Finite Group Databasebeta

← #29574907

Subgroups — #29574907

Order 15616.

484 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455274C211yesmaximal, characteristic
2#21444269C211yesmaximal, characteristic, complemented
3#21444217C211yesmaximal, characteristic, complemented
4#21444201C211yesmaximal, characteristic, complemented
5#21443714C211yesmaximal, characteristic, complemented
6#21443653C211yesmaximal, characteristic, complemented
7C61×#2925C211yesmaximal, characteristic, complemented
8C2×#14519797—21no—
9#16840312C2211yescharacteristic
10#16839984—21no—
11#16839977—21no—
12#16839972C411yescharacteristic
13#16839967C411yescharacteristic
14#16839962C411yescharacteristic
15#16839957C411yescharacteristic
16#16839815C2211yescharacteristic
17C2×C4⋊#92418C2211yescharacteristic
18#16839756—21no—
19C2×C4×#92418C2211yescharacteristic
20Q8⋊#92418—21no—
21D4⋊#92418—21no—
22#16839489—21no—
23#16839489—21no—
24#16839489—22no—
25C4×#41×C61C2211yescharacteristic
26C61×#433—22no—
27C61×#432—21no—
28C61×#431—21no—
29C61×#423C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C61×#408—21no—
32C61×#405—21no—
33C2×#11758222—21no—
34#14519797—42no—
35#14519797—42no—
36C2×#11758202—21no—
37C2×#11758200—21no—
38C2×#11758201—21no—
39C2×#11758199—21no—
40C22×#92418—21no—
41C22×#92418—21no—
42#14519777C2×C411yescharacteristic
43#14519774C2×C411yescharacteristic
44#14519765—21no—
45#14519751—21no—
46#14519751—21no—
47C4×D244—21no—
48C4×D244—21no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418C2×C411yescharacteristic
52C4⋊#92418C2×C411yescharacteristic
53#14519700—21no—
54#14519700—21no—
55#14519697—21no—
56#14519697—21no—
57C22⋊#92418—21no—
58C4×#92418—21no—
59C4×#92418—21no—
60C4×#92418—21no—
61C2×#41×C61D411yescharacteristic
62C2×M16×C61—21no—
63C22×C8×C61—21no—
64C4×Q8×C61C2×C411yescharacteristic
65C4×Q8×C61D411yescharacteristic
66C4×D4×C61—21no—
67C4×D4×C61—21no—
68C4×D4×C61C2×C411yescharacteristic
69C4×D4×C61D411yescharacteristic
70#117×C61—21no—
71#117×C61D411yescharacteristic
72C2×C42×C61—21no—
73C2×C42×C61C2311yescharacteristic
74C4⋊C8×C61—21no—
75C4⋊C8×C61—21no—
76C4⋊C8×C61D411yescharacteristic
77C4⋊C8×C61D411yescharacteristic
78C4⋊C8×C61D412yes—
79C22⋊C8×C61—22no—
80C22⋊C8×C61—22no—
81#97×C61—22no—
82C4×C8×C61—22no—
83#41×C61—21no—
84#41×C61—21no—
85#41×C61—21no—
86#41×C61—21no—
87C2×Q8×C61C22⋊C411yescharacteristic
88C2×D4×C61—21no—
89C2×D4×C61C22⋊C411yescharacteristic
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61#4111yescharacteristic
95C22×C4×C61#4111yescharacteristic
96C2×C22⋊D61—41no—
97#11758222—41no—
98#11758222—41no—
99#11758222—41no—
100#11758222—41no—
101C2×D244—21no—
102C2×D244—21no—
103C2×D244—21no—
104C2×C4×D61—41no—
105C2×Dic122—21no—
106M16×C61—41no—
107M16×C61—41no—
108C2×C8×C61—21no—
109C2×C8×C61—22no—
110C2×C8×C61—21no—
111C2×C8×C61—41no—
112C2×C8×C61—41no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61C22⋊C411yescharacteristic
116C4⋊C4×C61C22⋊C411yescharacteristic
117C22⋊C4×C61—21no—
118C22⋊C4×C61—21no—
119C22⋊C4×C61—21no—
120C42×C61—21no—
121C42×C61—21no—
122C42×C61—21no—
123C42×C61C22×C411yescharacteristic
124C42×C61C2×D411yescharacteristic
125C42×C61C2×D411yescharacteristic
126C42×C61C2×D411yescharacteristic
127#11758202—42no—
128#11758201—42no—
129#11758200—42no—
130#11758199—42no—
131#11758198—41no—
