Finite Group Databasebeta

← #11872817

Subgroups — #11872817

Order 1152.

882 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5798C211yesmaximal, characteristic
2#10594824C211yesmaximal, characteristic, complemented
3#10592917C211yesmaximal, characteristic
4C3×#5218C211yesmaximal, characteristic
5#10591489C211yesmaximal, characteristic, complemented
6#10591489C211yesmaximal, characteristic, complemented
7#10591440C211yesmaximal, characteristic, complemented
8Dic3×#214C211yesmaximal, characteristic, complemented
9#10591411C211yesmaximal, characteristic, complemented
10#10591409C211yesmaximal, characteristic, complemented
11#10591405C211yesmaximal, characteristic, complemented
12#10591401C211yesmaximal, characteristic, complemented
13#10591134C211yesmaximal, characteristic, complemented
14#10591102C211yesmaximal, characteristic, complemented
15#10591056C211yesmaximal, characteristic, complemented
16#82545—31nomaximal
17#80137—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×#3754C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21#64133C2211yescharacteristic
22C2×C3×#217—21no—
23C2×C3×#217—21no—
24C3×D4×Dic3—21no—
25C3×D4×Dic3—21no—
26C3×D4×Dic3C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C3×D4×Dic3C2211yescharacteristic
29C3×D4×Dic3C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C3×#926C2211yescharacteristic
33C3×#926C2211yescharacteristic
34C3×#924C2211yescharacteristic
35#63956—21no—
36#63956—21no—
37#63869C2211yescharacteristic, complemented
38#63866C2211yescharacteristic, complemented
39#63847—21no—
40#63846—21no—
41#63844C2211yescharacteristic, complemented
42Dic3×Dic6C2211yescharacteristic, complemented
43#63659C2211yescharacteristic
44#63659C2211yescharacteristic
45#63657C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#830C2211yescharacteristic
49#63576C2211yescharacteristic, complemented
50#63575C2211yescharacteristic, complemented
51#63574C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#518—31no—
62#5798D311yescharacteristic
63#5625—31no—
64#5518—31no—
65C3×#450—31no—
66#5218—31no—
67#5218—31no—
68#5218—61no—
69#5218D311yescharacteristic
70#5164—31no—
71#5162—31no—
72#5162—31no—
73Dic3×SD16—31no—
74#5045—31no—
75#5019—31no—
76#5019—31no—
77#5018—31no—
78#5018—31no—
79C4×#214—31no—
80C4×#214—31no—
81#5009—31no—
82#5009—31no—
83#5000—31no—
84#4996—31no—
85#4996—31no—
86#4766—31no—
87#4763—31no—
88#4758—31no—
89#4757—31no—
90#4723—31no—
91#4720—31no—
92C24×C32—21no—
93C2×C32×D4—22no—
94C2×C32×D4—22no—
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C2×C3×Dic6C2311yescharacteristic
105#3757—21no—
106#3754—22no—
107#3754—22no—
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109#3750—21no—
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112C3×#217—21no—
113C3×#217—21no—
114C3×#217—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×#217D411yescharacteristic
120C3×#214—22no—
121C3×#214—22no—
122C3×C4⋊Dic3D411yescharacteristic
123C3×C4⋊Dic3D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141#3123—91noSylow
142C22×C3×D4—21no—
143C22×C3×D4C2×D311yescharacteristic
144C22×C3×D4C2×D311yescharacteristic
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C3×C22⋊Q8—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150C3×C4×D4—31no—
151C3×C4×D4—31no—
152C3×C4×D4—61no—
153C3×C4×D4—61no—
154C3×#117—31no—
155C3×#117—31no—
156C2×C3×C22⋊C4—61no—
157C2×C3×C22⋊C4—61no—
158C2×#217—21no—
159C2×#217—21no—
160Q8×Dic3—31no—
161#944—31no—
162D4×Dic3—21no—
163D4×Dic3—21no—
164D4×Dic3C2×D311yescharacteristic
165D4×Dic3C2×D311yescharacteristic
166D4×Dic3C2×D311yescharacteristic
167D4×Dic3C2×D311yescharacteristic
168C2×#214—31no—
169C2×#214—31no—
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—61no—
173C2×#214—61no—
174C2×#214C2×D311yescharacteristic
175C2×#214C2×D311yescharacteristic
176#926C2×D311yescharacteristic
177#926C2×D311yescharacteristic
178#924—31no—
179#924—31no—
180#924—61no—
181#924C2×D311yescharacteristic
182#890—31no—
183#890—61no—
184#889—61no—
185#889—61no—
186#889—61no—
187#887—31no—
188#879—61no—
189#879—61no—
190#879—61no—
191#879—61no—
192#870—31no—
193#869—31no—
194C4×Dic6—31no—
195C4×Dic6—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×C22⋊C8—31no—
199#835—31no—
200#835—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—61no—
