Finite Group Databasebeta

← #29575090

Subgroups — #29575090

Order 15616.

670 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 103 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#21454848C211yesmaximal, characteristic, complemented
2#21449098C211yesmaximal, characteristic
3#21444263C212yesmaximal, complemented
4#21443713C212yesmaximal, complemented
5C4×#100×C61C211yesmaximal, characteristic, complemented
6C2×C4×D244C2211yescharacteristic
7C2×C4×C22⋊D61—21no—
8C2×C4×C22⋊D61—21no—
9#16839834—24no—
10#16839819C2212yes—
11#16839726—21no—
12C2×C22⋊#92418—21no—
13#16839698C411yescharacteristic
14#16839698C411yescharacteristic
15#16839697—21no—
16#16839671C411yescharacteristic
17#16839671C411yescharacteristic
18#16839670—21no—
19#16839608C2211yescharacteristic
20#16839491—24no—
21C2×C4×D4×C61C2211yescharacteristic
22C2×#100×C61—21no—
23C4×M16×C61C2212yes—
24C61×#343—21no—
25C22×D244C2×C411yescharacteristic
26C22×C22⋊D61—21no—
27C22×C22⋊D61—21no—
28C22×C4×D61—21no—
29C2×#11758194—22no—
30C22×#92418—22no—
31C4×D244—22no—
32C4×D244—22no—
33C4×C22⋊D61—44no—
34C4×C22⋊D61—44no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×C4×Dic61—21no—
44C4⋊#92418D414yescomplemented
45C22⋊#92418—22no—
46C22⋊#92418—22no—
47C22⋊#92418—22no—
48#14519688—22no—
49#14519684—21no—
50#14519684C2×C411yescharacteristic
51#14519684C2×C411yescharacteristic
52C22×D4×C61D411yescharacteristic
53C23×C4×C61D411yescharacteristic
54C23×C4×C61D411yescharacteristic
55C2×M16×C61—22no—
56C4×D4×C61—22no—
57C4×D4×C61—22no—
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C22⋊C4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61C2×C411yescharacteristic
61C2×C42×C61C2311yescharacteristic
62#100×C61—24no—
63#97×C61—22no—
64C4×C8×C61—22no—
65C24×C61C22⋊C411yescharacteristic
66C24×C61C22⋊C411yescharacteristic
67C23×D61—21no—
68C2×D4×C61—22no—
69C2×D4×C61—22no—
70C2×D4×C61—41no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—42no—
76C22×C4×C61—42no—
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61C22×C411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C2×C22⋊D61—42no—
83C2×C22⋊D61—42no—
84C2×C22⋊D61—42no—
85C2×C22⋊D61—42no—
86C2×C22⋊D61—42no—
87C2×C22⋊D61—42no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C2×D244—22no—
92C2×D244—42no—
93C2×C4×D61—42no—
94C2×C4×D61—42no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97M16×C61—24no—
98M16×C61—42no—
99C2×C8×C61—42no—
100C4⋊C4×C61—22no—
101C22⋊C4×C61—22no—
102C22⋊C4×C61—22no—
103C42×C61C2×D412yes—
104C42×C61#4112yes—
105C22⋊Dic61—42no—
106C22⋊Dic61—42no—
107#11758198—42no—
108#11758198—42no—
109#11758198—42no—
110C4⋊Dic61—22no—
111#11758196—42no—
112#11758196—42no—
113C4×Dic61—24no—
114#11758194—82no—
115C2×#92418—24no—
116C2×#92418—82no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61#10412yes—
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—
135D4×C61—44no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—22no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—41no—
142C2×C4×C61—42no—
143C2×C4×C61—42no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—81no—
147C2×C4×C61—81no—
148C2×C4×C61C4×D412yes—
149C2×C4×C61#12011yescharacteristic
150C2×C4×C61#12112yes—
151C2×C4×C61#12311yescharacteristic
152C22⋊D61—48no—
153C22⋊D61—48no—
154C2×Dic61—22no—
155C2×Dic61—22no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163D244—24no—
164D244—42no—
165C4×D61—82no—
166C4×D61—82no—
167C8×C61—44no—
168#92418—44no—
169#9031—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—22no—
173C22×C61—42no—
174C22×C61—42no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61#38611yescharacteristic
183C22×C61C2×#10411yescharacteristic
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—22no—
193C4×C61—21no—
194C4×C61—22no—
195C4×C61—41no—
196C4×C61—41no—
197C4×C61#45312yes—
198Dic61—42no—
199Dic61—42no—
200Dic61—81no—
201#2973—611no—
202#2397—611no—
203C4×#100D6111yescharacteristic, complemented
204#1490—612no—
205#1300—612no—
206C2×C61—21no—
207C2×C61—21no—
