Finite Group Databasebeta

← #11778308

Subgroups — #11778308

Order 1152.

562 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 78 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#10594973C211yesmaximal, characteristic
2#10592438C211yesmaximal, characteristic, complemented
3#10591354C211yesmaximal, characteristic, complemented
4#10591181C211yesmaximal, characteristic
5C3×#4470C211yesmaximal, characteristic
6C3×#4469C211yesmaximal, characteristic, complemented
7#10589154C211yesmaximal, characteristic, complemented
8#68294—31nomaximal
9#68132—31nomaximal
10C22×#634C2211yescharacteristic
11#64133C2211yescharacteristic
12C2×#3746—21no—
13C3×#930C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15Dic3×#67—21no—
16C2×Dic3⋊Dic3—21no—
17#63961—21no—
18#63896—21no—
19#63884—21no—
20#63861—21no—
21#63847—21no—
22C2×#3716—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63643—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63579—21no—
28#63567—21no—
29#5602—31no—
30#5515—31no—
31#5040—31no—
32#4979—31no—
33#4739—31no—
34#4739—31no—
35#4739—61no—
36#4738—31no—
37#4656—31no—
38C3×#327—31no—
39C3×#324—31no—
40#4470D311yescharacteristic
41#4469D311yescharacteristic, complemented
42#4467—31no—
43#4452—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—42no—
49C2×#634D411yescharacteristic
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D411yescharacteristic
53C22×C3×Dic3D411yescharacteristic
54C2×C3×D12D411yescharacteristic
55C2×D3×Dic3—21no—
56C2×C32×C8—21no—
57#3757—21no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59#3750—21no—
60#3746—42no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66#3724—21no—
67#3724—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—42no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73Dic32—21no—
74#3716—42no—
75#1603—91noSylow
76C22×Dic6—31no—
77C22×Dic6—31no—
78C22×Dic6—61no—
79C3×#121—31no—
80C2×C3×C4⋊C4—31no—
81#935—61no—
82#935—61no—
83D4×Dic3—61no—
84C2×#214—61no—
85#930C2×D311yescharacteristic
86#929—61no—
87C4×#67—61no—
88C2×C4⋊Dic3—61no—
89#924—31no—
90#924—31no—
91#924—61no—
92C2×Dic3⋊C4—61no—
93C2×Dic3⋊C4C2×D311yescharacteristic
94C2×Dic12—61no—
95C2×Dic12—61no—
96C2×Dic12—62no—
97C2×#204—61no—
98#898—61no—
99#896—61no—
100#894—61no—
101#889—61no—
102#889—61no—
103#879—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—
121C2×C32×C4—41no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129#634—22no—
130#634—22no—
131#634—41no—
132#634—41no—
133#634—41no—
134C3×#67—41no—
135C3×#67—41no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C3×D12—41no—
146D3×Dic3—81no—
147C32×C8—41no—
148C3×C3⋊C8—41no—
149#539—91no—
150#451—91no—
151#448—91no—
152#395—91no—
153#328—91no—
154#327—31no—
155#324—31no—
156C2×C3×D4—31no—
157C2×C3×D4—61no—
158C22×C3×C4—21no—
159C22×C3×C4—31no—
160C22×C3×C4—31no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C2×#67—21no—
165C22×Dic3—21no—
166C22×Dic3—61no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—121no—
170C22×Dic3D1211yescharacteristic
