Finite Group Databasebeta

← #29572783

Subgroups — #29572783

Order 15616.

540 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448358C211yesmaximal, characteristic
2#21445673C211yesmaximal, characteristic, complemented
3#21445673C211yesmaximal, characteristic, complemented
4C2×#16839501C211yesmaximal, characteristic
5C2×#16839501C211yesmaximal, characteristic
6#21443700C211yesmaximal, characteristic, complemented
7C61×#1295C211yesmaximal, characteristic, complemented
8C2×#14519765C2211yescharacteristic
9C2×#14519742C411yescharacteristic
10C2×#14519739C411yescharacteristic
11C2×#14519706—21no—
12C2×#14519706—21no—
13C2×#14519688C2211yescharacteristic
14C2×#14519688C2211yescharacteristic
15#16839667C411yescharacteristic
16#16839663C411yescharacteristic
17#16839651—21no—
18#16839651—21no—
19#16839609—21no—
20#16839609—21no—
21C42×Dic61C2211yescharacteristic
22#16839516—21no—
23#16839516—21no—
24#16839501—22no—
25#16839501—22no—
26C2×#97×C61C2211yescharacteristic
27C2×#97×C61C2211yescharacteristic
28C61×#382C2211yescharacteristic
29C22×Dic122C2×C411yescharacteristic
30C22×D244C2×C411yescharacteristic
31C22×C4×D61—21no—
32C22×#92418—21no—
33C22×#92418—21no—
34#14519765—21no—
35#14519765—21no—
36#14519765D412yes—
37#14519765Q812yes—
38#14519742—42no—
39#14519739—42no—
40C2×#11758196—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53#14519706—24no—
54#14519706—24no—
55#14519688—21no—
56#14519688—21no—
57#14519688—21no—
58#14519688—21no—
59#14519684—21no—
60#14519684—21no—
61C22×C8×C61—21no—
62C22×C8×C61—21no—
63C2×C4⋊C4×C61C2×C411yescharacteristic
64C2×C4⋊C4×C61C2×C411yescharacteristic
65C2×C42×C61C2311yescharacteristic
66#97×C61—21no—
67#97×C61—21no—
68#97×C61—21no—
69#97×C61—21no—
70#95×C61—21no—
71#95×C61—21no—
72C23×D61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61C22×C411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×Dic61—21no—
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C2×D244—21no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244C4⋊C412yes—
87C2×C4×D61—42no—
88C2×C4×D61—42no—
89C2×C4×D61—42no—
90C2×Dic122—21no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×Dic122C4⋊C412yes—
94C2×C8×C61—22no—
95C2×C8×C61—22no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C42×C61C2×D411yescharacteristic
103C42×C61C2×Q811yescharacteristic
104C42×C61#4111yescharacteristic
105C42×C61#4111yescharacteristic
106#11758198—22no—
107#11758198—22no—
108#11758198—22no—
109#11758198—22no—
110#11758198—42no—
111#11758198—42no—
112#11758198—42no—
113#11758196—42no—
114C4×Dic61—22no—
115C4×Dic61—22no—
116C4×Dic61—22no—
117C4×Dic61—41no—
118C4×Dic61—41no—
119C4×Dic61—41no—
120C4×Dic61—42no—
121C2×#92418—22no—
122C2×#92418—22no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126C2×#92418—41no—
127C23×C61C2×C22⋊C411yescharacteristic
128C22×D61—22no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61C2×C4⋊C411yescharacteristic
148C2×C4×C61#11711yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61C22⋊Q811yescharacteristic
152C2×C4×C61C22⋊Q811yescharacteristic
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—22no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61#10012yes—
166C2×Dic61#10412yes—
167C2×Dic61#10412yes—
168D244—42no—
169D244—42no—
170C4×D61—84no—
171Dic122—42no—
172Dic122—42no—
173C8×C61—42no—
174C8×C61—42no—
175#92418—42no—
176#92418—42no—
177#8581—611nomaximal, Sylow
178C22×C61#38011yescharacteristic
179C22×C61C2×#10011yescharacteristic
180C22×C61#41311yescharacteristic
181C22×C61C2×#10411yescharacteristic
182C22×C61C2×#10411yescharacteristic
183C22×C61#42111yescharacteristic
184C22×C61#42111yescharacteristic
185C2×D61—42no—
186C2×D61—42no—
187C2×D61—42no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—81no—
199C4×C61—81no—
200Dic61—22no—
201Dic61—22no—
202Dic61—22no—
203Dic61—42no—
204Dic61—41no—
205C4×#124—611no—
206#1767—611no—
207#1767—611no—
208C2×#329—611no—
209C2×#329—611no—
210#1295—611no—
211#1295D6111yescharacteristic, complemented
212C2×C61#152411yescharacteristic
213C2×C61#152711yescharacteristic
214C2×C61#153011yescharacteristic
215C2×C61#153511yescharacteristic
