Finite Group Databasebeta

← #29598182

Subgroups — #29598182

Order 15616.

446 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454529C211yesmaximal, characteristic
2C2×#16839580C211yesmaximal, characteristic, complemented
3C2×#16839547C211yesmaximal, characteristic, complemented
4C2×#16839546C211yesmaximal, characteristic, complemented
5C2×#16839545C211yesmaximal, characteristic, complemented
6M32×Dic61C211yesmaximal, characteristic, complemented
7C2×C61×#350C211yesmaximal, characteristic, complemented
8C2×#14519783C2211yescharacteristic
9#16840308C411yescharacteristic
10C2×#14519717C2211yescharacteristic
11C22×#11758185C2211yescharacteristic
12#16839838—21no—
13#16839838—21no—
14C8×C22⋊D61—21no—
15C8×C22⋊D61—21no—
16#16839785C411yescharacteristic
17#16839730C411yescharacteristic
18#16839729C411yescharacteristic
19C2×C8×Dic61C2211yescharacteristic
20#16839580—21no—
21#16839580—21no—
22#16839547—22no—
23#16839546—22no—
24#16839545—22no—
25#16839537—21no—
26C16×Dic61—21no—
27C2×#131×C61C2211yescharacteristic
28C2×M32×C61C2211yescharacteristic
29C22×C16×C61C2211yescharacteristic
30C61×#350—22no—
31C2×#11758222C2×C411yescharacteristic
32#14519783—21no—
33#14519783—21no—
34#14519783—21no—
35#14519783—21no—
36C2×#11758194C2×C411yescharacteristic
37C2×#11758189—21no—
38C22×#92418C2×C411yescharacteristic
39C2×C8×D61—21no—
40#14519775C811yescharacteristic
41#14519773C811yescharacteristic
42#14519766C811yescharacteristic
43#14519764C811yescharacteristic
44#14519749—21no—
45#14519749—21no—
46C4×C22⋊D61—21no—
47C4×C22⋊D61—21no—
48C2×C4×Dic61C2×C411yescharacteristic
49#14519717—21no—
50#14519717D412yescomplemented
51C2×#11758185—21no—
52C2×#11758185—21no—
53C2×#11758185—21no—
54C2×#11758185—21no—
55#14519706—21no—
56#14519706—21no—
57C22⋊#92418—21no—
58C22⋊#92418—21no—
59#14519689—21no—
60#14519689—21no—
61C8×Dic61D411yescharacteristic
62C8×Dic61D411yescharacteristic
63C8×Dic61D411yescharacteristic
64C8×Dic61D411yescharacteristic
65C2×#41×C61C2×C411yescharacteristic
66#131×C61—21no—
67#131×C61—21no—
68#131×C61—21no—
69#131×C61—21no—
70C2×M16×C61—21no—
71C2×M16×C61C2×C411yescharacteristic
72C22×C8×C61—21no—
73C22×C8×C61C2311yescharacteristic
74M32×C61—21no—
75M32×C61D412yescomplemented
76C2×C16×C61—21no—
77C2×C16×C61—21no—
78C2×C16×C61—21no—
79C2×C16×C61—21no—
80#41×C61—21no—
81#41×C61—21no—
82#41×C61—21no—
83#41×C61—21no—
84C2×Q8×C61C2×C811yescharacteristic
85C2×D4×C61—21no—
86C2×D4×C61C2×C811yescharacteristic
87C22×C4×C61—21no—
88C22×C4×C61C22×C411yescharacteristic
89C2×C22⋊D61—21no—
90C2×C22⋊D61—21no—
91C2×C22⋊D61—21no—
92C22×Dic61M1611yescharacteristic
93C22×Dic61M1611yescharacteristic
94#11758222—21no—
95#11758222—21no—
96#11758222—21no—
97#11758222—21no—
98C2×D244C2×C811yescharacteristic
99C2×C4×D61—21no—
100C2×Dic122C2×C811yescharacteristic
101M16×C61—21no—
102M16×C61—21no—
103M16×C61—41no—
104M16×C61—41no—
105C2×C8×C61—21no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61C2×D411yescharacteristic
109C2×C8×C61C2×D411yescharacteristic
110C2×C8×C61C2×D411yescharacteristic
111C2×C8×C61C2×D411yescharacteristic
112C2×C8×C61#4111yescharacteristic
113C2×C8×C61#4111yescharacteristic
114C22⋊Dic61—21no—
115C22⋊Dic61—21no—
116#11758198—21no—
117#11758198—21no—
118#11758196—21no—
119#11758196—21no—
120C4×Dic61C22⋊C411yescharacteristic
121C4×Dic61C22⋊C411yescharacteristic
122C4×Dic61C2×C811yescharacteristic
