Finite Group Databasebeta

← #30600889

Subgroups — #30600889

Order 15616.

444 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 78 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#21462513C211yesmaximal, characteristic
2#21461724C211yesmaximal, characteristic
3#21461259C211yesmaximal, characteristic
4#21461099C211yesmaximal, characteristic
5#21460719C211yesmaximal, characteristic
6#21460701C211yesmaximal, characteristic
7#21455765C211yesmaximal, characteristic
8#16840786—22no—
9#16840785—21no—
10#16840781—21no—
11#16840769—21no—
12#16840733C2211yescharacteristic
13D61⋊(C22⋊C8)C2211yescharacteristic
14D61⋊(C22⋊C8)C2211yescharacteristic
15#16840727—21no—
16#16840704C2211yescharacteristic
17#16840635—21no—
18#16840635—21no—
19#16840616—21no—
20#16840616—21no—
21#16840608—22no—
22C2×#14519753C2211yescharacteristic
23#117×D61C2211yescharacteristic
24#16840102—21no—
25#16840101—21no—
26#16840096—21no—
27#16840091—21no—
28#16839805C411yescharacteristic, complemented
29#16839804C411yescharacteristic, complemented
30#16839771C411yescharacteristic, complemented
31#16839725C2211yescharacteristic
32C61×#419C411yescharacteristic, complemented
33C2×#11758213—21no—
34C2×D61⋊C8—21no—
35C2×D61⋊C8—21no—
36C2×C4⋊#6923—21no—
37C2×C22⋊#6923—21no—
38#14519844—22no—
39C4⋊#92420—22no—
40#14519834—21no—
41#14519834—21no—
42#14519834D411yescharacteristic
43#14519834D411yescharacteristic
44C22⋊#92420—21no—
45C22⋊#92420—21no—
46C22⋊#92420D412yes—
47#14519832—22no—
48C4×#92420—22no—
49(C2×#6923)⋊C4—21no—
50C22×C4×D61C2311yescharacteristic
51C2×#11758194C2×C411yescharacteristic
52#14519753—21no—
53#14519753—21no—
54#14519753—21no—
55#14519753—21no—
56#14519736C2×C411yescharacteristic
57#14519735D411yescharacteristic
58#14519735D411yescharacteristic
59#14519734—21no—
60#14519733—21no—
61C2×C4⋊Dic61C2×C411yescharacteristic
62C2×#11758196—21no—
63C4⋊C4×D61D411yescharacteristic
64C4⋊C4×D61D411yescharacteristic
65C2×#11758198—21no—
66C22⋊C4×D61—21no—
67C42×D61—21no—
68#14519711—21no—
69#14519710—21no—
70#14519709—21no—
71#14519708—21no—
72#14519701—21no—
73#14519701—21no—
74#14519689—21no—
75#14519689—21no—
76C22×Q8×C61C2×C411yescharacteristic
77C2×M16×C61C2×C411yescharacteristic
78#117×C61C2×C411yescharacteristic
79#103×C61—21no—
80#103×C61—21no—
81C23×D61#4111yescharacteristic
82C22×#6923—41no—
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61—41no—
86C2×Q8×C61—41no—
87C22×C4×C61—21no—
88C22×C4×C61C22×C411yescharacteristic
89C22×Dic61—21no—
90C22×Dic61C2×D411yescharacteristic
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C4×D61C2×D411yescharacteristic
96C2×C4×D61C2×D411yescharacteristic
97C2×C4×D61C2×D411yescharacteristic
98C2×C4×D61#4111yescharacteristic
99C22⋊#6923—81no—
100C2×#92420—21no—
101C2×#92420—22no—
102C2×#92420—21no—
103C2×#92420—41no—
104C4⋊#6923—41no—
105C4⋊#6923—41no—
106#11758213—41no—
107#11758213—41no—
108D61⋊C8—41no—
109D61⋊C8—41no—
110D61⋊C8—41no—
111D61⋊C8—41no—
112M16×C61—41no—
