Finite Group Databasebeta

← #30599848

Subgroups — #30599848

Order 15616.

672 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840790C211yesmaximal, characteristic, complemented
2#21461941C211yesmaximal, characteristic, complemented
3C2×#16840610C211yesmaximal, characteristic, complemented
4C2×#16840610C211yesmaximal, characteristic, complemented
5#21460649C211yesmaximal, characteristic, complemented
6#21460641C211yesmaximal, characteristic, complemented
7C2×#16839844C211yesmaximal, characteristic
8C22×D61⋊C8—21no—
9#16840790—22no—
10#16840790—22no—
11C2×C4⋊#92420C2211yescharacteristic
12C2×C4⋊#92420C2211yescharacteristic
13C2×#14519834—21no—
14C2×#14519834—21no—
15C2×#14519834—21no—
16C2×C4×#92420C2211yescharacteristic
17C2×C4×#92420C2211yescharacteristic
18#16840610—22no—
19#16840610—22no—
20C22×D488C411yescharacteristic
21C2×#14519739C2211yescharacteristic
22C2×#14519739C2211yescharacteristic
23#16839844—22no—
24#16839844—22no—
25C2×#14519697C411yescharacteristic
26C2×#14519697C411yescharacteristic
27C2×C8×Dic61C2211yescharacteristic
28C2×#107×C61C411yescharacteristic
29C2×D61⋊C8—24no—
30C2×D61⋊C8—42no—
31C2×D61⋊C8—42no—
32C22×#92420—21no—
33C22×#92420—21no—
34C22×#92420—21no—
35C22×#92420D411yescharacteristic
36C22×#92420D411yescharacteristic
37C4⋊#92420—21no—
38C4⋊#92420—21no—
39C4⋊#92420—21no—
40C4⋊#92420D412yes—
41#14519834—24no—
42#14519834—42no—
43#14519834—42no—
44C4×#92420—21no—
45C4×#92420—21no—
46C4×#92420—21no—
47C4×#92420—21no—
48C22×D244C2×C411yescharacteristic
49C22×D244C2×C411yescharacteristic
50C22×C4×D61—21no—
51C22×C4×D61—21no—
52C2×D488—22no—
53C2×D488—22no—
54C2×D488C814yescomplemented
55C22×#92418C2×C411yescharacteristic
56#14519739—21no—
57#14519739—21no—
58#14519739—21no—
59#14519739—21no—
60#14519739—21no—
61#14519739—21no—
62#14519739D412yes—
63#14519739D412yes—
64C2×#11758198—21no—
65C2×#11758198—21no—
66C2×C4×Dic61C2311yescharacteristic
67#14519697—22no—
68#14519697—22no—
69C8×Dic61—21no—
70C8×Dic61—21no—
71C22×C8×C61C2×C411yescharacteristic
72C2×C4⋊C4×C61C2×C411yescharacteristic
73C2×C4⋊C4×C61C2×C411yescharacteristic
74#107×C61—22no—
75C23×D61—21no—
76C23×D61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61C22×C411yescharacteristic
80C22×Dic61C2×D411yescharacteristic
81C22×Dic61#4111yescharacteristic
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244C22⋊C412yes—
91C2×D244C2×C812yes—
92C2×D244C2×C812yescomplemented
93C2×D244M1612yes—
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C2×C4×D61—41no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×#92420—21no—
107C2×#92420—21no—
108C2×#92420—22no—
109C2×#92420—21no—
110C2×#92420—22no—
111C2×#92420—21no—
112C2×#92420—21no—
113C2×#92420—41no—
114C2×#92420—41no—
115C2×#92420—41no—
116C2×#92420—41no—
117C2×#92420—41no—
118C2×#92420—41no—
119C2×#92420—41no—
120C2×#92420D812yescomplemented
121D61⋊C8—48no—
122C2×C8×C61—21no—
123C2×C8×C61—21no—
124C2×C8×C61C2×C812yescomplemented
125C4⋊C4×C61—21no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61—21no—
128C4⋊C4×C61C22⋊C412yes—
129#11758198—22no—
130#11758198—22no—
131#11758198—41no—
132#11758198—41no—
133C4×Dic61C2×D411yescharacteristic
134C4×Dic61C2×D411yescharacteristic
135C4×Dic61C2×D411yescharacteristic
136C4×Dic61#4111yescharacteristic
137C2×#92418—21no—
138C2×#92418—21no—
139C2×#92418—21no—
140D488—28no—
141C23×C61C4×D411yescharacteristic
142C22×D61—22no—
143C22×D61—22no—
144C22×D61—22no—
145C22×D61—22no—
146C22×D61—41no—
147C22×D61—41no—
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—41no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C2×C4×C61—22no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61C2×C22⋊C411yescharacteristic
