Finite Group Databasebeta

← #11784136

Subgroups — #11784136

Order 1152.

657 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×#63815C211yesmaximal, characteristic
2C2×#63630C211yesmaximal, characteristic, complemented
3C2×C3×#805C211yesmaximal, characteristic
4#10591083C211yesmaximal, characteristic
5#10591057C211yesmaximal, characteristic, complemented
6C3×#4523C211yesmaximal, characteristic, complemented
7#10589165C211yesmaximal, characteristic, complemented
8#70370—31nomaximal
9#68740—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×#3711—21no—
18#63815—22no—
19#63815C414yescomplemented
20C2×D3×C3⋊C8—21no—
21#63630—22no—
22C3×#805C414yescomplemented
23#63565C412yescomplemented
24#63562C412yescomplemented
25#63554—21no—
26Dic3×C3⋊C8—21no—
27C2×#948—31no—
28C2×#907—31no—
29C2×C3×#104—31no—
30#5233—31no—
31#5122—31no—
32#5002—31no—
33#4997—31no—
34C2×#805D311yescharacteristic
35C2×#803—31no—
36C2×#803—31no—
37C2×#803—61no—
38C3×#339—31no—
39#4558—31no—
40#4558—31no—
41#4523D311yescharacteristic, complemented
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C2×C3×#67—21no—
45C3×#235—21no—
46C3×#235—21no—
47C3×#235C2×C412yes—
48C3×#235C2×C412yes—
49C2×C3×D12C2×C411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×Dic6C2×C411yescharacteristic
52C32×C42—21no—
53C32×C42C2×C412yes—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)C2×C412yes—
57C2×C3⋊(C3⋊C8)C2×C412yes—
58C2×C3⋊(C3⋊C8)D411yescharacteristic
59C2×C3⋊(C3⋊C8)D411yescharacteristic
60C2×C3⋊(C3⋊C8)D412yes—
61C3×#217—21no—
62C3×C4⋊Dic3C2×C412yes—
63C3×C4×Dic3—21no—
64C3×#208—21no—
65C3×#208—21no—
66C3×#208C2×C412yes—
67C3×#208C2×C412yes—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70#3711—24no—
71D3×C3⋊C8—24no—
72#1765—91noSylow
73C2×C3×#41—31no—
74C2×#235C2×D311yescharacteristic
75C2×C3×M16—31no—
76C2×C3×M16—31no—
77C3×#117—31no—
78C2×C3×C42—21no—
79C2×C3×C42C2×D311yescharacteristic
80C2×C3×C42C2×D311yescharacteristic
81#948—34no—
82#948—62no—
83#926C2×D311yescharacteristic
84C2×#208—61no—
85C2×#208C2×D311yescharacteristic
86C2×#208C2×D311yescharacteristic
87C22×C3⋊C8—31no—
88C22×C3⋊C8—31no—
89C22×C3⋊C8—31no—
90C22×C3⋊C8—31no—
91C22×C3⋊C8—61no—
92C22×C3⋊C8—61no—
93C22×C3⋊C8—61no—
94#907—34no—
95#907—62no—
96C2×ΓL(1,𝔽25)—61no—
97C2×D3×C8—61no—
98C3×#104—34no—
99#835—32no—
100#832—32no—
101#815—61no—
102C8×Dic3—61no—
103#810—32no—
104#809—32no—
105#805Dic314yescomplemented
106#803—61no—
107#803—62no—
108#803—62no—
109#803—64no—
110C4×C3⋊C8—61no—
111C23×C32#4111yescharacteristic
112C22×C3×D3—21no—
113C2×C32×C4—22no—
114C2×C32×C4—42no—
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C3×#67—22no—
122C3×#67—22no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—22no—
125C3×D12—21no—
126C3×D12C4212yes—
127C3×C4×D3—22no—
128C3×C4×D3—22no—
129C3×Dic6—21no—
130C3×Dic6C4212yes—
131C3⋊(C3⋊C8)—22no—
132C3⋊(C3⋊C8)C22⋊C412yes—
133C3⋊(C3⋊C8)C22⋊C412yes—
134C3×C3⋊C8—22no—
135C3×C3⋊C8—22no—
136C2×#131—91no—
137C2×#104—31no—
138#416—91no—
139#405—91no—
140C2×#97—91no—
141#341—91no—
142#339—31no—
143C3×#41—32no—
144C3×#41—32no—
