1222no—
197C2×#108—611no—
198C2×#108—611no—
199C2×#106—611no—
200#417—1221no—
201#413—1221no—
202#360—1222no—
203#359—1222no—
204#343—1221no—
205C61#1307011yescharacteristic, complemented, Sylow
206C2×#41—1221no—
207C2×#41D24411yescharacteristic
208#137—1222no—
209#137—2441no—
210AGL(1,ℤ/8)—1222no—
211AGL(1,ℤ/8)—2441no—
212#135—1221no—
213#135—1221no—
214#135—1221no—
215#135—1221no—
216#135—2442no—
217C2×Q16—611no—
218C2×SD16—1221no—
219C2×D8—611no—
220#131—21no—
221#131—21no—
222#131C4×D6112yes—
223#131C22⋊D6112yes—
224C2×M16—21no—
225C2×M16—1221no—
226C2×M16—1221no—
227C2×M16D24411yescharacteristic
228C22×C8—21no—
229C22×C8C22×D6111yescharacteristic
230C2×C4⋊C4—1221no—
231M32—24no—
232M32—21no—
233M32—21no—
234M32—21no—
235M32C22⋊D6112yes—
236C2×C16—24no—
237C2×C16—21no—
238C2×C16C22⋊D6112yes—
239#108—612no—
240#108—1221no—
241#108—1221no—
242#108—1221no—
243#106—1221no—
244#106—1221no—
245#103—2441no—
246#102—2441no—
247#101—1222no—
248#100—1222no—
249#41—21no—
250#41—21no—
251#41—2441no—
252#41—2441no—
253#41—2441no—
254#41—2441no—
255#41#1175819012yes—
256#41#1175819812yes—
257C2×Q8—1221no—
258C2×Q8D48811yescharacteristic
259C2×D4—21no—
260C2×D4—1221no—
261C2×D4—2441no—
262C2×D4D48811yescharacteristic
263C22×C4—21no—
264C22×C4—2441no—
265C22×C4—2441no—
266C22×C4C2×D24411yescharacteristic
267Q16—1221no—
268Q16—1221no—
269Q16—2442no—
270SD16—2442no—
271SD16—2442no—
272SD16—2441no—
273SD16—2441no—
274D8—1221no—
275D8—1221no—
276D8—2442no—
277M16—21no—
278M16—22no—
279M16—22no—
280M16—1222no—
281M16—2441no—
282M16—2441no—
283M16—2441no—
284M16#1175819812yes—
285C2×C8—21no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—2441no—
289C2×C8—2441no—
290C2×C8C2×C4×D6111yescharacteristic
291C2×C8#1175822211yescharacteristic
292C2×C8#1175822211yescharacteristic
293C2×C8C2×C22⋊D6111yescharacteristic
294C2×C8C2×C22⋊D6111yescharacteristic
295C2×C8C2×C22⋊D6111yescharacteristic
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C16—22no—
299C16—22no—
300C23—21no—
301C23—2441no—
302C23#1451979911yescharacteristic
303Q8—21no—
304Q8—2441no—
305Q8—2441no—
306Q8#1451969912yes—
307D4—22no—
308D4—22no—
309D4—21no—
310D4—4881no—
311D4—4881no—
312D4—2441no—
313D4—2441no—
314D4#1451969912yes—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—9761no—
319C2×C4—4881no—
320C2×C4—4881no—
321C2×C4—4881no—
322C2×C4—2441no—
323C2×C4C2×#1175819811yescharacteristic
324C2×C4#1451975111yescharacteristic
325C2×C4#1451975111yescharacteristic
326C2×C4C2×D48811yescharacteristic
327C2×C4C2×#1175819011yescharacteristic
328C2×C4#1451979911yescharacteristic
329C8—22no—
330C8—4881no—
331C8—2442no—
332C8C4×C22⋊D6111yescharacteristic
333C8C4×C22⋊D6111yescharacteristic
334C8#1451974611yescharacteristic
335C8#1451976011yescharacteristic
336C22—22no—
337C22—41no—
338C22—81no—
339C22—9761no—
340C22—4881no—
341C22#1683975911yescharacteristic
342C22#1683999111yescharacteristic
343C22#1683999811yescharacteristic
344C4—22no—
345C4—9761no—
346C4—4881no—
347C4#1683964111yescharacteristic
348C4C2×#1451969911yescharacteristic
349C4#1683999111yescharacteristic
350C4#1683999811yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—9761no—
356C2#2144624711yescharacteristic
subgroupG/H
centerC2#21446247
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#3407C2
socleC2×C61#1893
prime radical#21455539C2
cosocleC22×C8×C61C23
hypercenter#3407D61
hypocenterC61#13070
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3407

Complements

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

NH ≅ G/Ntype
2. C2×#16839573C2semidirect
3. #21447548C2semidirect
4. #21445878C2semidirect
5. #21443931C2semidirect
6. #21443918C2semidirect
7. C61×#3407C2semidirect
10. #16840037C4semidirect
11. #16840032C4semidirect
173. #3407D61semidirect
205. C61#13070semidirect

Maximal subgroups

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

subgroupindex
#214555392
C2×#168395732
#214475482
#214458782
#214439312
#214439182
C61×#34072
#1307061