Finite Group Databasebeta

← #11872286

Subgroups — #11872286

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 777 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5619C211yesmaximal, characteristic, complemented
2#10594992C211yesmaximal, characteristic, complemented
3#10592732C211yesmaximal, characteristic, complemented
4C3×#5037C211yesmaximal, characteristic, complemented
5#10591438C211yesmaximal, characteristic, complemented
6Dic3×#214C211yesmaximal, characteristic, complemented
7#10591430C211yesmaximal, characteristic, complemented
8#10591428C211yesmaximal, characteristic, complemented
9#10591161C211yesmaximal, characteristic, complemented
10#10591092C211yesmaximal, characteristic, complemented
11#10591056C211yesmaximal, characteristic, complemented
12#10590493C211yesmaximal, characteristic, complemented
13#10590478C211yesmaximal, characteristic, complemented
14#10590467C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#83434—31nomaximal
17#80073—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C32×#121C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C3×#940C2211yescharacteristic
22C3×#939—21no—
23C3×#938—21no—
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×#930C2211yescharacteristic
28C3×#926C2211yescharacteristic
29C3×#893C2211yescharacteristic
30C3×#890C2211yescharacteristic
31C3×#886—21no—
32C3×#883—21no—
33#67⋊Dic3—21no—
34#67⋊Dic3—21no—
35Dic3×D12C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37D3×C4⋊Dic3—21no—
38Dic3×Dic6C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic
40#63841—21no—
41C2×#3715C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63659C2211yescharacteristic
44#63659C2211yescharacteristic
45#63657C2211yescharacteristic
46#63634C2211yescharacteristic
47#63634C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#809C2211yescharacteristic
51#63573C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63565C2211yescharacteristic
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#540—31no—
62#5827—31no—
63#5619D311yescharacteristic, complemented
64#5523—31no—
65C3×#449—31no—
66#5238—31no—
67#5163—31no—
68Dic3×SD16—31no—
69#5152—31no—
70#5150—31no—
71#5075—31no—
72#5072—31no—
73#5066—31no—
74#5063—31no—
75#5037—31no—
76#5037D311yescharacteristic, complemented
77#5034—31no—
78#5033—31no—
79#5033—31no—
80#5033—61no—
81#5018—31no—
82C4×#214—31no—
83#5014—31no—
84C4×#213—31no—
85#5000—31no—
86#4817—31no—
87#4799—31no—
88#4763—31no—
89#4756—31no—
90#4735—31no—
91#4720—31no—
92C2×C32×D4—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×#235—22no—
102C3×#235—22no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×#217D411yescharacteristic
120C3×#214—22no—
121C3×#213—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3D411yescharacteristic
126C3×C4⋊Dic3D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139#3715—22no—
140#3713—22no—
141#3119—91noSylow
142C2×C3×#41—31no—
143C2×#235C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×D8—31no—
146C3×#127—31no—
147C3×#125—31no—
148C3×#123—61no—
149C3×#123—61no—
150C3×#121—21no—
151C3×#121—31no—
152C3×#121—61no—
153C3×#121—61no—
154C3×#121C2×D311yescharacteristic
155C3×#121C2×D311yescharacteristic
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×#117—31no—
159Q8×Dic3—31no—
160Q8×Dic3—31no—
161C2×#215—31no—
162#940C2×D311yescharacteristic
163#939—21no—
164#938—21no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—61no—
168D4×Dic3—61no—
169D4×Dic3C2×D311yescharacteristic
170C2×#214—31no—
171C2×#214C2×D311yescharacteristic
172C2×#213—31no—
173C2×#213—31no—
174C2×#213C2×D311yescharacteristic
175#930C2×D311yescharacteristic
176#926—61no—
177#926C2×D311yescharacteristic
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3—61no—
181C2×C4⋊Dic3—61no—
182#893C2×D311yescharacteristic
183#892—61no—
184D3×C4⋊C4—61no—
185#890C2×D311yescharacteristic
186#886—21no—
187#883—21no—
188#67⋊C4—61no—
189#67⋊C4—61no—
190C4×D12—31no—
191C4×D12—31no—
192C4×Dic6—31no—
193C4×Dic6—31no—
194C3×#103—31no—
195C3×#102—31no—
196C3×C22⋊C8—31no—
197#835—31no—
198#832—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—61no—
206#832—61no—
207#830—31no—
208#830—31no—
209#830—61no—
210#830C2×D311yescharacteristic
211#821—31no—
