Finite Group Databasebeta

← #29575642

Subgroups — #29575642

Order 15616.

530 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839817C211yesmaximal, characteristic
2#21454130C211yesmaximal, characteristic
3#21445582C211yesmaximal, characteristic
4C2×#16839503C211yesmaximal, characteristic, complemented
5C2×#16839503C211yesmaximal, characteristic, complemented
6#21443700C211yesmaximal, characteristic, complemented
7C61×#1295C211yesmaximal, characteristic, complemented
8C2×#14519769C2211yescharacteristic
9C2×C42×D61C2211yescharacteristic
10#16839817—22no—
11#16839817—22no—
12C2×#14519706—21no—
13C2×#14519689—21no—
14C2×#14519689—21no—
15C2×#14519688C2211yescharacteristic
16C2×#14519688C2211yescharacteristic
17#16839661C411yescharacteristic
18#16839661C411yescharacteristic
19#16839647—21no—
20#16839647—21no—
21#16839636—21no—
22#16839636—21no—
23#16839619C411yescharacteristic
24#16839619C411yescharacteristic
25#16839516—21no—
26#16839503—22no—
27#16839503—22no—
28C2×#97×C61C2211yescharacteristic
29C2×#97×C61C2211yescharacteristic
30C61×#382C2211yescharacteristic
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C22×#92418—21no—
35C22×#92418—21no—
36#14519769—21no—
37#14519769—21no—
38#14519769—21no—
39#14519769—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C42×D61—21no—
52C42×D61—21no—
53C42×D61—21no—
54C42×D61—21no—
55#14519706—24no—
56#14519689—24no—
57#14519689—24no—
58#14519688—21no—
59#14519688—21no—
60#14519688—21no—
61#14519688D412yes—
62#14519684—21no—
63#14519684—21no—
64#14519684—21no—
65#14519684—21no—
66C22×C8×C61—21no—
67C22×C8×C61—21no—
68C2×C4⋊C4×C61C2×C411yescharacteristic
69C2×C4⋊C4×C61C2×C411yescharacteristic
70C2×C42×C61C2311yescharacteristic
71#97×C61—21no—
72#97×C61—21no—
73#97×C61—21no—
74#97×C61D412yes—
75#95×C61—21no—
76#95×C61—21no—
77C23×D61C22⋊C411yescharacteristic
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61C22×C411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C2×C4×D61—22no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—22no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C8×C61—22no—
101C2×C8×C61—22no—
102C2×C8×C61—41no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C2×C8×C61—41no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61—41no—
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C42×C61#4111yescharacteristic
111C42×C61#4111yescharacteristic
112#11758198—42no—
113#11758198—42no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—42no—
119C4⋊Dic61—42no—
120#11758196—41no—
121#11758196—41no—
122#11758196—41no—
123#11758196—41no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—21no—
129C4×Dic61—21no—
130C2×#92418—22no—
131C2×#92418—22no—
132C2×#92418—41no—
133C2×#92418—41no—
134C2×#92418—41no—
135C2×#92418—41no—
136C23×C61C2×C22⋊C411yescharacteristic
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61#10112yes—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61C4×D411yescharacteristic
158C2×C4×C61#12011yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12311yescharacteristic
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61#10412yes—
177C4×D61—42no—
178C4×D61—42no—
179C4×D61—42no—
180C4×D61—42no—
181C4×D61—42no—
182C4×D61—42no—
183C8×C61—42no—
184C8×C61—42no—
185#92418—42no—
186#92418—42no—
187#9126—611nomaximal, Sylow
188C22×C61#38611yescharacteristic
189C22×C61C2×#10111yescharacteristic
190C22×C61#41311yescharacteristic
191C22×C61C2×#10411yescharacteristic
192C22×C61#42111yescharacteristic
193C22×C61#42111yescharacteristic
194C22×C61#42111yescharacteristic
195C2×D61—22no—
196C2×D61—22no—
197C2×D61—22no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—41no—
201C2×D61—41no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—81no—
209C4×C61—81no—
210Dic61—22no—
211Dic61—41no—
212Dic61—41no—
213Dic61—81no—
214Dic61—81no—
215C2×#432—611no—
216#2851—611no—
217#1749—611no—
218C2×#330—611no—
219C2×#330—611no—
220#1295—611no—
221#1295D6111yescharacteristic, complemented
222C2×C61#152911yescharacteristic
223C2×C61#153111yescharacteristic
224C2×C61#153411yescharacteristic
225C2×C61#153511yescharacteristic
226C2×C61#187111yescharacteristic
227C2×C61#189711yescharacteristic
