Finite Group Databasebeta

← #11872343

Subgroups — #11872343

Order 1152.

856 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5719C211yesmaximal, characteristic, complemented
2#10593887C211yesmaximal, characteristic, complemented
3#10592774C211yesmaximal, characteristic, complemented
4C3×#5072C211yesmaximal, characteristic, complemented
5#10591519C211yesmaximal, characteristic, complemented
6#10591519C211yesmaximal, characteristic, complemented
7#10591430C211yesmaximal, characteristic, complemented
8Dic3×#213C211yesmaximal, characteristic, complemented
9#10591415C211yesmaximal, characteristic, complemented
10#10591413C211yesmaximal, characteristic, complemented
11#10591405C211yesmaximal, characteristic, complemented
12#10591401C211yesmaximal, characteristic, complemented
13#10590292C211yesmaximal, characteristic, complemented
14#10590270C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#83434—31nomaximal
17#80316—31nomaximal
18C2×#3795C2211yescharacteristic
19C32×#127C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×#939—21no—
24C3×#939—21no—
25C3×#938C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C3×#935—21no—
28C3×#935—21no—
29C3×D4×Dic3C2211yescharacteristic
30C3×D4×Dic3C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34C3×#872C2211yescharacteristic
35C3×#870C2211yescharacteristic
36#63902—21no—
37Dic3×D12C2211yescharacteristic
38D3×C4⋊Dic3C2211yescharacteristic
39#63879—21no—
40#63878—21no—
41D3×Dic3⋊C4—21no—
42#63844C2211yescharacteristic
43#63659C2211yescharacteristic
44#63659C2211yescharacteristic
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×C4⋊(C3⋊C8)C2211yescharacteristic
49#63576C2211yescharacteristic
50#63575C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#540—31no—
62#5719D311yescharacteristic, complemented
63#5546—31no—
64#5523—31no—
65C3×#459—31no—
66#5158—31no—
67#5158—31no—
68#5152—31no—
69Dic3×D8—31no—
70#5075—31no—
71#5075—31no—
72#5075—61no—
73#5072D311yescharacteristic, complemented
74#5066—31no—
75#5063—31no—
76#5037—31no—
77#5037—31no—
78#5034—31no—
79#5033—31no—
80#5018—31no—
81C4×#214—31no—
82#5014—31no—
83C4×#213—31no—
84#5009—31no—
85#5000—31no—
86#4840—31no—
87#4829—31no—
88#4777—31no—
89#4774—31no—
90#4758—31no—
91#4757—31no—
92C2×C32×D4—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×#625—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3795—22no—
109#3795—22no—
110C32×C42C2311yescharacteristic
111#3754—22no—
112#3754—22no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115C4×C3⋊Dic3—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#213—22no—
123C3×#213—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3119—91noSylow
142C2×#237—31no—
143C2×#235—31no—
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C3×#127—21no—
147C3×#127C2×D311yescharacteristic
148C3×#127C2×D311yescharacteristic
149C3×#125—31no—
150C3×#123—61no—
151C3×#123—61no—
152C3×#121—31no—
153C3×#121—31no—
154C3×#121—61no—
155C3×#121—61no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×#117—31no—
160#939—21no—
161#939—21no—
162#938C2×D311yescharacteristic
163#938C2×D311yescharacteristic
164#935—21no—
165#935—21no—
166D4×Dic3—31no—
167D4×Dic3C2×D311yescharacteristic
168D4×Dic3C2×D311yescharacteristic
169C2×#214—31no—
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—31no—
173C2×#214—61no—
174C2×#214—61no—
175C2×#213C2×D311yescharacteristic
176C2×#213C2×D311yescharacteristic
177C4×#67—61no—
178C2×C4⋊Dic3—31no—
179C2×Dic3⋊C4—61no—
180#892—61no—
181D3×C4⋊C4—31no—
182D3×C4⋊C4—61no—
183#887—31no—
184#67⋊C4—61no—
185#67⋊C4—61no—
186#67⋊C4—61no—
187#877—61no—
188C4×D12—31no—
189C4×D12C2×D311yescharacteristic
190#872C2×D311yescharacteristic
191#870C2×D311yescharacteristic
192C4×Dic6—31no—
193C4×Dic6—31no—
194C4×Dic6—31no—
195C4×Dic6—61no—
196C3×C4⋊C8—31no—
197C3×#102—31no—
198C3×#102—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#832C2×D311yescharacteristic
208#832C2×D311yescharacteristic
209#830—31no—
210#830—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213#818—31no—
214#817—31no—
215#816—31no—
216#816—31no—
217#815—31no—
218C8×Dic3—31no—
219#810—31no—
220#810—31no—
221#809—31no—
