Finite Group Databasebeta

← #11778259

Subgroups — #11778259

Order 1152.

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

normal subgroups only

This group has 561 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×#4739C211yesmaximal, characteristic, complemented
3#10591310C211yesmaximal, characteristic
4#10591185C211yesmaximal, characteristic, complemented
5#10589334C211yesmaximal, characteristic
6C3×#4467C211yesmaximal, characteristic, complemented
7#10589153C211yesmaximal, characteristic, complemented
8#70980—31nomaximal
9#68318—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C2×#3752C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C3×#924C2211yescharacteristic
14C2×C3×Dic12—21no—
15#63982—21no—
16#63974—21no—
17C2×#3722—21no—
18#63895—21no—
19#63895—21no—
20#63888—21no—
21#63888—21no—
22C2×#3718—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95C2211yescharacteristic
26C3×#816—21no—
27#63579—21no—
28#63565—21no—
29#5634—31no—
30#5634—31no—
31C3×#451—31no—
32#5231—31no—
33#5228—31no—
34#5050—31no—
35#4739D311yescharacteristic, complemented
36#4673—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×Dic6—21no—
50C2×C3×Dic6—21no—
51C2×C3×Dic6—42no—
52C2×C3×Dic6D411yescharacteristic
53C2×C3×Dic6D411yescharacteristic
54C2×#627—21no—
55C2×#624—21no—
56C2×#624—21no—
57C2×C32×C8—21no—
58#3752—21no—
59#3752—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×#217—21no—
62C3×#217—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×C4⋊Dic3D411yescharacteristic
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—21no—
67C3×Dic12—42no—
68#3724—21no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—21no—
71#3722—21no—
72#3722—21no—
73#3722—42no—
74#3718—42no—
75#1602—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C2×C3×Q16—61no—
79C3×C22⋊Q8—31no—
80C3×C22⋊Q8—31no—
81#946—61no—
82#946—61no—
83C2×#216—61no—
84C2×#216—61no—
85C2×(C2×D3)⋊C4—31no—
86C2×(C2×D3)⋊C4—31no—
87C2×(C2×D3)⋊C4—61no—
88C2×(C2×D3)⋊C4—61no—
89C2×(C2×D3)⋊C4—61no—
90#924C2×D311yescharacteristic
91#924C2×D311yescharacteristic
92C2×Dic12—21no—
93#897—61no—
94#897—61no—
95#896—61no—
96#896—61no—
97#896—61no—
98#896—61no—
99D3×C22⋊C4—61no—
100D3×C22⋊C4—61no—
101#878—61no—
102#878—61no—
103C3×#103—61no—
104C3×C22⋊C8—21no—
105C3×C22⋊C8C2×D311yescharacteristic
106C3×C22⋊C8C2×D311yescharacteristic
107C3×#95—31no—
108#835—61no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95C2×D311yescharacteristic
112#830—31no—
113#830—31no—
114#830—61no—
115#816—21no—
116#810—61no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—21no—
119C22×C3⋊D3—21no—
120C22×C3⋊D3—41no—
121C22×C3⋊D3—41no—
122C22×C3⋊D3Q1612yescomplemented
123C2×C32×C4—41no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—41no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—21no—
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—
137C2×C3×Dic3—41no—
138C3×Dic6—22no—
139C3×Dic6—22no—
140C3×Dic6—41no—
141C3×Dic6—41no—
142C3×Dic6—41no—
143C3×Dic6—41no—
144#627—81no—
145#624—81no—
146#624—81no—
147C32×C8—41no—
148C3⋊(C3⋊C8)—41no—
149#543—91no—
150#451—31no—
151#451—91no—
152#393—91no—
153#328—31no—
154#328—91no—
155#323—91no—
156C23×D3—31no—
157C23×D3—31no—
158C23×D3—61no—
159C2×C3×Q8—31no—
160C2×C3×Q8—31no—
161C2×C3×Q8—61no—
