Finite Group Databasebeta

← #29697669

Subgroups — #29697669

Order 15616.

778 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839799C211yesmaximal, characteristic
2#21448700C212yesmaximal
3#21446552C211yesmaximal, characteristic, complemented
4#21446550C211yesmaximal, characteristic, complemented
5#21446404C212yesmaximal, complemented
6#21446402C212yesmaximal, complemented
7#21445912C212yesmaximal
8#21445845C211yesmaximal, characteristic
9#107×Dic61C211yesmaximal, characteristic, complemented
10C8×#11758198C211yesmaximal, characteristic
11C4×#107×C61C211yesmaximal, characteristic, complemented
12C22×C8×D61C2211yescharacteristic
13C2×#14519735C2212yes—
14#16839799C418yescomplemented
15C2×#14519711C2211yescharacteristic
16C2×#14519711C2211yescharacteristic
17C2×#14519708C2212yes—
18C2×#14519689C2211yescharacteristic
19C2×C8×Dic61C2211yescharacteristic
20#16839660C2212yes—
21#16839658C2212yes—
22#16839653—22no—
23#16839651—22no—
24#16839626—22no—
25#16839619C2212yes—
26C4⋊C4×Dic61C2212yes—
27C4×#11758198C2211yescharacteristic
28#16839608—22no—
29#16839525C2212yes—
30#16839524C2212yes—
31#16839524C2212yes—
32#16839524C2212yes—
33#16839517C2211yescharacteristic
34#16839516C2211yescharacteristic
35C2×#107×C61C2211yescharacteristic
36C2×#107×C61C2211yescharacteristic
37C2×C4×C8×C61C2211yescharacteristic
38C4×C4⋊C4×C61C2212yes—
39C61×#340C2212yes—
40C22×C4×D61C2311yescharacteristic
41C22×#92418C2311yescharacteristic
42C22×#92418C2311yescharacteristic
43C2×C8×D61—22no—
44C2×C8×D61—22no—
45C2×C8×D61C2×C414yes—
46#14519735—24no—
47#14519735C2×C418yes—
48C2×C4⋊Dic61C2312yes—
49C2×C4⋊Dic61C2312yes—
50C2×#11758196—22no—
51C2×#11758196—22no—
52C2×#11758198—22no—
53C2×#11758198—22no—
54C2×#11758198D411yescharacteristic
55C2×#11758198D411yescharacteristic
56C2×C4×Dic61—22no—
57C2×C4×Dic61—22no—
58C2×C4×Dic61C2311yescharacteristic
59#14519711—22no—
60#14519711C2×C414yes—
61#14519708C2×C418yes—
62#14519689—22no—
63C8×Dic61—22no—
64#14519684—22no—
65#14519684—22no—
66#14519684—22no—
67#14519684—22no—
68#14519684D411yescharacteristic
69#14519684D411yescharacteristic
70C22×C8×C61C2311yescharacteristic
71C22×C8×C61C2311yescharacteristic
72C2×C4⋊C4×C61C2312yes—
73C2×C4⋊C4×C61C2312yes—
74C2×C42×C61—22no—
75C2×C42×C61C2311yescharacteristic
76#107×C61—22no—
77#107×C61C2×C414yes—
78C4×C8×C61—22no—
79#95×C61—22no—
80C23×D61C2×D411yescharacteristic
81C22×C4×C61—22no—
82C22×C4×C61—22no—
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2411yescharacteristic
86C22×Dic61—22no—
87C22×Dic61—22no—
88C22×Dic61C2×D411yescharacteristic
89C22×Dic61C2×D411yescharacteristic
90C22×Dic61C2×D411yescharacteristic
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61C22×C412yes—
96C2×C4×D61#4112yes—
97C2×C8×C61—21no—
98C2×C8×C61—21no—
99C2×C8×C61—21no—
100C2×C8×C61C22×C412yes—
101C2×C8×C61#4112yes—
102C2×C8×C61#4112yes—
103C4⋊C4×C61—22no—
104C4⋊C4×C61—22no—
105C4⋊C4×C61—22no—
106C4⋊C4×C61C22×C414yes—
107C42×C61—21no—
108C42×C61—21no—
109C42×C61—44no—
110#11758198—28no—
111#11758198—22no—
112#11758198—22no—
113#11758198—82no—
114C4⋊Dic61—22no—
115C4⋊Dic61—22no—
116C4⋊Dic61—22no—
117C4⋊Dic61C22×C414yes—
118#11758196—82no—
119#11758196—82no—
120C4×Dic61—21no—
121C4×Dic61—21no—
122C4×Dic61—28no—
123C4×Dic61—44no—
124C2×#92418—21no—
125C2×#92418—21no—
126C2×#92418—21no—
127C2×#92418—21no—
