Finite Group Databasebeta

← #34077142

Subgroups — #34077142

Order 19328.

528 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012716C211yesmaximal, characteristic, complemented
2C2×#18012711C211yesmaximal, characteristic
3#23752148C211yesmaximal, characteristic, complemented
4#23752147C211yesmaximal, characteristic, complemented
5#23752146C211yesmaximal, characteristic, complemented
6#23752145C211yesmaximal, characteristic, complemented
7#23752128C211yesmaximal, characteristic, complemented
8#23752128C211yesmaximal, characteristic, complemented
9#23752127C211yesmaximal, characteristic, complemented
10#23752127C211yesmaximal, characteristic, complemented
11#23752126C211yesmaximal, characteristic, complemented
12#23752125C211yesmaximal, characteristic, complemented
13#23752124C211yesmaximal, characteristic, complemented
14#23752073C211yesmaximal, characteristic, complemented
15#394×C151C211yesmaximal, characteristic, complemented
16C22×Dic302C2211yescharacteristic
17C22×C22⋊D151C2211yescharacteristic
18C22×C22⋊D151C2211yescharacteristic
19C23×Dic151C2211yescharacteristic
20#18012716—24no—
21#18012711—24no—
22C2×C4⋊Dic151C2211yescharacteristic
23C2×C4⋊Dic151C2211yescharacteristic
24C2×Dic151⋊C4C2211yescharacteristic
25C2×Dic151⋊C4C2211yescharacteristic
26C2×Dic151⋊C4C2211yescharacteristic
27C2×Dic151⋊C4C2211yescharacteristic
28C2×Dic151⋊C4C2211yescharacteristic
29C2×C22⋊Dic151C2211yescharacteristic
30C2×C22⋊Dic151C2211yescharacteristic
31C2×C22⋊Dic151C2211yescharacteristic
32C2×C22⋊Dic151C2211yescharacteristic
33C2×C22⋊Dic151C2211yescharacteristic
34C2×(C2×D151)⋊C4C2211yescharacteristic
35C2×(C2×D151)⋊C4C2211yescharacteristic
36C2×(C2×D151)⋊C4C2211yescharacteristic
37C2×(C2×D151)⋊C4C2211yescharacteristic
38C2×(C2×D151)⋊C4C2211yescharacteristic
39C151⋊#95C2211yescharacteristic
40C151⋊#95C2211yescharacteristic
41C151⋊#95C2211yescharacteristic
42C151⋊#95C2211yescharacteristic
43C151⋊#95C2211yescharacteristic
44C151⋊#95C2211yescharacteristic
45C151⋊#95C2211yescharacteristic
46C22×D4×C151C2211yescharacteristic
47C2×C4⋊C4×C151C2211yescharacteristic
48C2×C22⋊C4×C151C2211yescharacteristic
49C2×C22⋊C4×C151C2211yescharacteristic
50C2×C22⋊C4×C151C2211yescharacteristic
51C2×C22⋊C4×C151C2211yescharacteristic
52#95×C151C2211yescharacteristic
53C23×D151C2311yescharacteristic
54C2×Dic302—22no—
55C2×Dic302—41no—
56C2×Dic302—41no—
57C2×C22⋊D151—22no—
58C2×C22⋊D151—22no—
59C2×C22⋊D151—41no—
60C2×C22⋊D151—41no—
61C2×C22⋊D151—41no—
62C2×C22⋊D151—41no—
63C22×Dic151—41no—
64C22×Dic151—41no—
65C22×Dic151D414yes—
66C22×Dic151C2311yescharacteristic
67C22×Dic151C2311yescharacteristic
68C22×Dic151C2311yescharacteristic
69C22×Dic151C2311yescharacteristic
70C22×Dic151C2311yescharacteristic
71C22×Dic151C2311yescharacteristic
72C22×Dic151C2311yescharacteristic
73C4⋊Dic151—22no—
74C4⋊Dic151—41no—
75Dic151⋊C4—22no—
76Dic151⋊C4—22no—
77Dic151⋊C4—22no—
78Dic151⋊C4—41no—
79Dic151⋊C4—41no—
80C22⋊Dic151—22no—
81C22⋊Dic151—22no—
82C22⋊Dic151—41no—
83C22⋊Dic151—41no—
84C22⋊Dic151—41no—
85(C2×D151)⋊C4—22no—
86(C2×D151)⋊C4—41no—
87(C2×D151)⋊C4—41no—
88(C2×D151)⋊C4—41no—
89(C2×D151)⋊C4—41no—
90C24×C151C2311yescharacteristic
91C24×C151C2311yescharacteristic
92C2×D4×C151—22no—
93C2×D4×C151—41no—
94C2×D4×C151—41no—
