Finite Group Databasebeta

← #49132810

Subgroups — #49132810

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×#22583631C211yesmaximal, characteristic, complemented
2#31827126C211yesmaximal, characteristic, complemented
3#31827114C211yesmaximal, characteristic, complemented
4#31826858C211yesmaximal, characteristic, complemented
5#31826711C211yesmaximal, characteristic, complemented
6#31826703C211yesmaximal, characteristic, complemented
7#31826682C211yesmaximal, characteristic, complemented
8#31826673C211yesmaximal, characteristic, complemented
9#31826626C211yesmaximal, characteristic, complemented
10#31826624C211yesmaximal, characteristic, complemented
11#31826621C211yesmaximal, characteristic, complemented
12#31826610C211yesmaximal, characteristic, complemented
13#31826566C211yesmaximal, characteristic, complemented
14#31826534C211yesmaximal, characteristic, complemented
15C2×#137×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985391C2211yescharacteristic
18#22583631—24no—
19C2×#17985382C2211yescharacteristic
20C2×#17985382C2211yescharacteristic
21C2×#17985381C2211yescharacteristic
22C2×#17985379C2211yescharacteristic
23C2×#17985377C2211yescharacteristic
24C2×C8×D283C2211yescharacteristic
25#22583608C2211yescharacteristic
26#22583599—21no—
27#22583599C2211yescharacteristic
28#22583593—21no—
29#22583591—21no—
30#22583589C2211yescharacteristic
31#22583586—21no—
32#22583586C2211yescharacteristic
33#22583586C2211yescharacteristic
34#22583584—21no—
35#22583584C2211yescharacteristic
36#22583582—21no—
37Q8×Dic283C2211yescharacteristic
38D4×Dic283C2211yescharacteristic
39C4×C22⋊D283—21no—
40C4×C22⋊D283C2211yescharacteristic
41C2×Dic283⋊C4—21no—
42#22583544C2211yescharacteristic
43Dic283⋊C8C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583534C2211yescharacteristic
48#22583532C2211yescharacteristic
49#22583531C2211yescharacteristic
50C22⋊(C283⋊C8)C2211yescharacteristic
51(C2×D283)⋊C8C2211yescharacteristic
52#22583520C2211yescharacteristic
53C2×#41×C283C2211yescharacteristic
54C22×Q8×C283C2211yescharacteristic
55#137×C283—24no—
56C2×Q16×C283C2211yescharacteristic
57C2×Q16×C283C2211yescharacteristic
58C2×SD16×C283C2211yescharacteristic
59C2×SD16×C283C2211yescharacteristic
60C2×M16×C283C2211yescharacteristic
61#17985393—22no—
62#17985393—41no—
63#17985391—22no—
64#17985391—41no—
65C2×Dic566C2311yescharacteristic
66C2×D1132—21no—
67C2×D1132C2311yescharacteristic
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70C2×C22⋊D283D411yescharacteristic
71C22×Dic283—21no—
72C22×Dic283—21no—
73C2×C4×D283—21no—
74C2×C4×D283C2311yescharacteristic
75#17985382—22no—
76#17985382—41no—
77#17985381—22no—
78#17985379—41no—
79#17985377—22no—
80C2×C283⋊C8C2311yescharacteristic
81C2×C283⋊C8C2311yescharacteristic
82C8×D283—22no—
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⋊Dic283D411yescharacteristic
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4—21no—
97(C2×D283)⋊C4—21no—
98(C2×D283)⋊C4—21no—
99(C2×D283)⋊C4—21no—
100(C2×D283)⋊C4D411yescharacteristic
101C4×Dic283—21no—
102C4×Dic283C2311yescharacteristic
103#41×C283—22no—
104#41×C283—41no—
105C2×Q8×C283—21no—
106C2×Q8×C283—22no—
107C2×Q8×C283—41no—
108C2×Q8×C283C2311yescharacteristic
109C2×Q8×C283C2311yescharacteristic
110C2×Q8×C283C2311yescharacteristic
111C2×D4×C283—21no—
112C2×D4×C283C2311yescharacteristic
113C22×C4×C283—21no—
114C22×C4×C283—21no—
115C22×C4×C283C2311yescharacteristic
116Q16×C283—22no—
117Q16×C283—22no—
118SD16×C283—22no—
119SD16×C283D414yescomplemented
120M16×C283—22no—
121C2×C8×C283C2311yescharacteristic
122C2×C8×C283C2311yescharacteristic
123C22×D283—21no—
124C22×D283C2×D411yescharacteristic
125Dic566—21no—
126Dic566—21no—
127D1132—21no—
128D1132—21no—
129D1132—42no—
130C22⋊D283—41no—
131C22⋊D283—42no—
132C22⋊D283—42no—
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×C283C2×D411yescharacteristic
