Finite Group Databasebeta

← #49132816

Subgroups — #49132816

Order 36224.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583639C211yesmaximal, characteristic, complemented
2#31827122C211yesmaximal, characteristic, complemented
3#31827114C211yesmaximal, characteristic, complemented
4#31826856C211yesmaximal, characteristic, complemented
5#31826708C211yesmaximal, characteristic, complemented
6#31826706C211yesmaximal, characteristic, complemented
7#31826678C211yesmaximal, characteristic, complemented
8#31826673C211yesmaximal, characteristic, complemented
9#31826627C211yesmaximal, characteristic, complemented
10#31826627C211yesmaximal, characteristic, complemented
11#31826619C211yesmaximal, characteristic, complemented
12#31826607C211yesmaximal, characteristic, complemented
13#31826566C211yesmaximal, characteristic, complemented
14#31826536C211yesmaximal, characteristic, complemented
15C2×#135×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18#22583639—24no—
19C2×Dic1132C2211yescharacteristic
20C2×#17985382C2211yescharacteristic
21C2×#17985382C2211yescharacteristic
22C2×#17985380C2211yescharacteristic
23C2×#17985380C2211yescharacteristic
24C2×#17985375C2211yescharacteristic
25#22583608C2211yescharacteristic
26#22583597—21no—
27#22583597C2211yescharacteristic
28#22583593—21no—
29#22583591—21no—
30#22583589—21no—
31#22583589C2211yescharacteristic
32#22583589C2211yescharacteristic
33#22583586C2211yescharacteristic
34#22583582—21no—
35#22583581—21no—
36#22583581C2211yescharacteristic
37Q8×Dic283C2211yescharacteristic
38D4×Dic283C2211yescharacteristic
39C4×C22⋊D283—21no—
40C4×C22⋊D283C2211yescharacteristic
41C2×Dic283⋊C4—21no—
42#22583544C2211yescharacteristic
43Dic283⋊C8C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583535C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583534C2211yescharacteristic
48#22583531C2211yescharacteristic
49#22583531C2211yescharacteristic
50C22⋊(C283⋊C8)C2211yescharacteristic
51(C2×D283)⋊C8C2211yescharacteristic
52#22583520C2211yescharacteristic
53C2×#41×C283C2211yescharacteristic
54C2×#41×C283C2211yescharacteristic
55#135×C283—24no—
56C2×Q16×C283C2211yescharacteristic
57C2×SD16×C283C2211yescharacteristic
58C2×SD16×C283C2211yescharacteristic
59C2×D8×C283C2211yescharacteristic
60C22×C8×C283C2211yescharacteristic
61#17985391—22no—
62#17985391—41no—
63C2×Dic566—21no—
64C2×Dic566C2311yescharacteristic
65C2×Dic566C2311yescharacteristic
66Q8×D283—22no—
67Q8×D283—41no—
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70C2×C22⋊D283D411yescharacteristic
71C22×Dic283—21no—
72C22×Dic283—21no—
73C2×C4×D283—21no—
74C2×C4×D283C2311yescharacteristic
75Dic1132—22no—
76#17985382—22no—
77#17985382—41no—
78#17985380—22no—
79#17985380—41no—
80#17985375—22no—
81C2×C283⋊C8C2311yescharacteristic
82C2×C283⋊C8C2311yescharacteristic
83C4⋊Dic283—21no—
84C4⋊Dic283C2311yescharacteristic
85C4⋊Dic283C2311yescharacteristic
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90Dic283⋊C4—21no—
91Dic283⋊C4D411yescharacteristic
92C22⋊Dic283—21no—
93C22⋊Dic283—21no—
94C22⋊Dic283—21no—
95C22⋊Dic283—21no—
96C22⋊Dic283—21no—
97C22⋊Dic283—21no—
98C22⋊Dic283D411yescharacteristic
99(C2×D283)⋊C4—21no—
100(C2×D283)⋊C4D411yescharacteristic
101C4×Dic283—21no—
102C4×Dic283C2311yescharacteristic
103#41×C283—22no—
