Finite Group Databasebeta

← #29576465

Subgroups — #29576465

Order 15616.

594 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840075C211yesmaximal, characteristic
2#21448688C211yesmaximal, characteristic, complemented
3#21446654C211yesmaximal, characteristic
4#21444388C211yesmaximal, characteristic
5#21443686C211yesmaximal, characteristic, complemented
6#21443665C211yesmaximal, characteristic, complemented
7C61×#1823C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×#14519736—21no—
10#16840075—21no—
11#16840075—21no—
12#16840075—22no—
13C2×#14519710C412yescomplemented
14C2×#14519697C412yescomplemented
15C2×#14519691—21no—
16C2×#14519691—21no—
17C2×C22⋊#92418C2211yescharacteristic
18#16839661—21no—
19#16839648—22no—
20#16839625—21no—
21#16839622C2211yescharacteristic
22C4⋊C4×Dic61—21no—
23C4×C22⋊Dic61C2211yescharacteristic
24#16839497—22no—
25C22×C4⋊C4×C61C2211yescharacteristic
26C2×C22⋊C8×C61C2211yescharacteristic
27C61×#380C2211yescharacteristic
28C61×#340—22no—
29C22×D244C2×C411yescharacteristic
30C22×C22⋊D61—21no—
31C22×#92418C2×C412yes—
32#14519751—21no—
33#14519751—21no—
34#14519751—21no—
35#14519751—21no—
36#14519736—42no—
37#14519736—42no—
38C2×C4⋊Dic61—22no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61D411yescharacteristic
43C2×C22⋊Dic61D411yescharacteristic
44C2×#11758198—21no—
45C2×C4×Dic61—22no—
46C2×C4×Dic61—21no—
47#14519710—22no—
48#14519710—22no—
49#14519697—22no—
50#14519697—22no—
51#14519691—42no—
52#14519691—42no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55#14519684—22no—
56#14519684—22no—
57#14519684—21no—
58#14519684D412yes—
59C23×C4×C61—21no—
60C23×C4×C61C2311yescharacteristic
61C22×C8×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61C2×C412yes—
67C2×C4⋊C4×C61D411yescharacteristic
68C2×C4⋊C4×C61D411yescharacteristic
69C2×C4⋊C4×C61D412yes—
70C2×C22⋊C4×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73#95×C61—21no—
74C24×C61C2×D411yescharacteristic
75C23×D61—21no—
76C22×C4×C61—22no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—22no—
80C22×C4×C61—42no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61C22×C411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61#4111yescharacteristic
91C22×C4×C61#4111yescharacteristic
92C2×C22⋊D61—41no—
93C2×C22⋊D61—41no—
94C2×C22⋊D61—41no—
95C2×C22⋊D61—41no—
96C2×C22⋊D61—41no—
97C2×C22⋊D61—41no—
98C22×Dic61—21no—
99C22×Dic61—21no—
100C22×Dic61—21no—
101C22×Dic61—22no—
102C2×D244—21no—
103C2×D244—21no—
104C2×D244—42no—
105C2×C8×C61—42no—
106C2×C8×C61—41no—
107C4⋊C4×C61—22no—
108C4⋊C4×C61—22no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—42no—
112C4⋊C4×C61C22⋊C412yes—
113C4⋊C4×C61C22⋊C412yes—
114C22⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C22⋊Dic61—21no—
117C22⋊Dic61—21no—
118C22⋊Dic61—21no—
119C22⋊Dic61—41no—
120C22⋊Dic61—41no—
121C22⋊Dic61D812yes—
122#11758198—41no—
123#11758198—41no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126C4⋊Dic61—44no—
127C4⋊Dic61—42no—
128C4×Dic61—44no—
129C4×Dic61—42no—
130C2×#92418—22no—
131C2×#92418—42no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61C4×D411yescharacteristic
135C23×C61#12011yescharacteristic
136C23×C61#12111yescharacteristic
137C23×C61C2×D811yescharacteristic
138C23×C61#13511yescharacteristic
139C23×C61AGL(1,ℤ/8)11yescharacteristic
140C23×C61AGL(1,ℤ/8)11yescharacteristic
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—81no—
145C22×D61—81no—
146C2×C4×C61—22no—
147C2×C4×C61—22no—
148C2×C4×C61—22no—
149C2×C4×C61—22no—
150C2×C4×C61—22no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—42no—
161C2×C4×C61—42no—
162C2×C4×C61—81no—
163C2×C4×C61—81no—
164C2×C4×C61—81no—
165C2×C4×C61C2×C22⋊C411yescharacteristic
166C2×C4×C61C4×D411yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12311yescharacteristic
169C22⋊D61—81no—
170C22⋊D61—81no—
171C22⋊D61—81no—
172C22⋊D61—81no—
173C2×Dic61—22no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—42no—
178C2×Dic61—41no—
179C2×Dic61—42no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—42no—
184C2×Dic61—41no—
185D244—42no—
186D244—81no—
187C8×C61—81no—
188#92418—42no—
189#9260—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61#38611yescharacteristic
201C22×C61C4×D811yescharacteristic
202C22×C61#44211yescharacteristic
203C22×C61#44711yescharacteristic
204C22×C61#44911yescharacteristic
205C22×C61#45911yescharacteristic
206C22×C61#46311yescharacteristic
207C2×D61—81no—
208C2×D61—81no—
209C2×D61—81no—
210C2×D61—161no—
211C2×D61—161no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—42no—
216C4×C61—42no—
217C4×C61—161no—
218C4×C61#41012yes—
219Dic61—42no—
220Dic61—82no—
221Dic61—81no—
222Dic61—81no—
223C2×#480—611no—
224#2344—611no—
225#1964—611no—
