Finite Group Databasebeta

← #11872341

Subgroups — #11872341

Order 1152.

862 conjugacy classes of subgroups.

The subgroup lattice has 785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5719C211yesmaximal, characteristic, complemented
2#10593890C211yesmaximal, characteristic, complemented
3#10592771C211yesmaximal, characteristic, complemented
4C3×#5075C211yesmaximal, characteristic, complemented
5#10591521C211yesmaximal, characteristic, complemented
6#10591521C211yesmaximal, characteristic, complemented
7#10591440C211yesmaximal, characteristic, complemented
8Dic3×#214C211yesmaximal, characteristic, complemented
9#10591415C211yesmaximal, characteristic, complemented
10#10591413C211yesmaximal, characteristic, complemented
11#10591404C211yesmaximal, characteristic, complemented
12#10591400C211yesmaximal, characteristic, complemented
13#10590308C211yesmaximal, characteristic, complemented
14#10590286C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#83434—31nomaximal
17#80364—31nomaximal
18C2×#3799C2211yescharacteristic
19C32×#127C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×#939—21no—
24C3×#939—21no—
25C3×#938C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C3×#935—21no—
28C3×#935—21no—
29C3×D4×Dic3C2211yescharacteristic
30C3×D4×Dic3C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic
33C3×#872C2211yescharacteristic
34C3×#870C2211yescharacteristic
35C3×C4×Dic6C2211yescharacteristic
36#63894C2211yescharacteristic
37D3×C4⋊Dic3C2211yescharacteristic
38#63883—21no—
39#63881—21no—
40#63880—21no—
41Dic3×Dic6C2211yescharacteristic
42#63836—21no—
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#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×#540—31no—
62#5719D311yescharacteristic, complemented
63#5574—31no—
64#5523—31no—
65C3×#460—31no—
66#5172—31no—
67#5172—31no—
68#5164—31no—
69Dic3×SD16—31no—
70#5075D311yescharacteristic, complemented
71#5072—31no—
72#5072—31no—
73#5072—61no—
74#5066—31no—
75#5063—31no—
76#5037—31no—
77#5037—31no—
78#5034—31no—
79#5033—31no—
80#5022—31no—
81#5018—31no—
82C4×#214—31no—
83#5014—31no—
84C4×#213—31no—
85#5000—31no—
86#4847—31no—
87#4840—31no—
88#4785—31no—
89#4777—31no—
90#4774—31no—
91#4756—31no—
92C2×C32×D4—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#624—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108#3799—22no—
109#3799—22no—
110C32×C42C2311yescharacteristic
111#3753—22no—
112#3753—22no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#214—22no—
122C3×#214—22no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
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#3119—91noSylow
142C2×#239—31no—
143C2×#235—31no—
144C2×C3×SD16—31no—
145C2×C3×SD16—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×Q8—31no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×#117—31no—
160Q8×Dic3—31no—
161#939—21no—
162#939—21no—
163#938C2×D311yescharacteristic
164#938C2×D311yescharacteristic
165#935—21no—
166#935—21no—
167D4×Dic3C2×D311yescharacteristic
168D4×Dic3C2×D311yescharacteristic
169C2×#214C2×D311yescharacteristic
170C2×#214C2×D311yescharacteristic
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—31no—
174C2×#213—31no—
175C2×#213—61no—
176C2×#213—61no—
177C2×C4⋊Dic3—31no—
178#893—31no—
179#893—61no—
180#892—61no—
181D3×C4⋊C4—31no—
182D3×C4⋊C4—61no—
183D3×C4⋊C4—61no—
184#67⋊C4—61no—
185#67⋊C4—61no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—61no—
190C4×D12—61no—
191#872—61no—
192#872C2×D311yescharacteristic
193#870C2×D311yescharacteristic
194C4×Dic6—31no—
195C4×Dic6C2×D311yescharacteristic
196C3×C4⋊C8—31no—
197C3×#102—31no—
198C3×#102—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#821—31no—
212#821—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215#818—31no—
