Finite Group Databasebeta

← #11803481

Subgroups — #11803481

Order 1152.

1277 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64086C211yesmaximal, characteristic
2C2×#63982C211yesmaximal, characteristic
3C2×C4×#627C211yesmaximal, characteristic, complemented
4C3×#4944C212yesmaximal
5#10591720C211yesmaximal, characteristic
6#10591701C212yesmaximal
7#10591396C211yesmaximal, characteristic, complemented
8#10591337C211yesmaximal, characteristic, complemented
9#10591332C212yesmaximal, complemented
10#10591257C211yesmaximal, characteristic, complemented
11#10591234C212yesmaximal, complemented
12#75460—32nomaximal
13C23×C3⋊Dic3C2211yescharacteristic
14C22×#627C2211yescharacteristic
15C2×C32×C22⋊C4C2211yescharacteristic
16C2×#3757C2211yescharacteristic
17C2×#3750C2211yescharacteristic
18C2×#3750C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21#64086—24no—
22C2×C3×#217C2212yes—
23C2×C3×#217C2212yes—
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2212yes—
26#63982C418yescomplemented
27C2×#3724C2211yescharacteristic
28C2×#3724C2211yescharacteristic
29C2×#3724C2211yescharacteristic
30C2×Dic3⋊Dic3C2212yes—
31C2×Dic3⋊Dic3C2212yes—
32C2×Dic32C2212yes—
33C4×#627—24no—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×#878—32no—
40C2×#877—32no—
41C2×#877—61no—
42C2×C4×Dic6—32no—
43C3×#388—32no—
44#4976—32no—
45#4972—32no—
46#4951—32no—
47#4944—32no—
48#4944D312yes—
49#4942—32no—
50#4933—32no—
51#4653—32no—
52#4649—32no—
53#4647—32no—
54#4646—32no—
55C24×C32C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3—22no—
59C22×C3⋊Dic3—22no—
60C22×C3⋊Dic3C2×C414yes—
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3⋊Dic3C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C2×#627—22no—
70C2×#627—22no—
71C2×#627C2×C414yes—
72C32×C22⋊C4—22no—
73#3757—22no—
74#3750—22no—
75#3750—22no—
76C4×C3⋊Dic3—22no—
77C4×C3⋊Dic3D414yes—
78C3×#217—42no—
79C3×#217C2×C418yes—
80C3×Dic3⋊C4—42no—
81C3×C4×Dic3—24no—
82#3724—22no—
83#3724—22no—
84#3724C2×C414yes—
85Dic3⋊Dic3—24no—
86Dic3⋊Dic3C2×C418yes—
87Dic32—42no—
88#2323—91noSylow
89C23×Dic3—32no—
90C23×Dic3—61no—
91C22×Dic6—32no—
92C2×C3×C4⋊C4—32no—
93C2×C3×C22⋊C4—21no—
94C2×C3×C22⋊C4—32no—
95C2×C3×C22⋊C4—32no—
96C2×C3×C22⋊C4C2×D312yes—
97C2×C3×C42—32no—
98C2×#217—32no—
99C2×#217—61no—
100C2×#217C2×D312yes—
101C2×#217C2×D312yes—
102C2×C4⋊Dic3—32no—
103C2×C4⋊Dic3—32no—
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4—32no—
107C2×Dic3⋊C4—32no—
108C2×Dic3⋊C4—32no—
109C2×Dic3⋊C4—32no—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4—61no—
112C2×Dic3⋊C4—61no—
113C2×Dic3⋊C4C2×D312yes—
114C2×C4×Dic3—32no—
115C2×C4×Dic3—32no—
116C2×C4×Dic3—32no—
117C2×C4×Dic3—32no—
118C2×C4×Dic3—61no—
119C2×C4×Dic3—61no—
120C2×C4×Dic3C2×D312yes—
121#878—316no—
122#877—68no—
123#877—68no—
124C4×Dic6—68no—
125C3×#95—32no—
126C3×#95—32no—
127C3⋊#95—32no—
128C3⋊#95—32no—
129C3⋊#95—32no—
130C3⋊#95—32no—
131C3⋊#95—32no—
132C3⋊#95—32no—
133C3⋊#95C2×D312yes—
134C3⋊#95C2×D312yes—
135C23×C32—21no—
136C23×C32—21no—
137C23×C32—21no—
138C23×C32—21no—
139C23×C32—21no—
140C23×C32—21no—
141C23×C32C22×C412yes—
142C23×C32C2411yescharacteristic
143C2×C32×C4—21no—
144C2×C32×C4—21no—
145C2×C32×C4—21no—
146C2×C32×C4—21no—
147C2×C32×C4—21no—
148C2×C32×C4C2×D412yes—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—28no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3C22×C412yes—
