Finite Group Databasebeta

← #11873340

Subgroups — #11873340

Order 1152.

771 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594357C211yesmaximal, characteristic
2#10594346C211yesmaximal, characteristic
3#10592572C211yesmaximal, characteristic, complemented
4C3×#4888C211yesmaximal, characteristic
5C3×#4877C211yesmaximal, characteristic, complemented
6#10590952C211yesmaximal, characteristic
7#10590808C211yesmaximal, characteristic, complemented
8#10590790C211yesmaximal, characteristic, complemented
9#10590698C211yesmaximal, characteristic
10#10590604C211yesmaximal, characteristic
11#10590561C211yesmaximal, characteristic, complemented
12#10590490C211yesmaximal, characteristic, complemented
13#10590485C211yesmaximal, characteristic, complemented
14#10590485C211yesmaximal, characteristic, complemented
15#10590428C211yesmaximal, characteristic
16#81499—31nomaximal
17#81211—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19C2×#3746C2211yescharacteristic
20#64096C2211yescharacteristic
21#64096C2211yescharacteristic
22C3×#897C2211yescharacteristic
23C3×#892C2211yescharacteristic
24C3×#890C2211yescharacteristic
25C3×#887C2211yescharacteristic
26C4×#627—21no—
27#63878—21no—
28#63877—21no—
29#63872—21no—
30#63866C2211yescharacteristic
31#63862—21no—
32#63858—21no—
33#63857C2211yescharacteristic
34#63855C2211yescharacteristic
35#63846—21no—
36#63844C2211yescharacteristic
37#63843C2211yescharacteristic
38#63843C2211yescharacteristic
39#63837—21no—
40C2×#3719C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C32×#107C2211yescharacteristic
44C8×C3⋊Dic3C2211yescharacteristic
45#63637C2211yescharacteristic
46#63637C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#808C2211yescharacteristic
54C3×#808C2211yescharacteristic
55#63576C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic
61#5698—31no—
62#5625—31no—
63#5572—31no—
64#5516—31no—
65C3×#485—31no—
66C3×#479—31no—
67#5063—31no—
68#5050—31no—
69#5031—31no—
70#4996—31no—
71#4888D311yescharacteristic
72#4877D311yescharacteristic, complemented
73#4873—31no—
74#4873—31no—
75#4873—61no—
76#4868—31no—
77#4857—31no—
78#4853—31no—
79#4853—31no—
80#4849—31no—
81#4840—31no—
82#4809—31no—
83#4809—31no—
84#4795—31no—
85#4795—31no—
86#4790—31no—
87#4790—31no—
88#4789—31no—
89#4789—31no—
90#4739—31no—
91#4720—31no—
92C2×#634C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×C4×D3C2311yescharacteristic
95C2×C3×Dic6C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×D3×Dic3—21no—
99D3×Dic6—22no—
100D3×Dic6—22no—
101C2×C32×C8C2311yescharacteristic
102C32×C4⋊C4C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104#3750—21no—
105#3750—21no—
106C4×C3⋊Dic3—21no—
107C4×C3⋊Dic3—21no—
108C4×C3⋊Dic3C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110#3746—22no—
111C3×(C2×D3)⋊C4—21no—
112C3×(C2×D3)⋊C4—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4—21no—
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)⋊Dic3D411yescharacteristic
134(C2×D3)⋊Dic3D411yescharacteristic
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138#3719—22no—
139#3719—22no—
140#3718—22no—
