Finite Group Databasebeta

← #29834599

Subgroups — #29834599

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840200C211yesmaximal, characteristic, complemented
2#21455539C211yesmaximal, characteristic, complemented
3C2×#16840032C211yesmaximal, characteristic, complemented
4#21447949C214yesmaximal, complemented
5#21447939C214yesmaximal, complemented
6#21447614C211yesmaximal, characteristic, complemented
7#21447569C211yesmaximal, characteristic, complemented
8C2×#16839576C211yesmaximal, characteristic, complemented
9C61×#3407C211yesmaximal, characteristic, complemented
10#16840560—21no—
11C2×#14519802—21no—
12C2×#14519799C2211yescharacteristic
13C22×D488C2211yescharacteristic
14#16840200—22no—
15#16840200—22no—
16C2×#14519722C2212yescomplemented
17C2×D976C2212yescomplemented
18#16840037C2212yescomplemented
19#16840032—22no—
20#16840032C2214yes—
21#16840032C2212yescomplemented
22#16840025—22no—
23C2×#14519713C2211yescharacteristic
24C2×#14519713C2211yescharacteristic
25#16839744—21no—
26C2×#14519693—21no—
27#16839592C2214yescomplemented
28#16839579C2212yescomplemented
29#16839576C2212yescomplemented
30#16839576C2214yescomplemented
31C2×#131×C61C2211yescharacteristic
32C61×#504—22no—
33C61×#504C2214yescomplemented
34C2×M32×C61—22no—
35C2×M32×C61C2211yescharacteristic
36C2×M32×C61C2211yescharacteristic
37C2×#11758222—21no—
38C22×D244—21no—
39#14519808—41no—
40#14519807—22no—
41#14519803—41no—
42#14519802—22no—
43#14519802—24no—
44#14519802—42no—
45#14519799—21no—
46#14519799—21no—
47#14519799—21no—
48#14519799—21no—
49#14519797—42no—
50C2×Dic244C2311yescharacteristic
51C2×#11758190—21no—
52C2×#11758201—41no—
53C2×D488—21no—
54C2×D488—21no—
55C2×D488—21no—
56C2×D488—21no—
57C2×D488—21no—
58C2×D488C2312yes—
59C2×D488C2311yescharacteristic
60C2×#11758199—41no—
61C2×#11758194—21no—
62C2×#11758194—21no—
63#14519722—24no—
64D976—24no—
65#14519713—21no—
66#14519713—21no—
67#14519713C2312yes—
68#14519713C2312yes—
69#14519695—22no—
70#14519693—24no—
71#14519693—22no—
72C2×#41×C61D411yescharacteristic
73#131×C61—21no—
74#131×C61—21no—
75#131×C61D412yes—
76#131×C61C2312yes—
77C2×M16×C61—21no—
78C2×M16×C61D411yescharacteristic
79C22×C8×C61—21no—
80C22×C8×C61C2311yescharacteristic
81M32×C61—21no—
82M32×C61—24no—
83M32×C61D412yes—
84M32×C61D412yes—
85M32×C61C2312yes—
86C2×C16×C61—21no—
87C2×C16×C61—24no—
88C2×C16×C61C2312yes—
89C23×D61—41no—
90#41×C61—21no—
91#41×C61—21no—
92#41×C61D812yes—
93#41×C61C2×D412yes—
94C2×Q8×C61D811yescharacteristic
95C2×D4×C61—21no—
96C2×D4×C61D811yescharacteristic
97C22×C4×C61—21no—
98C22×C4×C61C2×D411yescharacteristic
99C2×C22⋊D61—41no—
100#11758222—41no—
101#11758222—41no—
102#11758222—41no—
103#11758222—41no—
104C2×D244—22no—
105C2×D244—21no—
106C2×D244—41no—
107C2×D244—41no—
108C2×D244—41no—
109C2×D244—41no—
110C2×D244—41no—
111C2×C4×D61—41no—
112C2×Dic122—21no—
113M16×C61—21no—
114M16×C61—22no—
115M16×C61—22no—
116M16×C61C2×D412yes—
117C2×C8×C61—21no—
118C2×C8×C61—22no—
119C2×C8×C61—22no—
120C2×C8×C61C2×D411yescharacteristic
121C2×C8×C61C2×D411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61#4111yescharacteristic
124C2×C8×C61#4111yescharacteristic
125C2×C8×C61C2411yescharacteristic
126#11758202—42no—
127#11758201—42no—
128#11758201—44no—
129#11758200—42no—
130#11758199—44no—
131#11758199—42no—
132#11758194—22no—
133#11758194—22no—
134#11758194—41no—
135#11758194—41no—
136C2×#92418—41no—
137C2×#92418—41no—
138Dic244—21no—
139Dic244—21no—
