Finite Group Databasebeta

← #29598197

Subgroups — #29598197

Order 15616.

430 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839877C211yesmaximal, characteristic
2C2×#16839582C211yesmaximal, characteristic, complemented
3C2×#16839545C211yesmaximal, characteristic, complemented
4#21447434C211yesmaximal, characteristic, complemented
5#21447433C211yesmaximal, characteristic, complemented
6C2×#16839537C211yesmaximal, characteristic, complemented
7C2×C61×#350C211yesmaximal, characteristic, complemented
8C2×#14519797C411yescharacteristic
9C2×#14519783C2211yescharacteristic
10C2×#14519717C2211yescharacteristic
11C22×#11758185C2211yescharacteristic
12#16839877—22no—
13#16839877—22no—
14C2×#14519712C411yescharacteristic
15C2×#14519704C411yescharacteristic
16C2×#14519703C411yescharacteristic
17C2×C8×Dic61C2211yescharacteristic
18#16839582—22no—
19#16839545—22no—
20C22⋊#11758185—22no—
21#16839541—22no—
22#16839537—22no—
23C2×#131×C61C2211yescharacteristic
24C2×M32×C61C2211yescharacteristic
25C22×C16×C61C2211yescharacteristic
26C61×#350—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#14519783—21no—
37#14519783—21no—
38C2×#11758194C2×C411yescharacteristic
39C2×#11758189—21no—
40C22×#92418C2×C411yescharacteristic
41C2×C8×D61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43#14519717—21no—
44#14519717—21no—
45C2×#11758185—21no—
46C2×#11758185—21no—
47C2×#11758185—21no—
48C2×#11758185D412yes—
49#14519712—22no—
50#14519704—22no—
51#14519703—22no—
52C8×Dic61D412yes—
53C8×Dic61D412yes—
54C2×#41×C61C2×C411yescharacteristic
55#131×C61—21no—
56#131×C61—21no—
57#131×C61—21no—
58#131×C61—21no—
59C2×M16×C61—21no—
60C2×M16×C61C2×C411yescharacteristic
61C22×C8×C61—21no—
62C22×C8×C61C2311yescharacteristic
63M32×C61—21no—
64M32×C61—21no—
65C2×C16×C61—21no—
66C2×C16×C61—21no—
67C2×C16×C61—21no—
68C2×C16×C61D412yes—
69#41×C61—21no—
70#41×C61—21no—
71#41×C61—21no—
72#41×C61—21no—
73C2×Q8×C61C2×C811yescharacteristic
74C2×D4×C61—21no—
75C2×D4×C61C2×C811yescharacteristic
76C22×C4×C61—21no—
77C22×C4×C61C22×C411yescharacteristic
78C2×C22⋊D61—21no—
79C22×Dic61—21no—
80#11758222—21no—
81#11758222—21no—
82#11758222—21no—
83#11758222—21no—
84C2×D244C2×C811yescharacteristic
85C2×C4×D61—21no—
86C2×Dic122C2×C811yescharacteristic
87M16×C61—21no—
88M16×C61—21no—
89M16×C61—41no—
90M16×C61—41no—
91C2×C8×C61—21no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61C2×D411yescharacteristic
95C2×C8×C61C2×D411yescharacteristic
96C2×C8×C61C2×D411yescharacteristic
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61#4111yescharacteristic
99C2×C8×C61#4111yescharacteristic
100#11758202—22no—
101#11758201—22no—
102#11758200—22no—
103#11758199—22no—
104C4×Dic61—21no—
105C4×Dic61C22⋊C412yes—
106#11758194—21no—
107#11758194—21no—
108C2×#92418—21no—
109C2×#92418C22⋊C412yes—
110C2×#92418C2×C811yescharacteristic
111C2×#92418C2×C811yescharacteristic
112C2×#92418M1612yes—
113#11758189—41no—
114#11758189—41no—
115C8×D61—41no—
116C8×D61—41no—
117C16×C61—22no—
118C16×C61—41no—
119#11758185—22no—
120#11758185—41no—
121C23×C61—21no—
122C23×C61#13111yescharacteristic
123C22×D61—21no—
124Q8×C61—21no—
125Q8×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—41no—
129D4×C61—41no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61C2×C22⋊C411yescharacteristic
134C2×C4×C61C4×D411yescharacteristic
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61C22×C811yescharacteristic
137C2×C4×C61C2×M1611yescharacteristic
138C2×C4×C61#13111yescharacteristic
139C22⋊D61—41no—
140C22⋊D61—41no—
141C2×Dic61—22no—
142C2×Dic61—21no—
143C2×Dic61—42no—
144D244—21no—
145D244—21no—
146C4×D61—41no—
147C4×D61—41no—
148Dic122—21no—
149Dic122—21no—
150C8×C61—41no—
151C8×C61#12111yescharacteristic
152C8×C61#12111yescharacteristic
153C8×C61#12411yescharacteristic
154C8×C61#12711yescharacteristic
155#92418—41no—
156#92418C22⋊C812yes—
157#92418C22⋊C812yes—
158#13196—611nomaximal, Sylow
159C22×C61—22no—
160C22×C61—42no—
161C22×C61—41no—
162C22×C61#40811yescharacteristic
163C22×C61C8×D411yescharacteristic
164C22×C61#43611yescharacteristic
165C2×D61—42no—
166C2×D61—41no—
167C4×C61—41no—
168C4×C61#39011yescharacteristic
169C4×C61C2×C22⋊C811yescharacteristic
170C4×C61C8×D411yescharacteristic
171C4×C61#43611yescharacteristic
172Dic61—42no—
173Dic61—41no—
174C2×#443—611no—
175C2×#364—611no—
