Finite Group Databasebeta

← #11778297

Subgroups — #11778297

Order 1152.

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

normal subgroups only

This group has 567 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#10594980C211yesmaximal, characteristic
2#10592437C211yesmaximal, characteristic
3#10591354C211yesmaximal, characteristic, complemented
4#10591190C211yesmaximal, characteristic, complemented
5C3×#4469C211yesmaximal, characteristic, complemented
6C3×#4467C211yesmaximal, characteristic, complemented
7#10589151C211yesmaximal, characteristic
8#68326—31nomaximal
9#68132—31nomaximal
10C22×#634C2211yescharacteristic
11#64139C2211yescharacteristic
12C2×#3744—21no—
13C3×#924C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15#63966—21no—
16C2×Dic3⋊Dic3—21no—
17#63952—21no—
18#63897—21no—
19#63888—21no—
20#63848—21no—
21#63845—21no—
22C2×#3719—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63643—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63579—21no—
28#63567—21no—
29#5645—31no—
30#5515—31no—
31#5050—31no—
32#4979—31no—
33#4739—31no—
34#4738—31no—
35#4738—31no—
36#4738—61no—
37#4656—31no—
38C3×#328—31no—
39C3×#324—31no—
40#4470—31no—
41#4469D311yescharacteristic, complemented
42#4467D311yescharacteristic, complemented
43#4451—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—42no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D411yescharacteristic
53C22×C3×Dic3D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C2×#624—21no—
56C2×C32×C8—21no—
57#3752—21no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59#3744—42no—
60C3×#217—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66#3724—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—42no—
70#3722—21no—
71#3722—21no—
72#3722—21no—
73Dic32—21no—
74#3719—42no—
75#1603—91noSylow
76C22×Dic6—31no—
77C22×Dic6—31no—
78C22×Dic6—61no—
79C3×C22⋊Q8—31no—
80C2×C3×C4⋊C4—31no—
81#946—61no—
82C2×#216—61no—
83#930—31no—
84#930—31no—
85#930—61no—
86#929—61no—
87C4×#67—61no—
88C2×C4⋊Dic3—61no—
89#924C2×D311yescharacteristic
90C2×Dic3⋊C4—61no—
91C2×Dic3⋊C4C2×D311yescharacteristic
92C2×Dic12—61no—
93C2×#204—61no—
94C2×#204—61no—
95C2×#204—62no—
96#898—61no—
97#898—61no—
98#896—61no—
99#894—61no—
100#894—61no—
101#890—61no—
102#889—61no—
103#886—61no—
104#67⋊C4—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
124#638—41no—
125#638—41no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C4⋊(C3⋊D3)—41no—
131#634—22no—
132#634—22no—
133#634—41no—
134#634—41no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—21no—
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×Dic6—41no—
146#624—81no—
147C32×C8—41no—
148C3×C3⋊C8—41no—
149#539—91no—
150#451—91no—
151#448—91no—
152#395—91no—
153#328—31no—
154#327—91no—
155#324—31no—
156C2×C3×Q8—31no—
157C22×C3×C4—21no—
158C22×C3×C4—31no—
159C22×C3×C4—31no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C2×#67—61no—
164C2×#67—61no—
165C2×#67—121no—
166C22×Dic3—21no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—121no—
170C22×Dic3D1211yescharacteristic
171C22×Dic3D1211yescharacteristic
172C2×D12—31no—
173C2×D12—31no—
174C2×D12—61no—
175C2×C4×D3—61no—
176C2×C4×D3—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×Dic6D1211yescharacteristic
187C2×C3×C8—22no—
188C2×C3×C8—21no—
189C2×C3×C8—21no—
190C2×C3×C8—61no—
191C3×C4⋊C4—31no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195C3×C22⋊C4—61no—
196#217—21no—
197#216—122no—
198(C2×D3)⋊C4—61no—
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—121no—
207C4⋊Dic3—31no—
208C4⋊Dic3—31no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—122no—
213C4⋊Dic3D1211yescharacteristic
214Dic3⋊C4—21no—
215Dic3⋊C4—21no—
216Dic3⋊C4—21no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—61no—
220Dic3⋊C4—61no—
221Dic3⋊C4—122no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C2×C3⋊C8—21no—
225Dic12—122no—
226#204—122no—
227#204—122no—
228#204—124no—
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—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—91no—
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×C3C2×D1211yescharacteristic
267C23×C3D3×D411yescharacteristic
268C22×D3—61no—
269C22×D3—61no—
