Finite Group Databasebeta

← #29577869

Subgroups — #29577869

Order 15616.

518 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454859C211yesmaximal, characteristic
2#21451177C211yesmaximal, characteristic
3#21445808C211yesmaximal, characteristic
4#21444248C211yesmaximal, characteristic, complemented
5#21443679C211yesmaximal, characteristic, complemented
6#21443678C211yesmaximal, characteristic, complemented
7C61×#1487C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9#16839841—22no—
10#16839839—22no—
11#16839815C2211yescharacteristic
12#16839786C2211yescharacteristic
13C2×#14519693—21no—
14#16839724—22no—
15#16839697C412yes—
16#16839673C412yes—
17#16839664—21no—
18#16839660—21no—
19#16839633—22no—
20#16839628C2211yescharacteristic
21#16839530—21no—
22Q8⋊#92418—22no—
23C2×C4×Q8×C61C2211yescharacteristic
24C61×#431C2211yescharacteristic
25C61×#423C2211yescharacteristic
26C61×Q8⋊C8—22no—
27C22×D244D411yescharacteristic
28C22×C4×D61D412yes—
29C2×#11758194—21no—
30C2×#11758189—24no—
31C4×D244—21no—
32C4×D244—21no—
33C4×D244—21no—
34C4×D244—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61D411yescharacteristic
37C2×#11758196—22no—
38C2×#11758198—22no—
39C2×#11758198—22no—
40C2×#11758198C2×C412yes—
41C4⋊#92418—21no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44#14519693—42no—
45C22⋊#92418—21no—
46#14519689—24no—
47C4×#92418D412yes—
48#14519684—21no—
49#14519684—22no—
50#14519684C2×C412yes—
51C22×Q8×C61C2×C411yescharacteristic
52C2×M16×C61—21no—
53C4×Q8×C61—21no—
54C4×Q8×C61—21no—
55C4×Q8×C61—21no—
56C4×Q8×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C42×C61—21no—
60C2×C42×C61C2311yescharacteristic
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C22⋊C8×C61—21no—
65C4×C8×C61D412yes—
66C23×D61C22⋊C412yes—
67C2×Q8×C61—21no—
68C2×Q8×C61—21no—
69C2×Q8×C61—42no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—22no—
76C22×Dic61C22⋊C412yes—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244—21no—
83C2×C4×D61—22no—
84C2×C4×D61—22no—
85C2×C4×D61—82no—
86M16×C61—41no—
87M16×C61—41no—
88C2×C8×C61—22no—
89C2×C8×C61—41no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C42×C61—41no—
95C42×C61—41no—
96C42×C61C2×D411yescharacteristic
97C42×C61C2×D411yescharacteristic
98C42×C61#4111yescharacteristic
99C42×C61#4111yescharacteristic
100#11758198—22no—
101#11758198—22no—
102#11758198—44no—
103#11758198—82no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—41no—
107C4⋊Dic61—41no—
108#11758196—82no—
109#11758194—41no—
110#11758194—41no—
111C2×#92418—22no—
112C2×#92418—41no—
113#11758189—84no—
114C23×C61C2×C22⋊C411yescharacteristic
115C22×D61—22no—
116C22×D61—22no—
117C22×D61—22no—
118C22×D61—42no—
119C22×D61—42no—
120Q8×C61—22no—
121Q8×C61—22no—
122Q8×C61—41no—
123Q8×C61—41no—
124C2×C4×C61—22no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61C4×D411yescharacteristic
134C2×C4×C61#12011yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12311yescharacteristic
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C61#13711yescharacteristic
140C2×C4×C61#13711yescharacteristic
141C2×C4×C61#13711yescharacteristic
142C2×Dic61—22no—
143C2×Dic61—42no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61—42no—
147D244—41no—
148D244—41no—
149D244—41no—
150D244—41no—
151C4×D61—44no—
152C4×D61—82no—
153C8×C61—42no—
154C8×C61—81no—
155#92418—42no—
156#92418—81no—
157#9487—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61#38611yescharacteristic
161C22×C61#41711yescharacteristic
162C22×C61#41911yescharacteristic
163C2×D61—44no—
164C2×D61—42no—
165C2×D61—42no—
166C2×D61—42no—
167C2×D61—82no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—42no—
173C4×C61—81no—
174C4×C61#46811yescharacteristic
175C4×C61#46811yescharacteristic
176C4×C61#47011yescharacteristic
177C4×C61#47011yescharacteristic
178Dic61—42no—
179Dic61—82no—
180#2975—611no—
181#2580—611no—
182#1800—611no—
183#1487—611no—
184#1487D6111yescharacteristic, complemented
185#1286—611no—
