Finite Group Databasebeta

← #30598399

Subgroups — #30598399

Order 15616.

998 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 998 conjugacy classes of subgroups — too many to draw. Only its 112 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#21461683C211yesmaximal, characteristic, complemented
2#21461332C212yesmaximal, complemented
3#21461144C212yesmaximal, complemented
4#21461058C211yesmaximal, characteristic, complemented
5C2×#16840411C211yesmaximal, characteristic
6#16840779C2212yes—
7#16840765C2212yes—
8C2×#14519837—21no—
9#16840642—21no—
10#16840622—24no—
11D4⋊#92420—24no—
12#16840606—21no—
13#16840605—21no—
14C22×#11758224C411yescharacteristic
15#16840411—24no—
16#16840411—24no—
17C2×#14519775C2211yescharacteristic
18C2×#14519760—21no—
19C2×#14519758—21no—
20C2×#14519756C411yescharacteristic
21C2×#14519753C411yescharacteristic
22C2×#14519749—21no—
23C2×D4×Dic61C2211yescharacteristic
24C2×C4×C22⋊D61C2211yescharacteristic
25C22×#11758196—21no—
26C22×#41×C61C411yescharacteristic
27C2×#11758217—22no—
28#14519844—22no—
29#14519844—22no—
30C4⋊#92420—22no—
31#14519837—42no—
32C22⋊#92420—22no—
33C4×#92420—22no—
34C2×#11758224—22no—
35C2×#11758224—22no—
36C2×#11758224—44no—
37C22×Dic122C2×C411yescharacteristic
38C22×C22⋊D61—21no—
39C22×C22⋊D61D411yescharacteristic
40C23×Dic61—21no—
41C23×Dic61—21no—
42C22×C4×D61C2×C411yescharacteristic
43#14519775—22no—
44#14519775D414yes—
45#14519760—28no—
46#14519758—28no—
47#14519756—22no—
48#14519756—22no—
49#14519753—22no—
50#14519753—22no—
51#14519749—28no—
52D4×Dic61—22no—
53D4×Dic61D414yes—
54C4×C22⋊D61—22no—
55C4×C22⋊D61—22no—
56C2×C4⋊Dic61C2×C411yescharacteristic
57C2×#11758196—28no—
58C2×#11758196—21no—
59C2×#11758196—21no—
60C2×#11758196—21no—
61C2×#11758196—21no—
62C2×#11758196D411yescharacteristic
63C2×C22⋊Dic61—21no—
64C2×C22⋊Dic61—21no—
65C2×C22⋊Dic61D411yescharacteristic
66C2×#11758198—21no—
67C2×#11758198D411yescharacteristic
68C2×C4×Dic61C2311yescharacteristic
69C2×#41×C61—22no—
70C2×#41×C61—22no—
71C2×#41×C61—44no—
72C22×Q8×C61C2×C411yescharacteristic
73C22×D4×C61—21no—
74C22×D4×C61C2×C411yescharacteristic
75C23×C4×C61—21no—
76C23×C4×C61C2×C411yescharacteristic
77C24×C61—21no—
78C24×C61C22⋊C411yescharacteristic
79C23×D61C22⋊C411yescharacteristic
80#41×C61—48no—
81#41×C61—44no—
82#41×C61—44no—
83C2×Q8×C61—21no—
84C2×Q8×C61—42no—
85C2×Q8×C61C22⋊C412yes—
86C2×D4×C61—24no—
87C2×D4×C61—24no—
88C2×D4×C61—21no—
89C2×D4×C61—44no—
90C2×D4×C61C22⋊C412yes—
91C22×C4×C61—24no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—42no—
96C22×C4×C61—44no—
97C22×C4×C61C22⋊C411yescharacteristic
98C22×C4×C61C22×C411yescharacteristic
99C2×C22⋊D61—24no—
100C2×C22⋊D61—22no—
101C2×C22⋊D61—22no—
102C2×C22⋊D61—21no—
103C2×C22⋊D61—21no—
104C2×C22⋊D61—44no—
105C22×Dic61—24no—
106C22×Dic61—21no—
107C22×Dic61—21no—
108C22×Dic61—24no—
109C22×Dic61—44no—
110C22×Dic61—42no—
111C22×Dic61—41no—
112C22×Dic61—41no—
113C22×Dic61C22⋊C411yescharacteristic
114C22×Dic61C2×D411yescharacteristic
115C22×Dic61C2×D411yescharacteristic
116#11758224—44no—
117#11758224—48no—
118#11758224—44no—
119C2×C4×D61—21no—
120C2×C4×D61—21no—
121C2×C4×D61—42no—
122C2×Dic122—21no—
123C2×Dic122—42no—
124C2×Dic122C22⋊C412yes—
125#11758217—42no—
126#11758217—42no—
127C2×#92420—42no—
128C2×#92420—42no—
129C22⋊Dic61—24no—
130C22⋊Dic61—24no—
131C22⋊Dic61—22no—
132#11758198—24no—
133#11758198—22no—
134C4⋊Dic61—21no—
135C4⋊Dic61C22⋊C412yes—
136#11758196—24no—
