Finite Group Databasebeta

← #30598239

Subgroups — #30598239

Order 15616.

846 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 846 conjugacy classes of subgroups — too many to draw. Only its 114 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#21461545C211yesmaximal, characteristic, complemented
2#21461545C211yesmaximal, characteristic, complemented
3C2×#16840619C212yesmaximal, complemented
4C2×#16840618C212yesmaximal, complemented
5C2×#16840298C211yesmaximal, characteristic
6C2×C22⋊#92420—21no—
7C2×C22⋊#92420—21no—
8C2×#14519832C2212yes—
9C2×#14519832C2212yes—
10#16840628—21no—
11#16840628—21no—
12#16840619—24no—
13#16840618—24no—
14#16840298—24no—
15#16840298—24no—
16C2×#14519772—21no—
17C2×#14519768C2211yescharacteristic
18C2×#14519766C2211yescharacteristic
19C2×#14519761—21no—
20C2×#14519751C411yescharacteristic
21C2×Q8×Dic61C411yescharacteristic
22C2×#14519739C411yescharacteristic
23C2×#14519737—21no—
24C2×#14519735—21no—
25C22×C4×Dic61C2211yescharacteristic
26C2×C22⋊Q8×C61C411yescharacteristic
27C22×#92420—22no—
28C22×#92420—22no—
29C22⋊#92420—24no—
30C22⋊#92420—24no—
31#14519832—22no—
32#14519832—22no—
33#14519832—22no—
34#14519832—22no—
35C22×D244C2×C411yescharacteristic
36C22×C22⋊D61—21no—
37C23×Dic61D411yescharacteristic
38C23×Dic61D411yescharacteristic
39C22×C4×D61—21no—
40#14519772—28no—
41#14519768—22no—
42#14519768D414yes—
43#14519766—22no—
44#14519766D414yes—
45#14519761—28no—
46#14519751—22no—
47#14519751—22no—
48Q8×Dic61—22no—
49Q8×Dic61—22no—
50#14519739—22no—
51#14519739—22no—
52#14519737—28no—
53#14519735—28no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61—21no—
56C2×C4⋊Dic61C2×C411yescharacteristic
57C2×#11758196—21no—
58C2×#11758198—21no—
59C2×#11758198—21no—
60C2×#11758198—21no—
61C2×#11758198—21no—
62C2×C4×Dic61—21no—
63C2×C4×Dic61—22no—
64C2×C4×Dic61—22no—
65C2×C4×Dic61C2×C411yescharacteristic
66C2×C4×Dic61D411yescharacteristic
67C2×C4×Dic61D411yescharacteristic
68C2×C4×Dic61C2311yescharacteristic
69C22×Q8×C61C2×C411yescharacteristic
70C23×C4×C61C2×C411yescharacteristic
71C22⋊Q8×C61—22no—
72C22⋊Q8×C61—22no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61C2×C411yescharacteristic
75C2×C22⋊C4×C61—21no—
76C24×C61C22⋊C411yescharacteristic
77C23×D61—21no—
78C2×Q8×C61—21no—
79C2×Q8×C61—41no—
80C2×Q8×C61—41no—
81C2×Q8×C61C22⋊C412yes—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61C22⋊C411yescharacteristic
89C22×C4×C61C22×C411yescharacteristic
90C2×C22⋊D61—24no—
91C2×C22⋊D61—42no—
92C2×C22⋊D61—42no—
93C22×Dic61—22no—
94C22×Dic61—21no—
95C22×Dic61—22no—
96C22×Dic61—22no—
97C22×Dic61—22no—
98C22×Dic61—41no—
99C22×Dic61—41no—
100C22×Dic61C22⋊C411yescharacteristic
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C2×D411yescharacteristic
103C22×Dic61C2×D411yescharacteristic
104C2×D244—21no—
105C2×D244—41no—
106C2×D244—41no—
107C2×D244C22⋊C412yes—
108C2×C4×D61—24no—
109C2×C4×D61—42no—
110C2×C4×D61—42no—
111C2×#92420—24no—
112C2×#92420—24no—
113C2×#92420—42no—
114C2×#92420—42no—
115C2×#92420—42no—
116C2×#92420—42no—
117C4⋊C4×C61—24no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61C22⋊C412yes—
120C22⋊C4×C61—24no—
121#11758198—24no—
122#11758198—24no—
123#11758198—24no—
124#11758198—24no—
125C4⋊Dic61—24no—
126C4⋊Dic61—21no—
