Finite Group Databasebeta

← #29575206

Subgroups — #29575206

Order 15616.

544 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455815C211yesmaximal, characteristic
2#21446617C211yesmaximal, characteristic, complemented
3#21444468C211yesmaximal, characteristic, complemented
4#21444243C211yesmaximal, characteristic, complemented
5#21443714C211yesmaximal, characteristic, complemented
6#21443664C211yesmaximal, characteristic, complemented
7C61×#2932C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9#16840073C412yes—
10#16840039—21no—
11#16839954—21no—
12#16839895C412yes—
13C4×#11758199—22no—
14#16839815C2211yescharacteristic
15#16839815C2211yescharacteristic
16C2×C4⋊#92418C2211yescharacteristic
17C2×#14519689—21no—
18C2×#14519689—21no—
19#16839508—21no—
20#16839506—21no—
21#16839489—22no—
22C2×#131×C61—21no—
23C61×#532C2211yescharacteristic
24C61×#435—22no—
25C61×#435—22no—
26C61×#423C2211yescharacteristic
27C61×#408—21no—
28C2×#97×C61C2211yescharacteristic
29C22×D244C2×C411yescharacteristic
30C22×C4×D61—21no—
31C2×#11758199—22no—
32C22×#92418—21no—
33C4×D244—21no—
34C4×D244—21no—
35C4×D244—21no—
36C4×D244—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758198—21no—
39#14519710—22no—
40C4⋊#92418—21no—
41C4⋊#92418—21no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44#14519698—22no—
45#14519697—22no—
46C22⋊#92418—21no—
47C22⋊#92418C2×C412yes—
48#14519689—42no—
49#14519689—42no—
50C4×#92418—21no—
51C4×#92418—21no—
52C2×#41×C61—21no—
53#131×C61—42no—
54#131×C61—42no—
55C2×M16×C61—22no—
56C2×M16×C61—21no—
57C22×C8×C61—22no—
58C22×C8×C61D411yescharacteristic
59C22×C8×C61D411yescharacteristic
60C4⋊Q8×C61D411yescharacteristic
61#127×C61D411yescharacteristic
62#124×C61—21no—
63#121×C61—21no—
64#121×C61C2×C412yes—
65C4×D4×C61—21no—
66C4×D4×C61D412yes—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61D412yes—
70C22⋊C8×C61—24no—
71#97×C61—21no—
72#97×C61—21no—
73C23×D61—21no—
74#41×C61—41no—
75#41×C61—41no—
76#41×C61—41no—
77#41×C61—41no—
78C2×Q8×C61—21no—
79C2×D4×C61—22no—
80C2×D4×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61C22⋊C412yes—
83C22×C4×C61—22no—
84C22×C4×C61C22×C411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C22×Dic61—21no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244—42no—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97M16×C61—44no—
98M16×C61—41no—
99M16×C61—41no—
100C2×C8×C61—21no—
101C2×C8×C61—21no—
102C2×C8×C61—21no—
103C2×C8×C61—22no—
104C2×C8×C61—21no—
105C2×C8×C61—21no—
106C2×C8×C61—44no—
107C2×C8×C61D812yescomplemented
108C4⋊C4×C61—21no—
109C4⋊C4×C61C22⋊C412yes—
110C22⋊C4×C61—22no—
111C22⋊C4×C61—22no—
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61#4111yescharacteristic
116#11758199—44no—
117#11758198—41no—
118#11758198—41no—
119C4⋊Dic61—21no—
120C4⋊Dic61—21no—
121C2×#92418—22no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126C23×C61—22no—
127C23×C61C4×D411yescharacteristic
128C22×D61—22no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135Q8×C61—41no—
136Q8×C61—41no—
137D4×C61—42no—
138D4×C61—42no—
139D4×C61—42no—
140D4×C61—41no—
141D4×C61—41no—
142D4×C61—81no—
143C2×C4×C61—22no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—42no—
147C2×C4×C61—42no—
148C2×C4×C61C2×C22⋊C411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12311yescharacteristic
154C2×C4×C61C2×D811yescharacteristic
155C2×C4×C61#13511yescharacteristic
156C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161D244—22no—
162D244—22no—
163D244—41no—
164D244—41no—
165C4×D61—81no—
166C4×D61—81no—
167C4×D61—81no—
168C4×D61—81no—
169C8×C61—22no—
170C8×C61—42no—
171C8×C61—41no—
172#92418—42no—
173#92418—81no—
174#92418—81no—
175#9049—611nomaximal, Sylow
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—42no—
179C22×C61—42no—
180C22×C61—42no—
181C22×C61#38611yescharacteristic
182C22×C61C4×D811yescharacteristic
183C22×C61#44211yescharacteristic
184C2×D61—42no—
185C2×D61—42no—
186C2×D61—42no—
187C2×D61—81no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—81no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—42no—
196C4×C61#44711yescharacteristic
197C4×C61#44911yescharacteristic
198C4×C61#45911yescharacteristic
199C4×C61#46311yescharacteristic
200Dic61—81no—
201#3100—611no—
202#2932D6111yescharacteristic, complemented
203#1955—611no—
204#1540—611no—
205#1486—611no—
206#1301—611no—
207#1281—611no—
208C2×C61—21no—
209C2×C61—21no—
210C2×C61—82no—
211C2×C61#187911yescharacteristic
212C2×C61#188111yescharacteristic
213C2×C61#189111yescharacteristic
214D61—82no—
