Finite Group Databasebeta

← #11778293

Subgroups — #11778293

Order 1152.

533 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 533 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5602C211yesmaximal, characteristic
2C3×#5040C211yesmaximal, characteristic
3#10591344C211yesmaximal, characteristic, complemented
4#10591185C211yesmaximal, characteristic, complemented
5#10589403C211yesmaximal, characteristic
6#10589152C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#71889—31nomaximal
9#70974—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C32×#121C2211yescharacteristic
12C3×#935—21no—
13C3×#935—21no—
14C3×D4×Dic3—21no—
15C2×C3×#214—21no—
16C3×#924C2211yescharacteristic
17C2×C3×Dic3⋊C4C2211yescharacteristic
18C3×#889—21no—
19C3×#879—21no—
20C3×#878—21no—
21C2×#3724—21no—
22C2×#3718—21no—
23#63658C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#810—21no—
27#63579—21no—
28#63565—21no—
29C3×#539—31no—
30#5602D311yescharacteristic
31C3×#448—31no—
32#5230—31no—
33#5228—31no—
34#5050—31no—
35#5040D311yescharacteristic
36#4979—31no—
37#4538—31no—
38#4537—31no—
39#4537—31no—
40#4537—61no—
41#4528—31no—
42#4469—31no—
43#4467—31no—
44C2×C32×D4—21no—
45C2×C32×D4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—42no—
55C2×C3×Dic6D411yescharacteristic
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—21no—
60C3×#217—21no—
61C3×#217—21no—
62C3×#217—21no—
63C3×#214—42no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C3×C4×Dic3—21no—
72C2×C3×C3⋊C8—21no—
73#3724—42no—
74#3718—42no—
75#1603—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C2×C3×SD16—61no—
79C3×#126—61no—
80C3×#125—61no—
81C3×#123—61no—
82C3×#123—61no—
83C3×C22⋊Q8—31no—
84C3×C22⋊Q8—61no—
85C3×#121—21no—
86C3×#121C2×D311yescharacteristic
87C3×#121C2×D311yescharacteristic
88C3×C4×D4—61no—
89C2×C3×C4⋊C4—31no—
90C2×#216—61no—
91C2×#216—61no—
92#935—21no—
93#935—21no—
94D4×Dic3—21no—
95C2×#214—21no—
96#924C2×D311yescharacteristic
97C2×Dic3⋊C4—61no—
98C2×Dic3⋊C4—61no—
99C2×Dic3⋊C4C2×D311yescharacteristic
100#889—21no—
101#879—21no—
102#878—21no—
103C3×#103—61no—
104C3×C22⋊C8—31no—
105#835—61no—
106C3⋊#95—31no—
107C3⋊#95—31no—
108C3⋊#95—61no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111#830—31no—
112#830—31no—
113#830—61no—
114#830C2×D311yescharacteristic
115#810—21no—
116#810—61no—
117C23×C32—21no—
118C23×C32C2×D411yescharacteristic
119C32×D4—41no—
120C32×D4—41no—
121C32×D4—41no—
122C2×C32×C4—21no—
123C2×C32×C4—41no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—81no—
140C3×Dic6—22no—
141C3×Dic6—22no—
142C3×Dic6—41no—
143C3×Dic6—41no—
144C3×Dic6—41no—
145C3⋊(C3⋊C8)—41no—
146C3×C3⋊C8—41no—
147#539—31no—
148#451—91no—
149#448—31no—
150#395—91no—
151#328—91no—
152#327—91no—
153#324—91no—
154C2×C3×Q8—31no—
155C2×C3×Q8—61no—
156C2×C3×Q8—61no—
157C2×C3×Q8—122no—
158C2×C3×D4—21no—
159C2×C3×D4—21no—
160C2×C3×D4—21no—
161C2×C3×D4—41no—
162C2×C3×D4#6711yescharacteristic
163C2×C3×D4#6711yescharacteristic
164C22×C3×C4—21no—
165C22×C3×C4—31no—
166C22×C3×C4—31no—
167C22×C3×C4—61no—
168C22×C3×C4—61no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—121no—
176C22×Dic3#6711yescharacteristic
177C22×Dic3#6711yescharacteristic
178C2×Dic6—21no—
179C2×Dic6—21no—
180C2×Dic6—42no—
181C2×Dic6#6711yescharacteristic
182C3×SD16—122no—
183C2×C3×C8—61no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—31no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4#6711yescharacteristic
193C3×C4⋊C4#6711yescharacteristic
194C3×C22⋊C4—21no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—41no—
197C3×C22⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C22⋊C4—61no—
200C3×C22⋊C4—61no—
201C3×C42—61no—
202#217—21no—
203#217—21no—
204#217—21no—
205#217—21no—
206#216—122no—
207#216—122no—
208#214—42no—
209C4⋊Dic3—21no—
210C4⋊Dic3#6711yescharacteristic
211Dic3⋊C4—21no—
212Dic3⋊C4—21no—
213Dic3⋊C4—21no—
214Dic3⋊C4—21no—
215Dic3⋊C4—21no—
216Dic3⋊C4—122no—
217Dic3⋊C4—122no—
218C4×Dic3—21no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—121no—
223C22×C32—21no—
224C22×C32—21no—
225C22×C32—41no—
226C22×C32—41no—
227C22×C32—41no—
228C22×C32#12011yescharacteristic
229C22×C32#13511yescharacteristic
230C22×C32#13711yescharacteristic
231C32×C4—21no—
232C32×C4—21no—
233C32×C4—41no—
234C3⋊Dic3—42no—
235C3×Dic3—41no—
236C3×Dic3—41no—
237C3×Dic3—42no—
238C3×Dic3—41no—
239C3×Dic3—41no—
240C22×Q8—31no—
241C2×Q16—181no—
242C2×SD16—61no—
243#126—61no—
244#125—61no—
245#123—61no—