208C2×C61—42no—
209C2×C61—81no—
210C2×C61#187111yescharacteristic
211C2×C61#188711yescharacteristic
212C2×C61#189111yescharacteristic
213D61—82no—
214C2×C4×D4—611no—
215C2×C4×D4—1221no—
216C2×C4×D4—1221no—
217C2×C4×D4C2×D6111yescharacteristic
218#435—1224no—
219#432—612no—
220C2×#100—21no—
221#407—1221no—
222C2×C22⋊C8—1221no—
223C4×M16C2×D6112yes—
224#399—611no—
225#399—611no—
226#399—1221no—
227#392—611no—
228#392—611no—
229#392—1221no—
230#376—611no—
231#343—21no—
232D4⋊C8—1224no—
233C61#903111yescharacteristic, complemented, Sylow
234C22×D4—611no—
235C22×D4—1221no—
236C22×D4—1221no—
237C22×D4C22⋊D6111yescharacteristic
238C23×C4—1221no—
239C23×C4D24411yescharacteristic
240C23×C4D24411yescharacteristic
241C2×M16—22no—
242C2×M16—1222no—
243C22×C8—1222no—
244C4×D4—22no—
245C4×D4—22no—
246C4×D4—1222no—
247C4×D4—1222no—
248C4×D4—2444no—
249C4×D4—2444no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4C22⋊D6111yescharacteristic
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C22⋊C4C4×D6111yescharacteristic
260C2×C22⋊C4C4×D6111yescharacteristic
261C2×C42—1221no—
262C2×C42C22×D6111yescharacteristic
263C4⋊C8—614no—
264#100—24no—
265C22⋊C8—1222no—
266C22⋊C8—1222no—
267C22⋊C8—1222no—
268#97—22no—
269#97—1222no—
270C4×C8—22no—
271#95—611no—
272#95—611no—
273#95—1221no—
274C24—1221no—
275C24#1175819811yescharacteristic
276C24#1175819811yescharacteristic
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—41no—
280C2×D4—1222no—
281C2×D4—2442no—
282C2×D4—2442no—
283C2×D4—2442no—
284C2×D4—2442no—
285C2×D4—2442no—
286C2×D4—2442no—
287C2×D4—2442no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—2442no—
298C22×C4—2442no—
299C22×C4—2441no—
300C22×C4—2441no—
301C22×C4#1175819811yescharacteristic
302C22×C4#1175819811yescharacteristic
303C22×C4C2×C4×D6111yescharacteristic
304C22×C4C2×D24411yescharacteristic
305C22×C4C2×C22⋊D6111yescharacteristic
306M16—24no—
307M16—42no—
308M16—4882no—
309C2×C8—42no—
310C2×C8—1224no—
311C2×C8—4882no—
312C4⋊C4—22no—
313C4⋊C4—1222no—
314C4⋊C4—2442no—
315C4⋊C4—2442no—
316C22⋊C4—22no—
317C22⋊C4—22no—
318C22⋊C4—2442no—
319C22⋊C4—2442no—
320C22⋊C4—2442no—
321C22⋊C4—2442no—
322C22⋊C4—2442no—
323C42—1224no—
324C42D4×D6112yes—
325C42#1175822412yes—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—1222no—
336C23—2441no—
337C23—2441no—
338C23—2441no—
339C23—2441no—
340C23—2441no—
341C23—2441no—
342C23#1451970512yes—
343C23C2×#1175819811yescharacteristic
344D4—44no—
345D4—1224no—
346D4—2442no—
347D4—2448no—
348D4—2448no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—1222no—
362C2×C4—1222no—
363C2×C4—4882no—
364C2×C4—4882no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4#1451973712yes—
373C2×C4#1451974711yescharacteristic
374C2×C4#1451974912yes—
375C2×C4#1451976111yescharacteristic
376C8—44no—
377C8—2444no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22—42no—
382C22—42no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—81no—
389C22—81no—
390C22—4881no—
391C22—4881no—
392C22—4881no—
393C22—4881no—
394C22—2442no—
395C22—2442no—
396C22—2442no—
397C22#1683963911yescharacteristic
398C22C2×#1451970511yescharacteristic
399C22#1683978011yescharacteristic
400C4—21no—
401C4—22no—
402C4—22no—
403C4—41no—
404C4—41no—
405C4—4881no—
406C4—2442no—
407C4—2442no—
408C4#1683993212yes—
409C2—21no—
410C2—21no—
411C2—42no—
412C2—81no—
413C2—4882no—
414C2#2144611911yescharacteristic
415C2#2144621511yescharacteristic
416C2#2144623511yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC4×#100×C61C2
socleC22×C61#386
prime radical#21449098C2
cosocleC2×C42×C61C23
hypercenterC4×#100D61
hypocenterC61#9031
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
1. #21454848C2semidirect
3. #21444263C2semidirect
4. #21443713C2semidirect
5. C4×#100×C61C2semidirect
44. C4⋊#92418D4semidirect
203. C4×#100D61semidirect
233. C61#9031semidirect

Maximal subgroups

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

subgroupindex
#214548482
#214490982
#214442632
#214437132
C4×#100×C612
#903161