Finite Group Databasebeta

← #73377

Subgroups — #73377

Order 384.

610 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#930C211yesmaximal, characteristic
2C2×C4×#67C211yesmaximal, characteristic, complemented
3C2×C3×#95C211yesmaximal, characteristic, complemented
4#5213C211yesmaximal, characteristic, complemented
5#5213C211yesmaximal, characteristic, complemented
6#5213C211yesmaximal, characteristic, complemented
7#5210C211yesmaximal, characteristic, complemented
8#4675C211yesmaximal, characteristic, complemented
9#4675C211yesmaximal, characteristic, complemented
10#4672C211yesmaximal, characteristic, complemented
11#4669C211yesmaximal, characteristic, complemented
12#4665C211yesmaximal, characteristic, complemented
13#4664C211yesmaximal, characteristic, complemented
14#4660C211yesmaximal, characteristic, complemented
15#4655C211yesmaximal, characteristic, complemented
16#2444—31nomaximal, Sylow
17C23×C3×C4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C23×C3×C4C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×D12C2211yescharacteristic
23C22×C4×D3C2211yescharacteristic
24C2×#217C2211yescharacteristic
25C2×#217C2211yescharacteristic
26#930—24no—
27C4×#67—24no—
28C2×(C2×D3)⋊C4C2211yescharacteristic
29C2×(C2×D3)⋊C4C2211yescharacteristic
30C2×(C2×D3)⋊C4C2211yescharacteristic
31C2×(C2×D3)⋊C4C2211yescharacteristic
32C2×(C2×D3)⋊C4C2211yescharacteristic
33C2×(C2×D3)⋊C4C2211yescharacteristic
34C2×(C2×D3)⋊C4C2211yescharacteristic
35C2×(C2×D3)⋊C4C2211yescharacteristic
36C2×(C2×D3)⋊C4C2211yescharacteristic
37C2×C4⋊Dic3C2211yescharacteristic
38C2×Dic3⋊C4C2211yescharacteristic
39C2×Dic3⋊C4C2211yescharacteristic
40C2×Dic3⋊C4C2211yescharacteristic
41C2×C4×Dic3C2211yescharacteristic
42C3×#95C2211yescharacteristic
43C3×#95C2211yescharacteristic
44C3×#95C2211yescharacteristic
45C3×#95C2211yescharacteristic
46C3⋊#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C2×#121—31no—
55C2×C4×D4—31no—
56#400—31no—
57#397—31no—
58#397—31no—
59#394—31no—
60#388—31no—
61#387—31no—
62#386—31no—
63#386—31no—
64#386—31no—
65#386—31no—
66#385—31no—
67#381—31no—
68C2×#95D311yescharacteristic, complemented
69C24×C3C2311yescharacteristic
70C23×D3C2311yescharacteristic
71C23×D3C2311yescharacteristic
72C22×C3×C4—22no—
73C22×C3×C4—22no—
74C22×C3×C4—22no—
75C22×C3×C4—22no—
76C22×C3×C4—22no—
77C22×C3×C4—41no—
78C22×C3×C4—41no—
79C22×C3×C4—41no—
80C22×C3×C4—41no—
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C22×C3×C4C2311yescharacteristic
85C22×C3×C4C2311yescharacteristic
86C22×C3×C4C2311yescharacteristic
87C2×#67—22no—
88C2×#67—22no—
89C2×#67—22no—
90C2×#67—22no—
91C2×#67—22no—
92C2×#67D414yes—
93C22×Dic3C2311yescharacteristic
94C22×Dic3C2311yescharacteristic
95C22×Dic3C2311yescharacteristic
96C22×Dic3C2311yescharacteristic
97C22×Dic3C2311yescharacteristic
98C22×Dic3C2311yescharacteristic
99C2×D12—22no—
100C2×D12—22no—
101C2×D12—41no—
102C2×C4×D3—22no—
103C2×C4×D3—22no—
104C2×C4×D3—41no—
105#217—22no—
106#217—22no—
107(C2×D3)⋊C4—22no—
108(C2×D3)⋊C4—22no—
109(C2×D3)⋊C4—22no—
110(C2×D3)⋊C4—22no—
111(C2×D3)⋊C4—41no—