148Q8×C283—21no—
149Q8×C283—21no—
150Q8×C283—21no—
151Q8×C283—21no—
152Q8×C283—21no—
153Q8×C283—42no—
154Q8×C283C2×D412yes—
155D4×C283—21no—
156D4×C283—42no—
157D4×C283C2×D412yes—
158C2×C4×C283—21no—
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×C283C22×D411yescharacteristic
176C2×D283—21no—
177C2×D283—21no—
178C2×D283—21no—
179C2×D283—41no—
180C2×D283—41no—
181C2×D283—41no—
182C4×C283—21no—
183C4×C283—22no—
184C4×C283—41no—
185C4×C283—41no—
186C4×C283C22×D411yescharacteristic
187C4×C283H(5,𝔽2)11yescharacteristic
188Dic283—21no—
189Dic283—21no—
190Dic283—21no—
191Dic283—41no—
192Dic283—41no—
193Dic283—41no—
194C2×C283—41no—
195C2×C283—42no—
196C2×C283D4211yescharacteristic
197C2×C283#57511yescharacteristic
198C2×C283#57811yescharacteristic
199D283—41no—
200D283—81no—
201C283#326911yescharacteristic, complemented, Sylow
202#3269—2831nomaximal, Sylow
203C2×#137D28311yescharacteristic, complemented
204C2×#135—2831no—
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×#41—2831no—
220C2×#41C2×D28311yescharacteristic
221C22×Q8C2×D28311yescharacteristic
222#137—24no—
223#135—5664no—
224C2×Q16—2831no—
225C2×Q16—2831no—
226C2×Q16C2×D28311yescharacteristic
227C2×Q16C2×D28311yescharacteristic
228C2×SD16—2831no—
229C2×SD16—2831no—
230C2×SD16C2×D28311yescharacteristic
231C2×SD16C2×D28311yescharacteristic
232C2×D8—2831no—
233C2×M16C2×D28311yescharacteristic
234C22×C8—2831no—
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—41no—
265#41—5662no—
266#41—5662no—
267#41—11321no—
268#41—11321no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—2831no—
273C2×Q8C22×D28311yescharacteristic
274C2×Q8C22×D28311yescharacteristic
275C2×Q8C22×D28311yescharacteristic
276C2×D4—21no—
277C2×D4—2831no—
278C2×D4—2831no—
279C2×D4—5661no—
280C2×D4—5661no—
281C2×D4—5661no—
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—22no—
292Q16—5662no—
293Q16—11321no—
294SD16—22no—
295SD16—5662no—
296SD16—11321no—
297SD16C22⋊D28314yescomplemented
298D8—5662no—
299M16—22no—
300C2×C8—2831no—
301C2×C8—2831no—
302C2×C8—5662no—
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—2831no—
327C23—5661no—
328C23D4×D28311yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—42no—
335Q8—5661no—
336Q8—5661no—
337Q8C2×C22⋊D28312yes—
338D4—21no—
339D4—42no—
340D4—5661no—
341D4—5661no—
342D4—11322no—
343D4—11321no—
344D4—11322no—
345D4—11322no—
346D4C2×C22⋊D28312yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—2831no—
355C2×C4—2831no—
356C2×C4—2831no—
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—5661no—
378C22—5661no—
379C22—5661no—
380C22—11321no—
381C22—11321no—
382C22—11321no—
383C22C2×D4×D28311yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—41no—
388C4—5661no—
389C4—5661no—
390C4—5661no—
391C4—11321no—
392C4—11321no—
393C4—11321no—
394C4C22×C22⋊D28311yescharacteristic
395C4#2258365511yescharacteristic
396C2—41no—
397C2—42no—
398C2—11321no—
399C2—22641no—
400C2D4×C22⋊D28311yescharacteristic
401C2#3182726411yescharacteristic
402C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#137×C283C2
socleC22×C283C22×D4
hypercenterC2×#137D283
hypocenterC283#3269
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#22583631C2semidirect
2. #31827126C2semidirect
3. #31827114C2semidirect
4. #31826858C2semidirect
5. #31826711C2semidirect
6. #31826703C2semidirect
7. #31826682C2semidirect
8. #31826673C2semidirect
9. #31826626C2semidirect
10. #31826624C2semidirect
11. #31826621C2semidirect
12. #31826610C2semidirect
13. #31826566C2semidirect
14. #31826534C2semidirect
15. C2×#137×C283C2semidirect
119. SD16×C283D4semidirect
201. C283#3269semidirect
203. C2×#137D283semidirect
297. SD16C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836312
#318271262
#318271142
#318268582
#318267112
#318267032
#318266822
#318266732
#318266262
#318266242
#318266212
#318266102
#318265662
#318265342
C2×#137×C2832
#3269283