Finite Group Databasebeta

← #11861187

Subgroups — #11861187

Order 1152.

678 conjugacy classes of subgroups.

The subgroup lattice has 423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63513C211yesmaximal, characteristic
2#10589921C211yesmaximal, characteristic, complemented
3#10589847C211yesmaximal, characteristic, complemented
4C9×#421C211yesmaximal, characteristic, complemented
5C2×#63381C211yesmaximal, characteristic, complemented
6#10588685C211yesmaximal, characteristic, complemented
7#10588675C211yesmaximal, characteristic, complemented
8#10588504C214yesmaximal, complemented
9#10588503C214yesmaximal, complemented
10#78990—31nomaximal
11C2×C9×#41C2211yescharacteristic
12C2×#3697C2211yescharacteristic
13C2×C9×M16C2211yescharacteristic
14C9×#117C2211yescharacteristic
15#63513C412yescomplemented
16#63513C412yescomplemented
17#63513C2212yes—
18#63513C2212yes—
19#63510—22no—
20#63510C2214yescomplemented
21C2×#3675C411yescharacteristic, complemented
22C2×#3674C411yescharacteristic, complemented
23C2×#3673C411yescharacteristic, complemented
24C2×#3672C411yescharacteristic, complemented
25C2×#3667—22no—
26C2×#3667C2211yescharacteristic
27C2×#3667C2211yescharacteristic
28C22×C9⋊C8C2211yescharacteristic
29#63469C2214yescomplemented
30M16×D9—22no—
31#63464—22no—
32C9×#104C2214yescomplemented
33#63381C2212yescomplemented
34#63381C2212yescomplemented
35#63364C2214yescomplemented
36#63362C2212yescomplemented
37C4×C9⋊C8C2212yescomplemented
38C2×#950—31no—
39#5819—31no—
40#5745—31no—
41C3×#421D311yescharacteristic
42C2×#822—31no—
43#5005—31no—
44#4997—31no—
45#4824—34no—
46#4823—34no—
47C9×#41—21no—
48C9×#41—21no—
49C9×#41C2×C412yes—
50C9×#41C2312yes—
51C2×Q8×C9C2×C411yescharacteristic
52C2×D4×C9—21no—
53C2×D4×C9C2×C411yescharacteristic
54C22×C4×C9—21no—
55C22×C4×C9C2311yescharacteristic
56C2×#611—21no—
57#3697—21no—
58#3697—21no—
59#3697C2×C412yes—
60#3697C2312yes—
61C2×D36C2×C411yescharacteristic
62C2×C4×D9—21no—
63C2×Dic18C2×C411yescharacteristic
64C9×M16—21no—
65C9×M16C2312yes—
66C2×C8×C9—21no—
67C9×C4⋊C4—21no—
68C9×C22⋊C4—21no—
69C42×C9C2312yes—
70#3675C2×C412yes—
71#3675C2×C412yes—
72#3674C2×C412yes—
73#3674C2×C412yes—
74#3673C2×C412yes—
75#3673C2×C412yes—
76#3672C2×C412yes—
77#3672C2×C412yes—
78#3667—21no—
79#3667—24no—
80#3667D412yes—
81#3667D412yes—
82#3667C2312yes—
83C2×C9⋊C8—21no—
84C2×C9⋊C8—24no—
85C2×C9⋊C8C2×C411yescharacteristic
86C2×C9⋊C8C2×C411yescharacteristic
87C2×C9⋊C8C2×C411yescharacteristic
88C2×C9⋊C8C2×C411yescharacteristic
89C2×C9⋊C8C2311yescharacteristic
90C2×C9⋊C8C2311yescharacteristic
91C2×C9⋊C8C2312yes—
92#3663—24no—
93C8×D9—24no—
94#2957—91noSylow
95C2×C3×#41C2×D311yescharacteristic
96C2×#235—31no—
97C2×C3×M16C2×D311yescharacteristic
98C3×#117C2×D311yescharacteristic
99#950—32no—
100#950—32no—
101#950—32no—
102#950—32no—
103#948—34no—
104#948—62no—
105C2×#216—31no—
106C2×#215—31no—
107C2×#214—31no—
108C2×#213—31no—
109C2×#208—31no—
110C2×#208—31no—
111C2×#208—62no—
112C22×C3⋊C8—31no—
113#907—34no—
114D3×M16—62no—
115#901—62no—
116C3×#104C2×D314yes—
117#822—32no—
118#822—32no—
119#805—34no—
120#803—32no—
121C4×C3⋊C8—32no—
122C23×C9—21no—
123C23×C9#4111yescharacteristic
124C22×D9—21no—
125Q8×C9—21no—
126Q8×C9C22×C412yes—
127D4×C9—22no—
128D4×C9—22no—
129D4×C9—21no—
130D4×C9C22×C412yes—
131C2×C4×C9—21no—
