Finite Group Databasebeta

← #30606291

Subgroups — #30606291

Order 15616.

736 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 140 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
1D61⋊#413C212yesmaximal
2#21460911C212yesmaximal, complemented
3#21460910C212yesmaximal, complemented
4#21454261C211yesmaximal, characteristic
5C2×D61⋊M16—22no—
6#16840749—22no—
7#16840749C414yes—
8#16840748—22no—
9#16840748C2214yes—
10D61⋊#101—22no—
11D61⋊#100C414yes—
12C2×#41×D61C2211yescharacteristic
13C22×#11758189C411yescharacteristic
14C2×M16×D61C411yescharacteristic
15#16839730C2211yescharacteristic
16#16839729C411yescharacteristic
17#16839728C2211yescharacteristic
18#16839727—22no—
19#16839724—22no—
20C61×#408C411yescharacteristic
21C2×#11758213—42no—
22D61⋊M16—24no—
23D61⋊M16—24no—
24D61⋊M16—42no—
25D61⋊M16—42no—
26C2×#11758217—24no—
27C2×D61⋊C8—42no—
28#14519838—24no—
29#14519838—24no—
30#14519837—24no—
31#14519837C2×C418yes—
32C2×#11758226Q811yescharacteristic
33C2×#11758222D412yes—
34C2×#11758222C2311yescharacteristic
35C2×#11758224C2×C412yes—
36C2×#11758224D411yescharacteristic
37#41×D61—42no—
38#41×D61—42no—
39C2×Q8×D61D411yescharacteristic
40C2×D4×D61C2×C412yes—
41C2×D4×D61Q811yescharacteristic
42C22×C4×D61C2×C411yescharacteristic
43C22×C4×D61D412yes—
44C2×#11758194C2×C411yescharacteristic
45C2×#11758189—21no—
46C2×#11758189—21no—
47C2×#11758189—21no—
48C2×#11758189—42no—
49M16×D61—42no—
50C22×#92418C2×C411yescharacteristic
51C2×C8×D61—21no—
52C22⋊#92418—22no—
53#14519689—22no—
54#14519689—22no—
55C2×#41×C61C2×C411yescharacteristic
56C2×M16×C61C2×C411yescharacteristic
57C22×C8×C61C2×C411yescharacteristic
58C22⋊C8×C61—22no—
59C23×D61C4211yescharacteristic
60C23×D61C4⋊C412yes—
61#41×C61—41no—
62#41×C61—41no—
63C2×Q8×C61C4⋊C411yescharacteristic
64C2×D4×C61C4212yes—
65C2×D4×C61C4⋊C411yescharacteristic
66C22×C4×C61C22⋊C412yes—
67C22×C4×C61C22×C411yescharacteristic
68C2×C22⋊D61C22⋊C412yes—
69C2×C22⋊D61C4⋊C412yes—
70C2×C22⋊D61C22×C412yes—
71C22×Dic61C4211yescharacteristic
72C22×Dic61C22⋊C412yes—
73#11758226—42no—
74Q8×D61—42no—
75#11758224—42no—
76#11758224—42no—
77#11758224—42no—
78D4×D61—42no—
79D4×D61—42no—
80D4×D61—42no—
81#11758222—42no—
82#11758222—42no—
83#11758222—41no—
84#11758222—41no—
85C2×D244C4⋊C412yes—
86C2×D244C2×Q811yescharacteristic
87C2×C4×D61—22no—
88C2×C4×D61—22no—
89C2×C4×D61—22no—
90C2×C4×D61—22no—
91C2×C4×D61—22no—
92C2×C4×D61—22no—
93C2×C4×D61C22⋊C411yescharacteristic
94C2×C4×D61C22⋊C412yes—
95C2×C4×D61C22⋊C411yescharacteristic
96C2×C4×D61C4⋊C412yes—
97C2×C4×D61C4⋊C411yescharacteristic
98C2×C4×D61C4⋊C411yescharacteristic
99C2×C4×D61C2×D412yes—
100C2×Dic122C22⋊C412yes—
101C2×Dic122C2×D411yescharacteristic
102#11758217—28no—
103#11758217—44no—
104C2×#92420—44no—
105#11758213—44no—
106#11758213—44no—
107D61⋊C8—44no—
108D61⋊C8—44no—
109M16×C61—41no—
110C2×C8×C61—21no—
