Finite Group Databasebeta

← #11868734

Subgroups — #11868734

Order 1152.

800 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic
2C4×D3×Dic6C211yesmaximal, characteristic
3#10592790C211yesmaximal, characteristic, complemented
4C3×#5091C211yesmaximal, characteristic, complemented
5#10590600C212yesmaximal
6#10590493C212yesmaximal, complemented
7#10590492C212yesmaximal, complemented
8#10590436C212yesmaximal
9#10590336C211yesmaximal, characteristic
10#10590307C211yesmaximal, characteristic, complemented
11#10590285C211yesmaximal, characteristic, complemented
12#83367—31nomaximal
13#81108—31nomaximal
14C2×D3×Dic6C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C3×#946—21no—
18C3×Q8×Dic3—21no—
19C3×#897—21no—
20C3×#892C2212yes—
21C3×#890C2212yes—
22C3×#887—21no—
23C3×C42×D3C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26C4×#627—21no—
27D3×C4⋊Dic3C2211yescharacteristic
28D3×Dic3⋊C4—21no—
29C4×D3×Dic3—21no—
30#63844C2211yescharacteristic
31Dic3×Dic6C2211yescharacteristic
32#63837—21no—
33C2×#3711C2212yes—
34#63637C2212yes—
35#63634C2212yes—
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
37C3×#810C2212yes—
38C3×#807C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63574C2212yes—
41#63573C2212yes—
42Dic3⋊(C3⋊C8)C2212yes—
43#63567C2212yes—
44#63565C2212yes—
45C3×#533—31no—
46#5728D311yescharacteristic
47C4×D3×Q8—31no—
48C2×C4×Dic6—31no—
49C3×#477—31no—
50#5094—31no—
51#5094—31no—
52#5091—31no—
53#5091—31no—
54#5091—61no—
55#5091D311yescharacteristic, complemented
56#5063—32no—
57#5063—32no—
58#5020—31no—
59#5004—32no—
60#4995—32no—
61#4924—31no—
62#4881—32no—
63#4877—32no—
64#4851—31no—
65#4837—31no—
66#4802—32no—
67#4799—32no—
68C2×C32×Q8—21no—
69C2×#634C2311yescharacteristic
70C2×C3×C4×D3D411yescharacteristic
71C2×C3×C4×D3D411yescharacteristic
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×Dic6—21no—
74C2×C3×Dic6C2311yescharacteristic
75C2×#627—21no—
76C2×D3×Dic3—21no—
77C2×D3×Dic3—21no—
78D3×Dic6—22no—
79D3×Dic6Q814yescomplemented
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2312yes—
82C32×C42C2311yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—21no—
85C4×C3⋊Dic3—21no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—21no—
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3—21no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3C2311yescharacteristic
99C2×C3×C3⋊C8C2312yes—
100#3724—21no—
101Dic3⋊Dic3—21no—
102Dic3⋊Dic3—21no—
103Dic32—21no—
104Dic32—21no—
105#3711—24no—
106#3078—91noSylow
107C2×D3×Q8—31no—
108C22×Dic6—31no—
109C3×C4⋊Q8—21no—
110C3×C4⋊Q8—31no—
111C3×C4⋊Q8C2×D311yescharacteristic
112C3×C4⋊Q8C2×D311yescharacteristic
113C3×#125—32no—
114C3×C22⋊Q8—61no—
115C3×C22⋊Q8—61no—
116C3×C4×Q8—31no—
117C3×C4×Q8—61no—
118C3×C4×Q8—61no—
119C3×#117—32no—
120C2×C3×C42—31no—
121#946—21no—
122Q8×Dic3—21no—
123Q8×Dic3—31no—
124C2×C4⋊Dic3—31no—
125C2×Dic3⋊C4—61no—
