Finite Group Databasebeta

← #29574127

Subgroups — #29574127

Order 15616.

464 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 93 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#21454864C211yesmaximal, characteristic
2#21446119C211yesmaximal, characteristic
3#21446026C211yesmaximal, characteristic, complemented
4#21446001C211yesmaximal, characteristic, complemented
5#21444311C211yesmaximal, characteristic
6#21443705C211yesmaximal, characteristic, complemented
7C61×#1282C211yesmaximal, characteristic, complemented
8C22×#11758194C2211yescharacteristic
9#16840273C2211yescharacteristic
10#16839837—21no—
11#16839836—21no—
12#16839833—21no—
13C8×C22⋊D61—21no—
14#16839820—21no—
15C2×#14519713—21no—
16C2×#14519706—21no—
17C2×#14519705—21no—
18#16839727—21no—
19#16839726C2211yescharacteristic
20C4×C22⋊Dic61C2211yescharacteristic
21#16839527—21no—
22#16839522—21no—
23#16839516—21no—
24#16839500C411yescharacteristic, complemented
25#16839500C411yescharacteristic, complemented
26#16839497C411yescharacteristic, complemented
27#16839497C411yescharacteristic, complemented
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C4×C22⋊C4×C61C2211yescharacteristic
31C2×#11758222D411yescharacteristic
32C2×#11758194—21no—
33C2×#11758194—21no—
34C2×#11758194—42no—
35C2×#11758194D411yescharacteristic
36C2×#11758194D411yescharacteristic
37C2×#11758189—21no—
38C22×#92418—21no—
39C2×C8×D61—21no—
40#14519760—21no—
41#14519756C2×C411yescharacteristic
42#14519756Q811yescharacteristic
43#14519751C2×C411yescharacteristic
44#14519751Q811yescharacteristic
45#14519746—21no—
46C4×C22⋊D61—21no—
47C4×C22⋊D61—21no—
48#14519736D411yescharacteristic
49C2×C22⋊Dic61—21no—
50C2×C4×Dic61—21no—
51#14519713—42no—
52#14519706—21no—
53#14519706—21no—
54#14519706—42no—
55#14519705—42no—
56C22⋊#92418—21no—
57C22⋊#92418—21no—
58#14519689—21no—
59#14519689—21no—
60#14519687—21no—
61C8×Dic61—21no—
62#14519684C2×C411yescharacteristic
63#14519684C2×C411yescharacteristic
64C23×C4×C61C2311yescharacteristic
65C22×C8×C61—21no—
66C22×C8×C61D411yescharacteristic
67C22×C8×C61D411yescharacteristic
68C2×C22⋊C4×C61—21no—
69C2×C42×C61—21no—
70C22⋊C8×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73C22⋊C8×C61C2×C411yescharacteristic
74C22⋊C8×C61C2×C411yescharacteristic
75#95×C61—21no—
76C24×C61#4111yescharacteristic
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61C22×C411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×Q811yescharacteristic
85C22×C4×C61#4111yescharacteristic
86C2×C22⋊D61—21no—
87C2×C22⋊D61—21no—
88C2×C22⋊D61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91#11758222—41no—
92#11758222—41no—
93C2×D244C4⋊C411yescharacteristic
94C2×C4×D61—21no—
95C2×Dic122C4⋊C411yescharacteristic
96C2×C8×C61—21no—
97C2×C8×C61—21no—
98C2×C8×C61—21no—
99C2×C8×C61—21no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C2×C8×C61—41no—
104C22⋊C4×C61—22no—
105C22⋊C4×C61—41no—
106C42×C61—41no—
107C42×C61—41no—
108C22⋊Dic61—21no—
109C22⋊Dic61—21no—
110C22⋊Dic61—21no—
111C22⋊Dic61—42no—
112#11758198—21no—
113#11758198—21no—
114C4⋊Dic61C4⋊C411yescharacteristic
115C4⋊Dic61C4⋊C411yescharacteristic
116#11758196—21no—
117#11758196—21no—
118C4×Dic61—21no—
119C4×Dic61—41no—
120C4×Dic61—41no—
121#11758194—22no—
122#11758194—22no—
123#11758194—41no—
124#11758194—41no—
125#11758194—41no—
126#11758194—41no—
127C2×#92418—22no—
128C2×#92418—21no—
129C2×#92418—21no—
130C2×#92418—41no—
131C2×#92418—41no—
132#11758189—81no—
133C8×D61—81no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61C4×D411yescharacteristic
139C23×C61C22⋊Q811yescharacteristic
140C23×C61#12311yescharacteristic
141C22×D61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—42no—
152C2×C4×C61—81no—
153C2×C4×C61—81no—
154C2×C4×C61C2×C4⋊C411yescharacteristic
155C2×C4×C61C4×D411yescharacteristic
156C2×C4×C61#12011yescharacteristic
157C2×C4×C61C22⋊Q811yescharacteristic
158C22⋊D61—41no—
159C22⋊D61—41no—
160C22⋊D61—81no—
161C22⋊D61—81no—
162C2×Dic61—22no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171D244—41no—
172C4×D61—41no—
173C4×D61—41no—
174Dic122—41no—
175C8×C61—41no—
176C8×C61—41no—
177C8×C61—41no—
178C8×C61—41no—
179#92418—41no—
180#92418—42no—
181#92418—41no—
182#8875—611nomaximal, Sylow
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61#38511yescharacteristic
194C22×C61#44311yescharacteristic
195C22×C61#44411yescharacteristic
196C2×D61—41no—
197C2×D61—41no—
198C2×D61—41no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—82no—
203C4×C61B(4,𝔽2)11yescharacteristic
204C4×C61#45811yescharacteristic