95C22×C4×C151C2311yescharacteristic
96C22×C4×C151C2311yescharacteristic
97C22×C4×C151C2311yescharacteristic
98C22×C4×C151C2311yescharacteristic
99C22×C4×C151C2311yescharacteristic
100C4⋊C4×C151—41no—
101C22⋊C4×C151—22no—
102C22⋊C4×C151—41no—
103C22⋊C4×C151—41no—
104C22⋊C4×C151—41no—
105C22×D151—21no—
106C22×D151—21no—
107C22×D151—21no—
108C22×D151—21no—
109C22×D151—21no—
110C22×D151—21no—
111C22×D151—21no—
112Dic302—44no—
113C22⋊D151—44no—
114C22⋊D151—44no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—44no—
135C2×Dic151C2×D412yes—
136C2×Dic151C2×D412yes—
137C23×C151—21no—
138C23×C151—21no—
139C23×C151—21no—
140C23×C151—21no—
141C23×C151—21no—
142C23×C151—21no—
143C23×C151—21no—
144C23×C151—21no—
145C23×C151—21no—
146C23×C151—21no—
147C23×C151—21no—
148C23×C151—21no—
149C23×C151—21no—
150C23×C151C2×D412yes—
151C23×C151C2411yescharacteristic
152D4×C151—44no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C22×C151—22no—
169C22×C151—22no—
170C22×C151—22no—
171C22×C151—41no—
172C22×C151—41no—
173C22×C151—41no—
174C22×C151—41no—
175C22×C151—41no—
176C22×C151—41no—
177C22×C151—41no—
178C22×C151—41no—
179C22×C151—41no—
180C22×C151—41no—
181C22×C151—41no—
182C22×C151C22×D411yescharacteristic
183C22×C151H(5,𝔽2)11yescharacteristic
184C22×C151H(5,𝔽2)11yescharacteristic
185C22×C151H(5,𝔽2)11yescharacteristic
186C22×C151H(5,𝔽2)11yescharacteristic
187C22×C1512−1+411yescharacteristic
188C22×C1512−1+411yescharacteristic
189C2×D151—41no—
190C2×D151—41no—
191C2×D151—41no—
192C2×D151—41no—
193C2×D151—41no—
194C2×D151—41no—
195C2×D151—41no—
196C4×C151—41no—
197C4×C151—41no—
198C4×C151—41no—
199C4×C151—41no—
200C4×C151—41no—
201Dic151—22no—
202Dic151—22no—
203Dic151—41no—
204Dic151—41no—
205Dic151—41no—
206Dic151—41no—
207Dic151—41no—
208C2×C151—42no—
209C2×C151—81no—
210C2×C151#53411yescharacteristic
211C2×C151#53511yescharacteristic
212C2×C151#53611yescharacteristic
213C2×C151#56211yescharacteristic
214C2×C151#56211yescharacteristic
215C2×C151#56211yescharacteristic
216C2×C151#56211yescharacteristic
217D151—81no—
218C151#281611yescharacteristic, complemented, Sylow
219#2816—1511nomaximal, Sylow
220C2×C22⋊Q8—1511no—
221C2×#121—1511no—
222#399—1511no—
223#399—1511no—
224#398—1511no—
225#398—1511no—
226#394—1511no—
227#394—1511no—
228#394—1511no—
229#394—1511no—
230#394—1511no—
231#394D15111yescharacteristic, complemented
232#393—1511no—
233#393—1511no—
234#381—1511no—
235C22×Q8—1511no—
236C22×D4—1511no—
237C22×D4—1511no—
238C22×D4C2×D15111yescharacteristic
239C23×C4—1511no—
240C22⋊Q8—3024no—
241#121—3024no—
242C2×C4⋊C4—1511no—
243C2×C4⋊C4—1511no—
244C2×C4⋊C4—1511no—
245C2×C4⋊C4—1511no—
246C2×C4⋊C4—1511no—
247C2×C4⋊C4—1511no—
248C2×C4⋊C4—1511no—
249C2×C4⋊C4C2×D15111yescharacteristic
250C2×C22⋊C4—1511no—
251C2×C22⋊C4—1511no—
252C2×C22⋊C4—1511no—
253C2×C22⋊C4—1511no—
254C2×C22⋊C4—1511no—
255C2×C22⋊C4—1511no—
256C2×C22⋊C4—1511no—
257C2×C22⋊C4—1511no—
258C2×C22⋊C4—1511no—
259C2×C22⋊C4—1511no—
260C2×C22⋊C4C2×D15111yescharacteristic
261C2×C22⋊C4C2×D15111yescharacteristic
262C2×C22⋊C4C2×D15111yescharacteristic
263C2×C22⋊C4C2×D15111yescharacteristic
264#95—1511no—
265#95—1511no—
266#95—1511no—
267#95—1511no—
268#95—1511no—
269#95—1511no—
270#95—1511no—
271#95C2×D15111yescharacteristic
272C24—1511no—
273C24C22×D15111yescharacteristic
