Finite Group Databasebeta

← #46822434

Subgroups — #46822434

Order 34432.

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×#22575474C211yesmaximal, characteristic, complemented
2#31771266C211yesmaximal, characteristic, complemented
3#31771254C211yesmaximal, characteristic, complemented
4#31770998C211yesmaximal, characteristic, complemented
5#31770851C211yesmaximal, characteristic, complemented
6#31770843C211yesmaximal, characteristic, complemented
7#31770822C211yesmaximal, characteristic, complemented
8#31770813C211yesmaximal, characteristic, complemented
9#31770766C211yesmaximal, characteristic, complemented
10#31770764C211yesmaximal, characteristic, complemented
11#31770761C211yesmaximal, characteristic, complemented
12#31770750C211yesmaximal, characteristic, complemented
13#31770706C211yesmaximal, characteristic, complemented
14#31770674C211yesmaximal, characteristic, complemented
15C2×#137×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic
17C2×#16864401C2211yescharacteristic
18#22575474—24no—
19C2×#16864392C2211yescharacteristic
20C2×#16864392C2211yescharacteristic
21C2×#16864391C2211yescharacteristic
22C2×#16864389C2211yescharacteristic
23C2×#16864387C2211yescharacteristic
24C2×C8×D269C2211yescharacteristic
25#22575451C2211yescharacteristic
26#22575442—21no—
27#22575442C2211yescharacteristic
28#22575436—21no—
29#22575434—21no—
30#22575432C2211yescharacteristic
31#22575429—21no—
32#22575429C2211yescharacteristic
33#22575429C2211yescharacteristic
34#22575427—21no—
35#22575427C2211yescharacteristic
36#22575425—21no—
37Q8×Dic269C2211yescharacteristic
38D4×Dic269C2211yescharacteristic
39C4×C22⋊D269—21no—
40C4×C22⋊D269C2211yescharacteristic
41C2×#16864381—21no—
42#22575387C2211yescharacteristic
43#22575382C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575377C2211yescharacteristic
46#22575377C2211yescharacteristic
47#22575377C2211yescharacteristic
48#22575375C2211yescharacteristic
49#22575374C2211yescharacteristic
50C22⋊#14524130C2211yescharacteristic
51#22575365C2211yescharacteristic
52#22575363C2211yescharacteristic
53C2×#41×C269C2211yescharacteristic
54C22×Q8×C269C2211yescharacteristic
55#137×C269—24no—
56C2×Q16×C269C2211yescharacteristic
57C2×Q16×C269C2211yescharacteristic
58C2×SD16×C269C2211yescharacteristic
59C2×SD16×C269C2211yescharacteristic
60C2×M16×C269C2211yescharacteristic
61#16864403—22no—
62#16864403—41no—
63#16864401—22no—
64#16864401—41no—
65C2×Dic538C2311yescharacteristic
66C2×D1076—21no—
67C2×D1076C2311yescharacteristic
68C2×C22⋊D269—21no—
69C2×C22⋊D269—21no—
70C2×C22⋊D269D411yescharacteristic
71C22×Dic269—21no—
72C22×Dic269—21no—
73C2×C4×D269—21no—
74C2×C4×D269C2311yescharacteristic
75#16864392—22no—
76#16864392—41no—
77#16864391—22no—
78#16864389—41no—
79#16864387—22no—
80C2×#14524130C2311yescharacteristic
81C2×#14524130C2311yescharacteristic
82C8×D269—22no—
83C4⋊Dic269—21no—
84C4⋊Dic269C2311yescharacteristic
85C4⋊Dic269C2311yescharacteristic
86#16864381—21no—
87#16864381—21no—
88#16864381—21no—
89#16864381—21no—
90#16864381—21no—
91#16864381D411yescharacteristic
92C22⋊Dic269—21no—
93C22⋊Dic269—21no—
94C22⋊Dic269D411yescharacteristic
95#16864379—21no—
96#16864379—21no—
97#16864379—21no—
98#16864379—21no—
99#16864379—21no—
100#16864379D411yescharacteristic
101C4×Dic269—21no—
102C4×Dic269C2311yescharacteristic
