Finite Group Databasebeta

← #30595770

Subgroups — #30595770

Order 15616.

702 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 108 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
1C4×C22⋊#92420C211yesmaximal, characteristic, complemented
2#21461482C211yesmaximal, characteristic, complemented
3#21460636C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5#21454162C211yesmaximal, characteristic
6C22×#11758217—21no—
7C2×C22⋊#92420—21no—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519773C411yescharacteristic
13C2×#14519751C411yescharacteristic
14C2×#14519749—21no—
15C2×#14519749—21no—
16C22×C4×Dic61C2211yescharacteristic
17#16839665C2211yescharacteristic
18#16839663C2211yescharacteristic
19#16839662—21no—
20#16839662—21no—
21#16839631C411yescharacteristic
22C2×#121×C61C411yescharacteristic
23C2×#11758217—24no—
24C2×#11758217—42no—
25C2×#11758217—42no—
26C22×#92420—22no—
27C22×#92420—22no—
28C22⋊#92420—24no—
29C4×#92420—42no—
30C22×D244C2×C411yescharacteristic
31C22×C22⋊D61—21no—
32C22×C22⋊D61—21no—
33C22×C22⋊D61—21no—
34C23×Dic61D411yescharacteristic
35C23×Dic61D411yescharacteristic
36#14519773—42no—
37#14519751—42no—
38#14519749—44no—
39#14519749—42no—
40#14519749—42no—
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×C4×Dic61—42no—
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61C2311yescharacteristic
54C22×D4×C61—21no—
55C22×D4×C61C2×C411yescharacteristic
56C23×C4×C61C2×C411yescharacteristic
57#121×C61—42no—
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C22⋊C4×C61—21no—
60C24×C61—21no—
61C24×C61C22⋊C411yescharacteristic
62C23×D61—21no—
63C2×D4×C61—22no—
64C2×D4×C61—41no—
65C2×D4×C61—41no—
66C2×D4×C61—42no—
67C2×D4×C61—42no—
68C2×D4×C61—42no—
69C22×C4×C61—22no—
70C22×C4×C61—22no—
71C22×C4×C61—21no—
72C22×C4×C61—41no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C2×C22⋊D61—42no—
78C2×C22⋊D61—42no—
79C2×C22⋊D61—42no—
80C2×C22⋊D61—42no—
81C2×C22⋊D61—42no—
82C2×C22⋊D61—42no—
83C2×C22⋊D61—42no—
84C22×Dic61—22no—
85C22×Dic61—22no—
86C22×Dic61—22no—
87C22×Dic61—22no—
88C22×Dic61—21no—
89C22×Dic61—41no—
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C22⋊C411yescharacteristic
92C22×Dic61D812yes—
93C22×Dic61SD1612yes—
94C22×Dic61C2×D411yescharacteristic
95C22×Dic61C2×D411yescharacteristic
96C2×D244—22no—
97C2×D244—41no—
98C2×D244—41no—
99#11758217—48no—
100C2×#92420—24no—
101C2×#92420—24no—
102C2×#92420—42no—
103C2×#92420—42no—
104C2×#92420—42no—
105C2×#92420—42no—
106C4⋊C4×C61—41no—
107C22⋊C4×C61—42no—
108C22⋊Dic61—41no—
109C22⋊Dic61—41no—
110C22⋊Dic61—42no—
111#11758198—42no—
112#11758198—41no—
113#11758198—41no—
114#11758198—42no—
115C4⋊Dic61—41no—
116#11758196—42no—
117#11758196—42no—
118C4×Dic61—22no—
119C4×Dic61—22no—
120C4×Dic61—41no—
121C4×Dic61—41no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61#10212yes—
136C23×C61C2×C22⋊C411yescharacteristic
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144D4×C61—82no—
145D4×C61—84no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—44no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61#10012yes—
155C2×C4×C61#13112yes—
156C22⋊D61—84no—
157C22⋊D61—84no—
158C22⋊D61—84no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—24no—
166C2×Dic61—24no—
167C2×Dic61—44no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61#9912yes—
172C2×Dic61#10212yes—
173C2×Dic61#10412yes—
174C2×Dic61#10412yes—
175C2×Dic61C2×D811yescharacteristic
176C2×Dic61C2×SD1611yescharacteristic
177C2×Dic61AGL(1,ℤ/8)12yes—
178D244—82no—
179#92420—44no—
180#92420—44no—
181#7684—611nomaximal, Sylow
182C22×C61—22no—
183C22×C61—22no—
184C22×C61—22no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61#40811yescharacteristic
197C22×C61C2×#9911yescharacteristic
198C22×C61C2×#10011yescharacteristic
199C22×C61C2×#10211yescharacteristic
200C22×C61#41811yescharacteristic
201C22×C61C2×#10411yescharacteristic
202C22×C61C2×#10411yescharacteristic
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—81no—
206C2×D61—81no—
207C2×D61—81no—
208C2×D61—81no—
209C2×D61—81no—
210C4×C61—22no—
211C4×C61—22no—
212C4×C61—81no—
213Dic61—21no—
214Dic61—21no—
215Dic61—22no—
216Dic61—22no—
217Dic61—81no—
218Dic61#32714yes—
219#2856—611no—
220C4×C22⋊C8—611no—
221#1728—611no—
222#1270—612no—
223#1270—612no—
224C2×C61—42no—
225C2×C61—161no—
226C2×C61#147111yescharacteristic
227C2×C61#148411yescharacteristic
