Finite Group Databasebeta

← #29680377

Subgroups — #29680377

Order 15616.

616 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519783C211yesmaximal, characteristic
2#21445965C212yesmaximal, complemented
3#21445944C211yesmaximal, characteristic, complemented
4#21445942C211yesmaximal, characteristic, complemented
5#21445922C212yesmaximal
6#21445866C211yesmaximal, characteristic
7#21445862C211yesmaximal, characteristic
8#21445698C211yesmaximal, characteristic, complemented
9#21445620C212yesmaximal
10#21445574C212yesmaximal, complemented
11C61×#1772C211yesmaximal, characteristic, complemented
12C2×#14519783C2211yescharacteristic
13C2×#14519783C2211yescharacteristic
14C4×#11758222C2211yescharacteristic
15C2×#14519713C2211yescharacteristic
16#16839800C2211yescharacteristic
17#16839744C2212yes—
18#16839735C2212yes—
19#16839717C2212yes—
20#16839717C2211yescharacteristic
21#16839717C2211yescharacteristic
22#16839716C412yescomplemented
23#16839716C412yescomplemented
24C4×#11758194C2211yescharacteristic
25C4×#11758189C412yescomplemented
26C4×C8×D61C412yescomplemented
27#16839534C2212yes—
28#16839532C2212yes—
29#16839522C2212yes—
30#16839520C2212yes—
31#16839519C2212yes—
32#16839518C2212yes—
33#16839518C2212yes—
34C2×#108×C61C2211yescharacteristic
35C61×#427C2211yescharacteristic
36C61×#405C2212yes—
37C2×C4×C8×C61C2211yescharacteristic
38C61×#339C2212yes—
39C2×#11758222C2311yescharacteristic
40#14519783—21no—
41#14519783—21no—
42#14519783—21no—
43#14519783—21no—
44#14519783—21no—
45#14519783—21no—
46#14519783—21no—
47#14519783—21no—
48C2×#11758194C2312yes—
49C2×#11758194C2311yescharacteristic
50C2×#11758194C2311yescharacteristic
51C2×#11758189C2×C412yes—
52C2×#11758189C2×C412yes—
53C2×C8×D61C2×C412yes—
54C2×C8×D61C2×C412yes—
55C4×Dic122—21no—
56C4×D244—21no—
57C4×C22⋊D61—22no—
58#14519736C2312yes—
59#14519736C2311yescharacteristic
60#14519734C2×C412yes—
61C42×D61C2×C412yes—
62#14519713—21no—
63#14519713—21no—
64#14519711—21no—
65#14519709—21no—
66#14519695—22no—
67#14519693—22no—
68#14519691—24no—
69#14519688C2×C412yes—
70#14519687—22no—
71#14519687C2×C412yes—
72#14519687C2×C412yes—
73C4×#92418C2×C412yes—
74C8×Dic61—22no—
75C8×Dic61C2×C412yes—
76C8×Dic61C2×C412yes—
77C2×M16×C61C2312yes—
78C22×C8×C61C2311yescharacteristic
79C22×C8×C61C2311yescharacteristic
80#117×C61C2312yes—
81C2×C42×C61C2311yescharacteristic
82#108×C61—21no—
83#108×C61—21no—
84#107×C61—21no—
85#106×C61—21no—
86#97×C61—22no—
87C4×C8×C61—22no—
88C4×C8×C61C2×C411yescharacteristic
89C4×C8×C61C2×C411yescharacteristic
90C4×C8×C61C2×C411yescharacteristic
91C4×C8×C61C2×C411yescharacteristic
92C22×C4×C61—21no—
93C22×C4×C61C2411yescharacteristic
94C2×C22⋊D61#4112yes—
95#11758222—21no—
96#11758222—21no—
97#11758222—21no—
98#11758222—21no—
99C2×D244#4111yescharacteristic
100C2×C4×D61—22no—
101C2×C4×D61C22×C412yes—
102C2×Dic122#4111yescharacteristic
103M16×C61—22no—
104M16×C61—22no—
105C2×C8×C61—22no—
106C2×C8×C61C22×C411yescharacteristic
107C2×C8×C61C22×C411yescharacteristic
108C2×C8×C61C22×C411yescharacteristic
109C2×C8×C61C22×C411yescharacteristic
110C2×C8×C61#4111yescharacteristic
111C2×C8×C61#4111yescharacteristic
112C2×C8×C61#4111yescharacteristic
113C2×C8×C61#4111yescharacteristic
114C2×C8×C61#4111yescharacteristic
115C2×C8×C61#4111yescharacteristic
116C2×C8×C61#4111yescharacteristic
117C2×C8×C61#4111yescharacteristic
118C4⋊C4×C61—22no—
119C22⋊C4×C61—22no—
120C42×C61—21no—
121C42×C61—22no—
122C42×C61C22×C411yescharacteristic
123C42×C61C22×C411yescharacteristic
124C22⋊Dic61—21no—