132#11758198—41no—
133C4⋊Dic61—21no—
134C4⋊Dic61—21no—
135C2×#92418—22no—
136C2×#92418—21no—
137C2×#92418—21no—
138C2×#92418—41no—
139C2×#92418—41no—
140C2×#92418—41no—
141C2×#92418—41no—
142C2×#92418—41no—
143C23×C61—21no—
144C23×C61#12311yescharacteristic
145C22×D61—41no—
146Q8×C61—21no—
147Q8×C61—21no—
148D4×C61—21no—
149D4×C61—21no—
150D4×C61—41no—
151D4×C61—41no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—81no—
163C2×C4×C61C2×C22⋊C411yescharacteristic
164C2×C4×C61C4×D411yescharacteristic
165C2×C4×C61C4×D411yescharacteristic
166C2×C4×C61#12011yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#13511yescharacteristic
170C2×C4×C61#13511yescharacteristic
171C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
173C22⋊D61—81no—
174C22⋊D61—81no—
175C2×Dic61—41no—
176D244—42no—
177D244—41no—
178D244—41no—
179D244—41no—
180D244—41no—
181C4×D61—81no—
182C4×D61—81no—
183Dic122—41no—
184Dic122—41no—
185C8×C61—41no—
186C8×C61—41no—
187C8×C61—42no—
188#92418—42no—
189#92418—41no—
190#92418—41no—
191#92418—81no—
192#8996—611nomaximal, Sylow
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61#38611yescharacteristic
199C22×C61#48211yescharacteristic
200C22×C61#48211yescharacteristic
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—81no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—41no—
208C4×C61—41no—
209C4×C61—41no—
210C4×C61#41611yescharacteristic
211C4×C61#41811yescharacteristic
212C4×C61#44311yescharacteristic
213C4×C61#44411yescharacteristic
214C4×C61#44911yescharacteristic
215C4×C61#44911yescharacteristic
216Dic61—81no—
217#3035—611no—
218#2925D6111yescharacteristic, complemented
219#1492—611no—
220#1480—611no—
221#1476—611no—
222#1301—611no—
223#1277—611no—
224C2×C61—21no—
225C2×C61—21no—
226C2×C61—81no—
227C2×C61#187511yescharacteristic
228C2×C61#187611yescharacteristic
229C2×C61#188111yescharacteristic
230D61—161no—
231C2×#135—1221no—
232#532—611no—
233C4×#41C2×D6111yescharacteristic
234#464—1221no—
235#463—1221no—
236#462—611no—
237#461—611no—
238#460—611no—
239#459—611no—
240#433—22no—
241#432—21no—
242#431—21no—
243#431—611no—
244#423C2×D6111yescharacteristic
245C2×C4⋊C8—611no—
246C2×C4⋊C8C2×D6111yescharacteristic
247#416—1221no—
248#408—21no—
249#405—21no—
250C2×C4×C8—611no—
251Q8⋊C8—1221no—
252D4⋊C8—1221no—
253D4⋊C8—1221no—
254D4⋊C8—1221no—
255D4⋊C8—1222no—
256C61#899611yescharacteristic, complemented, Sylow
257C2×#41—1221no—
258C2×#41C22⋊D6111yescharacteristic
259#135—2442no—
260#135—2442no—
261C2×Q16—1221no—
262C2×SD16—1221no—
263C2×SD16—1221no—
264C2×D8—1221no—
265C2×M16—21no—
266C22×C8—21no—
267C22×C8—1221no—
268C22×C8—1221no—
269C4⋊Q8—611no—
270#127—611no—
271#124—1221no—
272#121—1221no—
273#121—1221no—
274C4×Q8C4×D6111yescharacteristic
275C4×Q8D24411yescharacteristic
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—1221no—
279C4×D4—1221no—
280C4×D4C4×D6111yescharacteristic
281C4×D4D24411yescharacteristic
282#117—21no—
283#117C22⋊D6111yescharacteristic
284C2×C42—21no—
285C2×C42C22×D6111yescharacteristic
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8—611no—
289C4⋊C8—611no—
290C4⋊C8—1221no—
291C4⋊C8—1221no—
292C4⋊C8C22⋊D6111yescharacteristic
293C4⋊C8C22⋊D6111yescharacteristic
294C4⋊C8C22⋊D6112yes—
295#103—1221no—
296#103—1221no—
297#102—1221no—
298#102—1221no—
299C22⋊C8—22no—
300C22⋊C8—22no—
301C22⋊C8—1221no—
