Finite Group Databasebeta

← #11895739

Subgroups — #11895739

Order 1152.

862 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×#5718C211yesmaximal, characteristic, complemented
2#10593938C211yesmaximal, characteristic, complemented
3#10592771C211yesmaximal, characteristic, complemented
4C3×#5071C211yesmaximal, characteristic, complemented
5#10591487C211yesmaximal, characteristic, complemented
6#10591477C211yesmaximal, characteristic, complemented
7#10591429C211yesmaximal, characteristic, complemented
8#10591429C211yesmaximal, characteristic, complemented
9#10591409C211yesmaximal, characteristic, complemented
10#10591408C211yesmaximal, characteristic, complemented
11#10591404C211yesmaximal, characteristic, complemented
12#10591400C211yesmaximal, characteristic, complemented
13#10590346C211yesmaximal, characteristic, complemented
14#10590270C211yesmaximal, characteristic, complemented
15#10590251C211yesmaximal, characteristic, complemented
16#83581—31nomaximal
17#81708—31nomaximal
18C2×C3×#237—21no—
19C32×#127C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×#940C2211yescharacteristic
24C3×#940C2211yescharacteristic
25C3×#939—21no—
26C3×#939—21no—
27C3×#938—21no—
28C3×D4×Dic3C2211yescharacteristic
29C3×D4×Dic3C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×#870C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33#63918C2211yescharacteristic
34#63895—21no—
35#63894C2211yescharacteristic
36#63894C2211yescharacteristic
37#63888—21no—
38#63883—21no—
39#63869C2211yescharacteristic
40#63865—21no—
41C2×#3714C2211yescharacteristic
42#63659C2211yescharacteristic
43#63659C2211yescharacteristic
44C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#803C2211yescharacteristic
50#63576C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#550—31no—
62#5718D311yescharacteristic, complemented
63#5690—31no—
64#5579—31no—
65C3×#490—31no—
66#5072—31no—
67#5072—31no—
68#5072—31no—
69#5072—31no—
70#5072—61no—
71#5071—31no—
72#5071D311yescharacteristic, complemented
73#5070—31no—
74#5066—31no—
75#5024—31no—
76#5014—31no—
77#5014—31no—
78C4×#213—31no—
79#5009—31no—
80#5009—31no—
81#5008—31no—
82#4786—31no—
83#4786—31no—
84#4785—31no—
85#4764—31no—
86#4763—31no—
87#4761—31no—
88#4760—31no—
89#4756—31no—
90#4711—31no—
91#4701—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—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C3×#237—44no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×Dic6D411yescharacteristic
108C2×#627—21no—
109C2×#624—21no—
110C2×#624—21no—
111C32×C42C2311yescharacteristic
112#3753—22no—
113#3753—22no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3D411yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4D411yescharacteristic
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137#3722—21no—
138#3714—22no—
139#3366—91noSylow
140C2×C3×#41—61no—
141C2×#237—21no—
142C3×#127—21no—
143C3×#127—31no—
144C3×#127—31no—
145C3×#127C2×D311yescharacteristic
146C3×#127C2×D311yescharacteristic
147C3×#125—31no—
148C3×#121—61no—
149C3×#121—61no—
150C3×#121—61no—
151C3×C4×Q8—31no—
152C3×C4×D4—31no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155#946—61no—
156#940C2×D311yescharacteristic
157#940C2×D311yescharacteristic
158#939—21no—
159#939—21no—
160#938—21no—
161D4×Dic3C2×D311yescharacteristic
162D4×Dic3C2×D311yescharacteristic
163C2×#213—31no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—31no—
167C2×#213—31no—
168C2×#213—61no—
169C2×#213—61no—
170C2×D24—31no—
171#897—61no—
172#896—61no—
173#896—61no—
174#896—61no—
175#896—61no—
176#893—31no—
177#893—31no—
178D3×C4⋊C4—61no—
179D3×C4⋊C4—61no—
180#890—31no—
181#888—31no—
182C4×D12—31no—
183C4×D12—31no—
184C4×D12—31no—
185C4×D12—31no—
186C4×D12—61no—
187C4×D12C2×D311yescharacteristic
188#870—31no—
189#870C2×D311yescharacteristic
190#869—31no—
191C4×Dic6C2×D311yescharacteristic
192C3×#102—31no—
193C3×#102—31no—
194C3×#102—31no—
195C3×#102—31no—
196C3×#97—31no—
197#832—31no—
198#832—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—61no—
205#832—61no—
206#832C2×D311yescharacteristic
207#832C2×D311yescharacteristic
208#832C2×D311yescharacteristic
209#832C2×D311yescharacteristic
210#821—31no—
211#821—31no—
212#817—31no—
213#815—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216C8×Dic3—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#808—31no—
221#808—31no—
222#808—31no—
223#807—31no—
