Finite Group Databasebeta

← #34080659

Subgroups — #34080659

Order 19328.

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×#18012760C211yesmaximal, characteristic, complemented
2#23752873C211yesmaximal, characteristic, complemented
3#23752861C211yesmaximal, characteristic, complemented
4#23752605C211yesmaximal, characteristic, complemented
5#23752458C211yesmaximal, characteristic, complemented
6#23752450C211yesmaximal, characteristic, complemented
7#23752429C211yesmaximal, characteristic, complemented
8#23752420C211yesmaximal, characteristic, complemented
9#23752373C211yesmaximal, characteristic, complemented
10#23752371C211yesmaximal, characteristic, complemented
11#23752368C211yesmaximal, characteristic, complemented
12#23752357C211yesmaximal, characteristic, complemented
13#23752313C211yesmaximal, characteristic, complemented
14#23752281C211yesmaximal, characteristic, complemented
15C2×#137×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18#18012760—24no—
19C2×#14558994C2211yescharacteristic
20C2×#14558994C2211yescharacteristic
21C2×#14558993C2211yescharacteristic
22C2×#14558991C2211yescharacteristic
23C2×#14558989C2211yescharacteristic
24C2×C8×D151C2211yescharacteristic
25#18012737C2211yescharacteristic
26#18012728—21no—
27#18012728C2211yescharacteristic
28#18012722—21no—
29#18012720—21no—
30#18012718C2211yescharacteristic
31#18012715—21no—
32#18012715C2211yescharacteristic
33#18012715C2211yescharacteristic
34#18012713—21no—
35#18012713C2211yescharacteristic
36#18012711—21no—
37Q8×Dic151C2211yescharacteristic
38D4×Dic151C2211yescharacteristic
39C4×C22⋊D151—21no—
40C4×C22⋊D151C2211yescharacteristic
41C2×Dic151⋊C4—21no—
42#18012673C2211yescharacteristic
43Dic151⋊C8C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012663C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012660C2211yescharacteristic
50C22⋊(C151⋊C8)C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52#18012649C2211yescharacteristic
53C2×#41×C151C2211yescharacteristic
54C22×Q8×C151C2211yescharacteristic
55#137×C151—24no—
56C2×Q16×C151C2211yescharacteristic
57C2×Q16×C151C2211yescharacteristic
58C2×SD16×C151C2211yescharacteristic
59C2×SD16×C151C2211yescharacteristic
60C2×M16×C151C2211yescharacteristic
61#14559005—22no—
62#14559005—41no—
63#14559003—22no—
64#14559003—41no—
65C2×Dic302C2311yescharacteristic
66C2×D604—21no—
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151D411yescharacteristic
71C22×Dic151—21no—
72C22×Dic151—21no—
73C2×C4×D151—21no—
74C2×C4×D151C2311yescharacteristic
75#14558994—22no—
76#14558994—41no—
77#14558993—22no—
78#14558991—41no—
79#14558989—22no—
80C2×C151⋊C8C2311yescharacteristic
81C2×C151⋊C8C2311yescharacteristic
82C8×D151—22no—
83C4⋊Dic151—21no—
84C4⋊Dic151C2311yescharacteristic
85C4⋊Dic151C2311yescharacteristic
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89Dic151⋊C4—21no—
90Dic151⋊C4—21no—
91Dic151⋊C4D411yescharacteristic
92C22⋊Dic151—21no—
93C22⋊Dic151—21no—
94C22⋊Dic151D411yescharacteristic
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4D411yescharacteristic
101C4×Dic151—21no—
102C4×Dic151C2311yescharacteristic
103#41×C151—22no—
104#41×C151—41no—
105C2×Q8×C151—21no—
106C2×Q8×C151—22no—
107C2×Q8×C151—41no—