226#1823D6111yescharacteristic, complemented
227#1519—611no—
228#1289—611no—
229#1282—611no—
230C2×C61—21no—
231C2×C61—21no—
232C2×C61—21no—
233C2×C61—21no—
234C2×C61—21no—
235C2×C61—21no—
236C2×C61#187911yescharacteristic
237C2×C61#189911yescharacteristic
238C2×C61#190511yescharacteristic
239D61—161no—
240C2×#121—611no—
241C2×#117—1221no—
242C22×C4⋊C4C2×D6111yescharacteristic
243#480—1221no—
244#480—1221no—
245#480—1222no—
246C2×#107—612no—
247C2×#102—612no—
248C2×#99—1221no—
249C2×#99—1221no—
250C2×C22⋊C8—611no—
251C2×C22⋊C8C2×D6111yescharacteristic
252#389—1221no—
253#387—1222no—
254#381—1221no—
255#380—611no—
256#380C2×D6111yescharacteristic
257C4×C4⋊C4—1221no—
258C4×C22⋊C4—611no—
259#340—22no—
260#327—1222no—
261C61#926011yescharacteristic, complemented, Sylow
262C22×D4—611no—
263C22×D4—1221no—
264C23×C4—21no—
265C23×C4C22×D6111yescharacteristic
266C22×C8—21no—
267C22×C8—612no—
268#121—1221no—
269#121—1221no—
270#121—1221no—
271#121—1221no—
272#117—2442no—
273#117—2442no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4—1222no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4C4×D6112yes—
282C2×C4⋊C4D24411yescharacteristic
283C2×C4⋊C4D24411yescharacteristic
284C2×C4⋊C4C22⋊D6112yes—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—611no—
287C2×C22⋊C4—611no—
288C2×C22⋊C4—1221no—
289C2×C22⋊C4—1221no—
290C2×C42—1222no—
291C2×C42—1221no—
292#107—1222no—
293#107—1222no—
294#102—1222no—
295#102—1222no—
296#99—2442no—
297#99—2442no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—1221no—
301C22⋊C8—1221no—
302#95—21no—
303#95—612no—
304#95—1222no—
305#95—1222no—
306#95—1221no—
307C24—1221no—
308C24D4×D6111yescharacteristic
309C2×D4—1221no—
310C2×D4—1221no—
311C2×D4—2442no—
312C2×D4—2441no—
313C2×D4—2441no—
314C2×D4—2441no—
315C2×D4—2441no—
316C2×D4—2441no—
317C2×D4—2441no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—42no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1222no—
331C22×C4—1221no—
332C22×C4C2×C4×D6111yescharacteristic
333C22×C4C2×D24411yescharacteristic
334C22×C4D4×D6111yescharacteristic
335C22×C4#1175822411yescharacteristic
336C22×C4#1175822411yescharacteristic
337C22×C4C2×C22⋊D6111yescharacteristic
338C2×C8—42no—
339C2×C8—41no—
340C2×C8—1222no—
341C2×C8—2442no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—42no—
347C4⋊C4—1221no—
348C4⋊C4—1221no—
349C4⋊C4—2442no—
350C4⋊C4—2444no—
351C4⋊C4#1175819812yes—
352C4⋊C4#1175819812yes—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—612no—
356C22⋊C4—1221no—
357C22⋊C4—1221no—
358C22⋊C4—1221no—
359C22⋊C4—2441no—
360C22⋊C4—2441no—
361C22⋊C4—2441no—
362C22⋊C4—2441no—
363C42—2442no—
364C42—2444no—
365C23—41no—
366C23—41no—
367C23—4881no—
368C23—4881no—
369C23—2441no—
370C23—2441no—
371C23—2441no—
372C23#1451973711yescharacteristic
373C23#1451974711yescharacteristic
374C23#1451974911yescharacteristic
375C23D8×D6111yescharacteristic
376C23#1451979811yescharacteristic
377C23#1451980111yescharacteristic
378C23#1451980411yescharacteristic
379D4—4881no—
380D4—4881no—
381D4—4881no—
382D4—4881no—
383D4—4881no—
384D4—2442no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—1222no—
405C2×C4—2441no—
406C2×C4—2442no—
407C2×C4—2442no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2442no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4C2×#1175819811yescharacteristic
417C2×C4#1451973711yescharacteristic
418C2×C4#1451974911yescharacteristic
419C2×C4#1451976111yescharacteristic
420C8—81no—
421C8—2442no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—9761no—
433C22—9761no—
434C22—4881no—
435C22—4881no—
436C22—4881no—
437C22#1683963911yescharacteristic
438C22#1683984211yescharacteristic
439C22#1683987111yescharacteristic
440C22#1683989711yescharacteristic
441C22#1683990811yescharacteristic
442C22#1683995511yescharacteristic
443C22#1683997911yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—42no—
448C4—42no—
449C4—161no—
450C4—4882no—
451C4—4881no—
452C4—4881no—
453C4—2442no—
454C4#1683973512yes—
455C2—21no—
456C2—21no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—9761no—
462C2#2144616511yescharacteristic
463C2#2144627511yescharacteristic
464C2#2144631111yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1823C2
socleC22×C61#386
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1823D61
hypocenterC61#9260
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
2. #21448688C2semidirect
5. #21443686C2semidirect
6. #21443665C2semidirect
7. C61×#1823C2semidirect
13. C2×#14519710C4semidirect
14. C2×#14519697C4semidirect
226. #1823D61semidirect
261. C61#9260semidirect

Maximal subgroups

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

subgroupindex
C2×#168400752
#214486882
#214466542
#214443882
#214436862
#214436652
C61×#18232
#926061