Finite Group Databasebeta

← #29571658

Subgroups — #29571658

Order 15616.

788 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 788 conjugacy classes of subgroups — too many to draw. Only its 117 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×#16840468C211yesmaximal, characteristic
2C4×#14519695C211yesmaximal, characteristic, complemented
3#21444421C211yesmaximal, characteristic, complemented
4#21444263C211yesmaximal, characteristic
5#21444261C211yesmaximal, characteristic
6#21444162C211yesmaximal, characteristic, complemented
7C61×#1528C211yesmaximal, characteristic, complemented
8#16840468—22no—
9#16840468—22no—
10#16840468—22no—
11#16840468—22no—
12C2×#14519776C411yescharacteristic
13C2×#14519768C411yescharacteristic
14C2×#14519757—21no—
15C2×#14519755—21no—
16C2×#14519755—21no—
17C2×C4×Dic122C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519739C411yescharacteristic
20C2×#14519739C411yescharacteristic
21C2×C4⋊C4×D61—21no—
22#16839819C2211yescharacteristic
23C2×#14519695—21no—
24C4×#11758194C2211yescharacteristic
25#16839530—21no—
26#16839504—22no—
27#16839491—22no—
28#16839489—22no—
29#16839487—21no—
30#16839487—21no—
31C2×#125×C61C2211yescharacteristic
32C61×#432C2211yescharacteristic
33C4×M16×C61C2211yescharacteristic
34C61×#330—22no—
35C22×Dic122—21no—
36C22×Dic122D411yescharacteristic
37C22×D244C2×C411yescharacteristic
38C22×C4×D61—21no—
39C22×C4×D61—21no—
40C22×C4×D61—21no—
41C2×#11758194—21no—
42#14519776—22no—
43#14519776—22no—
44#14519768—22no—
45#14519768—22no—
46#14519757—24no—
47#14519757—24no—
48#14519755—24no—
49#14519755—24no—
50#14519755—24no—
51#14519755—24no—
52C4×Dic122—21no—
53C4×Dic122—21no—
54C4×Dic122—21no—
55C4×Dic122—21no—
56C4×D244—21no—
57C4×D244—21no—
58C4×D244D412yes—
59C4×D244D412yes—
60#14519739—22no—
61#14519739—22no—
62#14519739—22no—
63#14519739—22no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61C2×C411yescharacteristic
66C2×C4⋊Dic61D411yescharacteristic
67C2×#11758196—21no—
68C2×#11758196—21no—
69C2×#11758196D411yescharacteristic
70C2×#11758196D411yescharacteristic
71C4⋊C4×D61—24no—
72C4⋊C4×D61—24no—
73C2×#11758198—21no—
74C2×#11758198—21no—
75C2×#11758198—21no—
76C2×C4×Dic61C2×C411yescharacteristic
77C2×C4×Dic61C2×C411yescharacteristic
78C4⋊#92418—21no—
79#14519695—24no—
80C22⋊#92418—21no—
81#14519688—21no—
82#14519688—21no—
83C4×#92418—21no—
84C2×M16×C61—21no—
85#125×C61—21no—
86#125×C61—21no—
87#125×C61D412yes—
88#125×C61D412yes—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61C2×C411yescharacteristic
92C2×C4⋊C4×C61C2×C411yescharacteristic
93C2×C42×C61C2311yescharacteristic
94C4⋊C8×C61—21no—
95C22⋊C8×C61—21no—
96#97×C61—21no—
97#97×C61—21no—
98C4×C8×C61—21no—
99C23×D61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61C22×C411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×Dic61—21no—
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C22⋊C411yescharacteristic
109C22×Dic61C22⋊C411yescharacteristic
110C2×D244—21no—
111C2×D244—24no—
112C2×D244C22⋊C412yes—
113C2×C4×D61—24no—
114C2×C4×D61—24no—
115C2×C4×D61—22no—
116C2×C4×D61—22no—
117C2×C4×D61—42no—
118C2×C4×D61—42no—
119C2×C4×D61—82no—
120C2×C4×D61—82no—
121C2×Dic122—21no—
122C2×Dic122—21no—
123C2×Dic122—22no—
124C2×Dic122—24no—
125C2×Dic122—41no—
126C2×Dic122—82no—
127M16×C61—22no—
128M16×C61—41no—
129C2×C8×C61—41no—
130C2×C8×C61—41no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—22no—
134C4⋊C4×C61—22no—
135C4⋊C4×C61—22no—
136C4⋊C4×C61—22no—
137C4⋊C4×C61C22⋊C412yes—
138C4⋊C4×C61C22⋊C412yes—