216#817—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—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)#4112yes—
251C4×C3⋊D3—81no—
252C3×#67—81no—
253C3×#67—81no—
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×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×Dic6—21no—
266C3×Dic6#4112yes—
267#626—24no—
268#624—24no—
269#624—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—31no—
282#459—91no—
283#449—91no—
284#449—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C2×C3×Q8—31no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
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—
308C2×#67—21no—
309C2×#67—21no—
310C2×#67—61no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—61no—
314#239—62no—
315#239—62no—
316#235—62no—
317#235—62no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—61no—
321C2×D12—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—121no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6C22×D311yescharacteristic
332C3×SD16—62no—
333C3×SD16—62no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—21no—
351C3×C42—31no—
352C3×C42—61no—
353C3×C42C22×D311yescharacteristic
354C3×C42C22×D311yescharacteristic
355#217—21no—
356#217—21no—
357#217—21no—
358#217—21no—
359#214—22no—
360#214—22no—
361#213—62no—
362#213—62no—
363#213—62no—
364#213—62no—
365#213—122no—
366#213—122no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—121no—
372(C2×D3)⋊C4#6711yescharacteristic
373(C2×D3)⋊C4#6711yescharacteristic
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4#6711yescharacteristic
388Dic3⋊C4#6711yescharacteristic
389C4×Dic3—21no—
390C4×Dic3—61no—
391C4×Dic3—61no—
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—41no—
410C2×C3⋊D3—41no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—41no—
419C3×Dic3—21no—
420C3×Dic3—22no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C2×#41—91no—
427C2×SD16—31no—
428C2×SD16—31no—
429C2×D8—91no—
430C2×D8—91no—
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—31no—
440C4×Q8—91no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—91no—
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—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—121no—
479C22×D3C2×#6711yescharacteristic
480C3×Q8—32no—
481C3×Q8—61no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—21no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—41no—
491C3×D4—41no—
492C3×D4—41no—
493C3×D4—41no—
494C3×D4—81no—
495C3×D4—81no—
496C3×D4—81no—
497C3×D4—81no—
498C3×D4—82no—
499C3×D4—82no—
500C3×D4—241no—
501C3×D4—241no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—241no—
515C2×C3×C4—241no—
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C2×#6711yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522#67—64no—
523#67—81no—
524#67—81no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—81no—
532C2×Dic3—81no—
533C2×Dic3—121no—
534C2×Dic3—241no—
535C2×Dic3C2×#6711yescharacteristic
536C2×Dic3C2×#6711yescharacteristic
537C2×Dic3C2×#6711yescharacteristic
538D12—32no—
539D12—32no—
540D12—62no—
541D12—64no—
542D12—61no—
543D12—61no—
544D12—121no—
545C4×D3—21no—
546C4×D3—21no—
547C4×D3—64no—
548C4×D3—64no—
549C4×D3—241no—
550C4×D3—241no—
551C4×D3—241no—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3—242no—
555Dic6—21no—
556Dic6#23712yes—
557C3×C8—61no—
558C3×C8—61no—
559C3⋊C8—21no—
560C3⋊C8—21no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—121no—
566C3⋊C8—121no—
567C2×C32—81no—
568C2×C32—81no—
569C2×C32#52511yescharacteristic
570C2×C32#57611yescharacteristic
571C2×C32#57711yescharacteristic
572C3⋊D3—42no—
573C3×D3—41no—
574#41—182no—
575#41—182no—
576C2×Q8—31no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—61no—