140D488—21no—
141D488—22no—
142D488—22no—
143D488—21no—
144D488—41no—
145D488—41no—
146#11758190—41no—
147#11758190—41no—
148C16×C61—22no—
149C16×C61C2×D414yes—
150C23×C61—21no—
151C23×C61#13511yescharacteristic
152C22×D61—41no—
153C22×D61—42no—
154C22×D61—81no—
155C22×D61—81no—
156C22×D61—162no—
157Q8×C61—21no—
158Q8×C61C2×D812yes—
159D4×C61—22no—
160D4×C61—22no—
161D4×C61—21no—
162D4×C61C2×D812yes—
163C2×C4×C61—21no—
164C2×C4×C61—22no—
165C2×C4×C61—22no—
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61C2×D811yescharacteristic
169C2×C4×C61C2×D811yescharacteristic
170C2×C4×C61#13511yescharacteristic
171C2×C4×C61C22×D411yescharacteristic
172C22⋊D61—81no—
173C22⋊D61—81no—
174C2×Dic61—41no—
175D244—41no—
176D244—42no—
177D244—42no—
178D244—41no—
179D244—81no—
180D244—81no—
181C4×D61—81no—
182C4×D61—81no—
183Dic122—41no—
184Dic122—41no—
185C8×C61—22no—
186C8×C61#12111yescharacteristic
187C8×C61#12111yescharacteristic
188C8×C61C22×D411yescharacteristic
189C8×C61C2×#4111yescharacteristic
190#92418—42no—
191#92418—42no—
192#33618—611nomaximal, Sylow
193C22×C61—22no—
194C22×C61—41no—
195C22×C61—81no—
196C22×C61#46611yescharacteristic
197C22×C61#46611yescharacteristic
198C22×C61C2×#13511yescharacteristic
199C2×D61—81no—
200C2×D61—82no—
201C2×D61—162no—
202C2×D61—162no—
203C2×D61—161no—
204C2×D61—162no—
205C4×C61—22no—
206C4×C61#46611yescharacteristic
207C4×C61#46611yescharacteristic
208C4×C61C2×#12111yescharacteristic
209C4×C61C22×D811yescharacteristic
210Dic61—81no—
211C2×#509—611no—
212#3407D6111yescharacteristic, complemented
213#3067—611no—
214C2×#472—611no—
215#2223—614no—
216#2221—614no—
217#2161—611no—
218#2148—611no—
219C2×#361—611no—
220C2×C61—21no—
221C2×C61—21no—
222C2×C61—21no—
223C2×C61—42no—
224C2×C61C2×#46611yescharacteristic
225D61—161no—
226D61—162no—
227#575—1221no—
228C2×AGL(1,ℤ/8)—1221no—
229C2×#135—611no—
230C22×D8—611no—
231C2×#131C2×D6111yescharacteristic
232#509—1222no—
233#509—1222no—
234C2×SD32—612no—
235C2×D16—612no—
236#504—22no—
237#504C2×D6114yescomplemented
238C2×M32—22no—
239C2×M32C2×D6111yescharacteristic
240C2×M32C2×D6111yescharacteristic
241#473—612no—
242#472—614no—
243#472—612no—
244#472—1222no—
245#471—1222no—
246C2×#108—611no—
247C2×#108—611no—
248#413—1221no—
249C2×#100—1221no—
250#368—614no—
251#362—612no—
252#361—614no—
253#361—612no—
254C61#3361811yescharacteristic, complemented, Sylow
255C2×#41—1221no—
256C2×#41D24411yescharacteristic
257C22×D4—1221no—
258#137—1222no—
259#137—2441no—
260AGL(1,ℤ/8)—1224no—
261AGL(1,ℤ/8)—1222no—
262AGL(1,ℤ/8)—2442no—
263AGL(1,ℤ/8)—2441no—
264#135—1221no—
265#135—1221no—
266#135—1221no—
267#135—1221no—
268#135—2442no—
269C2×Q16—611no—
270C2×SD16—1221no—
271C2×SD16—2441no—
272C2×D8—612no—
273C2×D8—611no—
274C2×D8—1221no—
275C2×D8—1221no—
276C2×D8—1221no—
277C2×D8—1221no—
278C2×D8—1221no—
279C2×D8—2441no—
280#131—21no—
281#131—21no—
282#131D24412yes—
283#131C22×D6112yes—
284C2×M16—21no—
285C2×M16—1221no—
286C2×M16—1221no—
287C2×M16D24411yescharacteristic
288C22×C8—21no—
289C22×C8C22×D6111yescharacteristic
290SD32—1224no—
291D16—1224no—
292M32—21no—
293M32—24no—
294M32C22⋊D6112yes—
295M32C22⋊D6112yes—
296M32C22×D6112yes—
297C2×C16—21no—
298C2×C16—24no—
299C2×C16C22×D6112yes—
300#108—612no—
301#108—612no—
302#108—1221no—
303#108—1221no—
304#101—1222no—
305#100—1224no—
306#100—1222no—
307C24—2441no—
308#41—21no—
309#41—21no—
310#41—2441no—
311#41—2441no—
312#41—2441no—
313#41—2441no—
314#41D48812yes—
315#41C2×D24412yes—