103#41×C269—22no—
104#41×C269—41no—
105C2×Q8×C269—21no—
106C2×Q8×C269—22no—
107C2×Q8×C269—41no—
108C2×Q8×C269C2311yescharacteristic
109C2×Q8×C269C2311yescharacteristic
110C2×Q8×C269C2311yescharacteristic
111C2×D4×C269—21no—
112C2×D4×C269C2311yescharacteristic
113C22×C4×C269—21no—
114C22×C4×C269—21no—
115C22×C4×C269C2311yescharacteristic
116Q16×C269—22no—
117Q16×C269—22no—
118SD16×C269—22no—
119SD16×C269D414yescomplemented
120M16×C269—22no—
121C2×C8×C269C2311yescharacteristic
122C2×C8×C269C2311yescharacteristic
123C22×D269—21no—
124C22×D269C2×D411yescharacteristic
125Dic538—21no—
126Dic538—21no—
127D1076—21no—
128D1076—21no—
129D1076—42no—
130C22⋊D269—41no—
131C22⋊D269—42no—
132C22⋊D269—42no—
133C2×Dic269—21no—
134C2×Dic269—21no—
135C2×Dic269—21no—
136C2×Dic269—42no—
137C2×Dic269—42no—
138C2×Dic269C2×D411yescharacteristic
139C2×Dic269C2×D411yescharacteristic
140C2×Dic269C2×D411yescharacteristic
141C4×D269—21no—
142C4×D269—21no—
143C4×D269—42no—
144#14524130—21no—
145#14524130—21no—
146C23×C269—21no—
147C23×C269C2×D411yescharacteristic
148Q8×C269—21no—
149Q8×C269—21no—
150Q8×C269—21no—
151Q8×C269—21no—
152Q8×C269—21no—
153Q8×C269—42no—
154Q8×C269C2×D412yes—
155D4×C269—21no—
156D4×C269—42no—
157D4×C269C2×D412yes—
158C2×C4×C269—21no—
159C2×C4×C269—21no—
160C2×C4×C269—21no—
161C2×C4×C269—21no—
162C2×C4×C269—21no—
163C2×C4×C269—42no—
164C2×C4×C269—42no—
165C2×C4×C269C2×D411yescharacteristic
166C2×C4×C269C2411yescharacteristic
167C8×C269—21no—
168C8×C269C2×D412yes—
169C22×C269—21no—
170C22×C269—22no—
171C22×C269—21no—
172C22×C269—21no—
173C22×C269—41no—
174C22×C269—41no—
175C22×C269C22×D411yescharacteristic
176C2×D269—21no—
177C2×D269—21no—
178C2×D269—21no—
179C2×D269—41no—
180C2×D269—41no—
181C2×D269—41no—
182C4×C269—21no—
183C4×C269—22no—
184C4×C269—41no—
185C4×C269—41no—
186C4×C269C22×D411yescharacteristic
187C4×C269H(5,𝔽2)11yescharacteristic
188Dic269—21no—
189Dic269—21no—
190Dic269—21no—
191Dic269—41no—
192Dic269—41no—
193Dic269—41no—
194C2×C269—41no—
195C2×C269—42no—
196C2×C269D4211yescharacteristic
197C2×C269#57511yescharacteristic
198C2×C269#57811yescharacteristic
199D269—41no—
200D269—81no—
201C269#326911yescharacteristic, complemented, Sylow
202#3269—2691nomaximal, Sylow
203C2×#137D26911yescharacteristic, complemented
204C2×#135—2691no—
205#548—2691no—
206#547—2691no—
207#497—2691no—
208#468—2691no—
209#467—2691no—
210#463—2691no—
211#462—2691no—
212#452—2691no—
213#452—2691no—
214#451—2691no—
215#449—2691no—
216#440—2691no—
217#435—2691no—
218C2×#41—2691no—
219C2×#41—2691no—
220C2×#41C2×D26911yescharacteristic
221C22×Q8C2×D26911yescharacteristic
222#137—24no—
223#135—5384no—
224C2×Q16—2691no—
225C2×Q16—2691no—
226C2×Q16C2×D26911yescharacteristic
227C2×Q16C2×D26911yescharacteristic
228C2×SD16—2691no—
229C2×SD16—2691no—
230C2×SD16C2×D26911yescharacteristic
231C2×SD16C2×D26911yescharacteristic
232C2×D8—2691no—
233C2×M16C2×D26911yescharacteristic
234C22×C8—2691no—
235C4⋊Q8—2691no—
236#124—2691no—
237#124—5381no—
238#123—5381no—
239#123—5381no—
240C22⋊Q8—2691no—
241C22⋊Q8—2691no—
242C22⋊Q8—2691no—
243C22⋊Q8—5381no—
244#121—2691no—
245#121—5381no—
246#121—5381no—
247C4×Q8—2691no—
248C4×D4—2691no—
249C4×D4—2691no—
250C4×D4—5381no—
251C2×C4⋊C4—5381no—
252#107—2691no—
253C4⋊C8—2691no—
254#103—2691no—
255#103—2691no—
256#103—2691no—
257#103—2691no—
