Finite Group Databasebeta

← #29575128

Subgroups — #29575128

Order 15616.

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

normal subgroups only

This group has 468 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#21455734C211yesmaximal, characteristic
2#21454864C211yesmaximal, characteristic
3#21445919C211yesmaximal, characteristic, complemented
4#21445888C211yesmaximal, characteristic, complemented
5#21444308C211yesmaximal, characteristic
6#21443707C211yesmaximal, characteristic, complemented
7C61×#1282C211yesmaximal, characteristic, complemented
8#16840273C2211yescharacteristic
9C2×#14519736C2211yescharacteristic
10#16840104—21no—
11#16840098C411yescharacteristic, complemented
12#16840093C411yescharacteristic, complemented
13#16840087—21no—
14#16840081C411yescharacteristic, complemented
15#16840076C411yescharacteristic, complemented
16#16839837—21no—
17#16839836—21no—
18#16839833—21no—
19C8×C22⋊D61—21no—
20#16839820—21no—
21#16839800—21no—
22#16839759—21no—
23#16839727—21no—
24#16839726C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26#16839522—21no—
27#16839522—21no—
28#16839516—21no—
29#16839516—21no—
30#16839498—21no—
31#16839495—21no—
32C2×C22⋊C8×C61C2211yescharacteristic
33C2×C22⋊C8×C61C2211yescharacteristic
34C4×C22⋊C4×C61C2211yescharacteristic
35C2×#11758222D411yescharacteristic
36C2×#11758194D411yescharacteristic
37C2×#11758194D411yescharacteristic
38C2×#11758189—21no—
39C22×#92418—21no—
40C2×C8×D61—21no—
41#14519760—21no—
42#14519756C2×C411yescharacteristic
43#14519756D411yescharacteristic
44#14519751C2×C411yescharacteristic
45#14519751D411yescharacteristic
46#14519746—21no—
47C4×C22⋊D61—21no—
48C4×C22⋊D61—21no—
49#14519736—21no—
50#14519736—21no—
51#14519736—21no—
52#14519736—21no—
53#14519736D411yescharacteristic
54C2×C4⋊Dic61C2×C411yescharacteristic
55C2×C4⋊Dic61C2×C411yescharacteristic
56C2×C22⋊Dic61—21no—
57C2×C4×Dic61—21no—
58#14519711—21no—
59#14519711—21no—
60#14519709—21no—
61#14519709—21no—
62#14519706—21no—
63#14519706—21no—
64#14519702—21no—
65#14519702—21no—
66#14519699—21no—
67#14519699—21no—
68C22⋊#92418—21no—
69C22⋊#92418—21no—
70C22⋊#92418—21no—
71C22⋊#92418—21no—
72#14519689—21no—
73#14519689—21no—
74#14519687—21no—
75C8×Dic61—21no—
76C23×C4×C61C2311yescharacteristic
77C22×C8×C61—21no—
78C22×C8×C61D411yescharacteristic
79C22×C8×C61D411yescharacteristic
80C2×C22⋊C4×C61—21no—
81C2×C42×C61—21no—
82C22⋊C8×C61—21no—
83C22⋊C8×C61—21no—
84C22⋊C8×C61—21no—
85C22⋊C8×C61C2×C411yescharacteristic
86C22⋊C8×C61C2×C411yescharacteristic
87#95×C61—21no—
88C24×C61#4111yescharacteristic
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61C22×C411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C2×C22⋊D61—21no—
99C2×C22⋊D61—21no—
100C2×C22⋊D61—21no—
101C22×Dic61—21no—
102C22×Dic61—21no—
103#11758222—41no—
104#11758222—41no—
105C2×D244C22⋊C411yescharacteristic
106C2×C4×D61—21no—
107C2×Dic122C22⋊C411yescharacteristic
108C2×C8×C61—21no—
109C2×C8×C61—21no—
110C2×C8×C61—21no—
111C2×C8×C61—21no—
112C2×C8×C61—41no—
113C2×C8×C61—41no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C22⋊C4×C61—22no—
117C22⋊C4×C61—41no—
118C42×C61—41no—
119C42×C61—41no—
120C22⋊Dic61—21no—
121C22⋊Dic61—21no—
