Finite Group Databasebeta

← #11778713

Subgroups — #11778713

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×#4677C211yesmaximal, characteristic
3#10591135C211yesmaximal, characteristic, complemented
4#10591132C211yesmaximal, characteristic, complemented
5#10589318C211yesmaximal, characteristic, complemented
6C3×#4452C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic
8#69716—31nomaximal
9#68322—31nomaximal
10#64133C2211yescharacteristic
11C2×C3×(C2×D3)⋊C4—21no—
12C2×C3×(C2×D3)⋊C4C2211yescharacteristic
13C2×C3×C4⋊Dic3—21no—
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C3×#924C2211yescharacteristic
16D3×#217—21no—
17#63964—21no—
18#63899—21no—
19#63896—21no—
20#63893—21no—
21#63887—21no—
22C32×#95C2211yescharacteristic
23#63657C2211yescharacteristic
24C3×#830C2211yescharacteristic
25#63576—21no—
26#63575—21no—
27#63567—21no—
28#63565—21no—
29#5634—31no—
30#5483—31no—
31C3×#399—31no—
32#5044—31no—
33#4970—31no—
34#4970—31no—
35#4722—31no—
36#4677D311yescharacteristic
37C3×#328—31no—
38#4525—31no—
39#4468—31no—
40#4452—31no—
41#4452—31no—
42#4452—61no—
43#4452D311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#634D411yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C2×C3×Dic6D411yescharacteristic
51C2×#627—21no—
52C2×D3×Dic3—21no—
53C2×D3×Dic3—21no—
54#3757—21no—
55C4⋊(C3⋊Dic3)D411yescharacteristic
56#3750—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#217—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—42no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—42no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C2×C3×C3⋊C8—21no—
68#3724—21no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73#1614—91noSylow
74C3×C22⋊Q8—31no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—61no—
77C2×C3×C22⋊C4—31no—
78C2×C3×C22⋊C4—61no—
79C2×#217—61no—
80#946—61no—
81C2×(C2×D3)⋊C4—21no—
82C2×(C2×D3)⋊C4C2×D311yescharacteristic
83C2×C4⋊Dic3—21no—
84C2×C4⋊Dic3C2×D311yescharacteristic
85#924—31no—
86#924—31no—
87#924—61no—
88#924—61no—
89#924C2×D311yescharacteristic
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×C22⋊C8—31no—
100C3×#95—21no—
101C3×#95C2×D311yescharacteristic
102C3×#95C2×D311yescharacteristic
103#835—61no—
104#830—31no—
105#830—31no—
106#830—61no—
107#830C2×D311yescharacteristic
108#818—61no—
109#816—61no—
110#810—61no—
111#810—61no—
112#807—61no—
113#807—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—22no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
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—
141C3⋊(C3⋊C8)—41no—
142C3×C3⋊C8—41no—
143#543—91no—
144#484—91no—
145#484—91no—
146#399—31no—
147#328—31no—
148#328—91no—
149#323—91no—
150C24×C3—31no—
151C23×D3#6711yescharacteristic
152C2×C3×Q8—31no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—31no—
157C22×C3×C4—41no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×Dic3—21no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C22×Dic3#6711yescharacteristic
165C2×C4×D3—61no—
166C2×C4×D3—61no—
167C2×Dic6—31no—
168C2×Dic6—31no—
169C2×Dic6—61no—
170C2×Dic6—61no—
171C2×Dic6—61no—
172C2×Dic6D1211yescharacteristic
173C2×C3×C8—61no—
174C3×C4⋊C4—31no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—122no—
179C3×C22⋊C4—61no—
180C3×C22⋊C4—61no—
181C3×C22⋊C4—61no—
182C3×C22⋊C4—122no—
183#217—21no—
184#217—61no—
185#217—61no—
186#217—61no—
187#217—61no—
188#217—121no—
189(C2×D3)⋊C4—21no—
190(C2×D3)⋊C4—21no—
191(C2×D3)⋊C4—42no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—61no—
194C4⋊Dic3—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3—31no—
197C4⋊Dic3—31no—
198C4⋊Dic3—42no—
199C4⋊Dic3—61no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3D1211yescharacteristic
203Dic3⋊C4—21no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
207Dic3⋊C4—61no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—121no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—121no—
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—
