Finite Group Databasebeta

← #11778301

Subgroups — #11778301

Order 1152.

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

normal subgroups only

This group has 579 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#10594974C211yesmaximal, characteristic
2#10592355C211yesmaximal, characteristic, complemented
3#10591190C211yesmaximal, characteristic, complemented
4#10591181C211yesmaximal, characteristic
5C3×#4452C211yesmaximal, characteristic, complemented
6C3×#4451C211yesmaximal, characteristic
7#10589148C211yesmaximal, characteristic, complemented
8#68326—31nomaximal
9#68294—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)—21no—
12C2×#3750C2211yescharacteristic
13C3×#930C2211yescharacteristic
14C3×#924C2211yescharacteristic
15#67⋊Dic3—21no—
16#63962—21no—
17#63887—21no—
18#63884—21no—
19#63858—21no—
20#63846—21no—
21C2×#3719—21no—
22C2×#3716—21no—
23C32×#95C2211yescharacteristic
24#63658—21no—
25C3×#830C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63567—21no—
28#63567—21no—
29#5645—31no—
30#5602—31no—
31#5050—31no—
32#5040—31no—
33#4739—31no—
34#4738—31no—
35#4656—31no—
36#4656—31no—
37#4656—61no—
38C3×#328—31no—
39C3×#327—31no—
40#4469—31no—
41#4469—31no—
42#4452D311yescharacteristic, complemented
43#4451D311yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3D411yescharacteristic
48C22×C3⋊Dic3D411yescharacteristic
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—42no—
52C2×C3×#67—21no—
53C2×C3×D12D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C2×D3×Dic3—21no—
56C4⋊(C3⋊Dic3)—42no—
57#3750—21no—
58#3750—21no—
59C3×#217—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72Dic32—21no—
73#3719—42no—
74#3716—42no—
75#1603—91noSylow
76C22×Dic6—31no—
77C22×Dic6—31no—
78C22×Dic6—61no—
79C3×C22⋊Q8—31no—
80C3×#121—31no—
81#946—61no—
82C2×#216—61no—
83#935—61no—
84#935—61no—
85D4×Dic3—61no—
86C2×#214—61no—
87#930C2×D311yescharacteristic
88C2×C4⋊Dic3—61no—
89C2×C4⋊Dic3—61no—
90C2×C4⋊Dic3—62no—
91#924C2×D311yescharacteristic
92C2×Dic3⋊C4—31no—
93C2×Dic3⋊C4—31no—
94C2×Dic3⋊C4—61no—
95C2×Dic12—61no—
96C2×#204—61no—
97#898—61no—
98#894—61no—
99#890—61no—
100#889—61no—
101#886—61no—
102#67⋊C4—61no—
103#879—61no—
104#878—61no—
105C3×C22⋊C8—31no—
106C3×C22⋊C8—31no—
107C3×#95—21no—
108C3×#95C2×D311yescharacteristic
109C3×#95C2×D311yescharacteristic
110C3⋊#95—61no—
111C3⋊#95—61no—
112C3⋊#95—62no—
113#830C2×D311yescharacteristic
114#830C2×D311yescharacteristic
115#816—61no—
116#816—61no—
117#810—61no—
118#810—61no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—21no—
121C2×C32×C4—22no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135#634—22no—
136#634—22no—
137#634—41no—
138#634—41no—
139C3×#67—41no—
140C3×#67—41no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C3×D12—41no—
145C3×Dic6—41no—
146D3×Dic3—81no—
147C3×C3⋊C8—41no—
148C3×C3⋊C8—41no—
149#539—91no—
150#451—91no—
151#448—91no—
152#395—91no—
153#328—31no—
154#327—31no—
155#324—91no—
156C2×C3×Q8—31no—
157C2×C3×D4—31no—
158C2×C3×D4—61no—
159C22×C3×C4—22no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C2×#67—21no—
166C22×Dic3—31no—
167C22×Dic3—31no—
168C22×Dic3—31no—
169C22×Dic3—31no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—61no—
173C22×Dic3—62no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C2×D12D1211yescharacteristic
177C2×C4×D3—61no—
178C2×Dic6—61no—
179C2×Dic6—61no—
180C2×Dic6—61no—
181C2×Dic6—61no—
182C2×Dic6—121no—
183C2×Dic6—121no—
184C2×Dic6—122no—
185C2×Dic6—122no—
186C2×Dic6—124no—
187C2×Dic6D1211yescharacteristic
188C2×C3×C8—61no—
189C2×C3×C8—61no—
190C3×C4⋊C4—31no—
191C3×C4⋊C4—31no—
192C3×C4⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195#217—21no—
196#217—61no—
197#217—61no—
198#217—61no—
199#216—122no—
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—61no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—122no—
209C4⋊Dic3—122no—
210C4⋊Dic3—124no—
211C4⋊Dic3D1211yescharacteristic
212C4⋊Dic3D1211yescharacteristic
213Dic3⋊C4—21no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—61no—
220Dic3⋊C4—61no—
221Dic3⋊C4—121no—
222Dic3⋊C4—121no—
223C4×Dic3—61no—
224C4×Dic3—61no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227Dic12—122no—
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—
239C32×C4—42no—
240C3⋊Dic3—41no—
241C3⋊Dic3—42no—
242C3⋊Dic3—41no—
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—31no—
