Finite Group Databasebeta

← #29580501

Subgroups — #29580501

Order 15616.

770 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 770 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×#16839917C211yesmaximal, characteristic, complemented
2#21449478C211yesmaximal, characteristic
3#21446805C211yesmaximal, characteristic, complemented
4#21445755C211yesmaximal, characteristic, complemented
5#21444387C211yesmaximal, characteristic
6#21443666C211yesmaximal, characteristic, complemented
7C61×#3187C211yesmaximal, characteristic
8C23×Dic122C2211yescharacteristic
9C22×#11758202—21no—
10C2×#14519764—21no—
11#16839917—22no—
12#16839917—22no—
13C2×#14519702—22no—
14C2×#14519700—21no—
15C2×C22⋊#92418C2211yescharacteristic
16#16839674—22no—
17#16839667—21no—
18#16839642—22no—
19#16839622C2211yescharacteristic
20C4×C22⋊Dic61C2211yescharacteristic
21#16839529—22no—
22#16839496—22no—
23C2×C22⋊Q8×C61C2211yescharacteristic
24C2×#121×C61C2211yescharacteristic
25C61×#483—21no—
26C61×#481—21no—
27C61×#465—22no—
28C61×#450—21no—
29C61×#448—21no—
30C2×C22⋊C8×C61C2211yescharacteristic
31C22×Dic122—21no—
32C22×Dic122—21no—
33C22×Dic122—21no—
34C22×Dic122—21no—
35C22×Dic122—21no—
36C22×Dic122—44no—
37C22×Dic122D412yes—
38C23×Dic61—21no—
39C2×#11758202—24no—
40C2×#11758202—44no—
41C22×#92418—21no—
42#14519764—44no—
43C2×C4⋊Dic61—21no—
44C2×C22⋊Dic61—24no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61D412yes—
47C2×C4×Dic61—21no—
48#14519702—44no—
49#14519700—24no—
50C22⋊#92418—21no—
51C22⋊#92418D412yes—
52#14519684—24no—
53#14519684—21no—
54#14519684—21no—
55C22×Q8×C61D411yescharacteristic
56C22×D4×C61—21no—
57C22×D4×C61D411yescharacteristic
58C23×C4×C61C2311yescharacteristic
59C2×SD16×C61—22no—
60C22×C8×C61D412yes—
61C22⋊Q8×C61—21no—
62C22⋊Q8×C61—21no—
63C22⋊Q8×C61—21no—
64C22⋊Q8×C61—21no—
65#121×C61—21no—
66#121×C61—21no—
67#121×C61—21no—
68#121×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61D411yescharacteristic
71C2×C4⋊C4×C61D411yescharacteristic
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74#106×C61—22no—
75#103×C61—22no—
76#102×C61—22no—
77C22⋊C8×C61—21no—
78C22⋊C8×C61—21no—
79C24×C61—21no—
80C24×C61C2×D411yescharacteristic
81C2×Q8×C61—21no—
82C2×Q8×C61—21no—
83C2×Q8×C61—42no—
84C2×D4×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—42no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—42no—
90C2×D4×C61—42no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—42no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61#4111yescharacteristic
101C22×Dic61—22no—
102C22×Dic61—22no—
103C22×Dic61—44no—
104C22×Dic61—41no—
105C22×Dic61—41no—
106C22×Dic61—41no—
107C2×Dic122—24no—
108C2×Dic122—24no—
109C2×Dic122—22no—
110C2×Dic122—22no—
111C2×Dic122—24no—
112C2×Dic122—44no—
113C2×Dic122—44no—
114C2×Dic122—44no—
115C2×Dic122—42no—
116C2×Dic122—42no—
117C2×Dic122—42no—
118C2×Dic122—41no—
119C2×Dic122—41no—
120SD16×C61—82no—
121C2×C8×C61—22no—
122C2×C8×C61—42no—
123C4⋊C4×C61—21no—
124C4⋊C4×C61—21no—
125C4⋊C4×C61—21no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61—41no—
128C4⋊C4×C61—41no—
129C22⋊C4×C61—41no—
130C22⋊C4×C61—41no—
131C22⋊C4×C61—41no—
132C22⋊C4×C61—41no—
133C22⋊Dic61—22no—
134C22⋊Dic61—22no—
135C22⋊Dic61—48no—
