Finite Group Databasebeta

← #29663369

Subgroups — #29663369

Order 15616.

562 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456998C212yesmaximal
2#21454794C211yesmaximal, characteristic
3#21445398C212yesmaximal, complemented
4#21445391C212yesmaximal, complemented
5#21445220C211yesmaximal, characteristic, complemented
6#21445215C211yesmaximal, characteristic, complemented
7#21445186C211yesmaximal, characteristic, complemented
8#21445181C211yesmaximal, characteristic, complemented
9#21444567C211yesmaximal, characteristic, complemented
10#21444529C212yesmaximal, complemented
11C61×#3170C211yesmaximal, characteristic, complemented
12#16840296C2211yescharacteristic
13#16840161—22no—
14#16840119—22no—
15#16840103—22no—
16#16840086—22no—
17#16840054C2212yes—
18#16840049C2212yes—
19#16840044C2212yes—
20#16840039C2212yes—
21#16839892C2211yescharacteristic
22C8×Dic122C2211yescharacteristic
23#16839841C2211yescharacteristic
24#16839833—21no—
25C8×D244C2211yescharacteristic
26C8×C22⋊D61—21no—
27#16839821—21no—
28#16839819C2211yescharacteristic
29#16839815C2212yes—
30#16839716—21no—
31#16839515C2211yescharacteristic
32#16839515C2211yescharacteristic
33#16839513C2212yes—
34#16839511C2212yes—
35#16839511C2212yes—
36#16839508C2212yes—
37#16839508C2212yes—
38C61×#533C2212yes—
39C61×#500C2211yescharacteristic
40C61×#494C2211yescharacteristic
41C61×#487C2212yes—
42C61×#467—21no—
43C61×#467—21no—
44C4×Q16×C61—21no—
45C4×Q16×C61—21no—
46C2×C4×C8×C61C2211yescharacteristic
47C2×#11758189—21no—
48C2×C8×D61—21no—
49#14519771—21no—
50#14519769D411yescharacteristic
51#14519765D411yescharacteristic
52#14519760—21no—
53#14519756D411yescharacteristic
54#14519751D411yescharacteristic
55C4×Dic122C2311yescharacteristic
56C4×D244C2311yescharacteristic
57C4×C22⋊D61—21no—
58#14519734—21no—
59#14519710—22no—
60#14519710—22no—
61#14519708—22no—
62#14519708—22no—
63C4⋊#92418C2311yescharacteristic
64C4⋊#92418C2311yescharacteristic
65C4⋊#92418C2312yes—
66C4⋊#92418C2312yes—
67#14519706—21no—
68#14519706—21no—
69#14519700—22no—
70#14519700—22no—
71#14519697—22no—
72#14519697—22no—
73C22⋊#92418—22no—
74C22⋊#92418—21no—
75#14519689—21no—
76#14519689—21no—
77#14519688—21no—
78#14519687—21no—
79C4×#92418—22no—
80C8×Dic61—21no—
81C2×Q16×C61—21no—
82C2×Q16×C61—21no—
83C22×C8×C61D411yescharacteristic
84C22×C8×C61D411yescharacteristic
85C4⋊Q8×C61C2312yes—
86C4⋊Q8×C61C2312yes—
87#125×C61—22no—
88C22⋊Q8×C61—22no—
89C22⋊Q8×C61—22no—
90C4×Q8×C61—22no—
91C4×Q8×C61—22no—
92#117×C61—22no—
93C2×C42×C61C2311yescharacteristic
94#107×C61—21no—
95#107×C61—21no—
96#103×C61—22no—
97#103×C61—22no—
98C4×C8×C61D411yescharacteristic
99C4×C8×C61D411yescharacteristic
100C4×C8×C61C2311yescharacteristic
101C4×C8×C61C2311yescharacteristic
102C2×Q8×C61—22no—
103C2×Q8×C61—22no—
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61#4111yescharacteristic
107C2×C22⋊D61—21no—
108C2×D244C2×D411yescharacteristic
109C2×C4×D61—21no—
110C2×Dic122C2×D411yescharacteristic
111Q16×C61—42no—
112Q16×C61—42no—
113C2×C8×C61—22no—
114C2×C8×C61—41no—
115C2×C8×C61C2×D411yescharacteristic
116C2×C8×C61C2×D411yescharacteristic
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2×D411yescharacteristic
119C4⋊C4×C61—22no—
