Finite Group Databasebeta

← #29579025

Subgroups — #29579025

Order 15616.

526 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454192C211yesmaximal, characteristic
2#21445673C211yesmaximal, characteristic, complemented
3#97×Dic61C211yesmaximal, characteristic, complemented
4C2×#16839504C211yesmaximal, characteristic, complemented
5C2×#16839501C211yesmaximal, characteristic
6C2×#16839501C211yesmaximal, characteristic
7C2×C61×#330C211yesmaximal, characteristic, complemented
8C2×#14519765C2211yescharacteristic
9C2×#14519706—21no—
10C2×#14519688C2211yescharacteristic
11C2×#14519688C2211yescharacteristic
12C2×#14519687—21no—
13C2×C8×Dic61—21no—
14#16839667C411yescharacteristic
15#16839667C411yescharacteristic
16#16839663C411yescharacteristic
17#16839663C411yescharacteristic
18#16839652—21no—
19#16839652—21no—
20#16839652—21no—
21#16839652—21no—
22C42×Dic61C2211yescharacteristic
23#16839516—21no—
24#16839504—22no—
25#16839501—22no—
26#16839501—22no—
27C2×#125×C61C2211yescharacteristic
28C2×#97×C61C2211yescharacteristic
29C2×#97×C61C2211yescharacteristic
30C61×#330—22no—
31C22×Dic122C2×C411yescharacteristic
32C22×D244C2×C411yescharacteristic
33C22×#92418—21no—
34C22×#92418—21no—
35#14519765—21no—
36#14519765—21no—
37#14519765—21no—
38#14519765—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51#14519706—24no—
52#14519688—21no—
53#14519688—21no—
54#14519688—21no—
55#14519688D412yes—
56#14519687—24no—
57C8×Dic61—24no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62C22×C8×C61—21no—
63C22×C8×C61—21no—
64#125×C61—21no—
65#125×C61—21no—
66#125×C61—21no—
67#125×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61C2×C411yescharacteristic
71C2×C4⋊C4×C61C2×C411yescharacteristic
72C2×C42×C61C2311yescharacteristic
73#97×C61—21no—
74#97×C61—21no—
75#97×C61—21no—
76#97×C61D412yes—
77C23×D61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61C22×C411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×Dic61—21no—
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C2×D244—21no—
89C2×D244—21no—
90C2×D244—41no—
91C2×D244—41no—
92C2×Dic122—21no—
93C2×Dic122—21no—
94C2×Dic122—41no—
95C2×Dic122—41no—
96C2×C8×C61—22no—
97C2×C8×C61—22no—
98C2×C8×C61—22no—
99C2×C8×C61—22no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61#4111yescharacteristic
113C42×C61#4111yescharacteristic
114#11758198—42no—
115#11758198—41no—
116#11758198—41no—
117#11758198—41no—
118#11758198—41no—
119#11758198—42no—
120#11758198—42no—
121#11758198—42no—
122C4×Dic61—22no—
123C4×Dic61—22no—
124C4×Dic61—22no—
125C4×Dic61—41no—
126C4×Dic61—41no—
127C4×Dic61—41no—
128C2×#92418—22no—
129C2×#92418—22no—
130C2×#92418—22no—
131C2×#92418—22no—
132C2×#92418—41no—
133C2×#92418—41no—
134C23×C61C2×C22⋊C411yescharacteristic
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61C4×D411yescharacteristic
155C2×C4×C61C4×D411yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12411yescharacteristic
159C2×C4×C61#12711yescharacteristic
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61#10412yes—
173C2×Dic61#10412yes—
174C2×Dic61#10412yes—
175D244—81no—
176D244—81no—
177Dic122—81no—
178Dic122—81no—
179C8×C61—24no—
180C8×C61—42no—
181#92418—24no—
182#92418—42no—
183#9687—611nomaximal, Sylow
184C22×C61#39011yescharacteristic
185C22×C61#41311yescharacteristic
186C22×C61#41311yescharacteristic
187C22×C61C2×#10411yescharacteristic
188C22×C61C2×#10411yescharacteristic
189C22×C61C2×#10411yescharacteristic
190C22×C61#42111yescharacteristic
191C2×D61—81no—
192C2×D61—81no—
193C2×D61—81no—
194C2×D61—81no—
195C2×D61—81no—
196C2×D61—81no—
197C2×D61—81no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—81no—
205C4×C61—81no—
206Dic61—22no—
207Dic61—22no—
208Dic61—22no—
209Dic61—41no—
210Dic61—81no—
211#2861—611no—
212#1767—611no—
213C4×#97—611no—
214C2×#330—611no—
215C2×#330D6111yescharacteristic, complemented
216C2×#329—611no—
217C2×#329—611no—
218C2×C61#152411yescharacteristic
219C2×C61#152411yescharacteristic
220C2×C61#152911yescharacteristic
221C2×C61#153211yescharacteristic
222C2×C61#196211yescharacteristic
223C2×C61#196711yescharacteristic
224C2×C61#198011yescharacteristic
