Finite Group Databasebeta

← #29576468

Subgroups — #29576468

Order 15616.

594 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 111 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×#16840076C211yesmaximal, characteristic
2#21448690C211yesmaximal, characteristic, complemented
3#21446654C211yesmaximal, characteristic
4#21445903C211yesmaximal, characteristic, complemented
5#21444386C211yesmaximal, characteristic
6#21443666C211yesmaximal, characteristic, complemented
7C61×#1289C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×#14519733—21no—
10C22×C4⋊Dic61C2211yescharacteristic
11#16840076—22no—
12#16840076—21no—
13#16840076—21no—
14C2×#14519711C412yescomplemented
15C2×#14519699C412yescomplemented
16C2×#14519691—21no—
17C2×#14519691—21no—
18C2×C22⋊#92418C2211yescharacteristic
19#16839658—21no—
20#16839645—22no—
21#16839623—21no—
22C4⋊C4×Dic61—21no—
23C4×C22⋊Dic61C2211yescharacteristic
24#16839524—22no—
25#16839495—22no—
26C2×C22⋊C8×C61C2211yescharacteristic
27C61×#380C2211yescharacteristic
28C61×#380C2211yescharacteristic
29C22×D244C2×C411yescharacteristic
30C22×C22⋊D61—21no—
31C23×Dic61—21no—
32C22×#92418—21no—
33#14519751—21no—
34#14519751—21no—
35#14519751—21no—
36#14519751—21no—
37#14519733—42no—
38#14519733—42no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×C4⋊Dic61C2×C412yes—
44C2×C4⋊Dic61D412yes—
45C2×C4⋊Dic61D411yescharacteristic
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758196—22no—
48C2×C22⋊Dic61D411yescharacteristic
49C2×C22⋊Dic61D411yescharacteristic
50C2×#11758198—21no—
51C2×C4×Dic61—22no—
52C2×C4×Dic61—21no—
53#14519711—22no—
54#14519711—22no—
55#14519699—22no—
56#14519699—22no—
57#14519691—42no—
58#14519691—42no—
59C22⋊#92418—21no—
60C22⋊#92418—21no—
61#14519684—22no—
62#14519684—22no—
63#14519684—21no—
64C23×C4×C61C2311yescharacteristic
65C22×C8×C61C2×C412yes—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C22⋊C4×C61—21no—
69C2×C22⋊C4×C61—21no—
70C22⋊C8×C61—21no—
71C22⋊C8×C61—21no—
72#95×C61—21no—
73#95×C61D412yes—
74C24×C61C2×D411yescharacteristic
75C23×D61—21no—
76C22×C4×C61—22no—
77C22×C4×C61—42no—
78C22×C4×C61—41no—
79C22×C4×C61C22×C411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61#4111yescharacteristic
84C22×C4×C61#4111yescharacteristic
85C2×C22⋊D61—41no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C22×Dic61—22no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—22no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—41no—
99C22×Dic61—41no—
100C22×Dic61—41no—
101C22×Dic61—41no—
102C2×D244—21no—
103C2×D244—21no—
104C2×D244—42no—
105C2×C8×C61—22no—
106C2×C8×C61—42no—
107C4⋊C4×C61—42no—
108C4⋊C4×C61—42no—
109C22⋊C4×C61—41no—
110C22⋊C4×C61—41no—
111C22⋊C4×C61—41no—
112C22⋊C4×C61—41no—
113C22⋊Dic61—21no—
114C22⋊Dic61—21no—
115C22⋊Dic61—21no—
116C22⋊Dic61D812yes—
117#11758198—41no—
118#11758198—41no—
119C4⋊Dic61—22no—
120C4⋊Dic61—22no—
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61—21no—
124C4⋊Dic61—21no—
125C4⋊Dic61C22⋊C412yes—
126C4⋊Dic61C22⋊C412yes—
127#11758196—44no—
128C4×Dic61—44no—
129C4×Dic61—42no—
130C2×#92418—42no—
131C2×#92418—41no—
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—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—42no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—81no—
156C2×C4×C61—81no—
157C2×C4×C61—81no—
158C2×C4×C61C2×C22⋊C411yescharacteristic
159C2×C4×C61C4×D411yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12311yescharacteristic
162C22⋊D61—81no—
163C22⋊D61—81no—
164C22⋊D61—81no—
165C22⋊D61—81no—
166C2×Dic61—22no—
167C2×Dic61—22no—
168C2×Dic61—22no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—42no—
172C2×Dic61—42no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185D244—42no—
186D244—81no—
187C8×C61—42no—
188#92418—81no—
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—82no—
216C4×C61—161no—
217C4×C61#41012yes—
218Dic61—42no—
219Dic61—42no—