316C2×Q8—1221no—
317C2×Q8D48811yescharacteristic
318C2×D4—21no—
319C2×D4—1222no—
320C2×D4—1221no—
321C2×D4—2441no—
322C2×D4—2441no—
323C2×D4—2441no—
324C2×D4—2441no—
325C2×D4—2441no—
326C2×D4—2441no—
327C2×D4D48811yescharacteristic
328C22×C4—21no—
329C22×C4—2441no—
330C22×C4C2×D24411yescharacteristic
331Q16—1221no—
332Q16—1221no—
333Q16—2442no—
334SD16—2444no—
335SD16—2442no—
336SD16—2442no—
337SD16—2441no—
338SD16—2441no—
339D8—1221no—
340D8—1222no—
341D8—1222no—
342D8—1221no—
343D8—2444no—
344D8—2442no—
345D8—2441no—
346D8—2441no—
347M16—21no—
348M16—22no—
349M16—22no—
350M16—1222no—
351M16—1222no—
352M16—2441no—
353M16—2441no—
354M16C2×D24412yes—
355C2×C8—21no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—2441no—
359C2×C8—2441no—
360C2×C8C2×D24411yescharacteristic
361C2×C8#1175822211yescharacteristic
362C2×C8#1175822211yescharacteristic
363C2×C8C2×C22⋊D6111yescharacteristic
364C2×C8C2×C22⋊D6111yescharacteristic
365C2×C8C23×D6111yescharacteristic
366C16—22no—
367C16C2×C22⋊D6114yes—
368C23—21no—
369C23—9762no—
370C23—4881no—
371C23—4881no—
372C23—2441no—
373C23—2442no—
374C23#1451979911yescharacteristic
375Q8—21no—
376Q8—2441no—
377Q8—2441no—
378Q8C2×D48812yes—
379D4—22no—
380D4—22no—
381D4—21no—
382D4—4881no—
383D4—4881no—
384D4—4881no—
385D4—4881no—
386D4—2442no—
387D4—2441no—
388D4—2442no—
389D4—2441no—
390D4C2×D48812yes—
391C2×C4—21no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—4881no—
395C2×C4—4881no—
396C2×C4—2441no—
397C2×C4#1451975111yescharacteristic
398C2×C4#1451975111yescharacteristic
399C2×C4C2×D48811yescharacteristic
400C2×C4C2×D48811yescharacteristic
401C2×C4#1451979911yescharacteristic
402C2×C4C22×D24411yescharacteristic
403C8—22no—
404C8—2442no—
405C8—2442no—
406C8#1451975111yescharacteristic
407C8#1451975111yescharacteristic
408C8C22×C22⋊D6111yescharacteristic
409C8C2×#1175822211yescharacteristic
410C22—22no—
411C22—41no—
412C22—81no—
413C22—9762no—
414C22—9761no—
415C22—9762no—
416C22—9762no—
417C22—4881no—
418C22—4882no—
419C22#1683999811yescharacteristic
420C22#1683999811yescharacteristic
421C22C2×#1451979911yescharacteristic
422C4—22no—
423C4—4881no—
424C4#1683999811yescharacteristic
425C4#1683999811yescharacteristic
426C4C2×#1451975111yescharacteristic
427C4C22×D48811yescharacteristic
428C2—21no—
429C2—21no—
430C2—21no—
431C2—42no—
432C2—9762no—
433C2—9761no—
434C2C2×#1683999811yescharacteristic
subgroupG/H
centerC2C2×#16839998
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3407C2
socleC2×C61C2×#466
hypercenter#3407D61
hypocenterC61#33618
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3407

Complements

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

NH ≅ G/Ntype
1. C2×#16840200C2semidirect
2. #21455539C2semidirect
3. C2×#16840032C2semidirect
4. #21447949C2semidirect
5. #21447939C2semidirect
6. #21447614C2semidirect
7. #21447569C2semidirect
8. C2×#16839576C2semidirect
9. C61×#3407C2semidirect
16. C2×#14519722C22semidirect
17. C2×D976C22semidirect
18. #16840037C22semidirect
21. #16840032C22semidirect
27. #16839592C22semidirect
28. #16839579C22semidirect
29. #16839576C22semidirect
30. #16839576C22semidirect
33. C61×#504C22semidirect
212. #3407D61semidirect
237. #504C2×D61semidirect
254. C61#33618semidirect

Maximal subgroups

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

subgroupindex
C2×#168402002
#214555392
C2×#168400322
#214479492
#214479392
#214476142
#214475692
C2×#168395762
C61×#34072
#3361861