Finite Group Databasebeta

← #11872975

Subgroups — #11872975

Order 1152.

830 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5682C211yesmaximal, characteristic, complemented
2#10593890C211yesmaximal, characteristic, complemented
3#10592756C211yesmaximal, characteristic, complemented
4C3×#5054C211yesmaximal, characteristic, complemented
5#10591657C211yesmaximal, characteristic, complemented
6Dic3×#216C211yesmaximal, characteristic, complemented
7#10591551C211yesmaximal, characteristic, complemented
8#10591540C211yesmaximal, characteristic, complemented
9#10591521C211yesmaximal, characteristic
10#10591440C211yesmaximal, characteristic, complemented
11#10591413C211yesmaximal, characteristic, complemented
12#10591400C211yesmaximal, characteristic, complemented
13#10590313C211yesmaximal, characteristic, complemented
14#10590310C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#83461—31nomaximal
17#80574—31nomaximal
18C2×#3799C2211yescharacteristic
19C32×#124C2211yescharacteristic
20C2×#3755C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C3×#886—21no—
30C3×#885—21no—
31C3×#879—21no—
32C3×#878—21no—
33C3×#872C2211yescharacteristic
34C3×#869C2211yescharacteristic
35C3×C4×Dic6C2211yescharacteristic
36#63894C2211yescharacteristic
37D3×C4⋊Dic3C2211yescharacteristic
38#63883—21no—
39#63881—21no—
40#63880—21no—
41Dic3×Dic6C2211yescharacteristic
42#63836—21no—
43#63662C2211yescharacteristic
44#63659C2211yescharacteristic
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×C4⋊(C3⋊C8)C2211yescharacteristic
49#63576C2211yescharacteristic
50#63576C2211yescharacteristic
51#63575C2211yescharacteristic
52#63575C2211yescharacteristic
53#63565C2211yescharacteristic
54#63565C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#542—31no—
62#5682D311yescharacteristic, complemented
63#5574—31no—
64#5523—31no—
65C3×#464—31no—
66#5187—31no—
67Dic3×Q16—31no—
68#5172—31no—
69#5164—31no—
70#5091—31no—
71#5087—31no—
72#5057—31no—
73#5057—31no—
74#5057—61no—
75#5054D311yescharacteristic, complemented
76#5047—31no—
77#5044—31no—
78#5037—31no—
79#5033—31no—
80C4×#216—31no—
81#5026—31no—
82#5021—31no—
83#5018—31no—
84C4×#213—31no—
85#5000—31no—
86#4846—31no—
87#4840—31no—
88#4817—31no—
89#4811—31no—
90#4774—31no—
91#4756—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6—21no—
100C2×C3×Dic6C2311yescharacteristic
101C2×#626—21no—
102C2×#624—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105#3799—22no—
106#3799—22no—
107C32×C22⋊C4—21no—
108C32×C22⋊C4—21no—
109C32×C42C2311yescharacteristic
110#3755—22no—
111#3753—22no—
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#216—22no—
119C3×#214—22no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140Dic32—21no—
141#3124—91noSylow
142C2×#239—31no—
143C2×#235—31no—
144C2×C3×Q16—31no—
145C2×C3×SD16—31no—
146C3×C4⋊Q8—31no—
147C3×#126—61no—
148C3×#124—21no—
149C3×#124—61no—
150C3×#124C2×D311yescharacteristic
151C3×#124C2×D311yescharacteristic
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—61no—
155C3×#121—31no—
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×D4—31no—
159C3×#117—31no—
160#946C2×D311yescharacteristic
161Q8×Dic3—31no—
162Q8×Dic3C2×D311yescharacteristic
163C2×#216C2×D311yescharacteristic
164C2×#215—31no—
165C2×#215—31no—
166C2×#215—61no—
167#938C2×D311yescharacteristic