113C2×C8×C61—21no—
114C4⋊C4×C61C22⋊C411yescharacteristic
115C4⋊C4×C61C22⋊C411yescharacteristic
116C22⋊C4×C61—21no—
117C42×C61—21no—
118C22⋊Dic61—21no—
119#11758198—21no—
120#11758198—21no—
121#11758198—41no—
122#11758198—41no—
123C4⋊Dic61—21no—
124C4⋊Dic61—21no—
125C4⋊Dic61C22⋊C411yescharacteristic
126C4⋊Dic61C22⋊C411yescharacteristic
127#11758196—21no—
128#11758196—21no—
129#11758196—41no—
130#11758196—41no—
131C4×Dic61—21no—
132C4×Dic61—21no—
133C4×Dic61—21no—
134#11758194—41no—
135C2×#92418—21no—
136C23×C61C4×D411yescharacteristic
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61#12111yescharacteristic
142C22×D61#12311yescharacteristic
143C2×#6923—81no—
144C2×#6923—81no—
145C2×#6923—81no—
146Q8×C61—41no—
147Q8×C61—41no—
148Q8×C61—81no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—41no—
154C2×C4×C61—81no—
155C2×C4×C61C2×C22⋊C411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—41no—
160C2×Dic61—42no—
161C2×Dic61—41no—
162C2×Dic61#12011yescharacteristic
163C2×Dic61#12111yescharacteristic
164C4×D61—21no—
165C4×D61—21no—
166C4×D61—21no—
167C4×D61—21no—
168C4×D61—41no—
169C4×D61—41no—
170C4×D61—41no—
171C4×D61—41no—
172C4×D61—81no—
173#92420—41no—
174#92420—41no—
175#92420—42no—
176#92420—81no—
177C8×C61—41no—
178#92418—41no—
179#9346—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61#38611yescharacteristic
184C2×D61—21no—
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—21no—
188C2×D61—21no—
189C2×D61—81no—
190C2×D61—81no—
191C2×D61#47111yescharacteristic
192C2×D61#47311yescharacteristic
193#6923—161no—
194C4×C61—21no—
195C4×C61—41no—
196C4×C61—41no—
197C4×C61—81no—
198C4×C61#41011yescharacteristic
199C4×C61#41011yescharacteristic
200Dic61—21no—
201Dic61—21no—
202Dic61—41no—
203Dic61—41no—
204Dic61—81no—
205#3095—611no—
206#2924—611no—
207#1825—611no—
208#1520—611no—
209#1472—611no—
210#1305—611no—
211#1298—611no—
212C2×C61—41no—
213C2×C61#188111yescharacteristic
214C2×C61#189911yescharacteristic
215C2×C61#190811yescharacteristic
216D61—21no—
217D61—21no—
218D61—41no—
219C2×C22⋊Q8—611no—
220C2×#117—611no—
221#485—1221no—
222#485—1221no—
223#484—1221no—
224#483—1221no—
225#433—1222no—
226#432—1221no—
227#431—1221no—
228#428—611no—
229#428—611no—
230#424—1221no—
231#419—611no—
232#419#692311yescharacteristic, complemented
233#407—611no—
234#407—611no—
235C2×C22⋊C8—611no—
236C2×C22⋊C8—611no—
237#405—1221no—
238#380—611no—
239#340—1221no—
240#340—1221no—
241#328—1221no—
242#328—1221no—
243#324—1222no—
244C61#934611yescharacteristic, complemented, Sylow
245C22×Q8C2×#692311yescharacteristic
246C23×C4—611no—
247C2×M16—611no—
248C2×M16—1221no—
249C2×M16C2×#692311yescharacteristic
250C22×C8—1221no—
251C22×C8—1221no—
252C22⋊Q8—1221no—
253C22⋊Q8—1221no—
254C22⋊Q8—1221no—
255C22⋊Q8—1221no—
256#117—611no—
257#117—611no—
258#117—611no—
259#117—1221no—
260#117—1221no—
261#117C2×#692311yescharacteristic
262C2×C4⋊C4—611no—
263C2×C4⋊C4—611no—
264C2×C4⋊C4—611no—
265C2×C4⋊C4—1221no—
