Finite Group Databasebeta

← #11778711

Subgroups — #11778711

Order 1152.

521 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 521 conjugacy classes of subgroups — too many to draw. Only its 80 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#10594981C211yesmaximal, characteristic
2C3×#4722C211yesmaximal, characteristic, complemented
3#10591350C211yesmaximal, characteristic
4#10591132C211yesmaximal, characteristic, complemented
5#10589334C211yesmaximal, characteristic
6C3×#4467C211yesmaximal, characteristic, complemented
7#10589153C211yesmaximal, characteristic, complemented
8#71176—31nomaximal
9#68322—31nomaximal
10C2×#3752C2211yescharacteristic
11C2×C3×C4⋊Dic3C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C3×#924C2211yescharacteristic
14#63982—21no—
15#63974—21no—
16C2×Dic3⋊Dic3—21no—
17C2×#3722—21no—
18#63895—21no—
19#63895—21no—
20#63888—21no—
21#63888—21no—
22C32×C22⋊C8C2211yescharacteristic
23#63657C2211yescharacteristic
24C3×C3⋊#95C2211yescharacteristic
25C3×#818—21no—
26C3×#816—21no—
27#63576—21no—
28#63565—21no—
29#5634—31no—
30#5634—31no—
31C3×#484—31no—
32#5044—31no—
33#4993—31no—
34#4970—31no—
35#4722D311yescharacteristic, complemented
36#4677—31no—
37C3×#328—31no—
38#4538—31no—
39#4468—31no—
40#4468—31no—
41#4468—61no—
42#4467D311yescharacteristic, complemented
43#4452—31no—
44C23×C3⋊D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C2×C3×Dic6D411yescharacteristic
50C2×C3×Dic6D411yescharacteristic
51C2×#627—21no—
52C2×#624—21no—
53C2×#624—21no—
54C2×C32×C8—21no—
55#3752—21no—
56#3752—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#217—21no—
59C3×#217—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66#3724—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—42no—
70#3722—21no—
71#3722—21no—
72#3722—42no—
73#1614—91noSylow
74C3×C22⋊Q8—31no—
75C3×C22⋊Q8—31no—
76C2×C3×C4⋊C4—31no—
77#946—61no—
78#946—61no—
79C2×(C2×D3)⋊C4—31no—
80C2×(C2×D3)⋊C4—31no—
81C2×(C2×D3)⋊C4—61no—
82C2×(C2×D3)⋊C4—61no—
83C2×(C2×D3)⋊C4—61no—
84C2×C4⋊Dic3—61no—
85C2×C4⋊Dic3C2×D311yescharacteristic
86#924C2×D311yescharacteristic
87#924C2×D311yescharacteristic
88C2×Dic3⋊C4—61no—
89#897—61no—
90#897—61no—
91#896—61no—
92#896—61no—
93#896—61no—
94#896—61no—
95D3×C22⋊C4—61no—
96D3×C22⋊C4—61no—
97#878—61no—
98#878—61no—
99C3×#107—61no—
100C3×#103—61no—
101C3×C22⋊C8—21no—
102C3×C22⋊C8C2×D311yescharacteristic
103C3×C22⋊C8C2×D311yescharacteristic
104C3×#95—31no—
105#835—61no—
106C3⋊#95C2×D311yescharacteristic
107#830—31no—
108#830—31no—
109#830—61no—
110#818—21no—
111#816—21no—
112#810—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—41no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—41no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C3×Dic6—41no—
137C3×Dic6—41no—
138#627—81no—
139#624—81no—
140#624—81no—
141C32×C8—41no—
142C3⋊(C3⋊C8)—41no—
143#543—91no—
144#484—31no—
145#484—91no—
146#399—91no—
147#328—31no—
148#328—91no—
149#323—91no—
150C23×D3—31no—
151C23×D3—31no—
152C23×D3—61no—
153C2×C3×Q8—31no—
154C2×C3×Q8—31no—
155C22×C3×C4—21no—
156C22×C3×C4—61no—
157C22×C3×C4—61no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C22×Dic3—21no—
161C22×Dic3—21no—
162C22×Dic3—31no—
163C22×Dic3—31no—
164C22×Dic3—61no—
165C2×C4×D3—61no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×Dic6—61no—
170C2×Dic6—61no—
171C2×Dic6D1211yescharacteristic
172C2×Dic6#6711yescharacteristic
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C2×C3×C8—41no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—31no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C22⋊C4—61no—
183C3×C22⋊C4—61no—
184#217—21no—
185#217—21no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4—61no—
189(C2×D3)⋊C4—61no—
190(C2×D3)⋊C4—61no—
191(C2×D3)⋊C4—61no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—121no—
195(C2×D3)⋊C4—121no—
196(C2×D3)⋊C4—122no—
197(C2×D3)⋊C4—122no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3—122no—
203C4⋊Dic3D1211yescharacteristic
204C4⋊Dic3#6711yescharacteristic
205Dic3⋊C4—21no—
206Dic3⋊C4—21no—
207Dic3⋊C4—61no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211Dic3⋊C4—122no—
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—
227C3⋊Dic3—41no—
228C3×Dic3—42no—
229C3×Dic3—41no—
230C3×Dic3—41no—
231C3×Dic3—41no—
232C3×Dic3—41no—
233C3×Dic3—81no—
234C22⋊Q8—31no—
235C22⋊Q8—31no—
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—91no—
244C2×C22⋊C4—181no—
245C2×C22⋊C4—181no—
246#107—61no—
