Finite Group Databasebeta

← #11873310

Subgroups — #11873310

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
1#10595348C211yesmaximal, characteristic
2#10595347C211yesmaximal, characteristic
3#10592881C211yesmaximal, characteristic, complemented
4C3×#5186C211yesmaximal, characteristic
5C3×#5184C211yesmaximal, characteristic, complemented
6#10591615C211yesmaximal, characteristic, complemented
7#10591595C211yesmaximal, characteristic
8#10591580C211yesmaximal, characteristic, complemented
9Dic3×#216C211yesmaximal, characteristic, complemented
10#10591559C211yesmaximal, characteristic
11#10591537C211yesmaximal, characteristic, complemented
12#10590820C211yesmaximal, characteristic, complemented
13#10590794C211yesmaximal, characteristic, complemented
14#10590709C211yesmaximal, characteristic
15#10590697C211yesmaximal, characteristic
16#80177—31nomaximal
17#79836—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21#64153C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27#63872C2211yescharacteristic
28#63867—21no—
29#63859—21no—
30#63858—21no—
31#63857C2211yescharacteristic
32#63855—21no—
33#63855C2211yescharacteristic
34#63846—21no—
35#63844C2211yescharacteristic
36#63843—21no—
37#63843C2211yescharacteristic
38Dic3×Dic6—21no—
39Dic3×Dic6C2211yescharacteristic
40#63841—21no—
41#63841C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43#63662C2211yescharacteristic
44#63643C2211yescharacteristic
45#63641C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53#63576C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57#63567C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5812—31no—
62#5625—31no—
63#5583—31no—
64#5572—31no—
65C3×#451—31no—
66C3×#441—31no—
67#5228—31no—
68#5186D311yescharacteristic
69#5184D311yescharacteristic, complemented
70#5182—31no—
71#5182—31no—
72#5182—31no—
73#5182—61no—
74Dic3×Q16—31no—
75#5045—31no—
76C4×#216—31no—
77C4×#216—31no—
78#4868—31no—
79#4857—31no—
80#4815—31no—
81#4809—31no—
82#4799—31no—
83#4799—31no—
84#4796—31no—
85#4795—31no—
86#4790—31no—
87#4789—31no—
88#4723—31no—
89#4720—31no—
90#4716—31no—
91#4709—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8—22no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6—21no—
100C2×C3×Dic6C2311yescharacteristic
101C32×Q16—22no—
102C2×C32×C8C2311yescharacteristic
103#3756—22no—
104C4⋊(C3⋊Dic3)—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106#3750—21no—
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#216—22no—
112C3×(C2×D3)⋊C4—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C3×C4×Dic3—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124#3724—21no—
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3D411yescharacteristic
135(C2×D3)⋊Dic3D411yescharacteristic
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139Dic32—21no—
140#3719—22no—
141#3127—91noSylow
142C22×C3×Q8—31no—
143C2×D3×Q8C2×D311yescharacteristic
144C2×C3×Q16—21no—
145C2×C3×Q16—31no—
146C2×C3×Q16C2×D311yescharacteristic
147C2×C3×Q16C2×D311yescharacteristic
148C3×C22⋊Q8—31no—
149C3×C4×Q8—31no—
150C3×C4×Q8—31no—
151#946C2×D311yescharacteristic
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154Q8×Dic3—31no—