163C2×C4×C61C4×D411yescharacteristic
164C2×C4×C61C22×C811yescharacteristic
165C2×C4×C61C2×M1611yescharacteristic
166C2×C4×C61#13111yescharacteristic
167C2×C4×C61#13111yescharacteristic
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61#12011yescharacteristic
171C2×Dic61#12111yescharacteristic
172C2×Dic61#12111yescharacteristic
173C2×Dic61#12311yescharacteristic
174C2×Dic61C2×D811yescharacteristic
175C2×Dic61#13511yescharacteristic
176C2×Dic61AGL(1,ℤ/8)11yescharacteristic
177C2×Dic61AGL(1,ℤ/8)11yescharacteristic
178D244—22no—
179D244—22no—
180D244—22no—
181D244—22no—
182D244—22no—
183D244—41no—
184D244—41no—
185D244C22⋊C814yescomplemented
186C4×D61—42no—
187C4×D61—42no—
188C4×D61—42no—
189C4×D61—42no—
190C4×D61—81no—
191C4×D61—81no—
192C4×D61—81no—
193C4×D61—81no—
194#92420—22no—
195#92420—42no—
196#92420—42no—
197#92420—41no—
198#92420—81no—
199C8×C61—22no—
200#92418—41no—
201#8947—611nomaximal, Sylow
202C22×C61#38611yescharacteristic
203C22×C61C8×D411yescharacteristic
204C22×C61#43511yescharacteristic
205C22×C61C4×D811yescharacteristic
206C22×C61#44211yescharacteristic
207C22×C61#44311yescharacteristic
208C22×C61#44411yescharacteristic
209C2×D61—24no—
210C2×D61—42no—
211C2×D61—42no—
212C2×D61—42no—
213C2×D61—42no—
214C2×D61—42no—
215C2×D61—42no—
216C2×D61—42no—
217C2×D61—42no—
218C2×D61—42no—
219C2×D61—81no—
220C2×D61—81no—
221C2×D61—81no—
222C2×D61—81no—
223C4×C61—42no—
224C4×C61—81no—
225C4×C61C2×C22⋊C811yescharacteristic
226C4×C61#40811yescharacteristic
227C4×C61C8×D411yescharacteristic
228C4×C61#43511yescharacteristic
229Dic61—21no—
230Dic61—21no—
231Dic61#44711yescharacteristic
232Dic61#44911yescharacteristic
233Dic61#45911yescharacteristic
234Dic61#46311yescharacteristic
235C2×C4×D8—611no—
236C2×C8×D4—611no—
237#1954—611no—
238C2×D4⋊C8—611no—
239C2×D4⋊C8—611no—
240#1277—611no—
241#1273—611no—
242C2×C61C8×D811yescharacteristic
243C2×C61#158011yescharacteristic
244C2×C61#158111yescharacteristic
245C2×C61#158611yescharacteristic
246C2×C61#186911yescharacteristic
247C2×C61#187611yescharacteristic
248C2×C61#187911yescharacteristic
249D61—44no—
250D61—82no—
251C22×D8—611no—
252C23×C8—1221no—
253C2×C4×D4—611no—
254C2×C4×D4—611no—
255C4×D8—1222no—
256C4×D8—1222no—
257C8×D4—1222no—
258C8×D4—1222no—
259C2×#107#692311yescharacteristic
260C2×C4⋊C8—611no—
261C2×C4⋊C8—611no—
262C2×#102—611no—
263C2×#102—611no—
264C2×C22⋊C8—1221no—
265C2×C22⋊C8—1221no—
266C2×C22⋊C8—1221no—
267C2×C4×C8—611no—
268C2×C4×C8—611no—
269C2×C4×C8—611no—
270D4⋊C8—1222no—
271D4⋊C8—1222no—
272C61#894711yescharacteristic, complemented, Sylow
273C22×D4—611no—
274C22×D4—611no—
275C23×C4—1221no—
276C23×C4—1221no—
277C2×D8—614no—
278C2×D8—1222no—
279C2×D8—1222no—
280C22×C8—611no—
281C22×C8—611no—
282C22×C8—611no—
283C22×C8—1221no—
284C22×C8—1221no—
285C22×C8—1224no—
286C22×C8—1221no—
287C22×C8—2442no—
288C22×C8—2442no—
289C22×C8C2×#692311yescharacteristic
290C4×D4—612no—
291C4×D4—612no—
292C4×D4—1221no—
293C4×D4—1221no—
294C4×D4—1221no—
295C4×D4—1221no—
296C4×D4—1221no—
297C4×D4—1221no—
298C2×C4⋊C4C2×#692311yescharacteristic
299C2×C4⋊C4C2×#692311yescharacteristic
300C2×C22⋊C4—1221no—
301C2×C22⋊C4—1221no—
302C2×C42—611no—
303#107—22no—
304C4⋊C8—612no—
305C4⋊C8—1221no—
306C4⋊C8—1221no—
307C4⋊C8—1221no—
308#102—1222no—
309#102—1222no—
310C22⋊C8—1224no—
311C22⋊C8—2442no—
312C22⋊C8—2442no—
313C4×C8—1221no—
314C4×C8—1221no—
315C4×C8—1221no—
316C4×C8—1221no—
317C4×C8—1221no—
318C4×C8—1221no—
319C24—1221no—
320C24—1221no—
321C2×D4—612no—
322C2×D4—612no—
323C2×D4—612no—
324C2×D4—612no—
325C2×D4—1221no—
326C2×D4—1221no—
327C2×D4—1221no—
328C2×D4—1221no—
329C2×D4—1221no—
330C2×D4—1221no—
331C2×D4—1221no—
