Finite Group Databasebeta

← #34078426

Subgroups — #34078426

Order 19328.

712 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012787C211yesmaximal, characteristic, complemented
2C2×#18012771C211yesmaximal, characteristic, complemented
3C2×#18012762C211yesmaximal, characteristic, complemented
4#23752792C211yesmaximal, characteristic, complemented
5#23752373C211yesmaximal, characteristic, complemented
6#23752372C211yesmaximal, characteristic, complemented
7#23752366C211yesmaximal, characteristic, complemented
8#23752360C211yesmaximal, characteristic, complemented
9#23752359C211yesmaximal, characteristic, complemented
10#23752352C211yesmaximal, characteristic, complemented
11#23752351C211yesmaximal, characteristic, complemented
12#23752212C211yesmaximal, characteristic, complemented
13#103×D151C211yesmaximal, characteristic, complemented
14#23752177C211yesmaximal, characteristic, complemented
15#451×C151C211yesmaximal, characteristic, complemented
16#18012787—24no—
17#18012787—24no—
18C2×#14559005—21no—
19C2×#14559005C2211yescharacteristic
20C2×#14559005C2211yescharacteristic
21C2×#14559005C2211yescharacteristic
22C2×#14559004—21no—
23C2×#14559004—21no—
24C2×#14559004C2211yescharacteristic
25C2×#14559004C2211yescharacteristic
26C2×Q8×D151—21no—
27C2×Q8×D151C2211yescharacteristic
28C2×Q8×D151C2211yescharacteristic
29#18012771—24no—
30#18012762—24no—
31C2×#14558994C2211yescharacteristic
32C2×#14558993C2211yescharacteristic
33C2×#14558991C2211yescharacteristic
34C2×#14558991C2211yescharacteristic
35C2×#14558991C2211yescharacteristic
36C2×D1208C2211yescharacteristic
37C2×#14558987C2211yescharacteristic
38C2×C8×D151C2211yescharacteristic
39#18012717—21no—
40#18012715C2211yescharacteristic
41#18012714—21no—
42#18012714C2211yescharacteristic
43#18012713C2211yescharacteristic
44#18012712—21no—
45#18012712—21no—
46C4⋊C4×D151C2211yescharacteristic
47#18012664C2211yescharacteristic
48#18012663C2211yescharacteristic
49#18012663C2211yescharacteristic
50#18012662C2211yescharacteristic
51#18012661C2211yescharacteristic
52#18012659C2211yescharacteristic
53C22⋊(C151⋊C8)C2211yescharacteristic
54(C2×D151)⋊C8C2211yescharacteristic
55(C2×D151)⋊C8C2211yescharacteristic
56C22×Q8×C151C2211yescharacteristic
57C2×Q16×C151C2211yescharacteristic
58C2×Q16×C151C2211yescharacteristic
59C22⋊Q8×C151C2211yescharacteristic
60#103×C151C2211yescharacteristic
61#103×C151C2211yescharacteristic
62C22⋊C8×C151C2211yescharacteristic
63#14559005—28no—
64#14559005—22no—
65#14559005—22no—
66#14559005—22no—
67#14559005—22no—
68#14559005—22no—
69#14559005D414yescomplemented
70#14559004—28no—
71#14559004—28no—
72#14559004—22no—
73#14559004—22no—
74#14559004—22no—
75#14559004—22no—
76C2×Dic302—21no—
77C2×Dic302—21no—
78C2×Dic302D411yescharacteristic