141#3127—91noSylow
142C2×D3×Q8—31no—
143C22×Dic6—31no—
144C3×#125—31no—
145C3×C22⋊Q8—31no—
146C3×C4×Q8—31no—
147C3×#117—31no—
148Q8×Dic3—31no—
149Q8×Dic3—31no—
150#944—31no—
151C2×#216—31no—
152C2×#216—31no—
153C2×#216—31no—
154C2×#216—31no—
155#926—31no—
156#924—31no—
157C2×Dic12—31no—
158C2×Dic12—31no—
159C2×Dic12—31no—
160C2×Dic12—31no—
161C2×Dic12—61no—
162#898—61no—
163#898—61no—
164#897—31no—
165#897C2×D311yescharacteristic
166#892—61no—
167#892C2×D311yescharacteristic
168#890—61no—
169#890—61no—
170#890—61no—
171#890C2×D311yescharacteristic
172#889—61no—
173#887—31no—
174#887—31no—
175#887—31no—
176#887—31no—
177#887—31no—
178#887—31no—
179#887—31no—
180#887—61no—
181#887—61no—
182#887—61no—
183#887C2×D311yescharacteristic
184#879—61no—
185#879—61no—
186#877—61no—
187#877—61no—
188#872—31no—
189#872—61no—
190#869—31no—
191C4×Dic6—31no—
192C4×Dic6—61no—
193C4×Dic6—61no—
194C4×Dic6—61no—
195C3×#107—21no—
196C3×#107C2×D311yescharacteristic
197C3×#107C2×D311yescharacteristic
198C3×#106—31no—
199C3×#106—31no—
200C3×C4⋊C8—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×C22⋊C8—31no—
206#830—31no—
207(C2×D3)⋊C8—31no—
208(C2×D3)⋊C8C2×D311yescharacteristic
209#816—31no—
210#816—31no—
211#816C2×D311yescharacteristic
212#816C2×D311yescharacteristic
213#815—31no—
214#815—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8C2×D311yescharacteristic
217C8×Dic3—31no—
218C8×Dic3—31no—
219C8×Dic3—61no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#810—61no—
228#810C2×D311yescharacteristic
229#810C2×D311yescharacteristic
230#808C2×D311yescharacteristic
231#808C2×D311yescharacteristic
232#807—31no—
233#807—31no—
234C4⋊(C3⋊C8)—31no—
235C22×C3×D3C2×D411yescharacteristic
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3C2×D411yescharacteristic
242C2×C3⋊Dic3C2×D411yescharacteristic
243#634—21no—
244#634—21no—
245#634—21no—
246#634#4112yes—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×C4×D3—21no—
255C3×C4×D3—21no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6#4112yes—
260#627—24no—
261D3×Dic3—24no—
262C32×C8—21no—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—91no—
267#519—91no—
268#485—31no—
269#485—91no—
270#479—31no—
271#479—91no—
272#462—91no—
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—31no—
282C2×C3×Q8—31no—
283C22×C3×C4—31no—
284C22×Dic3—61no—
285D3×Q8—62no—
286D3×Q8—62no—
287C2×C4×D3—61no—
288C2×C4×D3C22×D311yescharacteristic
289C2×Dic6—31no—
290C2×Dic6—31no—
291C2×Dic6—31no—
292C2×Dic6—31no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—62no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6—62no—
299C2×Dic6C22×D311yescharacteristic
300C2×Dic6C22×D311yescharacteristic
301C2×C3×C8—21no—
302C2×C3×C8—31no—
303C2×C3×C8—31no—
304C2×C3×C8C22×D311yescharacteristic
305C2×C3×C8C22×D311yescharacteristic
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C4⋊C4C22×D311yescharacteristic
317C3×C4⋊C4C22×D311yescharacteristic
318C3×C22⋊C4—61no—
319C3×C22⋊C4—61no—
320C3×C42—31no—
321C3×C42—61no—
322C3×C42—61no—
323#217—31no—
324#217—31no—
325#217—61no—
326#216—62no—
327#216—62no—