332C2×D4—1221no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—611no—
336C22×C4—611no—
337C22×C4—1222no—
338C22×C4—1222no—
339C22×C4—2441no—
340C22×C4—2441no—
341C22×C4—2441no—
342C22×C4—2441no—
343C22×C4—2441no—
344C22×C4—2441no—
345C22×C4—2441no—
346C22×C4—2441no—
347C22×C4—2441no—
348C22×C4—2441no—
349C22×C4C22×#692311yescharacteristic
350D8—1228no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—612no—
354C2×C8—1221no—
355C2×C8—1221no—
356C2×C8—1221no—
357C2×C8—1222no—
358C2×C8—1221no—
359C2×C8—1221no—
360C2×C8—1222no—
361C2×C8—1221no—
362C2×C8—1221no—
363C2×C8—1221no—
364C2×C8—2448no—
365C2×C8—2441no—
366C2×C8—2441no—
367C2×C8—2441no—
368C2×C8—2441no—
369C2×C8—2441no—
370C2×C8—2441no—
371C2×C8—2441no—
372C2×C8D61⋊C812yescomplemented
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4C22⋊#692312yes—
377C22⋊C4—1222no—
378C22⋊C4—1222no—
379C22⋊C4—2441no—
380C22⋊C4—2441no—
381C42—611no—
382C42—611no—
383C42—611no—
384C42—611no—
385C23—1222no—
386C23—1222no—
387C23—1222no—
388C23—1222no—
389C23—2441no—
390C23—2441no—
391C23—2441no—
392C23—2441no—
393C23—2441no—
394C23—2441no—
395C23—2441no—
396C23—2441no—
397C23—2441no—
398C23—2441no—
399C23D4×#692311yescharacteristic
400D4—614no—
401D4—1222no—
402D4—1222no—
403D4—1222no—
404D4—1222no—
405D4—1222no—
406D4—2441no—
407D4—2441no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—611no—
415C2×C4—611no—
416C2×C4—611no—
417C2×C4—611no—
418C2×C4—611no—
419C2×C4—611no—
420C2×C4—611no—
421C2×C4—611no—
422C2×C4—1221no—
423C2×C4—1221no—
424C2×C4—4881no—
425C2×C4—4881no—
426C2×C4—4881no—
427C2×C4—4881no—
428C2×C4—2442no—
429C2×C4—2442no—
430C2×C4—2442no—
431C2×C4—2442no—
432C2×C4C2×C22⋊#692311yescharacteristic
433C2×C4D4×#692311yescharacteristic
434C2×C4C2×D61⋊C811yescharacteristic
435C2×C4D61⋊M1611yescharacteristic
436C2×C4#1451986511yescharacteristic
437C2×C4#1451986511yescharacteristic
438C8—22no—
439C8—1222no—
440C8—4881no—
441C8—2441no—
442C8—2442no—
443C8—2442no—
444C8—2441no—
445C22—1224no—
446C22—4881no—
447C22—4881no—
448C22—4881no—
449C22—4881no—
450C22—2442no—
451C22—2442no—
452C22—2442no—
453C22—2442no—
454C22—2442no—
455C22—2442no—
456C22—2442no—
457C22—2442no—
458C22—2442no—
459C22#1684071011yescharacteristic
460C22#1684079011yescharacteristic
461C22#1684079211yescharacteristic
462C22D8×#692311yescharacteristic
463C22#1684080311yescharacteristic
464C22#1684080611yescharacteristic
465C22#1684080811yescharacteristic
466C4—42no—
467C4—81no—
468C4—611no—
469C4—611no—
470C4—611no—
471C4—611no—
472C4—1221no—
473C4—1221no—
474C4D61⋊(C22⋊C8)11yescharacteristic
475C4#1684073711yescharacteristic
476C4#1684079011yescharacteristic
477C4#1684079211yescharacteristic
478C2—4882no—
479C2—2444no—
480C2#2146140011yescharacteristic
481C2#2146141711yescharacteristic
482C2#2146141911yescharacteristic
483C2#2146143911yescharacteristic
484C2#2146179511yescharacteristic
485C2#2146180911yescharacteristic
486C2#2146181411yescharacteristic
subgroupG/H
centerC23D4×#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×#107×C61C4
socleC23×C61C4×D4
prime radicalC22×D488C4
cosocleC2×C4×Dic61C23
hypercenterC2×#107#6923
hypocenterC61#8947
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C2×#16840790C2semidirect
2. #21461941C2semidirect
3. C2×#16840610C2semidirect
4. C2×#16840610C2semidirect
5. #21460649C2semidirect
6. #21460641C2semidirect
54. C2×D488C8semidirect
92. C2×D244C2×C8semidirect
120. C2×#92420D8semidirect
124. C2×C8×C61C2×C8semidirect
185. D244C22⋊C8semidirect
272. C61#8947semidirect
372. C2×C8D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×#168407902
#214619412
C2×#168406102
#214606492
#214606412
C2×#168398442
#894761