Finite Group Databasebeta

← #11778712

Subgroups — #11778712

Order 1152.

512 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 82 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
1#10594971C211yesmaximal, characteristic
2C3×#4722C211yesmaximal, characteristic, complemented
3#10591324C211yesmaximal, characteristic
4#10591135C211yesmaximal, characteristic, complemented
5#10589333C211yesmaximal, characteristic, complemented
6C3×#4468C211yesmaximal, characteristic
7#10589152C211yesmaximal, characteristic, complemented
8#71176—31nomaximal
9#68117—31nomaximal
10#64133C2211yescharacteristic
11C2×C3×(C2×D3)⋊C4C2211yescharacteristic
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C3×#924C2211yescharacteristic
14D3×#217—21no—
15C2×#3724—21no—
16#63964—21no—
17C2×(C2×D3)⋊Dic3—21no—
18#63899—21no—
19#63896—21no—
20#63893—21no—
21#63887—21no—
22C32×C22⋊C8C2211yescharacteristic
23#63658C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×#818—21no—
26C3×#816—21no—
27#63575—21no—
28#63567—21no—
29#5634—31no—
30#5483—31no—
31C3×#484—31no—
32#4993—31no—
33#4970—31no—
34#4949—31no—
35#4722—31no—
36#4722D311yescharacteristic, complemented
37C3×#323—31no—
38#4538—31no—
39#4468D311yescharacteristic
40#4467—31no—
41#4467—31no—
42#4467—31no—
43#4467—61no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×#634D411yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C2×C3×Dic6D411yescharacteristic
51C2×#627—21no—
52C2×D3×Dic3—21no—
53C2×D3×Dic3—21no—
54C2×C32×C8—21no—
55#3757—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57#3750—21no—
58C3×#217—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66#3724—21no—
67#3724—42no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—42no—
73#1614—91noSylow
74C3×C22⋊Q8—31no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C22⋊C4—31no—
77C2×#217—61no—
78C2×#217—61no—
79#946—61no—
80C2×(C2×D3)⋊C4—61no—
81C2×(C2×D3)⋊C4C2×D311yescharacteristic
82C2×C4⋊Dic3C2×D311yescharacteristic
83#924—31no—
84#924—31no—
85#924—61no—
86#924—61no—
87#924C2×D311yescharacteristic
88C2×Dic3⋊C4—61no—
89C2×Dic3⋊C4—61no—
90#897—61no—
91#896—61no—
92#896—61no—
93D3×C22⋊C4—61no—
94#878—61no—
95#878—61no—
96#878—61no—
97#878—61no—
98#878—61no—
99C3×#107—61no—
100C3×#103—61no—
101C3×C22⋊C8—21no—
102C3×C22⋊C8—31no—
103C3×C22⋊C8C2×D311yescharacteristic
104C3×C22⋊C8C2×D311yescharacteristic
105C3⋊#95—31no—
106C3⋊#95—31no—
107C3⋊#95—61no—
108#830C2×D311yescharacteristic
109#818—21no—
110#818—61no—
111#816—21no—
112#816—61no—
113#810—61no—
114#807—61no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C22×C3×D3—21no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3Q1612yes—
121C2×C32×C4—41no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129#634—41no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C3×Dic6—41no—
138#627—81no—
139D3×Dic3—81no—
140D3×Dic3—81no—
141C32×C8—41no—
142C3×C3⋊C8—41no—
143#543—91no—
144#484—31no—
145#484—91no—
146#399—91no—
147#328—91no—
148#328—91no—
149#323—31no—
150C24×C3—31no—
151C23×D3D1211yescharacteristic
152C2×C3×Q8—31no—
153C22×C3×C4—21no—
154C22×C3×C4—31no—
