Finite Group Databasebeta

← #29579030

Subgroups — #29579030

Order 15616.

482 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454192C211yesmaximal, characteristic
2#21445673C211yesmaximal, characteristic, complemented
3#21445567C211yesmaximal, characteristic, complemented
4C2×#16839504C211yesmaximal, characteristic, complemented
5C2×#16839501C211yesmaximal, characteristic
6C2×#16839501C211yesmaximal, characteristic
7C2×C61×#330C211yesmaximal, characteristic, complemented
8C2×#14519765C2211yescharacteristic
9C2×#14519706—21no—
10C2×#14519688C2211yescharacteristic
11C2×#14519688C2211yescharacteristic
12#16839667C411yescharacteristic
13#16839667C411yescharacteristic
14#16839663C411yescharacteristic
15#16839663C411yescharacteristic
16#16839652—21no—
17#16839652—21no—
18#16839652—21no—
19#16839652—21no—
20C42×Dic61C2211yescharacteristic
21#16839516—21no—
22#16839516—21no—
23#16839516—21no—
24#16839504—22no—
25#16839501—22no—
26#16839501—22no—
27C2×#125×C61C2211yescharacteristic
28C2×#97×C61C2211yescharacteristic
29C2×#97×C61C2211yescharacteristic
30C61×#330—22no—
31C22×Dic122C2×C411yescharacteristic
32C22×D244C2×C411yescharacteristic
33C22×#92418—21no—
34C22×#92418—21no—
35#14519765—21no—
36#14519765—21no—
37#14519765—21no—
38#14519765—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51#14519706—24no—
52#14519688—21no—
53#14519688—21no—
54#14519688—21no—
55#14519688D412yes—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60C22×C8×C61—21no—
61C22×C8×C61—21no—
62#125×C61—21no—
63#125×C61—21no—
64#125×C61—21no—
65#125×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61C2×C411yescharacteristic
69C2×C4⋊C4×C61C2×C411yescharacteristic
70C2×C42×C61C2311yescharacteristic
71#97×C61—21no—
72#97×C61—21no—
73#97×C61—21no—
74#97×C61D412yes—
75C23×D61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61C22×C411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×Dic61—21no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—41no—
89C2×D244—41no—
90C2×Dic122—21no—
91C2×Dic122—21no—
92C2×Dic122—41no—
93C2×Dic122—41no—
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—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61—41no—
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C42×C61#4111yescharacteristic
111C42×C61#4111yescharacteristic
112#11758198—42no—
113#11758198—42no—
114#11758198—42no—
115#11758198—41no—
116#11758198—41no—
117#11758198—41no—
118#11758198—41no—
119#11758198—42no—
120C4×Dic61—22no—
121C4×Dic61—41no—
122C4×Dic61—41no—
123C4×Dic61—41no—
124C4×Dic61—41no—
125C4×Dic61—41no—
126C2×#92418—22no—
127C2×#92418—22no—
128C2×#92418—41no—
129C2×#92418—41no—
130C2×#92418—41no—
131C2×#92418—41no—
132C23×C61C2×C22⋊C411yescharacteristic
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61C4×D411yescharacteristic
153C2×C4×C61C4×D411yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61#12411yescharacteristic
157C2×C4×C61#12711yescharacteristic
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61#10412yes—
173D244—81no—
174D244—81no—
175Dic122—81no—
176Dic122—81no—
177C8×C61—42no—
178C8×C61—42no—
179#92418—42no—
180#92418—42no—
181#9688—611nomaximal, Sylow
182C22×C61#39011yescharacteristic
183C22×C61#41311yescharacteristic
184C22×C61#41311yescharacteristic
185C22×C61C2×#10411yescharacteristic
186C22×C61#42111yescharacteristic
187C22×C61#42111yescharacteristic
188C22×C61#42111yescharacteristic
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C2×D61—81no—
193C2×D61—81no—
194C2×D61—81no—
195C2×D61—81no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—81no—
203C4×C61—81no—
204Dic61—22no—
205Dic61—41no—
206Dic61—41no—
207Dic61—41no—
208Dic61—81no—
209#2861—611no—
210#1767—611no—
211#1745—611no—
212C2×#330—611no—
213C2×#330D6111yescharacteristic, complemented
214C2×#329—611no—
215C2×#329—611no—
216C2×C61#152911yescharacteristic
217C2×C61#153211yescharacteristic
218C2×C61#153511yescharacteristic
219C2×C61#153511yescharacteristic
220C2×C61#196311yescharacteristic
221C2×C61#196711yescharacteristic