222#809—31no—
223#808—31no—
224#808—31no—
225#808—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—
236C23×C32—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C32×D4—21no—
240C32×D4—21no—
241C32×D4—21no—
242C32×D4—21no—
243C32×D4—81no—
244C32×D4—81no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250#634—21no—
251#634#4112yes—
252C3×#67—81no—
253C3×#67—81no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—81no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—81no—
267#625—24no—
268D3×Dic3—24no—
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—31no—
283#449—91no—
284#449—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—31no—
297C2×C3×D4—41no—
298C2×C3×D4—41no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—21no—
310C2×#67—21no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318#237—62no—
319#237—62no—
320#235—62no—
321#235—62no—
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3C22×D311yescharacteristic
328C2×Dic6—31no—
329C2×Dic6—31no—
330C2×Dic6—61no—
331C3×D8—62no—
332C3×D8—62no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C22⋊C4—31no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—21no—
350C3×C42—31no—
351C3×C42C22×D311yescharacteristic
352C3×C42C22×D311yescharacteristic
353#217—21no—
354#217—21no—
355#217—21no—
356#217—21no—
357#217—61no—
358#214—62no—
359#214—62no—
360#214—62no—
361#214—62no—
362#214—122no—
363#214—122no—
364#213—22no—
365#213—22no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4#6711yescharacteristic
369(C2×D3)⋊C4#6711yescharacteristic
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—121no—
385Dic3⋊C4#6711yescharacteristic
386Dic3⋊C4#6711yescharacteristic
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—121no—
392C4×Dic3C22×D311yescharacteristic
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8C22×D311yescharacteristic
400C2×C3⋊C8C22×D311yescharacteristic
401C22×C32—41no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32C22×D411yescharacteristic
408C2×C3×D3—22no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—22no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C2×#41—91no—
427C2×SD16—91no—
428C2×SD16—91no—
429C2×D8—31no—
430C2×D8—31no—
431#127D3211yescharacteristic
432#125—31no—
433#123—61no—
434#123—61no—
435#121—31no—
436#121—31no—
437#121—61no—
438#121—61no—
439C4×Q8—91no—
440C4×Q8—91no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—31no—
444C4×D4—91no—
445C4×D4—181no—
446C4×D4—181no—
447#117—31no—
448#117—181no—
449C2×C4⋊C4—91no—
450C2×C4⋊C4—181no—
451#107—91no—
452#107—91no—
453#106—91no—
454#106—91no—
455C4⋊C8—31no—
456C4⋊C8—91no—
457#103—91no—
458#103—91no—
459#102—31no—
460#102—31no—
461#102—91no—
462#102—91no—
463#102—91no—
464#102—91no—
465C22⋊C8—91no—
466C22⋊C8—91no—
467#97—91no—
468C4×C8—91no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—31no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—61no—
477C22×D3—21no—
478C22×D3C2×#6711yescharacteristic
479C3×D4—21no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—21no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—32no—
488C3×D4—41no—
489C3×D4—41no—
490C3×D4—41no—
491C3×D4—41no—
492C3×D4—61no—
493C3×D4—81no—
494C3×D4—81no—
495C3×D4—81no—
496C3×D4—81no—
497C3×D4—82no—
498C3×D4—82no—
499C3×D4—241no—
500C3×D4—241no—
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—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—241no—
513C2×C3×C4—241no—
514C2×C3×C4—241no—
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4C2×#6711yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—64no—
522#67—64no—
523#67—81no—
524#67—81no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—64no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—81no—
534C2×Dic3—81no—
535C2×Dic3—121no—
536C2×Dic3—121no—
537C2×Dic3—241no—
538C2×Dic3—241no—
539C2×Dic3C2×#6711yescharacteristic
540C2×Dic3C2×#6711yescharacteristic
541C2×Dic3C2×#6711yescharacteristic
542D12—21no—
543D12#23712yes—
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—64no—
547C4×D3—81no—
548C4×D3—241no—
549C4×D3—241no—
550Dic6—32no—
551Dic6—32no—
552Dic6—62no—
553Dic6—61no—
554Dic6—61no—