176C2×#350—611no—
177C2×#350D6111yescharacteristic, complemented
178#2113—611no—
179#2113—611no—
180C2×#346—611no—
181C2×C61—21no—
182C2×C61—21no—
183C2×C61—81no—
184C2×C61#195411yescharacteristic
185C2×C61#217112yes—
186D61—81no—
187C2×#135—611no—
188C2×#131—611no—
189C2×#131C2×D6111yescharacteristic
190C2×M32—611no—
191C2×M32C2×D6111yescharacteristic
192C22×C16—611no—
193C22×C16C2×D6111yescharacteristic
194#443—1222no—
195#443—1222no—
196C2×#108—611no—
197C2×#104—611no—
198C2×#104—611no—
199C2×C4×C8—611no—
200#364—1222no—
201#350—22no—
202#350—1222no—
203C22⋊C16—1222no—
204C22⋊C16—1222no—
205#346—1222no—
206C61#1319611yescharacteristic, complemented, Sylow
207C2×#41—611no—
208C2×#41C4×D6111yescharacteristic
209#135—1222no—
210#135—1222no—
211C2×Q16—611no—
212C2×SD16—611no—
213C2×SD16—611no—
214C2×D8—611no—
215#131—21no—
216#131—21no—
217#131—21no—
218#131—21no—
219#131—1221no—
220#131—1221no—
221#131—1221no—
222#131—1221no—
223C2×M16—21no—
224C2×M16—611no—
225C2×M16—1221no—
226C2×M16C4×D6111yescharacteristic
227C22×C8—21no—
228C22×C8—611no—
229C22×C8—1221no—
230C22×C8C22×D6111yescharacteristic
231C2×C42—611no—
232M32—21no—
233M32—21no—
234M32—1221no—
235M32—1221no—
236C2×C16—21no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—612no—
240C2×C16—1221no—
241C2×C16—1221no—
242C2×C16—1221no—
243C2×C16C22⋊D6112yes—
244#108—1222no—
245#104—1222no—
246#104—1222no—
247C4×C8—612no—
248C4×C8—612no—
249#41—21no—
250#41—21no—
251#41—21no—
252#41—21no—
253#41—1221no—
254#41—1221no—
255#41—1221no—
256#41—1221no—
257C2×Q8—611no—
258C2×Q8C8×D6111yescharacteristic
259C2×D4—21no—
260C2×D4—611no—
261C2×D4—1221no—
262C2×D4C8×D6111yescharacteristic
263C22×C4—21no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4C2×C4×D6111yescharacteristic
267Q16—1222no—
268SD16—1222no—
269SD16—1222no—
270D8—1222no—
271M16—21no—
272M16—21no—
273M16—41no—
274M16—41no—
275M16—1221no—
276M16—1221no—
277M16—2441no—
278M16—2441no—
279C2×C8—21no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—612no—
283C2×C8—611no—
284C2×C8—611no—
285C2×C8—612no—
286C2×C8—1221no—
287C2×C8—2441no—
288C2×C8—2441no—
289C2×C8#1175822211yescharacteristic
290C2×C8D4×D6111yescharacteristic
291C2×C8D4×D6111yescharacteristic
292C2×C8D4×D6111yescharacteristic
293C2×C8#1175822411yescharacteristic
294C2×C8C2×C22⋊D6111yescharacteristic
295C42—612no—
296C42—1221no—
297C16—22no—
298C16—41no—
299C16—1222no—
300C16—2441no—
301C23—21no—
302C23—1221no—
303C23#1451978511yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1221no—
307Q8—1221no—
308D4—21no—
309D4—21no—
310D4—41no—
311D4—41no—
312D4—1221no—
313D4—1221no—
314D4—2441no—
315D4—2441no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—1222no—
320C2×C4—1221no—
321C2×C4—2442no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4C22⋊C4×D6111yescharacteristic
325C2×C4#1451973711yescharacteristic
326C2×C4C4×C22⋊D6111yescharacteristic
327C2×C4C2×C8×D6111yescharacteristic
328C2×C4M16×D6111yescharacteristic
329C2×C4#1451978311yescharacteristic
330C8—41no—
331C8—612no—
332C8—612no—
333C8—2441no—
334C8#1451974911yescharacteristic
335C8#1451975011yescharacteristic
336C8#1451976311yescharacteristic
337C8#1451977311yescharacteristic
338C22—22no—
339C22—41no—
340C22—42no—
341C22—2441no—
342C22—2442no—
343C22#1683972711yescharacteristic
344C22#1683982511yescharacteristic
345C22#1683983811yescharacteristic
346C4—41no—
347C4—2442no—
348C4—2441no—
349C4#1683966211yescharacteristic
350C4C22⋊C8×D6111yescharacteristic
351C4C8×C22⋊D6111yescharacteristic
352C4#1683983711yescharacteristic
353C2—21no—
354C2—21no—
355C2—81no—
356C2—4881no—
357C2#2144661111yescharacteristic
358C2#2144765812yes—
subgroupG/H
centerC2×C8D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC2×C61×#350C2
socleC22×C61C8×D4
prime radicalC2×#14519797C4
cosocleC22×C8×C61C23
hypercenterC2×#350D61
hypocenterC61#13196
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
2. C2×#16839582C2semidirect
3. C2×#16839545C2semidirect
4. #21447434C2semidirect
5. #21447433C2semidirect
6. C2×#16839537C2semidirect
7. C2×C61×#350C2semidirect
177. C2×#350D61semidirect
206. C61#13196semidirect

Maximal subgroups

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

subgroupindex
C2×#168398772
C2×#168395822
C2×#168395452
#214474342
#214474332
C2×#168395372
C2×C61×#3502
#1319661