224#807—31no—
225C4⋊(C3⋊C8)—31no—
226C4⋊(C3⋊C8)—31no—
227C4⋊(C3⋊C8)—31no—
228C4⋊(C3⋊C8)—31no—
229C4⋊(C3⋊C8)—61no—
230#803—31no—
231#803C2×D311yescharacteristic
232C4×C3⋊C8—31no—
233C23×C32—21no—
234C23×C32—21no—
235C22×C3⋊D3—21no—
236C22×C3×D3—21no—
237C32×D4—21no—
238C32×D4—21no—
239C32×D4—21no—
240C32×D4—21no—
241C32×D4—42no—
242C32×D4—81no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)#4112yescomplemented
249C4×C3⋊D3—81no—
250C3×#67—42no—
251C3×#67—42no—
252C3×#67—81no—
253C3×#67—81no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3—42no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12—21no—
265C3×C4×D3—42no—
266C3×Dic6—22no—
267#627—81no—
268#624—42no—
269#624—81no—
270C3⋊(C3⋊C8)—21no—
271C3⋊(C3⋊C8)—21no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274#554—91no—
275#550—31no—
276#490—31no—
277#490—91no—
278#486—91no—
279#478—91no—
280#478—91no—
281#476—91no—
282#459—91no—
283#459—91no—
284#459—91no—
285#446—91no—
286#442—91no—
287#442—91no—
288C4×D8—91no—
289C3×#41—124no—
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—31no—
298C2×C3×D4—41no—
299C2×C3×D4—41no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C2×#67—21no—
312C2×#67—21no—
313C2×#67—21no—
314C2×#67—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317#237—44no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—61no—
321C2×D12C22×D311yescharacteristic
322C2×C4×D3—21no—
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×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6#6711yescharacteristic
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—31no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C42—21no—
347C3×C42—31no—
348C3×C42—31no—
349C3×C42C22×D311yescharacteristic
350C3×C42C22×D311yescharacteristic
351#217—21no—
352#217—21no—
353#213—62no—
354#213—62no—
355#213—62no—
356#213—62no—
357#213—62no—
358#213—122no—
359#213—122no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—121no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3#6711yescharacteristic
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#6711yescharacteristic
384Dic3⋊C4#6711yescharacteristic
385C4×Dic3C22×D311yescharacteristic
386C4×Dic3C22×D311yescharacteristic
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—61no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8C22×D311yescharacteristic
394C2×C3⋊C8C22×D311yescharacteristic
395D24—62no—
396C22×C32—41no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32C22×D411yescharacteristic
403C2×C3⋊D3—22no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4C2×#4111yescharacteristic
412C32×C42−1+411yescharacteristic
413C3⋊Dic3—41no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3AGL(1,ℤ/8)12yes—
421C2×#41—61no—
422C2×D8—91no—
423C2×D8—91no—
424C2×D8—91no—
425C4⋊Q8—91no—
426#127—31no—
427#127—31no—
428#127D3211yescharacteristic
429#125—31no—
430#125—91no—
431C22⋊Q8—181no—
432C22⋊Q8—181no—
433C22⋊Q8—181no—
434#121—61no—
435#121—61no—
436#121—61no—
437C4×Q8—31no—
438C4×D4—31no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—91no—
444C2×C4⋊C4—181no—
445#107—91no—
446#106—91no—
447#106—91no—
448C4⋊C8—91no—
449C4⋊C8—91no—
450C4⋊C8—91no—
451#102—31no—
452#102—31no—
453#102—31no—
454#102—31no—
455#102—91no—
456#102—91no—
457#102—91no—
458#102—91no—
459#102—91no—
460#102—91no—
461#97—31no—
462#97—91no—
463C4×C8—91no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—61no—
471C22×D3—21no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—121no—
475C3×Q8—62no—
476C3×D4—21no—
477C3×D4—21no—
478C3×D4—21no—
479C3×D4—21no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—41no—
485C3×D4—41no—
486C3×D4—41no—
487C3×D4—41no—
488C3×D4—42no—
489C3×D4—42no—
490C3×D4—61no—
491C3×D4—61no—
492C3×D4—82no—
493C3×D4—81no—
494C3×D4—81no—
495C3×D4—82no—
496C3×D4—122no—
497C3×D4—122no—
498C3×D4—241no—
499C3×D4—241no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—31no—
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—122no—
511C2×C3×C4—122no—
512C2×C3×C4—122no—
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C2×#6711yescharacteristic
516C2×C3×C4C2×#6711yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519#67—42no—
520#67—42no—
521#67—81no—
522#67—81no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—42no—
527C2×Dic3—42no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—121no—
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533C2×Dic3C2×#6711yescharacteristic
