Finite Group Databasebeta

← #11778258

Subgroups — #11778258

Order 1152.

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

normal subgroups only

This group has 586 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#10592438C211yesmaximal, characteristic, complemented
3#10591322C211yesmaximal, characteristic
4#10591190C211yesmaximal, characteristic, complemented
5C3×#4468C211yesmaximal, characteristic
6C3×#4467C211yesmaximal, characteristic, complemented
7#10589154C211yesmaximal, characteristic, complemented
8#68318—31nomaximal
9#68115—31nomaximal
10C22×#634C2211yescharacteristic
11#64133C2211yescharacteristic
12C2×#3746—21no—
13C2×C3×(C2×D3)⋊C4C2211yescharacteristic
14C3×#924C2211yescharacteristic
15D3×#217—21no—
16#63964—21no—
17C2×(C2×D3)⋊Dic3—21no—
18#63899—21no—
19#63896—21no—
20#63893—21no—
21#63887—21no—
22C2×#3719—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63643—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63579—21no—
28#63567—21no—
29#5634—31no—
30#5483—31no—
31#5050—31no—
32#4947—31no—
33#4739—31no—
34#4739—31no—
35#4739—31no—
36#4739—61no—
37#4673—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×#634—21no—
48C2×#634—21no—
49C2×#634—42no—
50C2×#634D411yescharacteristic
51C22×C3×Dic3—21no—
52C22×C3×Dic3D411yescharacteristic
53C2×C3×Dic6D411yescharacteristic
54C2×#627—21no—
55C2×D3×Dic3—21no—
56C2×D3×Dic3—21no—
57C2×C32×C8—21no—
58#3757—21no—
59C4⋊(C3⋊Dic3)D411yescharacteristic
60#3750—21no—
61#3746—42no—
62C3×#217—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
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(C2×D3)⋊Dic3—42no—
74#3719—42no—
75#1602—91noSylow
76C22×Dic6—31no—
77C22×Dic6—31no—
78C22×Dic6—61no—
79C3×C22⋊Q8—31no—
80C2×C3×C22⋊C4—31no—
81C2×#217—61no—
82C2×#217—61no—
83#946—61no—
84C2×#216—61no—
85C2×(C2×D3)⋊C4—61no—
86C2×(C2×D3)⋊C4C2×D311yescharacteristic
87#924—31no—
88#924—31no—
89#924—61no—
90#924—61no—
91#924C2×D311yescharacteristic
92C2×Dic12—61no—
93C2×Dic12—61no—
94C2×Dic12—62no—
95C2×Dic12—61no—
96#897—61no—
97#896—61no—
98#896—61no—
99D3×C22⋊C4—61no—
100#878—61no—
101#878—61no—
102#878—61no—
103#878—61no—
104#878—61no—
105C3×C22⋊C8—21no—
106C3×C22⋊C8—31no—
107C3×C22⋊C8C2×D311yescharacteristic
108C3×C22⋊C8C2×D311yescharacteristic
109C3×#95—31no—
110C3⋊#95—61no—
111C3⋊#95—61no—
112C3⋊#95C2×D311yescharacteristic
113#830C2×D311yescharacteristic
114#816—61no—
115#816—61no—
116#816—62no—
117#816—61no—
118#810—61no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3Q1612yescomplemented
125C2×C32×C4—41no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133#634—22no—
134#634—22no—
135#634—41no—
136#634—41no—
137#634—41no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C3×Dic6—41no—
146#627—81no—
147D3×Dic3—81no—
148D3×Dic3—81no—
149C32×C8—41no—
150C3×C3⋊C8—41no—
151#543—91no—
152#451—91no—
153#451—91no—
154#393—91no—
155#328—31no—
156#328—91no—
157#323—31no—
158C24×C3—31no—
159C23×D3D1211yescharacteristic
160C2×C3×Q8—31no—
161C22×C3×C4—21no—
162C22×C3×C4—31no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C22×Dic3—21no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C22×Dic3—121no—
172C22×Dic3D1211yescharacteristic
173C2×C4×D3—61no—
