Finite Group Databasebeta

← #29662764

Subgroups — #29662764

Order 15616.

598 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#21455884C212yesmaximal
2#21454785C211yesmaximal, characteristic
3#21445370C212yesmaximal, complemented
4#21445363C212yesmaximal, complemented
5#21445334C211yesmaximal, characteristic, complemented
6#21445329C211yesmaximal, characteristic, complemented
7#21445310C211yesmaximal, characteristic, complemented
8#21445305C211yesmaximal, characteristic, complemented
9#21444567C211yesmaximal, characteristic, complemented
10#21444484C212yesmaximal, complemented
11C61×#3170C211yesmaximal, characteristic, complemented
12C4×#11758222C2211yescharacteristic
13#16840100—22no—
14#16840044C2212yes—
15#16840039C2212yes—
16#16839969C2212yes—
17#16839964C2212yes—
18#16839922—22no—
19#16839892C2211yescharacteristic
20#16839892C2211yescharacteristic
21C4×#11758202—22no—
22C4×#11758201—22no—
23#16839841C2211yescharacteristic
24#16839841C2211yescharacteristic
25#16839833—21no—
26#16839833—21no—
27#16839815C2212yes—
28#16839815C2211yescharacteristic
29#16839813—21no—
30C4×#11758189—21no—
31#16839515C2212yes—
32#16839513C2211yescharacteristic
33#16839513C2211yescharacteristic
34#16839508C2212yes—
35#16839508C2212yes—
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×#11758222D411yescharacteristic
48C2×#11758202—22no—
49C2×#11758201—22no—
50C2×#11758189—21no—
51C2×#11758189—21no—
52C4×Dic122D411yescharacteristic
53C4×Dic122C2311yescharacteristic
54C4×D244D411yescharacteristic
55C4×D244C2311yescharacteristic
56C4×C22⋊D61—21no—
57C4×C22⋊D61—21no—
58#14519736D411yescharacteristic
59#14519734—21no—
60C42×D61—21no—
61#14519710—22no—
62#14519708—22no—
63C4⋊#92418C2312yes—
64C4⋊#92418C2312yes—
65C4⋊#92418C2311yescharacteristic
66C4⋊#92418C2311yescharacteristic
67#14519706—21no—
68#14519706—21no—
69#14519701—22no—
70#14519701—22no—
71#14519700—22no—
72#14519697—22no—
73C22⋊#92418—21no—
74C22⋊#92418—22no—
75#14519689—21no—
76#14519689—21no—
77#14519687—21no—
78#14519687—21no—
79C4×#92418—21no—
80C4×#92418—22no—
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—
108#11758222—42no—
109C2×D244C2×D411yescharacteristic
110C2×C4×D61—21no—
111C2×C4×D61—21no—
112C2×C4×D61—21no—
113C2×Dic122C2×D411yescharacteristic
114Q16×C61—42no—
115Q16×C61—42no—
116C2×C8×C61—22no—
117C2×C8×C61—41no—
118C2×C8×C61C2×D411yescharacteristic
119C2×C8×C61C2×D411yescharacteristic
120C2×C8×C61C2×D411yescharacteristic
121C2×C8×C61C2×D411yescharacteristic
122C4⋊C4×C61—22no—
123C4⋊C4×C61—22no—
124C4⋊C4×C61—22no—
125C4⋊C4×C61—22no—
126C4⋊C4×C61—42no—
127C4⋊C4×C61—42no—
128C22⋊C4×C61—42no—
129C42×C61—42no—
130C42×C61C2×D411yescharacteristic
131C42×C61C2×D411yescharacteristic
132C42×C61#4111yescharacteristic
133C42×C61C2411yescharacteristic
134C22⋊Dic61—21no—
135#11758202—44no—
136#11758201—44no—
137#11758198—21no—
138#11758198—21no—
139C4⋊Dic61C2×D411yescharacteristic
140C4⋊Dic61C2×D411yescharacteristic
141#11758196—21no—
142#11758196—21no—
143C4×Dic61—21no—
144C4×Dic61—21no—
145C4×Dic61—21no—
146C2×#92418—21no—
