Finite Group Databasebeta

← #29574991

Subgroups — #29574991

Order 15616.

560 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454846C211yesmaximal, characteristic
2#21449079C211yesmaximal, characteristic
3#21445919C211yesmaximal, characteristic, complemented
4#21445916C211yesmaximal, characteristic, complemented
5C4×#14519691C211yesmaximal, characteristic
6#21443705C211yesmaximal, characteristic, complemented
7C61×#1297C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D61C2211yescharacteristic
9C2×#14519736C2211yescharacteristic
10#16839836—22no—
11#16839831—22no—
12#16839816—21no—
13C2×#14519691—21no—
14#16839726C2211yescharacteristic
15C22⋊C8×D61—21no—
16#16839702C411yescharacteristic, complemented
17#16839699C411yescharacteristic, complemented
18#16839694C411yescharacteristic, complemented
19#16839689C411yescharacteristic, complemented
20#16839687—21no—
21#16839678—21no—
22C4×C4⋊Dic61—21no—
23C4×#11758198—21no—
24C4×C22⋊Dic61C2211yescharacteristic
25#16839528—21no—
26#16839523—22no—
27#16839522—22no—
28C61×#407C2211yescharacteristic
29C4×C22⋊C4×C61C2211yescharacteristic
30C4×C22⋊C4×C61C2211yescharacteristic
31C22×C22⋊D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C2×#11758194D412yes—
34C2×C8×D61—22no—
35C4×C22⋊D61—21no—
36C4×C22⋊D61—21no—
37C4×C22⋊D61—21no—
38C4×C22⋊D61—21no—
39#14519736—21no—
40#14519736—21no—
41#14519736—21no—
42#14519736—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×#11758196C2×C411yescharacteristic
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61D411yescharacteristic
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198C2×C411yescharacteristic
54C2×C4×Dic61—21no—
55C2×C4×Dic61—21no—
56C2×C4×Dic61D411yescharacteristic
57#14519706—22no—
58#14519691—24no—
59C22⋊#92418—21no—
60C22⋊#92418—21no—
61#14519689—22no—
62#14519687—22no—
63#14519684—21no—
64#14519684—21no—
65#14519684—21no—
66#14519684—21no—
67#14519684—21no—
68C23×C4×C61C2311yescharacteristic
69C2×M16×C61D412yes—
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C42×C61—21no—
73C2×C42×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61—21no—
76#95×C61—21no—
77#95×C61C2×C411yescharacteristic
78#95×C61C2×C411yescharacteristic
79C24×C61C2×D411yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—42no—
84C22×C4×C61—41no—
85C22×C4×C61C22×C411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C22×C4×C61#4111yescharacteristic
91C2×C22⋊D61—21no—
92C2×C22⋊D61—21no—
93C2×C22⋊D61—22no—
94C2×C22⋊D61—41no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—41no—
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61C22⋊C411yescharacteristic
100C22×Dic61C22⋊C411yescharacteristic
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—42no—
104M16×C61—42no—
105C2×C8×C61—22no—
106C22⋊C4×C61—22no—
107C22⋊C4×C61—42no—
108C22⋊C4×C61—41no—
109C42×C61—42no—
110C42×C61—42no—
111C22⋊Dic61—21no—
112C22⋊Dic61—21no—
113C22⋊Dic61—22no—
114C22⋊Dic61—41no—
115C22⋊Dic61—41no—
116C22⋊Dic61—41no—
117#11758198—21no—
118#11758198—21no—
119#11758198—42no—
120#11758198—42no—
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61—21no—
124C4⋊Dic61—21no—
125C4⋊Dic61—42no—
126C4⋊Dic61—42no—
127#11758196—21no—
128#11758196—21no—
129C4×Dic61—21no—
130C4×Dic61—21no—
131C4×Dic61—41no—
132C4×Dic61—41no—
133C4×Dic61—42no—
134#11758194—42no—
135C2×#92418—22no—
136C8×D61—82no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61C2×C22⋊C411yescharacteristic
142C23×C61#12111yescharacteristic
143C23×C61#12111yescharacteristic
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—41no—
147C22×D61—41no—
148C22×D61#10412yes—
149C2×C4×C61—22no—
150C2×C4×C61—22no—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—42no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—81no—
163C2×C4×C61—81no—
164C2×C4×C61C4×D411yescharacteristic
165C2×C4×C61C4×D411yescharacteristic
166C2×C4×C61#12011yescharacteristic
167C2×C4×C61#12311yescharacteristic
168C22⋊D61—42no—
169C22⋊D61—42no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—42no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—81no—
185C2×Dic61—81no—
186C4×D61—42no—
187C4×D61—81no—
188C8×C61—42no—
189#92418—42no—
190#9011—611nomaximal, Sylow
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—81no—
200C22×C61—81no—
201C22×C61#38611yescharacteristic
202C22×C61C2×#10411yescharacteristic
203C22×C61#42111yescharacteristic
204C2×D61—22no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—42no—
208C2×D61—81no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—42no—
213C4×C61—81no—
214C4×C61—82no—
215C4×C61#45812yes—
216Dic61—41no—
217Dic61—41no—
218Dic61—41no—
219Dic61—82no—
220Dic61—81no—
221Dic61—81no—
222#2973—611no—
223#2395—611no—