126C2×C4×Dic3—61no—
127C2×#208—32no—
128C2×ΓL(1,𝔽25)—32no—
129#897—21no—
130#892C2×D312yes—
131D3×C4⋊C4—31no—
132D3×C4⋊C4—61no—
133#890C2×D312yes—
134#887—21no—
135#887—31no—
136#887—61no—
137C42×D3—61no—
138C42×D3C2×D311yescharacteristic
139#869C2×D311yescharacteristic
140C4×Dic6—31no—
141C4×Dic6—31no—
142C4×Dic6—31no—
143C4×Dic6—31no—
144C4×Dic6—61no—
145C4×Dic6—61no—
146C4×Dic6—61no—
147C4×Dic6—61no—
148C4×Dic6C2×D311yescharacteristic
149C3×#107—32no—
150C3×C4⋊C8—31no—
151C3×#103—32no—
152#835—32no—
153#817—32no—
154#816—32no—
155Dic3⋊C8—32no—
156#810—32no—
157#810—32no—
158#810—32no—
159#810—32no—
160#810—62no—
161#810C2×D312yes—
162#808—32no—
163#808—32no—
164#808—32no—
165#807—32no—
166#807—32no—
167#807—62no—
168#807C2×D312yes—
169C4⋊(C3⋊C8)—31no—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—32no—
172C4⋊(C3⋊C8)—61no—
173C4⋊(C3⋊C8)C2×D311yescharacteristic
174C22×C3×D3C2×D411yescharacteristic
175C32×Q8—42no—
176C2×C32×C4—22no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182#634—21no—
183#634C2×Q812yes—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3C2×D411yescharacteristic
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C3×C4×D3—22no—
191C3×C4×D3—41no—
192C3×C4×D3C2×Q812yes—
193C3×C4×D3#4112yes—
194C3×Dic6—21no—
195C3×Dic6—42no—
196C3×Dic6C2×Q812yes—
197#627—24no—
198D3×Dic3—24no—
199D3×Dic3—42no—
200C3⋊(C3⋊C8)—22no—
201C3×C3⋊C8—22no—
202#533—31no—
203C2×C4×Q8—91no—
204#479—92no—
205#479—92no—
206#477—31no—
207#477—91no—
208#475—91no—
209#475—91no—
210#428—92no—
211#423—91no—
212#419—92no—
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—31no—
216C2×C3×Q8—41no—
217C2×C3×Q8—61no—
218C22×C3×C4—31no—
219C22×C3×C4—31no—
220C22×C3×C4—31no—
221C22×Dic3—61no—
222C22×Dic3—61no—
223D3×Q8—34no—
224D3×Q8—62no—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C4×D3#6711yescharacteristic
228C2×C4×D3#6711yescharacteristic
229C2×C4×D3C22×D311yescharacteristic
230C2×Dic6—21no—
231C2×Dic6—31no—
232C2×Dic6—31no—
233C2×Dic6—34no—
234C2×Dic6—61no—
235C2×Dic6—62no—
236C2×Dic6—61no—
237C2×Dic6—61no—
238C2×Dic6C22×D311yescharacteristic
239C2×C3×C8—32no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—22no—
243C3×C4⋊C4—32no—
244C3×C4⋊C4—31no—
245C3×C4⋊C4—41no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4—62no—
248C3×C4⋊C4—61no—
249C3×C4⋊C4—61no—
250C3×C4⋊C4C22×D312yes—
251C3×C4⋊C4C22×D312yes—
252C3×C22⋊C4—62no—
253C3×C42—21no—
254C3×C42—31no—
255C3×C42—31no—
256C3×C42—31no—
257C3×C42—62no—
258C3×C42—61no—
259C3×C42C22×D311yescharacteristic
260C3×C42C22×D311yescharacteristic
261(C2×D3)⋊C4—22no—
262C4⋊Dic3—21no—
263C4⋊Dic3—22no—
264C4⋊Dic3—31no—
265C4⋊Dic3—31no—
266C4⋊Dic3—61no—
267C4⋊Dic3—61no—
268C4⋊Dic3—61no—
269C4⋊Dic3C22×D311yescharacteristic
270C4⋊Dic3C22×D312yes—
271Dic3⋊C4—21no—
272Dic3⋊C4—22no—
273Dic3⋊C4—61no—
274Dic3⋊C4—61no—
275Dic3⋊C4—61no—
276Dic3⋊C4—61no—
277Dic3⋊C4—61no—