212#821—31no—
213#817—31no—
214#817—31no—
215#815—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218C8×Dic3—31no—
219#810—31no—
220#810C2×D311yescharacteristic
221#809—31no—
222#809C2×D311yescharacteristic
223#808—31no—
224#808—31no—
225#807—31no—
226#807—31no—
227#807—31no—
228#807—31no—
229#807—61no—
230#807—61no—
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C23×C32C2×D411yescharacteristic
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C32×D4—21no—
240C32×D4—21no—
241C32×D4—81no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—81no—
250C3×#67—24no—
251C3×#67—81no—
252C3×#67—81no—
253C3×#67—81no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—81no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—24no—
266C3×C4×D3—81no—
267C3×Dic6—21no—
268C3×Dic6#4112yes—
269D3×Dic3—81no—
270D3×Dic3—81no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#540—31no—
276#520—91no—
277#481—91no—
278#480—91no—
279#479—91no—
280#478—91no—
281#460—91no—
282#459—91no—
283#449—31no—
284#449—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C3×#41—62no—
291C3×#41—62no—
292C2×C3×Q8—31no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—41no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C22×C3×C4—21no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C2×#67—21no—
312C2×#67—21no—
313C2×#67—21no—
314C2×#67—21no—
315C22×Dic3—21no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—121no—
321#235—22no—
322#235—22no—
323C2×D12C22×D311yescharacteristic
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×Dic6C22×D311yescharacteristic
330C3×SD16—62no—
331C3×D8—62no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C22⋊C4—21no—
343C3×C22⋊C4—21no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—41no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—31no—
351C3×C42—31no—
352#217—21no—
353#217—61no—
354#217—61no—
355#217#6711yescharacteristic
356#217#6711yescharacteristic
357#215—62no—
358#214—22no—
359#214—62no—
360#213—22no—
361#213—62no—
362#213—62no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367C4⋊Dic3—21no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—121no—
379C4⋊Dic3#6711yescharacteristic
380C4⋊Dic3#6711yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3C22×D311yescharacteristic
390C4×Dic3C22×D311yescharacteristic
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8C22×D311yescharacteristic
398C2×C3⋊C8C22×D311yescharacteristic
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32C22×D411yescharacteristic
406C2×C3×D3—22no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C32×C4—21no—
413C32×C4—41no—
414C32×C4C2×#4111yescharacteristic
415C32×C4C2×#4111yescharacteristic
416C3⋊Dic3—41no—
417C3⋊Dic3—41no—
418C3×Dic3—22no—
419C3×Dic3—21no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C2×#41—31no—
425C2×SD16—31no—
426C2×SD16—91no—
427C2×D8—31no—
428C2×D8—91no—
429#127—31no—
430#125—31no—
431#123—61no—
432#123—61no—
433#121—31no—
434#121—61no—
435#121—61no—
436#121D3211yescharacteristic
437C4×Q8—91no—
438C4×Q8—91no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—181no—
444C4×D4—181no—
445#117—31no—
446#117—181no—
447C2×C4⋊C4—91no—
448C2×C4⋊C4—181no—
449#107—91no—
450#107—91no—
451#106—91no—
452#106—91no—
453C4⋊C8—91no—
454C4⋊C8—91no—
455#103—31no—
456#103—91no—
457#102—31no—
458#102—91no—
459#102—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463C22⋊C8—31no—
464C22⋊C8—91no—
465#97—91no—
466C4×C8—91no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—41no—
471C23×C3—61no—
472C23×C3—61no—
473C23×C3D3×D411yescharacteristic
474C23×C3C2×#6711yescharacteristic
475C22×D3—21no—
476C22×D3—21no—
477C3×Q8—32no—
478C3×Q8—61no—
479C3×D4—21no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—21no—
483C3×D4—32no—
484C3×D4—41no—
485C3×D4—41no—
486C3×D4—64no—
487C3×D4—61no—
488C3×D4—61no—
489C3×D4—61no—
490C3×D4—81no—
491C3×D4—81no—
492C3×D4—82no—
493C3×D4—241no—
494C3×D4—241no—
495C3×D4—241no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—64no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—241no—
515C2×C3×C4—241no—
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4C2×#6711yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67—24no—
521#67—81no—
522#67—81no—
