Finite Group Databasebeta

← #11778710

Subgroups — #11778710

Order 1152.

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

normal subgroups only

This group has 524 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
2#10592421C211yesmaximal, characteristic, complemented
3#10591317C211yesmaximal, characteristic
4#10591103C211yesmaximal, characteristic, complemented
5C3×#4468C211yesmaximal, characteristic
6C3×#4467C211yesmaximal, characteristic, complemented
7#10589154C211yesmaximal, characteristic, complemented
8#68322—31nomaximal
9#68117—31nomaximal
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11#64133C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4C2211yescharacteristic
13C3×#924C2211yescharacteristic
14D3×#217—21no—
15C2×Dic3⋊Dic3—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#63645—21no—
24#63643—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63575—21no—
28#63566—21no—
29#5634—31no—
30#5483—31no—
31#5044—31no—
32#4949—31no—
33#4722—31no—
34#4722—31no—
35#4722—31no—
36#4722—61no—
37#4677—31no—
38C3×#328—31no—
39C3×#323—31no—
40#4468D311yescharacteristic
41#4467—31no—
42#4467D311yescharacteristic, complemented
43#4452—31no—
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)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59#3750—21no—
60C3×#217—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66#3724—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—42no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—42no—
73#1614—91noSylow
74C3×C22⋊Q8—31no—
75C2×C3×C22⋊C4—31no—
76C2×#217—61no—
77C2×#217—61no—
78#946—61no—
79C2×(C2×D3)⋊C4—61no—
80C2×(C2×D3)⋊C4C2×D311yescharacteristic
81C2×C4⋊Dic3—31no—
82C2×C4⋊Dic3—31no—
83C2×C4⋊Dic3—61no—
84C2×C4⋊Dic3—61no—
85#924—31no—
86#924—31no—
87#924—61no—
88#924—61no—
89#924C2×D311yescharacteristic
90C2×Dic3⋊C4—61no—
91#897—61no—
92#896—61no—
93#896—61no—
94D3×C22⋊C4—61no—
95#878—61no—
96#878—61no—
97#878—61no—
98#878—61no—
99#878—61no—
100C3×C22⋊C8—21no—
101C3×C22⋊C8—31no—
102C3×C22⋊C8C2×D311yescharacteristic
103C3×C22⋊C8C2×D311yescharacteristic
104C3×#95—31no—
105#835—61no—
106C3⋊#95C2×D311yescharacteristic
107#830C2×D311yescharacteristic
108#818—61no—
109#818—61no—
110#818—62no—
111#818—61no—
112#816—61no—
113#816—61no—
114#816—62no—
115#816—61no—
116#807—61no—
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C22×C3×D3Q1612yes—
123C2×C32×C4—41no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131#634—41no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C3×Dic6—41no—
140#627—81no—
141D3×Dic3—81no—
142D3×Dic3—81no—
143C32×C8—41no—
144C3×C3⋊C8—41no—
145#543—91no—
146#484—91no—
147#484—91no—
148#399—91no—
149#328—31no—
150#328—91no—
151#323—31no—
152C24×C3—31no—
153C23×D3D1211yescharacteristic
154C2×C3×Q8—31no—
155C22×C3×C4—21no—
156C22×C3×C4—31no—
157C22×C3×C4—61no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C22×Dic3—21no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—121no—