555Dic6—121no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—121no—
565C3⋊C8—121no—
566C2×C32—81no—
567C2×C32—81no—
568C2×C32#52511yescharacteristic
569C2×C32#57611yescharacteristic
570C2×C32#57711yescharacteristic
571C3×D3—41no—
572C3×D3—42no—
573#41—182no—
574#41—182no—
575C2×Q8—91no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—31no—
579C2×D4—61no—
580C2×D4—61no—
581C2×D4—181no—
582C2×D4C2×D3211yescharacteristic
583C2×D4C2×D3211yescharacteristic
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—181no—
591SD16—182no—
592SD16—182no—
593D8—62no—
594D8—62no—
595C2×C8—31no—
596C2×C8—31no—
597C2×C8—91no—
598C2×C8—91no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—91no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C22⋊C4—31no—
611C22⋊C4—31no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—181no—
618C42—31no—
619C42—181no—
620C42—181no—
621C42C2×D3211yescharacteristic
622C22×C3—21no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
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—41no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—62no—
638C22×C3—61no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3C2×D3×D411yescharacteristic
648C22×C3C22×#6711yescharacteristic
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—22no—
653C2×D3—41no—
654C2×D3—41no—
655C3×C4—22no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—41no—
663C3×C4—61no—
664C3×C4—61no—
665C3×C4—61no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4C2×#23711yescharacteristic
670C3×C4D3×#4111yescharacteristic
671C3×C4D3×#4111yescharacteristic
672C3×C4D3×#4111yescharacteristic
673Dic3—21no—
674Dic3—21no—
675Dic3—21no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—62no—
680Dic3—62no—
681Dic3—122no—
682Dic3—121no—
683Dic3—121no—
684Dic3—241no—
685C32#311911yescharacteristic, complemented, Sylow
686C23—21no—
687C23—21no—
688C23—31no—
689C23—61no—
690Q8—92no—
691Q8—181no—
692D4—21no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—32no—
697D4—61no—
698D4—81no—
699D4—81no—
700D4—184no—
701D4—241no—
702D4—241no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—184no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—241no—
715C2×C4—241no—
716C2×C4—241no—
717C2×C4—721no—
718C2×C4—721no—
719C2×C4D3×#6711yescharacteristic
720C2×C4D3×#6711yescharacteristic
721C2×C4C22×D3211yescharacteristic
722C8—61no—
723C8—61no—
724C8—181no—
725C8—181no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—81no—
730C2×C3—81no—
731C2×C3—81no—
732C2×C3—81no—
733C2×C3—121no—
734C2×C3—122no—
735C2×C3—161no—
736C2×C3—161no—
737C2×C3#560611yescharacteristic
738C2×C3#575711yescharacteristic
739C2×C3#577511yescharacteristic
740C2×C3#582811yescharacteristic
741C2×C3#583511yescharacteristic
742C2×C3#583611yescharacteristic
743D3—42no—
744D3—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—61no—
752C22—61no—
753C22—61no—
754C22—62no—
755C22—121no—
756C22—121no—
757C22C2×D3×#6711yescharacteristic
758C4—21no—
759C4—21no—
760C4—61no—
761C4—61no—
762C4—61no—
763C4—121no—
764C4—121no—
765C4—121no—
766C4—182no—
767C4—361no—
768C4D3×#23711yescharacteristic
769C4#6431211yescharacteristic
770C3—21no—
771C3#8031611yescharacteristic, complemented
772C3#8343411yescharacteristic, complemented
773C2—81no—
774C2—81no—
775C2—121no—
776C2—122no—
777C2#1059509611yescharacteristic
778C2#1059510611yescharacteristic
779C2#1059530111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5719C2semidirect
2. #10593887C2semidirect
3. #10592774C2semidirect
4. C3×#5072C2semidirect
5. #10591519C2semidirect
6. #10591519C2semidirect
7. #10591430C2semidirect
8. Dic3×#213C2semidirect
9. #10591415C2semidirect
10. #10591413C2semidirect
11. #10591405C2semidirect
12. #10591401C2semidirect
13. #10590292C2semidirect
14. #10590270C2semidirect
15. #10590253C2semidirect
62. #5719D3semidirect
73. #5072D3semidirect
685. C32#3119semidirect
771. C3#80316semidirect
772. C3#83434semidirect

Maximal subgroups

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

subgroupindex
C3×#57192
#105938872
#105927742
C3×#50722
#105915192
#105914302
Dic3×#2132
#105914152
#105914132
#105914052
#105914012
#105902922
#105902702
#105902532
#834343
#803163