Finite Group Databasebeta

← #29663990

Subgroups — #29663990

Order 15616.

638 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455628C211yesmaximal, characteristic
2#21455628C211yesmaximal, characteristic
3C8×#11758222C211yesmaximal, characteristic
4#21445274C214yesmaximal, complemented
5#21445267C214yesmaximal, complemented
6#21444578C211yesmaximal, characteristic, complemented
7#21444504C211yesmaximal, characteristic, complemented
8#21444500C211yesmaximal, characteristic, complemented
9C2×C61×#487C211yesmaximal, characteristic, complemented
10C4×#11758222C2211yescharacteristic
11#16840054—21no—
12#16840054C2212yes—
13#16840049—21no—
14#16840049C2212yes—
15#16840044—21no—
16#16840044C2212yes—
17#16840039—21no—
18#16840039C2212yes—
19C8×Dic122C2212yes—
20C8×D244C2212yes—
21C8×C22⋊D61—22no—
22#16839815C2211yescharacteristic
23#16839813—21no—
24#16839802—21no—
25#16839802—21no—
26#16839786C2211yescharacteristic
27#16839786C2211yescharacteristic
28#16839761—21no—
29#16839761—21no—
30C4×C8×D61—21no—
31#16839515C2214yes—
32#16839511C2214yes—
33#16839508C2214yes—
34C2×C4⋊Q8×C61C2211yescharacteristic
35C2×C4⋊Q8×C61C2211yescharacteristic
36C61×#487—21no—
37C61×#487—21no—
38C61×#487C2214yes—
39C2×#103×C61—22no—
40C2×C4×C8×C61C2211yescharacteristic
41C2×#11758222D411yescharacteristic
42C2×#11758194—21no—
43C2×#11758194—21no—
44C2×C8×D61—22no—
45C4×Dic122D411yescharacteristic
46C4×Dic122C2311yescharacteristic
47C4×D244D411yescharacteristic
48C4×D244C2311yescharacteristic
49C4×C22⋊D61—21no—
50C4×C22⋊D61—21no—
51#14519736D411yescharacteristic
52#14519734—21no—
53C42×D61—21no—
54#14519710—22no—
55#14519710—22no—
56#14519708—22no—
57#14519708—22no—
58C4⋊#92418—21no—
59C4⋊#92418—21no—
60C4⋊#92418C2312yes—
61C4⋊#92418C2312yes—
62C4⋊#92418C2312yes—
63#14519706—22no—
64#14519700—22no—
65#14519700—22no—
66#14519697—22no—
67#14519697—22no—
68C22⋊#92418—21no—
69#14519689—22no—
70C4×#92418—21no—
71C8×Dic61—22no—
72C22×Q8×C61—21no—
73C22×Q8×C61—21no—
74C22×C8×C61D412yes—
75C4⋊Q8×C61—21no—
76C4⋊Q8×C61—21no—
77C4⋊Q8×C61—21no—
78C4⋊Q8×C61—21no—
79C4⋊Q8×C61—21no—
80C4⋊Q8×C61—21no—
81C4⋊Q8×C61C2312yes—
82C4⋊Q8×C61C2312yes—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—21no—
87C2×C42×C61C2311yescharacteristic
88#103×C61—24no—
89#103×C61—24no—
90C4×C8×C61D411yescharacteristic
91C4×C8×C61D411yescharacteristic
92C4×C8×C61C2312yes—
93C2×Q8×C61—22no—
94C2×Q8×C61—22no—
95C2×Q8×C61—44no—
96C2×Q8×C61—41no—
97C2×Q8×C61—41no—
98C2×Q8×C61—82no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61#4111yescharacteristic
104C2×C22⋊D61—21no—
105#11758222—22no—
106#11758222Q1614yes—
107C2×D244C2×D411yescharacteristic
108C2×C4×D61—21no—
109C2×C4×D61—21no—
110C2×C4×D61—21no—
111C2×Dic122C2×D411yescharacteristic
112C2×C8×C61—42no—
113C2×C8×C61C2×D412yes—
114C2×C8×C61C2×D412yes—
115C4⋊C4×C61—22no—
116C4⋊C4×C61—22no—
117C4⋊C4×C61—22no—
118C4⋊C4×C61—22no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C4⋊C4×C61—41no—
122C4⋊C4×C61—41no—