79C2×Dic302C2311yescharacteristic
80Q8×D151—28no—
81Q8×D151—22no—
82Q8×D151—22no—
83Q8×D151—22no—
84Q8×D151D414yescomplemented
85C2×D604—21no—
86C2×D604—21no—
87C2×D604—21no—
88C2×D604—21no—
89C2×D604D411yescharacteristic
90C2×D604C2311yescharacteristic
91C2×D604C2311yescharacteristic
92C2×C22⋊D151—21no—
93C2×C22⋊D151—21no—
94C2×C22⋊D151D411yescharacteristic
95C2×C22⋊D151D411yescharacteristic
96C2×C4×D151—21no—
97C2×C4×D151—21no—
98C2×C4×D151—21no—
99C2×C4×D151—21no—
100C2×C4×D151—21no—
101C2×C4×D151—21no—
102C2×C4×D151—21no—
103C2×C4×D151C2311yescharacteristic
104C2×C4×D151C2311yescharacteristic
105#14558994—22no—
106#14558993—22no—
107#14558991—22no—
108#14558991—22no—
109#14558991—22no—
110D1208—22no—
111#14558987—22no—
112C2×C151⋊C8C2311yescharacteristic
113C2×C151⋊C8C2311yescharacteristic
114C8×D151—22no—
115C4⋊Dic151C2311yescharacteristic
116Dic151⋊C4—21no—
117Dic151⋊C4—21no—
118(C2×D151)⋊C4—21no—
119(C2×D151)⋊C4—21no—
120(C2×D151)⋊C4—21no—
121C2×Q8×C151—22no—
122C2×Q8×C151—22no—
123C2×Q8×C151—21no—
124C2×Q8×C151C2311yescharacteristic
125C2×Q8×C151C2311yescharacteristic
126C2×Q8×C151C2311yescharacteristic
127C22×C4×C151—21no—
128C22×C4×C151C2311yescharacteristic
129Q16×C151—22no—
130Q16×C151—22no—
131C2×C8×C151C2311yescharacteristic
132C2×C8×C151C2311yescharacteristic
133C4⋊C4×C151—21no—
134C4⋊C4×C151C2311yescharacteristic
135C22⋊C4×C151—21no—
136C22×D151—21no—
137C22×D151—21no—
138C22×D151C2×D411yescharacteristic
139C22×D151C2×D411yescharacteristic
140Dic302—24no—
141Dic302—21no—
142Dic302—22no—
143Dic302—24no—
144Dic302C2×D412yes—
145D604—24no—
146D604—24no—
147D604—22no—
148D604—21no—
149D604—21no—
150D604—21no—
151D604—42no—
152D604—81no—
153D604C2×D412yes—
154C22⋊D151—24no—
155C22⋊D151—22no—
156C22⋊D151—22no—
157C22⋊D151—81no—
158C2×Dic151—21no—
159C2×Dic151—21no—
160C2×Dic151C2×D411yescharacteristic
161C2×Dic151C2×D411yescharacteristic
162C4×D151—24no—
163C4×D151—24no—
164C4×D151—24no—
165C4×D151—24no—
166C4×D151—21no—
167C4×D151—21no—
168C4×D151—24no—
169C4×D151—42no—
170C4×D151—81no—
171C4×D151C2×D412yes—
172C4×D151C2×D412yes—
173C151⋊C8—21no—
174C151⋊C8—21no—
175C23×C151C2×D411yescharacteristic
176Q8×C151—24no—
177Q8×C151—21no—
178Q8×C151—21no—
179Q8×C151—21no—
180Q8×C151—21no—
181Q8×C151C2×D412yes—
182Q8×C151C2×D412yes—
183C2×C4×C151—24no—
184C2×C4×C151—21no—
185C2×C4×C151—21no—
186C2×C4×C151—21no—
187C2×C4×C151—21no—
188C2×C4×C151—21no—
189C2×C4×C151—21no—
190C2×C4×C151C2×D411yescharacteristic
191C2×C4×C151C2411yescharacteristic
192C8×C151—21no—
193C8×C151—21no—
194C22×C151—21no—
195C22×C151—21no—
196C22×C151—21no—
197C22×C151C22×D411yescharacteristic
198C2×D151—21no—
199C2×D151—21no—
200C2×D151—21no—
201C2×D151—22no—
202C2×D151—21no—
203C2×D151—21no—
204C2×D151—41no—