155C22×C3×C4—61no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×Dic3—21no—
159C22×Dic3—61no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163C22×Dic3—121no—
164C22×Dic3D1211yescharacteristic
165C2×C4×D3—61no—
166C2×C4×D3—61no—
167C2×Dic6—31no—
168C2×Dic6—31no—
169C2×Dic6—61no—
170C2×Dic6—61no—
171C2×Dic6—61no—
172C2×Dic6#6711yescharacteristic
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C2×C3×C8—41no—
176C2×C3×C8—61no—
177C3×C4⋊C4—31no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C22⋊C4—61no—
182C3×C22⋊C4—61no—
183C3×C22⋊C4—61no—
184#217—21no—
185#217—61no—
186#217—61no—
187#217—61no—
188#217—61no—
189#217—121no—
190#217—122no—
191(C2×D3)⋊C4—21no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—122no—
196C4⋊Dic3—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3—31no—
199C4⋊Dic3—31no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3#6711yescharacteristic
204Dic3⋊C4—21no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
207Dic3⋊C4—61no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211Dic3⋊C4—121no—
212Dic3⋊C4—122no—
213Dic3⋊C4—122no—
214C2×C3⋊C8—21no—
215C22×C32—21no—
216C22×C32—21no—
217C22×C32#12011yescharacteristic
218C22×C32C2×Q1611yescharacteristic
219C22×C32#13711yescharacteristic
220C2×C3×D3—22no—
221C2×C3×D3—41no—
222C2×C3×D3—41no—
223C2×C3×D3—42no—
224C2×C3×D3—81no—
225C32×C4—21no—
226C32×C4—21no—
227C3⋊Dic3—42no—
228C3⋊Dic3—41no—
229C3⋊Dic3—41no—
230C3×Dic3—41no—
231C3×Dic3—41no—
232C3×Dic3—41no—
233C3×Dic3—81no—
234C22⋊Q8—31no—
235C22⋊Q8—91no—
236C22⋊Q8—181no—
237C22⋊Q8—181no—
238C22⋊Q8—181no—
239C22⋊Q8—181no—
240C22⋊Q8—181no—
241C2×C4⋊C4—31no—
242C2×C4⋊C4—181no—
243C2×C22⋊C4—31no—
244C2×C22⋊C4—181no—
245C2×C22⋊C4—181no—
246#107—61no—
247#107—181no—
248#103—61no—
249#103—181no—
250C22⋊C8—31no—
251C22⋊C8D3211yescharacteristic
252#95—91no—
253C23×C3—21no—
254C23×C3—32no—
255C23×C3—61no—
256C23×C3—61no—
257C23×C3—121no—
258C23×C3—121no—
259C23×C3C2×D1211yescharacteristic
260C23×C3D3×D411yescharacteristic
261C22×D3—21no—
262C22×D3—21no—
263C22×D3—41no—
264C22×D3—41no—
265C22×D3Dic1212yes—
266C3×Q8—121no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—61no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—81no—
275C2×C3×C4—121no—
276C2×C3×C4—121no—
277C2×C3×C4—121no—
278C2×C3×C4—121no—
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4C2×#6711yescharacteristic
283C2×Dic3—21no—
284C2×Dic3—21no—
285C2×Dic3—21no—
286C2×Dic3—41no—
287C2×Dic3—41no—
288C2×Dic3—41no—
289C2×Dic3—41no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—121no—
297C2×Dic3—121no—
298C2×Dic3—122no—
299C2×Dic3—121no—
300C2×Dic3—121no—
301C2×Dic3—121no—
302C2×Dic3—121no—
303C2×Dic3—241no—
304C2×Dic3—241no—
305C2×Dic3—241no—
306C2×Dic3—241no—
307C4×D3—241no—
308C4×D3—241no—
309Dic6—41no—
310Dic6—121no—
311Dic6—121no—
312Dic6—241no—
313Dic6—241no—
314Dic6—241no—
315C3×C8—41no—
316C3×C8—41no—
317C3×C8—81no—
318C3×C8—121no—
319C3⋊C8—41no—
320C2×C32—21no—
321C2×C32—21no—
322C2×C32#45111yescharacteristic
323C2×C32#45311yescharacteristic
324C2×C32#45811yescharacteristic
325C3×D3—42no—
326C24—31no—