120C4⋊C4×C61—22no—
121C4⋊C4×C61—22no—
122C4⋊C4×C61—22no—
123C4⋊C4×C61—42no—
124C4⋊C4×C61—42no—
125C22⋊C4×C61—42no—
126C42×C61—42no—
127C42×C61C2×D411yescharacteristic
128C42×C61C2×D411yescharacteristic
129C42×C61#4111yescharacteristic
130C42×C61C2411yescharacteristic
131C22⋊Dic61—21no—
132#11758198—21no—
133#11758198—21no—
134#11758198—21no—
135#11758198—21no—
136C4⋊Dic61C2×D411yescharacteristic
137C4⋊Dic61C2×D411yescharacteristic
138#11758196—21no—
139#11758196—21no—
140#11758196—21no—
141#11758196—21no—
142C4×Dic61—21no—
143C2×#92418—21no—
144C2×#92418—22no—
145C2×#92418—22no—
146C2×#92418—21no—
147#11758189—42no—
148C8×D61—42no—
149C23×C61#12111yescharacteristic
150C22×D61—21no—
151Q8×C61—42no—
152Q8×C61—42no—
153Q8×C61—82no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—41no—
159C2×C4×C61—42no—
160C2×C4×C61—42no—
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61#12111yescharacteristic
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61C22×D411yescharacteristic
165C2×C4×C61C22×D411yescharacteristic
166C2×C4×C61C2×#4111yescharacteristic
167C22⋊D61—42no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171D244—21no—
172D244—21no—
173C4×D61—41no—
174C4×D61—41no—
175Dic122—21no—
176Dic122—21no—
177C8×C61—21no—
178C8×C61—21no—
179C8×C61—21no—
180C8×C61#13512yes—
181#92418—41no—
182#92418—41no—
183#92418—42no—
184#92418—42no—
185#19220—611nomaximal, Sylow
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61C2×#12111yescharacteristic
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—82no—
198C4×C61—82no—
199C4×C61C2×#13511yescharacteristic
200C4×C61#57511yescharacteristic
201C4×C61#57811yescharacteristic
202C4×C61#57811yescharacteristic
203Dic61—41no—
204Dic61—41no—
205Dic61—41no—
206#3233—612no—
207#3170D6111yescharacteristic, complemented
208#2966—611no—
209#1704—612no—
210#1703—612no—
211#1676—611no—
212#1675—611no—
213#1670—611no—
214#1669—611no—
215#1564—611no—
216#1554—612no—
217C2×C61—41no—
218C2×C61#303511yescharacteristic
219C2×C61#305911yescharacteristic
220C2×C61#306711yescharacteristic
221D61—81no—
222#533C2×D6112yes—
223#529—611no—
224#500C2×D6111yescharacteristic
225#499—1222no—
226#494C2×D6111yescharacteristic
227#488—1222no—
228#487C2×D6112yes—
229#485—1222no—
230#482—1222no—
231#477—612no—
232#476—612no—
233#475—612no—
234#474—612no—
235#467—21no—
236#467—21no—
237#446—611no—
238C8×Q8—611no—
239C4×Q16—21no—
240C4×Q16—21no—
241#436—611no—
242#435—1221no—
243C8×D4—611no—
244C8×D4—1221no—
245#433—1221no—
246#432—611no—
247#431—612no—
248#405—1221no—
249C2×C4×C8C2×D6111yescharacteristic
250#335—611no—
251#335—611no—
252#334—612no—
253#333—612no—
254#333—612no—
255#332—612no—
256#332—612no—
257C61#1922011yescharacteristic, complemented, Sylow
258C2×Q16—21no—
259C2×Q16—21no—
260C2×M16—1221no—
261C22×C8—1221no—
262C22×C8C22⋊D6111yescharacteristic
263C22×C8C22⋊D6111yescharacteristic
264C4⋊Q8C22×D6112yes—
265C4⋊Q8C22×D6112yes—
266#126—1221no—
267#125—22no—
268#125—611no—
269#124—611no—
270#123—1221no—
271C22⋊Q8—22no—
272C22⋊Q8—22no—
273C22⋊Q8—611no—
274#121—611no—
275C4×Q8—22no—
276C4×Q8—22no—
277C4×Q8—611no—
278C4×D4—611no—
279C4×D4—1221no—
280#117—22no—
281#117—1221no—
282C2×C42C22×D6111yescharacteristic
283#107—21no—