158C2×C3⋊Dic3C22×C412yes—
159C2×C3⋊Dic3C2×D412yes—
160C2×C3⋊Dic3C2×D412yes—
161C2×C3⋊Dic3#4112yes—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3C22×C414yes—
173C2×C3×Dic3C22×C414yes—
174#627—28no—
175C2×C22⋊Q8—91no—
176C2×C4×Q8—91no—
177C2×#117—91no—
178#391—91no—
179#389—92no—
180#389—91no—
181#388—32no—
182#388—92no—
183#387—92no—
184#380—91no—
185C4×C4⋊C4—91no—
186C24×C3—21no—
187C24×C3C22×D312yes—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—32no—
191C22×C3×C4—32no—
192C22×C3×C4—32no—
193C22×C3×C4—32no—
194C22×C3×C4C22×D312yes—
195C22×C3×C4C22×D312yes—
196C22×Dic3—32no—
197C22×Dic3—38no—
198C22×Dic3—32no—
199C22×Dic3—32no—
200C22×Dic3—32no—
201C22×Dic3—61no—
202C22×Dic3—61no—
203C22×Dic3—64no—
204C22×Dic3—61no—
205C22×Dic3—61no—
206C22×Dic3—64no—
207C22×Dic3—64no—
208C22×Dic3—64no—
209C22×Dic3—64no—
210C22×Dic3C22×D312yes—
211C22×Dic3C22×D312yes—
212C22×Dic3C22×D312yes—
213C22×Dic3C22×D312yes—
214C2×Dic6—38no—
215C2×Dic6—64no—
216C2×Dic6—64no—
217C3×C4⋊C4—122no—
218C3×C22⋊C4—24no—
219C3×C22⋊C4—24no—
220C3×C22⋊C4—38no—
221C3×C22⋊C4—122no—
222C3×C42—64no—
223#217—42no—
224#217—64no—
225#217—64no—
226#217C4×D318yes—
227C4⋊Dic3—38no—
228C4⋊Dic3—64no—
229Dic3⋊C4—38no—
230Dic3⋊C4—38no—
231Dic3⋊C4—42no—
232Dic3⋊C4—64no—
233Dic3⋊C4—64no—
234Dic3⋊C4—64no—
235Dic3⋊C4—64no—
236Dic3⋊C4—64no—
237Dic3⋊C4—64no—
238Dic3⋊C4—64no—
239C4×Dic3—24no—
240C4×Dic3—38no—
241C4×Dic3—64no—
242C4×Dic3—64no—
243C4×Dic3—64no—
244C4×Dic3—122no—
245C4×Dic3—122no—
246C22×C32—22no—
247C22×C32—22no—
248C22×C32—22no—
249C22×C32—41no—
250C22×C32—41no—
251C22×C32—41no—
252C22×C32—41no—
253C22×C32C23×C411yescharacteristic
254C22×C32C22×D411yescharacteristic
255C22×C32C2×#4111yescharacteristic
256C22×C32H(5,𝔽2)11yescharacteristic
257C22×C322−1+411yescharacteristic
258C22×C322−1+411yescharacteristic
259C22×C322−1+411yescharacteristic
260C32×C4—22no—
261C32×C4—41no—
262C3⋊Dic3—22no—
263C3⋊Dic3—22no—
264C3⋊Dic3—41no—
265C3⋊Dic3C4×D414yes—
266C3×Dic3—24no—
267C3×Dic3—24no—
268C3×Dic3—42no—
269C3×Dic3—42no—
270C22×Q8—91no—
271C23×C4—91no—
272C22⋊Q8—98no—
273C4×Q8—184no—
274#117—184no—
275C2×C4⋊C4—32no—
276C2×C4⋊C4—91no—
277C2×C4⋊C4—92no—
278C2×C4⋊C4—91no—
279C2×C4⋊C4—92no—
280C2×C4⋊C4—91no—
281C2×C4⋊C4—91no—
282C2×C4⋊C4—91no—
283C2×C22⋊C4—32no—
284C2×C22⋊C4—32no—
285C2×C22⋊C4—91no—
286C2×C22⋊C4D3211yescharacteristic
287C2×C42—32no—
288C2×C42—91no—
289C2×C42—91no—
290C2×C42—92no—
291#95—32no—
292#95—32no—
293#95—92no—
294#95—92no—
295#95—92no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—22no—
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—22no—
304C23×C3—21no—
305C23×C3—22no—
306C23×C3—41no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3—41no—
310C23×C3C2×C4×D314yes—
311C23×C3C23×D312yes—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—34no—
320C2×C3×C4—34no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4D3×D414yes—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—34no—
347C2×Dic3—34no—
348C2×Dic3—34no—
349C2×Dic3—34no—
350C2×Dic3—34no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—616no—
357C2×Dic3—62no—
358C2×Dic3—616no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—121no—
369C2×Dic3—121no—
370C2×Dic3—121no—
371C2×Dic3—121no—
372C2×Dic3C2×C4×D314yes—
373C2×Dic3C2×C4×D314yes—
374Dic6—616no—