155Q8×Dic3—31no—
156Q8×Dic3—61no—
157Q8×Dic3—61no—
158Q8×Dic3—61no—
159Q8×Dic3C2×D311yescharacteristic
160Q8×Dic3C2×D311yescharacteristic
161#944—31no—
162#944—31no—
163#944—61no—
164C2×#216—31no—
165C2×#216—31no—
166C2×#216—31no—
167C2×#216—61no—
168C2×#216C2×D311yescharacteristic
169#926—31no—
170#926—31no—
171#926—61no—
172#926—61no—
173#924—31no—
174C2×Dic12—31no—
175#898—61no—
176#897—31no—
177#892—31no—
178#892—61no—
179#890—31no—
180#890—31no—
181#890—61no—
182#889—61no—
183#889—61no—
184#887—31no—
185#887—31no—
186#887—61no—
187#879—61no—
188#879—61no—
189#876—61no—
190#872—31no—
191#872—61no—
192#870—61no—
193C4×Dic6—31no—
194C4×Dic6—31no—
195C4×Dic6—61no—
196C3×#106—31no—
197C3×#103—31no—
198C3×#103—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×C22⋊C8—31no—
202C3×#97—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—61no—
207#835C2×D311yescharacteristic
208#835C2×D311yescharacteristic
209#835C2×D311yescharacteristic
210#830—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8C2×D311yescharacteristic
213#818—31no—
214#817—31no—
215#817C2×D311yescharacteristic
216#816—31no—
217#816—31no—
218#816—31no—
219#816—61no—
220#816C2×D311yescharacteristic
221#815C2×D311yescharacteristic
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227C8×Dic3—31no—
228#810—31no—
229#810—31no—
230#808—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234C4×C3⋊C8—31no—
235C22×C3×D3C2×D411yescharacteristic
236C32×Q8—21no—
237C32×Q8—21no—
238C32×Q8—21no—
239C32×Q8#4112yes—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2411yescharacteristic
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C2×D411yescharacteristic
246C2×C3⋊Dic3C2×D411yescharacteristic
247#634—21no—
248#634—21no—
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—24no—
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×Dic6—24no—
260C3×Dic6—21no—
261C3×Dic6#4112yes—
262C32×C8—21no—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—91no—
267#519—91no—
268#485—91no—
269#485—91no—
270#479—91no—
271#479—91no—
272#462—91no—
273#462—91no—
274#451—31no—
275#451—91no—
276#441—31no—
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×Q8—61no—
285C2×C3×Q8—62no—
286C2×C3×Q8—62no—
287C2×C3×Q8C22×D311yescharacteristic
288C2×C3×Q8C22×D311yescharacteristic
289C2×C3×Q8C22×D311yescharacteristic
290C2×C3×Q8C22×D311yescharacteristic
291C22×C3×C4—31no—
292C22×C3×C4—61no—
293D3×Q8—22no—
294D3×Q8—22no—
295C2×C4×D3—21no—
296C2×C4×D3C22×D311yescharacteristic
297C2×Dic6—21no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—61no—
301C2×Dic6C22×D311yescharacteristic
302C3×Q16—22no—
303C3×Q16—22no—
304C3×Q16—42no—
305C3×Q16—62no—
306C2×C3×C8—21no—
307C2×C3×C8—31no—
308C2×C3×C8—31no—
309C2×C3×C8C22×D311yescharacteristic
310C2×C3×C8C22×D311yescharacteristic
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C22⋊C4—61no—
318C3×C42—31no—
319C3×C42—61no—
320C3×C42—61no—
321#217—31no—
322#217—31no—
323#217—61no—
324#217—61no—
325#216—22no—
326#216—62no—
327#216—62no—
328#216—62no—
329#216—122no—
330(C2×D3)⋊C4—21no—
331(C2×D3)⋊C4—31no—