205C2×D151—41no—
206C2×D151—41no—
207C2×D151—41no—
208C2×D151—41no—
209C2×D151#12012yes—
210C4×C151—22no—
211C4×C151—22no—
212C4×C151—21no—
213C4×C151—41no—
214C4×C151—41no—
215C4×C151C22×D411yescharacteristic
216C4×C151C22×D411yescharacteristic
217Dic151—22no—
218Dic151—21no—
219Dic151—41no—
220Dic151#12012yes—
221C2×C151—41no—
222C2×C151C2×#12011yescharacteristic
223C2×C151#57711yescharacteristic
224C2×C151#57811yescharacteristic
225D151—22no—
226D151—41no—
227D151—42no—
228D151—81no—
229C151#301311yescharacteristic, complemented, Sylow
230#3013—1511nomaximal, Sylow
231C2×2−1+4—1511no—
232C2×#137—1511no—
233C2×#135—1511no—
234#537—1511no—
235#452—1511no—
236#452—1511no—
237#451—1511no—
238#451D15111yescharacteristic, complemented
239#449—1511no—
240#449—1511no—
241#448—1511no—
242#448—1511no—
243#417—1511no—
244C2×#103—1511no—
245#408—1511no—
2462−1+4—3024no—
2472−1+4—3024no—
248C2×#41—3021no—
249C2×#41—3021no—
250C2×#41—3021no—
251C2×#41—1511no—
252C2×#41—1511no—
253C2×#41—1511no—
254C2×#41—1511no—
255C2×#41—1511no—
256C22×Q8—3021no—
257C22×Q8—1511no—
258C22×Q8—1511no—
259C22×Q8C2×D15111yescharacteristic
260#137—3024no—
261#135—3024no—
262C2×Q16—1511no—
263C2×Q16C2×D15111yescharacteristic
264C2×Q16C2×D15111yescharacteristic
265C2×SD16—1511no—
266C2×SD16—1511no—
267C2×SD16—1511no—
268C2×SD16—1511no—
269C2×D8—1511no—
270C2×M16—1511no—
271C22×C8—1511no—
272C22⋊Q8—3021no—
273C22⋊Q8—1511no—
274C22⋊Q8C2×D15111yescharacteristic
275#121—3021no—
276#121—3021no—
277#121—3021no—
278#121—1511no—
279#121—1511no—
280C2×C4⋊C4—1511no—
281#103—1511no—
282#103—1511no—
283#103—1511no—
284#103—1511no—
285#103C2×D15111yescharacteristic
286#103C2×D15111yescharacteristic
287#102—1511no—
288#102—1511no—
289C22⋊C8—1511no—
290C22⋊C8—1511no—
291C22⋊C8—1511no—
292C22⋊C8C2×D15111yescharacteristic
293#41—3028no—
294#41—3028no—
295#41—3022no—
296#41—3022no—
297#41—3022no—
298#41—3022no—
299#41—3028no—
300#41—3022no—
301#41—3022no—
302#41—3022no—
303#41—3022no—
304#41—3022no—
305#41—1514no—
306C2×Q8—22no—
307C2×Q8—22no—
308C2×Q8—21no—
309C2×Q8—3021no—
310C2×Q8—3021no—
311C2×Q8—3028no—
312C2×Q8—3022no—
313C2×Q8—3022no—
314C2×Q8—3022no—
315C2×Q8—1514no—
316C2×Q8—1511no—
317C2×Q8—1511no—
318C2×Q8C22×D15111yescharacteristic
319C2×Q8C22×D15111yescharacteristic
320C2×Q8C22×D15111yescharacteristic
321C2×D4—3021no—
322C2×D4—3021no—
323C2×D4—3021no—
324C2×D4—3021no—
325C2×D4—3021no—
326C2×D4—3021no—
327C2×D4—1511no—
328C2×D4—1511no—
329C2×D4—1511no—
330C2×D4—1511no—
331C2×D4—1511no—
332C22×C4—21no—
333C22×C4—3021no—
334C22×C4—3021no—
335C22×C4—3021no—
336C22×C4—3021no—
337C22×C4—3021no—
338C22×C4—3021no—
339C22×C4—3021no—
340C22×C4—1511no—
341C22×C4—1511no—
342C22×C4C22×D15111yescharacteristic
343Q16—22no—
344Q16—22no—
345Q16—3022no—