128C2×#92418—21no—
129C2×#92418C22×C412yes—
130C8×D61—28no—
131C23×C61C22×D411yescharacteristic
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61C4×D412yes—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—24no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—42no—
146C2×C4×C61—42no—
147C2×C4×C61—42no—
148C2×C4×C61—42no—
149C2×C4×C61—42no—
150C2×C4×C61#13512yes—
151C2×C4×C61C23×C411yescharacteristic
152C2×C4×C61C2×#4111yescharacteristic
153C2×C4×C61C2×#4111yescharacteristic
154C2×C4×C61C2×#4111yescharacteristic
155C2×C4×C612−1+411yescharacteristic
156C2×C4×C612−1+411yescharacteristic
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—24no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—42no—
166C2×Dic61—42no—
167C2×Dic61—42no—
168C2×Dic61—42no—
169C2×Dic61—42no—
170C2×Dic61C4×D412yes—
171C2×Dic61#13512yes—
172C4×D61—22no—
173C4×D61—22no—
174C4×D61—22no—
175C4×D61—22no—
176C8×C61—41no—
177C8×C61#11714yes—
178#92418—22no—
179#92418—41no—
180#22613—611nomaximal, Sylow
181C22×C61C2×C4×D411yescharacteristic
182C22×C61#54711yescharacteristic
183C22×C61#54711yescharacteristic
184C22×C61C2×#13511yescharacteristic
185C22×C61C2×#13511yescharacteristic
186C22×C61#57611yescharacteristic
187C22×C61#57811yescharacteristic
188C2×D61—22no—
189C2×D61—22no—
190C2×D61—22no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C4×C61—22no—
196C4×C61—41no—
197C4×C61—44no—
198C4×C61—82no—
199C4×C61C2×#11711yescharacteristic
200C4×C61#51911yescharacteristic
201C4×C61#55211yescharacteristic
202C4×C61#55211yescharacteristic
203Dic61—22no—
204Dic61—22no—
205Dic61—41no—
206Dic61—44no—
207Dic61—82no—
208C2×#427—611no—
209#2346—612no—
210#1942—611no—
211#1942—611no—
212#1920—612no—
213#1920—612no—
214#1825—612no—
215#1808—611no—
216C4×#107—611no—
217C4×#107D6111yescharacteristic, complemented
218C8×C22⋊C4—611no—
219C2×C61#234411yescharacteristic
220C2×C61C4×#13511yescharacteristic
221C2×C61#295111yescharacteristic
222C2×C61#333611yescharacteristic
223C2×C61#333611yescharacteristic
224C2×C61#334111yescharacteristic
225C2×C61#334111yescharacteristic
226D61—42no—
227C23×C8—611no—
228C2×#117—612no—
229#427—618no—
230C2×#107—611no—
231C2×#107—611no—
232C2×#107C2×D6111yescharacteristic
233C2×#107C2×D6111yescharacteristic
234C2×#106—612no—
235C2×C22⋊C8—611no—
236C2×C4×C8—611no—
237C2×C4×C8C2×D6111yescharacteristic
238#389—612no—
239#389—612no—
240#388—1222no—
241#388—1222no—
242#382—1222no—
243#380—612no—
244C4×C4⋊C4—612no—
245C4×C4⋊C4C2×D6112yes—
246C4×C22⋊C4—611no—
247#376—1222no—
248#340—612no—
249#340—612no—
250#340—612no—
251#340—612no—
252#340C2×D6112yes—
253#336—611no—
254#336—611no—
255C61#2261311yescharacteristic, complemented, Sylow
256C23×C4—611no—
257C22×C8—611no—
258C22×C8—614no—
259C22×C8—611no—
260C22×C8—1222no—
261C22×C8—1222no—
262C22×C8C22×D6111yescharacteristic
263C22×C8C22×D6111yescharacteristic
264#117—618no—
265#117—1224no—
266C2×C4⋊C4—612no—
267C2×C4⋊C4—612no—
268C2×C4⋊C4—1222no—
269C2×C4⋊C4—1222no—
270C2×C4⋊C4C22×D6112yes—
271C2×C4⋊C4C22×D6112yes—
272C2×C22⋊C4—611no—
273C2×C22⋊C4—611no—
274C2×C22⋊C4—1222no—
275C2×C22⋊C4—1222no—
276C2×C42—22no—
277C2×C42—611no—
278C2×C42—1222no—
279C2×C42—1222no—
280C2×C42C22×D6111yescharacteristic
281#107—22no—
282#107—614no—
283#107—1222no—
284#107C4×D6114yes—
285#106—618no—
286C22⋊C8—1222no—
287C4×C8—22no—
288C4×C8—1222no—
