Finite Group Databasebeta

← #29580502

Subgroups — #29580502

Order 15616.

770 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 770 conjugacy classes of subgroups — too many to draw. Only its 99 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#21456572C211yesmaximal, characteristic
2C2×#16839917C211yesmaximal, characteristic, complemented
3#21449477C211yesmaximal, characteristic
4#21445753C211yesmaximal, characteristic, complemented
5#21444386C211yesmaximal, characteristic
6#21443667C211yesmaximal, characteristic, complemented
7C61×#1996C211yesmaximal, characteristic, complemented
8C23×Dic122C2211yescharacteristic
9C22×#11758202—21no—
10C2×#14519765—21no—
11C2×#14519751C2211yescharacteristic
12#16840090—21no—
13#16840080—21no—
14#16839993—22no—
15#16839917—22no—
16#16839917—22no—
17#16839912—21no—
18#16839901—21no—
19C2×#14519700—22no—
20C2×#14519700—21no—
21C2×C22⋊#92418C2211yescharacteristic
22C2×C22⋊#92418C2211yescharacteristic
23#16839675—22no—
24#16839668—21no—
25#16839639—22no—
26#16839495—22no—
27C2×C22⋊Q8×C61C2211yescharacteristic
28C61×#380C2211yescharacteristic
29C4×C22⋊C4×C61C2211yescharacteristic
30C61×#342—22no—
31C22×Dic122—21no—
32C22×Dic122—21no—
33C22×Dic122—21no—
34C22×Dic122—21no—
35C22×Dic122—21no—
36C22×Dic122—44no—
37C22×Dic122D412yes—
38C22×D244D411yescharacteristic
39C22×C22⋊D61—21no—
40C23×Dic61—21no—
41C2×#11758202—24no—
42C2×#11758202—44no—
43C2×#11758201—22no—
44C22×#92418—21no—
45C22×#92418D412yes—
46#14519765—44no—
47#14519751—21no—
48#14519751—21no—
49#14519751—21no—
50#14519751—21no—
51C2×C4⋊Dic61D411yescharacteristic
52C2×#11758198—24no—
53C2×#11758198—21no—
54#14519708—22no—
55#14519701—22no—
56#14519700—24no—
57#14519700—44no—
58#14519697—22no—
59C22⋊#92418—21no—
60C22⋊#92418—21no—
61C22⋊#92418—21no—
62C22⋊#92418D412yes—
63#14519684—24no—
64C22×Q8×C61D411yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C22⋊Q8×C61—21no—
67C22⋊Q8×C61—21no—
68C22⋊Q8×C61—21no—
69C22⋊Q8×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61D411yescharacteristic
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61D412yes—
76C2×C42×C61—21no—
77#95×C61—21no—
78#95×C61—21no—
79C24×C61C2×D411yescharacteristic
80C23×D61—21no—
81C2×Q8×C61—21no—
82C2×Q8×C61—21no—
83C2×Q8×C61—42no—
84C22×C4×C61—22no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61—42no—
88C22×C4×C61—41no—
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61#4111yescharacteristic
95C2×C22⋊D61—41no—
96C2×C22⋊D61—41no—
97C2×C22⋊D61—42no—
98C2×C22⋊D61—42no—
99C22×Dic61—22no—
100C22×Dic61—21no—
101C22×Dic61—44no—
102C22×Dic61—41no—
103C22×Dic61—41no—
104C2×D244—21no—
105C2×D244—21no—
106C2×D244—42no—
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—
120C4⋊C4×C61—21no—
121C4⋊C4×C61—21no—
122C4⋊C4×C61—42no—
123C4⋊C4×C61—41no—
124C4⋊C4×C61—41no—
125C22⋊C4×C61—22no—
126C22⋊C4×C61—22no—
127C22⋊C4×C61—41no—
128C22⋊C4×C61—41no—
129C22⋊C4×C61—42no—
130C42×C61—42no—
131#11758202—48no—
132#11758201—82no—
133#11758198—48no—
134#11758198—41no—
135#11758198—41no—
136C4⋊Dic61—21no—
137C4⋊Dic61—21no—
138C2×#92418—22no—
139C2×#92418—22no—
140C2×#92418—42no—
141C2×#92418—42no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61#12011yescharacteristic
145C23×C61#12111yescharacteristic
146C23×C61#12711yescharacteristic
147C23×C61#13512yes—
148C23×C61#13712yes—
149C22×D61—42no—
150C22×D61—42no—
151C22×D61—41no—
152C22×D61—42no—
153Q8×C61—42no—
154Q8×C61—42no—
155C2×C4×C61—22no—
156C2×C4×C61—22no—
157C2×C4×C61—22no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—42no—
162C2×C4×C61—42no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—42no—
166C2×C4×C61—81no—
167C2×C4×C61—81no—
168C2×C4×C61—81no—
169C2×C4×C61—81no—
170C2×C4×C61—81no—
171C2×C4×C61#12011yescharacteristic
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C22⋊D61—82no—
176C22⋊D61—81no—
177C22⋊D61—81no—
178C2×Dic61—24no—
179C2×Dic61—44no—
180C2×Dic61—44no—
181C2×Dic61—42no—
182C2×Dic61—42no—
183C2×Dic61—41no—
184C2×Dic61—42no—
185D244—42no—
186D244—81no—
187Dic122—24no—
188Dic122—24no—
189Dic122—42no—
190Dic122—42no—
191Dic122—44no—
192Dic122—44no—
193#92418—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#39211yescharacteristic
205C22×C61#45212yes—
206C22×C61#46412yes—
207C22×C61#49511yescharacteristic
208C22×C61#49711yescharacteristic
209C2×D61—84no—
210C2×D61—81no—
211C2×D61—81no—
212C2×D61—81no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—82no—
217C4×C61—81no—
218C4×C61—81no—