125C22⋊Dic61—22no—
126#11758198—22no—
127C4⋊Dic61—21no—
128C4⋊Dic61—22no—
129#11758196—22no—
130C4×Dic61—22no—
131C4×Dic61—22no—
132C4×Dic61C22×C412yes—
133#11758194—21no—
134#11758194—21no—
135#11758194—21no—
136#11758194—21no—
137#11758194—22no—
138#11758194—22no—
139C2×#92418—22no—
140C2×#92418C22×C412yes—
141C2×#92418C22×C412yes—
142#11758189—22no—
143#11758189—22no—
144#11758189—22no—
145#11758189—22no—
146C8×D61—22no—
147C8×D61—22no—
148C8×D61—22no—
149C8×D61—22no—
150C23×C61C2×#4111yescharacteristic
151C22×D61#11712yes—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61C23×C411yescharacteristic
157C2×C4×C61C2×#4111yescharacteristic
158C2×C4×C61C2×#4111yescharacteristic
159C2×C4×C61C2×#4111yescharacteristic
160C2×C4×C61C2×#4111yescharacteristic
161C2×C4×C61C2×#4111yescharacteristic
162C22⋊D61—22no—
163C22⋊D61—22no—
164C2×Dic61—22no—
165C2×Dic61—42no—
166C2×Dic61#11712yes—
167D244—21no—
168D244—21no—
169C4×D61—22no—
170C4×D61—22no—
171C4×D61—44no—
172Dic122—21no—
173Dic122—21no—
174C8×C61—42no—
175C8×C61#11711yescharacteristic
176C8×C61#11711yescharacteristic
177C8×C61#11711yescharacteristic
178C8×C61#11711yescharacteristic
179C8×C61#11711yescharacteristic
180C8×C61#11711yescharacteristic
181C8×C61#11711yescharacteristic
182C8×C61#11711yescharacteristic
183#92418—22no—
184#92418—22no—
185#92418—42no—
186#20787—611nomaximal, Sylow
187C22×C61—41no—
188C22×C61C2×#11711yescharacteristic
189C22×C61#52911yescharacteristic
190C22×C61#52911yescharacteristic
191C2×D61—22no—
192C2×D61—42no—
193C4×C61—22no—
194C4×C61—41no—
195C4×C61—82no—
196C4×C61C2×#11711yescharacteristic
197C4×C61C2×#11711yescharacteristic
198C4×C61#52911yescharacteristic
199C4×C61#52911yescharacteristic
200Dic61—22no—
201Dic61—42no—
202Dic61—82no—
203C4×#131—611no—
204#1841—612no—
205#1833—611no—
206#1833—611no—
207#1827—612no—
208#1813—611no—
209#1812—611no—
210#1772—611no—
211#1772D6111yescharacteristic, complemented
212#1757—612no—
213#1747—612no—
214C2×C61—21no—
215C2×C61—21no—
216C2×C61—21no—
217C2×C61#228311yescharacteristic
218D61—42no—
219C2×#131—611no—
220C2×#131—611no—
221C4×#41—611no—
222C2×#108—611no—
223C2×#108C2×D6111yescharacteristic
224#427—611no—
225#427C2×D6111yescharacteristic
226#413—612no—
227#410—612no—
228#405—611no—
229#405—611no—
230#405—612no—
231#405—612no—
232#405—612no—
233#405C2×D6112yes—
234C4×M16—611no—
235C4×M16—612no—
236C2×C4×C8—612no—
237C2×C4×C8C2×D6111yescharacteristic
238#344—612no—
239#344—612no—
240#339—612no—
241#339C2×D6112yes—
242#338—612no—
243H(3,ℤ/4)—612no—
244H(3,ℤ/4)—612no—
245H(3,ℤ/4)—612no—
246C61#2078711yescharacteristic, complemented, Sylow
247C2×#41—611no—
248#131—1221no—
249#131—1221no—
250#131—1221no—
251#131—1221no—
252#131—1221no—
253#131—1221no—
254#131—1221no—
255#131—1221no—
256C2×M16—611no—
257C2×M16—611no—
258C2×M16—612no—
259C2×M16—612no—
260C2×M16—612no—
261C2×M16C22×D6112yes—
262C22×C8—612no—
263C22×C8—612no—
264C22×C8C22×D6111yescharacteristic
265C22×C8C22×D6111yescharacteristic
266C4×Q8—1221no—
267C4×D4—1221no—
268C4×D4—1222no—
269#117—611no—
270#117—612no—
271#117—612no—
272#117C22×D6112yes—
273C2×C42—612no—
274C2×C42C22×D6111yescharacteristic
275#108—21no—
276#108—21no—
277#108—1221no—
278#108—1221no—
279#107—21no—
280#107—1221no—
281#106—21no—
282#106—1221no—
283#101—1222no—
284#100—1222no—
285#99—1224no—
286#97—22no—
287#97—612no—
288#97—612no—
289#97—612no—
290#97—1222no—
291C4×C8—22no—
292C4×C8—612no—
293C4×C8—612no—
294C4×C8—612no—
295C4×C8—1222no—
296C4×C8C4×D6111yescharacteristic