278Dic3⋊C4—61no—
279Dic3⋊C4—121no—
280C4×Dic3—21no—
281C4×Dic3—22no—
282C4×Dic3—61no—
283C4×Dic3—61no—
284C4×Dic3—61no—
285C4×Dic3—61no—
286C4×Dic3—61no—
287C4×Dic3—61no—
288C4×Dic3—121no—
289C4×Dic3#6711yescharacteristic
290C4×Dic3#6711yescharacteristic
291C4×Dic3C22×D311yescharacteristic
292#208—64no—
293C2×C3⋊C8—32no—
294C2×C3⋊C8—32no—
295C2×C3⋊C8—62no—
296C2×C3⋊C8C22×D312yes—
297ΓL(1,𝔽25)—64no—
298C22×C32C22×D411yescharacteristic
299C2×C3×D3—21no—
300C2×C3×D3—21no—
301C2×C3×D3C22⋊Q812yes—
302C32×C4—21no—
303C32×C4—42no—
304C32×C4#13712yes—
305C32×C4C22×Q811yescharacteristic
306C32×C4C2×#4111yescharacteristic
307C3⋊Dic3—22no—
308C3⋊Dic3—41no—
309C3×Dic3—22no—
310C3×Dic3—21no—
311C3×Dic3—21no—
312C3×Dic3—42no—
313C3×Dic3—41no—
314C3×Dic3C22⋊Q812yes—
315C22×Q8—91no—
316C2×M16—92no—
317C4⋊Q8—31no—
318C4⋊Q8D3211yescharacteristic
319#125—32no—
320C22⋊Q8—61no—
321C22⋊Q8—61no—
322C4×Q8—31no—
323C4×Q8—61no—
324C4×Q8—61no—
325C4×Q8—91no—
326C4×Q8—91no—
327C4×Q8—91no—
328C4×Q8—181no—
329C4×Q8—181no—
330#117—32no—
331C2×C4⋊C4—91no—
332C2×C4⋊C4—181no—
333C2×C42—31no—
334C2×C42—181no—
335#107—32no—
336#107—92no—
337#106—92no—
338#106—92no—
339C4⋊C8—31no—
340C4⋊C8—92no—
341C4⋊C8—91no—
342#103—32no—
343#103—92no—
344#103—92no—
345#103—92no—
346C23×C3—31no—
347C22×D3C2×#6711yescharacteristic
348C3×Q8—32no—
349C3×Q8—42no—
350C3×Q8—42no—
351C3×Q8—61no—
352C3×Q8—82no—
353C3×Q8—122no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—31no—
360C2×C3×C4—32no—
361C2×C3×C4—32no—
362C2×C3×C4—31no—
363C2×C3×C4—31no—
364C2×C3×C4—42no—
365C2×C3×C4—61no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—61no—
369C2×C3×C4—121no—
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4C2×#6711yescharacteristic
373C2×C3×C4C2×#6711yescharacteristic
374C2×C3×C4C23×D311yescharacteristic
375C2×C3×C4C23×D311yescharacteristic
376C2×Dic3—21no—
377C2×Dic3—21no—
378C2×Dic3—22no—
379C2×Dic3—64no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—121no—
385C2×Dic3—121no—
386C2×Dic3—122no—
387C2×Dic3C2×#6711yescharacteristic
388C2×Dic3C2×#6711yescharacteristic
389C2×Dic3C2×#6711yescharacteristic
390C4×D3—22no—
391C4×D3—41no—
392C4×D3—64no—
393C4×D3—122no—
394C4×D3D3×Q812yes—
395C4×D3#23912yes—
396Dic6—21no—
397Dic6—32no—
398Dic6—32no—
399Dic6—42no—
400Dic6—62no—
401Dic6—64no—
402Dic6—61no—
403Dic6—61no—
404Dic6—64no—
405Dic6—121no—
406Dic6D3×Q812yes—
407C3×C8—62no—
408C3⋊C8—22no—
409C3⋊C8—62no—
410C3⋊C8—62no—
411C3⋊C8—122no—
412C2×C32C2×C22⋊Q811yescharacteristic
413C2×C32C2×#13711yescharacteristic
414C2×C32#57511yescharacteristic
415C3×D3—22no—
416C2×Q8—21no—
417C2×Q8—31no—
418C2×Q8—61no—
419C2×Q8—94no—
420C2×Q8—91no—
421C2×Q8—181no—
422C2×Q8—182no—
423C22×C4—31no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—181no—
427C22×C4—181no—
428M16—184no—
429C2×C8—32no—
430C2×C8—92no—
431C4⋊C4—21no—
432C4⋊C4—32no—
433C4⋊C4—31no—
434C4⋊C4—62no—
435C4⋊C4—62no—