523#67—81no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—81no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3—241no—
534C2×Dic3—241no—
535C2×Dic3—241no—
536C2×Dic3—241no—
537C2×Dic3—242no—
538C2×Dic3C2×#6711yescharacteristic
539C2×Dic3C2×#6711yescharacteristic
540C2×Dic3C2×#6711yescharacteristic
541C2×Dic3C2×#6711yescharacteristic
542D12—21no—
543D12—21no—
544D12—21no—
545D12#23712yes—
546C4×D3—24no—
547C4×D3—81no—
548C4×D3—241no—
549C4×D3—241no—
550Dic6—21no—
551Dic6#23712yes—
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—81no—
564C2×C32#52511yescharacteristic
565C2×C32#57611yescharacteristic
566C2×C32#57711yescharacteristic
567C3×D3—42no—
568C3×D3—81no—
569#41—62no—
570#41—62no—
571C2×Q8—31no—
572C2×D4—21no—
573C2×D4—31no—
574C2×D4—31no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4C2×D3211yescharacteristic
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4—181no—
586C22×C4C2×D3211yescharacteristic
587SD16—62no—
588SD16—182no—
589D8—62no—
590D8—182no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—91no—
594C2×C8—91no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4C2×D3211yescharacteristic
606C22⋊C4—21no—
607C22⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C42—31no—
615C42—31no—
616C42—181no—
617C42—181no—
618C22×C3—22no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—62no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3C2×D3×D411yescharacteristic
644C22×C3C22×#6711yescharacteristic
645C2×D3—22no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—62no—
663C3×C4—81no—
664C3×C4—121no—
665C3×C4C2×#23711yescharacteristic
666C3×C4C2×#23711yescharacteristic
667C3×C4D3×#4111yescharacteristic
668C3×C4D3×#4111yescharacteristic
669Dic3—21no—
670Dic3—21no—
671Dic3—21no—
672Dic3—21no—
673Dic3—22no—
674Dic3—41no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—241no—
680Dic3—241no—
681C32#311911yescharacteristic, complemented, Sylow
682C23—21no—
683C23—61no—
684C23—61no—
685C23D3×#6711yescharacteristic
686Q8—32no—
687Q8—61no—
688D4—21no—
689D4—21no—
690D4—32no—
691D4—64no—
692D4—61no—
693D4—61no—
694D4—61no—
695D4—81no—
696D4—241no—
697D4—241no—
698D4—241no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—64no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—241no—
712C2×C4—241no—
713C2×C4—721no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4D3×#6711yescharacteristic
717C2×C4C22×D3211yescharacteristic
718C8—61no—
719C8—61no—
720C8—181no—
721C8—181no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—42no—
726C2×C3—41no—
727C2×C3—41no—
728C2×C3—81no—
729C2×C3—81no—
730C2×C3—122no—
731C2×C3—161no—
732C2×C3—241no—
733C2×C3#558611yescharacteristic
734C2×C3#577011yescharacteristic
735C2×C3#577411yescharacteristic
736C2×C3#582811yescharacteristic
737C2×C3#583511yescharacteristic
738C2×C3#583611yescharacteristic
739D3—42no—
740D3—81no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—62no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22C2×D3×#6711yescharacteristic
754C4—21no—
755C4—41no—
756C4—61no—
757C4—61no—
758C4—62no—
759C4—61no—
760C4—61no—
761C4—121no—
762C4—361no—
763C4—361no—
764C4D3×#23711yescharacteristic
765C4D3×#23711yescharacteristic
766C3—21no—
767C3#8007311yescharacteristic, complemented
768C3#8343411yescharacteristic, complemented
769C2—41no—
770C2—81no—
771C2—122no—
772C2—241no—
773C2#1059509711yescharacteristic
774C2#1059515411yescharacteristic
775C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5619C2semidirect
2. #10594992C2semidirect
3. #10592732C2semidirect
4. C3×#5037C2semidirect
5. #10591438C2semidirect
6. Dic3×#214C2semidirect
7. #10591430C2semidirect
8. #10591428C2semidirect
9. #10591161C2semidirect
10. #10591092C2semidirect
11. #10591056C2semidirect
12. #10590493C2semidirect
13. #10590478C2semidirect
14. #10590467C2semidirect
15. #10590452C2semidirect
63. #5619D3semidirect
76. #5037D3semidirect
681. C32#3119semidirect
767. C3#80073semidirect
768. C3#83434semidirect

Maximal subgroups

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

subgroupindex
C3×#56192
#105949922
#105927322
C3×#50372
#105914382
Dic3×#2142
#105914302
#105914282
#105911612
#105910922
#105910562
#105904932
#105904782
#105904672
#105904522
#834343
#800733