Finite Group Databasebeta

← #29576393

Subgroups — #29576393

Order 15616.

512 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840049C211yesmaximal, characteristic
2M16×D244C211yesmaximal, characteristic
3#21444504C211yesmaximal, characteristic, complemented
4#21444243C211yesmaximal, characteristic
5#21443693C211yesmaximal, characteristic, complemented
6#21443670C211yesmaximal, characteristic, complemented
7C61×#1997C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×C4×D244C2211yescharacteristic
10#16840049—21no—
11#16840049—21no—
12#16840049—21no—
13#16840049—21no—
14#16839841—21no—
15#16839835—22no—
16C8×D244—21no—
17#16839815C2211yescharacteristic
18C2×#14519708C412yes—
19#16839786C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519697C412yes—
22#16839725—21no—
23#16839508—22no—
24#16839489—21no—
25#16839489—21no—
26C2×C4⋊Q8×C61C2211yescharacteristic
27C61×#423C2211yescharacteristic
28C4×M16×C61C2211yescharacteristic
29C61×#343—21no—
30C61×#343—21no—
31C22×D244C2×C411yescharacteristic
32C22×C4×D61—21no—
33C2×#11758194—21no—
34C2×#11758189—22no—
35M16×D61—42no—
36M16×D61—42no—
37C22×#92418C2×C412yes—
38C2×C8×D61—22no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244D411yescharacteristic
42C4×D244D411yescharacteristic
43C4×D244D411yescharacteristic
44C4×D244D411yescharacteristic
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×#11758198—21no—
47#14519708—22no—
48#14519708—22no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53C4⋊#92418D412yes—
54#14519697—22no—
55#14519697—22no—
56C22⋊#92418—21no—
57#14519689—22no—
58#14519689—22no—
59C4×#92418—21no—
60C22×Q8×C61—21no—
61C2×M16×C61—21no—
62C2×M16×C61D411yescharacteristic
63C2×M16×C61D411yescharacteristic
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61—21no—
67C4⋊Q8×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61C2×C412yes—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73#97×C61—21no—
74C4×C8×C61—21no—
75C23×D61—21no—
76C2×Q8×C61—41no—
77C2×Q8×C61—41no—
78C2×Q8×C61—82no—
79C22×C4×C61—22no—
80C22×C4×C61C22×C411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C22×Dic61—21no—
84C2×D244—22no—
85C2×D244—21no—
86C2×D244—41no—
87C2×D244C22⋊C411yescharacteristic
88C2×D244C22⋊C411yescharacteristic
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97M16×C61—21no—
98M16×C61—21no—
99M16×C61—21no—
100M16×C61—41no—
101M16×C61—41no—
102M16×C61SD1612yes—
103C2×C8×C61—21no—
104C2×C8×C61—21no—
105C2×C8×C61—41no—
106C4⋊C4×C61—22no—
107C4⋊C4×C61—22no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C42×C61#4111yescharacteristic
114#11758198—21no—
115#11758198—21no—
116#11758198—21no—
117#11758198—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61C22⋊C411yescharacteristic
120C4⋊Dic61C22⋊C411yescharacteristic
121#11758194—41no—
122#11758194—41no—
123C2×#92418—22no—
124C2×#92418—22no—
125C2×#92418—42no—
126C2×#92418—41no—
127#11758189—44no—
128C8×D61—44no—
129C23×C61C4×D411yescharacteristic
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—42no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—81no—
136Q8×C61—82no—
137Q8×C61—82no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61—82no—
143C2×C4×C61C2×C22⋊C411yescharacteristic
144C2×C4×C61C4×D411yescharacteristic
145C2×C4×C61#12011yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12311yescharacteristic
149C2×C4×C61C2×SD1611yescharacteristic
150C2×C4×C61#13511yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C61#13711yescharacteristic
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157D244—21no—
158D244—21no—
159D244—21no—
160D244—42no—
161D244#10112yes—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61—41no—
165C4×D61—41no—
166C4×D61—41no—
167C4×D61—41no—
168C4×D61—41no—
169C4×D61—41no—
170C8×C61—22no—
171C8×C61—41no—
172C8×C61—81no—
173#92418—42no—
174#92418—42no—
175#92418—81no—
176#9249—611nomaximal, Sylow
177C22×C61—21no—
178C22×C61—21no—
179C22×C61#38611yescharacteristic
180C22×C61C4×SD1611yescharacteristic
181C22×C61#44011yescharacteristic
182C2×D61—22no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—82no—
189C2×D61—82no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—82no—
194C4×C61C2×#10111yescharacteristic
195C4×C61#41311yescharacteristic
196C4×C61#45011yescharacteristic
197C4×C61#45211yescharacteristic
198C4×C61#46111yescharacteristic
199C4×C61#46311yescharacteristic
200Dic61—41no—
201Dic61—41no—
202C2×#476—611no—
203D4×M16—611no—
204#1997D6111yescharacteristic, complemented