112(C2×D3)⋊C4—41no—
113(C2×D3)⋊C4—41no—
114(C2×D3)⋊C4—41no—
115(C2×D3)⋊C4—41no—
116C4⋊Dic3—22no—
117Dic3⋊C4—22no—
118Dic3⋊C4—22no—
119Dic3⋊C4—41no—
120C4×Dic3—22no—
121C22×D4—31no—
122C22×D4—31no—
123C22×D4—31no—
124C23×C4—31no—
125C23×C4C2×D311yescharacteristic
126C23×C4C2×D311yescharacteristic
127C23×C4C2×D311yescharacteristic
128#121—64no—
129C4×D4—64no—
130C2×C4⋊C4—31no—
131C2×C4⋊C4—31no—
132C2×C4⋊C4—31no—
133C2×C4⋊C4—31no—
134C2×C22⋊C4—31no—
135C2×C22⋊C4—31no—
136C2×C22⋊C4—31no—
137C2×C22⋊C4—31no—
138C2×C22⋊C4—31no—
139C2×C22⋊C4—31no—
140C2×C22⋊C4—31no—
141C2×C22⋊C4—31no—
142C2×C22⋊C4—31no—
143C2×C22⋊C4—31no—
144C2×C22⋊C4—31no—
145C2×C42—31no—
146#95—31no—
147#95—31no—
148#95—31no—
149#95—31no—
150#95—31no—
151#95—31no—
152#95—31no—
153#95—31no—
154#95C2×D311yescharacteristic
155#95C2×D311yescharacteristic
156#95C2×D311yescharacteristic
157#95C2×D311yescharacteristic
158C23×C3—21no—
159C23×C3—21no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3C2×D412yes—
163C23×C3#4112yes—
164C23×C3#4112yes—
165C23×C3C2411yescharacteristic
166C22×D3—21no—
167C22×D3—21no—
168C22×D3—21no—
169C22×D3—21no—
170C22×D3—21no—
171C22×D3—21no—
172C22×D3—21no—
173C22×D3—21no—
174C22×D3—21no—
175C22×D3—21no—
176C22×D3—21no—
177C22×D3—21no—
178C22×D3—21no—
179C22×D3C2×D412yes—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—44no—
197C2×C3×C4—44no—
198C2×C3×C4—44no—
199C2×C3×C4#4112yes—
200C2×C3×C4#4112yes—
201#67—28no—
202#67—44no—
203C2×Dic3—21no—
204C2×Dic3—21no—
205C2×Dic3—21no—
206C2×Dic3—21no—
207C2×Dic3—21no—
208C2×Dic3—21no—
209C2×Dic3—21no—
210C2×Dic3—21no—
211C2×Dic3—21no—
212C2×Dic3—21no—
213C2×Dic3—21no—
214C2×Dic3—21no—
215C2×Dic3—21no—
216C2×Dic3—21no—
217C2×Dic3—21no—
218C2×Dic3—21no—
219C2×Dic3—21no—
220C2×Dic3C2×D412yes—
221D12—44no—
222C4×D3—44no—
223C24—31no—
224C24—31no—
225C24C22×D311yescharacteristic
226C2×D4—34no—
227C2×D4—62no—
228C2×D4—62no—
229C2×D4—62no—
230C2×D4—62no—
231C2×D4—62no—
232C2×D4—62no—
233C2×D4—62no—
234C2×D4—121no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—31no—
241C22×C4—31no—
242C22×C4—31no—
243C22×C4—31no—
244C22×C4—31no—
245C22×C4—31no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—62no—
251C22×C4—62no—
252C22×C4—121no—
253C22×C4C22×D311yescharacteristic
254C22×C4C22×D311yescharacteristic
255C22×C4C22×D311yescharacteristic
256C22×C4C22×D311yescharacteristic
257C22×C4C22×D311yescharacteristic
258C22×C4C22×D311yescharacteristic
259C4⋊C4—62no—
260C4⋊C4—62no—
261C4⋊C4—62no—
262C4⋊C4—121no—
263C22⋊C4—62no—
264C22⋊C4—62no—
265C22⋊C4—62no—
266C22⋊C4—62no—
267C22⋊C4—62no—
268C22⋊C4—62no—
269C22⋊C4—121no—
270C22⋊C4—121no—
271C22⋊C4—121no—
272C22⋊C4—121no—
273C22⋊C4—121no—
274C42—62no—
275C22×C3—22no—
276C22×C3—22no—
277C22×C3—22no—
278C22×C3—22no—
279C22×C3—22no—
280C22×C3—22no—
281C22×C3#12314yes—
282C22×C3C22×D411yescharacteristic
283C22×C3C2×#4111yescharacteristic
284C22×C3C2×#4111yescharacteristic
285C22×C3C2×#4111yescharacteristic
286C22×C3C2×#4111yescharacteristic
287C22×C3H(5,𝔽2)11yescharacteristic
288C22×C3H(5,𝔽2)11yescharacteristic
289C2×D3—22no—
290C2×D3—22no—