216C2×C61#180011yescharacteristic
217C2×C61#180611yescharacteristic
218C2×C61#180611yescharacteristic
219D61—82no—
220C2×#124—611no—
221C2×C4×Q8—611no—
222C2×C4×D4—611no—
223C2×C4⋊C8—1221no—
224C2×C4⋊C8—1221no—
225C2×#97—611no—
226C2×#97—611no—
227C2×#97C2×D6111yescharacteristic
228C2×#97C2×D6111yescharacteristic
229#391—611no—
230#390—611no—
231#388—1221no—
232#388—1221no—
233#382C2×D6111yescharacteristic
234C4×C22⋊C4—1221no—
235C4×C22⋊C4—1221no—
236C43—611no—
237#336—1221no—
238#336—1221no—
239#329—1222no—
240#329—1222no—
241C61#858111yescharacteristic, complemented, Sylow
242C22×Q8—611no—
243C22×D4—611no—
244C23×C4—1221no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—1221no—
248C22×C8—1221no—
249#124—612no—
250#124—612no—
251#124—1221no—
252#124—1221no—
253C4×Q8—2442no—
254C4×D4—2442no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4C4×D6111yescharacteristic
257C2×C4⋊C4C4×D6111yescharacteristic
258C2×C22⋊C4—1221no—
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C42—611no—
264C2×C42—611no—
265C2×C42—611no—
266C2×C42—611no—
267C2×C42—611no—
268C2×C42—611no—
269C2×C42—1221no—
270C2×C42C22×D6111yescharacteristic
271C4⋊C8—1224no—
272C4⋊C8—1224no—
273#97—21no—
274#97—21no—
275#97—21no—
276#97—21no—
277#97—1221no—
278#97—1221no—
279#97—1221no—
280#97—1221no—
281#95—21no—
282#95—21no—
283#95—1221no—
284#95—1221no—
285C24—1221no—
286C2×Q8—612no—
287C2×Q8—1221no—
288C2×Q8—2441no—
289C2×Q8—2441no—
290C2×D4—612no—
291C2×D4—1221no—
292C2×D4—2441no—
293C2×D4—2441no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—1221no—
301C22×C4—2442no—
302C22×C4—2442no—
303C22×C4—2442no—
304C22×C4C2×C4×D6111yescharacteristic
305C22×C4D4×D6111yescharacteristic
306C22×C4D4×D6111yescharacteristic
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—1222no—
314C2×C8—1222no—
315C2×C8—2441no—
316C2×C8—2441no—
317C2×C8—2441no—
318C2×C8—2441no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—2442no—
322C22⋊C4—1222no—
323C22⋊C4—1222no—
324C22⋊C4—1222no—
325C22⋊C4—1222no—
326C22⋊C4—2442no—
327C22⋊C4—2442no—
328C22⋊C4—2442no—
329C42—1222no—
330C42—1222no—
331C42—1222no—
332C42—2441no—
333C42—2441no—
334C42—2441no—
335C42—2442no—
336C42#1175822211yescharacteristic
337C42#1175822211yescharacteristic
338C42D4×D6111yescharacteristic
339C42Q8×D6111yescharacteristic
340C23—1222no—
341C23—2441no—
342C23—2441no—
343C23—2441no—
344C23—2441no—
345C23—2441no—
346C23—2441no—
347C23C22⋊C4×D6111yescharacteristic
348Q8—2442no—
349Q8—2442no—
350D4—2442no—
351D4—2442no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—612no—
365C2×C4—612no—
366C2×C4—612no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1222no—
377C2×C4—4884no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4C4⋊C4×D6111yescharacteristic
381C2×C4#1451973411yescharacteristic
382C2×C4#1451975011yescharacteristic
383C2×C4#1451975011yescharacteristic
384C2×C4#1451975511yescharacteristic
385C2×C4#1451975511yescharacteristic
386C8—42no—
387C8—42no—
388C8—2442no—
389C8—2442no—
390C22—4881no—
391C22—4881no—
392C22—4881no—
393C22—4881no—
394C22—2442no—
395C22—2442no—
396C22—2442no—
397C22#1683962111yescharacteristic
398C22#100×D6111yescharacteristic
399C22#1683974511yescharacteristic
400C22#104×D6111yescharacteristic
401C22#104×D6111yescharacteristic
402C22#1683977711yescharacteristic
403C22#1683977711yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—81no—
411C4—81no—
412C4—1222no—
413C4—1222no—
414C4—1222no—
415C4—2441no—
416C4—2442no—
417C2—4882no—
418C2#2144440611yescharacteristic
419C2#2144441511yescharacteristic
420C2#2144442811yescharacteristic
421C2#2144444911yescharacteristic
422C2#2144581011yescharacteristic
423C2#2144583811yescharacteristic
424C2#2144583811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1295D61
hypocenterC61#8581
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
2. #21445673C2semidirect
3. #21445673C2semidirect
6. #21443700C2semidirect
7. C61×#1295C2semidirect
211. #1295D61semidirect
241. C61#8581semidirect

Maximal subgroups

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

subgroupindex
#214483582
#214456732
C2×#168395012
#214437002
C61×#12952
#858161