328#216—62no—
329#216—62no—
330(C2×D3)⋊C4—21no—
331(C2×D3)⋊C4—21no—
332(C2×D3)⋊C4—31no—
333(C2×D3)⋊C4—31no—
334(C2×D3)⋊C4—61no—
335C4⋊Dic3—21no—
336C4⋊Dic3—21no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3C22×D311yescharacteristic
345C4⋊Dic3C22×D311yescharacteristic
346Dic3⋊C4—21no—
347Dic3⋊C4—21no—
348Dic3⋊C4—31no—
349Dic3⋊C4—31no—
350Dic3⋊C4—61no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—121no—
362Dic3⋊C4—121no—
363C4×Dic3—21no—
364C4×Dic3—21no—
365C4×Dic3—31no—
366C4×Dic3—31no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—121no—
379C4×Dic3—121no—
380C4×Dic3C22×D311yescharacteristic
381C2×C3⋊C8—31no—
382C2×C3⋊C8—31no—
383C2×C3⋊C8—61no—
384C2×C3⋊C8C22×D311yescharacteristic
385C2×C3⋊C8C22×D311yescharacteristic
386Dic12—62no—
387Dic12—62no—
388Dic12—64no—
389Dic12—62no—
390Dic12—62no—
391C22×C32C22×D411yescharacteristic
392C2×C3×D3—21no—
393C2×C3×D3—21no—
394C2×C3×D3—21no—
395C32×C4—41no—
396C32×C4—41no—
397C32×C4C2×#4111yescharacteristic
398C32×C4C2×#4111yescharacteristic
399C3⋊Dic3—21no—
400C3⋊Dic3—22no—
401C3⋊Dic3—21no—
402C3⋊Dic3—41no—
403C3×Dic3—22no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C22×Q8—91no—
411C2×Q16—91no—
412C2×Q16—91no—
413C2×Q16—91no—
414C2×Q16—91no—
415C4⋊Q8—91no—
416#126—181no—
417#126—181no—
418#125—31no—
419#125—181no—
420#125—181no—
421C22⋊Q8—31no—
422C22⋊Q8—91no—
423C4×Q8—31no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×Q8—91no—
429C4×Q8—181no—
430C4×Q8—181no—
431#117—31no—
432#117—91no—
433#117—181no—
434#117—181no—
435#107—91no—
436#107D3211yescharacteristic
437#106—31no—
438#106—31no—
439C4⋊C8—31no—
440C4⋊C8—91no—
441#103—31no—
442#103—31no—
443#103—31no—
444#103—31no—
445#103—91no—
446#103—91no—
447#103—91no—
448#103—91no—
449C22⋊C8—31no—
450C22⋊C8—91no—
451#97—91no—
452C4×C8—91no—
453C23×C3—31no—
454C22×D3D3×D411yescharacteristic
455C3×Q8—32no—
456C3×Q8—61no—
457C3×Q8—61no—
458C3×Q8—61no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4C23×D311yescharacteristic
476C2×C3×C4C23×D311yescharacteristic
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—31no—
482C2×Dic3—31no—
483C2×Dic3—31no—
484C2×Dic3—31no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—64no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—121no—
493C2×Dic3—121no—
494C2×Dic3D3×D411yescharacteristic
495C2×Dic3D3×D411yescharacteristic
496C2×Dic3D3×D411yescharacteristic
497C4×D3—21no—
498C4×D3—21no—
499C4×D3—64no—
500Dic6—21no—
501Dic6—21no—
502Dic6—21no—
503Dic6—32no—
504Dic6—32no—
505Dic6—62no—
506Dic6—64no—
507Dic6—64no—
508Dic6—61no—
509Dic6—61no—
510Dic6—62no—
511Dic6—61no—
512Dic6—61no—
513Dic6—61no—
514Dic6—61no—
515Dic6—121no—
516Dic6—121no—
517Dic6#23912yes—
518C3×C8—22no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—61no—
522C3×C8—61no—
523C3⋊C8—21no—
524C3⋊C8—21no—
525C3⋊C8—61no—
526C3⋊C8—61no—
527C3⋊C8—121no—
528C2×C32#52511yescharacteristic
529C2×C32#57811yescharacteristic
530C2×C32#57811yescharacteristic
531C3×D3—41no—
532C2×Q8—31no—
533C2×Q8—31no—
534C2×Q8—91no—
535C2×Q8—91no—
536C2×Q8—181no—
537C2×Q8—182no—
538C2×Q8—182no—
539C22×C4—31no—
540C22×C4—181no—