174C2×C4×D3—61no—
175C2×Dic6—31no—
176C2×Dic6—31no—
177C2×Dic6—61no—
178C2×Dic6—62no—
179C2×Dic6—61no—
180C2×Dic6—61no—
181C2×Dic6—61no—
182C2×Dic6—61no—
183C2×Dic6—61no—
184C2×Dic6—61no—
185C2×Dic6—121no—
186C2×Dic6—122no—
187C2×Dic6—122no—
188C2×Dic6—124no—
189C2×Dic6D1211yescharacteristic
190C2×C3×C8—22no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—61no—
194C3×C4⋊C4—31no—
195C3×C4⋊C4—61no—
196C3×C22⋊C4—61no—
197C3×C22⋊C4—61no—
198C3×C22⋊C4—61no—
199#217—21no—
200#217—61no—
201#217—61no—
202#217—61no—
203#217—61no—
204#217—121no—
205#217—122no—
206#216—122no—
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—21no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—61no—
211(C2×D3)⋊C4—122no—
212C4⋊Dic3—31no—
213C4⋊Dic3—31no—
214C4⋊Dic3—61no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3D1211yescharacteristic
218Dic3⋊C4—21no—
219Dic3⋊C4—61no—
220Dic3⋊C4—61no—
221Dic3⋊C4—61no—
222Dic3⋊C4—61no—
223Dic3⋊C4—61no—
224Dic3⋊C4—61no—
225Dic3⋊C4—121no—
226C2×C3⋊C8—21no—
227Dic12—122no—
228Dic12—122no—
229Dic12—124no—
230Dic12—122no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32#12011yescharacteristic
234C22×C32C2×Q1611yescharacteristic
235C22×C32#13711yescharacteristic
236C2×C3×D3—22no—
237C2×C3×D3—41no—
238C2×C3×D3—41no—
239C2×C3×D3—42no—
240C2×C3×D3—81no—
241C32×C4—21no—
242C32×C4—21no—
243C3⋊Dic3—42no—
244C3⋊Dic3—41no—
245C3⋊Dic3—41no—
246C3×Dic3—41no—
247C3×Dic3—41no—
248C3×Dic3—41no—
249C3×Dic3—81no—
250C22×Q8—91no—
251C2×Q16—181no—
252C2×Q16—181no—
253C22⋊Q8—31no—
254C22⋊Q8—91no—
255C22⋊Q8—181no—
256C22⋊Q8—181no—
257C22⋊Q8—181no—
258C22⋊Q8—181no—
259C22⋊Q8—181no—
260C2×C22⋊C4—31no—
261C2×C22⋊C4—181no—
262C2×C22⋊C4—181no—
263#103—181no—
264#103—181no—
265C22⋊C8—31no—
266C22⋊C8D3211yescharacteristic
267#95—31no—
268#95—181no—
269C23×C3—21no—
270C23×C3—32no—
271C23×C3—61no—
272C23×C3—61no—
273C23×C3—121no—
274C23×C3—121no—
275C23×C3C2×D1211yescharacteristic
276C23×C3D3×D411yescharacteristic
277C22×D3—21no—
278C22×D3—21no—
279C22×D3—41no—
280C22×D3—41no—
281C22×D3Dic1212yescomplemented
282C3×Q8—121no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—42no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—121no—
292C2×C3×C4—121no—
293C2×C3×C4—121no—
294C2×C3×C4—121no—
295C2×C3×C4C2×D1211yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×Dic3—21no—
300C2×Dic3—21no—
301C2×Dic3—21no—
302C2×Dic3—41no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312C2×Dic3—122no—
313C2×Dic3—121no—
314C2×Dic3—121no—
315C2×Dic3—122no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—122no—
319C2×Dic3—121no—
320C2×Dic3—121no—
321C2×Dic3—241no—
322C2×Dic3—241no—
323C4×D3—241no—
324C4×D3—241no—
325Dic6—41no—
326Dic6—64no—
327Dic6—62no—
328Dic6—62no—
329Dic6—62no—
330Dic6—62no—
331Dic6—122no—
332Dic6—122no—
333Dic6—121no—
334Dic6—121no—
335Dic6—121no—
336Dic6—121no—
337Dic6—122no—
338Dic6—121no—
339Dic6—121no—
340Dic6—122no—
341Dic6—241no—
342Dic6—241no—
343C3×C8—42no—
344C3×C8—41no—
345C3×C8—41no—
346C3×C8—121no—
347C3⋊C8—41no—
348C2×C32—21no—
349C2×C32—21no—
350C2×C32#45111yescharacteristic
351C2×C32#45511yescharacteristic
352C2×C32B(4,𝔽2)11yescharacteristic
353C3×D3—42no—
354C24—31no—