139C42×C61C2×D411yescharacteristic
140C42×C61C2×D411yescharacteristic
141C42×C61C2×D411yescharacteristic
142C42×C61C2×D411yescharacteristic
143#11758198—24no—
144#11758198—24no—
145#11758198—22no—
146#11758198—22no—
147C4⋊Dic61—24no—
148C4⋊Dic61—21no—
149C4⋊Dic61—21no—
150C4⋊Dic61—21no—
151C4⋊Dic61C22⋊C412yes—
152#11758196—24no—
153#11758196—24no—
154#11758196—21no—
155#11758196—21no—
156#11758196—21no—
157#11758196—21no—
158C4×Dic61—21no—
159C4×Dic61—21no—
160C4×Dic61—21no—
161C4×Dic61—21no—
162#11758194—22no—
163#11758194—41no—
164C2×#92418—41no—
165C2×#92418—41no—
166C23×C61C2×C22⋊C411yescharacteristic
167C22×D61—24no—
168C22×D61—22no—
169C22×D61—42no—
170C22×D61—41no—
171C22×D61—41no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—22no—
177C2×C4×C61—41no—
178C2×C4×C61—42no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61C2×C22⋊C411yescharacteristic
182C2×C4×C61C2×C22⋊C411yescharacteristic
183C2×C4×C61#12011yescharacteristic
184C2×C4×C61#12011yescharacteristic
185C2×C4×C61#12011yescharacteristic
186C2×C4×C61#12011yescharacteristic
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—22no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—42no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61#10412yes—
199D244—24no—
200D244—22no—
201D244#10114yescomplemented
202C4×D61—48no—
203C4×D61—82no—
204C4×D61—82no—
205C4×D61—84no—
206Dic122—42no—
207Dic122—42no—
208Dic122—84no—
209C8×C61—42no—
210C8×C61—81no—
211#92418—42no—
212#92418—81no—
213#8372—611nomaximal, Sylow
214C22×C61—21no—
215C22×C61—21no—
216C22×C61#37911yescharacteristic
217C22×C61C2×#10411yescharacteristic
218C22×C61#42111yescharacteristic
219C2×D61—24no—
220C2×D61—44no—
221C2×D61—44no—
222C2×D61—42no—
223C2×D61—42no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—21no—
229C4×C61—42no—
230C4×C61—42no—
231C4×C61C2×#10112yes—
232Dic61—22no—
233Dic61—41no—
234Dic61—42no—
235Dic61—41no—
236Dic61—41no—
237C2×#554—611no—
238C4×#101—611no—
239#1528—611no—
240#1528D6111yescharacteristic, complemented
241#1490—611no—
242#1490—611no—
243#1467—611no—
244C2×C61—21no—
245C2×C61—21no—
246C2×C61#178411yescharacteristic
247C2×C61#178911yescharacteristic
248C2×C61#179511yescharacteristic
249D61—44no—
250#554—1222no—
251#554—1222no—
252#554—1222no—
253#554—1222no—
254C2×C4⋊Q8—611no—
255C2×#125—611no—
256C2×#125C2×D6111yescharacteristic
257C2×C22⋊Q8—1221no—
258C2×C22⋊Q8—1221no—
259C2×C22⋊Q8—1221no—
260C2×C4×Q8—611no—
261C2×C4×D4—611no—
262C2×C4×D4—611no—
263C2×C4×D4—611no—
264C22×C4⋊C4—1221no—
265#432—611no—
266#432C2×D6111yescharacteristic
267C2×#101—1221no—
268C4×M16—611no—
269C4×M16C2×D6111yescharacteristic
270#343—1221no—
271#330—22no—
272#330—1222no—
273D4⋊C8—1222no—
274D4⋊C8—1222no—
275#324—1221no—
276#324—1221no—
277C61#837211yescharacteristic, complemented, Sylow
278C22×Q8—611no—
279C22×Q8—1221no—
280C22×D4—611no—
281C23×C4—1221no—
282C23×C4—1221no—
283C23×C4—1221no—
284C2×M16—21no—
285C2×M16—1221no—
286C4⋊Q8—1222no—
287C4⋊Q8—1222no—
288#125—21no—
289#125—21no—
290#125—1222no—
291#125—1222no—
292#125D24412yes—
293#125C22⋊D6112yes—
294C22⋊Q8—1224no—
295C22⋊Q8—1224no—
296C22⋊Q8—1224no—
297C22⋊Q8—1224no—
298C22⋊Q8—1224no—
299C22⋊Q8—1224no—
300C4×Q8—1221no—
301C4×Q8—1221no—
302C4×Q8—1221no—
303C4×Q8—1221no—
304C4×D4—612no—
305C4×D4—612no—
306C4×D4—1222no—
307C4×D4—1222no—
308C4×D4—1222no—
309C4×D4—1222no—
310C4×D4—1221no—
311C4×D4—1221no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—611no—
315C2×C4⋊C4—611no—
316C2×C4⋊C4—611no—
317C2×C4⋊C4—611no—
318C2×C4⋊C4—1224no—