145C3×#41—61no—
146C3×#41—61no—
147C2×C3×Q8—31no—
148C2×C3×D4—31no—
149C2×C3×D4—61no—
150C22×C3×C4—22no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—61no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C2×#67—21no—
158#235—21no—
159#235—21no—
160#235C4×D312yes—
161#235C2×Dic312yes—
162C2×D12C4×D311yescharacteristic
163C2×C4×D3—21no—
164C2×Dic6C4×D311yescharacteristic
165C3×M16—32no—
166C3×M16—32no—
167C3×M16—61no—
168C3×M16—61no—
169C2×C3×C8—61no—
170C2×C3×C8—61no—
171C3×C4⋊C4—32no—
172C3×C22⋊C4—61no—
173C3×C42—22no—
174C3×C42—21no—
175C3×C42—21no—
176C3×C42—22no—
177C3×C42—61no—
178C3×C42C4×D312yes—
179C3×C42C2×Dic312yes—
180#217—21no—
181C4⋊Dic3C4×D312yes—
182C4×Dic3—21no—
183#208—21no—
184#208—21no—
185#208—64no—
186#208C4×D312yes—
187#208C2×Dic312yes—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—32no—
191C2×C3⋊C8—32no—
192C2×C3⋊C8—31no—
193C2×C3⋊C8—31no—
194C2×C3⋊C8—32no—
195C2×C3⋊C8—32no—
196C2×C3⋊C8—31no—
197C2×C3⋊C8—31no—
198C2×C3⋊C8—32no—
199C2×C3⋊C8—32no—
200C2×C3⋊C8—62no—
201C2×C3⋊C8—62no—
202C2×C3⋊C8—62no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—64no—
206C2×C3⋊C8—62no—
207C2×C3⋊C8—62no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212ΓL(1,𝔽25)—64no—
213D3×C8—64no—
214C22×C32—22no—
215C22×C32#11711yescharacteristic
216C22×C32C4×D411yescharacteristic
217C22×C32C4×D411yescharacteristic
218C2×C3×D3—22no—
219C2×C3×D3—42no—
220C32×C4—42no—
221C32×C4C2×C4211yescharacteristic
222C32×C4C2×C22⋊C411yescharacteristic
223C32×C4C4×D411yescharacteristic
224C32×C4C4×D411yescharacteristic
225C3×Dic3—22no—
226C3×Dic3—42no—
227C2×#41—31no—
228#131—94no—
229#131—182no—
230C2×M16—31no—
231C2×M16—31no—
232C2×M16—181no—
233C22×C8—91no—
234C22×C8—91no—
235C22×C8—181no—
236#117—31no—
237C2×C42D3211yescharacteristic
238#104—34no—
239#103—92no—
240#102—92no—
241#97—182no—
242#97—181no—
243C4×C8—181no—
244C23×C3—21no—
245C23×C3—61no—
246C23×C3#23711yescharacteristic
247C23×C3#23711yescharacteristic
248C22×D3—21no—
249C3×Q8—32no—
250C3×Q8—61no—
251C3×D4—32no—
252C3×D4—62no—
253C3×D4—62no—
254C3×D4—61no—
255C2×C3×C4—24no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—44no—
265C2×C3×C4—42no—
266C2×C3×C4—42no—
267C2×C3×C4—61no—
268C2×C3×C4—62no—
269C2×C3×C4—62no—
270C2×C3×C4—62no—
271C2×C3×C4C2×C4×D311yescharacteristic
272C2×C3×C4C2×C4×D311yescharacteristic
273C2×C3×C4C2×C4×D311yescharacteristic
274C2×C3×C4C2×C4×D311yescharacteristic
275C2×C3×C4C2×C4×D311yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4#23711yescharacteristic
281C2×C3×C4#23911yescharacteristic
282C2×C3×C4C22×Dic311yescharacteristic
283#67—22no—
284#67—22no—
285C2×Dic3—21no—
286C2×Dic3—22no—
287D12—21no—
288D12C4×Dic312yes—
289C4×D3—22no—
290C4×D3—22no—
291Dic6—21no—
292Dic6C4×Dic312yes—
293C3×C8—62no—
294C3×C8—62no—
295C3⋊C8—22no—
296C3⋊C8—22no—
297C3⋊C8—32no—
298C3⋊C8—32no—
299C3⋊C8—32no—
300C3⋊C8—32no—
301C3⋊C8—62no—
302C3⋊C8—62no—
303C3⋊C8—64no—
304C3⋊C8—62no—
305C3⋊C8—62no—
306C2×C32—21no—
307C2×C32—21no—
308C2×C32C4×C22⋊C411yescharacteristic
309C2×C32#44412yes—
310C3×D3—42no—
311#41—32no—
312#41—32no—