162C2×C3×Q8—61no—
163C2×C3×Q8—122no—
164C22×C3×C4—21no—
165C22×C3×C4—61no—
166C22×C3×C4—61no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×Dic3—21no—
170C22×Dic3—21no—
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—61no—
174C2×C4×D3—61no—
175C2×C4×D3—61no—
176C2×C4×D3—61no—
177C2×C4×D3—61no—
178C2×Dic6—21no—
179C2×Dic6—21no—
180C2×Dic6—42no—
181C2×Dic6—61no—
182C2×Dic6—61no—
183C2×Dic6D1211yescharacteristic
184C2×Dic6#6711yescharacteristic
185C3×Q16—122no—
186C2×C3×C8—21no—
187C2×C3×C8—21no—
188C2×C3×C8—41no—
189C3×C4⋊C4—31no—
190C3×C4⋊C4—31no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195#217—21no—
196#217—21no—
197#216—122no—
198#216—122no—
199(C2×D3)⋊C4—61no—
200(C2×D3)⋊C4—61no—
201(C2×D3)⋊C4—61no—
202(C2×D3)⋊C4—61no—
203(C2×D3)⋊C4—61no—
204(C2×D3)⋊C4—61no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—121no—
208(C2×D3)⋊C4—121no—
209(C2×D3)⋊C4—122no—
210(C2×D3)⋊C4—122no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3D1211yescharacteristic
214C4⋊Dic3#6711yescharacteristic
215Dic3⋊C4—21no—
216Dic3⋊C4—21no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—61no—
220Dic3⋊C4—61no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—121no—
224Dic12—42no—
225C22×C32—21no—
226C22×C32—21no—
227C22×C32#12011yescharacteristic
228C22×C32C2×Q1611yescharacteristic
229C22×C32#13711yescharacteristic
230C2×C3⋊D3—22no—
231C2×C3⋊D3—41no—
232C2×C3⋊D3—41no—
233C2×C3⋊D3—42no—
234C2×C3⋊D3—81no—
235C32×C4—21no—
236C32×C4—21no—
237C3⋊Dic3—41no—
238C3×Dic3—41no—
239C3×Dic3—41no—
240C3×Dic3—41no—
241C3×Dic3—41no—
242C3×Dic3—42no—
243C3×Dic3—81no—
244C22×Q8—31no—
245C2×Q16—61no—
246C2×Q16—181no—
247C22⋊Q8—31no—
248C22⋊Q8—31no—
249C22⋊Q8—181no—
250C22⋊Q8—181no—
251C22⋊Q8—181no—
252C22⋊Q8—181no—
253C22⋊Q8—181no—
254C2×C22⋊C4—91no—
255C2×C22⋊C4—181no—
256C2×C22⋊C4—181no—
257#103—61no—
258#103—181no—
259C22⋊C8—91no—
260C22⋊C8D3211yescharacteristic
261#95—31no—
262#95—181no—
263C23×C3—21no—
264C23×C3D3×D411yescharacteristic
265C23×C3D3×D411yescharacteristic
266C22×D3—32no—
267C22×D3—32no—
268C22×D3—62no—
269C22×D3—61no—
270C22×D3—61no—
271C22×D3—61no—
272C22×D3—61no—
273C22×D3—121no—
274C22×D3—121no—
275C22×D3—121no—
276C22×D3—121no—
277C22×D3—121no—
278C22×D3—121no—
279C22×D3—241no—
280C22×D3—241no—
281C3×Q8—62no—
282C3×Q8—62no—
283C3×Q8—121no—
284C3×Q8—121no—
285C3×Q8—121no—
286C3×Q8—121no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—62no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
296C2×C3×C4—81no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4C2×D1211yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4C2×#6711yescharacteristic
306C2×Dic3—22no—
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—41no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320C2×Dic3—121no—
321C2×Dic3—241no—
322C4×D3—241no—
323C4×D3—241no—
324C4×D3—241no—
325C4×D3—241no—
326Dic6—22no—
327Dic6—22no—
328Dic6—41no—
329Dic6—41no—
330Dic6—41no—
331Dic6—41no—
332Dic6—241no—
333Dic6—241no—
334C3×C8—41no—
335C3×C8—41no—
336C3×C8—81no—
337C3⋊C8—121no—
338C3⋊C8—121no—
339C3⋊C8—241no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32#45111yescharacteristic
343C2×C32#45511yescharacteristic
344C2×C32B(4,𝔽2)11yescharacteristic
345C3⋊D3—42no—
346C24—91no—
347C2×Q8—31no—
348C2×Q8—31no—