122C22⋊Dic61—21no—
123C22⋊Dic61—41no—
124C22⋊Dic61—41no—
125#11758198—21no—
126#11758198—21no—
127C4⋊Dic61—21no—
128C4⋊Dic61—21no—
129C4⋊Dic61—21no—
130C4⋊Dic61—21no—
131C4⋊Dic61C22⋊C411yescharacteristic
132C4⋊Dic61C22⋊C411yescharacteristic
133#11758196—21no—
134#11758196—21no—
135C4×Dic61—21no—
136C4×Dic61—41no—
137C4×Dic61—41no—
138#11758194—41no—
139#11758194—41no—
140C2×#92418—21no—
141C2×#92418—21no—
142C2×#92418—41no—
143C2×#92418—41no—
144C2×#92418—41no—
145#11758189—81no—
146C8×D61—81no—
147C23×C61—21no—
148C23×C61—21no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61C4×D411yescharacteristic
152C23×C61#12111yescharacteristic
153C23×C61#12311yescharacteristic
154C22×D61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—42no—
165C2×C4×C61—81no—
166C2×C4×C61—81no—
167C2×C4×C61C2×C22⋊C411yescharacteristic
168C2×C4×C61C4×D411yescharacteristic
169C2×C4×C61#12011yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C22⋊D61—41no—
172C22⋊D61—41no—
173C22⋊D61—81no—
174C22⋊D61—81no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—42no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183D244—41no—
184C4×D61—41no—
185C4×D61—41no—
186Dic122—41no—
187C8×C61—41no—
188C8×C61—41no—
189C8×C61—41no—
190C8×C61—41no—
191#92418—41no—
192#92418—41no—
193#92418—81no—
194#9038—611nomaximal, Sylow
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—81no—
204C22×C61—81no—
205C22×C61#38611yescharacteristic
206C22×C61#44311yescharacteristic
207C22×C61#44411yescharacteristic
208C2×D61—41no—
209C2×D61—41no—
210C2×D61—41no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—82no—
215C4×C61#45811yescharacteristic
216C4×C61#45811yescharacteristic
217Dic61—41no—
218Dic61—41no—
219Dic61—41no—
220Dic61—81no—
221Dic61—81no—
222#3091—611no—
223#2976—611no—
224#1826—611no—
225#1818—611no—
226#1501—611no—
227#1298—611no—
228#1282D6111yescharacteristic, complemented
229C2×C61—21no—
230C2×C61—21no—
231C2×C61—41no—
232C2×C61—41no—
233C2×C61#187611yescharacteristic
234C2×C61#188111yescharacteristic
235C2×C61#189011yescharacteristic
236D61—81no—
237#525—611no—
238C2×#117—611no—
239#485—1221no—
240#484—611no—
241#483—611no—
242#482—1221no—
243#481—611no—
244#480—611no—
245#436—1221no—
246#435—1221no—
247#435—1221no—
248C8×D4—1221no—
249#433—1221no—
250#427—1221no—
251#416—1221no—
252#408—1221no—
253#407—611no—
254C2×C22⋊C8—611no—
255C2×C22⋊C8C2×D6111yescharacteristic
256C2×C22⋊C8C2×D6111yescharacteristic
257C4×C22⋊C4C2×D6111yescharacteristic
258#339—1221no—
259#339—1221no—
260#336—1221no—
261#336—1221no—
262#328—1221no—
263#327—1221no—
264C61#903811yescharacteristic, complemented, Sylow
265C2×#41—611no—
266C23×C4C22×D6111yescharacteristic
267C2×M16—611no—
268C2×M16—611no—
269C2×M16—1221no—
270C22×C8—21no—
271C22×C8—1221no—
272C22×C8—1221no—
273C22×C8D24411yescharacteristic
274C22×C8D24411yescharacteristic
275#123—1221no—
276C22⋊Q8—611no—
277C22⋊Q8—611no—
278#121—611no—
279#121—611no—
280#120—1221no—
281C4×D4—1221no—
282C4×D4—1221no—
283#117—611no—
284#117—1221no—
285#117—1221no—
286#117—1221no—
287#117—1221no—
288C2×C4⋊C4—611no—
289C2×C4⋊C4—611no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—1221no—
292C2×C42—21no—
293C2×C42—1221no—