205Dic61—42no—
206Dic61—41no—
207Dic61—41no—
208Dic61—41no—
209Dic61—81no—
210#2976—611no—
211#1871—611no—
212#1855—611no—
213#1851—611no—
214#1501—611no—
215#1297—611no—
216#1282D6111yescharacteristic, complemented
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—41no—
220C2×C61—41no—
221C2×C61#186111yescharacteristic
222C2×C61#186611yescharacteristic
223C2×C61#186711yescharacteristic
224D61—81no—
225C22×M16—611no—
226#525—611no—
227#436—1221no—
228#435—1221no—
229#435—1221no—
230C8×D4—1221no—
231#433—1221no—
232C2×#108—1221no—
233C2×C4⋊C8—1221no—
234C2×#104—1221no—
235#408—1221no—
236#407—611no—
237C2×C22⋊C8C2×D6111yescharacteristic
238C2×C22⋊C8C2×D6111yescharacteristic
239C4×C22⋊C4—611no—
240C4×C22⋊C4C2×D6111yescharacteristic
241#341—1221no—
242#339—1221no—
243#336—1221no—
244#328—611no—
245#328—611no—
246#327—611no—
247#327—611no—
248C61#887511yescharacteristic, complemented, Sylow
249C2×#41—611no—
250C23×C4C22×D6111yescharacteristic
251C2×M16—611no—
252C2×M16—611no—
253C2×M16—1221no—
254C2×M16—1221no—
255C2×M16—1221no—
256C2×M16—2442no—
257C22×C8—21no—
258C22×C8—1221no—
259C22×C8—1221no—
260C22×C8D24411yescharacteristic
261C22×C8D24411yescharacteristic
262#123—1221no—
263C22⋊Q8—611no—
264C22⋊Q8—611no—
265#121—611no—
266#121—611no—
267#120—1221no—
268C4×D4—1221no—
269C4×D4—1221no—
270#117—611no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—1221no—
273C2×C42—21no—
274C2×C42—1221no—
275#108—2442no—
276C4⋊C8—1221no—
277C4⋊C8—1221no—
278C4⋊C8—2442no—
279#104—2442no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—1221no—
284C22⋊C8—1221no—
285C22⋊C8—1221no—
286C22⋊C8—1221no—
287C22⋊C8C4×D6111yescharacteristic
288C22⋊C8C4×D6111yescharacteristic
289#97—1221no—
290C4×C8—1221no—
291#95—21no—
292#95—611no—
293#95—611no—
294C24#1175822211yescharacteristic
295#41—2441no—
296#41—2441no—
297C2×Q8—611no—
298C2×D4—611no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4—1221no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4C2×C4×D6111yescharacteristic
309C22×C4C2×D24411yescharacteristic
310C22×C4D4×D6111yescharacteristic
311C22×C4D4×D6111yescharacteristic
312C22×C4#1175822411yescharacteristic
313C22×C4Q8×D6111yescharacteristic
314M16—1222no—
315M16—1222no—
316M16—4881no—
317M16—2441no—
318M16—2441no—
319M16—2441no—
320M16—2441no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—1222no—
330C2×C8—1221no—
331C2×C8—1221no—
332C2×C8—4881no—
333C2×C8—2441no—
334C2×C8—2441no—
335C4⋊C4—611no—
336C4⋊C4—611no—
337C4⋊C4—1221no—
338C4⋊C4—1221no—
339C22⋊C4—22no—
340C22⋊C4—41no—
341C22⋊C4—1221no—
342C22⋊C4—1221no—
343C22⋊C4—1221no—
344C22⋊C4—1221no—
345C22⋊C4—1221no—
346C22⋊C4—2442no—
347C42—41no—
348C42—41no—
349C42—1221no—
350C42—2441no—
351C42—2441no—
352C23—21no—
353C23—21no—
354C23—41no—
355C23—41no—
356C23—1221no—
357C23C4×D24411yescharacteristic
358C23#1451975511yescharacteristic
359C23#1451975911yescharacteristic
360Q8—2441no—
361D4—4881no—
362D4—4881no—
363D4—2441no—
364D4—2441no—
365D4—2441no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—1222no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4C4⋊C4×D6111yescharacteristic
390C2×C4#1451973711yescharacteristic
391C2×C4#1451974711yescharacteristic
392C2×C4#1451975711yescharacteristic
393C8—41no—
394C8—41no—
395C8—41no—
396C8—41no—
397C8—2442no—
398C8—2441no—
399C8—2441no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—81no—
409C22—81no—
410C22—2441no—
411C22—2441no—
412C22—2441no—
413C22#1683963611yescharacteristic
414C22#1683988011yescharacteristic
415C22#1683988511yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—82no—
420C4—4881no—
421C4—2442no—
422C4—2441no—
423C4—2441no—
424C4—2441no—
425C4#1683995011yescharacteristic
426C4#1683995311yescharacteristic
427C2—21no—
428C2—21no—
429C2—41no—
430C2—41no—
431C2—4881no—
432C2#2144606211yescharacteristic
433C2#2144609711yescharacteristic
434C2#2144610111yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1282C2
socleC22×C61#385
prime radical#16840273C22
cosocleC23×C4×C61C23
hypercenter#1282D61
hypocenterC61#8875
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
3. #21446026C2semidirect
4. #21446001C2semidirect
6. #21443705C2semidirect
7. C61×#1282C2semidirect
24. #16839500C4semidirect
25. #16839500C4semidirect
26. #16839497C4semidirect
27. #16839497C4semidirect
216. #1282D61semidirect
248. C61#8875semidirect

Maximal subgroups

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

subgroupindex
#214548642
#214461192
#214460262
#214460012
#214443112
#214437052
C61×#12822
#887561