137#11758196—24no—
138#11758196—22no—
139#11758196—24no—
140#11758196—24no—
141C4×Dic61C2×D412yes—
142C4×Dic61C2×D412yes—
143C23×C61—24no—
144C23×C61—22no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61—42no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61C2×C22⋊C411yescharacteristic
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61—41no—
158C22×D61—41no—
159Q8×C61—42no—
160Q8×C61—42no—
161D4×C61—24no—
162D4×C61—22no—
163D4×C61—48no—
164D4×C61#10014yescomplemented
165C2×C4×C61—22no—
166C2×C4×C61—21no—
167C2×C4×C61—22no—
168C2×C4×C61—42no—
169C2×C4×C61—42no—
170C2×C4×C61—48no—
171C2×C4×C61—42no—
172C2×C4×C61—41no—
173C2×C4×C61C2×C22⋊C411yescharacteristic
174C2×C4×C61C2×C22⋊C411yescharacteristic
175C22⋊D61—48no—
176C22⋊D61—42no—
177C22⋊D61—42no—
178C2×Dic61—22no—
179C2×Dic61—21no—
180C2×Dic61—22no—
181C2×Dic61—41no—
182C2×Dic61—42no—
183C2×Dic61—48no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—44no—
187C2×Dic61—44no—
188C2×Dic61—41no—
189C2×Dic61#12012yes—
190C2×Dic61#12012yes—
191C2×Dic61#13512yes—
192C2×Dic61AGL(1,ℤ/8)11yescharacteristic
193C2×Dic61#13711yescharacteristic
194C4×D61—42no—
195C4×D61—42no—
196Dic122—42no—
197Dic122—42no—
198#92420—82no—
199#92420—82no—
200#8393—611nomaximal, Sylow
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—24no—
204C22×C61—44no—
205C22×C61—44no—
206C22×C61—42no—
207C22×C61—42no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—41no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61#37911yescharacteristic
214C22×C61#41611yescharacteristic
215C22×C61#41711yescharacteristic
216C2×D61—41no—
217C2×D61—41no—
218C2×D61—41no—
219C2×D61—81no—
220C2×D61—81no—
221C4×C61—21no—
222C4×C61—41no—
223C4×C61—42no—
224C4×C61C2×#10012yes—
225Dic61—22no—
226Dic61—42no—
227Dic61—41no—
228Dic61—42no—
229Dic61#44912yes—
230Dic61#45212yes—
231C2×#547—611no—
232#1800—611no—
233#1548—612no—
234#1486—612no—
235#1460—611no—
236C2×C61—21no—
237C2×C61—21no—
238C2×C61—44no—
239C2×C61—81no—
240C2×C61#178311yescharacteristic
241C2×C61#178811yescharacteristic
242C2×C61#179611yescharacteristic
243D61—81no—
244C22×#41—611no—
245C22×#41#692311yescharacteristic
246#547—1224no—
247#547—1224no—
248C2×C4⋊Q8—611no—
249C2×#123—1221no—
250C2×#123—1221no—
251C2×C22⋊Q8—611no—
252C2×C22⋊Q8—611no—
253C2×#121—1221no—
254C2×C4×D4—611no—
255C2×C4×D4—611no—
256C22×C4⋊C4—1221no—
257#431—612no—
258#423—612no—
259C2×#100—1221no—
260#343—1221no—
261#333—1224no—
262D4⋊C8—1224no—
263#323—1221no—
264#323—1221no—
265C61#839311yescharacteristic, complemented, Sylow
266C2×#41—22no—
267C2×#41—22no—
268C2×#41—44no—
269C2×#41—1222no—
270C2×#41—1222no—
271C2×#41—2444no—
272C22×Q8—611no—
273C22×Q8C2×#692311yescharacteristic
274C22×D4—21no—
275C22×D4—611no—
276C22×D4—1221no—
277C22×D4C2×#692311yescharacteristic
278C23×C4—21no—
279C23×C4—611no—
280C23×C4—1221no—
281C23×C4—1221no—
282C23×C4C2×#692311yescharacteristic
283C2×M16—1222no—
284C4⋊Q8—614no—
285C4⋊Q8—1222no—
286#123—1228no—
287#123—1228no—
288C22⋊Q8—1222no—
289C22⋊Q8—1222no—
290C22⋊Q8—1222no—
291C22⋊Q8—1222no—
292#121—1228no—
293C4×D4—614no—
294C4×D4—1222no—
295C4×D4—1222no—
296C4×D4—1222no—
297C2×C4⋊C4—611no—
298C2×C4⋊C4—611no—
299C2×C4⋊C4—1221no—
300C2×C4⋊C4—1221no—
301C2×C4⋊C4—1221no—
302C2×C4⋊C4—1228no—
303C2×C4⋊C4—1221no—
304C2×C22⋊C4—611no—
305C2×C22⋊C4—611no—
306C2×C22⋊C4—1221no—
307C2×C22⋊C4—1221no—
308C2×C22⋊C4—1221no—
309C2×C42—611no—
310C4⋊C8—1222no—
311C4⋊C8—1222no—
312C4⋊C8—1222no—