166C22×Dic3D1211yescharacteristic
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×Dic6—31no—
170C2×Dic6—31no—
171C2×Dic6—61no—
172C2×Dic6—61no—
173C2×Dic6—61no—
174C2×Dic6D1211yescharacteristic
175C2×C3×C8—22no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—61no—
179C3×C4⋊C4—31no—
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—31no—
197C4⋊Dic3—31no—
198C4⋊Dic3—61no—
199C4⋊Dic3—61no—
200C4⋊Dic3—61no—
201C4⋊Dic3—62no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204C4⋊Dic3—61no—
205C4⋊Dic3—61no—
206C4⋊Dic3—121no—
207C4⋊Dic3—122no—
208C4⋊Dic3D1211yescharacteristic
209Dic3⋊C4—21no—
210Dic3⋊C4—61no—
211Dic3⋊C4—61no—
212Dic3⋊C4—61no—
213Dic3⋊C4—61no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216Dic3⋊C4—121no—
217Dic3⋊C4—122no—
218C2×C3⋊C8—21no—
219C22×C32—21no—
220C22×C32—21no—
221C22×C32#12011yescharacteristic
222C22×C32C2×Q1611yescharacteristic
223C22×C32#13711yescharacteristic
224C2×C3×D3—22no—
225C2×C3×D3—41no—
226C2×C3×D3—41no—
227C2×C3×D3—42no—
228C2×C3×D3—81no—
229C32×C4—21no—
230C32×C4—21no—
231C3⋊Dic3—41no—
232C3⋊Dic3—41no—
233C3⋊Dic3—81no—
234C3×Dic3—42no—
235C3×Dic3—41no—
236C3×Dic3—41no—
237C3×Dic3—41no—
238C22⋊Q8—31no—
239C22⋊Q8—91no—
240C22⋊Q8—181no—
241C22⋊Q8—181no—
242C22⋊Q8—181no—
243C22⋊Q8—181no—
244C22⋊Q8—181no—
245C2×C4⋊C4—91no—
246C2×C4⋊C4—181no—
247C2×C22⋊C4—31no—
248C2×C22⋊C4—181no—
249C2×C22⋊C4—181no—
250#107—181no—
251#107—181no—
252#103—181no—
253#103—181no—
254C22⋊C8—31no—
255C22⋊C8D3211yescharacteristic
256#95—31no—
257C23×C3—21no—
258C23×C3—32no—
259C23×C3—61no—
260C23×C3—61no—
261C23×C3—121no—
262C23×C3—121no—
263C23×C3C2×D1211yescharacteristic
264C23×C3D3×D411yescharacteristic
265C22×D3—21no—
266C22×D3—21no—
267C22×D3—41no—
268C22×D3—41no—
269C22×D3Dic1212yes—
270C3×Q8—121no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—42no—
276C2×C3×C4—62no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—121no—
281C2×C3×C4—121no—
282C2×C3×C4—121no—
283C2×C3×C4C2×D1211yescharacteristic
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×Dic3—22no—
288C2×Dic3—21no—
289C2×Dic3—21no—
290C2×Dic3—21no—
291C2×Dic3—41no—
292C2×Dic3—41no—
293C2×Dic3—41no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—121no—
299C2×Dic3—121no—
300C2×Dic3—121no—
301C2×Dic3—122no—
302C2×Dic3—121no—
303C2×Dic3—121no—
304C2×Dic3—121no—
305C2×Dic3—121no—
306C2×Dic3—121no—
307C2×Dic3—241no—
308C2×Dic3—241no—
309C2×Dic3—241no—
310C2×Dic3—241no—
311C4×D3—241no—
312C4×D3—241no—
313Dic6—41no—
314Dic6—121no—
315Dic6—121no—
316Dic6—122no—
317Dic6—241no—
318Dic6—241no—
319C3×C8—42no—
320C3×C8—41no—
321C3×C8—41no—
322C3×C8—121no—
323C3⋊C8—41no—
324C2×C32—21no—
325C2×C32—21no—
326C2×C32#45111yescharacteristic
327C2×C32#45311yescharacteristic
328C2×C32#45811yescharacteristic
329C3×D3—42no—
330C24—31no—
331C2×Q8—31no—
332C2×Q8—91no—
333C2×Q8—181no—
334C22×C4—31no—
335C22×C4—61no—
336C22×C4—181no—
