Finite Group Databasebeta

← #49132812

Subgroups — #49132812

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×#22583640C211yesmaximal, characteristic, complemented
2C2×#22583630C211yesmaximal, characteristic, complemented
3#31827124C211yesmaximal, characteristic, complemented
4#31826857C211yesmaximal, characteristic, complemented
5#31826713C211yesmaximal, characteristic, complemented
6#31826704C211yesmaximal, characteristic, complemented
7#31826680C211yesmaximal, characteristic, complemented
8#31826672C211yesmaximal, characteristic, complemented
9#31826627C211yesmaximal, characteristic, complemented
10#31826625C211yesmaximal, characteristic, complemented
11#31826620C211yesmaximal, characteristic, complemented
12#31826610C211yesmaximal, characteristic, complemented
13#31826565C211yesmaximal, characteristic, complemented
14#31826537C211yesmaximal, characteristic, complemented
15#547×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C22×Dic566C2211yescharacteristic
18#22583640—24no—
19#22583630—24no—
20C2×#17985382C2211yescharacteristic
21C2×#17985382C2211yescharacteristic
22C2×#17985382C2211yescharacteristic
23C2×#17985382C2211yescharacteristic
24C2×#17985380C2211yescharacteristic
25C2×#17985380C2211yescharacteristic
26C2×#17985379C2211yescharacteristic
27C2×#17985379C2211yescharacteristic
28C2×#17985377C2211yescharacteristic
29C2×#17985376C2211yescharacteristic
30C22×C283⋊C8C2211yescharacteristic
31#22583598C2211yescharacteristic
32#22583596—21no—
33#22583589C2211yescharacteristic
34#22583588—21no—
35#22583584C2211yescharacteristic
36#22583582—21no—
37C4×Dic566C2211yescharacteristic
38(C22⋊D283)⋊C4—21no—
39#22583543C2211yescharacteristic
40C4⋊(C283⋊C8)C2211yescharacteristic
41#22583534C2211yescharacteristic
42#22583534C2211yescharacteristic
43#22583533C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583531C2211yescharacteristic
46#22583530C2211yescharacteristic
47C22⋊(C283⋊C8)C2211yescharacteristic
48C22⋊(C283⋊C8)C2211yescharacteristic
49#22583521C2211yescharacteristic
50C2×#41×C283C2211yescharacteristic
51C2×#41×C283C2211yescharacteristic
52C4⋊Q8×C283C2211yescharacteristic
53#123×C283—21no—
54#123×C283—21no—
55C22⋊Q8×C283C2211yescharacteristic
56C22⋊Q8×C283C2211yescharacteristic
57#121×C283—21no—
58C4×D4×C283C2211yescharacteristic
59C4×D4×C283C2211yescharacteristic
60C2×C4⋊C4×C283—21no—
61#17985392—22no—
62#17985392—41no—
63C2×Dic566—22no—
64C2×Dic566—21no—
65C2×Dic566—41no—
66C2×Dic566C2311yescharacteristic
67C2×Dic566C2311yescharacteristic
68C2×D1132C2311yescharacteristic
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71C22×Dic283—21no—
72C2×C4×D283—21no—
73#17985382—22no—
74#17985382—22no—
75#17985382—22no—
76#17985382—41no—
77#17985380—22no—
78#17985380D414yescomplemented
79#17985379—22no—
80#17985379—41no—
81#17985377—22no—
82#17985376—22no—
83C2×C283⋊C8—22no—
84C2×C283⋊C8C2311yescharacteristic
85C2×C283⋊C8C2311yescharacteristic
86C2×C283⋊C8C2311yescharacteristic
87C2×C283⋊C8C2311yescharacteristic
88C4⋊Dic283C2311yescharacteristic
89Dic283⋊C4—21no—
90Dic283⋊C4—21no—