108C2×Q8×C151C2311yescharacteristic
109C2×Q8×C151C2311yescharacteristic
110C2×Q8×C151C2311yescharacteristic
111C2×D4×C151—21no—
112C2×D4×C151C2311yescharacteristic
113C22×C4×C151—21no—
114C22×C4×C151—21no—
115C22×C4×C151C2311yescharacteristic
116Q16×C151—22no—
117Q16×C151—22no—
118SD16×C151—22no—
119SD16×C151D414yescomplemented
120M16×C151—22no—
121C2×C8×C151C2311yescharacteristic
122C2×C8×C151C2311yescharacteristic
123C22×D151—21no—
124C22×D151C2×D411yescharacteristic
125Dic302—21no—
126Dic302—21no—
127D604—21no—
128D604—21no—
129D604—42no—
130C22⋊D151—41no—
131C22⋊D151—42no—
132C22⋊D151—42no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—42no—
137C2×Dic151—42no—
138C2×Dic151C2×D411yescharacteristic
139C2×Dic151C2×D411yescharacteristic
140C2×Dic151C2×D411yescharacteristic
141C4×D151—21no—
142C4×D151—21no—
143C4×D151—42no—
144C151⋊C8—21no—
145C151⋊C8—21no—
146C23×C151—21no—
147C23×C151C2×D411yescharacteristic
148Q8×C151—21no—
149Q8×C151—21no—
150Q8×C151—21no—
151Q8×C151—21no—
152Q8×C151—21no—
153Q8×C151—42no—
154Q8×C151C2×D412yes—
155D4×C151—21no—
156D4×C151—42no—
157D4×C151C2×D412yes—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151—42no—
164C2×C4×C151—42no—
165C2×C4×C151C2×D411yescharacteristic
166C2×C4×C151C2411yescharacteristic
167C8×C151—21no—
168C8×C151C2×D412yes—
169C22×C151—21no—
170C22×C151—22no—
171C22×C151—21no—
172C22×C151—21no—
173C22×C151—41no—
174C22×C151—41no—
175C22×C151C22×D411yescharacteristic
176C2×D151—21no—
177C2×D151—21no—
178C2×D151—21no—
179C2×D151—41no—
180C2×D151—41no—
181C2×D151—41no—
182C4×C151—21no—
183C4×C151—22no—
184C4×C151—41no—
185C4×C151—41no—
186C4×C151C22×D411yescharacteristic
187C4×C151H(5,𝔽2)11yescharacteristic
188Dic151—21no—
189Dic151—21no—
190Dic151—21no—
191Dic151—41no—
192Dic151—41no—
193Dic151—41no—
194C2×C151—41no—
195C2×C151—42no—
196C2×C151D4211yescharacteristic
197C2×C151#57511yescharacteristic
198C2×C151#57811yescharacteristic
199D151—41no—
200D151—81no—
201C151#326911yescharacteristic, complemented, Sylow
202#3269—1511nomaximal, Sylow
203C2×#137D15111yescharacteristic, complemented
204C2×#135—1511no—
205#548—1511no—
206#547—1511no—
207#497—1511no—
208#468—1511no—
209#467—1511no—
210#463—1511no—
211#462—1511no—
212#452—1511no—
213#452—1511no—
214#451—1511no—
215#449—1511no—
216#440—1511no—
217#435—1511no—
218C2×#41—1511no—
219C2×#41—1511no—
220C2×#41C2×D15111yescharacteristic
221C22×Q8C2×D15111yescharacteristic
222#137—24no—
223#135—3024no—
224C2×Q16—1511no—
225C2×Q16—1511no—
226C2×Q16C2×D15111yescharacteristic
227C2×Q16C2×D15111yescharacteristic
228C2×SD16—1511no—
229C2×SD16—1511no—
230C2×SD16C2×D15111yescharacteristic
231C2×SD16C2×D15111yescharacteristic
232C2×D8—1511no—
233C2×M16C2×D15111yescharacteristic
234C22×C8—1511no—
235C4⋊Q8—1511no—
236#124—3021no—
237#124—1511no—
238#123—3021no—
239#123—3021no—
240C22⋊Q8—3021no—
241C22⋊Q8—1511no—
242C22⋊Q8—1511no—
243C22⋊Q8—1511no—
244#121—3021no—
245#121—3021no—
246#121—1511no—
247C4×Q8—1511no—
248C4×D4—3021no—
249C4×D4—1511no—
250C4×D4—1511no—
251C2×C4⋊C4—3021no—
252#107—1511no—
253C4⋊C8—1511no—
254#103—1511no—
255#103—1511no—
256#103—1511no—
257#103—1511no—
258#102—1511no—
259#102—1511no—
260C22⋊C8—1511no—
261C22⋊C8—1511no—