123C42×C61C2×D411yescharacteristic
124C42×C61C2×D411yescharacteristic
125C42×C61#4111yescharacteristic
126C42×C61C2411yescharacteristic
127C22⋊Dic61—21no—
128#11758198—21no—
129#11758198—21no—
130C4⋊Dic61C2×D411yescharacteristic
131C4⋊Dic61C2×D411yescharacteristic
132#11758196—21no—
133#11758196—21no—
134C4×Dic61—21no—
135C4×Dic61—21no—
136C4×Dic61—21no—
137#11758194—42no—
138#11758194—42no—
139C2×#92418—22no—
140C2×#92418—22no—
141C2×#92418—22no—
142C8×D61—44no—
143C23×C61#12111yescharacteristic
144C22×D61—21no—
145Q8×C61—44no—
146Q8×C61—82no—
147Q8×C61—82no—
148Q8×C61—82no—
149C2×C4×C61—22no—
150C2×C4×C61—22no—
151C2×C4×C61—42no—
152C2×C4×C61—42no—
153C2×C4×C61—82no—
154C2×C4×C61—82no—
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61C2×Q1612yes—
159C2×C4×C61#13512yes—
160C2×C4×C61C22×D411yescharacteristic
161C2×C4×C61C22×D411yescharacteristic
162C2×C4×C61C2×#4111yescharacteristic
163C22⋊D61—24no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167D244—21no—
168D244C2×Q1612yes—
169C4×D61—24no—
170C4×D61—42no—
171C4×D61—42no—
172Dic122—21no—
173Dic122C2×Q1612yes—
174C8×C61—22no—
175C8×C61—22no—
176#92418—42no—
177#92418—42no—
178#92418—42no—
179#19277—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61#46712yes—
183C22×C61C2×#12111yescharacteristic
184C2×D61—22no—
185C2×D61—41no—
186C2×D61—41no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—82no—
190C4×C61—82no—
191C4×C61#46712yes—
192C4×C61#47112yes—
193C4×C61C22×Q1611yescharacteristic
194C4×C61C2×#13511yescharacteristic
195C4×C61#57512yes—
196Dic61—22no—
197Dic61—41no—
198Dic61—41no—
199C2×#487D6111yescharacteristic, complemented
200#3079—611no—
201#3079—611no—
202C8×#41—611no—
203#1684—614no—
204#1683—614no—
205#1567—611no—
206#1549—611no—
207#1548—611no—
208C2×C61—22no—
209C2×C61#304011yescharacteristic
210C2×C61C2×#46711yescharacteristic
211C2×C61C2×#47111yescharacteristic
212D61—42no—
213C2×C4⋊Q8C2×D6111yescharacteristic
214C2×C4⋊Q8C2×D6111yescharacteristic
215C4×#41—611no—
216#487—21no—
217#487—21no—
218#487C2×D6114yes—
219#477—612no—
220#477—1221no—
221#476—612no—
222#476—1221no—
223#475—612no—
224#475—1221no—
225#474—612no—
226#474—1221no—
227C8×Q8—612no—
228C8×D4—612no—
229C8×D4—1222no—
230#431—611no—
231#431—1221no—
232#428—1221no—
233#428—1221no—
234#423—611no—
235#423—611no—
236#417—1221no—
237#417—1221no—
238C2×#103—22no—
239C2×C4×C8—1221no—
240C2×C4×C8C2×D6111yescharacteristic
241#335—614no—
242#333—614no—
243#332—614no—
244C61#1927711yescharacteristic, complemented, Sylow
245C2×#41—611no—
246C22×Q8—21no—
247C22×Q8—21no—
248C2×M16—1221no—
249C2×M16—1221no—
250C22×C8—1222no—
251C22×C8C22⋊D6112yes—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8C22×D6112yes—
259C4⋊Q8C22×D6112yes—
260C4×Q8—611no—
261C4×Q8—611no—
262C4×D4—611no—
263C4×D4—611no—
264C4×D4—1221no—
265C4×D4—1221no—
266#117—611no—
267#117—1221no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C42—1221no—
273C2×C42C22×D6111yescharacteristic
274#107—1222no—