171C22×Dic3D1211yescharacteristic
172C2×D12D1211yescharacteristic
173C2×C4×D3—61no—
174C2×Dic6—31no—
175C2×Dic6—31no—
176C2×Dic6—61no—
177C2×Dic6—62no—
178C2×Dic6—61no—
179C2×Dic6—61no—
180C2×Dic6—61no—
181C2×Dic6—61no—
182C2×Dic6—121no—
183C2×Dic6—122no—
184C2×Dic6—122no—
185C2×Dic6—124no—
186C2×C3×C8—22no—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C2×C3×C8—61no—
190C3×C4⋊C4—31no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4—61no—
193C3×C22⋊C4—61no—
194#217—61no—
195#217—61no—
196#217—61no—
197#217—61no—
198#217—61no—
199#217—121no—
200#214—122no—
201(C2×D3)⋊C4—21no—
202(C2×D3)⋊C4—61no—
203(C2×D3)⋊C4—61no—
204(C2×D3)⋊C4—61no—
205C4⋊Dic3—31no—
206C4⋊Dic3—31no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—122no—
210C4⋊Dic3D1211yescharacteristic
211Dic3⋊C4—21no—
212Dic3⋊C4—21no—
213Dic3⋊C4—61no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—61no—
220Dic3⋊C4—121no—
221Dic3⋊C4—122no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C2×C3⋊C8—21no—
225Dic12—122no—
226Dic12—122no—
227Dic12—124no—
228#204—122no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32#12011yescharacteristic
232C22×C32#13511yescharacteristic
233C22×C32#13711yescharacteristic
234C2×C3×D3—41no—
235C2×C3×D3—41no—
236C2×C3×D3—41no—
237C32×C4—21no—
238C32×C4—21no—
239C3⋊Dic3—42no—
240C3⋊Dic3—41no—
241C3⋊Dic3—41no—
242C3×Dic3—42no—
243C3×Dic3—41no—
244C3×Dic3—41no—
245C3×Dic3—41no—
246C22×Q8—91no—
247C2×Q16—181no—
248C2×SD16—181no—
249#126—181no—
250#125—181no—
251#123—181no—
252#123—181no—
253C22⋊Q8—91no—
254C22⋊Q8—181no—
255#121—31no—
256C4×D4—181no—
257C2×C4⋊C4—31no—
258C2×C4⋊C4—181no—
259#103—181no—
260#103—181no—
261C22⋊C8—31no—
262C22⋊C8D3211yescharacteristic
263#95—31no—
264#95—181no—
265C23×C3—21no—
266C23×C3—61no—
267C23×C3C2×D1211yescharacteristic
268C23×C3D3×D411yescharacteristic
269C22×D3—21no—
270C3×D4—121no—
271C3×D4—121no—
272C3×D4—121no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—42no—
278C2×C3×C4—62no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—121no—
285C2×C3×C4—121no—
286C2×C3×C4—121no—
287C2×C3×C4C2×D1211yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291#67—41no—
292#67—41no—
293C2×Dic3—22no—
294C2×Dic3—21no—
295C2×Dic3—21no—
296C2×Dic3—21no—
297C2×Dic3—21no—
298C2×Dic3—21no—
299C2×Dic3—41no—
300C2×Dic3—41no—
301C2×Dic3—41no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—122no—
309C2×Dic3—121no—
310C2×Dic3—121no—
311C2×Dic3—122no—
312C2×Dic3—121no—
313C2×Dic3—121no—
314C2×Dic3—122no—
315C2×Dic3—121no—
316C2×Dic3—121no—
317C2×Dic3—241no—
318D12—41no—
319C4×D3—241no—
320Dic6—62no—
321Dic6—64no—
322Dic6—62no—
323Dic6—62no—
324Dic6—62no—
325Dic6—122no—
326Dic6—122no—
327Dic6—121no—
328Dic6—121no—
329Dic6—121no—
330Dic6—121no—
331Dic6—122no—
332Dic6—121no—
333Dic6—121no—
334Dic6—122no—
335C3×C8—42no—
336C3×C8—41no—
337C3×C8—41no—
338C3×C8—121no—
339C3⋊C8—41no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32#45211yescharacteristic
343C2×C32#45611yescharacteristic
344C2×C32B(4,𝔽2)11yescharacteristic