127C4⋊Dic61—24no—
128C4⋊Dic61C22⋊C412yes—
129#11758196—24no—
130C4×Dic61—24no—
131C4×Dic61—21no—
132C4×Dic61—21no—
133C4×Dic61—22no—
134C4×Dic61—22no—
135C4×Dic61C2×D412yes—
136C4×Dic61C2×D412yes—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—21no—
140C23×C61—21no—
141C23×C61—21no—
142C23×C61—21no—
143C23×C61#10412yes—
144C23×C61C2×C22⋊C411yescharacteristic
145C22×D61—22no—
146C22×D61—41no—
147C22×D61—41no—
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—41no—
152Q8×C61—42no—
153Q8×C61—42no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—22no—
158C2×C4×C61—22no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—42no—
162C2×C4×C61—42no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61C2×C22⋊C411yescharacteristic
168C2×C4×C61C2×C22⋊C411yescharacteristic
169C22⋊D61—48no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—22no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—44no—
181C2×Dic61—44no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61#10412yes—
185C2×Dic61#12012yes—
186C2×Dic61#12012yes—
187D244—42no—
188D244—42no—
189C4×D61—48no—
190#92420—44no—
191#92420—44no—
192#8336—611nomaximal, Sylow
193C22×C61—22no—
194C22×C61—22no—
195C22×C61—22no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61#37911yescharacteristic
201C22×C61#41311yescharacteristic
202C22×C61#41311yescharacteristic
203C22×C61C2×#10411yescharacteristic
204C22×C61C2×#10411yescharacteristic
205C22×C61#42111yescharacteristic
206C22×C61#42111yescharacteristic
207C2×D61—42no—
208C2×D61—42no—
209C2×D61—42no—
210C2×D61—81no—
211C2×D61—81no—
212C2×D61—81no—
213C2×D61—81no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—41no—
217C4×C61—42no—
218C4×C61—42no—
219Dic61—22no—
220Dic61—22no—
221Dic61—22no—
222Dic61—41no—
223Dic61—42no—
224C2×#529—611no—
225#1749—611no—
226#1749—611no—
227C2×#330—612no—
228C2×#329—612no—
229C2×C61—42no—
230C2×C61#152411yescharacteristic
231C2×C61#152911yescharacteristic
232C2×C61#153211yescharacteristic
233C2×C61#153511yescharacteristic
234C2×C61#178511yescharacteristic
235C2×C61#178911yescharacteristic
236C2×C61#178911yescharacteristic
237D61—82no—
238#529—1224no—
239#529—1224no—
240C2×#126—1221no—
241C2×#125—611no—
242C2×#124—611no—
243C2×#123—1221no—
244C2×C22⋊Q8#692311yescharacteristic
245C2×#121—611no—
246C2×C4×Q8—611no—
247C2×C4×D4—611no—
248C2×C4×D4—1221no—
249C2×#117—1221no—
250C22×C42—611no—
251C2×C22⋊C8—1221no—
252C2×C22⋊C8—1221no—
253C2×#97—612no—
254C2×#97—612no—
255#336—1221no—
256#336—1221no—
257#330—1224no—
258#329—1224no—
259C61#833611yescharacteristic, complemented, Sylow
260C22×Q8C2×#692311yescharacteristic
261C22×D4—611no—
262C22×D4—1221no—
263C23×C4—611no—
264C23×C4—611no—
265C23×C4—1221no—
266C23×C4C2×#692311yescharacteristic
267C22×C8—1222no—
268C22×C8—1222no—
269#126—1228no—
270#125—614no—
271#125—1222no—
272#124—614no—
273#124—1222no—
274#123—1228no—
275C22⋊Q8—22no—
276C22⋊Q8—22no—
277#121—1222no—
278#121—1222no—
279C4×Q8—1222no—
280C4×Q8—1222no—
281C4×D4—1228no—
282C4×D4—1222no—
283C4×D4—1222no—
284#117—1228no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—611no—
287C2×C4⋊C4—1221no—
288C2×C4⋊C4—1221no—
289C2×C4⋊C4—1221no—
290C2×C4⋊C4C2×#692311yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—1221no—