275#107—1222no—
276#106—1222no—
277#106—1222no—
278C4⋊C8—612no—
279C4⋊C8—612no—
280C4⋊C8—612no—
281C4⋊C8—1222no—
282C4⋊C8—1221no—
283C4⋊C8—1221no—
284#103—24no—
285#103—24no—
286#103—1222no—
287#103—1222no—
288#102—1222no—
289#102—1222no—
290C22⋊C8—1221no—
291C22⋊C8—1222no—
292C4×C8—1222no—
293C4×C8—1221no—
294C4×C8C22⋊D6111yescharacteristic
295C4×C8C22⋊D6111yescharacteristic
296C4×C8C22×D6112yes—
297#41—614no—
298#41—1222no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—44no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—82no—
305C2×Q8—611no—
306C2×D4—611no—
307C2×D4—1221no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4D4×D6111yescharacteristic
314C22×C4#1175822411yescharacteristic
315C22×C4C2×C22⋊D6111yescharacteristic
316M16—2442no—
317M16—2442no—
318C2×C8—42no—
319C2×C8—1222no—
320C2×C8—1222no—
321C2×C8—1222no—
322C2×C8—2444no—
323C2×C8C2×C22⋊D6112yes—
324C2×C8C2×C22⋊D6112yes—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—611no—
334C4⋊C4—611no—
335C4⋊C4—1221no—
336C4⋊C4—1221no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C42—1221no—
341C42—1221no—
342C42—1221no—
343C42D4×D6111yescharacteristic
344C42#1175822411yescharacteristic
345C42C2×C22⋊D6111yescharacteristic
346C42C23×D6111yescharacteristic
347C23—1221no—
348C23#1451974811yescharacteristic
349Q8—44no—
350Q8—82no—
351Q8—82no—
352Q8—82no—
353Q8—612no—
354Q8—1221no—
355D4—612no—
356D4—1224no—
357D4—1221no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4—1221no—
365C2×C4—1224no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4#1451974811yescharacteristic
371C2×C4#1451974811yescharacteristic
372C2×C4#1451974811yescharacteristic
373C2×C4Q16×D6112yes—
374C2×C4#1451980012yes—
375C2×C4C2×D4×D6111yescharacteristic
376C2×C4C22×C22⋊D6111yescharacteristic
377C2×C4C2×#1175822411yescharacteristic
378C8—22no—
379C8—22no—
380C8—2442no—
381C8—2442no—
382C8—2442no—
383C22—21no—
384C22—21no—
385C22—1222no—
386C22—2441no—
387C22—2441no—
388C22#1684000012yes—
389C22C2×#1451974811yescharacteristic
390C4—21no—
391C4—21no—
392C4—82no—
393C4—82no—
394C4—1222no—
395C4—2441no—
396C4—2441no—
397C4#1684000012yes—
398C4#1684002212yes—
399C4C2×Q16×D6111yescharacteristic
400C4C2×#1451980011yescharacteristic
401C4#1684056012yes—
402C2—22no—
403C2—2442no—
404C2#2145530911yescharacteristic
405C2C2×#1684000011yescharacteristic
406C2C2×#1684002211yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#487C2
socleC22×C61C2×#121
prime radicalC2×#11758222D4
hypercenterC2×#487D61
hypocenterC61#19277
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
4. #21445274C2semidirect
5. #21445267C2semidirect
6. #21444578C2semidirect
7. #21444504C2semidirect
8. #21444500C2semidirect
9. C2×C61×#487C2semidirect
199. C2×#487D61semidirect
244. C61#19277semidirect

Maximal subgroups

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

subgroupindex
#214556282
C8×#117582222
#214452742
#214452672
#214445782
#214445042
#214445002
C2×C61×#4872
#1927761