534C2×Dic3C2×#6711yescharacteristic
535D12—21no—
536D12—21no—
537D12—32no—
538D12—32no—
539D12—62no—
540D12—61no—
541D12—61no—
542D12—121no—
543C4×D3—42no—
544C4×D3—122no—
545C4×D3—122no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—241no—
550C4×D3—242no—
551Dic6—22no—
552Dic6—241no—
553Dic6—241no—
554C3×C8—61no—
555C3×C8—61no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—121no—
563C3⋊C8—121no—
564C2×C32—81no—
565C2×C32—81no—
566C2×C32#54811yescharacteristic
567C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
568C2×C32#57611yescharacteristic
569C3⋊D3—42no—
570C3×D3—81no—
571#41—124no—
572C2×Q8—31no—
573C2×Q8—181no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—31no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4—61no—
580C2×D4—61no—
581C2×D4—91no—
582C2×D4C2×D3211yescharacteristic
583C2×D4C2×D3211yescharacteristic
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590D8—182no—
591D8—182no—
592D8—182no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8—91no—
596C2×C8—91no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—31no—
616C42—31no—
617C42C2×D3211yescharacteristic
618C22×C3—21no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
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—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C22×#6711yescharacteristic
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—62no—
646C2×D3—62no—
647C2×D3—122no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—241no—
653C2×D3—241no—
654C3×C4—22no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—32no—
662C3×C4—41no—
663C3×C4—61no—
664C3×C4—61no—
665C3×C4—61no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4D3×#4111yescharacteristic
670C3×C4D3×#4111yescharacteristic
671C3×C4#101011yescharacteristic
672C3×C4#101011yescharacteristic
673Dic3—21no—
674Dic3—21no—
675Dic3—21no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—121no—
680Dic3—121no—
681Dic3—241no—
682Dic3#93212yes—
683C32#336611yescharacteristic, complemented, Sylow
684C23—21no—
685C23—21no—
686C23—61no—
687C23—181no—
688Q8—62no—
689Q8—721no—
690D4—21no—
691D4—21no—
692D4—21no—
693D4—21no—
694D4—42no—
695D4—61no—
696D4—61no—
697D4—81no—
698D4—92no—
699D4—122no—
700D4—122no—
701D4—181no—
702D4—241no—
703D4—241no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—181no—
715C2×C4—362no—
716C2×C4—721no—
717C2×C4—721no—
718C2×C4D3×#6711yescharacteristic
719C2×C4D3×#6711yescharacteristic
720C2×C4C22×D3211yescharacteristic
721C8—61no—
722C8—61no—
723C8—181no—
724C8—181no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—81no—
729C2×C3—81no—
730C2×C3—81no—
731C2×C3—81no—
732C2×C3—161no—
733C2×C3—161no—
734C2×C3—241no—
735C2×C3#567711yescharacteristic
736C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
737C2×C3#577411yescharacteristic
738C2×C3C2×#93211yescharacteristic
739C2×C3#583111yescharacteristic
740C2×C3#583511yescharacteristic
741D3—81no—
742D3—122no—
743D3—122no—
744D3—242no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22—182no—
755C22—361no—
756C22—361no—
757C22C2×D3×#6711yescharacteristic
758C4—21no—
759C4—21no—
760C4—32no—
761C4—61no—
762C4—61no—
763C4—61no—
764C4—121no—
765C4—121no—
766C4—121no—
767C4—361no—
768C4#6430911yescharacteristic
769C4#6431211yescharacteristic
770C3—21no—
771C3#8170811yescharacteristic, complemented
772C3#8358111yescharacteristic, complemented
773C2—81no—
774C2—81no—
775C2—241no—
776C2—362no—
777C2D3×#93211yescharacteristic
778C2#1059509711yescharacteristic
779C2#1059523711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3366
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×#5718C2semidirect
2. #10593938C2semidirect
3. #10592771C2semidirect
4. C3×#5071C2semidirect
5. #10591487C2semidirect
6. #10591477C2semidirect
7. #10591429C2semidirect
8. #10591429C2semidirect
9. #10591409C2semidirect
10. #10591408C2semidirect
11. #10591404C2semidirect
12. #10591400C2semidirect
13. #10590346C2semidirect
14. #10590270C2semidirect
15. #10590251C2semidirect
62. #5718D3semidirect
72. #5071D3semidirect
248. C4⋊(C3⋊D3)#41semidirect
683. C32#3366semidirect
771. C3#81708semidirect
772. C3#83581semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
#105939382
#105927712
C3×#50712
#105914872
#105914772
#105914292
#105914092
#105914082
#105914042
#105914002
#105903462
#105902702
#105902512
#835813
#817083