215C2×#131—21no—
216#532C2×D6111yescharacteristic
217C2×C4×D4—611no—
218#480—612no—
219#474—1221no—
220#459—1221no—
221#447—612no—
222C4×D8—1222no—
223#435—22no—
224#435—22no—
225#431—611no—
226#431—611no—
227#423C2×D6111yescharacteristic
228C2×C4⋊C8—611no—
229#408—21no—
230C2×C22⋊C8—1221no—
231C2×C22⋊C8—1221no—
232C2×#97C2×D6111yescharacteristic
233#332—1221no—
234#331—1221no—
235D4⋊C8—1222no—
236C61#904911yescharacteristic, complemented, Sylow
237C2×#41—21no—
238C22×D4—611no—
239C23×C4—1221no—
240C2×D8—1222no—
241#131—42no—
242#131—42no—
243C2×M16—22no—
244C2×M16—21no—
245C22×C8—22no—
246C22×C8—1221no—
247C22×C8C22⋊D6111yescharacteristic
248C22×C8C22⋊D6111yescharacteristic
249C4⋊Q8D24411yescharacteristic
250#127D24411yescharacteristic
251#124—21no—
252#121—21no—
253#121C4×D6112yes—
254C4×D4—21no—
255C4×D4—1221no—
256C4×D4—1221no—
257C4×D4—1221no—
258C4×D4—1221no—
259C4×D4C22⋊D6112yes—
260C2×C4⋊C4—611no—
261C2×C22⋊C4—1221no—
262C2×C42C22×D6111yescharacteristic
263#107—1222no—
264C4⋊C8—21no—
265C4⋊C8—1221no—
266C4⋊C8—1221no—
267C4⋊C8—1221no—
268C4⋊C8—1221no—
269C4⋊C8C22⋊D6112yes—
270#102—1222no—
271#102—1222no—
272C22⋊C8—24no—
273C22⋊C8—612no—
274C22⋊C8—1221no—
275C22⋊C8—2442no—
276C22⋊C8—2442no—
277#97—21no—
278#97—21no—
279C4×C8—1221no—
280C4×C8—1221no—
281C24—1221no—
282#41—41no—
283#41—41no—
284#41—41no—
285#41—41no—
286C2×Q8—21no—
287C2×D4—22no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—1221no—
291C2×D4—1221no—
292C2×D4—2442no—
293C2×D4#1175819812yes—
294C22×C4—22no—
295C22×C4—1221no—
296C22×C4—2441no—
297C22×C4—2441no—
298C22×C4—2441no—
299C22×C4—2441no—
300C22×C4—2441no—
301C22×C4—2441no—
302C22×C4C2×C4×D6111yescharacteristic
303C22×C4#1175822211yescharacteristic
304C22×C4C2×C22⋊D6111yescharacteristic
305D8—2444no—
306M16—44no—
307M16—41no—
308M16—41no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—44no—
316C2×C8—1222no—
317C2×C8—2441no—
318C2×C8—2441no—
319C2×C8—2441no—
320C2×C8—2441no—
321C2×C8#1175819912yescomplemented
322C4⋊C4—21no—
323C4⋊C4—1221no—
324C4⋊C4—1221no—
325C4⋊C4#1175819812yes—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—2441no—
329C22⋊C4—2441no—
330C42C2×D24411yescharacteristic
331C42#1175822211yescharacteristic
332C42C2×C22⋊D6111yescharacteristic
333C42C2×C22⋊D6111yescharacteristic
334C23—22no—
335C23—1222no—
336C23—2441no—
337C23—2441no—
338C23—2441no—
339C23—2441no—
340C23—2441no—
341C23—2441no—
342C23C4×C22⋊D6111yescharacteristic
343Q8—41no—
344Q8—41no—
345D4—42no—
346D4—42no—
347D4—42no—
348D4—41no—
349D4—41no—
350D4—81no—
351D4—1222no—
352D4—1222no—
353D4—2441no—
354D4—2441no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—4881no—
361C2×C4—4881no—
362C2×C4—4881no—
363C2×C4—4881no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4C2×#1175819811yescharacteristic
368C2×C4C4×C22⋊D6111yescharacteristic
369C2×C4#1451974611yescharacteristic
370C2×C4#1451975111yescharacteristic
371C2×C4#1451975111yescharacteristic
372C2×C4#1451976011yescharacteristic
373C2×C4C2×#1175819911yescharacteristic
374C2×C4#1451979711yescharacteristic
375C2×C4#1451980211yescharacteristic
376C2×C4#1451980311yescharacteristic
377C8—22no—
378C8—42no—
379C8—41no—
380C8—4881no—
381C8—4881no—
382C8—2442no—
383C22—21no—
384C22—21no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22—4881no—
389C22—4881no—
390C22—4881no—
391C22—4881no—
392C22—2442no—
393C22—2442no—
394C22—2442no—
395C22#1683964111yescharacteristic
396C22C4×#1175819911yescharacteristic
397C22#1683987211yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—42no—
403C4—4881no—
404C4#1683989611yescharacteristic
405C4#1683990711yescharacteristic
406C4#1683995711yescharacteristic
407C4#1683997711yescharacteristic
408C2—21no—
409C2—21no—
410C2—82no—
411C2—4882no—
412C2#2144616711yescharacteristic
413C2#2144618111yescharacteristic
414C2#2144623711yescharacteristic
subgroupG/H
centerC2×C4#14519746
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2932C2
socleC22×C61#386
prime radical#21455815C2
cosocleC2×C42×C61C23
hypercenter#2932D61
hypocenterC61#9049
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. #21446617C2semidirect
3. #21444468C2semidirect
4. #21444243C2semidirect
5. #21443714C2semidirect
6. #21443664C2semidirect
7. C61×#2932C2semidirect
107. C2×C8×C61D8semidirect
202. #2932D61semidirect
236. C61#9049semidirect
321. C2×C8#11758199semidirect

Maximal subgroups

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

subgroupindex
#214558152
#214466172
#214444682
#214442432
#214437142
#214436642
C61×#29322
#904961