104#41×C283—22no—
105#41×C283—41no—
106#41×C283—41no—
107C2×Q8×C283C2311yescharacteristic
108C2×Q8×C283C2311yescharacteristic
109C2×D4×C283—21no—
110C2×D4×C283—21no—
111C2×D4×C283C2311yescharacteristic
112C2×D4×C283C2311yescharacteristic
113C22×C4×C283—21no—
114C22×C4×C283—21no—
115C22×C4×C283C2311yescharacteristic
116Q16×C283—22no—
117SD16×C283—22no—
118SD16×C283D414yescomplemented
119D8×C283—22no—
120C2×C8×C283—22no—
121C2×C8×C283C2311yescharacteristic
122C2×C8×C283C2311yescharacteristic
123C22×D283C2×D411yescharacteristic
124Dic566—21no—
125Dic566—21no—
126Dic566—21no—
127Dic566—21no—
128Dic566—42no—
129C22⋊D283—41no—
130C22⋊D283—42no—
131C22⋊D283—42no—
132C2×Dic283—21no—
133C2×Dic283—21no—
134C2×Dic283—21no—
135C2×Dic283—21no—
136C2×Dic283—42no—
137C2×Dic283—42no—
138C2×Dic283C2×D411yescharacteristic
139C2×Dic283C2×D411yescharacteristic
140C2×Dic283C2×D411yescharacteristic
141C4×D283—21no—
142C4×D283—21no—
143C4×D283—42no—
144C283⋊C8—21no—
145C283⋊C8—21no—
146C23×C283—21no—
147C23×C283—21no—
148C23×C283C2×D411yescharacteristic
149Q8×C283—21no—
150Q8×C283—21no—
151Q8×C283—21no—
152Q8×C283C2×D412yes—
153D4×C283—21no—
154D4×C283—21no—
155D4×C283—21no—
156D4×C283—42no—
157D4×C283—42no—
158D4×C283C2×D412yes—
159C2×C4×C283—21no—
160C2×C4×C283—21no—
161C2×C4×C283—21no—
162C2×C4×C283—21no—
163C2×C4×C283—42no—
164C2×C4×C283—42no—
165C2×C4×C283C2×D411yescharacteristic
166C2×C4×C283C2411yescharacteristic
167C8×C283—21no—
168C8×C283C2×D412yes—
169C22×C283—21no—
170C22×C283—22no—
171C22×C283—21no—
172C22×C283—21no—
173C22×C283—41no—
174C22×C283—41no—
175C22×C283—41no—
176C22×C283—41no—
177C22×C283—41no—
178C22×C283C22×D411yescharacteristic
179C2×D283—21no—
180C2×D283—21no—
181C2×D283—21no—
182C4×C283—21no—
183C4×C283—22no—
184C4×C283—41no—
185C4×C283C22×D411yescharacteristic
186C4×C283H(5,𝔽2)11yescharacteristic
187Dic283—21no—
188Dic283—21no—
189Dic283—21no—
190Dic283—41no—
191Dic283—41no—
192Dic283—41no—
193Dic283—41no—
194C2×C283—41no—
195C2×C283—42no—
196C2×C283—81no—
197C2×C283D4211yescharacteristic
198C2×C283#57511yescharacteristic
199C2×C283#57811yescharacteristic
200D283—41no—
201C283#326911yescharacteristic, complemented, Sylow
202#3269—2831nomaximal, Sylow
203C2×#137—2831no—
204C2×#135D28311yescharacteristic, complemented
205#548—2831no—
206#547—2831no—
207#497—2831no—
208#468—2831no—
209#467—2831no—
210#463—2831no—
211#462—2831no—
212#452—2831no—
213#452—2831no—
214#451—2831no—
215#449—2831no—
216#440—2831no—
217#435—2831no—
218C2×#41—2831no—
219C2×#41C2×D28311yescharacteristic
220C2×#41C2×D28311yescharacteristic
221C22×Q8—2831no—
222#137—5664no—
223#135—24no—
224C2×Q16—2831no—
225C2×Q16—2831no—
226C2×Q16—2831no—
227C2×Q16C2×D28311yescharacteristic
228C2×SD16—2831no—
229C2×SD16—2831no—
230C2×SD16C2×D28311yescharacteristic
231C2×SD16C2×D28311yescharacteristic
232C2×D8C2×D28311yescharacteristic
233C2×M16—2831no—
234C22×C8C2×D28311yescharacteristic
235C4⋊Q8—2831no—
236#124—2831no—
237#124—5661no—
238#123—5661no—
239#123—5661no—
240C22⋊Q8—2831no—
241C22⋊Q8—2831no—
242C22⋊Q8—2831no—
243C22⋊Q8—5661no—
244#121—2831no—
245#121—5661no—
246#121—5661no—
247C4×Q8—2831no—
248C4×D4—2831no—
249C4×D4—2831no—
250C4×D4—5661no—
251C2×C4⋊C4—5661no—
252#107—2831no—
253C4⋊C8—2831no—
254#103—2831no—
255#103—2831no—
256#103—2831no—
257#103—2831no—