132C2×C4×C9—22no—
133C2×C4×C9—22no—
134C2×C4×C9—22no—
135C2×C4×C9C22×C411yescharacteristic
136C2×C4×C9C22×C411yescharacteristic
137C2×C4×C9C2×D411yescharacteristic
138C2×C4×C9C2×D411yescharacteristic
139C2×C4×C9#4111yescharacteristic
140C2×C4×C9C2411yescharacteristic
141#611—22no—
142#611—22no—
143C2×Dic9—21no—
144D36—21no—
145D36C22×C412yes—
146C4×D9—22no—
147C4×D9—22no—
148Dic18—21no—
149Dic18C22×C412yes—
150C8×C9—22no—
151C9⋊C8—22no—
152C9⋊C8C22×C411yescharacteristic
153C9⋊C8C22×C411yescharacteristic
154C9⋊C8C22×C411yescharacteristic
155C9⋊C8C22×C411yescharacteristic
156C9⋊C8C2×D414yes—
157C2×#135—91no—
158#568—91no—
159#568—91no—
160#444—94no—
161#443—94no—
162C2×#108—91no—
163#421—91no—
164#421D911yescharacteristic, complemented
165#405—91no—
166C3×#41—21no—
167C3×#41—21no—
168C3×#41C4×D312yes—
169C3×#41C22×D312yes—
170C2×C3×Q8C4×D311yescharacteristic
171C2×C3×D4—21no—
172C2×C3×D4C4×D311yescharacteristic
173C22×C3×C4—21no—
174C22×C3×C4C22×D311yescharacteristic
175C2×#67—61no—
176#235—32no—
177#235—32no—
178#235—61no—
179#235—61no—
180C2×D12—31no—
181C2×C4×D3—61no—
182C2×Dic6—31no—
183C3×M16—21no—
184C3×M16C22×D312yes—
185C2×C3×C8—21no—
186C3×C4⋊C4—21no—
187C3×C22⋊C4—21no—
188C3×C42C22×D312yes—
189#216—32no—
190#216—32no—
191#215—32no—
192#215—32no—
193#214—32no—
194#214—32no—
195#213—32no—
196#213—32no—
197#208—32no—
198#208—32no—
199#208—32no—
200#208—64no—
201#208—61no—
202C2×C3⋊C8—31no—
203C2×C3⋊C8—31no—
204C2×C3⋊C8—31no—
205C2×C3⋊C8—31no—
206C2×C3⋊C8—31no—
207C2×C3⋊C8—32no—
208C2×C3⋊C8—31no—
209C2×C3⋊C8—64no—
210C2×C3⋊C8—61no—
211ΓL(1,𝔽25)—64no—
212D3×C8—64no—
213C22×C9—22no—
214C22×C9—41no—
215C22×C9—81no—
216C22×C9C4×D411yescharacteristic
217C22×C9C4×D411yescharacteristic
218C22×C9C2×#4111yescharacteristic
219C2×D9—22no—
220C2×D9—81no—
221C4×C9—22no—
222C4×C9—42no—
223C4×C9C4×D411yescharacteristic
224C4×C9C4×D411yescharacteristic
225C4×C9C23×C411yescharacteristic
226C4×C9C22×D411yescharacteristic
227Dic9—22no—
228C2×#41—91no—
229C2×#41C2×D911yescharacteristic
230#135—92no—
231#135—92no—
232#135—92no—
233#135—92no—
234C2×Q16—91no—
235C2×SD16—91no—
236C2×SD16—91no—
237C2×D8—91no—
238#131—94no—
239#131—94no—
240#131—182no—
241#131—182no—
242C2×M16—91no—
243C2×M16—91no—
244C2×M16—182no—
245C2×M16—182no—
246C2×M16C2×D911yescharacteristic
247C22×C8—91no—
248#117C2×D911yescharacteristic
249#108—92no—
250#108—92no—
251#104—94no—
252#104C2×D914yescomplemented
253#97—92no—
254C4×C8—92no—
255C23×C3—21no—
256C23×C3#23711yescharacteristic
257C22×D3—61no—
258C3×Q8—21no—
259C3×Q8C2×C4×D312yes—
260C3×D4—22no—
261C3×D4—22no—
262C3×D4—21no—
263C3×D4C2×C4×D312yes—
264C2×C3×C4—21no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4C2×C4×D311yescharacteristic
269C2×C3×C4C2×C4×D311yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4#23711yescharacteristic
273C2×C3×C4C23×D311yescharacteristic
274#67—62no—
275#67—62no—
276C2×Dic3—61no—
277D12—32no—
278D12—61no—
279C4×D3—62no—
280C4×D3—62no—
281Dic6—32no—
282Dic6—61no—
283C3×C8—22no—
284C3⋊C8—31no—
285C3⋊C8—31no—
286C3⋊C8—31no—
287C3⋊C8—31no—
288C3⋊C8—34no—
289C3⋊C8—62no—
290C2×C9—21no—
291C2×C9—21no—
292C2×C9—21no—
293C2×C9—42no—
294C2×C9C2×C4×D411yescharacteristic
295D9—42no—
296#41—21no—
297#41—21no—
298#41—92no—
299#41—92no—
300#41—181no—
301#41—181no—
302#41C4×D912yes—