332(C2×D3)⋊C4—31no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335C4⋊Dic3—21no—
336C4⋊Dic3—21no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—121no—
350C4⋊Dic3C22×D311yescharacteristic
351C4⋊Dic3C22×D311yescharacteristic
352C4⋊Dic3C22×D311yescharacteristic
353Dic3⋊C4—21no—
354Dic3⋊C4—31no—
355Dic3⋊C4—31no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—121no—
368Dic3⋊C4—121no—
369C4×Dic3—21no—
370C4×Dic3—21no—
371C4×Dic3—31no—
372C4×Dic3—31no—
373C4×Dic3—61no—
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—61no—
383C4×Dic3—61no—
384C4×Dic3—121no—
385C4×Dic3C22×D311yescharacteristic
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—61no—
389C2×C3⋊C8C22×D311yescharacteristic
390C2×C3⋊C8C22×D311yescharacteristic
391Dic12—62no—
392C22×C32C22×D411yescharacteristic
393C2×C3×D3—21no—
394C2×C3×D3—21no—
395C2×C3×D3—21no—
396C32×C4—22no—
397C32×C4—41no—
398C32×C4C2×#4111yescharacteristic
399C32×C4C2×#4111yescharacteristic
400C3⋊Dic3—21no—
401C3⋊Dic3—21no—
402C3⋊Dic3—41no—
403C3⋊Dic3—41no—
404C3×Dic3—21no—
405C3×Dic3—22no—
406C3×Dic3—21no—
407C3×Dic3—21no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C22×Q8—31no—
412C2×Q16—31no—
413C2×Q16—91no—
414C2×Q16—91no—
415C2×Q16D3211yescharacteristic
416C4⋊Q8—91no—
417#126—181no—
418#126—181no—
419#125—91no—
420#125—181no—
421#125—181no—
422C22⋊Q8—31no—
423C22⋊Q8—91no—
424C4×Q8—31no—
425C4×Q8—31no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×Q8—91no—
429C4×Q8—91no—
430C4×Q8—181no—
431C4×Q8—181no—
432#117—91no—
433#117—91no—
434#117—181no—
435#117—181no—
436#107—91no—
437#107—91no—
438#106—31no—
439#106—91no—
440C4⋊C8—91no—
441C4⋊C8—91no—
442#103—31no—
443#103—31no—
444#103—31no—
445#103—31no—
446#103—91no—
447#103—91no—
448#103—91no—
449#103—91no—
450C22⋊C8—31no—
451C22⋊C8—91no—
452#97—31no—
453C4×C8—91no—
454C23×C3—31no—
455C22×D3D3×D411yescharacteristic
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—21no—
461C3×Q8—21no—
462C3×Q8—22no—
463C3×Q8—32no—
464C3×Q8—41no—
465C3×Q8—41no—
466C3×Q8—41no—
467C3×Q8—64no—
468C3×Q8—61no—
469C3×Q8#23512yes—
470C3×Q8#23712yes—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—64no—
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×C4C23×D311yescharacteristic
489C2×C3×C4C23×D311yescharacteristic
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—121no—
505C2×Dic3—121no—
506C2×Dic3D3×D411yescharacteristic
507C2×Dic3D3×D411yescharacteristic
508C2×Dic3D3×D411yescharacteristic
509C4×D3—24no—
510C4×D3—21no—
511C4×D3—21no—
512Dic6—24no—
513Dic6—21no—
514Dic6—61no—
515Dic6—61no—
516Dic6—61no—
517Dic6—61no—
518Dic6—121no—
519Dic6—121no—
520Dic6#23712yes—
521C3×C8—21no—
522C3×C8—21no—
523C3×C8—41no—
524C3×C8—61no—
525C3×C8—61no—
526C3⋊C8—21no—
527C3⋊C8—21no—
528C3⋊C8—61no—
529C3⋊C8—61no—
530C3⋊C8—121no—
531C2×C32#52511yescharacteristic
532C2×C32#57811yescharacteristic
533C2×C32#57811yescharacteristic
534C3×D3—41no—
535C2×Q8—31no—
536C2×Q8—61no—
537C2×Q8—62no—
538C2×Q8—62no—
539C2×Q8—91no—
540C2×Q8C2×D3211yescharacteristic
541C2×Q8C2×D3211yescharacteristic
542C22×C4—31no—
543C22×C4—61no—
544Q16—22no—
545Q16—62no—
546Q16—182no—
547Q16—182no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—91no—