266C2×C4⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C42—1221no—
271#107—1221no—
272#107—1221no—
273#106—1221no—
274#106—1221no—
275C4⋊C8—1222no—
276C4⋊C8—1222no—
277#103—21no—
278#103—21no—
279#103—1221no—
280#103—1221no—
281C22⋊C8—612no—
282C22⋊C8—611no—
283C22⋊C8—611no—
284C22⋊C8—1221no—
285C22⋊C8—1221no—
286C22⋊C8—1221no—
287C22⋊C8—1221no—
288C22⋊C8—1221no—
289C22⋊C8—1221no—
290#97—1222no—
291C4×C8—1222no—
292#95—1221no—
293C24—611no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—41no—
297C2×Q8—41no—
298C22×C4—21no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—611no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4C22×#692311yescharacteristic
311M16—41no—
312M16—2441no—
313M16—2441no—
314M16—2441no—
315C2×C8—21no—
316C2×C8—1221no—
317C2×C8—1222no—
318C2×C8—1221no—
319C2×C8—1221no—
320C2×C8—2441no—
321C2×C8—2441no—
322C2×C8—2441no—
323C2×C8—2441no—
324C2×C8—2441no—
325C4⋊C4—611no—
326C4⋊C4—611no—
327C4⋊C4—1221no—
328C4⋊C4—1221no—
329C4⋊C4—1221no—
330C4⋊C4—1221no—
331C4⋊C4—2441no—
332C4⋊C4—2441no—
333C4⋊C4—2441no—
334C4⋊C4—2441no—
335C4⋊C4C22⋊#692311yescharacteristic
336C4⋊C4C22⋊#692311yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C22⋊C4—4881no—
342C22⋊C4—2441no—
343C22⋊C4—2441no—
344C42—21no—
345C42—1221no—
346C42—1221no—
347C42—1221no—
348C23—611no—
349C23—611no—
350C23—1221no—
351C23—1221no—
352C23—2441no—
353C23—2441no—
354C23D4×#692311yescharacteristic
355Q8—41no—
356Q8—41no—
357Q8—81no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—611no—
365C2×C4—611no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—4881no—
373C2×C4—4881no—
374C2×C4—4881no—
375C2×C4—4881no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2442no—
382C2×C4—2441no—
383C2×C4C2×C22⋊#692311yescharacteristic
384C2×C4D4×#692311yescharacteristic
385C8—41no—
386C8—4881no—
387C8—2441no—
388C8—2441no—
389C8—2442no—
390C8—2441no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—611no—
395C22—611no—
396C22—1221no—
397C22—1221no—
398C22—1221no—
399C22—1221no—
400C22—1221no—
401C22—4881no—
402C22—4881no—
403C22#1684071011yescharacteristic
404C4—21no—
405C4—41no—
406C4—41no—
407C4—81no—
408C4—1221no—
409C4—1221no—
410C4—9761no—
411C4—4881no—
412C4—2441no—
413C4—2441no—
414C4#1684074111yescharacteristic
415C4#1684074211yescharacteristic
416C2—41no—
417C2—1221no—
418C2—1221no—
419C2—2441no—
420C2#2146181611yescharacteristic
421C2#2146184211yescharacteristic
422C2#2146185911yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#419C4
socleC22×C61#386
prime radicalC23×D61#41
cosocleC22×C4×D61C23
hypercenter#419#6923
hypocenterC61#9346
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
28. #16839805C4semidirect
29. #16839804C4semidirect
30. #16839771C4semidirect
32. C61×#419C4semidirect
232. #419#6923semidirect
244. C61#9346semidirect

Maximal subgroups

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

subgroupindex
#214625132
#214617242
#214612592
#214610992
#214607192
#214607012
#214557652
#934661