Finite Group Databasebeta

← #29573545

Subgroups — #29573545

Order 15616.

546 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 87 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#21448432C211yesmaximal, characteristic
2#21444145C211yesmaximal, characteristic
3#21444145C211yesmaximal, characteristic
4#21443726C211yesmaximal, characteristic, complemented
5#21443725C211yesmaximal, characteristic, complemented
6#21443724C211yesmaximal, characteristic, complemented
7C61×#1305C211yesmaximal, characteristic, complemented
8C22×#11758198C2211yescharacteristic
9C2×C22⋊C4×D61C411yescharacteristic
10C2×C22⋊C4×D61C411yescharacteristic
11#16839726C2211yescharacteristic
12#16839726C2211yescharacteristic
13#16839636—21no—
14#16839636—21no—
15#16839633—21no—
16#16839633—21no—
17#16839622C2211yescharacteristic
18#16839620C411yescharacteristic
19#16839620C411yescharacteristic
20#16839485—21no—
21#16839485—21no—
22#16839485—21no—
23#16839485—21no—
24C61×#407C2211yescharacteristic
25C61×#407C2211yescharacteristic
26C61×#380C2211yescharacteristic
27C24×D61C2×C411yescharacteristic
28C23×Dic61C2×C411yescharacteristic
29C22×C4×D61—21no—
30C22×C4×D61—21no—
31C2×#11758194—21no—
32C2×#11758194—21no—
33C2×C4⋊Dic61—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×C22⋊Dic61C2×C411yescharacteristic
37C2×C22⋊Dic61C2×C411yescharacteristic
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198D411yescharacteristic
45C2×#11758198D411yescharacteristic
46C2×#11758198D411yescharacteristic
47C2×#11758198D411yescharacteristic
48C22⋊C4×D61—42no—
49C22⋊C4×D61—42no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C23×C4×C61C2311yescharacteristic
58C2×M16×C61—21no—
59C2×M16×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C22⋊C4×C61C2×C411yescharacteristic
62C2×C22⋊C4×C61C2×C411yescharacteristic
63C22⋊C8×C61—21no—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66C22⋊C8×C61—21no—
67#95×C61—21no—
68C24×C61C22×C411yescharacteristic
69C23×D61—21no—
70C23×D61—21no—
71C23×D61—22no—
72C23×D61—22no—
73C23×D61—81no—
74C23×D61—81no—
75C23×D61C22⋊C411yescharacteristic
76C23×D61C22⋊C411yescharacteristic
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—81no—
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C22×C4×C61#4111yescharacteristic
84C22×C4×C61#4111yescharacteristic
85C22×C4×C61#4111yescharacteristic
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—81no—
91C22×Dic61C22⋊C411yescharacteristic
92C22×Dic61C22⋊C411yescharacteristic
93C2×C4×D61—42no—
94C2×C4×D61—42no—
95C2×C4×D61—81no—
96C2×C4×D61—81no—
97C2×C4×D61—81no—
98C2×C4×D61—81no—
99M16×C61—81no—
100M16×C61—81no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C4⋊C4×C61—81no—
104C22⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C22⋊Dic61—41no—
107C22⋊Dic61—41no—
108#11758198—21no—
109#11758198—21no—
110#11758198—21no—
111#11758198—21no—
112#11758198—21no—
113#11758198—21no—
114#11758198—21no—
115#11758198—21no—
116#11758198—42no—
117#11758198—42no—
118C4⋊Dic61—81no—
119#11758196—81no—
120#11758196—81no—
121#11758194—81no—
122#11758194—81no—
123C2×#92418—41no—
124C2×#92418—41no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61C2×C22⋊C411yescharacteristic
130C23×C61#11711yescharacteristic
131C23×C61#11711yescharacteristic
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—24no—
137C22×D61—24no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—81no—
143C22×D61—81no—
144C22×D61—81no—
145C22×D61—81no—
146C22×D61—84no—
147C22×D61—84no—
148C22×D61#10012yes—
149C22×D61#10112yes—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
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—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61#12311yescharacteristic
163C2×C4×C61#12311yescharacteristic
164C2×C4×C61#12311yescharacteristic
165C2×C4×C61#12311yescharacteristic
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—81no—
177C2×Dic61—81no—
178C4×D61—84no—
179C4×D61—84no—
180C8×C61—81no—
181C8×C61—81no—
182#92418—81no—
183#92418—81no—
184#8756—611nomaximal, Sylow
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—42no—
194C22×C61—42no—
195C22×C61#38111yescharacteristic
196C22×C61C2×#10011yescharacteristic
197C22×C61C2×#10111yescharacteristic
198C2×D61—22no—
199C2×D61—22no—
200C2×D61—42no—
201C2×D61—42no—
202C2×D61—41no—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—41no—
206C2×D61—42no—
207C2×D61—42no—
208C2×D61—84no—
209C2×D61—84no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—81no—
215C4×C61—81no—
216Dic61—41no—
217Dic61—41no—
218Dic61—81no—
219Dic61—81no—
220#2315—611no—
221#1462—611no—