313#100—2442no—
314C22⋊C8—1222no—
315C4×C8—1222no—
316C24—21no—
317C24—611no—
318C24C22⋊#692311yescharacteristic
319#41—48no—
320#41—44no—
321#41—44no—
322#41—2448no—
323#41—2444no—
324#41—2444no—
325C2×Q8—21no—
326C2×Q8—42no—
327C2×Q8—612no—
328C2×Q8—1221no—
329C2×Q8—2442no—
330C2×Q8C22⋊#692312yes—
331C2×D4—24no—
332C2×D4—24no—
333C2×D4—21no—
334C2×D4—44no—
335C2×D4—1221no—
336C2×D4—1222no—
337C2×D4—1222no—
338C2×D4—1221no—
339C2×D4—1224no—
340C2×D4—2444no—
341C2×D4C22⋊#692312yes—
342C22×C4—24no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—42no—
347C22×C4—44no—
348C22×C4—611no—
349C22×C4—611no—
350C22×C4—611no—
351C22×C4—1224no—
352C22×C4—1224no—
353C22×C4—1221no—
354C22×C4—1221no—
355C22×C4—1221no—
356C22×C4—1221no—
357C22×C4—2442no—
358C22×C4—2442no—
359C22×C4—2441no—
360C22×C4—2441no—
361C22×C4—2444no—
362C22×C4C22⋊#692311yescharacteristic
363C22×C4C22×#692311yescharacteristic
364M16—2442no—
365M16—2442no—
366C2×C8—2442no—
367C2×C8—2442no—
368C4⋊C4—612no—
369C4⋊C4—1222no—
370C4⋊C4—1224no—
371C4⋊C4—1224no—
372C4⋊C4—1224no—
373C4⋊C4—1224no—
374C4⋊C4—1221no—
375C22⋊C4—1222no—
376C22⋊C4—1224no—
377C22⋊C4—1222no—
378C22⋊C4—1224no—
379C22⋊C4—1224no—
380C42—612no—
381C42—612no—
382C23—24no—
383C23—22no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—42no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—1221no—
393C23—1221no—
394C23—1221no—
395C23—2441no—
396C23—2441no—
397C23C2×C22⋊#692311yescharacteristic
398Q8—42no—
399Q8—42no—
400Q8—2442no—
401Q8—2442no—
402D4—24no—
403D4—22no—
404D4—48no—
405D4—2442no—
406D4—2442no—
407D4—2448no—
408D4#1451983714yescomplemented
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—22no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—48no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—612no—
418C2×C4—611no—
419C2×C4—611no—
420C2×C4—612no—
421C2×C4—612no—
422C2×C4—1222no—
423C2×C4—1221no—
424C2×C4—1222no—
425C2×C4—2442no—
426C2×C4—2444no—
427C2×C4—2444no—
428C2×C4—2441no—
429C2×C4—2442no—
430C2×C4—2448no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4—2442no—
434C2×C4—2441no—
435C2×C4C2×C22⋊#692311yescharacteristic
436C2×C4C2×C22⋊#692311yescharacteristic
437C8—4882no—
438C8—4882no—
439C22—21no—
440C22—21no—
441C22—24no—
442C22—44no—
443C22—44no—
444C22—42no—
445C22—42no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—81no—
450C22—81no—
451C22—4881no—
452C22—4881no—
453C22—2441no—
454C22—2441no—
455C22—2441no—
456C22#1684070311yescharacteristic
457C22#1684075211yescharacteristic
458C22#1684075311yescharacteristic
459C4—21no—
460C4—41no—
461C4—42no—
462C4—612no—
463C4—612no—
464C4—1222no—
465C4—2441no—
466C4—2442no—
467C4—2442no—
468C4C2×#1451983712yes—
469C2—21no—
470C2—21no—
471C2—44no—
472C2—81no—
473C2—4881no—
474C2#2146165111yescharacteristic
475C2#2146165911yescharacteristic
476C2#2146167211yescharacteristic
subgroupG/H
centerC22#16840703
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×#41×C61C4
socleC22×C61#379
prime radicalC2×#16840411C2
cosocleC2×C4×Dic61C23
hypercenterC22×#41#6923
hypocenterC61#8393
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. #21461683C2semidirect
2. #21461332C2semidirect
3. #21461144C2semidirect
4. #21461058C2semidirect
164. D4×C61#100semidirect
265. C61#8393semidirect
408. D4#14519837semidirect

Maximal subgroups

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

subgroupindex
#214616832
#214613322
#214611442
#214610582
C2×#168404112
#839361