346SD16—3022no—
347SD16—3022no—
348SD16—3022no—
349SD16—3022no—
350D8—3022no—
351M16—3022no—
352C2×C8—3022no—
353C2×C8—1511no—
354C2×C8—1511no—
355C2×C8C22×D15111yescharacteristic
356C2×C8C22×D15111yescharacteristic
357C4⋊C4—21no—
358C4⋊C4—3021no—
359C4⋊C4—3021no—
360C4⋊C4—1511no—
361C4⋊C4C22×D15111yescharacteristic
362C22⋊C4—21no—
363C22⋊C4—3021no—
364C22⋊C4—3021no—
365C22⋊C4—3021no—
366C23—3021no—
367C23—3021no—
368C23—1511no—
369C23—1511no—
370C23D4×D15111yescharacteristic
371Q8—24no—
372Q8—21no—
373Q8—21no—
374Q8—21no—
375Q8—21no—
376Q8—3024no—
377Q8—3024no—
378Q8—3022no—
379Q8—3021no—
380Q8—1512no—
381Q8D4×D15112yes—
382Q8D4×D15112yes—
383D4—3024no—
384D4—3024no—
385D4—3022no—
386D4—3024no—
387D4—3022no—
388D4—3022no—
389D4—3021no—
390D4—3021no—
391D4—3021no—
392D4—6042no—
393D4—1512no—
394D4—12081no—
395D4—12081no—
396C2×C4—24no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—3024no—
404C2×C4—3024no—
405C2×C4—3024no—
406C2×C4—3024no—
407C2×C4—3024no—
408C2×C4—3021no—
409C2×C4—3021no—
410C2×C4—3021no—
411C2×C4—3021no—
412C2×C4—6042no—
413C2×C4—1511no—
414C2×C4—1511no—
415C2×C4—1512no—
416C2×C4—1512no—
417C2×C4—12081no—
418C2×C4D4×D15111yescharacteristic
419C2×C4C23×D15111yescharacteristic
420C8—21no—
421C8—21no—
422C8—3021no—
423C8—3021no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—3021no—
428C22—3021no—
429C22—3021no—
430C22—3021no—
431C22—3021no—
432C22—3022no—
433C22—6041no—
434C22—6041no—
435C22—6041no—
436C22—6041no—
437C22—6041no—
438C22—1512no—
439C22C2×D4×D15111yescharacteristic
440C4—22no—
441C4—22no—
442C4—21no—
443C4—41no—
444C4—41no—
445C4—3022no—
446C4—3021no—
447C4—6041no—
448C4—1512no—
449C4C2×D4×D15111yescharacteristic
450C4C2×D4×D15111yescharacteristic
451C2—41no—
452C2—3022no—
453C2—6041no—
454C2—6042no—
455C2—12081no—
456C2#120×D15111yescharacteristic
457C2#2375302111yescharacteristic
458C2#2375302511yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#451×C151C2
socleC22×C151C22×D4
hypercenter#451D151
hypocenterC151#3013
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×#18012787C2semidirect
2. C2×#18012771C2semidirect
3. C2×#18012762C2semidirect
4. #23752792C2semidirect
5. #23752373C2semidirect
6. #23752372C2semidirect
7. #23752366C2semidirect
8. #23752360C2semidirect
9. #23752359C2semidirect
10. #23752352C2semidirect
11. #23752351C2semidirect
12. #23752212C2semidirect
13. #103×D151C2semidirect
14. #23752177C2semidirect
15. #451×C151C2semidirect
69. #14559005D4semidirect
84. Q8×D151D4semidirect
229. C151#3013semidirect
238. #451D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127872
C2×#180127712
C2×#180127622
#237527922
#237523732
#237523722
#237523662
#237523602
#237523592
#237523522
#237523512
#237522122
#103×D1512
#237521772
#451×C1512
#3013151