Finite Group Databasebeta

← D61×#1694 #29662637

Subgroups — D61×#1694 #29662637

Order 15616.

682 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#500×D61C211yesmaximal, characteristic
2#462×D61C212yesmaximal
3#446×D61C211yesmaximal, characteristic
4#21445338C211yesmaximal, characteristic, complemented
5#21445337C211yesmaximal, characteristic, complemented
6#21445336C212yesmaximal, complemented
7#21445335C212yesmaximal, complemented
8#21445334C211yesmaximal, characteristic, complemented
9#334×D61C211yesmaximal, characteristic
10#332×D61C212yesmaximal
11C61×#1694C211yesmaximal, characteristic, complemented
12C2×Q16×D61—22no—
13C4⋊Q8×D61C2212yes—
14C4×Q8×D61C2211yescharacteristic
15#16840167C2211yescharacteristic
16#16840166—21no—
17#16840166—21no—
18#16840165C2212yes—
19#16839973C2212yes—
20#16839972C2212yes—
21#16839971—22no—
22#16839970—22no—
23#16839969C2212yes—
24#16839893C2211yescharacteristic
25#16839892C2211yescharacteristic
26#16839891—21no—
27#16839890—21no—
28#16839889C2211yescharacteristic
29#107×D61—21no—
30#107×D61—21no—
31C4⋊C8×D61—21no—
32C4⋊C8×D61C2211yescharacteristic
33C4⋊C8×D61C2212yes—
34#103×D61—22no—
35#97×D61—21no—
36C4×C8×D61C2211yescharacteristic
37#16839513C2211yescharacteristic
38#16839512C2212yes—
39#16839509C2212yes—
40#16839508C2212yes—
41#16839507C2212yes—
42C61×#500C2211yescharacteristic
43C61×#462C2212yes—
44C61×#446C2211yescharacteristic
45C61×#334C2211yescharacteristic
46C61×#332C2212yes—
47C2×Q8×D61—22no—
48C2×Q8×D61D411yescharacteristic
49C2×Dic244—22no—
50C2×#11758202—22no—
51C2×#11758202—22no—
52Q16×D61—48no—
53C2×C8×D61—21no—
54C2×C8×D61—22no—
55C2×C8×D61D411yescharacteristic
56C2×C8×D61D411yescharacteristic
57#14519777C2312yes—
58#14519776—22no—
59#14519776—22no—
60#14519775—22no—
61Q8×Dic61D411yescharacteristic
62C4×Dic122—21no—
63C4×Dic122C2311yescharacteristic
64#14519742—21no—
65#14519742D411yescharacteristic
66C4⋊C4×D61—21no—
67C4⋊C4×D61—22no—
68C4⋊C4×D61—22no—
69C4⋊C4×D61D411yescharacteristic
70C42×D61—21no—
71C42×D61C2311yescharacteristic
72#14519711—21no—
73#14519711—21no—
74#14519710—22no—
75#14519710—22no—
76C4⋊#92418—21no—
77C4⋊#92418C2312yes—
78C4⋊#92418C2311yescharacteristic
79#14519706—21no—
80#14519706—22no—
81#14519706—21no—
82#14519706—21no—
83#14519702—22no—
84#14519701—22no—
85#14519700—22no—
86#14519688—21no—
87#14519687—21no—
88#14519687—21no—
89C4×#92418C2311yescharacteristic
90C8×Dic61D411yescharacteristic
91C8×Dic61D411yescharacteristic
92C2×Q16×C61—22no—
93C4⋊Q8×C61C2312yes—
94C4×Q8×C61C2311yescharacteristic
95#107×C61—21no—
96#107×C61—21no—
97C4⋊C8×C61—21no—
98C4⋊C8×C61C2312yes—
99C4⋊C8×C61C2311yescharacteristic
100#103×C61—22no—
101#97×C61—21no—
102C4×C8×C61C2311yescharacteristic
103C2×Q8×C61—22no—
104C2×Q8×C61C2×D411yescharacteristic
105Q8×D61—24no—
106Q8×D61—44no—
107Q8×D61—44no—
108C2×C4×D61—21no—
109C2×C4×D61—21no—
110C2×C4×D61—42no—
111C2×C4×D61C2×D411yescharacteristic
112C2×C4×D61C2×D411yescharacteristic
113C2×C4×D61#4111yescharacteristic
114C2×Dic122—21no—
115C2×Dic122—22no—
116C2×Dic122—42no—
117C2×Dic122C2×D411yescharacteristic
118Q16×C61—44no—
119C2×C8×C61—21no—
120C2×C8×C61—22no—
121C2×C8×C61C2×D411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C4⋊C4×C61—21no—
124C4⋊C4×C61—22no—
125C4⋊C4×C61—22no—
126C4⋊C4×C61C2×D411yescharacteristic
127C42×C61—21no—