294#107—1221no—
295#107—1221no—
296#106—1221no—
297#106—1221no—
298C4⋊C8—1221no—
299C4⋊C8—1221no—
300#103—1221no—
301#103—1221no—
302#102—1221no—
303#102—1221no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—1221no—
308C22⋊C8—1221no—
309C22⋊C8—1221no—
310C22⋊C8—1221no—
311C22⋊C8—1221no—
312C22⋊C8—1221no—
313C22⋊C8C4×D6111yescharacteristic
314C22⋊C8C4×D6111yescharacteristic
315#97—1221no—
316C4×C8—1221no—
317#95—21no—
318C24#1175822211yescharacteristic
319#41—2441no—
320#41—2441no—
321C2×Q8—611no—
322C2×D4—611no—
323C2×D4—1221no—
324C2×D4—1221no—
325C2×D4—1221no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4C2×C4×D6111yescharacteristic
333C22×C4C2×D24411yescharacteristic
334C22×C4D4×D6111yescharacteristic
335C22×C4D4×D6111yescharacteristic
336C22×C4D4×D6111yescharacteristic
337C22×C4#1175822611yescharacteristic
338M16—4881no—
339M16—2441no—
340M16—2441no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—1221no—
350C2×C8—1221no—
351C2×C8—4881no—
352C2×C8—2441no—
353C2×C8—2441no—
354C2×C8—2441no—
355C4⋊C4—611no—
356C4⋊C4—611no—
357C4⋊C4—1221no—
358C4⋊C4—1221no—
359C4⋊C4—1221no—
360C4⋊C4—1221no—
361C4⋊C4—1221no—
362C4⋊C4—1221no—
363C22⋊C4—22no—
364C22⋊C4—41no—
365C22⋊C4—1221no—
366C22⋊C4—1221no—
367C22⋊C4—1221no—
368C22⋊C4—1221no—
369C22⋊C4—1221no—
370C22⋊C4—2441no—
371C22⋊C4—2441no—
372C42—41no—
373C42—41no—
374C42—1221no—
375C42—2441no—
376C42—2441no—
377C23—21no—
378C23—21no—
379C23—41no—
380C23—41no—
381C23—1221no—
382C23C4×D24411yescharacteristic
383C23#1451975011yescharacteristic
384C23#1451976211yescharacteristic
385Q8—2441no—
386D4—4881no—
387D4—4881no—
388D4—2441no—
389D4—2441no—
390D4—2441no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—2442no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4C22⋊C4×D6111yescharacteristic
414C2×C4#1451973911yescharacteristic
415C2×C4#1451974711yescharacteristic
416C2×C4#1451975211yescharacteristic
417C8—41no—
418C8—41no—
419C8—41no—
420C8—41no—
421C8—4881no—
422C8—2441no—
423C8—2441no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—81no—
433C22—81no—
434C22—2441no—
435C22—2441no—
436C22—2441no—
437C22#1683964011yescharacteristic
438C22#1683988011yescharacteristic
439C22#1683988511yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—82no—
444C4—4881no—
445C4—4881no—
446C4—2441no—
447C4—2441no—
448C4—2441no—
449C4#1683995311yescharacteristic
450C4#1683995311yescharacteristic
451C2—21no—
452C2—21no—
453C2—41no—
454C2—41no—
455C2—4881no—
456C2#2144614511yescharacteristic
457C2#2144618011yescharacteristic
458C2#2144623111yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1282C2
socleC22×C61#386
prime radical#16840273C22
cosocleC23×C4×C61C23
hypercenter#1282D61
hypocenterC61#9038
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. #21445919C2semidirect
4. #21445888C2semidirect
6. #21443707C2semidirect
7. C61×#1282C2semidirect
11. #16840098C4semidirect
12. #16840093C4semidirect
14. #16840081C4semidirect
15. #16840076C4semidirect
228. #1282D61semidirect
264. C61#9038semidirect

Maximal subgroups

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

subgroupindex
#214557342
#214548642
#214459192
#214458882
#214443082
#214437072
C61×#12822
#903861