Finite Group Databasebeta

← #11873324

Subgroups — #11873324

Order 1152.

770 conjugacy classes of subgroups.

The subgroup lattice has 701 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5731C211yesmaximal, characteristic
2#10593885C211yesmaximal, characteristic
3#10592789C211yesmaximal, characteristic, complemented
4C3×#5090C211yesmaximal, characteristic, complemented
5#10591653C211yesmaximal, characteristic
6#10591653C211yesmaximal, characteristic
7#10591576C211yesmaximal, characteristic, complemented
8Dic3×#216C211yesmaximal, characteristic, complemented
9#10591559C211yesmaximal, characteristic
10#10591558C211yesmaximal, characteristic
11#10591541C211yesmaximal, characteristic, complemented
12#10591537C211yesmaximal, characteristic, complemented
13#10590292C211yesmaximal, characteristic, complemented
14#10590286C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic
16#83451—31nomaximal
17#80461—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19C32×C4⋊Q8C2211yescharacteristic
20C2×#3756C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C3×#898—21no—
30C3×#898—21no—
31C3×#889—21no—
32C3×#889—21no—
33C3×#872C2211yescharacteristic
34C3×#870C2211yescharacteristic
35C3×C4×Dic6C2211yescharacteristic
36#63878—21no—
37#63877—21no—
38#63844C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic
40#63841C2211yescharacteristic
41#63838—21no—
42#63837—21no—
43#63662C2211yescharacteristic
44#63662C2211yescharacteristic
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×C4⋊(C3⋊C8)C2211yescharacteristic
49#63576C2211yescharacteristic
50#63575C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#541—31no—
62#5731D311yescharacteristic
63#5572—31no—
64#5516—31no—
65C3×#462—31no—
66#5186—31no—
67#5186—31no—
68#5184—31no—
69Dic3×Q16—31no—
70#5090—31no—
71#5090—31no—
72#5090—61no—
73#5090D311yescharacteristic, complemented
74#5063—31no—
75#5063—31no—
76#5050—31no—
77#5050—31no—
78#5045—31no—
79#5045—31no—
80#5030—31no—
81#5030—31no—
82C4×#216—31no—
83C4×#216—31no—
84#5022—31no—
85#5000—31no—
86#4840—31no—
87#4829—31no—
88#4815—31no—
89#4814—31no—
90#4790—31no—
91#4789—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×D3×Dic3—21no—
99D3×Dic6—22no—
100D3×Dic6—22no—
101C32×C4⋊C4—21no—
102C32×C4⋊C4—21no—
103C32×C42C2311yescharacteristic
104#3756—22no—
105#3756—22no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#216—22no—
112C3×#216—22no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4D411yescharacteristic
116C3×(C2×D3)⋊C4D411yescharacteristic
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4D411yescharacteristic
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32—21no—
140Dic32—21no—
141#3127—91noSylow
142C2×D3×Q8—31no—
143C22×Dic6—31no—
144C2×C3×Q16—31no—
145C2×C3×Q16—31no—
146C3×C4⋊Q8—21no—
147C3×C4⋊Q8C2×D311yescharacteristic
148C3×C4⋊Q8C2×D311yescharacteristic
149C3×#126—61no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#125—61no—
153C3×#125—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×Q8—31no—
159C3×#117—31no—
160#946C2×D311yescharacteristic
161#946C2×D311yescharacteristic
162Q8×Dic3—31no—