284#107—21no—
285#107—1222no—
286#107—1222no—
287#106—1222no—
288#106—1222no—
289C4⋊C8—611no—
290C4⋊C8—611no—
291C4⋊C8—612no—
292C4⋊C8—612no—
293C4⋊C8—1221no—
294C4⋊C8—1221no—
295#103—22no—
296#103—22no—
297#103—1222no—
298#103—1222no—
299#102—1222no—
300#102—1222no—
301C22⋊C8—1222no—
302C22⋊C8—1221no—
303C22⋊C8—1221no—
304C22⋊C8—1221no—
305#97—1221no—
306#97—1221no—
307C4×C8—1221no—
308C4×C8—1222no—
309C4×C8C22⋊D6111yescharacteristic
310C4×C8C22⋊D6111yescharacteristic
311C4×C8C22×D6111yescharacteristic
312C4×C8C22×D6111yescharacteristic
313C2×Q8—22no—
314C2×Q8—22no—
315C2×Q8—611no—
316C2×D4—611no—
317C2×D4—1221no—
318C22×C4—1221no—
319C22×C4D4×D6111yescharacteristic
320C22×C4#1175822411yescharacteristic
321C22×C4C2×C22⋊D6111yescharacteristic
322Q16—42no—
323Q16—42no—
324M16—2442no—
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—1222no—
328C2×C8—1222no—
329C2×C8—1221no—
330C2×C8—1221no—
331C2×C8—2442no—
332C2×C8C2×C22⋊D6111yescharacteristic
333C2×C8C2×C22⋊D6111yescharacteristic
334C2×C8C2×C22⋊D6111yescharacteristic
335C2×C8C2×C22⋊D6111yescharacteristic
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—611no—
343C4⋊C4—611no—
344C4⋊C4—1221no—
345C4⋊C4—1221no—
346C4⋊C4—1221no—
347C4⋊C4—1221no—
348C22⋊C4—42no—
349C22⋊C4—1221no—
350C22⋊C4—1221no—
351C22⋊C4—1221no—
352C22⋊C4—1221no—
353C22⋊C4—1221no—
354C42—42no—
355C42—1221no—
356C42D4×D6111yescharacteristic
357C42#1175822411yescharacteristic
358C42C2×C22⋊D6111yescharacteristic
359C42C23×D6111yescharacteristic
360C23—1221no—
361C23#1451974811yescharacteristic
362Q8—42no—
363Q8—42no—
364Q8—82no—
365Q8—1221no—
366Q8—1221no—
367D4—1221no—
368D4—1221no—
369D4—2442no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4#1451974811yescharacteristic
383C2×C4#1451974811yescharacteristic
384C2×C4#1451974811yescharacteristic
385C2×C4C2×D4×D6111yescharacteristic
386C2×C4C22×C22⋊D6111yescharacteristic
387C2×C4C2×#1175822411yescharacteristic
388C8—21no—
389C8—21no—
390C8—21no—
391C8—2441no—
392C8—2441no—
393C8—2442no—
394C8—2442no—
395C8#1451979712yes—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—2441no—
400C22—2441no—
401C22—2441no—
402C22C2×#1451974811yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—82no—
408C4—82no—
409C4—2441no—
410C4—2441no—
411C4—2441no—
412C4C2×#1451979711yescharacteristic
413C4#1684056011yescharacteristic
414C4#1684057511yescharacteristic
415C4#1684057511yescharacteristic
416C2—41no—
417C2—4881no—
418C2#2145526811yescharacteristic
419C2#2145547011yescharacteristic
420C2#2145553511yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3170C2
socleC22×C61C2×#121
prime radical#14519751D4
hypercenter#3170D61
hypocenterC61#19220
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
3. #21445398C2semidirect
4. #21445391C2semidirect
5. #21445220C2semidirect
6. #21445215C2semidirect
7. #21445186C2semidirect
8. #21445181C2semidirect
9. #21444567C2semidirect
10. #21444529C2semidirect
11. C61×#3170C2semidirect
207. #3170D61semidirect
257. C61#19220semidirect

Maximal subgroups

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

subgroupindex
#214569982
#214547942
#214453982
#214453912
#214452202
#214452152
#214451862
#214451812
#214445672
#214445292
C61×#31702
#1922061