136C22⋊Dic61—42no—
137#11758202—48no—
138C4⋊Dic61—42no—
139C4×Dic61—42no—
140C2×#92418—22no—
141C2×#92418—42no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61—42no—
145C23×C61—42no—
146C23×C61—41no—
147C23×C61—42no—
148C23×C61#12011yescharacteristic
149C23×C61#12111yescharacteristic
150C23×C61#12711yescharacteristic
151C23×C61#13512yes—
152C23×C61#13712yes—
153Q8×C61—42no—
154Q8×C61—42no—
155D4×C61—42no—
156D4×C61—81no—
157D4×C61—82no—
158D4×C61—81no—
159D4×C61—81no—
160C2×C4×C61—22no—
161C2×C4×C61—22no—
162C2×C4×C61—22no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—42no—
170C2×C4×C61—81no—
171C2×C4×C61—81no—
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61#12011yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×Dic61—24no—
177C2×Dic61—44no—
178C2×Dic61—44no—
179C2×Dic61—42no—
180C2×Dic61—42no—
181C2×Dic61—42no—
182C2×Dic61—42no—
183C2×Dic61—42no—
184C2×Dic61—81no—
185C2×Dic61—81no—
186C2×Dic61—81no—
187Dic122—24no—
188Dic122—24no—
189Dic122—42no—
190Dic122—42no—
191Dic122—44no—
192Dic122—44no—
193C8×C61—42no—
194#92418—42no—
195#9956—611nomaximal, Sylow
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—42no—
203C22×C61—42no—
204C22×C61—84no—
205C22×C61—81no—
206C22×C61—81no—
207C22×C61—81no—
208C22×C61#39211yescharacteristic
209C22×C61#45212yes—
210C22×C61#46412yes—
211C22×C61#49511yescharacteristic
212C22×C61#49711yescharacteristic
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—81no—
217C4×C61—81no—
218C4×C61—81no—
219C4×C61B(4,𝔽2)12yes—
220Dic61—44no—
221Dic61—82no—
222Dic61—161no—
223#3187D6111yescharacteristic
224C2×#451—611no—
225#2436—611no—
226#1996—611no—
227#1787—611no—
228#1519—611no—
229#1282—611no—
230C2×C61—22no—
231C2×C61—21no—
232C2×C61—22no—
233C2×C61—21no—
234C2×C61—161no—
235C2×C61#200911yescharacteristic
236C2×C61#201511yescharacteristic
237C2×C61#202111yescharacteristic
238C23×Q8—611no—
239C22×Q16—1221no—
240C2×#124—1221no—
241C2×C22⋊Q8C2×D6111yescharacteristic
242C2×#121C2×D6111yescharacteristic
243#483—21no—
244#481—21no—
245#465—22no—
246#451—1222no—
247#451—1222no—
248#450—21no—
249#448—21no—
250C2×#103—1221no—
251C2×#103—1222no—
252C2×C22⋊C8—611no—
253C2×C22⋊C8C2×D6111yescharacteristic
254#393—1222no—
255#391—1221no—
256#386—1222no—
257#380—611no—
258C4×C22⋊C4—611no—
259#342—1222no—
260#327—1222no—
261C61#995611yescharacteristic, complemented, Sylow
262C22×Q8—612no—
263C22×Q8—1221no—
264C22×Q8—1221no—
265C22×Q8—1221no—
266C22×Q8—1221no—
267C22×Q8—1221no—
268C22×Q8—2444no—
269C22×Q8C22⋊D6111yescharacteristic
270C22×D4—21no—
271C22×D4C22⋊D6111yescharacteristic
272C23×C4—1221no—
273C23×C4C22×D6111yescharacteristic
274C2×Q16—1224no—
275C2×Q16—2444no—
276C2×SD16—22no—
277C22×C8—1221no—
278C22×C8C22⋊D6112yes—
279#124—2444no—
280C22⋊Q8—21no—
281C22⋊Q8—21no—
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284#121—21no—
285#121—21no—
286#121—21no—
287#121—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—1221no—
290C2×C4⋊C4C22⋊D6111yescharacteristic
291C2×C4⋊C4C22⋊D6111yescharacteristic
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—612no—
295C2×C22⋊C4—1224no—
296C2×C22⋊C4—1221no—
297C2×C42—1221no—
298#106—22no—
299#103—22no—
300#103—1224no—
301#103—2444no—