128C42×C61C2411yescharacteristic
129#11758202—44no—
130#11758202—44no—
131C4⋊Dic61—21no—
132C4⋊Dic61—22no—
133C4⋊Dic61—22no—
134C4⋊Dic61C2×D411yescharacteristic
135#11758196—21no—
136#11758196—21no—
137#11758196—21no—
138#11758196—42no—
139#11758196—42no—
140C4×Dic61—21no—
141C4×Dic61—21no—
142C4×Dic61—21no—
143C4×Dic61C2×D411yescharacteristic
144C4×Dic61C2×D411yescharacteristic
145C4×Dic61#4111yescharacteristic
146C2×#92418—21no—
147C2×#92418—22no—
148C2×#92418C2×D411yescharacteristic
149C2×#92418C2×D411yescharacteristic
150Dic244—44no—
151C8×D61—22no—
152C8×D61—44no—
153C8×D61—42no—
154C8×D61Q1614yescomplemented
155C22×D61#12111yescharacteristic
156Q8×C61—22no—
157Q8×C61—42no—
158Q8×C61—42no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—42no—
162C2×C4×C61C22×D411yescharacteristic
163C2×C4×C61C22×D411yescharacteristic
164C2×C4×C61C2×#4111yescharacteristic
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—42no—
168C2×Dic61#12111yescharacteristic
169C2×Dic61#12111yescharacteristic
170C2×Dic61#12111yescharacteristic
171C4×D61—22no—
172C4×D61—42no—
173C4×D61—42no—
174C4×D61—84no—
175C4×D61C2×Q1612yes—
176C4×D61AGL(1,ℤ/8)14yes—
177C4×D61#13712yes—
178Dic122—22no—
179Dic122—42no—
180Dic122—42no—
181Dic122—42no—
182Dic122—84no—
183C8×C61—21no—
184C8×C61—42no—
185C8×C61—41no—
186C8×C61C2×Q1612yescomplemented
187#92418—21no—
188#92418—42no—
189#92418—41no—
190#92418C2×Q1612yescomplemented
191C2×#1694—611nomaximal, Sylow
192C22×C61C2×#12111yescharacteristic
193C2×D61#46212yes—
194C2×D61#46912yes—
195C2×D61#47312yes—
196C4×C61—21no—
197C4×C61—41no—
198C4×C61—41no—
199C4×C61—82no—
200C4×C61C22×Q1611yescharacteristic
201C4×C61C2×AGL(1,ℤ/8)12yes—
202C4×C61C2×#13711yescharacteristic
203Dic61—21no—
204Dic61—41no—
205Dic61—41no—
206Dic61—82no—
207Dic61#46212yes—
208Dic61#46912yes—
209C2×#500—611no—
210C2×#462—612no—
211C2×#446—611no—
212#1694—611no—
213#1694—612no—
214#1694—611no—
215#1694—611no—
216#1694—612no—
217#1694D6111yescharacteristic, direct product factor
218C2×#334—611no—
219C2×#332—612no—
220C2×C61C2×#46211yescharacteristic
221C2×C61C2×#46911yescharacteristic
222C2×C61C2×#47311yescharacteristic
223D61#169414yesdirect product factor
224C22×Q16—1222no—
225C2×C4⋊Q8—612no—
226C2×C4×Q8—611no—
227#500—612no—
228#500—611no—
229#500—1221no—
230#500—1221no—
231#500C2×D6111yescharacteristic
232#462—612no—
233#462—612no—
234#462—612no—
235#462—1222no—
236#462—1222no—
237#462C2×D6112yes—
238#446—611no—
239#446—611no—
240#446—611no—
241#446—1221no—
242#446—1221no—
243#446C2×D6111yescharacteristic
244C2×#107—1221no—
245C2×#107—1221no—
246C2×C4⋊C8—611no—
247C2×C4⋊C8—612no—
248C2×C4⋊C8—1221no—
249C2×#103—1222no—
250C2×#97—1221no—
251C2×C4×C8—611no—
252#334—612no—
253#334—611no—
254#334C2×D6111yescharacteristic
255#332—612no—
256#332—612no—
257#332—612no—
258#332C2×D6112yes—
259C61C2×#169411yescharacteristic, complemented, Sylow
260C22×Q8—611no—
261C22×Q8—1222no—
262C2×Q16—22no—
263C2×Q16—1222no—
264C2×Q16—1222no—
265C2×Q16—1222no—
266C2×Q16—2448no—
267C22×C8—611no—
268C22×C8—611no—
269C22×C8—1222no—
270C22×C8—1221no—
271C4⋊Q8—612no—
272C4⋊Q8—1222no—
273C4⋊Q8—1222no—
274C4⋊Q8—1222no—
275C4⋊Q8C22×D6112yes—
276C4×Q8—611no—
277C4×Q8—611no—
278C4×Q8—611no—
279C4×Q8—1221no—
280C4×Q8—1221no—
281C4×Q8C22×D6111yescharacteristic
282C2×C4⋊C4—611no—
283C2×C4⋊C4—1221no—
284C2×C4⋊C4—1222no—