580C2×D4—61no—
581C2×D4—91no—
582C2×D4—181no—
583C2×D4C2×D3211yescharacteristic
584C2×D4C2×D3211yescharacteristic
585C22×C4—31no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—181no—
591C22×C4—181no—
592SD16—62no—
593SD16—62no—
594D8—182no—
595D8—182no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—91no—
599C2×C8—91no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—91no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C22⋊C4—31no—
612C22⋊C4—31no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C42—31no—
620C42—61no—
621C42—181no—
622C42C2×D3211yescharacteristic
623C22×C3—21no—
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—41no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3C2×D3×D411yescharacteristic
646C22×C3C22×#6711yescharacteristic
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—122no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—241no—
658C2×D3—241no—
659C3×C4—22no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—41no—
667C3×C4—61no—
668C3×C4—61no—
669C3×C4—62no—
670C3×C4—61no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4C2×#23711yescharacteristic
675C3×C4D3×#4111yescharacteristic
676C3×C4D3×#4111yescharacteristic
677C3×C4D3×#4111yescharacteristic
678Dic3—21no—
679Dic3—21no—
680Dic3—21no—
681Dic3—22no—
682Dic3—41no—
683Dic3—41no—
684Dic3—41no—
685Dic3—121no—
686Dic3—121no—
687Dic3—241no—
688C32#311911yescharacteristic, complemented, Sylow
689C23—21no—
690C23—21no—
691C23—31no—
692C23—181no—
693Q8—32no—
694Q8—61no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—81no—
700D4—81no—
701D4—92no—
702D4—184no—
703D4—181no—
704D4—241no—
705D4—241no—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—184no—
716C2×C4—181no—
717C2×C4—241no—
718C2×C4—241no—
719C2×C4—721no—
720C2×C4—721no—
721C2×C4—721no—
722C2×C4D3×#6711yescharacteristic
723C2×C4D3×#6711yescharacteristic
724C2×C4C22×D3211yescharacteristic
725C8—61no—
726C8—61no—
727C8—181no—
728C8—181no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—81no—
733C2×C3—81no—
734C2×C3—81no—
735C2×C3—81no—
736C2×C3—121no—
737C2×C3—161no—
738C2×C3—161no—
739C2×C3#560611yescharacteristic
740C2×C3#576211yescharacteristic
741C2×C3#577411yescharacteristic
742C2×C3#582811yescharacteristic
743C2×C3#583511yescharacteristic
744C2×C3#583611yescharacteristic
745D3—41no—
746D3—122no—
747D3—122no—
748D3—242no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—61no—
756C22—61no—
757C22—61no—
758C22—182no—
759C22—361no—
760C22—361no—
761C22C2×D3×#6711yescharacteristic
762C4—21no—
763C4—21no—
764C4—61no—
765C4—61no—
766C4—61no—
767C4—62no—
768C4—121no—
769C4—121no—
770C4—121no—
771C4—361no—
772C4D3×#23711yescharacteristic
773C4#6431211yescharacteristic
774C3—21no—
775C3#8036411yescharacteristic, complemented
776C3#8343411yescharacteristic, complemented
777C2—81no—
778C2—81no—
779C2—121no—
780C2—362no—
781C2#1059509711yescharacteristic
782C2#1059510511yescharacteristic
783C2#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. #10593890C2semidirect
3. #10592771C2semidirect
4. C3×#5075C2semidirect
5. #10591521C2semidirect
6. #10591521C2semidirect
7. #10591440C2semidirect
8. Dic3×#214C2semidirect
9. #10591415C2semidirect
10. #10591413C2semidirect
11. #10591404C2semidirect
12. #10591400C2semidirect
13. #10590308C2semidirect
14. #10590286C2semidirect
15. #10590253C2semidirect
62. #5719D3semidirect
70. #5075D3semidirect
688. C32#3119semidirect
775. C3#80364semidirect
776. C3#83434semidirect

Maximal subgroups

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

subgroupindex
C3×#57192
#105938902
#105927712
C3×#50752
#105915212
#105914402
Dic3×#2142
#105914152
#105914132
#105914042
#105914002
#105903082
#105902862
#105902532
#834343
#803643