186#1286—611no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61#189111yescharacteristic
190C2×C61#189411yescharacteristic
191C2×C61#191111yescharacteristic
192D61—82no—
193C2×C4×Q8C2×D6111yescharacteristic
194C2×C4×D4—611no—
195#436—1222no—
196#436—1222no—
197#431—611no—
198#431C2×D6111yescharacteristic
199#423—611no—
200#423C2×D6111yescharacteristic
201C2×#100—1221no—
202#407—1222no—
203#399—612no—
204#393—612no—
205#390—1221no—
206#389—1221no—
207#385—1222no—
208#382—611no—
209#343—1221no—
210Q8⋊C8—22no—
211Q8⋊C8—1222no—
212C61#948711yescharacteristic, complemented, Sylow
213C22×Q8C4×D6111yescharacteristic
214C22×D4—611no—
215C23×C4—612no—
216C2×M16—21no—
217C2×M16—1224no—
218C2×M16—1221no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×D4—1221no—
224C4×D4—1221no—
225C4×D4—1221no—
226C4×D4—1221no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—1222no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4C4×D6111yescharacteristic
232C2×C22⋊C4—612no—
233C2×C22⋊C4—1222no—
234C2×C22⋊C4—1222no—
235C2×C42—21no—
236C2×C42C22×D6111yescharacteristic
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—1221no—
241C4⋊C8—1221no—
242C4⋊C8—1221no—
243#100—2442no—
244C22⋊C8—21no—
245C22⋊C8—1224no—
246C22⋊C8—1221no—
247C4×C8—612no—
248C4×C8C22⋊D6112yes—
249#95—612no—
250#95—1222no—
251#95—1221no—
252C24—612no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—42no—
256C2×D4—1221no—
257C2×D4—1221no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—612no—
265C22×C4—1222no—
266C22×C4—1222no—
267C22×C4—1222no—
268C22×C4—4882no—
269C22×C4C2×C4×D6111yescharacteristic
270C22×C4D4×D6111yescharacteristic
271C22×C4D4×D6111yescharacteristic
272M16—41no—
273M16—41no—
274M16—4884no—
275M16—2441no—
276M16—2441no—
277C2×C8—22no—
278C2×C8—41no—
279C2×C8—1222no—
280C2×C8—2441no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—4882no—
288C4⋊C4—2441no—
289C4⋊C4—2441no—
290C22⋊C4—1222no—
291C22⋊C4—1222no—
292C22⋊C4—4882no—
293C22⋊C4—2444no—
294C42—41no—
295C42—41no—
296C42#1175822211yescharacteristic
297C42D4×D6111yescharacteristic
298C42#1175822411yescharacteristic
299C42C2×C22⋊D6111yescharacteristic
300C23—1222no—
301C23—1222no—
302C23—1222no—
303C23—2442no—
304C23—2442no—
305C23C22⋊C4×D6111yescharacteristic
306Q8—22no—
307Q8—22no—
308Q8—41no—
309Q8—41no—
310D4—2441no—
311D4—2441no—
312D4—2441no—
313D4—2441no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—1222no—
323C2×C4—4882no—
324C2×C4—2444no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4#1451973711yescharacteristic
330C2×C4C4×C22⋊D6111yescharacteristic
331C2×C4#1451974511yescharacteristic
332C2×C4#1451974811yescharacteristic
333C2×C4#1451975011yescharacteristic
334C2×C4#1451975911yescharacteristic
335C2×C4#1451980411yescharacteristic
336C2×C4#1451980611yescharacteristic
337C2×C4#1451980911yescharacteristic
338C2×C4#1451980911yescharacteristic
339C8—42no—
340C8—81no—
341C8—4881no—
342C8—2442no—
343C22—21no—
344C22—21no—
345C22—4882no—
346C22—2444no—
347C22—2442no—
348C22—2442no—
349C22—2442no—
350C22#1683963811yescharacteristic
351C22#1683976211yescharacteristic
352C22#1683976911yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—42no—
358C4—81no—
359C4—4882no—
360C4—2442no—
361C4#1684000511yescharacteristic
362C4#1684001111yescharacteristic
363C4#1684001711yescharacteristic
364C4#1684001911yescharacteristic
365C2—21no—
366C2—21no—
367C2—4882no—
368C2#2144623411yescharacteristic
369C2#2144624911yescharacteristic
370C2#2144634811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1487C2
socleC22×C61#386
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1487D61
hypocenterC61#9487
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
4. #21444248C2semidirect
5. #21443679C2semidirect
6. #21443678C2semidirect
7. C61×#1487C2semidirect
184. #1487D61semidirect
212. C61#9487semidirect

Maximal subgroups

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

subgroupindex
#214548592
#214511772
#214458082
#214442482
#214436792
#214436782
C61×#14872
#948761