Finite Group Databasebeta

← #29598200

Subgroups — #29598200

Order 15616.

424 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839877C211yesmaximal, characteristic
2C2×#16839582C211yesmaximal, characteristic, complemented
3#21447448C211yesmaximal, characteristic, complemented
4#21447440C211yesmaximal, characteristic, complemented
5#21447439C211yesmaximal, characteristic, complemented
6M32×Dic61C211yesmaximal, characteristic, complemented
7C61×#2117C211yesmaximal, characteristic, complemented
8C2×#14519797C411yescharacteristic
9C2×#14519783C2211yescharacteristic
10C2×#14519717C2211yescharacteristic
11C2×#14519717C2211yescharacteristic
12#16839877—21no—
13#16839877—21no—
14#16839877—21no—
15#16839877—21no—
16C2×#14519712C411yescharacteristic
17C2×#14519704C411yescharacteristic
18C2×#14519703C411yescharacteristic
19C2×C8×Dic61C2211yescharacteristic
20#16839582—21no—
21#16839582—21no—
22#16839547—22no—
23#16839544—22no—
24#16839543—22no—
25#16839537—21no—
26C16×Dic61—21no—
27C2×#131×C61C2211yescharacteristic
28C2×M32×C61C2211yescharacteristic
29C2×M32×C61C2211yescharacteristic
30C61×#350—22no—
31C2×#11758222C2×C411yescharacteristic
32#14519797—21no—
33#14519797—21no—
34#14519797—21no—
35#14519797—21no—
36C2×#11758202C811yescharacteristic
37C2×#11758200C811yescharacteristic
38C2×#11758201C811yescharacteristic
39C2×#11758199C811yescharacteristic
40#14519783—21no—
41#14519783—21no—
42#14519783—21no—
43#14519783—21no—
44C2×#11758194C2×C411yescharacteristic
45C2×#11758189—21no—
46C22×#92418C2×C411yescharacteristic
47C2×C8×D61—21no—
48C2×C4×Dic61C2×C411yescharacteristic
49#14519717—21no—
50#14519717—21no—
51#14519717—21no—
52#14519717D412yes—
53C2×#11758185—21no—
54C2×#11758185—21no—
55#14519712—21no—
56#14519712—21no—
57#14519704—21no—
58#14519704—21no—
59#14519703—21no—
60#14519703—21no—
61C8×Dic61D411yescharacteristic
62C8×Dic61D411yescharacteristic
63C8×Dic61D411yescharacteristic
64C8×Dic61D411yescharacteristic
65C2×#41×C61C2×C411yescharacteristic
66#131×C61—21no—
67#131×C61—21no—
68#131×C61—21no—
69#131×C61—21no—
70C2×M16×C61—21no—
71C2×M16×C61C2×C411yescharacteristic
72C22×C8×C61—21no—
73C22×C8×C61C2311yescharacteristic
74M32×C61—21no—
75M32×C61—21no—
76M32×C61—21no—
77M32×C61D412yes—
78C2×C16×C61—21no—
79C2×C16×C61—21no—
80#41×C61—21no—
81#41×C61—21no—
82#41×C61—21no—
83#41×C61—21no—
84C2×Q8×C61C2×C811yescharacteristic
85C2×D4×C61—21no—
86C2×D4×C61C2×C811yescharacteristic
87C22×C4×C61—21no—
88C22×C4×C61C22×C411yescharacteristic
89C2×C22⋊D61—21no—
90C22×Dic61—21no—
91#11758222—21no—
92#11758222—21no—
93#11758222—21no—
94#11758222—21no—
95C2×D244C2×C811yescharacteristic
96C2×C4×D61—21no—
97C2×Dic122C2×C811yescharacteristic
98M16×C61—21no—
99M16×C61—21no—
100M16×C61—41no—
101M16×C61—41no—
102C2×C8×C61—21no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C2×C8×C61C2×D411yescharacteristic
106C2×C8×C61C2×D411yescharacteristic
107C2×C8×C61C2×D411yescharacteristic
108C2×C8×C61C2×D411yescharacteristic
109C2×C8×C61#4111yescharacteristic
110C2×C8×C61#4111yescharacteristic
111#11758202—21no—
112#11758202—21no—
113#11758201—21no—
114#11758201—21no—
115#11758200—21no—
116#11758200—21no—
117#11758199—21no—
118#11758199—21no—
119C4×Dic61—21no—