147C2×#92418—21no—
148C2×#92418—22no—
149C2×#92418—22no—
150#11758189—42no—
151#11758189—42no—
152C23×C61#12111yescharacteristic
153C22×D61—21no—
154Q8×C61—42no—
155Q8×C61—42no—
156Q8×C61—42no—
157Q8×C61—42no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—22no—
161C2×C4×C61—22no—
162C2×C4×C61—42no—
163C2×C4×C61—42no—
164C2×C4×C61#12111yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61C22×D411yescharacteristic
168C2×C4×C61C22×D411yescharacteristic
169C2×C4×C61C2×#4111yescharacteristic
170C22⋊D61—42no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174D244—22no—
175C4×D61—42no—
176C4×D61—41no—
177C4×D61—41no—
178C4×D61—42no—
179Dic122—22no—
180C8×C61—21no—
181C8×C61—21no—
182C8×C61—21no—
183C8×C61#13512yes—
184#92418—41no—
185#92418—41no—
186#92418—42no—
187#92418—42no—
188#19161—611nomaximal, Sylow
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61C2×#12111yescharacteristic
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—41no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—82no—
200C4×C61—82no—
201C4×C61#47312yes—
202C4×C61C2×#13511yescharacteristic
203C4×C61#57512yes—
204C4×C61#57511yescharacteristic
205Dic61—41no—
206Dic61—41no—
207Dic61—41no—
208#3170D6111yescharacteristic, complemented
209#3107—612no—
210#2965—611no—
211#1700—612no—
212#1699—612no—
213#1694—611no—
214#1693—611no—
215#1690—611no—
216#1689—611no—
217#1564—611no—
218#1544—612no—
219C2×C61—41no—
220C2×C61#303511yescharacteristic
221C2×C61#305411yescharacteristic
222C2×C61C2×#47311yescharacteristic
223D61—81no—
224#533C2×D6112yes—
225C4×#41—611no—
226#500C2×D6111yescharacteristic
227#494C2×D6111yescharacteristic
228#487C2×D6112yes—
229#485—1222no—
230#475—612no—
231#474—612no—
232#467—21no—
233#467—21no—
234#462—612no—
235#461—612no—
236#452—1222no—
237#446—611no—
238#446—611no—
239C4×Q16—21no—
240C4×Q16—21no—
241C4×Q16—1222no—
242C4×SD16—1222no—
243#436—611no—
244#436—611no—
245#435—1221no—
246#435—1221no—
247#431—611no—
248#431—612no—
249#431—1221no—
250C4×M16—1221no—
251C2×C4×C8C2×D6111yescharacteristic
252#335—612no—
253#334—611no—
254#334—611no—
255#332—612no—
256#332—612no—
257#332—612no—
258#332—612no—
259C61#1916111yescharacteristic, complemented, Sylow
260C2×#41—611no—
261C2×Q16—21no—
262C2×Q16—21no—
263C2×Q16—1222no—
264C2×SD16—1222no—
265C2×M16—1221no—
266C2×M16—1221no—
267C22×C8C22⋊D6111yescharacteristic
268C22×C8C22⋊D6111yescharacteristic
269C4⋊Q8C22×D6112yes—
270C4⋊Q8C22×D6112yes—
271#125—22no—
272C22⋊Q8—22no—
273C22⋊Q8—22no—
274C4×Q8—22no—
275C4×Q8—22no—
276C4×Q8—611no—
277C4×Q8—611no—
278C4×D4—611no—
279C4×D4—611no—
280C4×D4—1221no—
281C4×D4—1221no—
282#117—22no—
283#117—611no—
284#117—1221no—
285C2×C42—1221no—
286C2×C42C22×D6111yescharacteristic
287#107—21no—
288#107—21no—
289#107—1222no—
290#106—1222no—
291C4⋊C8—611no—
292C4⋊C8—611no—
293C4⋊C8—612no—
294C4⋊C8—612no—
295C4⋊C8—1221no—
296C4⋊C8—1221no—
297#103—22no—
298#103—22no—
299#103—1222no—
300#103—1222no—
301#103—1222no—
302#102—1222no—
303C22⋊C8—1222no—
304C22⋊C8—1221no—
305C22⋊C8—1221no—
306C22⋊C8—1221no—