246#123—61no—
247C22⋊Q8—31no—
248C22⋊Q8—61no—
249#121D3211yescharacteristic
250C4×D4—61no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—181no—
253#103—61no—
254#103—181no—
255C22⋊C8—31no—
256C22⋊C8—91no—
257#95—91no—
258#95—181no—
259C23×C3—21no—
260C23×C3—21no—
261C23×C3—21no—
262C23×C3—41no—
263C23×C3D3×D411yescharacteristic
264C23×C3C2×#6711yescharacteristic
265C3×Q8—62no—
266C3×Q8—62no—
267C3×Q8—121no—
268C3×Q8—121no—
269C3×Q8—121no—
270C3×D4—41no—
271C3×D4—41no—
272C3×D4—41no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—41no—
276C3×D4—81no—
277C3×D4—81no—
278C3×D4—81no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—62no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—61no—
292C2×C3×C4—61no—
293C2×C3×C4—81no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4—241no—
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302C2×Dic3—22no—
303C2×Dic3—21no—
304C2×Dic3—21no—
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—81no—
315C2×Dic3—122no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320C2×Dic3—241no—
321C2×Dic3—241no—
322Dic6—22no—
323Dic6—22no—
324Dic6—41no—
325Dic6—41no—
326Dic6—41no—
327C3×C8—121no—
328C3⋊C8—41no—
329C3⋊C8—121no—
330C3⋊C8—121no—
331C3⋊C8—241no—
332C2×C32—21no—
333C2×C32—21no—
334C2×C32—81no—
335C2×C32#45211yescharacteristic
336C2×C32#45611yescharacteristic
337C2×C32B(4,𝔽2)11yescharacteristic
338C2×Q8—31no—
339C2×Q8—61no—
340C2×Q8—61no—
341C2×Q8—122no—
342C2×D4—21no—
343C2×D4#62511yescharacteristic
344C22×C4—31no—
345C22×C4—31no—
346C22×C4—61no—
347C22×C4—61no—
348C22×C4—181no—
349C22×C4C2×D3211yescharacteristic
350Q16—362no—
351SD16—122no—
352C2×C8—61no—
353C2×C8—181no—
354C4⋊C4—31no—
355C4⋊C4—61no—
356C4⋊C4—61no—
357C4⋊C4—61no—
358C4⋊C4—61no—
359C4⋊C4—61no—
360C4⋊C4—61no—
361C4⋊C4—362no—
362C4⋊C4#62511yescharacteristic
363C22⋊C4—21no—
364C22⋊C4—61no—
365C22⋊C4—61no—
366C22⋊C4—61no—
367C22⋊C4—61no—
368C42—61no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—41no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—81no—
385C22×C3—81no—
386C22×C3—81no—
387C22×C3#91511yescharacteristic
388C22×C3#91611yescharacteristic
389C22×C3#93711yescharacteristic
390C22×C3#95011yescharacteristic
391C22×C3#95111yescharacteristic
392C22×C3#95311yescharacteristic
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—41no—
398C3×C4—41no—
399C3×C4—41no—
400C3×C4—41no—
401C3×C4—81no—
402C3×C4—121no—
403C3×C4—121no—
404C3×C4—122no—
405C3×C4—121no—
406C3×C4—121no—
407Dic3—41no—
408Dic3—41no—
409Dic3—41no—
410Dic3—41no—
411Dic3—42no—
412Dic3—122no—
413Dic3—122no—
414Dic3—242no—
415C32#160311yescharacteristic, complemented, Sylow
416C23—21no—
417C23D3×#6711yescharacteristic
418Q8—62no—
419Q8—62no—
420Q8—121no—
421Q8—121no—
422Q8—121no—
423D4—41no—
424D4—41no—
425D4—41no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—62no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—121no—
436C2×C4—121no—
437C2×C4—121no—
438C2×C4—182no—
439C2×C4—241no—
440C2×C4—361no—
441C2×C4—361no—
442C2×C4C2×#62511yescharacteristic
443C2×C4D3×#6711yescharacteristic
444C8—121no—
445C8—361no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—41no—
454C2×C3—41no—
455C2×C3—81no—
456C2×C3—81no—
457C2×C3—161no—
458C2×C3#503211yescharacteristic
459C2×C3#517311yescharacteristic
460C2×C3#520511yescharacteristic
461C2×C3#523911yescharacteristic
462C2×C3#524411yescharacteristic
463C2×C3#524611yescharacteristic
464C22—21no—
465C22—21no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22#6392911yescharacteristic
470C22#6393511yescharacteristic
471C22#6397611yescharacteristic
472C4—21no—
473C4—21no—
474C4—41no—
475C4—122no—
476C4—121no—
477C4—121no—
478C4—121no—
479C4—121no—
480C4—362no—
481C3—21no—
482C3#7097411yescharacteristic, complemented
483C3#7188911yescharacteristic, complemented
484C2—21no—
485C2—21no—
486C2—81no—
487C2#1059146111yescharacteristic
488C2#1059153011yescharacteristic
489C2#1059168711yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC32×#121C22
socleC22×C32#120
hypercenter#121D32
hypocenterC32#1603
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
3. #10591344C2semidirect
4. #10591185C2semidirect
6. #10589152C2semidirect
7. #10589147C2semidirect
415. C32#1603semidirect
482. C3#70974semidirect
483. C3#71889semidirect

Maximal subgroups

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

subgroupindex
C3×#56022
C3×#50402
#105913442
#105911852
#105894032
#105891522
#105891472
#718893
#709743