436C4⋊C4—61no—
437C4⋊C4—61no—
438C4⋊C4—91no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C4⋊C4—181no—
442C4⋊C4—181no—
443C4⋊C4C2×D3212yes—
444C22⋊C4—62no—
445C42—31no—
446C42—31no—
447C42—31no—
448C42—62no—
449C42—61no—
450C42—181no—
451C42—181no—
452C42—181no—
453C42C2×D3211yescharacteristic
454C22×C3—21no—
455C22×C3—32no—
456C22×C3—61no—
457C22×C3—61no—
458C22×C3C2×D3×D411yescharacteristic
459C22×C3C22×#6711yescharacteristic
460C2×D3—21no—
461C2×D3—21no—
462C2×D3#94612yes—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—22no—
468C3×C4—32no—
469C3×C4—41no—
470C3×C4—42no—
471C3×C4—42no—
472C3×C4—61no—
473C3×C4—61no—
474C3×C4—62no—
475C3×C4—82no—
476C3×C4—122no—
477C3×C4—121no—
478C3×C4#91812yes—
479C3×C4#95112yes—
480C3×C4C2×D3×Q811yescharacteristic
481C3×C4C2×D3×Q811yescharacteristic
482C3×C4C2×#23911yescharacteristic
483C3×C4D3×#4111yescharacteristic
484Dic3—21no—
485Dic3—21no—
486Dic3—22no—
487Dic3—41no—
488Dic3—42no—
489Dic3—62no—
490Dic3—62no—
491Dic3—122no—
492Dic3—121no—
493Dic3—121no—
494Dic3—241no—
495Dic3#94612yes—
496C32#307811yescharacteristic, complemented, Sylow
497C23—31no—
498Q8—32no—
499Q8—42no—
500Q8—61no—
501Q8—92no—
502Q8—122no—
503Q8—184no—
504Q8—181no—
505C2×C4—22no—
506C2×C4—31no—
507C2×C4—32no—
508C2×C4—32no—
509C2×C4—31no—
510C2×C4—31no—
511C2×C4—61no—
512C2×C4—62no—
513C2×C4—61no—
514C2×C4—62no—
515C2×C4—121no—
516C2×C4—184no—
517C2×C4—181no—
518C2×C4—181no—
519C2×C4—362no—
520C2×C4D3×#6711yescharacteristic
521C2×C4D3×#6711yescharacteristic
522C2×C4C22×D3211yescharacteristic
523C8—62no—
524C8—182no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—62no—
529C2×C3D3×C22⋊Q811yescharacteristic
530C2×C3C2×#91811yescharacteristic
531C2×C3#577311yescharacteristic
532C2×C3C2×#94611yescharacteristic
533C2×C3#582211yescharacteristic
534C2×C3C2×#95111yescharacteristic
535D3—22no—
536C22—32no—
537C22—61no—
538C22—61no—
539C22C2×D3×#6711yescharacteristic
540C4—21no—
541C4—32no—
542C4—42no—
543C4—61no—
544C4—62no—
545C4—61no—
546C4—121no—
547C4—122no—
548C4—182no—
549C4—361no—
550C4#6394312yes—
551C4D32×Q811yescharacteristic
552C4D3×#23911yescharacteristic
553C3—21no—
554C3#8110811yescharacteristic, complemented
555C3#8336711yescharacteristic, complemented
556C2—62no—
557C2#1059509511yescharacteristic
558C2C2×#6394311yescharacteristic
559C2D3×#94611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32#3078
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10592790C2semidirect
4. C3×#5091C2semidirect
6. #10590493C2semidirect
7. #10590492C2semidirect
10. #10590307C2semidirect
11. #10590285C2semidirect
55. #5091D3semidirect
79. D3×Dic6Q8semidirect
496. C32#3078semidirect
554. C3#81108semidirect
555. C3#83367semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
C4×D3×Dic62
#105927902
C3×#50912
#105906002
#105904932
#105904922
#105904362
#105903362
#105903072
#105902852
#833673
#811083