228C2×C61#149211yescharacteristic
229C2×C61C2×#32711yescharacteristic
230C2×C61#150711yescharacteristic
231C2×C61#152511yescharacteristic
232C2×C61#154511yescharacteristic
233D61—161no—
234C22×M16—1221no—
235C2×#127—611no—
236C2×#121—611no—
237C2×#121—1221no—
238C2×#121—1221no—
239C2×#121#692311yescharacteristic
240C22×C42—611no—
241C2×C22⋊C8—1221no—
242C2×C4×C8—1221no—
243#390—611no—
244#390—611no—
245#390—1221no—
246#390—1221no—
247#384—611no—
248#336—612no—
249#336—612no—
250#336—1221no—
251C61#768411yescharacteristic, complemented, Sylow
252C22×D4—21no—
253C22×D4—611no—
254C22×D4—1221no—
255C22×D4—1221no—
256C22×D4—1221no—
257C22×D4C2×#692311yescharacteristic
258C23×C4—611no—
259C23×C4—611no—
260C23×C4C2×#692311yescharacteristic
261C2×M16—1224no—
262C2×M16—2442no—
263C2×M16—2442no—
264C22×C8—1222no—
265C22×C8—1222no—
266#127—2442no—
267#121—42no—
268#121—2442no—
269#121—2442no—
270#121—2444no—
271#121—2442no—
272C2×C4⋊C4—611no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4—1221no—
275C2×C4⋊C4C2×#692311yescharacteristic
276C2×C22⋊C4—21no—
277C2×C22⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280C2×C22⋊C4—1221no—
281C2×C22⋊C4—1221no—
282C2×C42—611no—
283C2×C42—611no—
284C2×C42—611no—
285C2×C42—611no—
286C2×C42—2442no—
287C22⋊C8—1224no—
288C4×C8—2442no—
289C24—21no—
290C24—1221no—
291C24C22⋊#692311yescharacteristic
292C2×D4—22no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—42no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4—1222no—
299C2×D4—2441no—
300C2×D4—2441no—
301C2×D4—2442no—
302C2×D4—2442no—
303C2×D4—2442no—
304C2×D4—2442no—
305C2×D4—2442no—
306C2×D4—2442no—
307C2×D4—2442no—
308C2×D4—2442no—
309C2×D4—2442no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—41no—
314C22×C4—611no—
315C22×C4—612no—
316C22×C4—612no—
317C22×C4—611no—
318C22×C4—611no—
319C22×C4—611no—
320C22×C4—1222no—
321C22×C4—1222no—
322C22×C4—1222no—
323C22×C4—1222no—
324C22×C4—1221no—
325C22×C4—2441no—
326C22×C4C22⋊#692311yescharacteristic
327C22×C4C22×#692311yescharacteristic
328M16—2448no—
329C2×C8—1224no—
330C2×C8—1224no—
331C2×C8—2442no—
332C2×C8—2442no—
333C2×C8—2442no—
334C2×C8—2442no—
335C4⋊C4—41no—
336C4⋊C4—2441no—
337C4⋊C4—2442no—
338C4⋊C4—2442no—
339C22⋊C4—42no—
340C22⋊C4—2441no—
341C22⋊C4—2441no—
342C22⋊C4—2442no—
343C22⋊C4—2441no—
344C22⋊C4—2441no—
345C22⋊C4—2442no—
346C22⋊C4—2442no—
347C42—1222no—
348C42—1222no—
349C42—2441no—
350C42—2441no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—2441no—
365C23—2441no—
366C23—2441no—
367C23—2441no—
368C23—2441no—
369C23—2441no—
370C23—2441no—
371C23#1451983912yes—
372C23C2×C22⋊#692311yescharacteristic
373D4—82no—
374D4—84no—
375D4—4882no—
376D4—4884no—
377D4—4884no—
378D4—4884no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—44no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—612no—
388C2×C4—612no—
389C2×C4—612no—
390C2×C4—611no—
391C2×C4—611no—
392C2×C4—612no—
393C2×C4—612no—
394C2×C4—1224no—
395C2×C4—1224no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—2444no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4#1451983712yes—
407C2×C4#1451986412yes—
408C8—2444no—
409C8—2444no—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—4881no—
425C22—4881no—
426C22—4881no—
427C22—4881no—
428C22—4881no—
429C22—4881no—
430C22—4881no—
431C22#1684073511yescharacteristic
432C22D61⋊#9911yescharacteristic
433C22C2×#1451983711yescharacteristic
434C22C2×#1451983911yescharacteristic
435C22#1684075411yescharacteristic
436C22D61⋊#10411yescharacteristic
437C22D61⋊#10411yescharacteristic
438C4—22no—
439C4—22no—
440C4—81no—
441C4—614no—
442C4—1221no—
443C4—1221no—
444C4—1222no—
445C4—1222no—
446C4—4881no—
447C2—42no—
448C2—161no—
449C2—9761no—
450C2#2146109511yescharacteristic
451C2#2146113811yescharacteristic
452C2#2146116411yescharacteristic
453C2D61⋊#32711yescharacteristic
454C2#2146121411yescharacteristic
455C2#2146127311yescharacteristic
456C2#2146132611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#121×C61C4
socleC23×C61C2×C22⋊C4
prime radical#21454162C2
cosocleC2×C4×Dic61C23
hypercenterC2×#121#6923
hypocenterC61#7684
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C4×C22⋊#92420C2semidirect
2. #21461482C2semidirect
3. #21460636C2semidirect
4. #21460635C2semidirect
251. C61#7684semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#924202
#214614822
#214606362
#214606352
#214541622
#768461