541Q16—182no—
542Q16—182no—
543Q16—182no—
544Q16—182no—
545C2×C8—31no—
546C2×C8—31no—
547C2×C8—91no—
548C2×C8C2×D3211yescharacteristic
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4C2×D3211yescharacteristic
566C4⋊C4C2×D3211yescharacteristic
567C22⋊C4—61no—
568C22⋊C4—61no—
569C22⋊C4—91no—
570C22⋊C4—91no—
571C22⋊C4—181no—
572C42—31no—
573C42—61no—
574C42—61no—
575C42—91no—
576C42—181no—
577C42—181no—
578C42—181no—
579C42—181no—
580C42—181no—
581C22×C3—21no—
582C22×C3—61no—
583C22×C3—61no—
584C22×C3—61no—
585C22×C3C2×D3×D411yescharacteristic
586C22×C3C2×D3×D411yescharacteristic
587C2×D3—21no—
588C2×D3—21no—
589C2×D3—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—62no—
597C3×C4—61no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—81no—
601C3×C4—81no—
602C3×C4—121no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4C2×#23911yescharacteristic
606C3×C4D3×#4111yescharacteristic
607C3×C4D3×#4111yescharacteristic
608C3×C4D3×#4111yescharacteristic
609Dic3—21no—
610Dic3—21no—
611Dic3—21no—
612Dic3—22no—
613Dic3—41no—
614Dic3—41no—
615Dic3—41no—
616Dic3—62no—
617Dic3—62no—
618Dic3—61no—
619Dic3—61no—
620Dic3—61no—
621Dic3—61no—
622Dic3—62no—
623Dic3—122no—
624Dic3—121no—
625Dic3—122no—
626Dic3—121no—
627Dic3—121no—
628C32#312711yescharacteristic, complemented, Sylow
629C23—31no—
630Q8—32no—
631Q8—61no—
632Q8—61no—
633Q8—61no—
634Q8—92no—
635Q8—184no—
636Q8—181no—
637Q8—181no—
638Q8—181no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—91no—
651C2×C4—91no—
652C2×C4—184no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4C22×D3211yescharacteristic
656C8—21no—
657C8—61no—
658C8—61no—
659C8—181no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—121no—
664C2×C3#562711yescharacteristic
665C2×C3#565611yescharacteristic
666C2×C3#577111yescharacteristic
667C2×C3#577111yescharacteristic
668C2×C3#577911yescharacteristic
669C2×C3#577911yescharacteristic
670D3—41no—
671C22—61no—
672C22—61no—
673C22—61no—
674C22D32×D411yescharacteristic
675C4—41no—
676C4—41no—
677C4—61no—
678C4—62no—
679C4—61no—
680C4—61no—
681C4—121no—
682C4—121no—
683C4—121no—
684C4—182no—
685C4—181no—
686C4—181no—
687C4—361no—
688C4#6430611yescharacteristic
689C4D3×#23911yescharacteristic
690C3—21no—
691C3#8121111yescharacteristic, complemented
692C3#8149911yescharacteristic, complemented
693C2—121no—
694C2#1059461511yescharacteristic
695C2#1059473711yescharacteristic
696C2#1059476911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#107D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
3. #10592572C2semidirect
5. C3×#4877C2semidirect
7. #10590808C2semidirect
8. #10590790C2semidirect
11. #10590561C2semidirect
12. #10590490C2semidirect
13. #10590485C2semidirect
14. #10590485C2semidirect
72. #4877D3semidirect
628. C32#3127semidirect
691. C3#81211semidirect
692. C3#81499semidirect

Maximal subgroups

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

subgroupindex
#105943572
#105943462
#105925722
C3×#48882
C3×#48772
#105909522
#105908082
#105907902
#105906982
#105906042
#105905612
#105904902
#105904852
#105904282
#814993
#812113