327C2×Q8—31no—
328C2×Q8—91no—
329C2×Q8—181no—
330C22×C4—31no—
331C22×C4—61no—
332C22×C4—181no—
333C22×C4—181no—
334C22×C4—181no—
335C22×C4C2×D3211yescharacteristic
336C2×C8—21no—
337C2×C8—61no—
338C4⋊C4—31no—
339C4⋊C4—61no—
340C4⋊C4—61no—
341C4⋊C4—61no—
342C4⋊C4—91no—
343C4⋊C4—181no—
344C4⋊C4—181no—
345C4⋊C4—181no—
346C4⋊C4—181no—
347C4⋊C4—362no—
348C22⋊C4—61no—
349C22⋊C4—61no—
350C22⋊C4—61no—
351C22⋊C4—181no—
352C22⋊C4—181no—
353C22⋊C4—181no—
354C22⋊C4—362no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—62no—
365C22×C3—122no—
366C22×C3—121no—
367C22×C3—121no—
368C22×C3—241no—
369C22×C3#88211yescharacteristic
370C22×C3C2×Dic1211yescharacteristic
371C22×C3#90911yescharacteristic
372C22×C3D3×Q1611yescharacteristic
373C22×C3#91811yescharacteristic
374C22×C3#93711yescharacteristic
375C2×D3—22no—
376C2×D3—41no—
377C2×D3—41no—
378C2×D3—42no—
379C2×D3—81no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—41no—
385C3×C4—41no—
386C3×C4—121no—
387C3×C4—121no—
388C3×C4—121no—
389C3×C4—241no—
390Dic3—41no—
391Dic3—41no—
392Dic3—41no—
393Dic3—81no—
394Dic3—122no—
395Dic3—122no—
396Dic3—121no—
397Dic3—121no—
398Dic3—121no—
399Dic3—121no—
400Dic3—241no—
401Dic3—241no—
402Dic3—242no—
403C32#161411yescharacteristic, complemented, Sylow
404C23—32no—
405C23—61no—
406C23—61no—
407C23—121no—
408C23—121no—
409C23D3×D1211yescharacteristic
410Q8—121no—
411Q8—361no—
412Q8—721no—
413C2×C4—41no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—61no—
417C2×C4—121no—
418C2×C4—121no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—182no—
422C2×C4—181no—
423C2×C4—181no—
424C2×C4—361no—
425C2×C4—361no—
426C2×C4—721no—
427C2×C4—721no—
428C2×C4#380211yescharacteristic
429C2×C4D3×#6711yescharacteristic
430C8—41no—
431C8—121no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3—122no—
442C2×C3#473911yescharacteristic
443C2×C3#474211yescharacteristic
444C2×C3#474711yescharacteristic
445C2×C3#505311yescharacteristic
446C2×C3#518611yescharacteristic
447C2×C3#519811yescharacteristic
448D3—42no—
449C22—21no—
450C22—21no—
451C22—62no—
452C22—122no—
453C22—121no—
454C22—121no—
455C22—241no—
456C22D3×Dic1211yescharacteristic
457C22#6380111yescharacteristic
458C22#6392211yescharacteristic
459C4—21no—
460C4—21no—
461C4—121no—
462C4—121no—
463C4—121no—
464C4—241no—
465C4—362no—
466C4—361no—
467C4—361no—
468C3—21no—
469C3#6811711yescharacteristic, complemented
470C3#7117611yescharacteristic, complemented
471C2—21no—
472C2—21no—
473C2—122no—
474C2#1059040811yescharacteristic
475C2#1059094911yescharacteristic
476C2#1059101411yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radicalC23×C3×D3D4
hypercenterC22⋊C8D32
hypocenterC32#1614
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4722C2semidirect
4. #10591135C2semidirect
5. #10589333C2semidirect
7. #10589152C2semidirect
36. #4722D3semidirect
403. C32#1614semidirect
469. C3#68117semidirect
470. C3#71176semidirect

Maximal subgroups

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

subgroupindex
#105949712
C3×#47222
#105913242
#105911352
#105893332
C3×#44682
#105891522
#711763
#681173