289#95—22no—
290#95—611no—
291#95—611no—
292#95—1222no—
293#95—1222no—
294#95—1222no—
295#95—1222no—
296C24—611no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—612no—
302C22×C4—612no—
303C22×C4—611no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1222no—
309C22×C4—1222no—
310C22×C4D4×D6111yescharacteristic
311C22×C4D4×D6111yescharacteristic
312C22×C4C23×D6111yescharacteristic
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—612no—
317C2×C8—1221no—
318C2×C8—1221no—
319C2×C8—1228no—
320C2×C8—1221no—
321C2×C8—1221no—
322C2×C8—1221no—
323C2×C8C2×C4×D6112yes—
324C2×C8#1175822212yes—
325C2×C8#1175822212yes—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—614no—
330C4⋊C4—1222no—
331C4⋊C4—1222no—
332C4⋊C4—1222no—
333C4⋊C4—4882no—
334C4⋊C4—4882no—
335C4⋊C4C2×C4×D6114yes—
336C22⋊C4—1222no—
337C22⋊C4—1228no—
338C22⋊C4—1222no—
339C22⋊C4—4882no—
340C42—21no—
341C42—21no—
342C42—44no—
343C42—1228no—
344C42—1221no—
345C42—1221no—
346C42—2444no—
347C23—612no—
348C23—1221no—
349C23—1221no—
350C23—1221no—
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23C2×D4×D6111yescharacteristic
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—24no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—612no—
367C2×C4—612no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1222no—
373C2×C4—1222no—
374C2×C4—1222no—
375C2×C4—1222no—
376C2×C4—1224no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—2442no—
381C2×C4—2442no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4#1451979612yes—
386C2×C4C22×C4×D6111yescharacteristic
387C2×C4#41×D6111yescharacteristic
388C2×C4C2×#1175822211yescharacteristic
389C2×C4C2×#1175822211yescharacteristic
390C2×C4#1451982411yescharacteristic
391C2×C4#1451982511yescharacteristic
392C8—41no—
393C8—1222no—
394C8—2441no—
395C8#1451973414yes—
396C22—1222no—
397C22—1222no—
398C22—1222no—
399C22—2441no—
400C22—2441no—
401C22—2441no—
402C22—2441no—
403C22C4×D4×D6111yescharacteristic
404C22#1684041311yescharacteristic
405C22#1684041711yescharacteristic
406C22#135×D6111yescharacteristic
407C22C2×#1451979611yescharacteristic
408C22#1684056411yescharacteristic
409C22#1684057511yescharacteristic
410C4—22no—
411C4—41no—
412C4—44no—
413C4—82no—
414C4—1222no—
415C4—1222no—
416C4—4882no—
417C4—2441no—
418C4—2444no—
419C4C2×#1451973411yescharacteristic
420C4#1684023811yescharacteristic
421C4#1684045111yescharacteristic
422C4#1684045311yescharacteristic
423C2—2442no—
424C2#2144868411yescharacteristic
425C2C4×#1451979611yescharacteristic
426C2#2145469411yescharacteristic
427C2#2145818311yescharacteristic
428C2#2145818911yescharacteristic
429C2#2145823911yescharacteristic
430C2#2145824311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#107×C61C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenterC4×#107D61
hypocenterC61#22613
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
3. #21446552C2semidirect
4. #21446550C2semidirect
5. #21446404C2semidirect
6. #21446402C2semidirect
9. #107×Dic61C2semidirect
11. C4×#107×C61C2semidirect
14. #16839799C4semidirect
217. C4×#107D61semidirect
255. C61#22613semidirect

Maximal subgroups

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

subgroupindex
C2×#168397992
#214487002
#214465522
#214465502
#214464042
#214464022
#214459122
#214458452
#107×Dic612
C8×#117581982
C4×#107×C612
#2261361