222C2×C61#198011yescharacteristic
223D61—161no—
224C2×#125C2×D6111yescharacteristic
225C2×#124—611no—
226C2×C4⋊C8—1221no—
227C2×#97—611no—
228C2×#97—611no—
229C2×#97C2×D6111yescharacteristic
230C2×#97C2×D6111yescharacteristic
231#391—611no—
232#391—611no—
233#390—611no—
234#390—611no—
235#388—1221no—
236#388—1221no—
237#388—1221no—
238#388—1221no—
239C43—611no—
240#336—1221no—
241#336—1221no—
242#336—1221no—
243#330—22no—
244#330—1222no—
245#329—1222no—
246#329—1222no—
247C61#968811yescharacteristic, complemented, Sylow
248C22×Q8—611no—
249C22×D4—611no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—1221no—
253C22×C8—1221no—
254#125—21no—
255#125—21no—
256#125—21no—
257#125—21no—
258#124—1221no—
259#124—1221no—
260#124—1221no—
261#124—1221no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4C4×D6111yescharacteristic
265C2×C4⋊C4C4×D6111yescharacteristic
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C42—611no—
273C2×C42—611no—
274C2×C42—611no—
275C2×C42—611no—
276C2×C42—611no—
277C2×C42—611no—
278C2×C42C22×D6111yescharacteristic
279C4⋊C8—1224no—
280#97—21no—
281#97—21no—
282#97—21no—
283#97—612no—
284#97—1221no—
285#97—1221no—
286#97—1221no—
287#97C22⋊D6112yes—
288#95—1221no—
289#95—1221no—
290#95—1221no—
291#95—1221no—
292C24—1221no—
293C2×Q8—1221no—
294C2×Q8—1221no—
295C2×Q8—2441no—
296C2×Q8—2441no—
297C2×D4—1221no—
298C2×D4—1221no—
299C2×D4—2441no—
300C2×D4—2441no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—611no—
306C22×C4—611no—
307C22×C4—1221no—
308C22×C4C2×C4×D6111yescharacteristic
309C22×C4D4×D6111yescharacteristic
310C22×C4D4×D6111yescharacteristic
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—1222no—
318C2×C8—1222no—
319C2×C8—2441no—
320C2×C8—2441no—
321C2×C8—2441no—
322C2×C8—2441no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C22⋊C4—2442no—
332C22⋊C4—2442no—
333C22⋊C4—2442no—
334C22⋊C4—2442no—
335C22⋊C4—2441no—
336C22⋊C4—2441no—
337C22⋊C4—2441no—
338C22⋊C4—2441no—
339C42—1222no—
340C42—2441no—
341C42—2441no—
342C42—2441no—
343C42—2441no—
344C42—2441no—
345C42#1175822211yescharacteristic
346C42D4×D6111yescharacteristic
347C42#1175822411yescharacteristic
348C42C2×C22⋊D6111yescharacteristic
349C23—2441no—
350C23—2441no—
351C23—2441no—
352C23—2441no—
353C23—2441no—
354C23—2441no—
355C23—2441no—
356C23C22⋊C4×D6111yescharacteristic
357Q8—4881no—
358Q8—4881no—
359D4—4881no—
360D4—4881no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—612no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4#1451973711yescharacteristic
389C2×C4C4×C22⋊D6111yescharacteristic
390C2×C4#1451974911yescharacteristic
391C2×C4#1451975011yescharacteristic
392C2×C4#1451976311yescharacteristic
393C2×C4#1451977311yescharacteristic
394C8—42no—
395C8—42no—
396C8—2442no—
397C8—2442no—
398C22—4881no—
399C22—4881no—
400C22—4881no—
401C22—4881no—
402C22—4881no—
403C22—4881no—
404C22—4881no—
405C22#1683966211yescharacteristic
406C22#1683974511yescharacteristic
407C22#1683974511yescharacteristic
408C22#104×D6111yescharacteristic
409C22#1683977711yescharacteristic
410C22#1683977711yescharacteristic
411C22#1683977711yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—81no—
419C4—81no—
420C4—1222no—
421C4—4881no—
422C4—2441no—
423C4—2441no—
424C4—2441no—
425C2—9761no—
426C2#2144442511yescharacteristic
427C2#2144443811yescharacteristic
428C2#2144444911yescharacteristic
429C2#2144444911yescharacteristic
430C2#2144664911yescharacteristic
431C2#2144666711yescharacteristic
432C2#2144673611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#330C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenterC2×#330D61
hypocenterC61#9688
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
2. #21445673C2semidirect
3. #21445567C2semidirect
4. C2×#16839504C2semidirect
7. C2×C61×#330C2semidirect
213. C2×#330D61semidirect
247. C61#9688semidirect

Maximal subgroups

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

subgroupindex
#214541922
#214456732
#214455672
C2×#168395042
C2×#168395012
C2×C61×#3302
#968861