297C4×C8C4×D6111yescharacteristic
298C4×C8C4×D6111yescharacteristic
299C4×C8C4×D6111yescharacteristic
300#41—1221no—
301#41—1221no—
302#41—1221no—
303#41—1221no—
304C2×Q8—611no—
305C2×D4—612no—
306C2×D4—611no—
307C22×C4—21no—
308C22×C4—612no—
309C22×C4—1222no—
310C22×C4C23×D6111yescharacteristic
311M16—22no—
312M16—22no—
313M16—1221no—
314M16—1221no—
315M16—1221no—
316M16—1221no—
317M16—1222no—
318M16—1222no—
319M16—1222no—
320M16—1222no—
321M16—1222no—
322M16—1222no—
323C2×C8—22no—
324C2×C8—612no—
325C2×C8—612no—
326C2×C8—1222no—
327C2×C8—1222no—
328C2×C8—1222no—
329C2×C8—1222no—
330C2×C8—1222no—
331C2×C8C2×C4×D6111yescharacteristic
332C2×C8C2×C4×D6111yescharacteristic
333C2×C8C2×C4×D6111yescharacteristic
334C2×C8C2×C4×D6111yescharacteristic
335C2×C8#1175822211yescharacteristic
336C2×C8#1175822211yescharacteristic
337C2×C8#1175822211yescharacteristic
338C2×C8#1175822211yescharacteristic
339C2×C8#1175822411yescharacteristic
340C2×C8#1175822411yescharacteristic
341C2×C8#1175822611yescharacteristic
342C2×C8#1175822611yescharacteristic
343C4⋊C4—22no—
344C4⋊C4—1222no—
345C4⋊C4—1221no—
346C4⋊C4—1222no—
347C22⋊C4—22no—
348C22⋊C4—1222no—
349C22⋊C4—1221no—
350C22⋊C4—1222no—
351C42—21no—
352C42—22no—
353C42—612no—
354C42—1222no—
355C42—1222no—
356C42C2×C4×D6111yescharacteristic
357C42C2×C4×D6111yescharacteristic
358C23—612no—
359C23#41×D6111yescharacteristic
360Q8—1221no—
361Q8—1221no—
362D4—1222no—
363D4—1222no—
364D4—1221no—
365D4—1221no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—612no—
371C2×C4—1222no—
372C2×C4—1222no—
373C2×C4—1222no—
374C2×C4—2444no—
375C2×C4—2442no—
376C2×C4C22×C4×D6111yescharacteristic
377C2×C4#41×D6111yescharacteristic
378C2×C4C2×#1175822411yescharacteristic
379C2×C4C2×#1175822211yescharacteristic
380C2×C4C2×#1175822211yescharacteristic
381C2×C4C2×#1175822611yescharacteristic
382C8—42no—
383C8—1222no—
384C8—1222no—
385C8—2442no—
386C8#1451973411yescharacteristic
387C8#1451973411yescharacteristic
388C8#1451973411yescharacteristic
389C8#1451973411yescharacteristic
390C8#1451973511yescharacteristic
391C8#1451973511yescharacteristic
392C8#1451973511yescharacteristic
393C8#1451973511yescharacteristic
394C22—41no—
395C22—1222no—
396C22—2442no—
397C22#117×D6111yescharacteristic
398C22#1684029411yescharacteristic
399C22#1684029911yescharacteristic
400C4—22no—
401C4—41no—
402C4—82no—
403C4—1222no—
404C4—4882no—
405C4—2442no—
406C4C2×#1451973411yescharacteristic
407C4C2×#1451973511yescharacteristic
408C4#1684029411yescharacteristic
409C4#1684029911yescharacteristic
410C2—21no—
411C2—21no—
412C2—21no—
413C2—2442no—
414C2#2144821511yescharacteristic
subgroupG/H
centerC8#14519735
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1772C2
socleC2×C61#2283
prime radicalC2×#11758222C23
cosocleC22×C4×C61C24
hypercenter#1772D61
hypocenterC61#20787
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C8 ◁ C22×C8 ◁ #1772

Complements

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

NH ≅ G/Ntype
2. #21445965C2semidirect
3. #21445944C2semidirect
4. #21445942C2semidirect
8. #21445698C2semidirect
10. #21445574C2semidirect
11. C61×#1772C2semidirect
22. #16839716C4semidirect
23. #16839716C4semidirect
25. C4×#11758189C4semidirect
26. C4×C8×D61C4semidirect
211. #1772D61semidirect
246. C61#20787semidirect

Maximal subgroups

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

subgroupindex
C4×#145197832
#214459652
#214459442
#214459422
#214459222
#214458662
#214458622
#214456982
#214456202
#214455742
C61×#17722
#2078761