123C4×Dic61C2×C811yescharacteristic
124#11758194—21no—
125#11758194—21no—
126C2×#92418—21no—
127C2×#92418—21no—
128C2×#92418—21no—
129C2×#92418C22⋊C411yescharacteristic
130C2×#92418C22⋊C411yescharacteristic
131#11758189—41no—
132#11758189—41no—
133C8×D61—41no—
134C8×D61—41no—
135C16×C61—22no—
136C16×C61—41no—
137#11758185—22no—
138#11758185—41no—
139C23×C61—21no—
140C23×C61C2×M1611yescharacteristic
141C22×D61—21no—
142Q8×C61—21no—
143Q8×C61—21no—
144D4×C61—21no—
145D4×C61—21no—
146D4×C61—41no—
147D4×C61—41no—
148C2×C4×C61—21no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61C2×C22⋊C411yescharacteristic
152C2×C4×C61C4×D411yescharacteristic
153C2×C4×C61C4×D411yescharacteristic
154C2×C4×C61C22×C811yescharacteristic
155C2×C4×C61#13111yescharacteristic
156C2×C4×C61#13111yescharacteristic
157C22⋊D61—42no—
158C22⋊D61—41no—
159C22⋊D61—41no—
160C22⋊D61—42no—
161C2×Dic61—22no—
162C2×Dic61—21no—
163C2×Dic61—41no—
164C2×Dic61C22⋊C811yescharacteristic
165C2×Dic61C22⋊C811yescharacteristic
166C2×Dic61C22⋊C811yescharacteristic
167C2×Dic61C22⋊C811yescharacteristic
168D244—21no—
169D244—21no—
170C4×D61—41no—
171C4×D61—41no—
172Dic122—21no—
173Dic122—21no—
174C8×C61—41no—
175C8×C61#12111yescharacteristic
176C8×C61#12111yescharacteristic
177C8×C61#12411yescharacteristic
178C8×C61#12711yescharacteristic
179#92418—21no—
180#92418—21no—
181#92418—41no—
182#13193—611nomaximal, Sylow
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61C2×C22⋊C811yescharacteristic
189C22×C61#43611yescharacteristic
190C22×C61#43611yescharacteristic
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C4×C61—41no—
195C4×C61#39011yescharacteristic
196C4×C61#40811yescharacteristic
197C4×C61C8×D411yescharacteristic
198C4×C61C8×D411yescharacteristic
199Dic61—21no—
200Dic61—21no—
201Dic61—21no—
202Dic61—41no—
203Dic61#35012yescomplemented
204#2931—611no—
205C2×C4⋊C16—611no—
206C2×#350—611no—
207C2×#350—611no—
208C2×#350—611no—
209C2×#350D6111yescharacteristic, complemented
210C4×M32—611no—
211C2×C61—21no—
212C2×C61—21no—
213C2×C61—81no—
214C2×C61#195411yescharacteristic
215C2×C61C2×#35011yescharacteristic
216C2×C61#211711yescharacteristic
217D61—81no—
218C2×#131—611no—
219C2×#131C2×D6111yescharacteristic
220#532—611no—
221C2×M32—611no—
222C2×M32C2×D6111yescharacteristic
223C22×C16—611no—
224C22×C16C2×D6111yescharacteristic
225#436—1221no—
226#436—1221no—
227C8×D4—1221no—
228C8×D4—1221no—
229#423—611no—
230#408—611no—
231#408—611no—
232C2×C4×C8—611no—
233C4⋊C16—1221no—
234C4⋊C16—1221no—
235#350—22no—
236#350—1222no—
237#350—1222no—
238#350—1222no—
239#346—1221no—
240C4×C16—1221no—
241C61#1319311yescharacteristic, complemented, Sylow
242C2×#41—611no—
243C2×#41C4×D6111yescharacteristic
244#131—21no—
245#131—21no—
246#131—21no—
247#131—21no—
248#131—1221no—
249#131—1221no—
250#131—1221no—
251#131—1221no—
252C2×M16—21no—
253C2×M16—611no—
254C2×M16—1221no—
255C2×M16C4×D6111yescharacteristic
256C22×C8—21no—
257C22×C8—611no—
258C22×C8—1221no—
259C22×C8C22×D6111yescharacteristic
260C4⋊Q8—611no—
261#127—611no—
262#124—611no—
263#124—611no—
264#121—1221no—
265#121—1221no—
266C4×D4—1221no—
267C4×D4—1221no—
268C2×C42—611no—
269M32—21no—
270M32—612no—
271M32—1221no—
272M32C22⋊D6112yescomplemented
273C2×C16—21no—
274C2×C16—21no—
275C2×C16—21no—
276C2×C16—21no—
277C2×C16—1221no—
278C2×C16—1221no—
279C2×C16—1221no—
280C2×C16—1221no—
281C4⋊C8—1221no—