225D61—161no—
226C2×#125C2×D6111yescharacteristic
227C2×#124—611no—
228C2×C4⋊C8—1221no—
229C2×#97—611no—
230C2×#97—611no—
231C2×#97—1221no—
232C2×#97C2×D6111yescharacteristic
233C2×#97C2×D6111yescharacteristic
234C2×C4×C8—1221no—
235#391—611no—
236#391—611no—
237#390—611no—
238#390—611no—
239#388—1221no—
240#388—1221no—
241#388—1221no—
242#388—1221no—
243C43—611no—
244#336—1221no—
245#330—22no—
246#330—1222no—
247#329—1222no—
248#329—1222no—
249C61#968711yescharacteristic, complemented, Sylow
250C22×Q8—611no—
251C22×D4—611no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—1221no—
255C22×C8—1221no—
256#125—21no—
257#125—21no—
258#125—21no—
259#125—21no—
260#124—1221no—
261#124—1221no—
262#124—1221no—
263#124—1221no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4C4×D6111yescharacteristic
267C2×C4⋊C4C4×D6111yescharacteristic
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—1221no—
274C2×C42—611no—
275C2×C42—611no—
276C2×C42—611no—
277C2×C42—611no—
278C2×C42—611no—
279C2×C42—611no—
280C2×C42C22×D6111yescharacteristic
281C4⋊C8—1224no—
282#97—21no—
283#97—21no—
284#97—21no—
285#97—612no—
286#97—1224no—
287#97—1221no—
288#97—1221no—
289#97—1221no—
290#97C22⋊D6112yes—
291C4×C8—1224no—
292#95—1221no—
293#95—1221no—
294#95—1221no—
295#95—1221no—
296C24—1221no—
297C2×Q8—1221no—
298C2×Q8—1221no—
299C2×Q8—2441no—
300C2×Q8—2441no—
301C2×D4—1221no—
302C2×D4—1221no—
303C2×D4—2441no—
304C2×D4—2441no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—611no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—1221no—
312C22×C4C2×C4×D6111yescharacteristic
313C22×C4D4×D6111yescharacteristic
314C22×C4D4×D6111yescharacteristic
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—1222no—
322C2×C8—1222no—
323C2×C8—1222no—
324C2×C8—1222no—
325C2×C8—2441no—
326C2×C8—2441no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C22⋊C4—2442no—
336C22⋊C4—2442no—
337C22⋊C4—2442no—
338C22⋊C4—2442no—
339C22⋊C4—2441no—
340C22⋊C4—2441no—
341C22⋊C4—2441no—
342C22⋊C4—2441no—
343C42—1222no—
344C42—1222no—
345C42—1222no—
346C42—2441no—
347C42—2441no—
348C42—2441no—
349C42#1175822211yescharacteristic
350C42D4×D6111yescharacteristic
351C42#1175822411yescharacteristic
352C42C2×C22⋊D6111yescharacteristic
353C23—2441no—
354C23—2441no—
355C23—2441no—
356C23—2441no—
357C23—2441no—
358C23—2441no—
359C23—2441no—
360C23C22⋊C4×D6111yescharacteristic
361Q8—4881no—
362Q8—4881no—
363D4—4881no—
364D4—4881no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—612no—
378C2×C4—612no—
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—1221no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4#1451973711yescharacteristic
393C2×C4C4×C22⋊D6111yescharacteristic
394C2×C4#1451974911yescharacteristic
395C2×C4#1451975011yescharacteristic
396C2×C4#1451976311yescharacteristic
397C2×C4#1451977311yescharacteristic
398C8—24no—
399C8—42no—
400C8—1224no—
401C8—2442no—
402C22—4881no—
403C22—4881no—
404C22—4881no—
405C22—4881no—
406C22—4881no—
407C22—4881no—
408C22—4881no—
409C22#1683966211yescharacteristic
410C22#1683974511yescharacteristic
411C22#1683974511yescharacteristic
412C22#104×D6111yescharacteristic
413C22#104×D6111yescharacteristic
414C22#104×D6111yescharacteristic
415C22#1683977711yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—81no—
423C4—81no—
424C4—1222no—
425C4—1222no—
426C4—1222no—
427C4—4881no—
428C4—2441no—
429C2—9761no—
430C2#2144440611yescharacteristic
431C2#2144440611yescharacteristic
432C2#2144442511yescharacteristic
433C2#2144443811yescharacteristic
434C2#2144664511yescharacteristic
435C2#2144666711yescharacteristic
436C2#2144673611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#330C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenterC2×#330D61
hypocenterC61#9687
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
2. #21445673C2semidirect
3. #97×Dic61C2semidirect
4. C2×#16839504C2semidirect
7. C2×C61×#330C2semidirect
215. C2×#330D61semidirect
249. C61#9687semidirect

Maximal subgroups

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

subgroupindex
#214541922
#214456732
#97×Dic612
C2×#168395042
C2×#168395012
C2×C61×#3302
#968761