274C24C22×D15111yescharacteristic
275C2×Q8—3022no—
276C2×Q8—6041no—
277C2×Q8—6041no—
278C2×D4—22no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—3022no—
282C2×D4—3022no—
283C2×D4—6041no—
284C2×D4—6041no—
285C2×D4—6041no—
286C2×D4—6041no—
287C22×C4—6041no—
288C22×C4—6041no—
289C22×C4—1511no—
290C22×C4—1511no—
291C22×C4—1511no—
292C22×C4—1511no—
293C22×C4—1511no—
294C22×C4—1511no—
295C22×C4—1511no—
296C22×C4—1514no—
297C22×C4C22×D15111yescharacteristic
298C22×C4C22×D15111yescharacteristic
299C22×C4C22×D15111yescharacteristic
300C22×C4C22×D15111yescharacteristic
301C22×C4C22×D15111yescharacteristic
302C4⋊C4—41no—
303C4⋊C4—3022no—
304C4⋊C4—3022no—
305C4⋊C4—3022no—
306C4⋊C4—3022no—
307C4⋊C4—6041no—
308C4⋊C4—6041no—
309C4⋊C4—6041no—
310C22⋊C4—22no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—3022no—
315C22⋊C4—3022no—
316C22⋊C4—3022no—
317C22⋊C4—6041no—
318C22⋊C4—6041no—
319C22⋊C4—6041no—
320C22⋊C4—6041no—
321C22⋊C4—6041no—
322C22⋊C4—6041no—
323C22⋊C4—6041no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—3021no—
338C23—3021no—
339C23—3021no—
340C23—3021no—
341C23—3021no—
342C23—3021no—
343C23—3021no—
344C23D4×D15112yes—
345C23C23×D15111yescharacteristic
346Q8—6044no—
347D4—44no—
348D4—6044no—
349D4—6044no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—3021no—
366C2×C4—3021no—
367C2×C4—3021no—
368C2×C4—3021no—
369C2×C4—3021no—
370C2×C4—3021no—
371C2×C4—3021no—
372C2×C4—3021no—
373C2×C4—3021no—
374C2×C4—3021no—
375C2×C4—3021no—
376C2×C4—3021no—
377C2×C4—3021no—
378C2×C4—3021no—
379C2×C4—3021no—
380C2×C4—3021no—
381C2×C4—3021no—
382C2×C4—3021no—
383C2×C4—3021no—
384C2×C4—6044no—
385C2×C4—1512no—
386C2×C4—1512no—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—6041no—
402C22—6041no—
403C22—6041no—
404C22—6041no—
405C22—6041no—
406C22—6041no—
407C22—6041no—
408C22C2×D4×D15111yescharacteristic
409C22#1801278411yescharacteristic
410C22#1801278411yescharacteristic
411C22#1801278411yescharacteristic
412C22#1801278511yescharacteristic
413C22#1801278611yescharacteristic
414C22#1801278611yescharacteristic
415C4—41no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—3022no—
421C4—3022no—
422C4—6041no—
423C4—6041no—
424C4—6041no—
425C4—6041no—
426C4—6041no—
427C2—42no—
428C2—81no—
429C2—12081no—
430C2#2375277011yescharacteristic
431C2#2375277711yescharacteristic
432C2#2375278411yescharacteristic
433C2#2375295611yescharacteristic
434C2#2375295711yescharacteristic
435C2#2375295711yescharacteristic
436C2#2375295911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#394×C151C2
prime radicalC2×#18012711C2
hypercenter#394D151
hypocenterC151#2816
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#18012716C2semidirect
3. #23752148C2semidirect
4. #23752147C2semidirect
5. #23752146C2semidirect
6. #23752145C2semidirect
7. #23752128C2semidirect
8. #23752128C2semidirect
9. #23752127C2semidirect
10. #23752127C2semidirect
11. #23752126C2semidirect
12. #23752125C2semidirect
13. #23752124C2semidirect
14. #23752073C2semidirect
15. #394×C151C2semidirect
218. C151#2816semidirect
231. #394D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127162
C2×#180127112
#237521482
#237521472
#237521462
#237521452
#237521282
#237521272
#237521262
#237521252
#237521242
#237520732
#394×C1512
#2816151