337C22×C4—181no—
338C22×C4—181no—
339C22×C4C2×D3211yescharacteristic
340C2×C8—21no—
341C2×C8—61no—
342C4⋊C4—31no—
343C4⋊C4—61no—
344C4⋊C4—91no—
345C4⋊C4—181no—
346C4⋊C4—181no—
347C4⋊C4—181no—
348C4⋊C4—181no—
349C4⋊C4—181no—
350C4⋊C4—181no—
351C4⋊C4—362no—
352C22⋊C4—61no—
353C22⋊C4—61no—
354C22⋊C4—61no—
355C22⋊C4—181no—
356C22⋊C4—181no—
357C22⋊C4—181no—
358C22⋊C4—362no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3—62no—
369C22×C3—122no—
370C22×C3—121no—
371C22×C3—121no—
372C22×C3—241no—
373C22×C3#88211yescharacteristic
374C22×C3#88211yescharacteristic
375C22×C3C2×Dic1211yescharacteristic
376C22×C3#90911yescharacteristic
377C22×C3#91511yescharacteristic
378C22×C3D3×Q1611yescharacteristic
379C2×D3—22no—
380C2×D3—41no—
381C2×D3—41no—
382C2×D3—42no—
383C2×D3—81no—
384C3×C4—22no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—41no—
390C3×C4—122no—
391C3×C4—121no—
392C3×C4—121no—
393C3×C4—121no—
394Dic3—42no—
395Dic3—41no—
396Dic3—41no—
397Dic3—41no—
398Dic3—121no—
399Dic3—121no—
400Dic3—121no—
401Dic3—121no—
402Dic3—241no—
403Dic3—241no—
404Dic3—242no—
405Dic3—241no—
406Dic3—241no—
407C32#161411yescharacteristic, complemented, Sylow
408C23—32no—
409C23—61no—
410C23—61no—
411C23—121no—
412C23—121no—
413C23D3×D1211yescharacteristic
414Q8—121no—
415Q8—361no—
416Q8—721no—
417C2×C4—41no—
418C2×C4—62no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C4—121no—
425C2×C4—181no—
426C2×C4—181no—
427C2×C4—361no—
428C2×C4—361no—
429C2×C4—361no—
430C2×C4—721no—
431C2×C4—721no—
432C2×C4D3×D1211yescharacteristic
433C2×C4#381111yescharacteristic
434C8—41no—
435C8—121no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—41no—
444C2×C3—41no—
445C2×C3—122no—
446C2×C3#473911yescharacteristic
447C2×C3#474211yescharacteristic
448C2×C3#474211yescharacteristic
449C2×C3#474711yescharacteristic
450C2×C3#480911yescharacteristic
451C2×C3#482211yescharacteristic
452D3—42no—
453C22—21no—
454C22—21no—
455C22—62no—
456C22—122no—
457C22—121no—
458C22—121no—
459C22—241no—
460C22D3×Dic1211yescharacteristic
461C22#6380011yescharacteristic
462C22#6392311yescharacteristic
463C4—21no—
464C4—21no—
465C4—122no—
466C4—121no—
467C4—121no—
468C4—121no—
469C4—361no—
470C4—361no—
471C4—721no—
472C3—21no—
473C3#6811711yescharacteristic, complemented
474C3#6832211yescharacteristic, complemented
475C2—21no—
476C2—21no—
477C2—122no—
478C2#1059040911yescharacteristic
479C2#1059095211yescharacteristic
480C2#1059101511yescharacteristic
subgroupG/H
centerC22#63923
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. #10592421C2semidirect
4. #10591103C2semidirect
6. C3×#4467C2semidirect
7. #10589154C2semidirect
42. #4467D3semidirect
407. C32#1614semidirect
473. C3#68117semidirect
474. C3#68322semidirect

Maximal subgroups

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

subgroupindex
#105949712
#105924212
#105913172
#105911032
C3×#44682
C3×#44672
#105891542
#683223
#681173