258#102—2831no—
259#102—2831no—
260C22⋊C8—2831no—
261C22⋊C8—2831no—
262#97—2831no—
263#41—22no—
264#41—22no—
265#41—41no—
266#41—41no—
267#41—5662no—
268#41—11321no—
269C2×Q8—2831no—
270C2×Q8—2831no—
271C2×Q8—5661no—
272C2×Q8—5662no—
273C2×Q8—11321no—
274C2×Q8C22×D28311yescharacteristic
275C2×Q8C22×D28311yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—2831no—
279C2×D4—5661no—
280C2×D4—5661no—
281C2×D4C22×D28311yescharacteristic
282C2×D4C22×D28311yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—2831no—
286C22×C4—5661no—
287C22×C4—5661no—
288C22×C4—5661no—
289C22×C4C22×D28311yescharacteristic
290Q16—22no—
291Q16—5662no—
292Q16—5662no—
293Q16—11321no—
294SD16—22no—
295SD16—5662no—
296SD16—11321no—
297SD16C22⋊D28314yescomplemented
298D8—22no—
299M16—5662no—
300C2×C8—22no—
301C2×C8—2831no—
302C2×C8—2831no—
303C2×C8C22×D28311yescharacteristic
304C2×C8C22×D28311yescharacteristic
305C4⋊C4—2831no—
306C4⋊C4—2831no—
307C4⋊C4—2831no—
308C4⋊C4—5661no—
309C4⋊C4—5661no—
310C4⋊C4—5661no—
311C4⋊C4—5661no—
312C4⋊C4—5661no—
313C4⋊C4—5661no—
314C22⋊C4—2831no—
315C22⋊C4—2831no—
316C22⋊C4—5661no—
317C22⋊C4—5661no—
318C22⋊C4—5661no—
319C22⋊C4—5661no—
320C22⋊C4—5661no—
321C22⋊C4—5661no—
322C22⋊C4—5661no—
323C42—2831no—
324C42—5661no—
325C23—21no—
326C23—21no—
327C23—2831no—
328C23D4×D28311yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—5661no—
333Q8—5661no—
334Q8—5661no—
335Q8—5661no—
336Q8—11322no—
337Q8C2×C22⋊D28312yes—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—11321no—
344D4—11322no—
345D4—11322no—
346D4C2×C22⋊D28312yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—2831no—
354C2×C4—2831no—
355C2×C4—2831no—
356C2×C4—5661no—
357C2×C4—5661no—
358C2×C4—5661no—
359C2×C4—5661no—
360C2×C4—5661no—
361C2×C4—5661no—
362C2×C4—11322no—
363C2×C4—11322no—
364C2×C4—11322no—
365C2×C4D4×D28311yescharacteristic
366C2×C4C23×D28311yescharacteristic
367C8—21no—
368C8—5661no—
369C8—5661no—
370C8C2×C22⋊D28312yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—5661no—
381C22—5661no—
382C22—5661no—
383C22C2×D4×D28311yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—5661no—
388C4—5661no—
389C4—5661no—
390C4—11321no—
391C4—11321no—
392C4—11321no—
393C4—11321no—
394C4C22×C22⋊D28311yescharacteristic
395C4#2258365511yescharacteristic
396C2—41no—
397C2—42no—
398C2—81no—
399C2—11321no—
400C2D4×C22⋊D28311yescharacteristic
401C2#3182726211yescharacteristic
402C2#3182727911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#135×C283C2
socleC22×C283C22×D4
hypercenterC2×#135D283
hypocenterC283#3269
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#22583639C2semidirect
2. #31827122C2semidirect
3. #31827114C2semidirect
4. #31826856C2semidirect
5. #31826708C2semidirect
6. #31826706C2semidirect
7. #31826678C2semidirect
8. #31826673C2semidirect
9. #31826627C2semidirect
10. #31826627C2semidirect
11. #31826619C2semidirect
12. #31826607C2semidirect
13. #31826566C2semidirect
14. #31826536C2semidirect
15. C2×#135×C283C2semidirect
118. SD16×C283D4semidirect
201. C283#3269semidirect
204. C2×#135D283semidirect
297. SD16C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836392
#318271222
#318271142
#318268562
#318267082
#318267062
#318266782
#318266732
#318266272
#318266192
#318266072
#318265662
#318265362
C2×#135×C2832
#3269283