345C3×D3—81no—
346C2×Q8—91no—
347C2×Q8—181no—
348C2×Q8—181no—
349C2×Q8—362no—
350C2×D4—31no—
351C2×D4—61no—
352C22×C4—31no—
353C22×C4—31no—
354C22×C4—61no—
355C22×C4—181no—
356C22×C4—181no—
357C22×C4C2×D3211yescharacteristic
358Q16—362no—
359SD16—362no—
360C2×C8—21no—
361C2×C8—61no—
362C4⋊C4—31no—
363C4⋊C4—61no—
364C4⋊C4—61no—
365C4⋊C4—91no—
366C4⋊C4—181no—
367C4⋊C4—181no—
368C4⋊C4—181no—
369C4⋊C4—181no—
370C4⋊C4—362no—
371C22⋊C4—61no—
372C22⋊C4—181no—
373C22⋊C4—181no—
374C22⋊C4—181no—
375C22⋊C4—181no—
376C42—181no—
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—121no—
387C22×C3—121no—
388C22×C3—121no—
389C22×C3#88211yescharacteristic
390C22×C3#88211yescharacteristic
391C22×C3#90411yescharacteristic
392C22×C3#90911yescharacteristic
393C22×C3#91211yescharacteristic
394C22×C3#91511yescharacteristic
395C2×D3—41no—
396C2×D3—41no—
397C2×D3—41no—
398C3×C4—22no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—41no—
404C3×C4—122no—
405C3×C4—121no—
406C3×C4—121no—
407C3×C4—121no—
408Dic3—42no—
409Dic3—41no—
410Dic3—41no—
411Dic3—41no—
412Dic3—124no—
413Dic3—122no—
414Dic3—122no—
415Dic3—121no—
416Dic3—121no—
417Dic3—121no—
418Dic3—121no—
419Dic3—241no—
420Dic3—241no—
421C32#160311yescharacteristic, complemented, Sylow
422C23—61no—
423C23D3×D1211yescharacteristic
424Q8—182no—
425Q8—182no—
426Q8—361no—
427Q8—361no—
428Q8—361no—
429D4—121no—
430D4—121no—
431D4—121no—
432C2×C4—41no—
433C2×C4—62no—
434C2×C4—61no—
435C2×C4—61no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—121no—
440C2×C4—121no—
441C2×C4—121no—
442C2×C4—182no—
443C2×C4—181no—
444C2×C4—181no—
445C2×C4—361no—
446C2×C4—361no—
447C2×C4—721no—
448C2×C4D3×D1211yescharacteristic
449C2×C4#381111yescharacteristic
450C8—41no—
451C8—121no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—41no—
460C2×C3—41no—
461C2×C3—241no—
462C2×C3#473311yescharacteristic
463C2×C3#474111yescharacteristic
464C2×C3#474111yescharacteristic
465C2×C3#475211yescharacteristic
466C2×C3#478311yescharacteristic
467C2×C3#482611yescharacteristic
468D3—81no—
469C22—21no—
470C22—21no—
471C22—121no—
472C22—121no—
473C22—121no—
474C22#6380011yescharacteristic
475C22#6380711yescharacteristic
476C22#6392311yescharacteristic
477C4—21no—
478C4—21no—
479C4—122no—
480C4—121no—
481C4—121no—
482C4—121no—
483C4—361no—
484C4—362no—
485C4—361no—
486C3—21no—
487C3#6813211yescharacteristic, complemented
488C3#6829411yescharacteristic, complemented
489C2—21no—
490C2—21no—
491C2—241no—
492C2#1059041011yescharacteristic
493C2#1059096911yescharacteristic
494C2#1059102111yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC22⋊C8D32
hypocenterC32#1603
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
3. #10591354C2semidirect
6. C3×#4469C2semidirect
7. #10589154C2semidirect
41. #4469D3semidirect
421. C32#1603semidirect
487. C3#68132semidirect
488. C3#68294semidirect

Maximal subgroups

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

subgroupindex
#105949732
#105924382
#105913542
#105911812
C3×#44702
C3×#44692
#105891542
#682943
#681323