206#832—61no—
207#832C2×D311yescharacteristic
208#832C2×D311yescharacteristic
209#830—31no—
210#830—31no—
211#830—61no—
212#830C2×D311yescharacteristic
213#818—31no—
214#817—31no—
215#816—31no—
216#816—31no—
217#815—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220C8×Dic3—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32—24no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—81no—
239C23×C32—81no—
240C23×C32C2×D411yescharacteristic
241C32×D4—24no—
242C32×D4—21no—
243C32×D4—21no—
244C32×D4#4112yes—
245C32×D4#4112yes—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252#634—21no—
253#634—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3—81no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—91no—
273#518—31no—
274#485—91no—
275#485—91no—
276#478—91no—
277#478—91no—
278#461—91no—
279#461—91no—
280#450—31no—
281#450—91no—
282#440—91no—
283#440—91no—
284C4×SD16—91no—
285C4×SD16—91no—
286#433—91no—
287C24×C3—21no—
288C24×C3—21no—
289C24×C3—41no—
290C2×C3×Q8—31no—
291C2×C3×D4—22no—
292C2×C3×D4—22no—
293C2×C3×D4—22no—
294C2×C3×D4—22no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—41no—
300C2×C3×D4—42no—
301C2×C3×D4—42no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—21no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—61no—
320C2×Dic6C22×D311yescharacteristic
321C3×SD16—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×C22⋊C4—31no—
332C3×C22⋊C4—31no—
333C3×C22⋊C4—61no—
334C3×C22⋊C4—61no—
335C3×C22⋊C4—61no—
336C3×C22⋊C4—61no—
337C3×C22⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C42—31no—
340C3×C42—31no—
341C3×C42—61no—
342#217—21no—
343#217—21no—
344#217—21no—
345#217—21no—
346#217—21no—
347#217—21no—
348#217—61no—
349#217—61no—
350#217—121no—
351#217#6711yescharacteristic
352#217#6711yescharacteristic
353#214—22no—
354#214—22no—
355#214—62no—
356#214—62no—
357#214—62no—
358#214—62no—
359#214—122no—
360#214—122no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3#6711yescharacteristic
369C4⋊Dic3#6711yescharacteristic
370C4⋊Dic3C22×D311yescharacteristic
371C4⋊Dic3C22×D311yescharacteristic
372C4⋊Dic3C22×D311yescharacteristic
373Dic3⋊C4—21no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—121no—
385C4×Dic3—21no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3C22×D311yescharacteristic
391C4×Dic3C22×D311yescharacteristic
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8C22×D311yescharacteristic
399C2×C3⋊C8C22×D311yescharacteristic
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—22no—
403C22×C32—22no—
404C22×C32—21no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32—84no—
410C22×C32C22×D411yescharacteristic
411C32×C4—21no—
412C32×C4C2×#4111yescharacteristic
413C32×C4C2×#4111yescharacteristic
414C3⋊Dic3—41no—
415C3⋊Dic3—41no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—21no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C22×D4D3211yescharacteristic
425C2×SD16—31no—
426C2×SD16—31no—
427C2×SD16—91no—
428C2×SD16—91no—
429C4⋊Q8—91no—
430#126—181no—
431#126—181no—
432#125—91no—
433#125—181no—
434#125—181no—
435C22⋊Q8—31no—
436C22⋊Q8—91no—
437C4×Q8—91no—
438C4×Q8—91no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—61no—
444C4×D4—61no—
445#117—31no—
446#117—31no—
447C2×C22⋊C4—61no—
448C2×C22⋊C4—61no—
449#107—91no—
450#107—91no—
451#106—91no—
452#106—91no—
453C4⋊C8—91no—
454C4⋊C8—91no—
455#103—91no—
456#103—91no—
457#103—91no—
458#103—91no—
459#102—31no—
460#102—31no—
461#102—91no—
462#102—91no—
463C22⋊C8—31no—
464C22⋊C8—91no—
465#97—91no—
466C4×C8—91no—
467C23×C3—24no—
468C23×C3—24no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—44no—
477C23×C3—81no—
478C23×C3—81no—
479C23×C3—81no—
480C23×C3—81no—
481C23×C3—82no—
482C23×C3—82no—
483C23×C3D3×D411yescharacteristic
484C23×C3C2×#6711yescharacteristic
485C3×Q8—61no—
486C3×Q8—61no—
487C3×D4—24no—
488C3×D4—24no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—21no—
493C3×D4—22no—
494C3×D4—22no—
495C3×D4—41no—
496C3×D4—41no—
497C3×D4—44no—
498C3×D4#23512yes—
499C3×D4#23512yes—
500C3×D4#23712yes—
501C3×D4#23712yes—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—241no—
519C2×C3×C4—241no—
520C2×C3×C4—241no—
521C2×C3×C4—241no—
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4C2×#6711yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—81no—
535C2×Dic3—81no—
536C2×Dic3—81no—