220Dic61—42no—
221Dic61—81no—
222Dic61—81no—
223C2×#480—611no—
224#2344—611no—
225#1964—611no—
226#1823—611no—
227#1519—611no—
228#1289D6111yescharacteristic, complemented
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⋊C4—611no—
243#480—1222no—
244#480—1221no—
245#480—1221no—
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#380C2×D6111yescharacteristic
256#380C2×D6111yescharacteristic
257C4×C4⋊C4—1221no—
258C4×C22⋊C4—611no—
259#340—1222no—
260#327—1222no—
261C61#926011yescharacteristic, complemented, Sylow
262C22×D4—611no—
263C22×D4—1221no—
264C23×C4—1221no—
265C23×C4C22×D6111yescharacteristic
266C22×C8—1221no—
267C22×C8C4×D6112yes—
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—612no—
277C2×C4⋊C4—612no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4—611no—
281C2×C4⋊C4—1221no—
282C2×C4⋊C4—1221no—
283C2×C4⋊C4—1221no—
284C2×C4⋊C4—1222no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—611no—
288C2×C22⋊C4—611no—
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—1222no—
304#95—1222no—
305#95—1221no—
306#95D24412yes—
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—42no—
320C22×C4—41no—
321C22×C4—1222no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1222no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—2441no—
329C22×C4—2441no—
330C22×C4—2441no—
331C22×C4—2441no—
332C22×C4C2×C4×D6111yescharacteristic
333C22×C4C2×D24411yescharacteristic
334C22×C4#1175822211yescharacteristic
335C22×C4D4×D6111yescharacteristic
336C22×C4D4×D6111yescharacteristic
337C22×C4#1175822611yescharacteristic
338C2×C8—22no—
339C2×C8—42no—
340C2×C8—2442no—
341C2×C8—2441no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—612no—
345C4⋊C4—612no—
346C4⋊C4—1222no—
347C4⋊C4—1222no—
348C4⋊C4—1221no—
349C4⋊C4—1221no—
350C4⋊C4—1221no—
351C4⋊C4—1221no—
352C4⋊C4—2444no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—612no—
358C22⋊C4—1221no—
359C22⋊C4—1221no—
360C22⋊C4—1221no—
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#1451973911yescharacteristic
373C23#1451974711yescharacteristic
374C23#1451975011yescharacteristic
375C23D8×D6111yescharacteristic
376C23#1451980011yescharacteristic
377C23#1451980411yescharacteristic
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—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—1222no—
398C2×C4—1222no—
399C2×C4—1222no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2442no—
409C2×C4—2442no—
410C2×C4—2442no—
411C2×C4—2442no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4C22⋊C4×D6111yescharacteristic
417C2×C4C4×D24411yescharacteristic
418C2×C4#1451975211yescharacteristic
419C2×C4#1451976211yescharacteristic
420C8—42no—
421C8—4881no—
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#1683964011yescharacteristic
438C22#1683984411yescharacteristic
439C22#1683987311yescharacteristic
440C22#1683989711yescharacteristic
441C22#1683991011yescharacteristic
442C22#1683995611yescharacteristic
443C22#1683998011yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—82no—
448C4—161no—
449C4—4881no—
450C4—4881no—
451C4—2442no—
452C4—2442no—
453C4—2442no—
454C4#1683973412yes—
455C2—21no—
456C2—21no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—9761no—
462C2#2144616811yescharacteristic
463C2#2144627611yescharacteristic
464C2#2144631411yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1289C2
socleC22×C61#386
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1289D61
hypocenterC61#9260
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
2. #21448690C2semidirect
4. #21445903C2semidirect
6. #21443666C2semidirect
7. C61×#1289C2semidirect
14. C2×#14519711C4semidirect
15. C2×#14519699C4semidirect
228. #1289D61semidirect
261. C61#9260semidirect

Maximal subgroups

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

subgroupindex
C2×#168400762
#214486902
#214466542
#214459032
#214443862
#214436662
C61×#12892
#926061