349C2×Q8—61no—
350C2×Q8—61no—
351C2×Q8—122no—
352C2×Q8—181no—
353C22×C4—61no—
354C22×C4—61no—
355C22×C4—91no—
356C22×C4—181no—
357C22×C4—181no—
358C22×C4C2×D3211yescharacteristic
359Q16—122no—
360Q16—362no—
361C2×C8—21no—
362C2×C8—181no—
363C4⋊C4—31no—
364C4⋊C4—31no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—181no—
368C4⋊C4—181no—
369C4⋊C4—181no—
370C22⋊C4—61no—
371C22⋊C4—61no—
372C22⋊C4—181no—
373C22⋊C4—181no—
374C22⋊C4—181no—
375C22⋊C4—181no—
376C22⋊C4—362no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3#88211yescharacteristic
387C22×C3#91511yescharacteristic
388C22×C3D3×Q1611yescharacteristic
389C22×C3D3×Q1611yescharacteristic
390C22×C3#91811yescharacteristic
391C22×C3#93711yescharacteristic
392C2×D3—62no—
393C2×D3—62no—
394C2×D3—122no—
395C2×D3—121no—
396C2×D3—121no—
397C2×D3—121no—
398C2×D3—121no—
399C2×D3—122no—
400C2×D3—122no—
401C2×D3—241no—
402C2×D3—241no—
403C2×D3—242no—
404C2×D3—241no—
405C2×D3—241no—
406C2×D3—242no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—41no—
412C3×C4—41no—
413C3×C4—121no—
414C3×C4—121no—
415C3×C4—122no—
416C3×C4—121no—
417C3×C4—121no—
418C3×C4—241no—
419Dic3—41no—
420Dic3—41no—
421Dic3—42no—
422Dic3—41no—
423Dic3—41no—
424Dic3—81no—
425Dic3—121no—
426Dic3—121no—
427Dic3—241no—
428C32#160211yescharacteristic, complemented, Sylow
429C23—92no—
430C23—181no—
431C23—181no—
432C23—361no—
433C23—361no—
434C23#380211yescharacteristic
435Q8—62no—
436Q8—62no—
437Q8—121no—
438Q8—121no—
439Q8—121no—
440Q8—121no—
441Q8—721no—
442C2×C4—41no—
443C2×C4—62no—
444C2×C4—61no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—121no—
449C2×C4—121no—
450C2×C4—121no—
451C2×C4—121no—
452C2×C4—121no—
453C2×C4—181no—
454C2×C4—361no—
455C2×C4—721no—
456C2×C4—721no—
457C2×C4D3×D1211yescharacteristic
458C2×C4D3×#6711yescharacteristic
459C8—41no—
460C8—361no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—41no—
469C2×C3—41no—
470C2×C3#474111yescharacteristic
471C2×C3#480911yescharacteristic
472C2×C3#482511yescharacteristic
473C2×C3#503211yescharacteristic
474C2×C3#518611yescharacteristic
475C2×C3#520211yescharacteristic
476D3—122no—
477D3—122no—
478D3—242no—
479C22—21no—
480C22—21no—
481C22—182no—
482C22—362no—
483C22—361no—
484C22—361no—
485C22—721no—
486C22#6380211yescharacteristic
487C22#6381111yescharacteristic
488C22#6392211yescharacteristic
489C4—21no—
490C4—21no—
491C4—121no—
492C4—121no—
493C4—122no—
494C4—121no—
495C4—121no—
496C4—241no—
497C4—361no—
498C3—21no—
499C3#6831811yescharacteristic, complemented
500C3#7098011yescharacteristic, complemented
501C2—21no—
502C2—21no—
503C2—362no—
504C2#1059040711yescharacteristic
505C2#1059095011yescharacteristic
506C2#1059101111yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radicalC23×C3⋊D3D4
hypercenterC22⋊C8D32
hypocenterC32#1602
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×#4739C2semidirect
4. #10591185C2semidirect
6. C3×#4467C2semidirect
7. #10589153C2semidirect
35. #4739D3semidirect
42. #4467D3semidirect
122. C22×C3⋊D3Q16semidirect
428. C32#1602semidirect
499. C3#68318semidirect
500. C3#70980semidirect

Maximal subgroups

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

subgroupindex
#105949812
C3×#47392
#105913102
#105911852
#105893342
C3×#44672
#105891532
#709803
#683183