537C2×Dic3—81no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3C2×#6711yescharacteristic
541C2×Dic3C2×#6711yescharacteristic
542C2×Dic3C2×#6711yescharacteristic
543C2×Dic3C2×#6711yescharacteristic
544Dic6—21no—
545Dic6—21no—
546Dic6—61no—
547Dic6—61no—
548Dic6—61no—
549Dic6—61no—
550Dic6—121no—
551Dic6—121no—
552C3×C8—61no—
553C3×C8—61no—
554C3⋊C8—21no—
555C3⋊C8—21no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—121no—
561C3⋊C8—121no—
562C2×C32—41no—
563C2×C32—42no—
564C2×C32—42no—
565C2×C32#52511yescharacteristic
566C2×C32#57711yescharacteristic
567C2×C32#57711yescharacteristic
568C24—21no—
569C2×Q8—31no—
570C2×Q8—91no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4C2×D3211yescharacteristic
575C2×D4C2×D3211yescharacteristic
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4C2×D3211yescharacteristic
581SD16—62no—
582SD16—62no—
583SD16—182no—
584SD16—182no—
585C2×C8—31no—
586C2×C8—31no—
587C2×C8—91no—
588C2×C8—91no—
589C4⋊C4—31no—
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—61no—
595C4⋊C4—91no—
596C4⋊C4—181no—
597C4⋊C4—181no—
598C4⋊C4—181no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C22⋊C4—31no—
604C22⋊C4—31no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—181no—
612C42—31no—
613C42—31no—
614C42—61no—
615C42—181no—
616C42—181no—
617C22×C3—22no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—21no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—84no—
646C22×C3—84no—
647C22×C3—88no—
648C22×C3C2×D3×D411yescharacteristic
649C22×C3C22×#6711yescharacteristic
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—41no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4C2×#23511yescharacteristic
664C3×C4C2×#23511yescharacteristic
665C3×C4C2×#23711yescharacteristic
666C3×C4C2×#23711yescharacteristic
667Dic3—21no—
668Dic3—21no—
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—241no—
680Dic3—241no—
681C32#312311yescharacteristic, complemented, Sylow
682C23—24no—
683C23—21no—
684C23—21no—
685C23—81no—
686C23—81no—
687C23D3×#6711yescharacteristic
688Q8—61no—
689Q8—61no—
690Q8—181no—
691Q8—181no—
692D4—24no—
693D4—21no—
694D4—21no—
695D4#380412yes—
696D4#380412yes—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—181no—
708C2×C4—181no—
709C2×C4—241no—
710C2×C4—241no—
711C2×C4—241no—
712C2×C4—241no—
713C2×C4D3×#6711yescharacteristic
714C2×C4C22×D3211yescharacteristic
715C8—61no—
716C8—61no—
717C8—181no—
718C8—181no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—42no—
723C2×C3—41no—
724C2×C3—42no—
725C2×C3—42no—
726C2×C3—41no—
727C2×C3—42no—
728C2×C3—42no—
729C2×C3—82no—
730C2×C3—82no—
731C2×C3#558611yescharacteristic
732C2×C3#576211yescharacteristic
733C2×C3#577511yescharacteristic
734C2×C3#579111yescharacteristic
735C2×C3#583611yescharacteristic
736C2×C3#583611yescharacteristic
737C22—21no—
738C22—21no—
739C22—21no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—84no—
747C22C2×D3×#6711yescharacteristic
748C4—21no—
749C4—61no—
750C4—61no—
751C4—61no—
752C4—61no—
753C4—121no—
754C4—121no—
755C4—121no—
756C4—121no—
757C4—361no—
758C4—361no—
759C4C2×#380411yescharacteristic
760C4C2×#380411yescharacteristic
761C3—21no—
762C3#8013711yescharacteristic, complemented
763C3#8254511yescharacteristic, complemented
764C2—41no—
765C2—42no—
766C2—42no—
767C2#1059510511yescharacteristic
768C2#1059510611yescharacteristic
769C2#1059549811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10594824C2semidirect
5. #10591489C2semidirect
6. #10591489C2semidirect
7. #10591440C2semidirect
8. Dic3×#214C2semidirect
9. #10591411C2semidirect
10. #10591409C2semidirect
11. #10591405C2semidirect
12. #10591401C2semidirect
13. #10591134C2semidirect
14. #10591102C2semidirect
15. #10591056C2semidirect
37. #63869C22semidirect
38. #63866C22semidirect
41. #63844C22semidirect
42. Dic3×Dic6C22semidirect
49. #63576C22semidirect
50. #63575C22semidirect
51. #63574C22semidirect
52. #63573C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63565C22semidirect
58. #63565C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
681. C32#3123semidirect
762. C3#80137semidirect
763. C3#82545semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
#105948242
#105929172
C3×#52182
#105914892
#105914402
Dic3×#2142
#105914112
#105914092
#105914052
#105914012
#105911342
#105911022
#105910562
#825453
#801373