282C4⋊C8—1221no—
283C22⋊C8—1221no—
284C22⋊C8—1221no—
285C22⋊C8—1221no—
286C22⋊C8—1221no—
287C4×C8—611no—
288C4×C8—611no—
289C4×C8—611no—
290C4×C8—611no—
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295#41—1221no—
296#41—1221no—
297#41—1221no—
298#41—1221no—
299C2×Q8—611no—
300C2×Q8C8×D6111yescharacteristic
301C2×D4—21no—
302C2×D4—611no—
303C2×D4—1221no—
304C2×D4—1221no—
305C2×D4—1221no—
306C2×D4C8×D6111yescharacteristic
307C22×C4—21no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—1221no—
311C22×C4C2×C4×D6111yescharacteristic
312M16—21no—
313M16—21no—
314M16—41no—
315M16—41no—
316M16—1221no—
317M16—1221no—
318M16—2441no—
319M16—2441no—
320C2×C8—21no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—611no—
324C2×C8—611no—
325C2×C8—1221no—
326C2×C8—1221no—
327C2×C8—1221no—
328C2×C8—2441no—
329C2×C8—2441no—
330C2×C8#1175822211yescharacteristic
331C2×C8D4×D6111yescharacteristic
332C2×C8D4×D6111yescharacteristic
333C2×C8D4×D6111yescharacteristic
334C2×C8#1175822411yescharacteristic
335C2×C8C2×C22⋊D6111yescharacteristic
336C4⋊C4—1221no—
337C4⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C22⋊C4—1221no—
342C42—611no—
343C42—611no—
344C42—611no—
345C42—611no—
346C16—22no—
347C16—41no—
348C16—1222no—
349C16—2441no—
350C23—21no—
351C23—1221no—
352C23M16×D6111yescharacteristic
353Q8—21no—
354Q8—21no—
355Q8—1221no—
356Q8—1221no—
357D4—21no—
358D4—21no—
359D4—41no—
360D4—41no—
361D4—1221no—
362D4—1221no—
363D4—2442no—
364D4—2442no—
365D4—2441no—
366D4—2441no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—611no—
371C2×C4—611no—
372C2×C4—611no—
373C2×C4—611no—
374C2×C4—1222no—
375C2×C4—1221no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4C22⋊C4×D6111yescharacteristic
380C2×C4#1451973711yescharacteristic
381C2×C4C4×C22⋊D6111yescharacteristic
382C2×C4C2×C8×D6111yescharacteristic
383C2×C4#1451978311yescharacteristic
384C2×C4#1451978511yescharacteristic
385C8—41no—
386C8—1221no—
387C8—1221no—
388C8—2441no—
389C8#1451974911yescharacteristic
390C8#1451975011yescharacteristic
391C8#1451976311yescharacteristic
392C8#1451977311yescharacteristic
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—2441no—
399C22—2441no—
400C22—2441no—
401C22C22⋊C8×D6111yescharacteristic
402C22#1683983711yescharacteristic
403C22#1683983811yescharacteristic
404C4—41no—
405C4—612no—
406C4—1221no—
407C4—1221no—
408C4—1221no—
409C4—2441no—
410C4#1683966211yescharacteristic
411C4#1683972711yescharacteristic
412C4#1683982511yescharacteristic
413C4C8×C22⋊D6111yescharacteristic
414C2—21no—
415C2—21no—
416C2—81no—
417C2—4881no—
418C2#2144661111yescharacteristic
419C2#350×D6111yescharacteristic
420C2#2144744511yescharacteristic
subgroupG/H
centerC2×C8D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC2×C61×#350C2
socleC22×C61C2×C22⋊C8
prime radical#16840308C4
cosocleC22×C8×C61C23
hypercenterC2×#350D61
hypocenterC61#13193
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
2. C2×#16839580C2semidirect
3. C2×#16839547C2semidirect
4. C2×#16839546C2semidirect
5. C2×#16839545C2semidirect
6. M32×Dic61C2semidirect
7. C2×C61×#350C2semidirect
50. #14519717D4semidirect
75. M32×C61D4semidirect
203. Dic61#350semidirect
209. C2×#350D61semidirect
241. C61#13193semidirect
272. M32C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214545292
C2×#168395802
C2×#168395472
C2×#168395462
C2×#168395452
M32×Dic612
C2×C61×#3502
#1319361