303#41C22×D912yes—
304C2×Q8—91no—
305C2×Q8C4×D911yescharacteristic
306C2×D4—21no—
307C2×D4—91no—
308C2×D4—181no—
309C2×D4C4×D911yescharacteristic
310C22×C4—21no—
311C22×C4—181no—
312C22×C4C22×D911yescharacteristic
313Q16—92no—
314Q16—92no—
315SD16—92no—
316SD16—92no—
317SD16—92no—
318SD16—92no—
319D8—92no—
320D8—92no—
321M16—21no—
322M16—92no—
323M16—92no—
324M16—92no—
325M16—184no—
326M16—184no—
327M16—181no—
328M16C22×D912yes—
329C2×C8—21no—
330C2×C8—91no—
331C2×C8—91no—
332C2×C8—91no—
333C2×C8—91no—
334C2×C8—91no—
335C2×C8—92no—
336C2×C8—91no—
337C2×C8—184no—
338C2×C8—184no—
339C2×C8—181no—
340C4⋊C4—21no—
341C22⋊C4—21no—
342C42C22×D912yes—
343C22×C3—22no—
344C22×C3—41no—
345C22×C3—81no—
346C22×C3#67⋊C411yescharacteristic
347C22×C3#67⋊C411yescharacteristic
348C22×C3C2×#23711yescharacteristic
349C2×D3—62no—
350C2×D3—241no—
351C3×C4—22no—
352C3×C4—42no—
353C3×C4#67⋊C411yescharacteristic
354C3×C4#67⋊C411yescharacteristic
355C3×C4C22×C4×D311yescharacteristic
356C3×C4C2×D3×D411yescharacteristic
357Dic3—62no—
358C9#295711yescharacteristic, complemented, Sylow
359C23—21no—
360C23—181no—
361C23#369911yescharacteristic
362Q8—21no—
363Q8—92no—
364Q8—181no—
365Q8C2×C4×D912yes—
366D4—22no—
367D4—22no—
368D4—21no—
369D4—92no—
370D4—182no—
371D4—182no—
372D4—181no—
373D4C2×C4×D912yes—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—181no—
379C2×C4—182no—
380C2×C4—182no—
381C2×C4C2×C4×D911yescharacteristic
382C2×C4C2×C4×D911yescharacteristic
383C2×C4D4×D911yescharacteristic
384C2×C4D4×D911yescharacteristic
385C2×C4#369911yescharacteristic
386C2×C4C23×D911yescharacteristic
387C8—22no—
388C8—91no—
389C8—91no—
390C8—91no—
391C8—91no—
392C8—94no—
393C8—182no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—42no—
398C2×C3C2×#67⋊C411yescharacteristic
399D3—122no—
400C22—22no—
401C22—41no—
402C22—81no—
403C22—182no—
404C22—721no—
405C22#611⋊C411yescharacteristic
406C22#611⋊C411yescharacteristic
407C22C2×#369911yescharacteristic
408C4—22no—
409C4—42no—
410C4—182no—
411C4#611⋊C411yescharacteristic
412C4#611⋊C411yescharacteristic
413C4C22×C4×D911yescharacteristic
414C4C2×D4×D911yescharacteristic
415C3#7899011yescharacteristic
416C2—21no—
417C2—21no—
418C2—21no—
419C2—42no—
420C2—362no—
421C2C2×#611⋊C411yescharacteristic
subgroupG/H
centerC4C2×D4×D9
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC9×#421C2
socleC2×C3C2×#67⋊C4
prime radicalC2×#63513C2
cosocleC2×C4×C9C24
hypercenter#421D9
hypocenterC9#2957
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #10589921C2semidirect
3. #10589847C2semidirect
4. C9×#421C2semidirect
5. C2×#63381C2semidirect
6. #10588685C2semidirect
7. #10588675C2semidirect
8. #10588504C2semidirect
9. #10588503C2semidirect
15. #63513C4semidirect
16. #63513C4semidirect
20. #63510C22semidirect
21. C2×#3675C4semidirect
22. C2×#3674C4semidirect
23. C2×#3673C4semidirect
24. C2×#3672C4semidirect
29. #63469C22semidirect
32. C9×#104C22semidirect
33. #63381C22semidirect
34. #63381C22semidirect
35. #63364C22semidirect
36. #63362C22semidirect
37. C4×C9⋊C8C22semidirect
164. #421D9semidirect
252. #104C2×D9semidirect
358. C9#2957semidirect

Maximal subgroups

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

subgroupindex
C2×#635132
#105899212
#105898472
C9×#4212
C2×#633812
#105886852
#105886752
#105885042
#105885032
#789903