91C22⋊Dic283—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95C4×Dic283—21no—
96#41×C283—22no—
97#41×C283—22no—
98#41×C283—41no—
99#41×C283—41no—
100C2×Q8×C283C2311yescharacteristic
101C2×Q8×C283C2311yescharacteristic
102C2×D4×C283—21no—
103C2×D4×C283—21no—
104C2×D4×C283D411yescharacteristic
105C2×D4×C283C2311yescharacteristic
106C22×C4×C283—21no—
107C22×C4×C283—21no—
108C22×C4×C283—21no—
109C22×C4×C283C2311yescharacteristic
110C22×C4×C283C2311yescharacteristic
111C4⋊C4×C283—21no—
112C4⋊C4×C283—21no—
113C4⋊C4×C283—21no—
114C4⋊C4×C283—21no—
115C4⋊C4×C283D411yescharacteristic
116C4⋊C4×C283C2311yescharacteristic
117C22⋊C4×C283—21no—
118C22⋊C4×C283—21no—
119C22⋊C4×C283—21no—
120C22⋊C4×C283D411yescharacteristic
121C22⋊C4×C283D411yescharacteristic
122C42×C283C2311yescharacteristic
123C22×D283—21no—
124Dic566—21no—
125Dic566—21no—
126Dic566—21no—
127Dic566—42no—
128Dic566C2×D412yes—
129D1132—21no—
130D1132—21no—
131C22⋊D283—42no—
132C22⋊D283—42no—
133C2×Dic283—21no—
134C2×Dic283—21no—
135C2×Dic283—21no—
136C2×Dic283—42no—
137C4×D283—42no—
138C283⋊C8—21no—
139C283⋊C8—21no—
140C283⋊C8—21no—
141C283⋊C8C2×D412yes—
142C23×C283—21no—
143C23×C283C2×D411yescharacteristic
144C23×C283C2×D411yescharacteristic
145Q8×C283—21no—
146Q8×C283—21no—
147Q8×C283—21no—
148Q8×C283—21no—
149D4×C283—21no—
150D4×C283—41no—
151D4×C283—42no—
152D4×C283—42no—
153D4×C283C2×D412yes—
154C2×C4×C283—21no—
155C2×C4×C283—21no—
156C2×C4×C283—21no—
157C2×C4×C283—21no—
158C2×C4×C283—21no—
159C2×C4×C283—21no—
160C2×C4×C283—21no—
161C2×C4×C283—42no—
162C2×C4×C283—42no—
163C2×C4×C283—42no—
164C2×C4×C283C2×D411yescharacteristic
165C2×C4×C283C2×D411yescharacteristic
166C2×C4×C283C2×D411yescharacteristic
167C2×C4×C283C2×D411yescharacteristic
168C2×C4×C283C2411yescharacteristic
169C22×C283—21no—
170C22×C283—21no—
171C22×C283—22no—
172C22×C283—21no—
173C22×C283—21no—
174C22×C283—21no—
175C22×C283—21no—
176C22×C283—41no—
177C22×C283—41no—
178C22×C283C22×D411yescharacteristic
179C2×D283—41no—
180C2×D283—41no—
181C2×D283—41no—
182C4×C283—21no—
183C4×C283—21no—
184C4×C283—21no—
185C4×C283—21no—
186C4×C283—41no—
187C4×C283—41no—
188C4×C283—41no—
189C4×C283C22×D411yescharacteristic
190C4×C283H(5,𝔽2)11yescharacteristic
191Dic283—22no—
192Dic283—41no—
193Dic283—41no—
194C2×C283—41no—
195C2×C283—41no—
196C2×C283—42no—
197C2×C283D4211yescharacteristic
198C2×C283#57511yescharacteristic
199C2×C283#57811yescharacteristic
200D283—81no—
201C283#326911yescharacteristic, complemented, Sylow
202#3269—2831nomaximal, Sylow
203C2×#137—2831no—
204C2×#135—2831no—
205#548—2831no—
206#547D28311yescharacteristic, complemented
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—5664no—
224C2×Q16—2831no—
225C2×Q16—2831no—
226C2×Q16—2831no—
227C2×Q16—2831no—
228C2×SD16—2831no—
229C2×SD16—2831no—
230C2×SD16—2831no—
231C2×SD16—2831no—
232C2×D8—2831no—
233C2×M16—2831no—
234C22×C8—2831no—
235C4⋊Q8C2×D28311yescharacteristic
236#124—2831no—
237#124—5661no—
238#123—21no—
239#123—21no—
240C22⋊Q8—2831no—
241C22⋊Q8—5661no—
242C22⋊Q8C2×D28311yescharacteristic
243C22⋊Q8C2×D28311yescharacteristic