291C2×D3—22no—
292C2×D3—41no—
293C2×D3—41no—
294C2×D3—41no—
295C2×D3—41no—
296C2×D3—41no—
297C2×D3—41no—
298C2×D3—41no—
299C2×D3—41no—
300C2×D3—41no—
301C2×D3—41no—
302C2×D3—41no—
303C3×C4—22no—
304C3×C4—22no—
305C3×C4—41no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4—41no—
309Dic3—22no—
310Dic3—41no—
311Dic3—41no—
312Dic3—41no—
313Dic3—41no—
314Dic3—41no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—32no—
320C23—61no—
321C23—61no—
322C23—61no—
323C23—61no—
324C23—61no—
325C23—61no—
326C23—61no—
327C23—61no—
328C23—61no—
329C23—61no—
330C23—61no—
331C23—61no—
332C23—61no—
333C23#23512yes—
334C23D3×D412yes—
335C23#23912yes—
336C23C23×D311yescharacteristic
337D4—68no—
338D4—124no—
339D4—124no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—32no—
357C2×C4—44no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—61no—
361C2×C4—61no—
362C2×C4—61no—
363C2×C4—61no—
364C2×C4—61no—
365C2×C4—61no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—61no—
369C2×C4—61no—
370C2×C4—61no—
371C2×C4—61no—
372C2×C4—61no—
373C2×C4—61no—
374C2×C4—61no—
375C2×C4—61no—
376C2×C4—61no—
377C2×C4—124no—
378C2×C4#23512yes—
379C2×C4#23512yes—
380C2×C3—24no—
381C2×C3C2×#12311yescharacteristic
382C2×C3#52911yescharacteristic
383C2×C3#53811yescharacteristic
384C2×C3#54611yescharacteristic
385C2×C3#54611yescharacteristic
386C2×C3#55311yescharacteristic
387C2×C3#55311yescharacteristic
388D3—42no—
389D3—81no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—62no—
397C22—62no—
398C22—62no—
399C22—121no—
400C22—121no—
401C22—121no—
402C22—121no—
403C22—121no—
404C22—121no—
405C22—121no—
406C22—121no—
407C22—121no—
408C22—121no—
409C22—121no—
410C22#89414yes—
411C22C2×#23511yescharacteristic
412C22C2×#23511yescharacteristic
413C22C2×#23511yescharacteristic
414C22C2×D3×D411yescharacteristic
415C22#100411yescharacteristic
416C22#100411yescharacteristic
417C22C2×#23911yescharacteristic
418C4—22no—
419C4—22no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—62no—
425C4—121no—
426C4—121no—
427C4—121no—
428C4—121no—
429C4—121no—
430C3#244411yescharacteristic, complemented, Sylow
431C2—24no—
432C2—122no—
433C2—241no—
434C2#547911yescharacteristic
435C2#549011yescharacteristic
436C2#549011yescharacteristic
437C2#549411yescharacteristic
438C2C2×#89411yescharacteristic
439C2#551411yescharacteristic
440C2#551411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC2×C3×#95C2
prime radicalC2×#930C2
hypercenterC2×#95D3
hypocenterC3#2444
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
2. C2×C4×#67C2semidirect
3. C2×C3×#95C2semidirect
4. #5213C2semidirect
5. #5213C2semidirect
6. #5213C2semidirect
7. #5210C2semidirect
8. #4675C2semidirect
9. #4675C2semidirect
10. #4672C2semidirect
11. #4669C2semidirect
12. #4665C2semidirect
13. #4664C2semidirect
14. #4660C2semidirect
15. #4655C2semidirect
68. C2×#95D3semidirect
430. C3#2444semidirect

Maximal subgroups

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

subgroupindex
C2×#9302
C2×C4×#672
C2×C3×#952
#52132
#52102
#46752
#46722
#46692
#46652
#46642
#46602
#46552
#24443