228C2×C61#190111yescharacteristic
229D61—42no—
230C2×#125—611no—
231C22×C42—611no—
232#432—1222no—
233#432—1222no—
234C2×C4⋊C8—1221no—
235C2×C22⋊C8—1221no—
236C2×C22⋊C8—1221no—
237C2×#97—611no—
238C2×#97—611no—
239C2×#97C2×D6111yescharacteristic
240C2×#97C2×D6111yescharacteristic
241#389—611no—
242#389—611no—
243#387—1221no—
244#387—1221no—
245#385—1221no—
246#385—1221no—
247#382C2×D6111yescharacteristic
248#380—611no—
249#380—611no—
250#336—1221no—
251#330—1222no—
252#330—1222no—
253C61#912611yescharacteristic, complemented, Sylow
254C23×C4—611no—
255C23×C4—611no—
256C23×C4—611no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—1221no—
260C22×C8—1221no—
261#125—1221no—
262#125—1221no—
263#125—1221no—
264#125—1221no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—1221no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4—1221no—
270C2×C4⋊C4—1221no—
271C2×C4⋊C4C4×D6111yescharacteristic
272C2×C4⋊C4C4×D6111yescharacteristic
273C2×C22⋊C4—1221no—
274C2×C22⋊C4—1221no—
275C2×C42—611no—
276C2×C42—611no—
277C2×C42—611no—
278C2×C42—1221no—
279C2×C42—1221no—
280C2×C42—1221no—
281C2×C42—1221no—
282C2×C42C22×D6111yescharacteristic
283C4⋊C8—1224no—
284C22⋊C8—1224no—
285C22⋊C8—1224no—
286#97—21no—
287#97—21no—
288#97—21no—
289#97—612no—
290#97—1221no—
291#97—1221no—
292#97—1221no—
293#97D24412yes—
294#95—21no—
295#95—21no—
296#95—1221no—
297#95—1221no—
298#95—1221no—
299#95—1221no—
300C24—611no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—611no—
306C22×C4—1222no—
307C22×C4—1222no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4—2441no—
317C22×C4—2441no—
318C22×C4—2441no—
319C22×C4—2441no—
320C22×C4C2×C4×D6111yescharacteristic
321C22×C4D4×D6111yescharacteristic
322C22×C4D4×D6111yescharacteristic
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—1222no—
330C2×C8—1222no—
331C2×C8—2441no—
332C2×C8—2441no—
333C2×C8—2441no—
334C2×C8—2441no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—1221no—
338C4⋊C4—1221no—
339C4⋊C4—1221no—
340C4⋊C4—1221no—
341C4⋊C4—2442no—
342C4⋊C4—2442no—
343C4⋊C4—2441no—
344C4⋊C4—2441no—
345C4⋊C4—2441no—
346C4⋊C4—2441no—
347C22⋊C4—2442no—
348C22⋊C4—2442no—
349C42—1221no—
350C42—1221no—
351C42—1221no—
352C42—1221no—
353C42—1221no—
354C42—1221no—
355C42C2×D24411yescharacteristic
356C42#1175822211yescharacteristic
357C42D4×D6111yescharacteristic
358C42#1175822611yescharacteristic
359C23—612no—
360C23—1221no—
361C23—1221no—
362C23—1221no—
363C23—1221no—
364C23—1221no—
365C23—1221no—
366C23C22⋊C4×D6111yescharacteristic
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—612no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4—2442no—
391C2×C4—2442no—
392C2×C4—2442no—
393C2×C4—2442no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4#1451973911yescharacteristic
401C2×C4C4×D24411yescharacteristic
402C2×C4#1451974711yescharacteristic
403C2×C4#1451975011yescharacteristic
404C2×C4#1451975211yescharacteristic
405C2×C4#1451976211yescharacteristic
406C8—42no—
407C8—42no—
408C8—2442no—
409C8—2442no—
410C22—1222no—
411C22—1222no—
412C22—1222no—
413C22—2441no—
414C22—2441no—
415C22—2441no—
416C22—2441no—
417C22#1683964011yescharacteristic
418C22#101×D6111yescharacteristic
419C22#1683974311yescharacteristic
420C22#104×D6111yescharacteristic
421C22#1683977711yescharacteristic
422C22#1683977711yescharacteristic
423C22#1683977711yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—81no—
431C4—81no—
432C4—1222no—
433C4—4881no—
434C4—4881no—
435C4—2441no—
436C4—2441no—
437C2—2442no—
438C2#2144442311yescharacteristic
439C2#2144443211yescharacteristic
440C2#2144444411yescharacteristic
441C2#2144444711yescharacteristic
442C2#2144612011yescharacteristic
443C2#2144626611yescharacteristic
444C2#2144628611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1295D61
hypocenterC61#9126
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
4. C2×#16839503C2semidirect
5. C2×#16839503C2semidirect
6. #21443700C2semidirect
7. C61×#1295C2semidirect
221. #1295D61semidirect
253. C61#9126semidirect

Maximal subgroups

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

subgroupindex
C2×#168398172
#214541302
#214455822
C2×#168395032
#214437002
C61×#12952
#912661