262#97—1511no—
263#41—22no—
264#41—41no—
265#41—3022no—
266#41—3022no—
267#41—6041no—
268#41—6041no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—1511no—
273C2×Q8C22×D15111yescharacteristic
274C2×Q8C22×D15111yescharacteristic
275C2×Q8C22×D15111yescharacteristic
276C2×D4—21no—
277C2×D4—3021no—
278C2×D4—3021no—
279C2×D4—3021no—
280C2×D4—1511no—
281C2×D4—1511no—
282C2×D4C22×D15111yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—3021no—
286C22×C4—3021no—
287C22×C4—3021no—
288C22×C4—1511no—
289C22×C4C22×D15111yescharacteristic
290Q16—22no—
291Q16—22no—
292Q16—3022no—
293Q16—6041no—
294SD16—22no—
295SD16—3022no—
296SD16—6041no—
297SD16C22⋊D15114yescomplemented
298D8—3022no—
299M16—22no—
300C2×C8—3022no—
301C2×C8—1511no—
302C2×C8—1511no—
303C2×C8C22×D15111yescharacteristic
304C2×C8C22×D15111yescharacteristic
305C4⋊C4—3021no—
306C4⋊C4—3021no—
307C4⋊C4—3021no—
308C4⋊C4—3021no—
309C4⋊C4—3021no—
310C4⋊C4—3021no—
311C4⋊C4—1511no—
312C4⋊C4—1511no—
313C4⋊C4—1511no—
314C22⋊C4—3021no—
315C22⋊C4—3021no—
316C22⋊C4—3021no—
317C22⋊C4—3021no—
318C22⋊C4—3021no—
319C22⋊C4—3021no—
320C22⋊C4—3021no—
321C22⋊C4—1511no—
322C22⋊C4—1511no—
323C42—3021no—
324C42—1511no—
325C23—21no—
326C23—3021no—
327C23—1511no—
328C23D4×D15111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—42no—
335Q8—3021no—
336Q8—3021no—
337Q8C2×C22⋊D15112yes—
338D4—21no—
339D4—42no—
340D4—3021no—
341D4—3021no—
342D4—6042no—
343D4—6041no—
344D4—6042no—
345D4—6042no—
346D4C2×C22⋊D15112yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—3021no—
355C2×C4—3021no—
356C2×C4—3021no—
357C2×C4—3021no—
358C2×C4—3021no—
359C2×C4—6042no—
360C2×C4—6042no—
361C2×C4—6042no—
362C2×C4—1511no—
363C2×C4—1511no—
364C2×C4—1511no—
365C2×C4D4×D15111yescharacteristic
366C2×C4C23×D15111yescharacteristic
367C8—21no—
368C8—3021no—
369C8—3021no—
370C8C2×C22⋊D15112yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—3021no—
378C22—3021no—
379C22—3021no—
380C22—6041no—
381C22—6041no—
382C22—6041no—
383C22C2×D4×D15111yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—41no—
388C4—3021no—
389C4—3021no—
390C4—3021no—
391C4—6041no—
392C4—6041no—
393C4—6041no—
394C4C22×C22⋊D15111yescharacteristic
395C4#1801278411yescharacteristic
396C2—41no—
397C2—42no—
398C2—6041no—
399C2—12081no—
400C2D4×C22⋊D15111yescharacteristic
401C2#2375301111yescharacteristic
402C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#137×C151C2
socleC22×C151C22×D4
hypercenterC2×#137D151
hypocenterC151#3269
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#18012760C2semidirect
2. #23752873C2semidirect
3. #23752861C2semidirect
4. #23752605C2semidirect
5. #23752458C2semidirect
6. #23752450C2semidirect
7. #23752429C2semidirect
8. #23752420C2semidirect
9. #23752373C2semidirect
10. #23752371C2semidirect
11. #23752368C2semidirect
12. #23752357C2semidirect
13. #23752313C2semidirect
14. #23752281C2semidirect
15. C2×#137×C151C2semidirect
119. SD16×C151D4semidirect
201. C151#3269semidirect
203. C2×#137D151semidirect
297. SD16C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127602
#237528732
#237528612
#237526052
#237524582
#237524502
#237524292
#237524202
#237523732
#237523712
#237523682
#237523572
#237523132
#237522812
C2×#137×C1512
#3269151