120C4×Dic61C22⋊C411yescharacteristic
121C4×Dic61C22⋊C411yescharacteristic
122#11758194—21no—
123#11758194—21no—
124C2×#92418—21no—
125C2×#92418C22⋊C411yescharacteristic
126C2×#92418C22⋊C411yescharacteristic
127C2×#92418C2×C811yescharacteristic
128C2×#92418C2×C811yescharacteristic
129C2×#92418M1611yescharacteristic
130C2×#92418M1611yescharacteristic
131#11758189—41no—
132#11758189—41no—
133C8×D61—41no—
134C8×D61—41no—
135C16×C61—22no—
136C16×C61—41no—
137#11758185—22no—
138#11758185—41no—
139C23×C61—21no—
140C23×C61#13111yescharacteristic
141C22×D61—21no—
142Q8×C61—21no—
143Q8×C61—21no—
144D4×C61—21no—
145D4×C61—21no—
146D4×C61—41no—
147D4×C61—41no—
148C2×C4×C61—21no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61C2×C22⋊C411yescharacteristic
152C2×C4×C61C4×D411yescharacteristic
153C2×C4×C61C4×D411yescharacteristic
154C2×C4×C61C22×C811yescharacteristic
155C2×C4×C61C2×M1611yescharacteristic
156C2×C4×C61#13111yescharacteristic
157C22⋊D61—41no—
158C22⋊D61—41no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—42no—
163D244—21no—
164D244—21no—
165C4×D61—41no—
166C4×D61—41no—
167Dic122—21no—
168Dic122—21no—
169C8×C61—41no—
170C8×C61#12111yescharacteristic
171C8×C61#12111yescharacteristic
172C8×C61#12411yescharacteristic
173C8×C61#12711yescharacteristic
174#92418—41no—
175#92418C22⋊C811yescharacteristic
176#92418C22⋊C811yescharacteristic
177#92418C22⋊C811yescharacteristic
178#92418C22⋊C811yescharacteristic
179#13197—611nomaximal, Sylow
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—81no—
183C22×C61#40811yescharacteristic
184C22×C61C8×D411yescharacteristic
185C22×C61#43611yescharacteristic
186C2×D61—41no—
187C2×D61—81no—
188C4×C61—41no—
189C4×C61#39011yescharacteristic
190C4×C61C2×C22⋊C811yescharacteristic
191C4×C61C8×D411yescharacteristic
192C4×C61#43611yescharacteristic
193Dic61—22no—
194Dic61—41no—
195Dic61—41no—
196C2×#443—611no—
197C2×#364—611no—
198#2117—611no—
199#2117D6111yescharacteristic, complemented
200#2115—611no—
201#2115—611no—
202C4×M32—611no—
203C2×C61—21no—
204C2×C61—21no—
205C2×C61—21no—
206C2×C61—81no—
207C2×C61#195411yescharacteristic
208D61—81no—
209C2×#135—611no—
210C2×#131—611no—
211C2×#131C2×D6111yescharacteristic
212C2×M32—611no—
213C2×M32—611no—
214C2×M32C2×D6111yescharacteristic
215C2×M32C2×D6111yescharacteristic
216#443—1221no—
217#443—1221no—
218#443—1221no—
219#443—1221no—
220C2×#108—611no—
221C2×#104—611no—
222C2×#104—611no—
223C2×C4×C8—611no—
224#364—1221no—
225#364—1221no—
226#350—22no—
227#350—1222no—
228#349—1222no—
229#349—1222no—
230#346—1221no—
231C4×C16—1221no—
232C61#1319711yescharacteristic, complemented, Sylow
233C2×#41—611no—
234C2×#41C4×D6111yescharacteristic
235#135—1221no—
236#135—1221no—
237#135—1221no—
238#135—1221no—
239C2×Q16—611no—
240C2×SD16—611no—
241C2×SD16—611no—
242C2×D8—611no—
243#131—21no—
244#131—21no—
245#131—21no—
246#131—21no—
247#131—1221no—
248#131—1221no—
249#131—1221no—
250#131—1221no—
251C2×M16—21no—
252C2×M16—611no—
253C2×M16—1221no—
254C2×M16C4×D6111yescharacteristic
255C22×C8—21no—
256C22×C8—611no—
257C22×C8—1221no—
258C22×C8C22×D6111yescharacteristic
259C2×C42—611no—
260M32—21no—
261M32—21no—
262M32—21no—
263M32—612no—
264M32—1221no—
265M32—1221no—
266M32—1221no—