302#97—22no—
303C4×C8—22no—
304C4×C8—1221no—
305C4×C8—1221no—
306C4×C8—1221no—
307#41—21no—
308#41—21no—
309#41—21no—
310#41—21no—
311#41—2441no—
312#41—2441no—
313#41—2441no—
314#41—2441no—
315C2×Q8—1221no—
316C2×Q8#1175819811yescharacteristic
317C2×D4—21no—
318C2×D4—1221no—
319C2×D4—1221no—
320C2×D4—1221no—
321C2×D4—2441no—
322C2×D4#1175819811yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—2441no—
327C22×C4#1175822211yescharacteristic
328C22×C4#1175822211yescharacteristic
329C22×C4C2×C22⋊D6111yescharacteristic
330Q16—2442no—
331SD16—2442no—
332SD16—2442no—
333D8—2442no—
334M16—41no—
335M16—41no—
336C2×C8—21no—
337C2×C8—22no—
338C2×C8—21no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—1222no—
342C2×C8—1221no—
343C2×C8—1221no—
344C2×C8—2441no—
345C2×C8—2441no—
346C2×C8—2441no—
347C2×C8—2441no—
348C2×C8—2441no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—1221no—
352C4⋊C4—1221no—
353C4⋊C4#1175819811yescharacteristic
354C4⋊C4#1175819811yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—2441no—
359C22⋊C4—2441no—
360C42—21no—
361C42—21no—
362C42—21no—
363C42C2×C4×D6111yescharacteristic
364C42C2×D24411yescharacteristic
365C42C2×C22⋊D6111yescharacteristic
366C42C2×C22⋊D6111yescharacteristic
367C23—21no—
368C23—2441no—
369C23#1451976011yescharacteristic
370Q8—21no—
371Q8—21no—
372Q8—2441no—
373Q8—2441no—
374D4—21no—
375D4—21no—
376D4—41no—
377D4—41no—
378D4—4881no—
379D4—4881no—
380D4—2442no—
381D4—2441no—
382D4—2441no—
383D4—2441no—
384D4—2441no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—81no—
396C2×C4—4881no—
397C2×C4—4881no—
398C2×C4—2441no—
399C2×C4C2×#1175819811yescharacteristic
400C2×C4C4×C22⋊D6111yescharacteristic
401C2×C4C4×C22⋊D6111yescharacteristic
402C2×C4#1451974611yescharacteristic
403C2×C4#1451975111yescharacteristic
404C2×C4#1451975111yescharacteristic
405C2×C4#1451979711yescharacteristic
406C2×C4#1451979711yescharacteristic
407C2×C4#1451980211yescharacteristic
408C2×C4#1451980211yescharacteristic
409C8—41no—
410C8—41no—
411C8—42no—
412C8—4881no—
413C8—2442no—
414C8—2441no—
415C8—2441no—
416C22—21no—
417C22—21no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—4881no—
422C22—4881no—
423C22—4881no—
424C22#1683964111yescharacteristic
425C22#1684008611yescharacteristic
426C22#1684008611yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—4881no—
434C4#1683975611yescharacteristic
435C4#1683976611yescharacteristic
436C4#1683987711yescharacteristic
437C4#1683988211yescharacteristic
438C4#1683990711yescharacteristic
439C4#1683990711yescharacteristic
440C2—21no—
441C2—21no—
442C2—81no—
443C2—9761no—
444C2#2144614111yescharacteristic
445C2#2144614611yescharacteristic
446C2#2144618111yescharacteristic
subgroupG/H
centerC2×C4#14519746
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2925C2
socleC22×C61#386
prime radical#21455274C2
cosocleC2×C42×C61C23
hypercenter#2925D61
hypocenterC61#8996
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #21444269C2semidirect
3. #21444217C2semidirect
4. #21444201C2semidirect
5. #21443714C2semidirect
6. #21443653C2semidirect
7. C61×#2925C2semidirect
218. #2925D61semidirect
256. C61#8996semidirect

Maximal subgroups

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

subgroupindex
#214552742
#214442692
#214442172
#214442012
#214437142
#214436532
C61×#29252
#899661