319C2×C4⋊C4—1224no—
320C2×C4⋊C4—1221no—
321C2×C4⋊C4—1221no—
322C2×C4⋊C4—1221no—
323C2×C4⋊C4C4×D6111yescharacteristic
324C2×C4⋊C4C4×D6111yescharacteristic
325C2×C22⋊C4—1221no—
326C2×C22⋊C4—1221no—
327C2×C22⋊C4—1221no—
328C2×C42—611no—
329C2×C42—611no—
330C2×C42C22×D6111yescharacteristic
331C4⋊C8—21no—
332C4⋊C8—1221no—
333#101—1224no—
334C22⋊C8—21no—
335C22⋊C8—1221no—
336#97—21no—
337#97—21no—
338#97—1221no—
339#97—1221no—
340C4×C8—21no—
341C4×C8—1221no—
342C24—1221no—
343C2×Q8—1222no—
344C2×Q8—1224no—
345C2×Q8—1221no—
346C2×Q8—1221no—
347C2×Q8—4882no—
348C2×Q8—2441no—
349C2×D4—612no—
350C2×D4—1224no—
351C2×D4—1221no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—611no—
355C22×C4—611no—
356C22×C4—611no—
357C22×C4—611no—
358C22×C4—1224no—
359C22×C4—1224no—
360C22×C4—1221no—
361C22×C4—1222no—
362C22×C4—1222no—
363C22×C4—4882no—
364C22×C4—4882no—
365C22×C4—2442no—
366C22×C4—2442no—
367C22×C4C2×C4×D6111yescharacteristic
368C22×C4D4×D6111yescharacteristic
369C22×C4D4×D6111yescharacteristic
370M16—22no—
371M16—41no—
372M16—1222no—
373M16—2441no—
374C2×C8—41no—
375C2×C8—41no—
376C2×C8—2441no—
377C2×C8—2441no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—612no—
385C4⋊C4—1224no—
386C4⋊C4—1224no—
387C4⋊C4—1224no—
388C4⋊C4—1221no—
389C4⋊C4—1221no—
390C4⋊C4—1221no—
391C4⋊C4—1221no—
392C4⋊C4—1221no—
393C4⋊C4—1221no—
394C4⋊C4—1221no—
395C4⋊C4#1175819812yes—
396C4⋊C4#1175819812yes—
397C22⋊C4—1224no—
398C22⋊C4—1224no—
399C22⋊C4—1222no—
400C22⋊C4—1222no—
401C42—1221no—
402C42—1221no—
403C42—1221no—
404C42—1221no—
405C42C2×D24411yescharacteristic
406C42D4×D6111yescharacteristic
407C42D4×D6111yescharacteristic
408C42C2×C22⋊D6111yescharacteristic
409C23—1224no—
410C23—1222no—
411C23—2442no—
412C23—2441no—
413C23—2441no—
414C23C22⋊C4×D6111yescharacteristic
415Q8—4884no—
416Q8—2442no—
417Q8—2442no—
418D4—614no—
419D4—1224no—
420D4—1222no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—612no—
431C2×C4—1221no—
432C2×C4—1221no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1222no—
439C2×C4—4882no—
440C2×C4—4882no—
441C2×C4—4884no—
442C2×C4—2448no—
443C2×C4—2442no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4C22⋊C4×D6111yescharacteristic
447C2×C4C2×#1175819811yescharacteristic
448C2×C4#1451974511yescharacteristic
449C2×C4#1451974511yescharacteristic
450C2×C4#1451974711yescharacteristic
451C2×C4#1451974711yescharacteristic
452C8—42no—
453C8—81no—
454C8—4881no—
455C8—2442no—
456C22—21no—
457C22—21no—
458C22—1224no—
459C22—2444no—
460C22—2444no—
461C22—2442no—
462C22—2442no—
463C22#1683961711yescharacteristic
464C22#104×D6111yescharacteristic
465C22#1683977711yescharacteristic
466C4—21no—
467C4—21no—
468C4—21no—
469C4—21no—
470C4—21no—
471C4—42no—
472C4—42no—
473C4—1222no—
474C4—2441no—
475C4—2441no—
476C4—2442no—
477C4—2441no—
478C4#101×D6112yes—
479C2—21no—
480C2—21no—
481C2—2444no—
482C2#2144574111yescharacteristic
483C2#2144576111yescharacteristic
484C2#2144578811yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1528C2
socleC22×C61#379
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1528D61
hypocenterC61#8372
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
2. C4×#14519695C2semidirect
3. #21444421C2semidirect
6. #21444162C2semidirect
7. C61×#1528C2semidirect
201. D244#101semidirect
240. #1528D61semidirect
277. C61#8372semidirect

Maximal subgroups

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

subgroupindex
C2×#168404682
C4×#145196952
#214444212
#214442632
#214442612
#214441622
C61×#15282
#837261