270C22×D3—121no—
271C3×Q8—121no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—42no—
277C2×C3×C4—62no—
278C2×C3×C4—61no—
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—121no—
292#67—121no—
293#67—121no—
294#67—121no—
295#67—241no—
296#67—241no—
297C2×Dic3—22no—
298C2×Dic3—21no—
299C2×Dic3—21no—
300C2×Dic3—21no—
301C2×Dic3—21no—
302C2×Dic3—21no—
303C2×Dic3—21no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—122no—
312C2×Dic3—121no—
313C2×Dic3—122no—
314C2×Dic3—121no—
315C2×Dic3—121no—
316C2×Dic3—122no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319D12—121no—
320D12—121no—
321D12—122no—
322C4×D3—241no—
323C4×D3—241no—
324Dic6—41no—
325Dic6—64no—
326Dic6—62no—
327Dic6—62no—
328Dic6—62no—
329Dic6—62no—
330Dic6—122no—
331Dic6—122no—
332Dic6—121no—
333Dic6—121no—
334Dic6—121no—
335Dic6—121no—
336Dic6—122no—
337C3×C8—42no—
338C3×C8—41no—
339C3×C8—41no—
340C3×C8—121no—
341C3⋊C8—41no—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32#45211yescharacteristic
345C2×C32#45611yescharacteristic
346C2×C32B(4,𝔽2)11yescharacteristic
347C3⋊D3—81no—
348C2×Q8—31no—
349C2×Q8—181no—
350C2×Q8—181no—
351C2×Q8—362no—
352C2×D4—91no—
353C2×D4—181no—
354C22×C4—31no—
355C22×C4—31no—
356C22×C4—61no—
357C22×C4—181no—
358C22×C4—181no—
359C22×C4C2×D3211yescharacteristic
360Q16—362no—
361SD16—362no—
362C2×C8—21no—
363C2×C8—61no—
364C4⋊C4—31no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—91no—
369C4⋊C4—181no—
370C4⋊C4—181no—
371C4⋊C4—181no—
372C4⋊C4—362no—
373C22⋊C4—61no—
374C22⋊C4—181no—
375C22⋊C4—181no—
376C22⋊C4—181no—
377C22⋊C4—181no—
378C42—181no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3#88211yescharacteristic
389C22×C3#88211yescharacteristic
390C22×C3#90411yescharacteristic
391C22×C3#90911yescharacteristic
392C22×C3#91611yescharacteristic
393C22×C3#91811yescharacteristic
394C2×D3—121no—
395C2×D3—121no—
396C2×D3—121no—
397C2×D3—121no—
398C2×D3—121no—
399C2×D3—121no—
400C2×D3—241no—
401C2×D3—241no—
402C2×D3—241no—
403C3×C4—22no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—41no—
409C3×C4—122no—
410C3×C4—121no—
411C3×C4—121no—
412C3×C4—121no—
413C3×C4—121no—
414Dic3—42no—
415Dic3—41no—
416Dic3—41no—
417Dic3—41no—
418Dic3—41no—
419Dic3—124no—
420Dic3—121no—
421Dic3—122no—
422Dic3—122no—
423Dic3—121no—
424Dic3—241no—
425C32#160311yescharacteristic, complemented, Sylow
426C23—181no—
427C23D3×D1211yescharacteristic
428Q8—121no—
429Q8—182no—
430Q8—182no—
431Q8—361no—
432Q8—361no—
433D4—361no—
434D4—361no—
435D4—361no—
436C2×C4—41no—
437C2×C4—62no—
438C2×C4—61no—
439C2×C4—61no—
440C2×C4—61no—
441C2×C4—61no—
442C2×C4—61no—
443C2×C4—61no—
444C2×C4—121no—
445C2×C4—121no—
446C2×C4—121no—
447C2×C4—182no—
448C2×C4—181no—
449C2×C4—361no—
450C2×C4—361no—
451C2×C4—721no—
452C2×C4D3×D1211yescharacteristic
453C2×C4#381111yescharacteristic
454C8—41no—
455C8—121no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—41no—
464C2×C3—41no—
465C2×C3#473311yescharacteristic
466C2×C3#474111yescharacteristic
467C2×C3#474111yescharacteristic
468C2×C3#475211yescharacteristic
469C2×C3#480811yescharacteristic
470C2×C3#482611yescharacteristic
471D3—241no—
472D3—241no—
473D3—481no—
474C22—21no—
475C22—21no—
476C22—361no—
477C22—361no—
478C22—361no—
479C22#6380111yescharacteristic
480C22#6380611yescharacteristic
481C22#6392311yescharacteristic
482C4—21no—
483C4—21no—
484C4—122no—
485C4—121no—
486C4—121no—
487C4—121no—
488C4—121no—
489C4—362no—
490C4—361no—
491C3—21no—
492C3#6813211yescharacteristic, complemented
493C3#6832611yescharacteristic, complemented
494C2—21no—
495C2—21no—
496C2—721no—
497C2#1059041011yescharacteristic
498C2#1059097011yescharacteristic
499C2#1059102111yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#64139C22
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
3. #10591354C2semidirect
4. #10591190C2semidirect
5. C3×#4469C2semidirect
6. C3×#4467C2semidirect
41. #4469D3semidirect
42. #4467D3semidirect
425. C32#1603semidirect
492. C3#68132semidirect
493. C3#68326semidirect

Maximal subgroups

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

subgroupindex
#105949802
#105924372
#105913542
#105911902
C3×#44692
C3×#44672
#105891512
#683263
#681323