267M32C22⋊D6112yes—
268C2×C16—21no—
269C2×C16—21no—
270C2×C16—1221no—
271C2×C16—1221no—
272#108—1221no—
273#108—1221no—
274#104—1221no—
275#104—1221no—
276#104—1221no—
277#104—1221no—
278C4×C8—611no—
279C4×C8—611no—
280C4×C8—611no—
281C4×C8—611no—
282#41—21no—
283#41—21no—
284#41—21no—
285#41—21no—
286#41—1221no—
287#41—1221no—
288#41—1221no—
289#41—1221no—
290C2×Q8—611no—
291C2×Q8C8×D6111yescharacteristic
292C2×D4—21no—
293C2×D4—611no—
294C2×D4—1221no—
295C2×D4C8×D6111yescharacteristic
296C22×C4—21no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4C2×C4×D6111yescharacteristic
300Q16—1221no—
301Q16—1221no—
302SD16—1221no—
303SD16—1221no—
304SD16—1221no—
305SD16—1221no—
306D8—1221no—
307D8—1221no—
308M16—21no—
309M16—21no—
310M16—41no—
311M16—41no—
312M16—1221no—
313M16—1221no—
314M16—2441no—
315M16—2441no—
316C2×C8—21no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—611no—
320C2×C8—611no—
321C2×C8—611no—
322C2×C8—611no—
323C2×C8—611no—
324C2×C8—611no—
325C2×C8—1221no—
326C2×C8—2441no—
327C2×C8—2441no—
328C2×C8#1175822211yescharacteristic
329C2×C8D4×D6111yescharacteristic
330C2×C8D4×D6111yescharacteristic
331C2×C8D4×D6111yescharacteristic
332C2×C8#1175822411yescharacteristic
333C2×C8C2×C22⋊D6111yescharacteristic
334C42—611no—
335C42—611no—
336C42—1221no—
337C16—22no—
338C16—41no—
339C16—1222no—
340C16—2441no—
341C23—21no—
342C23—1221no—
343C23#1451978511yescharacteristic
344Q8—21no—
345Q8—21no—
346Q8—1221no—
347Q8—1221no—
348D4—21no—
349D4—21no—
350D4—41no—
351D4—41no—
352D4—1221no—
353D4—1221no—
354D4—2441no—
355D4—2441no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—2442no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4C22⋊C4×D6111yescharacteristic
366C2×C4#1451973711yescharacteristic
367C2×C4C4×C22⋊D6111yescharacteristic
368C2×C4C2×C8×D6111yescharacteristic
369C2×C4M16×D6111yescharacteristic
370C2×C4#1451978311yescharacteristic
371C8—41no—
372C8—611no—
373C8—611no—
374C8—611no—
375C8—611no—
376C8—2441no—
377C8#1451974911yescharacteristic
378C8#1451975011yescharacteristic
379C8#1451976311yescharacteristic
380C8#1451977311yescharacteristic
381C22—41no—
382C22—41no—
383C22—81no—
384C22—4881no—
385C22—2441no—
386C22#1683972711yescharacteristic
387C22#1683982511yescharacteristic
388C22#1683983811yescharacteristic
389C4—41no—
390C4—1222no—
391C4—2441no—
392C4—2441no—
393C4#1683966211yescharacteristic
394C4C22⋊C8×D6111yescharacteristic
395C4C8×C22⋊D6111yescharacteristic
396C4#1683983711yescharacteristic
397C2—21no—
398C2—21no—
399C2—21no—
400C2—81no—
401C2—4881no—
402C2#2144661111yescharacteristic
subgroupG/H
centerC8#14519749
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#2117C2
socleC2×C61#1954
prime radicalC2×#14519797C4
cosocleC22×C8×C61C23
hypercenter#2117D61
hypocenterC61#13197
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
2. C2×#16839582C2semidirect
3. #21447448C2semidirect
4. #21447440C2semidirect
5. #21447439C2semidirect
6. M32×Dic61C2semidirect
7. C61×#2117C2semidirect
199. #2117D61semidirect
232. C61#13197semidirect

Maximal subgroups

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

subgroupindex
C2×#168398772
C2×#168395822
#214474482
#214474402
#214474392
M32×Dic612
C61×#21172
#1319761