313#41—61no—
314#41—61no—
315C2×Q8—31no—
316C2×D4—31no—
317C2×D4—61no—
318C22×C4—21no—
319C22×C4—61no—
320C22×C4C2×D3211yescharacteristic
321M16—32no—
322M16—32no—
323M16—61no—
324M16—61no—
325M16—184no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8—92no—
329C2×C8—91no—
330C2×C8—91no—
331C2×C8—92no—
332C2×C8—92no—
333C2×C8—184no—
334C2×C8—181no—
335C2×C8—181no—
336C4⋊C4—32no—
337C22⋊C4—61no—
338C42—21no—
339C42—61no—
340C42D3×Dic312yes—
341C22×C3—24no—
342C22×C3—22no—
343C22×C3—22no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—62no—
348C22×C3—122no—
349C22×C3#87711yescharacteristic
350C22×C3#67⋊C411yescharacteristic
351C22×C3#67⋊C411yescharacteristic
352C22×C3#67⋊C411yescharacteristic
353C22×C3#89211yescharacteristic
354C22×C3D4×Dic311yescharacteristic
355C2×D3—22no—
356C2×D3—42no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—44no—
362C3×C4—42no—
363C3×C4—42no—
364C3×C4—62no—
365C3×C4—122no—
366C3×C4C42×D311yescharacteristic
367C3×C4D3×C22⋊C411yescharacteristic
368C3×C4D3×C22⋊C411yescharacteristic
369C3×C4#67⋊C411yescharacteristic
370C3×C4#89311yescharacteristic
371C3×C4#89311yescharacteristic
372C3×C4C2×C4×Dic311yescharacteristic
373C3×C4D4×Dic311yescharacteristic
374Dic3—22no—
375Dic3—42no—
376C32#176511yescharacteristic, complemented, Sylow
377C23—61no—
378C23#380511yescharacteristic
379Q8—32no—
380Q8—61no—
381D4—32no—
382D4—62no—
383D4—62no—
384D4—61no—
385C2×C4—22no—
386C2×C4—42no—
387C2×C4—61no—
388C2×C4—62no—
389C2×C4—62no—
390C2×C4—62no—
391C2×C4#379611yescharacteristic
392C2×C4C4×D3211yescharacteristic
393C2×C4C4×D3211yescharacteristic
394C2×C4#380211yescharacteristic
395C2×C4C2×D3×Dic311yescharacteristic
396C2×C4#381111yescharacteristic
397C8—62no—
398C8—62no—
399C8—92no—
400C8—92no—
401C8—182no—
402C2×C3—22no—
403C2×C3—22no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—22no—
410C2×C3—122no—
411C2×C3#466611yescharacteristic
412C2×C3#482312yes—
413C2×C3#482312yes—
414C2×C3Dic3×C22⋊C411yescharacteristic
415D3—42no—
416C22—22no—
417C22—62no—
418C22—122no—
419C22#6387811yescharacteristic
420C22#6390211yescharacteristic
421C22#67⋊Dic311yescharacteristic
422C4—42no—
423C4—62no—
424C4—122no—
425C4C4×D3×Dic311yescharacteristic
426C4#6388111yescharacteristic
427C4#6389811yescharacteristic
428C4#6392111yescharacteristic
429C3—21no—
430C3#6874011yescharacteristic, complemented
431C3#7037011yescharacteristic, complemented
432C2—21no—
433C2—21no—
434C2—122no—
435C2#1059039012yes—
436C2#1059136811yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1765
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#63630C2semidirect
5. #10591057C2semidirect
6. C3×#4523C2semidirect
7. #10589165C2semidirect
19. #63815C4semidirect
22. C3×#805C4semidirect
23. #63565C4semidirect
24. #63562C4semidirect
41. #4523D3semidirect
105. #805Dic3semidirect
376. C32#1765semidirect
430. C3#68740semidirect
431. C3#70370semidirect

Maximal subgroups

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

subgroupindex
C2×#638152
C2×#636302
C2×C3×#8052
#105910832
#105910572
C3×#45232
#105891652
#703703
#687403