247#107—181no—
248#103—61no—
249#103—181no—
250C22⋊C8—91no—
251C22⋊C8D3211yescharacteristic
252#95—31no—
253C23×C3—21no—
254C23×C3D3×D411yescharacteristic
255C23×C3D3×D411yescharacteristic
256C22×D3—32no—
257C22×D3—32no—
258C22×D3—62no—
259C22×D3—61no—
260C22×D3—61no—
261C22×D3—61no—
262C22×D3—61no—
263C22×D3—121no—
264C22×D3—121no—
265C22×D3—121no—
266C22×D3—121no—
267C22×D3—121no—
268C22×D3—121no—
269C22×D3—241no—
270C22×D3—241no—
271C3×Q8—121no—
272C3×Q8—121no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—62no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—61no—
282C2×C3×C4—81no—
283C2×C3×C4—121no—
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×C4C2×#6711yescharacteristic
292C2×Dic3—22no—
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—21no—
296C2×Dic3—21no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—41no—
300C2×Dic3—41no—
301C2×Dic3—41no—
302C2×Dic3—61no—
303C2×Dic3—61no—
304C2×Dic3—121no—
305C2×Dic3—121no—
306C2×Dic3—121no—
307C2×Dic3—241no—
308C4×D3—241no—
309C4×D3—241no—
310C4×D3—241no—
311C4×D3—241no—
312Dic6—41no—
313Dic6—41no—
314Dic6—241no—
315Dic6—241no—
316C3×C8—41no—
317C3×C8—41no—
318C3×C8—81no—
319C3⋊C8—121no—
320C3⋊C8—121no—
321C3⋊C8—241no—
322C2×C32—21no—
323C2×C32—21no—
324C2×C32#45111yescharacteristic
325C2×C32#45311yescharacteristic
326C2×C32#45811yescharacteristic
327C3⋊D3—42no—
328C24—91no—
329C2×Q8—31no—
330C2×Q8—31no—
331C2×Q8—181no—
332C22×C4—61no—
333C22×C4—61no—
334C22×C4—91no—
335C22×C4—181no—
336C22×C4—181no—
337C22×C4C2×D3211yescharacteristic
338C2×C8—21no—
339C2×C8—181no—
340C4⋊C4—31no—
341C4⋊C4—31no—
342C4⋊C4—61no—
343C4⋊C4—61no—
344C4⋊C4—61no—
345C4⋊C4—61no—
346C4⋊C4—181no—
347C4⋊C4—181no—
348C4⋊C4—181no—
349C4⋊C4—362no—
350C22⋊C4—61no—
351C22⋊C4—61no—
352C22⋊C4—181no—
353C22⋊C4—181no—
354C22⋊C4—181no—
355C22⋊C4—181no—
356C22⋊C4—362no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3#88211yescharacteristic
367C22×C3#91511yescharacteristic
368C22×C3D3×Q1611yescharacteristic
369C22×C3D3×Q1611yescharacteristic
370C22×C3#91811yescharacteristic
371C22×C3#93711yescharacteristic
372C2×D3—62no—
373C2×D3—62no—
374C2×D3—122no—
375C2×D3—121no—
376C2×D3—121no—
377C2×D3—121no—
378C2×D3—121no—
379C2×D3—122no—
380C2×D3—122no—
381C2×D3—241no—
382C2×D3—241no—
383C2×D3—242no—
384C2×D3—241no—
385C2×D3—241no—
386C2×D3—242no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—41no—
392C3×C4—41no—
393C3×C4—122no—
394C3×C4—121no—
395C3×C4—121no—
396C3×C4—121no—
397C3×C4—121no—
398C3×C4—241no—
399Dic3—42no—
400Dic3—41no—
401Dic3—41no—
402Dic3—41no—
403Dic3—41no—
404Dic3—81no—
405Dic3—121no—
406Dic3—121no—
407Dic3—241no—
408C32#161411yescharacteristic, complemented, Sylow
409C23—92no—
410C23—181no—
411C23—181no—
412C23—361no—
413C23—361no—
414C23#380211yescharacteristic
415Q8—121no—
416Q8—121no—
417Q8—721no—
418C2×C4—41no—
419C2×C4—62no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—121no—
425C2×C4—121no—
426C2×C4—121no—
427C2×C4—121no—
428C2×C4—121no—
429C2×C4—181no—
430C2×C4—361no—
431C2×C4—721no—
432C2×C4—721no—
433C2×C4D3×D1211yescharacteristic
434C2×C4D3×#6711yescharacteristic
435C8—41no—
436C8—361no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—41no—
445C2×C3—41no—
446C2×C3#474211yescharacteristic
447C2×C3#480911yescharacteristic
448C2×C3#482211yescharacteristic
449C2×C3#505311yescharacteristic
450C2×C3#518611yescharacteristic
451C2×C3#519811yescharacteristic
452D3—122no—
453D3—122no—
454D3—242no—
455C22—21no—
456C22—21no—
457C22—182no—
458C22—362no—
459C22—361no—
460C22—361no—
461C22—721no—
462C22#6380211yescharacteristic
463C22#6381111yescharacteristic
464C22#6392211yescharacteristic
465C4—21no—
466C4—21no—
467C4—122no—
468C4—121no—
469C4—121no—
470C4—121no—
471C4—121no—
472C4—241no—
473C4—361no—
474C3—21no—
475C3#6832211yescharacteristic, complemented
476C3#7117611yescharacteristic, complemented
477C2—21no—
478C2—21no—
479C2—362no—
480C2#1059040811yescharacteristic
481C2#1059095011yescharacteristic
482C2#1059101311yescharacteristic
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. #10591132C2semidirect
6. C3×#4467C2semidirect
7. #10589153C2semidirect
35. #4722D3semidirect
42. #4467D3semidirect
408. C32#1614semidirect
475. C3#68322semidirect
476. C3#71176semidirect

Maximal subgroups

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

subgroupindex
#105949812
C3×#47222
#105913502
#105911322
#105893342
C3×#44672
#105891532
#711763
#683223