168D4×Dic3C2×D311yescharacteristic
169C2×#214C2×D311yescharacteristic
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—61no—
173C2×C4⋊Dic3—31no—
174#893—31no—
175#893—61no—
176#892—61no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—61no—
179D3×C4⋊C4—61no—
180#886—21no—
181#885—21no—
182#67⋊C4—61no—
183#67⋊C4—61no—
184#879—21no—
185#878—21no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—61no—
190C4×D12—61no—
191#872—61no—
192#872C2×D311yescharacteristic
193#869C2×D311yescharacteristic
194C4×Dic6—31no—
195C4×Dic6C2×D311yescharacteristic
196C3×C4⋊C8—31no—
197C3×#103—31no—
198C3×#102—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—61no—
204#835C2×D311yescharacteristic
205#832—31no—
206#832—31no—
207#832—61no—
208#832C2×D311yescharacteristic
209#830—31no—
210#830—31no—
211#821—31no—
212#821—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215#818—31no—
216#818—31no—
217#815—31no—
218C8×Dic3—31no—
219#810—31no—
220#810—31no—
221#809—31no—
222#809—31no—
223#807—31no—
224#807—31no—
225#807—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—
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×Q8—21no—
239C32×Q8—21no—
240C32×D4—21no—
241C32×D4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)#4112yes—
249C4×C3⋊D3—81no—
250C3×#67—81no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—81no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×Dic6—21no—
262C3×Dic6—81no—
263C3×Dic6#4112yes—
264#626—24no—
265#624—24no—
266#624—81no—
267D3×Dic3—81no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#542—31no—
273#520—91no—
274#484—91no—
275#480—91no—
276#477—91no—
277#474—91no—
278#464—31no—
279#463—91no—
280#452—91no—
281#449—91no—
282#440—91no—
283#440—91no—
284C4×Q16—91no—
285C4×D8—91no—
286#433—91no—
287C2×C3×Q8—21no—
288C2×C3×Q8—31no—
289C2×C3×Q8—61no—
290C2×C3×Q8C22×D311yescharacteristic
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×D4—21no—
293C2×C3×D4—61no—
294C2×C3×D4C22×D311yescharacteristic
295C2×C3×D4C22×D311yescharacteristic
296C22×C3×C4—31no—
297C22×C3×C4—61no—
298C2×#67—21no—
299C2×#67—61no—
300C22×Dic3—21no—
301C22×Dic3—61no—
302#239—62no—
303#239—62no—
304#235—62no—
305#235—62no—
306C2×D12—31no—
307C2×D12—31no—
308C2×D12—61no—
309C2×D12—61no—
310C2×C4×D3—61no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—121no—
318C2×C4×D3C22×D311yescharacteristic
319C2×Dic6—21no—
320C2×Dic6C22×D311yescharacteristic
321C3×Q16—62no—
322C3×SD16—62no—
323C2×C3×C8—31no—
324C2×C3×C8—31no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C22⋊C4—21no—
335C3×C22⋊C4—21no—
336C3×C22⋊C4—21no—
337C3×C22⋊C4—21no—
338C3×C22⋊C4—31no—
339C3×C22⋊C4—31no—
340C3×C22⋊C4—41no—
341C3×C22⋊C4—41no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C42—21no—
346C3×C42—31no—
347C3×C42—61no—
348C3×C42—61no—
349C3×C42C22×D311yescharacteristic
350C3×C42C22×D311yescharacteristic
351#217—21no—
352#217—21no—
353#216—22no—
354#215—62no—
355#215—62no—
356#215—122no—
357#214—22no—
358#213—62no—
359#213—62no—
360#213—122no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—121no—
367(C2×D3)⋊C4#6711yescharacteristic
368(C2×D3)⋊C4#6711yescharacteristic
369C4⋊Dic3—21no—
370C4⋊Dic3—21no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4#6711yescharacteristic
384Dic3⋊C4#6711yescharacteristic