254C22⋊Q8—181no—
255#121—31no—
256C4×D4—181no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—181no—
259#103—181no—
260#103—181no—
261C22⋊C8—31no—
262C22⋊C8—31no—
263#95—181no—
264#95D3211yescharacteristic
265C23×C3—21no—
266C23×C3—61no—
267C23×C3D3×D411yescharacteristic
268C23×C3D3×D411yescharacteristic
269C22×D3—21no—
270C3×Q8—121no—
271C3×D4—121no—
272C3×D4—121no—
273C3×D4—121no—
274C2×C3×C4—24no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—42no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4C2×D1211yescharacteristic
292C2×C3×C4C2×D1211yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295#67—41no—
296#67—41no—
297C2×Dic3—21no—
298C2×Dic3—21no—
299C2×Dic3—21no—
300C2×Dic3—64no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312C2×Dic3—121no—
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—121no—
322C2×Dic3—121no—
323C2×Dic3—122no—
324C2×Dic3—241no—
325D12—41no—
326C4×D3—241no—
327Dic6—41no—
328Dic6—62no—
329Dic6—62no—
330Dic6—62no—
331Dic6—62no—
332Dic6—122no—
333Dic6—122no—
334Dic6—121no—
335Dic6—121no—
336Dic6—121no—
337Dic6—121no—
338Dic6—122no—
339Dic6—122no—
340C3×C8—121no—
341C3×C8—121no—
342C3⋊C8—41no—
343C3⋊C8—41no—
344C2×C32—21no—
345C2×C32—21no—
346C2×C32#45211yescharacteristic
347C2×C32#45611yescharacteristic
348C2×C32B(4,𝔽2)11yescharacteristic
349C3×D3—81no—
350C2×Q8—31no—
351C2×Q8—181no—
352C2×Q8—181no—
353C2×Q8—362no—
354C2×D4—31no—
355C2×D4—61no—
356C22×C4—21no—
357C22×C4—91no—
358C22×C4—91no—
359C22×C4—181no—
360C22×C4—181no—
361C22×C4C2×D3211yescharacteristic
362Q16—362no—
363SD16—362no—
364C2×C8—61no—
365C2×C8—61no—
366C4⋊C4—31no—
367C4⋊C4—31no—
368C4⋊C4—61no—
369C4⋊C4—181no—
370C4⋊C4—181no—
371C4⋊C4—181no—
372C4⋊C4—181no—
373C4⋊C4—181no—
374C4⋊C4—362no—
375C22⋊C4—61no—
376C22⋊C4—61no—
377C22⋊C4—181no—
378C22⋊C4—181no—
379C22⋊C4—181no—
380C42—181no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—121no—
391C22×C3—121no—
392C22×C3—121no—
393C22×C3#88211yescharacteristic
394C22×C3#88211yescharacteristic
395C22×C3#91211yescharacteristic
396C22×C3#91511yescharacteristic
397C22×C3#91611yescharacteristic
398C22×C3#91811yescharacteristic
399C2×D3—41no—
400C2×D3—41no—
401C2×D3—41no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—41no—
407C3×C4—41no—
408C3×C4—44no—
409C3×C4—42no—
410C3×C4—42no—
411C3×C4—121no—
412C3×C4—121no—
413C3×C4—121no—
414Dic3—41no—
415Dic3—41no—
416Dic3—41no—
417Dic3—124no—
418Dic3—122no—
419Dic3—122no—
420Dic3—122no—
421Dic3—121no—
422Dic3—121no—
423Dic3—121no—
424Dic3—121no—
425Dic3—241no—
426C32#160311yescharacteristic, complemented, Sylow
427C23—61no—
428C23#381111yescharacteristic
429Q8—121no—
430Q8—182no—
431Q8—182no—
432Q8—361no—
433Q8—361no—
434D4—121no—
435D4—121no—
436D4—121no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—61no—
442C2×C4—61no—
443C2×C4—61no—
444C2×C4—182no—
445C2×C4—181no—
446C2×C4—181no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—361no—
450C2×C4—361no—
451C2×C4—361no—
452C2×C4—721no—
453C2×C4D3×D1211yescharacteristic
454C2×C4D3×D1211yescharacteristic
455C8—121no—
456C8—121no—
457C2×C3—22no—
458C2×C3—22no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—241no—
467C2×C3#474111yescharacteristic
468C2×C3#474111yescharacteristic
469C2×C3#478311yescharacteristic
470C2×C3#480811yescharacteristic
471C2×C3#482611yescharacteristic
472C2×C3#482611yescharacteristic
473D3—81no—
474C22—21no—
475C22—21no—
476C22—121no—
477C22—121no—
478C22—121no—
479C22#6392311yescharacteristic
480C22#6393611yescharacteristic
481C22#6395111yescharacteristic
482C4—21no—
483C4—21no—
484C4—42no—
485C4—121no—
486C4—121no—
487C4—121no—
488C4—361no—
489C4—362no—
490C4—361no—
491C3—21no—
492C3#6829411yescharacteristic, complemented
493C3#6832611yescharacteristic, complemented
494C2—21no—
495C2—21no—
496C2—241no—
497C2#1059040111yescharacteristic
498C2#1059041011yescharacteristic
499C2#1059061811yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenter#95D32
hypocenterC32#1603
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10592355C2semidirect
3. #10591190C2semidirect
5. C3×#4452C2semidirect
7. #10589148C2semidirect
42. #4452D3semidirect
426. C32#1603semidirect
492. C3#68294semidirect
493. C3#68326semidirect

Maximal subgroups

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

subgroupindex
#105949742
#105923552
#105911902
#105911812
C3×#44522
C3×#44512
#105891482
#683263
#682943