111C2×C8×C61—21no—
112C2×C8×C61—41no—
113#11758194—41no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—41no—
117#11758189—42no—
118#11758189—42no—
119#11758189—42no—
120C8×D61—42no—
121C23×C61#9512yes—
122C23×C61C2×C4211yescharacteristic
123C22×D61—22no—
124C22×D61—22no—
125C22×D61—22no—
126C22×D61—82no—
127C22×D61—81no—
128C22×D61#9511yescharacteristic
129C22×D61#9511yescharacteristic
130C22×D61C2×C4⋊C412yes—
131Q8×C61—41no—
132D4×C61—42no—
133D4×C61—41no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—22no—
137C2×C4×C61—22no—
138C2×C4×C61#9512yes—
139C2×C4×C61C2×C22⋊C411yescharacteristic
140C2×C4×C61C2×C4⋊C411yescharacteristic
141C22⋊D61—42no—
142C22⋊D61—42no—
143C22⋊D61—42no—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—22no—
147C2×Dic61#9511yescharacteristic
148C2×Dic61#9511yescharacteristic
149C2×Dic61C2×C22⋊C412yes—
150D244—42no—
151D244—41no—
152C4×D61—22no—
153C4×D61—22no—
154C4×D61—22no—
155C4×D61—21no—
156C4×D61—21no—
157C4×D61—22no—
158C4×D61—22no—
159C4×D61—22no—
160C4×D61—22no—
161C4×D61—22no—
162C4×D61#9912yes—
163C4×D61#9912yes—
164Dic122—42no—
165Dic122—41no—
166#92420—48no—
167C8×C61—41no—
168C8×C61—41no—
169#92418—41no—
170#92418—41no—
171#12579—611nomaximal, Sylow
172C22×C61—22no—
173C22×C61—21no—
174C22×C61—42no—
175C22×C61—41no—
176C22×C61C2×#9511yescharacteristic
177C2×D61—21no—
178C2×D61—22no—
179C2×D61—41no—
180C2×D61—44no—
181C2×D61—41no—
182C2×D61—42no—
183C2×D61—82no—
184C2×D61—82no—
185C2×D61#34212yes—
186C4×C61—22no—
187C4×C61—21no—
188C4×C61C2×#9911yescharacteristic
189C4×C61C2×#9911yescharacteristic
190Dic61—22no—
191Dic61—21no—
192Dic61#34212yes—
193C2×#413—612no—
194#2879—611no—
195#1392—612no—
196#1392—612no—
197C2×C61—21no—
198C2×C61—42no—
199C2×C61—41no—
200C2×C61C2×#34211yescharacteristic
201D61—22no—
202D61—42no—
203D61—41no—
204C22×#41—611no—
205C22×M16—611no—
206C22×M16—611no—
207C22×M16—1222no—
208#413—614no—
209#413—614no—
210#413—1222no—
211#413—1222no—
212C2×#101—1222no—
213C2×#100—614no—
214#408—611no—
215#408—611no—
216#408—611no—
217#408—1222no—
218#408#692311yescharacteristic
219#407—1222no—
220C61#1257911yescharacteristic, complemented, Sylow
221C2×#41—611no—
222C2×#41—612no—
223C2×#41—611no—
224C2×#41—612no—
225C2×#41—611no—
226C2×#41—2442no—
227C2×#41—2442no—
228C2×#41C2×#692311yescharacteristic
229C22×Q8—611no—
230C22×D4—612no—
231C22×D4—611no—
232C23×C4—612no—
233C23×C4—611no—
234C2×M16—611no—
235C2×M16—1221no—
236C2×M16—1221no—
237C2×M16—1221no—
238C2×M16—1224no—
239C2×M16—1224no—
240C2×M16—1224no—
241C2×M16—2442no—
242C2×M16—2442no—
243C2×M16—2442no—
244C2×M16—2442no—
245C2×M16—2442no—
246C2×M16C2×#692311yescharacteristic
247C22×C8—611no—
248C22×C8—1221no—
249C22×C8—2442no—
250C22×C8C2×#692311yescharacteristic
251#101—1224no—
252#101—1224no—
253#100—618no—
254#100—1224no—
255C22⋊C8—22no—
256C22⋊C8—1222no—