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3C22×D311yescharacteristic
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398C22×C32—41no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32C22×D411yescharacteristic
402C2×C3⋊D3—22no—
403C2×C3⋊D3—41no—
404C2×C3⋊D3—41no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—41no—
411C32×C4C2×#4111yescharacteristic
412C32×C4C2×#4111yescharacteristic
413C3⋊Dic3—41no—
414C3×Dic3—21no—
415C3×Dic3—22no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C2×#41—91no—
422C2×Q16—31no—
423C2×SD16—31no—
424C2×SD16—91no—
425C2×D8—91no—
426C4⋊Q8—31no—
427#126—61no—
428#124—61no—
429#124D3211yescharacteristic
430#123—61no—
431C22⋊Q8—31no—
432C22⋊Q8—61no—
433#121—31no—
434C4×Q8—31no—
435C4×Q8—31no—
436C4×Q8—91no—
437C4×D4—31no—
438C4×D4—91no—
439C4×D4—91no—
440C4×D4—181no—
441C4×D4—181no—
442#117—31no—
443#117—181no—
444C2×C4⋊C4—91no—
445C2×C4⋊C4—181no—
446#107—91no—
447#107—91no—
448#107—91no—
449#107—91no—
450C4⋊C8—31no—
451C4⋊C8—91no—
452#103—31no—
453#103—91no—
454#103—91no—
455#103—91no—
456#102—31no—
457#102—91no—
458#102—91no—
459#102—91no—
460C22⋊C8—91no—
461C22⋊C8—91no—
462#97—91no—
463C4×C8—91no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—31no—
467C23×C3—41no—
468C22×D3—61no—
469C22×D3—61no—
470C22×D3—121no—
471C22×D3C2×#6711yescharacteristic
472C3×Q8—21no—
473C3×Q8—21no—
474C3×Q8—21no—
475C3×Q8—21no—
476C3×Q8—32no—
477C3×Q8—41no—
478C3×Q8—41no—
479C3×Q8—61no—
480C3×Q8—241no—
481C3×D4—21no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—21no—
485C3×D4—41no—
486C3×D4—41no—
487C3×D4—241no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—41no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—241no—
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4C2×#6711yescharacteristic
507C2×C3×C4C2×#6711yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510#67—64no—
511#67—81no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—81no—
519C2×Dic3—121no—
520C2×Dic3—241no—
521C2×Dic3C2×#6711yescharacteristic
522C2×Dic3C2×#6711yescharacteristic
523C2×Dic3C2×#6711yescharacteristic
524D12—32no—
525D12—32no—
526D12—62no—
527D12—64no—
528D12—61no—
529D12—61no—
530D12—121no—
531C4×D3—21no—
532C4×D3—21no—
533C4×D3—64no—
534C4×D3—64no—
535C4×D3—241no—
536C4×D3—241no—
537C4×D3—241no—
538C4×D3—241no—
539C4×D3—241no—
540C4×D3—242no—
541Dic6—21no—
542Dic6—81no—
543Dic6#23712yes—
544C3×C8—61no—
545C3×C8—61no—
546C3⋊C8—21no—
547C3⋊C8—21no—
548C3⋊C8—61no—
549C3⋊C8—61no—
550C3⋊C8—61no—
551C3⋊C8—61no—
552C3⋊C8—121no—
553C3⋊C8—121no—
554C2×C32—81no—
555C2×C32#52511yescharacteristic
556C2×C32#57611yescharacteristic
557C2×C32#57811yescharacteristic
558C3⋊D3—42no—
559C3×D3—41no—
560#41—182no—
561#41—182no—
562C2×Q8—31no—
563C2×Q8—61no—
564C2×Q8C2×D3211yescharacteristic
565C2×D4—61no—
566C2×D4—91no—
567C2×D4—181no—
568C2×D4C2×D3211yescharacteristic
569C22×C4—31no—
570C22×C4—61no—
571C22×C4—181no—
572C22×C4—181no—
573C22×C4—181no—
574C22×C4—181no—
575Q16—62no—
576SD16—62no—
577SD16—182no—
578D8—182no—
579C2×C8—31no—
580C2×C8—31no—
581C2×C8—91no—
582C2×C8—91no—
583C4⋊C4—31no—
584C4⋊C4—31no—
585C4⋊C4—31no—
586C4⋊C4—31no—
587C4⋊C4—31no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—91no—
593C4⋊C4—181no—
594C4⋊C4—181no—
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—31no—