205#1549—611no—
206#1486—611no—
207#1292—611no—
208#1283—611no—
209C2×C61—21no—
210C2×C61—21no—
211C2×C61#187711yescharacteristic
212C2×C61#190111yescharacteristic
213C2×C61#190311yescharacteristic
214D61—42no—
215D61—81no—
216C22×M16—1221no—
217C2×C4⋊Q8C2×D6111yescharacteristic
218C2×C4×D4—611no—
219#476—1221no—
220#476—1221no—
221#476—1221no—
222#476—1221no—
223#436—1221no—
224#435—1222no—
225C8×D4—1221no—
226#431—611no—
227C2×#106—612no—
228#423—611no—
229#423C2×D6111yescharacteristic
230C2×C4⋊C8—611no—
231C2×#102—612no—
232#407—1221no—
233C4×M16C2×D6111yescharacteristic
234#343—21no—
235#343—21no—
236#332—1222no—
237D4⋊C8—1221no—
238D4⋊C8—1221no—
239C61#924911yescharacteristic, complemented, Sylow
240C22×Q8—21no—
241C22×D4—611no—
242C23×C4—1221no—
243C2×M16—21no—
244C2×M16—1222no—
245C2×M16—1221no—
246C2×M16—2442no—
247C2×M16—2442no—
248C2×M16C22⋊D6111yescharacteristic
249C2×M16C22⋊D6111yescharacteristic
250C22×C8—612no—
251C22×C8—1222no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4×D4—611no—
257C4×D4—611no—
258C4×D4—611no—
259C4×D4—611no—
260C4×D4—1221no—
261C4×D4—1221no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—611no—
264C2×C4⋊C4C4×D6112yes—
265C2×C22⋊C4—1221no—
266C2×C42C22×D6111yescharacteristic
267#106—1222no—
268#106—1222no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—612no—
272C4⋊C8—1221no—
273C4⋊C8—1221no—
274C4⋊C8—1221no—
275C4⋊C8—1221no—
276#102—1222no—
277#102—1222no—
278C22⋊C8—1222no—
279C22⋊C8—1222no—
280C22⋊C8—1221no—
281#97—21no—
282C4×C8—21no—
283C4×C8—1221no—
284C24—1221no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—82no—
288C2×D4—611no—
289C2×D4—611no—
290C2×D4—1222no—
291C2×D4—1221no—
292C2×D4—2441no—
293C22×C4—22no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—2441no—
300C22×C4—2441no—
301C22×C4—2441no—
302C22×C4—2441no—
303C22×C4C2×C4×D6111yescharacteristic
304C22×C4#1175822211yescharacteristic
305C22×C4C2×C22⋊D6111yescharacteristic
306M16—21no—
307M16—21no—
308M16—21no—
309M16—41no—
310M16—41no—
311M16—2444no—
312M16—2441no—
313M16—2441no—
314M16#1175820112yes—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—41no—
318C2×C8—1222no—
319C2×C8—1222no—
320C2×C8—2444no—
321C2×C8—2441no—
322C2×C8—2442no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—611no—
328C4⋊C4—611no—
329C4⋊C4—1221no—
330C22⋊C4—1221no—
331C22⋊C4—1221no—
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C42D4×D6111yescharacteristic
335C42D4×D6111yescharacteristic
336C42D4×D6111yescharacteristic
337C42#1175822411yescharacteristic
338C23—1221no—
339C23—1221no—
340C23—4881no—
341C23—2442no—
342C23—2441no—
343C23—2441no—
344C23C4×C22⋊D6111yescharacteristic
345Q8—82no—
346Q8—82no—
347D4—612no—
348D4—1221no—
349D4—1221no—
350D4—1221no—
351D4—2442no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—82no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4C22⋊C4×D6111yescharacteristic
370C2×C4#1451973711yescharacteristic
371C2×C4#1451974511yescharacteristic
372C2×C4#1451974811yescharacteristic
373C2×C4#1451975011yescharacteristic
374C2×C4#1451975911yescharacteristic
375C2×C4C2×#1175820111yescharacteristic
376C2×C4#1451979711yescharacteristic
377C2×C4#1451980211yescharacteristic
378C2×C4#1451980811yescharacteristic
379C8—22no—
380C8—41no—
381C8—81no—
382C8—4881no—
383C8—2442no—
384C8—2442no—
385C22—21no—
386C22—21no—
387C22—1222no—
388C22—4882no—
389C22—4882no—
390C22—2441no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22#1683963811yescharacteristic
396C22C4×#1175820111yescharacteristic
397C22#1683986011yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—82no—
402C4—2441no—
403C4—2441no—
404C4#101×D6111yescharacteristic
405C4#1683974511yescharacteristic
406C4#1683991211yescharacteristic
407C4#1683992211yescharacteristic
408C4#1683996411yescharacteristic
409C4#1683997411yescharacteristic
410C2—21no—
411C2—21no—
412C2—4881no—
413C2—2442no—
414C2#2144615611yescharacteristic
415C2#2144628411yescharacteristic
416C2#2144630211yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1997C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1997D61
hypocenterC61#9249
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
3. #21444504C2semidirect
5. #21443693C2semidirect
6. #21443670C2semidirect
7. C61×#1997C2semidirect
204. #1997D61semidirect
239. C61#9249semidirect

Maximal subgroups

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

subgroupindex
C2×#168400492
M16×D2442
#214445042
#214442432
#214436932
#214436702
C61×#19972
#924961