355C2×Q8—31no—
356C2×Q8—91no—
357C2×Q8—181no—
358C2×Q8—181no—
359C2×Q8—181no—
360C2×Q8—362no—
361C22×C4—31no—
362C22×C4—61no—
363C22×C4—181no—
364C22×C4—181no—
365C22×C4—181no—
366C22×C4C2×D3211yescharacteristic
367Q16—362no—
368Q16—362no—
369C2×C8—21no—
370C2×C8—61no—
371C4⋊C4—31no—
372C4⋊C4—61no—
373C4⋊C4—91no—
374C4⋊C4—181no—
375C4⋊C4—181no—
376C4⋊C4—181no—
377C4⋊C4—181no—
378C22⋊C4—61no—
379C22⋊C4—61no—
380C22⋊C4—61no—
381C22⋊C4—181no—
382C22⋊C4—181no—
383C22⋊C4—181no—
384C22⋊C4—362no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3—62no—
395C22×C3—122no—
396C22×C3—121no—
397C22×C3—121no—
398C22×C3—241no—
399C22×C3#88211yescharacteristic
400C22×C3#88211yescharacteristic
401C22×C3C2×Dic1211yescharacteristic
402C22×C3#90911yescharacteristic
403C22×C3#91511yescharacteristic
404C22×C3D3×Q1611yescharacteristic
405C2×D3—22no—
406C2×D3—41no—
407C2×D3—41no—
408C2×D3—42no—
409C2×D3—81no—
410C3×C4—22no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—41no—
416C3×C4—121no—
417C3×C4—121no—
418C3×C4—121no—
419C3×C4—241no—
420Dic3—41no—
421Dic3—41no—
422Dic3—41no—
423Dic3—81no—
424Dic3—124no—
425Dic3—122no—
426Dic3—122no—
427Dic3—121no—
428Dic3—121no—
429Dic3—121no—
430Dic3—121no—
431Dic3—241no—
432Dic3—241no—
433C32#160211yescharacteristic, complemented, Sylow
434C23—32no—
435C23—61no—
436C23—61no—
437C23—121no—
438C23—121no—
439C23D3×D1211yescharacteristic
440Q8—121no—
441Q8—182no—
442Q8—182no—
443Q8—361no—
444Q8—361no—
445Q8—361no—
446Q8—721no—
447C2×C4—41no—
448C2×C4—61no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—121no—
452C2×C4—121no—
453C2×C4—121no—
454C2×C4—121no—
455C2×C4—182no—
456C2×C4—181no—
457C2×C4—181no—
458C2×C4—361no—
459C2×C4—361no—
460C2×C4—721no—
461C2×C4—721no—
462C2×C4D3×D1211yescharacteristic
463C2×C4#381111yescharacteristic
464C8—41no—
465C8—121no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—41no—
474C2×C3—41no—
475C2×C3—122no—
476C2×C3#473911yescharacteristic
477C2×C3#474111yescharacteristic
478C2×C3#474111yescharacteristic
479C2×C3#474611yescharacteristic
480C2×C3#480911yescharacteristic
481C2×C3#482511yescharacteristic
482D3—42no—
483C22—21no—
484C22—21no—
485C22—62no—
486C22—122no—
487C22—121no—
488C22—121no—
489C22—241no—
490C22D3×Dic1211yescharacteristic
491C22#6380011yescharacteristic
492C22#6392311yescharacteristic
493C4—21no—
494C4—21no—
495C4—121no—
496C4—121no—
497C4—121no—
498C4—241no—
499C4—361no—
500C4—362no—
501C4—361no—
502C3—21no—
503C3#6811511yescharacteristic, complemented
504C3#6831811yescharacteristic, complemented
505C2—21no—
506C2—21no—
507C2—122no—
508C2#1059041011yescharacteristic
509C2#1059095211yescharacteristic
510C2#1059101611yescharacteristic
subgroupG/H
centerC22#63923
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. #10592438C2semidirect
4. #10591190C2semidirect
6. C3×#4467C2semidirect
7. #10589154C2semidirect
42. #4467D3semidirect
124. C22×C3×D3Q16semidirect
281. C22×D3Dic12semidirect
433. C32#1602semidirect
503. C3#68115semidirect
504. C3#68318semidirect

Maximal subgroups

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

subgroupindex
#105949712
#105924382
#105913222
#105911902
C3×#44682
C3×#44672
#105891542
#683183
#681153