Finite Group Databasebeta

← #29573126

Subgroups — #29573126

Order 15616.

494 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839839C211yesmaximal, characteristic
2#21445946C211yesmaximal, characteristic, complemented
3#21445820C211yesmaximal, characteristic
4#21445816C211yesmaximal, characteristic
5C2×#16839512C211yesmaximal, characteristic, complemented
6#21443703C211yesmaximal, characteristic, complemented
7C61×#1296C211yesmaximal, characteristic, complemented
8C22×#11758189—21no—
9C2×C4×D244C2211yescharacteristic
10#16839839—22no—
11#16839839C414yescomplemented
12C2×C4⋊#92418C2211yescharacteristic
13C2×#14519699—21no—
14C2×#14519697—21no—
15C2×#14519689—21no—
16C2×C4×#92418C2211yescharacteristic
17#16839632C2211yescharacteristic
18#16839525—21no—
19#16839524—21no—
20#16839524—21no—
21#16839524—21no—
22#16839512—22no—
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C61×#384C2211yescharacteristic
26C22×D244D411yescharacteristic
27C22×C4×D61—21no—
28C2×#11758189—24no—
29C2×#11758189—42no—
30C2×#11758189—42no—
31C22×#92418—21no—
32C22×#92418D411yescharacteristic
33C22×#92418D411yescharacteristic
34C4×D244—21no—
35C4×D244—21no—
36C4×D244C2×C412yes—
37C4×D244Q812yes—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758198—21no—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45#14519699—42no—
46#14519697—42no—
47#14519689—24no—
48C4×#92418C2×C412yes—
49C4×#92418D412yes—
50C22×C8×C61—21no—
51C22×C8×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C42×C61C2311yescharacteristic
56C4⋊C8×C61—21no—
57C4⋊C8×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61C2×C412yes—
60C23×D61—21no—
61C22×C4×C61—41no—
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61#4111yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—41no—
67C2×D244—21no—
68C2×D244—21no—
69C2×D244—21no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244C4⋊C412yes—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C8×C61—22no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—81no—
90C42×C61C22×C411yescharacteristic
91C42×C61C2×D411yescharacteristic
92C42×C61C2×Q811yescharacteristic
93C42×C61#4111yescharacteristic
94#11758198—22no—
95#11758198—22no—
96C4⋊Dic61—21no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—81no—
102C4⋊Dic61C4⋊C412yes—
103C2×#92418—21no—
104C2×#92418—21no—
105C2×#92418—21no—
106C2×#92418—21no—
107C2×#92418—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418C22⋊C412yes—
111C2×#92418C22⋊C412yes—
112#11758189—48no—
113C23×C61#12111yescharacteristic
114C22×D61—22no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—81no—
124C2×C4×C61—81no—
125C2×C4×C61—81no—
126C2×C4×C61C2×C22⋊C411yescharacteristic
127C2×C4×C61C2×C4⋊C411yescharacteristic
128C2×C4×C61#11711yescharacteristic
129C2×C4×C61#12111yescharacteristic
130C2×C4×C61C22⋊Q811yescharacteristic
131C2×C4×C61C22⋊Q811yescharacteristic
132C2×C4×C61#13511yescharacteristic
133C2×C4×C61#13511yescharacteristic
134C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C61#13711yescharacteristic
139C2×C4×C61#13711yescharacteristic
140C2×Dic61—22no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—81no—
144C2×Dic61—81no—
145C2×Dic61—81no—
146D244—22no—
147D244—22no—
148D244—41no—
149D244—41no—
150C4×D61—42no—
151C4×D61—42no—
152C4×D61—42no—
153C4×D61—42no—
154C8×C61—42no—
155C8×C61—81no—
156#92418—22no—
157#92418—22no—
158#92418—81no—
159#8656—611nomaximal, Sylow
160C22×C61#38011yescharacteristic
161C22×C61#46311yescharacteristic
162C22×C61#46311yescharacteristic
163C22×C61#46911yescharacteristic
164C22×C61#47011yescharacteristic
165C22×C61#47111yescharacteristic
166C22×C61#47111yescharacteristic
167C2×D61—42no—
168C2×D61—42no—
169C2×D61—42no—
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—161no—
177C4×C61#41611yescharacteristic
178C4×C61#41811yescharacteristic
179C4×C61#42811yescharacteristic
180C4×C61#42811yescharacteristic
181C4×C61#46811yescharacteristic
182C4×C61#46811yescharacteristic
183C4×C61#47811yescharacteristic
184C4×C61#47811yescharacteristic
185Dic61—42no—
186Dic61—161no—
187C2×#436—611no—
188#1834—611no—
189#1802—611no—
190#1802—611no—
191C2×#334—611no—
192#1296—611no—
193#1296D6111yescharacteristic, complemented
194C2×C61#170111yescharacteristic
195C2×C61#170111yescharacteristic
196C2×C61#170311yescharacteristic
197C2×C61#170311yescharacteristic
198C2×C61#180411yescharacteristic
199C2×C61#180911yescharacteristic