307#97—1221no—
308#97—1221no—
309C4×C8—1222no—
310C4×C8—1221no—
311C4×C8C22⋊D6111yescharacteristic
312C4×C8C22⋊D6111yescharacteristic
313C4×C8C22×D6111yescharacteristic
314C4×C8C22×D6111yescharacteristic
315#41—2442no—
316C2×Q8—22no—
317C2×Q8—22no—
318C2×Q8—611no—
319C2×D4—611no—
320C2×D4—1221no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4D4×D6111yescharacteristic
325C22×C4#1175822411yescharacteristic
326C22×C4C2×C22⋊D6111yescharacteristic
327Q16—42no—
328Q16—42no—
329Q16—2444no—
330SD16—2444no—
331M16—2442no—
332M16—2442no—
333C2×C8—22no—
334C2×C8—41no—
335C2×C8—1222no—
336C2×C8—1222no—
337C2×C8—1221no—
338C2×C8—1221no—
339C2×C8C2×C22⋊D6111yescharacteristic
340C2×C8C2×C22⋊D6111yescharacteristic
341C2×C8C2×C22⋊D6111yescharacteristic
342C2×C8C2×C22⋊D6111yescharacteristic
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—42no—
348C4⋊C4—42no—
349C4⋊C4—611no—
350C4⋊C4—611no—
351C4⋊C4—1221no—
352C4⋊C4—1221no—
353C22⋊C4—42no—
354C22⋊C4—1221no—
355C22⋊C4—1221no—
356C22⋊C4—1221no—
357C42—42no—
358C42—1221no—
359C42—1221no—
360C42—1221no—
361C42D4×D6111yescharacteristic
362C42#1175822411yescharacteristic
363C42C2×C22⋊D6111yescharacteristic
364C42C23×D6111yescharacteristic
365C23—1221no—
366C23#1451974811yescharacteristic
367Q8—42no—
368Q8—42no—
369Q8—42no—
370Q8—42no—
371Q8—1222no—
372D4—1222no—
373D4—2442no—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—21no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—2442no—
384C2×C4—2441no—
385C2×C4—2442no—
386C2×C4—2441no—
387C2×C4#1451974811yescharacteristic
388C2×C4#1451974811yescharacteristic
389C2×C4#1451974811yescharacteristic
390C2×C4C2×D4×D6111yescharacteristic
391C2×C4C22×C22⋊D6111yescharacteristic
392C2×C4C2×#1175822411yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8—2441no—
397C8—2442no—
398C8—2442no—
399C8—2441no—
400C8#1451979712yes—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—2441no—
405C22—2441no—
406C22—2441no—
407C22C2×#1451974811yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—82no—
412C4—82no—
413C4—2441no—
414C4—2441no—
415C4—2441no—
416C4#1684003412yes—
417C4C2×#1451979711yescharacteristic
418C4#1684055912yes—
419C4#1684056011yescharacteristic
420C2—41no—
421C2—4881no—
422C2#2145526811yescharacteristic
423C2#2145542411yescharacteristic
424C2C2×#1684003411yescharacteristic
subgroupG/H
centerC2×C4#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3170C2
socleC22×C61C2×#121
prime radicalC2×#11758222D4
hypercenter#3170D61
hypocenterC61#19161
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
3. #21445370C2semidirect
4. #21445363C2semidirect
5. #21445334C2semidirect
6. #21445329C2semidirect
7. #21445310C2semidirect
8. #21445305C2semidirect
9. #21444567C2semidirect
10. #21444484C2semidirect
11. C61×#3170C2semidirect
208. #3170D61semidirect
259. C61#19161semidirect

Maximal subgroups

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

subgroupindex
#214558842
#214547852
#214453702
#214453632
#214453342
#214453292
#214453102
#214453052
#214445672
#214444842
C61×#31702
#1916161