219C4×C61—161no—
220C4×C61B(4,𝔽2)12yes—
221Dic61—44no—
222Dic61—81no—
223#3187—611no—
224C2×#451—611no—
225#2436—611no—
226#1996D6111yescharacteristic, complemented
227#1787—611no—
228#1519—611no—
229#1282—611no—
230C2×C61—22no—
231C2×C61—21no—
232C2×C61—22no—
233C2×C61—21no—
234C2×C61#200911yescharacteristic
235C2×C61#201511yescharacteristic
236C2×C61#202111yescharacteristic
237D61—161no—
238C23×Q8—611no—
239C22×Q16—1221no—
240C2×#124—1221no—
241C2×C22⋊Q8C2×D6111yescharacteristic
242C2×#121—611no—
243#483—1221no—
244#481—1221no—
245#465—1222no—
246#451—1222no—
247#451—1222no—
248#450—1221no—
249#448—1221no—
250C2×#103—1221no—
251C2×#103—1222no—
252C2×C22⋊C8—611no—
253C2×C22⋊C8—611no—
254#393—1222no—
255#391—1221no—
256#386—1222no—
257#380C2×D6111yescharacteristic
258C4×C22⋊C4C2×D6111yescharacteristic
259#342—22no—
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×Q8D24411yescharacteristic
270C22×D4—611no—
271C22×D4—1221no—
272C23×C4—1221no—
273C23×C4C22×D6111yescharacteristic
274C2×Q16—1224no—
275C2×Q16—2444no—
276C2×SD16—1222no—
277C22×C8—612no—
278C22×C8—1221no—
279#124—2444no—
280C22⋊Q8—21no—
281C22⋊Q8—21no—
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284#121—1221no—
285#121—1221no—
286#121—1221no—
287#121—1221no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—611no—
291C2×C4⋊C4D24411yescharacteristic
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—1224no—
295C2×C22⋊C4—1221no—
296C2×C22⋊C4C22⋊D6112yes—
297C2×C42—21no—
298#106—1222no—
299#103—1224no—
300#103—1222no—
301#103—2444no—
302#102—1222no—
303C22⋊C8—612no—
304C22⋊C8—1221no—
305C22⋊C8—1221no—
306C22⋊C8—1221no—
307#95—21no—
308#95—21no—
309#95—1224no—
310C24—1221no—
311C24C2×C22⋊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—1221no—
329C2×D4—1221no—
330C2×D4—2442no—
331C2×D4—2442no—
332C2×D4—2441no—
333C2×D4—2441no—
334C2×D4—2442no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—42no—
339C22×C4—41no—
340C22×C4—1222no—
341C22×C4—1221no—
342C22×C4—2444no—
343C22×C4—2441no—
344C22×C4—2441no—
345C22×C4C2×D24411yescharacteristic
346C22×C4#1175822211yescharacteristic
347C22×C4D4×D6111yescharacteristic
348C22×C4D4×D6111yescharacteristic
349C22×C4D4×D6111yescharacteristic
350C22×C4D4×D6111yescharacteristic
351Q16—2448no—
352SD16—4882no—
353C2×C8—1222no—
354C2×C8—1222no—
355C2×C8—2442no—
356C2×C8—2442no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—42no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—1221no—
363C4⋊C4—1221no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—42no—
369C22⋊C4—2448no—
370C22⋊C4—2441no—
371C22⋊C4—2441no—
372C42—42no—
373C23—41no—
374C23—41no—
375C23—2442no—
376C23—2442no—
377C23—2442no—
378C23—2441no—
379C23#1451974511yescharacteristic
380C23#1451975111yescharacteristic
381C23#1451977311yescharacteristic
382C23#1451979712yes—
383C23#1451980812yes—
384Q8—42no—
385Q8—42no—
386Q8—1224no—
387Q8—1224no—
388Q8—2442no—
389Q8—2444no—
390Q8—2442no—
391Q8—2444no—
392D4—4881no—
393D4—4882no—
394D4—4881no—
395D4—4881no—
396D4—2442no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—1224no—
414C2×C4—2442no—
415C2×C4—2441no—
416C2×C4—2442no—
417C2×C4—2444no—
418C2×C4—2444no—
419C2×C4—2442no—
420C2×C4#1451974711yescharacteristic
421C2×C4#1451974711yescharacteristic
422C2×C4#1451975011yescharacteristic
423C2×C4#1451975011yescharacteristic
424C8—2442no—
425C8—2442no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—42no—
433C22—42no—
434C22—4884no—
435C22—4881no—
436C22—4881no—
437C22—4881no—
438C22#1683967111yescharacteristic
439C22#1683992212yes—
440C22#1683998412yes—
441C22#1684014411yescharacteristic
442C22#1684015411yescharacteristic
443C4—21no—
444C4—21no—
445C4—21no—
446C4—82no—
447C4—81no—
448C4—81no—
449C4—161no—
450C4—4881no—
451C4—2444no—
452C4#1683995012yes—
453C2—22no—
454C2—21no—
455C2—22no—
456C2—21no—
457C2—9761no—
458C2#2144687811yescharacteristic
459C2#2144691211yescharacteristic
460C2#2144694411yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1996C2
socleC22×C61#392
prime radicalC2×#14519751C22
hypercenter#1996D61
hypocenterC61#9956
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. C2×#16839917C2semidirect
4. #21445753C2semidirect
6. #21443667C2semidirect
7. C61×#1996C2semidirect
226. #1996D61semidirect
261. C61#9956semidirect

Maximal subgroups

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

subgroupindex
#214565722
C2×#168399172
#214494772
#214457532
#214443862
#214436672
C61×#19962
#995661