163Q8×Dic3C2×D311yescharacteristic
164Q8×Dic3C2×D311yescharacteristic
165C2×#216—31no—
166C2×#216—31no—
167C2×#216—31no—
168C2×#216—31no—
169C2×#216—61no—
170C2×#216—61no—
171C2×#216C2×D311yescharacteristic
172C2×#216C2×D311yescharacteristic
173#926—31no—
174#898—21no—
175#898—21no—
176#892—31no—
177#892—61no—
178#889—21no—
179#889—21no—
180#887—31no—
181#887—61no—
182#887—61no—
183#887—61no—
184#877—61no—
185#877—61no—
186#872—61no—
187#872C2×D311yescharacteristic
188#870C2×D311yescharacteristic
189C4×Dic6—31no—
190C4×Dic6—31no—
191C4×Dic6—31no—
192C4×Dic6—31no—
193C4×Dic6—61no—
194C4×Dic6—61no—
195C4×Dic6C2×D311yescharacteristic
196C3×C4⋊C8—31no—
197C3×#103—31no—
198C3×#103—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—61no—
206#835—61no—
207#835C2×D311yescharacteristic
208#835C2×D311yescharacteristic
209#830—31no—
210#830—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213#818—31no—
214#817—31no—
215#816—31no—
216#816—31no—
217#815—31no—
218C8×Dic3—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#808—31no—
224#808—31no—
225#808—31no—
226#807—31no—
227#807—31no—
228#807—31no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233#803—31no—
234C4×C3⋊C8—31no—
235C22×C3×D3C2×D411yescharacteristic
236C32×Q8—21no—
237C32×Q8—21no—
238C32×Q8—21no—
239C32×Q8—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247#634—21no—
248#634#4112yes—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×C4×D3—21no—
257C3×C4×D3—21no—
258C3×Dic6—21no—
259C3×Dic6#4112yes—
260#627—24no—
261D3×Dic3—24no—
262C3⋊(C3⋊C8)—21no—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—31no—
267#519—91no—
268#485—91no—
269#485—91no—
270#479—91no—
271#479—91no—
272#462—31no—
273#462—91no—
274#451—91no—
275#451—91no—
276#441—91no—
277#441—91no—
278C4×Q16—91no—
279C4×Q16—91no—
280#433—91no—
281C2×C3×Q8—21no—
282C2×C3×Q8—21no—
283C2×C3×Q8—31no—
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×Q8C22×D311yescharacteristic
286C2×C3×Q8C22×D311yescharacteristic
287C2×C3×Q8C22×D311yescharacteristic
288C22×C3×C4—31no—
289C22×Dic3—61no—
290D3×Q8—62no—
291D3×Q8—62no—
292C2×C4×D3—61no—
293C2×C4×D3C22×D311yescharacteristic
294C2×Dic6—31no—
295C2×Dic6—31no—
296C2×Dic6—61no—
297C2×Dic6—62no—
298C2×Dic6—61no—
299C2×Dic6—61no—
300C2×Dic6—62no—
301C2×Dic6C22×D311yescharacteristic
302C3×Q16—62no—
303C3×Q16—62no—
304C2×C3×C8—31no—
305C2×C3×C8—31no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—41no—
316C3×C4⋊C4—41no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C22⋊C4—31no—
325C3×C22⋊C4—31no—
326C3×C22⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C42—21no—
329C3×C42—31no—
330C3×C42—61no—
331C3×C42—61no—
332C3×C42—61no—
333C3×C42C22×D311yescharacteristic
334C3×C42C22×D311yescharacteristic
335#217—61no—
336#216—22no—
337#216—22no—
338#216—62no—
339#216—62no—
340#216—62no—
341#216—62no—
342#216—122no—
343#216—122no—
344(C2×D3)⋊C4—21no—
345(C2×D3)⋊C4—21no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4#6711yescharacteristic
348(C2×D3)⋊C4#6711yescharacteristic
349C4⋊Dic3—21no—
350C4⋊Dic3—21no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3C22×D311yescharacteristic