227C32×C4—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—61no—
243C2×C22⋊C4—31no—
244C2×C22⋊C4—61no—
245C2×C22⋊C4—181no—
246#107—181no—
247#107—181no—
248#103—181no—
249#103—181no—
250C22⋊C8—31no—
251C22⋊C8—91no—
252#95D3211yescharacteristic
253C23×C3—21no—
254C23×C3—32no—
255C23×C3—61no—
256C23×C3—61no—
257C23×C3—121no—
258C23×C3—121no—
259C23×C3D3×D411yescharacteristic
260C23×C3C2×#6711yescharacteristic
261C22×D3—21no—
262C22×D3—21no—
263C22×D3—41no—
264C22×D3—41no—
265C22×D3#21612yes—
266C3×Q8—121no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—42no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—81no—
282C2×C3×C4—81no—
283C2×C3×C4—81no—
284C2×C3×C4—121no—
285C2×C3×C4—121no—
286C2×C3×C4—121no—
287C2×C3×C4—121no—
288C2×C3×C4C2×D1211yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×Dic3—21no—
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—41no—
296C2×Dic3—41no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—61no—
300C2×Dic3—61no—
301C2×Dic3—61no—
302C2×Dic3—61no—
303C2×Dic3—121no—
304C2×Dic3—121no—
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—121no—
316C3⋊C8—41no—
317C3⋊C8—121no—
318C3⋊C8—121no—
319C3⋊C8—241no—
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—21no—
331C22×C4—31no—
332C22×C4—61no—
333C22×C4—181no—
334C22×C4—181no—
335C22×C4C2×D3211yescharacteristic
336C2×C8—61no—
337C2×C8—181no—
338C4⋊C4—31no—
339C4⋊C4—61no—
340C4⋊C4—61no—
341C4⋊C4—61no—
342C4⋊C4—91no—
343C4⋊C4—122no—
344C4⋊C4—181no—
345C4⋊C4—181no—
346C4⋊C4—181no—
347C4⋊C4—181no—
348C22⋊C4—61no—
349C22⋊C4—61no—
350C22⋊C4—61no—
351C22⋊C4—122no—
352C22⋊C4—181no—
353C22⋊C4—181no—
354C22⋊C4—181no—
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×C3#91511yescharacteristic
371C22×C3D3×Q1611yescharacteristic
372C22×C3#93711yescharacteristic
373C22×C3C2×#21611yescharacteristic
374C22×C3#95111yescharacteristic
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—42no—
387C3×C4—42no—
388C3×C4—82no—
389C3×C4—121no—
390C3×C4—121no—
391C3×C4—121no—
392C3×C4—241no—
393Dic3—41no—
394Dic3—41no—
395Dic3—41no—
396Dic3—81no—
397Dic3—121no—
398Dic3—121no—
399Dic3—121no—
400Dic3—121no—
401Dic3—241no—
402Dic3—241no—
403C32#161411yescharacteristic, complemented, Sylow
404C23—32no—
405C23—61no—
406C23—61no—
407C23—121no—
408C23—121no—
409C23D3×#6711yescharacteristic
410Q8—121no—
411Q8—361no—
412Q8—721no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—121no—
421C2×C4—121no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C4—181no—
425C2×C4—181no—
426C2×C4—721no—
427C2×C4—721no—
428C2×C4D3×D1211yescharacteristic
429C2×C4#380211yescharacteristic
430C8—121no—
431C8—361no—
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#474211yescharacteristic
443C2×C3#480911yescharacteristic
444C2×C3#482211yescharacteristic
445C2×C3#505011yescharacteristic
446C2×C3#505311yescharacteristic
447C2×C3#507711yescharacteristic
448D3—42no—
449C22—21no—
450C22—21no—
451C22—62no—
452C22—122no—
453C22—121no—
454C22—121no—
455C22—241no—
456C22#6392211yescharacteristic
457C22#6392911yescharacteristic
458C22D3×#21611yescharacteristic
459C4—21no—
460C4—21no—
461C4—42no—
462C4—121no—
463C4—121no—
464C4—121no—
465C4—241no—
466C4—361no—
467C4—361no—
468C3—21no—
469C3#6832211yescharacteristic, complemented
470C3#6971611yescharacteristic, complemented
471C2—21no—
472C2—21no—
473C2—122no—
474C2#1059039511yescharacteristic
475C2#1059040811yescharacteristic
476C2#1059060411yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radicalC23×C3×D3D4
hypercenter#95D32
hypocenterC32#1614
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
3. #10591135C2semidirect
4. #10591132C2semidirect
5. #10589318C2semidirect
6. C3×#4452C2semidirect
43. #4452D3semidirect
403. C32#1614semidirect
469. C3#68322semidirect
470. C3#69716semidirect

Maximal subgroups

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

subgroupindex
#105949712
C3×#46772
#105911352
#105911322
#105893182
C3×#44522
#105891452
#697163
#683223