258#102—2691no—
259#102—2691no—
260C22⋊C8—2691no—
261C22⋊C8—2691no—
262#97—2691no—
263#41—22no—
264#41—41no—
265#41—5382no—
266#41—5382no—
267#41—10761no—
268#41—10761no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—2691no—
273C2×Q8C22×D26911yescharacteristic
274C2×Q8C22×D26911yescharacteristic
275C2×Q8C22×D26911yescharacteristic
276C2×D4—21no—
277C2×D4—2691no—
278C2×D4—2691no—
279C2×D4—5381no—
280C2×D4—5381no—
281C2×D4—5381no—
282C2×D4C22×D26911yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—2691no—
286C22×C4—5381no—
287C22×C4—5381no—
288C22×C4—5381no—
289C22×C4C22×D26911yescharacteristic
290Q16—22no—
291Q16—22no—
292Q16—5382no—
293Q16—10761no—
294SD16—22no—
295SD16—5382no—
296SD16—10761no—
297SD16C22⋊D26914yescomplemented
298D8—5382no—
299M16—22no—
300C2×C8—2691no—
301C2×C8—2691no—
302C2×C8—5382no—
303C2×C8C22×D26911yescharacteristic
304C2×C8C22×D26911yescharacteristic
305C4⋊C4—2691no—
306C4⋊C4—2691no—
307C4⋊C4—2691no—
308C4⋊C4—5381no—
309C4⋊C4—5381no—
310C4⋊C4—5381no—
311C4⋊C4—5381no—
312C4⋊C4—5381no—
313C4⋊C4—5381no—
314C22⋊C4—2691no—
315C22⋊C4—2691no—
316C22⋊C4—5381no—
317C22⋊C4—5381no—
318C22⋊C4—5381no—
319C22⋊C4—5381no—
320C22⋊C4—5381no—
321C22⋊C4—5381no—
322C22⋊C4—5381no—
323C42—2691no—
324C42—5381no—
325C23—21no—
326C23—2691no—
327C23—5381no—
328C23D4×D26911yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—42no—
335Q8—5381no—
336Q8—5381no—
337Q8C2×C22⋊D26912yes—
338D4—21no—
339D4—42no—
340D4—5381no—
341D4—5381no—
342D4—10762no—
343D4—10761no—
344D4—10762no—
345D4—10762no—
346D4C2×C22⋊D26912yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—2691no—
355C2×C4—2691no—
356C2×C4—2691no—
357C2×C4—5381no—
358C2×C4—5381no—
359C2×C4—5381no—
360C2×C4—5381no—
361C2×C4—5381no—
362C2×C4—10762no—
363C2×C4—10762no—
364C2×C4—10762no—
365C2×C4D4×D26911yescharacteristic
366C2×C4C23×D26911yescharacteristic
367C8—21no—
368C8—5381no—
369C8—5381no—
370C8C2×C22⋊D26912yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—5381no—
378C22—5381no—
379C22—5381no—
380C22—10761no—
381C22—10761no—
382C22—10761no—
383C22C2×D4×D26911yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—41no—
388C4—5381no—
389C4—5381no—
390C4—5381no—
391C4—10761no—
392C4—10761no—
393C4—10761no—
394C4C22×C22⋊D26911yescharacteristic
395C4#2257549811yescharacteristic
396C2—41no—
397C2—42no—
398C2—10761no—
399C2—21521no—
400C2D4×C22⋊D26911yescharacteristic
401C2#3177140411yescharacteristic
402C2#3177142111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC2×#137×C269C2
socleC22×C269C22×D4
hypercenterC2×#137D269
hypocenterC269#3269
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#22575474C2semidirect
2. #31771266C2semidirect
3. #31771254C2semidirect
4. #31770998C2semidirect
5. #31770851C2semidirect
6. #31770843C2semidirect
7. #31770822C2semidirect
8. #31770813C2semidirect
9. #31770766C2semidirect
10. #31770764C2semidirect
11. #31770761C2semidirect
12. #31770750C2semidirect
13. #31770706C2semidirect
14. #31770674C2semidirect
15. C2×#137×C269C2semidirect
119. SD16×C269D4semidirect
201. C269#3269semidirect
203. C2×#137D269semidirect
297. SD16C22⋊D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754742
#317712662
#317712542
#317709982
#317708512
#317708432
#317708222
#317708132
#317707662
#317707642
#317707612
#317707502
#317707062
#317706742
C2×#137×C2692
#3269269