356C4⋊Dic3C22×D311yescharacteristic
357C4⋊Dic3C22×D311yescharacteristic
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360Dic3⋊C4—21no—
361Dic3⋊C4—21no—
362Dic3⋊C4—21no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—121no—
369Dic3⋊C4#6711yescharacteristic
370Dic3⋊C4#6711yescharacteristic
371C4×Dic3—21no—
372C4×Dic3—21no—
373C4×Dic3—21no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—121no—
383C4×Dic3C22×D311yescharacteristic
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—61no—
389C2×C3⋊C8—61no—
390C2×C3⋊C8C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392C22×C32C22×D411yescharacteristic
393C2×C3×D3—21no—
394C2×C3×D3—21no—
395C2×C3×D3—21no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4—41no—
399C32×C4—41no—
400C32×C4C2×#4111yescharacteristic
401C32×C4C2×#4111yescharacteristic
402C3⋊Dic3—22no—
403C3⋊Dic3—41no—
404C3×Dic3—22no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—21no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C22×Q8—91no—
412C2×Q16—31no—
413C2×Q16—31no—
414C2×Q16—91no—
415C2×Q16—91no—
416C4⋊Q8D3211yescharacteristic
417#126—61no—
418#126—61no—
419#125—31no—
420#125—61no—
421#125—61no—
422C22⋊Q8—31no—
423C22⋊Q8—31no—
424C4×Q8—31no—
425C4×Q8—31no—
426C4×Q8—31no—
427C4×Q8—91no—
428C4×Q8—91no—
429C4×Q8—91no—
430C4×Q8—181no—
431C4×Q8—181no—
432#117—31no—
433#117—91no—
434#117—181no—
435#117—181no—
436#107—91no—
437#107—91no—
438#106—91no—
439#106—91no—
440C4⋊C8—31no—
441C4⋊C8—91no—
442#103—31no—
443#103—31no—
444#103—91no—
445#103—91no—
446#103—91no—
447#103—91no—
448#103—91no—
449#103—91no—
450C22⋊C8—91no—
451C22⋊C8—91no—
452#97—91no—
453C4×C8—91no—
454C23×C3—31no—
455C22×D3C2×#6711yescharacteristic
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—21no—
461C3×Q8—21no—
462C3×Q8—21no—
463C3×Q8—21no—
464C3×Q8—32no—
465C3×Q8—41no—
466C3×Q8—41no—
467C3×Q8—41no—
468C3×Q8—41no—
469C3×Q8—61no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4D3×D411yescharacteristic
489C2×C3×C4D3×D411yescharacteristic
490C2×C3×C4C2×#6711yescharacteristic
491C2×C3×C4C2×#6711yescharacteristic
492C2×C3×C4C23×D311yescharacteristic
493C2×C3×C4C23×D311yescharacteristic
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—64no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—121no—
504C2×Dic3—121no—
505C2×Dic3C2×#6711yescharacteristic
506C2×Dic3C2×#6711yescharacteristic
507C2×Dic3C2×#6711yescharacteristic
508C4×D3—21no—
509C4×D3—21no—
510C4×D3—64no—
511Dic6—21no—
512Dic6—32no—
513Dic6—32no—
514Dic6—62no—
515Dic6—64no—
516Dic6—64no—
517Dic6—61no—
518Dic6—61no—
519Dic6—121no—
520Dic6#23712yes—
521C3×C8—61no—
522C3×C8—61no—
523C3⋊C8—21no—
524C3⋊C8—21no—
525C3⋊C8—61no—
526C3⋊C8—61no—
527C3⋊C8—61no—
528C3⋊C8—61no—
529C3⋊C8—121no—
530C3⋊C8—121no—
531C2×C32#52511yescharacteristic
532C2×C32#57811yescharacteristic
533C2×C32#57811yescharacteristic
534C3×D3—41no—
535C2×Q8—31no—
536C2×Q8—91no—
537C2×Q8—181no—
538C2×Q8—182no—
539C2×Q8—182no—
540C2×Q8C2×D3211yescharacteristic
541C2×Q8C2×D3211yescharacteristic
542C22×C4—31no—
543C22×C4—181no—
544Q16—62no—
545Q16—62no—