285C2×C4⋊C4—1222no—
286C2×C42—611no—
287C2×C42—1221no—
288#107—21no—
289#107—21no—
290#107—1222no—
291#107—1222no—
292#107—1221no—
293#107—1221no—
294C4⋊C8—21no—
295C4⋊C8—611no—
296C4⋊C8—612no—
297C4⋊C8—1221no—
298C4⋊C8—1221no—
299C4⋊C8—1222no—
300C4⋊C8—1221no—
301C4⋊C8—1221no—
302C4⋊C8C22×D6111yescharacteristic
303C4⋊C8C22×D6112yes—
304#103—22no—
305#103—1222no—
306#103—1222no—
307#103—1222no—
308#97—21no—
309#97—1221no—
310#97—1221no—
311#97—1221no—
312C4×C8—611no—
313C4×C8—611no—
314C4×C8—611no—
315C4×C8C22×D6111yescharacteristic
316C2×Q8—22no—
317C2×Q8—611no—
318C2×Q8—1221no—
319C2×Q8—1224no—
320C2×Q8—1222no—
321C2×Q8—2442no—
322C2×Q8—2444no—
323C2×Q8—2444no—
324C2×Q8D4×D6111yescharacteristic
325C22×C4—611no—
326C22×C4—611no—
327C22×C4—611no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—2442no—
331Q16—44no—
332Q16—2444no—
333Q16—2444no—
334Q16—2444no—
335C2×C8—21no—
336C2×C8—22no—
337C2×C8—611no—
338C2×C8—614no—
339C2×C8—611no—
340C2×C8—1222no—
341C2×C8—1221no—
342C2×C8—1222no—
343C2×C8—2442no—
344C2×C8—2444no—
345C2×C8D4×D6111yescharacteristic
346C2×C8D4×D6111yescharacteristic
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—611no—
351C4⋊C4—1221no—
352C4⋊C4—1221no—
353C4⋊C4—1221no—
354C4⋊C4—1221no—
355C4⋊C4—1222no—
356C4⋊C4—1222no—
357C4⋊C4—2442no—
358C4⋊C4—2442no—
359C4⋊C4D4×D6111yescharacteristic
360C42—21no—
361C42—611no—
362C42—611no—
363C42—611no—
364C42—1221no—
365C42—1221no—
366C42—1221no—
367C42C23×D6111yescharacteristic
368C23—611no—
369Q8—22no—
370Q8—42no—
371Q8—42no—
372Q8—1222no—
373Q8—4884no—
374Q8—2442no—
375Q8—2442no—
376Q8—2442no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—611no—
381C2×C4—611no—
382C2×C4—612no—
383C2×C4—614no—
384C2×C4—612no—
385C2×C4—611no—
386C2×C4—1222no—
387C2×C4—1221no—
388C2×C4—1221no—
389C2×C4—4884no—
390C2×C4—2442no—
391C2×C4—2442no—
392C2×C4—2442no—
393C2×C4C2×D4×D6111yescharacteristic
394C2×C4C2×D4×D6111yescharacteristic
395C2×C4#41×D6111yescharacteristic
396C8—21no—
397C8—42no—
398C8—41no—
399C8—612no—
400C8—1221no—
401C8—2442no—
402C8—2441no—
403C8Q16×D6112yescomplemented
404C22—612no—
405C22—612no—
406C22—612no—
407C22#121×D6111yescharacteristic
408C4—21no—
409C4—41no—
410C4—41no—
411C4—82no—
412C4—612no—
413C4—612no—
414C4—1221no—
415C4—4882no—
416C4—2441no—
417C4—2441no—
418C4C2×Q16×D6111yescharacteristic
419C4AGL(1,ℤ/8)×D6112yes—
420C4#137×D6111yescharacteristic
421C2—614no—
422C2#462×D6111yescharacteristic
423C2#469×D6111yescharacteristic
424C2#473×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1694C2
socleC22×C61C2×#121
prime radicalC22×D61#121
hypercenter#1694D61
hypocenterC61C2×#1694
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1694

Complements

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

NH ≅ G/Ntype
4. #21445338C2semidirect
5. #21445337C2semidirect
6. #21445336C2semidirect
7. #21445335C2semidirect
8. #21445334C2semidirect
11. C61×#1694C2semidirect
154. C8×D61Q16semidirect
186. C8×C61C2×Q16semidirect
190. #92418C2×Q16semidirect
217. #1694D61direct (N × H)
223. D61#1694direct (N × H)
259. C61C2×#1694semidirect
403. C8Q16×D61semidirect

Maximal subgroups

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

subgroupindex
#500×D612
#462×D612
#446×D612
#214453382
#214453372
#214453362
#214453352
#214453342
#334×D612
#332×D612
C61×#16942
C2×#169461