551C2×C8C2×D3211yescharacteristic
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—91no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C4⋊C4—181no—
568C4⋊C4—181no—
569C4⋊C4—181no—
570C22⋊C4—61no—
571C22⋊C4—91no—
572C22⋊C4—91no—
573C22⋊C4—181no—
574C22⋊C4—181no—
575C42—31no—
576C42—61no—
577C42—61no—
578C42—91no—
579C42—181no—
580C42—181no—
581C42—181no—
582C42—181no—
583C42—181no—
584C22×C3—21no—
585C22×C3—61no—
586C22×C3—61no—
587C22×C3—61no—
588C22×C3C2×D3×D411yescharacteristic
589C22×C3C2×D3×D411yescharacteristic
590C2×D3—21no—
591C2×D3—21no—
592C2×D3—21no—
593C3×C4—22no—
594C3×C4—22no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—42no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—61no—
601C3×C4—61no—
602C3×C4—61no—
603C3×C4—62no—
604C3×C4—81no—
605C3×C4—121no—
606C3×C4—121no—
607C3×C4—121no—
608C3×C4C2×#23511yescharacteristic
609C3×C4C2×#23711yescharacteristic
610C3×C4C2×#23711yescharacteristic
611C3×C4D3×#4111yescharacteristic
612Dic3—21no—
613Dic3—21no—
614Dic3—21no—
615Dic3—22no—
616Dic3—41no—
617Dic3—41no—
618Dic3—41no—
619Dic3—62no—
620Dic3—61no—
621Dic3—61no—
622Dic3—61no—
623Dic3—61no—
624Dic3—121no—
625Dic3—121no—
626Dic3—121no—
627Dic3—121no—
628Dic3—121no—
629Dic3—241no—
630Dic3—241no—
631C32#312711yescharacteristic, complemented, Sylow
632C23—31no—
633Q8—21no—
634Q8—21no—
635Q8—21no—
636Q8—32no—
637Q8—64no—
638Q8—61no—
639Q8—181no—
640Q8—181no—
641Q8#380412yes—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—64no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—91no—
655C2×C4—91no—
656C2×C4—181no—
657C2×C4—181no—
658C2×C4C22×D3211yescharacteristic
659C8—21no—
660C8—61no—
661C8—61no—
662C8—181no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—121no—
667C2×C3#554711yescharacteristic
668C2×C3#558611yescharacteristic
669C2×C3#576611yescharacteristic
670C2×C3#577911yescharacteristic
671C2×C3#577911yescharacteristic
672C2×C3#577911yescharacteristic
673D3—41no—
674C22—61no—
675C22—61no—
676C22—61no—
677C22D32×D411yescharacteristic
678C4—22no—
679C4—41no—
680C4—61no—
681C4—62no—
682C4—61no—
683C4—61no—
684C4—121no—
685C4—121no—
686C4—121no—
687C4—181no—
688C4—181no—
689C4—361no—
690C4—361no—
691C4D3×#23711yescharacteristic
692C4C2×#380411yescharacteristic
693C3—21no—
694C3#7983611yescharacteristic, complemented
695C3#8017711yescharacteristic, complemented
696C2—121no—
697C2#1059476611yescharacteristic
698C2#1059476911yescharacteristic
699C2#1059512911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC2×Q16D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. #10592881C2semidirect
5. C3×#5184C2semidirect
6. #10591615C2semidirect
8. #10591580C2semidirect
9. Dic3×#216C2semidirect
11. #10591537C2semidirect
12. #10590820C2semidirect
13. #10590794C2semidirect
69. #5184D3semidirect
631. C32#3127semidirect
694. C3#79836semidirect
695. C3#80177semidirect

Maximal subgroups

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

subgroupindex
#105953482
#105953472
#105928812
C3×#51862
C3×#51842
#105916152
#105915952
#105915802
Dic3×#2162
#105915592
#105915372
#105908202
#105907942
#105907092
#105906972
#801773
#798363