375C2×C32—42no—
376C2×C32C2×C4×D411yescharacteristic
377C2×C32#51911yescharacteristic
378C2×C32#52011yescharacteristic
379C2×C32#53611yescharacteristic
380C2×C32#53711yescharacteristic
381C2×C32#54111yescharacteristic
382C2×C32#54211yescharacteristic
383C24C2×D3211yescharacteristic
384C2×Q8—94no—
385C2×Q8—182no—
386C2×Q8—182no—
387C22×C4—32no—
388C22×C4—32no—
389C22×C4—32no—
390C22×C4—32no—
391C22×C4—91no—
392C22×C4—91no—
393C22×C4—91no—
394C22×C4—94no—
395C22×C4—91no—
396C22×C4—182no—
397C22×C4—182no—
398C22×C4C2×D3211yescharacteristic
399C22×C4C2×D3211yescharacteristic
400C4⋊C4—94no—
401C4⋊C4—98no—
402C4⋊C4—122no—
403C4⋊C4—182no—
404C4⋊C4—182no—
405C4⋊C4—184no—
406C4⋊C4—182no—
407C4⋊C4—182no—
408C22⋊C4—22no—
409C22⋊C4—38no—
410C22⋊C4—122no—
411C22⋊C4—182no—
412C42—64no—
413C42—94no—
414C42—182no—
415C42—362no—
416C22×C3—24no—
417C22×C3—24no—
418C22×C3—24no—
419C22×C3—24no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—42no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3C22×C4×D312yes—
438C22×C3C2×D3×D412yes—
439C22×C3#100412yes—
440C22×C3D3×#4112yes—
441C22×C3#101012yes—
442C22×C3#101012yes—
443C22×C3#101012yes—
444C3×C4—24no—
445C3×C4—42no—
446C3×C4—42no—
447C3×C4—42no—
448C3×C4—64no—
449C3×C4—64no—
450C3×C4—122no—
451C3×C4—122no—
452Dic3—24no—
453Dic3—24no—
454Dic3—38no—
455Dic3—42no—
456Dic3—42no—
457Dic3—64no—
458Dic3—64no—
459Dic3—64no—
460Dic3—64no—
461Dic3—122no—
462Dic3—122no—
463Dic3—122no—
464C32#232311yescharacteristic, complemented, Sylow
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23C4×D3212yes—
472C23C22×D3211yescharacteristic
473Q8—188no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—34no—
480C2×C4—34no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—92no—
492C2×C4—92no—
493C2×C4—92no—
494C2×C4—92no—
495C2×C4—92no—
496C2×C4—188no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4#381112yes—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—44no—
513C2×C3—44no—
514C2×C3#551612yes—
515C2×C3C4×D3×D412yes—
516C2×C3#554612yes—
517C2×C3#560812yes—
518C2×C3#564812yes—
519C2×C3#566912yes—
520C2×C3#570112yes—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22C2×C4×D3211yescharacteristic
529C22#6430611yescharacteristic
530C22#6430911yescharacteristic
531C22#6430911yescharacteristic
532C22#6430911yescharacteristic
533C22#6431311yescharacteristic
534C22C2×#381111yescharacteristic
535C4—22no—
536C4—41no—
537C4—64no—
538C4—64no—
539C4—94no—
540C4—122no—
541C4—122no—
542C4—182no—
543C4—182no—
544C4—361no—
545C3—21no—
546C3#7546012yescomplemented
547C2—42no—
548C2#1059405111yescharacteristic
549C2#1059422411yescharacteristic
550C2#1059424511yescharacteristic
551C2#1059424911yescharacteristic
552C2C4×#381111yescharacteristic
553C2#1059524011yescharacteristic
554C2#1059527111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2323
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#627C2semidirect
7. #10591396C2semidirect
8. #10591337C2semidirect
9. #10591332C2semidirect
10. #10591257C2semidirect
11. #10591234C2semidirect
26. #63982C4semidirect
464. C32#2323semidirect
546. C3#75460semidirect

Maximal subgroups

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

subgroupindex
C2×#640862
C2×#639822
C2×C4×#6272
C3×#49442
#105917202
#105917012
#105913962
#105913372
#105913322
#105912572
#105912342
#754603