200C2×C61#181511yescharacteristic
201D61—82no—
202C22×M16—1221no—
203C2×C4×D4—611no—
204#436—614no—
205#436—1222no—
206C2×C4⋊C8—611no—
207C2×C4⋊C8C2×D6111yescharacteristic
208C2×C4⋊C8C2×D6111yescharacteristic
209C2×#102—1221no—
210C2×#102—1221no—
211C2×C22⋊C8—1221no—
212C2×C4×C8—611no—
213#384—611no—
214#384C2×D6111yescharacteristic
215#340—1221no—
216#340—1221no—
217#340—1221no—
218#340—1221no—
219#334—1222no—
220C61#865611yescharacteristic, complemented, Sylow
221C22×D4—611no—
222C23×C4—1221no—
223C2×M16—1224no—
224C2×M16—2442no—
225C2×M16—2442no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—611no—
229C22×C8—611no—
230C22×C8—1221no—
231C4×D4—612no—
232C4×D4—612no—
233C4×D4—1221no—
234C4×D4—1221no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C42C22×D6111yescharacteristic
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—1221no—
248C4⋊C8—1221no—
249C4⋊C8C4×D6112yes—
250#102—2442no—
251#102—2442no—
252C22⋊C8—1224no—
253C4×C8—612no—
254C4×C8—612no—
255C24—1221no—
256C2×D4—612no—
257C2×D4—1221no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C22×C4—41no—
263C22×C4—1221no—
264C22×C4—1222no—
265C22×C4—1222no—
266C22×C4—2441no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4—2441no—
270C22×C4—2441no—
271C22×C4#1175822211yescharacteristic
272C22×C4D4×D6111yescharacteristic
273C22×C4D4×D6111yescharacteristic
274M16—2448no—
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—612no—
282C2×C8—612no—
283C2×C8—1221no—
284C2×C8—1221no—
285C2×C8—1221no—
286C2×C8—1221no—
287C2×C8—2441no—
288C2×C8—2441no—
289C2×C8—2441no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—81no—
295C4⋊C4—612no—
296C4⋊C4—1221no—
297C4⋊C4—4881no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C22⋊C4—1222no—
303C22⋊C4—1222no—
304C42C2×C4×D6111yescharacteristic
305C42#1175822211yescharacteristic
306C42D4×D6111yescharacteristic
307C42Q8×D6111yescharacteristic
308C23—1222no—
309C23—2441no—
310C23—2441no—
311C23—2441no—
312C23—2441no—
313C23—2441no—
314C23—2441no—
315C23#1451975011yescharacteristic
316D4—1222no—
317D4—1222no—
318D4—2441no—
319D4—2441no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—1222no—
326C2×C4—4881no—
327C2×C4—4881no—
328C2×C4—4881no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4—2442no—
334C2×C4—2442no—
335C2×C4C22⋊C4×D6111yescharacteristic
336C2×C4C4⋊C4×D6111yescharacteristic
337C2×C4#1451973411yescharacteristic
338C2×C4#1451975011yescharacteristic
339C2×C4#1451975511yescharacteristic
340C2×C4#1451975511yescharacteristic
341C2×C4#1451979811yescharacteristic
342C2×C4#1451980011yescharacteristic
343C2×C4#1451980111yescharacteristic
344C2×C4#1451980111yescharacteristic
345C2×C4#1451980411yescharacteristic
346C2×C4#1451980411yescharacteristic
347C2×C4#1451980611yescharacteristic
348C2×C4#1451980911yescharacteristic
349C8—42no—
350C8—81no—
351C8—1222no—
352C8—1222no—
353C8—4881no—
354C22—4881no—
355C22—4881no—
356C22—4881no—
357C22—4881no—
358C22—2442no—
359C22—2442no—
360C22—2442no—
361C22#1683962111yescharacteristic
362C22#1683997611yescharacteristic
363C22#1683998011yescharacteristic
364C22#1684001411yescharacteristic
365C22#1684001911yescharacteristic
366C22#1684002411yescharacteristic
367C22#1684002811yescharacteristic
368C4—21no—
369C4—21no—
370C4—161no—
371C4—9761no—
372C4—2442no—
373C4#1683975711yescharacteristic
374C4#1683976511yescharacteristic
375C4#1683980111yescharacteristic
376C4#1683980311yescharacteristic
377C4#1684000711yescharacteristic
378C4#1684001111yescharacteristic
379C4#1684006111yescharacteristic
380C4#1684006511yescharacteristic
381C2—4882no—
382C2#2144537911yescharacteristic
383C2#2144538311yescharacteristic
384C2#2144539311yescharacteristic
385C2#2144539711yescharacteristic
386C2#2144582811yescharacteristic
387C2#2144585111yescharacteristic
388C2#2144587711yescharacteristic
subgroupG/H
centerC23#14519750
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#121
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1296D61
hypocenterC61#8656
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #21445946C2semidirect
5. C2×#16839512C2semidirect
6. #21443703C2semidirect
7. C61×#1296C2semidirect
11. #16839839C4semidirect
193. #1296D61semidirect
220. C61#8656semidirect

Maximal subgroups

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

subgroupindex
C2×#168398392
#214459462
#214458202
#214458162
C2×#168395122
#214437032
C61×#12962
#865661