224#1826—611no—
225#1826—611no—
226C4×#99—611no—
227#1297—611no—
228#1297D6111yescharacteristic, complemented
229C2×C61—21no—
230C2×C61—21no—
231C2×C61—41no—
232C2×C61—41no—
233C2×C61#187111yescharacteristic
234C2×C61#188411yescharacteristic
235C2×C61#189011yescharacteristic
236D61—42no—
237C2×C4×D4—611no—
238C2×#117—611no—
239#435—1222no—
240#435—1222no—
241#432—1221no—
242C2×#99—1221no—
243#407—611no—
244#407C2×D6111yescharacteristic
245C2×C22⋊C8—1221no—
246#400—611no—
247#399—611no—
248#398—611no—
249#397—611no—
250#397—1221no—
251#394—1221no—
252C4×C4⋊C4—1221no—
253C4×C22⋊C4—611no—
254C4×C22⋊C4—1221no—
255C4×C22⋊C4C2×D6111yescharacteristic
256C4×C22⋊C4C2×D6111yescharacteristic
257#342—1221no—
258#339—1222no—
259#339—1222no—
260C61#901111yescharacteristic, complemented, Sylow
261C22×D4—611no—
262C23×C4—611no—
263C23×C4C22×D6111yescharacteristic
264C2×M16—612no—
265C2×M16D24412yes—
266C22×C8—1222no—
267C4×D4—1221no—
268C4×D4—1221no—
269C4×D4—1221no—
270C4×D4—1221no—
271#117—1221no—
272#117—1221no—
273#117—1221no—
274#117—1221no—
275C2×C4⋊C4—611no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4—1221no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—611no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—1221no—
285C2×C22⋊C4—1221no—
286C2×C22⋊C4—1221no—
287C2×C22⋊C4—1221no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—611no—
291C2×C42—1221no—
292C2×C42—1221no—
293C4⋊C8—1222no—
294#99—1224no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—1222no—
298C22⋊C8—1221no—
299C22⋊C8—1221no—
300#97—1222no—
301#95—21no—
302#95—1221no—
303#95—1221no—
304#95—1221no—
305#95—1221no—
306#95—1221no—
307#95C4×D6111yescharacteristic
308#95C4×D6111yescharacteristic
309C24—611no—
310C24D4×D6111yescharacteristic
311C2×D4—1222no—
312C2×D4—1221no—
313C2×D4—1221no—
314C2×D4—2441no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—42no—
318C22×C4—41no—
319C22×C4—611no—
320C22×C4—611no—
321C22×C4—611no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—2442no—
327C22×C4—2441no—
328C22×C4C2×C4×D6111yescharacteristic
329C22×C4C2×D24411yescharacteristic
330C22×C4#1175822211yescharacteristic
331C22×C4D4×D6111yescharacteristic
332C22×C4D4×D6111yescharacteristic
333C22×C4#1175822611yescharacteristic
334M16—42no—
335M16—2442no—
336C2×C8—22no—
337C2×C8—1222no—
338C2×C8—4882no—
339C4⋊C4—1221no—
340C4⋊C4—1221no—
341C4⋊C4—1221no—
342C4⋊C4—1221no—
343C4⋊C4—1221no—
344C4⋊C4—1221no—
345C4⋊C4—2442no—
346C4⋊C4—2442no—
347C22⋊C4—22no—
348C22⋊C4—42no—
349C22⋊C4—41no—
350C22⋊C4—1221no—
351C22⋊C4—1221no—
352C22⋊C4—1221no—
353C22⋊C4—1221no—
354C22⋊C4—1222no—
355C22⋊C4—2442no—
356C22⋊C4—2442no—
357C22⋊C4—2441no—
358C22⋊C4—2441no—
359C22⋊C4—2441no—
360C42—42no—
361C42—42no—
362C42—1221no—
363C42—1221no—
364C42—2442no—
365C42—2441no—
366C42—2441no—
367C23—21no—
368C23—21no—
369C23—41no—
370C23—41no—
371C23—612no—
372C23—1221no—
373C23—1221no—
374C23—2441no—
375C23—2441no—
376C23C22⋊C4×D6111yescharacteristic
377C23#1451975011yescharacteristic
378C23#1451975211yescharacteristic
379D4—2442no—
380D4—2442no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—4881no—
402C2×C4—4881no—
403C2×C4—4881no—
404C2×C4—2442no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2442no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4#1451973911yescharacteristic
415C2×C4C4×D24411yescharacteristic
416C2×C4#1451974711yescharacteristic
417C2×C4#1451976211yescharacteristic
418C8—42no—
419C8—2442no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—81no—
429C22—81no—
430C22—1222no—
431C22—4881no—
432C22—2442no—
433C22—2441no—
434C22—2441no—
435C22#1683964011yescharacteristic
436C22#104×D6111yescharacteristic
437C22#1683977711yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—42no—
442C4—81no—
443C4—82no—
444C4—4882no—
445C4—4881no—
446C4—4881no—
447C4—2441no—
448C4—2441no—
449C4—2441no—
450C4#1683995312yes—
451C2—21no—
452C2—21no—
453C2—41no—
454C2—41no—
455C2—2442no—
456C2#2144612011yescharacteristic
457C2#2144620111yescharacteristic
458C2#2144623111yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1297C2
socleC22×C61#386
prime radicalC22×C22⋊D61D4
cosocleC23×C4×C61C23
hypercenter#1297D61
hypocenterC61#9011
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
3. #21445919C2semidirect
4. #21445916C2semidirect
6. #21443705C2semidirect
7. C61×#1297C2semidirect
16. #16839702C4semidirect
17. #16839699C4semidirect
18. #16839694C4semidirect
19. #16839689C4semidirect
228. #1297D61semidirect
260. C61#9011semidirect

Maximal subgroups

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

subgroupindex
#214548462
#214490792
#214459192
#214459162
C4×#145196912
#214437052
C61×#12972
#901161