244#121—21no—
245#121—2831no—
246#121—5661no—
247C4×Q8—2831no—
248C4×D4—5661no—
249C4×D4C2×D28311yescharacteristic
250C4×D4C2×D28311yescharacteristic
251C2×C4⋊C4—21no—
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—5662no—
272C2×Q8—5661no—
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—21no—
286C22×C4—5661no—
287C22×C4—5661no—
288C22×C4C22×D28311yescharacteristic
289C22×C4C22×D28311yescharacteristic
290Q16—5662no—
291Q16—5662no—
292Q16—5662no—
293Q16—11321no—
294SD16—2834no—
295SD16—5662no—
296SD16—5662no—
297SD16—11321no—
298D8—5662no—
299M16—5662no—
300C2×C8—2831no—
301C2×C8—2831no—
302C2×C8—2831no—
303C2×C8—2831no—
304C2×C8—5662no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—2831no—
310C4⋊C4—5661no—
311C4⋊C4—5661no—
312C4⋊C4C22⋊D28311yescharacteristic
313C4⋊C4C22×D28311yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—5661no—
318C22⋊C4—5661no—
319C22⋊C4—5661no—
320C22⋊C4—5661no—
321C22⋊C4C22⋊D28311yescharacteristic
322C22⋊C4C22⋊D28311yescharacteristic
323C42—5661no—
324C42C22×D28311yescharacteristic
325C23—21no—
326C23—5661no—
327C23C2×C22⋊D28311yescharacteristic
328C23C2×C22⋊D28311yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—2832no—
334Q8—5661no—
335Q8—5661no—
336Q8—5661no—
337Q8—11322no—
338D4—21no—
339D4—41no—
340D4—42no—
341D4—42no—
342D4—5661no—
343D4—5661no—
344D4—11322no—
345D4—11322no—
346D4D4×D28312yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—5661no—
358C2×C4—5661no—
359C2×C4—5661no—
360C2×C4—11322no—
361C2×C4—11322no—
362C2×C4C2×C22⋊D28311yescharacteristic
363C2×C4C2×C22⋊D28311yescharacteristic
364C2×C4C2×C22⋊D28311yescharacteristic
365C2×C4C2×C22⋊D28311yescharacteristic
366C2×C4C23×D28311yescharacteristic
367C8—2832no—
368C8—5661no—
369C8—5661no—
370C8—5661no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—22no—
378C22—41no—
379C22—41no—
380C22—11321no—
381C22—11321no—
382C22—11321no—
383C22C22×C22⋊D28311yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—5662no—
392C4—11321no—
393C4—11321no—
394C4C2×D4×D28311yescharacteristic
395C4#2258365511yescharacteristic
396C2—41no—
397C2—41no—
398C2—42no—
399C2—22641no—
400C2D4×C22⋊D28311yescharacteristic
401C2#3182726311yescharacteristic
402C2#3182728011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#547×C283C2
socleC22×C283C22×D4
hypercenter#547D283
hypocenterC283#3269
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C2×#22583640C2semidirect
2. C2×#22583630C2semidirect
3. #31827124C2semidirect
4. #31826857C2semidirect
5. #31826713C2semidirect
6. #31826704C2semidirect
7. #31826680C2semidirect
8. #31826672C2semidirect
9. #31826627C2semidirect
10. #31826625C2semidirect
11. #31826620C2semidirect
12. #31826610C2semidirect
13. #31826565C2semidirect
14. #31826537C2semidirect
15. #547×C283C2semidirect
78. #17985380D4semidirect
201. C283#3269semidirect
206. #547D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836402
C2×#225836302
#318271242
#318268572
#318267132
#318267042
#318266802
#318266722
#318266272
#318266252
#318266202
#318266102
#318265652
#318265372
#547×C2832
#3269283