293C2×C22⋊C4—1221no—
294C2×C22⋊C4—1221no—
295C2×C22⋊C4—1221no—
296C2×C42—611no—
297C2×C42—611no—
298C2×C42—611no—
299C2×C42—611no—
300C2×C42—1222no—
301C2×C42—1222no—
302C2×C42—1221no—
303C22⋊C8—1224no—
304C22⋊C8—1224no—
305#97—1222no—
306#97—1222no—
307#97—1222no—
308#97—1222no—
309C24—1221no—
310C24C22⋊#692311yescharacteristic
311C2×Q8—21no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8C22⋊#692312yes—
315C2×D4—612no—
316C2×D4—1224no—
317C2×D4—1221no—
318C2×D4—2441no—
319C2×D4—2441no—
320C2×D4—2442no—
321C2×D4—2442no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—611no—
332C22×C4—1224no—
333C22×C4—1222no—
334C22×C4—1222no—
335C22×C4—1222no—
336C22×C4—1222no—
337C22×C4—1221no—
338C22×C4—2442no—
339C22×C4—2442no—
340C22×C4—2441no—
341C22×C4—2441no—
342C22×C4C22⋊#692311yescharacteristic
343C22×C4C22×#692311yescharacteristic
344C2×C8—1224no—
345C2×C8—1224no—
346C2×C8—2442no—
347C2×C8—2442no—
348C2×C8—2442no—
349C2×C8—2442no—
350C4⋊C4—24no—
351C4⋊C4—21no—
352C4⋊C4—612no—
353C4⋊C4—1224no—
354C4⋊C4—1224no—
355C4⋊C4—1224no—
356C4⋊C4—1221no—
357C4⋊C4C22⋊#692312yes—
358C22⋊C4—24no—
359C22⋊C4—1224no—
360C22⋊C4—1224no—
361C22⋊C4—1224no—
362C22⋊C4—1224no—
363C42—612no—
364C42—612no—
365C42—1222no—
366C42—1222no—
367C42—1224no—
368C42—1221no—
369C42—1221no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—1222no—
377C23—2441no—
378C23—2441no—
379C23—2441no—
380C23—2441no—
381C23—2441no—
382C23—2441no—
383C23#1451984212yes—
384C23C2×C22⋊#692311yescharacteristic
385Q8—42no—
386Q8—42no—
387D4—2442no—
388D4—2442no—
389D4—2448no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—612no—
404C2×C4—612no—
405C2×C4—612no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—1221no—
414C2×C4—1221no—
415C2×C4—1222no—
416C2×C4—2448no—
417C2×C4—2444no—
418C2×C4—2444no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4C2×C22⋊#692311yescharacteristic
422C2×C4C2×C22⋊#692311yescharacteristic
423C8—2444no—
424C8—2444no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—4881no—
433C22—4881no—
434C22—4881no—
435C22—4881no—
436C22—2442no—
437C22—2442no—
438C22—2442no—
439C22#1684070311yescharacteristic
440C22#1684074911yescharacteristic
441C22#1684074911yescharacteristic
442C22D61⋊#10411yescharacteristic
443C22C2×#1451984211yescharacteristic
444C22#1684075911yescharacteristic
445C22#1684076111yescharacteristic
446C4—21no—
447C4—21no—
448C4—41no—
449C4—42no—
450C4—42no—
451C4—1222no—
452C4—1222no—
453C4—1222no—
454C4—2441no—
455C4—2442no—
456C2—42no—
457C2—4882no—
458C2#2146127211yescharacteristic
459C2#2146128711yescharacteristic
460C2#2146129711yescharacteristic
461C2#2146130611yescharacteristic
462C2#2146165611yescharacteristic
463C2#2146166111yescharacteristic
464C2#2146166211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C22⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519751C4
cosocleC2×C4×Dic61C23
hypercenterC2×C22⋊Q8#6923
hypocenterC61#8336
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #21461545C2semidirect
2. #21461545C2semidirect
3. C2×#16840619C2semidirect
4. C2×#16840618C2semidirect
259. C61#8336semidirect

Maximal subgroups

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

subgroupindex
#214615452
C2×#168406192
C2×#168406182
C2×#168402982
#833661