546Q16—182no—
547Q16—182no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—91no—
551C2×C8—91no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—31no—
557C4⋊C4—31no—
558C4⋊C4—31no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—91no—
567C4⋊C4—181no—
568C4⋊C4—181no—
569C4⋊C4—181no—
570C22⋊C4—31no—
571C22⋊C4—31no—
572C22⋊C4—61no—
573C22⋊C4—61no—
574C22⋊C4—181no—
575C42—31no—
576C42—61no—
577C42—61no—
578C42—61no—
579C42—181no—
580C42—181no—
581C42—181no—
582C42—181no—
583C42C2×D3211yescharacteristic
584C22×C3—21no—
585C22×C3—61no—
586C22×C3—61no—
587C22×C3—61no—
588C22×C3C2×D3×D411yescharacteristic
589C22×C3C22×#6711yescharacteristic
590C2×D3—21no—
591C2×D3—21no—
592C2×D3—21no—
593C3×C4—22no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—61no—
606C3×C4—61no—
607C3×C4—62no—
608C3×C4—61no—
609C3×C4—81no—
610C3×C4—81no—
611C3×C4—121no—
612C3×C4—121no—
613C3×C4—121no—
614C3×C4C2×#23711yescharacteristic
615C3×C4D3×#4111yescharacteristic
616C3×C4D3×#4111yescharacteristic
617C3×C4D3×#4111yescharacteristic
618Dic3—21no—
619Dic3—21no—
620Dic3—21no—
621Dic3—22no—
622Dic3—41no—
623Dic3—41no—
624Dic3—41no—
625Dic3—62no—
626Dic3—62no—
627Dic3—122no—
628Dic3—121no—
629Dic3—121no—
630Dic3—241no—
631C32#312711yescharacteristic, complemented, Sylow
632C23—31no—
633Q8—21no—
634Q8—21no—
635Q8—21no—
636Q8—21no—
637Q8—32no—
638Q8—61no—
639Q8—92no—
640Q8—184no—
641Q8—181no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—184no—
654C2×C4—181no—
655C2×C4—181no—
656C2×C4D3×#6711yescharacteristic
657C2×C4D3×#6711yescharacteristic
658C2×C4C22×D3211yescharacteristic
659C8—61no—
660C8—61no—
661C8—181no—
662C8—181no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—121no—
667C2×C3#560611yescharacteristic
668C2×C3#576611yescharacteristic
669C2×C3#577911yescharacteristic
670C2×C3#582811yescharacteristic
671C2×C3#583811yescharacteristic
672C2×C3#583811yescharacteristic
673D3—41no—
674C22—61no—
675C22—61no—
676C22—61no—
677C22C2×D3×#6711yescharacteristic
678C4—21no—
679C4—21no—
680C4—41no—
681C4—41no—
682C4—61no—
683C4—61no—
684C4—62no—
685C4—61no—
686C4—121no—
687C4—121no—
688C4—121no—
689C4—182no—
690C4—361no—
691C4D3×#23711yescharacteristic
692C4#6431211yescharacteristic
693C3—21no—
694C3#8046111yescharacteristic, complemented
695C3#8345111yescharacteristic, complemented
696C2—121no—
697C2#1059530111yescharacteristic
698C2#1059532711yescharacteristic
699C2#1059532811yescharacteristic
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#3127
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. #10592789C2semidirect
4. C3×#5090C2semidirect
7. #10591576C2semidirect
8. Dic3×#216C2semidirect
11. #10591541C2semidirect
12. #10591537C2semidirect
13. #10590292C2semidirect
14. #10590286C2semidirect
73. #5090D3semidirect
631. C32#3127semidirect
694. C3#80461semidirect
695. C3#83451semidirect

Maximal subgroups

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

subgroupindex
C3×#57312
#105938852
#105927892
C3×#50902
#105916532
#105915762
Dic3×#2162
#105915592
#105915582
#105915412
#105915372
#105902922
#105902862
#105902532
#834513
#804613