598C22⋊C4—31no—
599C22⋊C4—61no—
600C22⋊C4—61no—
601C22⋊C4—61no—
602C22⋊C4—181no—
603C22⋊C4—181no—
604C42—31no—
605C42—61no—
606C42—61no—
607C42—181no—
608C42C2×D3211yescharacteristic
609C22×C3—21no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3C2×D3×D411yescharacteristic
623C22×C3C22×#6711yescharacteristic
624C2×D3—21no—
625C2×D3—21no—
626C2×D3—21no—
627C2×D3—62no—
628C2×D3—62no—
629C2×D3—122no—
630C2×D3—121no—
631C2×D3—121no—
632C2×D3—121no—
633C2×D3—121no—
634C2×D3—241no—
635C2×D3—241no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—62no—
649C3×C4—61no—
650C3×C4—81no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4C2×#23711yescharacteristic
655C3×C4D3×#4111yescharacteristic
656C3×C4D3×#4111yescharacteristic
657C3×C4D3×#4111yescharacteristic
658Dic3—21no—
659Dic3—21no—
660Dic3—21no—
661Dic3—22no—
662Dic3—41no—
663Dic3—41no—
664Dic3—41no—
665Dic3—121no—
666Dic3—121no—
667Dic3—241no—
668C32#312411yescharacteristic, complemented, Sylow
669C23—21no—
670C23—31no—
671C23—181no—
672Q8—21no—
673Q8—21no—
674Q8—32no—
675Q8—61no—
676Q8—241no—
677D4—21no—
678D4—21no—
679D4—92no—
680D4—184no—
681D4—181no—
682D4—241no—
683C2×C4—21no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—184no—
694C2×C4—181no—
695C2×C4—241no—
696C2×C4—721no—
697C2×C4—721no—
698C2×C4—721no—
699C2×C4D3×#6711yescharacteristic
700C2×C4D3×#6711yescharacteristic
701C2×C4C22×D3211yescharacteristic
702C8—61no—
703C8—61no—
704C8—181no—
705C8—181no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—81no—
710C2×C3—81no—
711C2×C3—121no—
712C2×C3—161no—
713C2×C3#560611yescharacteristic
714C2×C3#576911yescharacteristic
715C2×C3#577911yescharacteristic
716C2×C3#582811yescharacteristic
717C2×C3#583511yescharacteristic
718C2×C3#583811yescharacteristic
719D3—41no—
720D3—122no—
721D3—122no—
722D3—242no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—61no—
727C22—61no—
728C22—61no—
729C22—182no—
730C22—361no—
731C22—361no—
732C22C2×D3×#6711yescharacteristic
733C4—21no—
734C4—21no—
735C4—41no—
736C4—61no—
737C4—61no—
738C4—61no—
739C4—62no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—361no—
744C4D3×#23711yescharacteristic
745C4#6431211yescharacteristic
746C3—21no—
747C3#8057411yescharacteristic, complemented
748C3#8346111yescharacteristic, complemented
749C2—81no—
750C2—121no—
751C2—362no—
752C2#1059530111yescharacteristic
753C2#1059545611yescharacteristic
754C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
prime radical#10591521C2
hypercenter#124D32
hypocenterC32#3124
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#5682C2semidirect
2. #10593890C2semidirect
3. #10592756C2semidirect
4. C3×#5054C2semidirect
5. #10591657C2semidirect
6. Dic3×#216C2semidirect
7. #10591551C2semidirect
8. #10591540C2semidirect
10. #10591440C2semidirect
11. #10591413C2semidirect
12. #10591400C2semidirect
13. #10590313C2semidirect
14. #10590310C2semidirect
15. #10590253C2semidirect
62. #5682D3semidirect
75. #5054D3semidirect
668. C32#3124semidirect
747. C3#80574semidirect
748. C3#83461semidirect

Maximal subgroups

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

subgroupindex
C3×#56822
#105938902
#105927562
C3×#50542
#105916572
Dic3×#2162
#105915512
#105915402
#105915212
#105914402
#105914132
#105914002
#105903132
#105903102
#105902532
#834613
#805743