257C22⋊C8—1222no—
258C22⋊C8—1222no—
259C24—612no—
260C24—611no—
261#41—41no—
262#41—41no—
263#41—2441no—
264#41—2442no—
265#41—2441no—
266#41—2442no—
267#41—2442no—
268#41—2442no—
269#41—2442no—
270#41—2442no—
271C2×Q8—612no—
272C2×Q8—611no—
273C2×Q8—2442no—
274C2×Q8C4⋊#692311yescharacteristic
275C2×D4—612no—
276C2×D4—612no—
277C2×D4—612no—
278C2×D4—612no—
279C2×D4—611no—
280C2×D4—2442no—
281C2×D4—2442no—
282C2×D4—2442no—
283C2×D4C4×#692312yes—
284C2×D4C4⋊#692311yescharacteristic
285C22×C4—611no—
286C22×C4—612no—
287C22×C4—611no—
288C22×C4—612no—
289C22×C4—612no—
290C22×C4—612no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—1222no—
295C22×C4—1222no—
296C22×C4—1222no—
297C22×C4—1222no—
298C22×C4—1222no—
299C22×C4—1222no—
300C22×C4C22⋊#692312yes—
301C22×C4C22×#692311yescharacteristic
302M16—41no—
303M16—1228no—
304M16—2442no—
305M16—2442no—
306M16—2442no—
307M16—2444no—
308M16—2444no—
309M16—2444no—
310M16—2441no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—41no—
314C2×C8—1221no—
315C2×C8—1221no—
316C2×C8—2442no—
317C2×C8—2444no—
318C2×C8—2444no—
319C2×C8—2444no—
320C2×C8—2441no—
321C23—611no—
322C23—611no—
323C23—612no—
324C23—1222no—
325C23—1222no—
326C23—1222no—
327C23—4881no—
328C23—4882no—
329C23(C2×#6923)⋊C412yes—
330C23C2×C4×#692311yescharacteristic
331Q8—41no—
332Q8—2442no—
333Q8—2441no—
334D4—42no—
335D4—41no—
336D4—2442no—
337D4—2441no—
338D4—2442no—
339D4—2442no—
340D4—2442no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—22no—
345C2×C4—611no—
346C2×C4—612no—
347C2×C4—612no—
348C2×C4—611no—
349C2×C4—612no—
350C2×C4—1222no—
351C2×C4—1222no—
352C2×C4—1222no—
353C2×C4—1222no—
354C2×C4—1222no—
355C2×C4—1222no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—1222no—
359C2×C4—1221no—
360C2×C4—1222no—
361C2×C4—1222no—
362C2×C4—1221no—
363C2×C4(C2×#6923)⋊C412yes—
364C2×C4C2×C22⋊#692311yescharacteristic
365C2×C4C2×C4⋊#692311yescharacteristic
366C8—41no—
367C8—41no—
368C8—2448no—
369C8—2441no—
370C8—2441no—
371C22—22no—
372C22—21no—
373C22—42no—
374C22—41no—
375C22—612no—
376C22—1221no—
377C22—1222no—
378C22—4882no—
379C22—4882no—
380C22—2441no—
381C22—2441no—
382C22—2442no—
383C22—2444no—
384C22C2×(C2×#6923)⋊C411yescharacteristic
385C4—22no—
386C4—21no—
387C4—612no—
388C4—1222no—
389C4—1221no—
390C4D61⋊#9911yescharacteristic
391C4D61⋊#9911yescharacteristic
392C2—21no—
393C2—41no—
394C2—42no—
395C2—1222no—
396C2—2441no—
397C2—2442no—
398C2#2146151611yescharacteristic
subgroupG/H
centerC4D61⋊#99
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC2×C61C2×#342
prime radicalC2×#41×D61C22
cosocleC2×#11758222C23
hypercenter#408#6923
hypocenterC61#12579
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #21460911C2semidirect
3. #21460910C2semidirect
220. C61#12579semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4132
#214609112
#214609102
#214542612
#1257961