302#102—22no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8—612no—
306C22⋊C8—1221no—
307#95—1224no—
308#95—1221no—
309#95—1221no—
310C24—21no—
311C24D4×D6111yescharacteristic
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—42no—
315C2×Q8—1224no—
316C2×Q8—1224no—
317C2×Q8—1224no—
318C2×Q8—1222no—
319C2×Q8—1222no—
320C2×Q8—2442no—
321C2×Q8—2442no—
322C2×Q8—2442no—
323C2×Q8—2444no—
324C2×Q8—2444no—
325C2×Q8—2444no—
326C2×Q8—2441no—
327C2×Q8—2441no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—42no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—42no—
334C2×D4—42no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—42no—
339C22×C4—1222no—
340C22×C4—1222no—
341C22×C4—2444no—
342C22×C4—2441no—
343C22×C4—2441no—
344C22×C4—2441no—
345C22×C4D4×D6111yescharacteristic
346C22×C4D4×D6111yescharacteristic
347C22×C4#1175822411yescharacteristic
348C22×C4C2×C22⋊D6111yescharacteristic
349C22×C4C2×C22⋊D6111yescharacteristic
350C22×C4C2×C22⋊D6111yescharacteristic
351Q16—2448no—
352SD16—82no—
353C2×C8—22no—
354C2×C8—42no—
355C2×C8—1222no—
356C2×C8—2442no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—2442no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—1222no—
369C22⋊C4—1222no—
370C22⋊C4—2448no—
371C22⋊C4—2442no—
372C42—2442no—
373C23—41no—
374C23—41no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23—41no—
379C23#1451974511yescharacteristic
380C23#1451974911yescharacteristic
381C23#1451977311yescharacteristic
382C23#1451979812yes—
383C23#1451980612yes—
384Q8—42no—
385Q8—42no—
386Q8—1224no—
387Q8—1224no—
388Q8—2442no—
389Q8—2442no—
390Q8—2444no—
391Q8—2444no—
392D4—42no—
393D4—81no—
394D4—82no—
395D4—81no—
396D4—81no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—1224no—
410C2×C4—4881no—
411C2×C4—4881no—
412C2×C4—4881no—
413C2×C4—2442no—
414C2×C4—2442no—
415C2×C4—2442no—
416C2×C4—2442no—
417C2×C4—2444no—
418C2×C4—2444no—
419C2×C4—2442no—
420C2×C4#1451974511yescharacteristic
421C2×C4#1451974611yescharacteristic
422C2×C4#1451974811yescharacteristic
423C2×C4#1451974911yescharacteristic
424C8—42no—
425C8—2442no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—42no—
433C22—42no—
434C22—84no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22#1683967011yescharacteristic
439C22#1683992112yes—
440C22#1683998212yes—
441C22#1684014311yescharacteristic
442C22#1684015311yescharacteristic
443C4—21no—
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—9761no—
450C4—4882no—
451C4—2444no—
452C4#1683994912yes—
453C2—21no—
454C2—22no—
455C2—22no—
456C2—21no—
457C2—161no—
458C2#2144687611yescharacteristic
459C2#2144691111yescharacteristic
460C2#2144694311yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#3187C2
socleC22×C61#392
prime radicalC2×#121×C61C22
hypercenter#3187D61
hypocenterC61#9956
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3187

Complements

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

NH ≅ G/Ntype
1. C2×#16839917C2semidirect
3. #21446805C2semidirect
4. #21445755C2semidirect
6. #21443666C2semidirect
261. C61#9956semidirect

Maximal subgroups

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

subgroupindex
C2×#168399172
#214494782
#214468052
#214457552
#214443872
#214436662
C61×#31872
#995661