222#1462—611no—
223#1305—611no—
224#1305—611no—
225#1305—611no—
226#1305D6111yescharacteristic, complemented
227C2×C61—21no—
228C2×C61—21no—
229C2×C61—41no—
230C2×C61—41no—
231C2×C61#182111yescharacteristic
232C2×C61#182811yescharacteristic
233C2×C61#182911yescharacteristic
234D61—42no—
235D61—42no—
236C22×C22⋊C4—611no—
237C22×C22⋊C4—611no—
238C22×C22⋊C4—611no—
239#407—611no—
240#407—611no—
241#407C2×D6111yescharacteristic
242#407C2×D6111yescharacteristic
243#385—1221no—
244#385—1221no—
245#385—1221no—
246#385—1221no—
247#380—611no—
248#380—611no—
249#380—611no—
250#380C2×D6111yescharacteristic
251#323—1221no—
252#323—1221no—
253#323—1221no—
254#323—1221no—
255C61#875611yescharacteristic, complemented, Sylow
256C25—611no—
257C23×C4—611no—
258C23×C4—1221no—
259C23×C4—1221no—
260C23×C4C22×D6111yescharacteristic
261C2×M16—21no—
262C2×M16—21no—
263C2×M16—1221no—
264C2×M16—1221no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—1221no—
267C2×C4⋊C4—1221no—
268C2×C4⋊C4—1221no—
269C2×C22⋊C4—611no—
270C2×C22⋊C4—611no—
271C2×C22⋊C4—611no—
272C2×C22⋊C4—611no—
273C2×C22⋊C4—611no—
274C2×C22⋊C4—611no—
275C2×C22⋊C4—1221no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280C2×C22⋊C4—1221no—
281C2×C22⋊C4—2442no—
282C2×C22⋊C4—2442no—
283C2×C22⋊C4C4×D6111yescharacteristic
284C2×C22⋊C4C4×D6111yescharacteristic
285C22⋊C8—21no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—1221no—
290C22⋊C8—1221no—
291C22⋊C8—1221no—
292C22⋊C8—1221no—
293#95—21no—
294#95—1221no—
295#95—1221no—
296#95—1221no—
297C24—611no—
298C24—611no—
299C24—1222no—
300C24—1222no—
301C24—1221no—
302C24—1221no—
303C24—4881no—
304C24—4881no—
305C24C2×C4×D6111yescharacteristic
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—81no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—4881no—
316C22×C4—4881no—
317C22×C4—4881no—
318C22×C4—4881no—
319C22×C4—4881no—
320C22×C4—2442no—
321C22×C4—2442no—
322C22×C4#1175822211yescharacteristic
323C22×C4#1175822211yescharacteristic
324C22×C4D4×D6111yescharacteristic
325C22×C4D4×D6111yescharacteristic
326C22×C4#1175822411yescharacteristic
327C22×C4#1175822611yescharacteristic
328M16—81no—
329M16—81no—
330M16—4881no—
331M16—4881no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—2441no—
335C2×C8—2441no—
336C4⋊C4—81no—
337C4⋊C4—4881no—
338C4⋊C4—4881no—
339C4⋊C4—4881no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—1221no—
343C22⋊C4—1221no—
344C22⋊C4—1221no—
345C22⋊C4—1221no—
346C22⋊C4—1221no—
347C22⋊C4—1221no—
348C22⋊C4—1221no—
349C22⋊C4—1221no—
350C22⋊C4—2442no—
351C22⋊C4—2442no—
352C22⋊C4—2441no—
353C22⋊C4—2441no—
354C23—21no—
355C23—21no—
356C23—41no—
357C23—41no—
358C23—612no—
359C23—612no—
360C23—1224no—
361C23—1224no—
362C23—1221no—
363C23—1221no—
364C23—1221no—
365C23—1221no—
366C23—4881no—
367C23—4881no—
368C23—4881no—
369C23—4881no—
370C23—4884no—
371C23—4884no—
372C23—2441no—
373C23—2441no—
374C23—2441no—
375C23—2441no—
376C23C22⋊C4×D6111yescharacteristic
377C23#1451973411yescharacteristic
378C23#1451973511yescharacteristic
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—4884no—
394C2×C4—4884no—
395C2×C4—4881no—
396C2×C4—4881no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4#1451975911yescharacteristic
406C2×C4#1451975911yescharacteristic
407C2×C4#1451976211yescharacteristic
408C2×C4#1451976211yescharacteristic
409C8—81no—
410C8—81no—
411C8—4881no—
412C8—4881no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—42no—
422C22—42no—
423C22—1222no—
424C22—1222no—
425C22—4884no—
426C22—4884no—
427C22—2442no—
428C22—2442no—
429C22—2442no—
430C22—2442no—
431C22—2441no—
432C22—2441no—
433C22—2441no—
434C22—2441no—
435C22#1683962411yescharacteristic
436C22#100×D6111yescharacteristic
437C22#101×D6111yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—81no—
443C4—81no—
444C4—4881no—
445C4—4881no—
446C4—2441no—
447C4—2441no—
448C2—21no—
449C2—21no—
450C2—41no—
451C2—41no—
452C2—2442no—
453C2—2442no—
454C2#2144589811yescharacteristic
455C2#2144592611yescharacteristic
456C2#2144592911yescharacteristic
subgroupG/H
centerC22#16839624
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1305C2
socleC22×C61#381
prime radicalC24×D61C2×C4
cosocleC23×C4×C61C23
hypercenter#1305D61
hypocenterC61#8756
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
4. #21443726C2semidirect
5. #21443725C2semidirect
6. #21443724C2semidirect
7. C61×#1305C2semidirect
226. #1305D61semidirect
255. C61#8756semidirect

Maximal subgroups

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

subgroupindex
#214484322
#214441452
#214437262
#214437252
#214437242
C61×#13052
#875661