Finite Group Databasebeta

← #11872221

Subgroups — #11872221

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595396C211yesmaximal, characteristic, complemented
2#10594604C211yesmaximal, characteristic, complemented
3#10592487C211yesmaximal, characteristic, complemented
4C3×#4819C211yesmaximal, characteristic, complemented
5C3×#4814C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591572C211yesmaximal, characteristic, complemented
8#10591568C211yesmaximal, characteristic, complemented
9#10590944C211yesmaximal, characteristic
10#10590777C211yesmaximal, characteristic, complemented
11#10590764C211yesmaximal, characteristic, complemented
12#10590698C211yesmaximal, characteristic, complemented
13#10590558C211yesmaximal, characteristic, complemented
14#10590505C211yesmaximal, characteristic, complemented
15#10590462C211yesmaximal, characteristic, complemented
16#81496—31nomaximal
17#80508—31nomaximal
18C2×D3×D12C2211yescharacteristic
19Q8×C3⋊Dic3C2211yescharacteristic, complemented
20C2×#3755C2211yescharacteristic
21#64102C2211yescharacteristic
22C3×#947C2211yescharacteristic, complemented
23C3×#946C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C2×C3×D24C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#892C2211yescharacteristic
28#63921—21no—
29D3×(C2×D3)⋊C4—21no—
30#63918C2211yescharacteristic, complemented
31#63915—21no—
32#63908C2211yescharacteristic
33C4×#626—21no—
34#63898C2211yescharacteristic
35#63898C2211yescharacteristic, complemented
36#63894C2211yescharacteristic
37#63893—21no—
38#63891—21no—
39#63880—21no—
40#63862—21no—
41#63855C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×#103C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45C8×C3⋊Dic3C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#818C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic, complemented
52C3×#808C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#5682—31no—
62#5643—31no—
63#5545—31no—
64#5521—31no—
65C3×#485—31no—
66C3×#463—31no—
67#5169—31no—
68#5164—31no—
69#5156—31no—
70Dic3×D8—31no—
71#5057—31no—
72#5046—31no—
73#5008—31no—
74#5003—31no—
75#4890—31no—
76#4872—31no—
77#4870—31no—
78#4869—31no—
79#4846—31no—
80#4840—31no—
81#4819—31no—
82#4819D311yescharacteristic, complemented
83#4817—31no—
84#4814D311yescharacteristic, complemented
85#4788—31no—
86#4788—31no—
87#4788—61no—
88#4785—31no—
89#4784—31no—
90#4732—31no—
91#4720—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×#627—21no—
101C2×#626—21no—
102C2×#625—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12—22no—
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110#3755—22no—
111#3752—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#215—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D24—22no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140#3714—22no—
141#3118—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C2×C3×SD16—31no—
145C2×C3×D8—31no—
146C3×#124—31no—
147C3×C22⋊Q8—31no—
148C3×C4×D4—31no—
149C3×#117—31no—
150#947C2×D311yescharacteristic, complemented
151#946C2×D311yescharacteristic
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154Q8×Dic3—61no—
155C2×#215—31no—
156C2×#215—31no—
157C2×#215—61no—
158C2×#215C2×D311yescharacteristic
159#938—31no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162C2×#213—31no—
163#930—31no—
164C4×#67—61no—
165C2×(C2×D3)⋊C4—61no—
166#926—31no—
167C2×D24—31no—
168C2×D24C2×D311yescharacteristic
169#898—61no—
170#897—61no—
171#893—31no—
172#893—31no—
173#893—31no—
174#893—31no—
175#893—31no—
176#893—61no—
177#893C2×D311yescharacteristic
178#892C2×D311yescharacteristic
179#888—31no—
180#886—61no—
181#885—61no—
182#885—61no—
183#883—61no—
184#67⋊C4—61no—
185D3×C22⋊C4—61no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188#879—61no—
189#878—61no—
190C4×D12—31no—
191C4×D12—61no—
192C4×D12—61no—
193#872—31no—
194#869—31no—
195C3×#107—31no—
196C3×#106—31no—
197C3×C4⋊C8—31no—
198C3×#103—21no—
199C3×#103—31no—
200C3×#103C2×D311yescharacteristic, complemented
201C3×#103C2×D311yescharacteristic, complemented
202C3×#102—31no—
203C3×C22⋊C8—31no—
204#835C2×D311yescharacteristic, complemented
205#832—31no—
206#832—31no—
207#832—31no—
208#830—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—61no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8C2×D311yescharacteristic
216#818—31no—
217#818C2×D311yescharacteristic, complemented
218#815—31no—
219#815—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8C2×D311yescharacteristic, complemented
222C8×Dic3—31no—
223C8×Dic3—31no—
224C8×Dic3—61no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809C2×D311yescharacteristic, complemented
229#808—31no—
230#808—31no—
231#808—61no—
232#808C2×D311yescharacteristic, complemented
233#807—31no—
234C4⋊(C3⋊C8)—31no—
235C22×C3⋊D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—24no—
240C2×D32—81no—
241C2×D32—81no—
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)#4112yes—
252C4×C3⋊D3—81no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12#4112yes—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—81no—
265#627—81no—
266#626—24no—
267#625—81no—
268#624—81no—
269D3×Dic3—81no—
270D3×Dic3—81no—
271C32×C8—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—91no—
276#518—91no—
277#485—31no—
278#482—91no—
279#476—91no—
280#474—91no—
281#463—31no—
282#463—91no—
283#450—91no—
284#447—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C23×D3—61no—
291C23×D3—61no—
292C2×C3×Q8—21no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—61no—
299C2×#67—61no—
300C2×#67—61no—
301C2×#67—61no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304D3×D4—62no—
305D3×D4—62no—
306C2×D12—31no—
307C2×D12—31no—
308C2×D12—61no—
309C2×D12—62no—
310C2×D12—61no—
311C2×D12—62no—
312C2×D12C22×D311yescharacteristic
313C2×D12C22×D311yescharacteristic
314C2×C4×D3—21no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—121no—
322C2×C4×D3C22×D311yescharacteristic
323C2×Dic6—61no—
324C2×Dic6—61no—
325C3×SD16—62no—
326C3×D8—62no—
327C2×C3×C8—21no—
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C22×D311yescharacteristic
332C3×C4⋊C4—21no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C42—31no—
344C3×C42—61no—
345#217—31no—
346#217—31no—
347#217—61no—
348#217—61no—
349#217—61no—
350#215—22no—
351#215—62no—
352#215—62no—
353#215—64no—
354#213—62no—
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—31no—
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—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—121no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—121no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—31no—
383Dic3⋊C4—31no—
384Dic3⋊C4—61no—
385C4×Dic3—21no—
386C4×Dic3—31no—
387C4×Dic3—31no—
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—61no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398D24—22no—
399D24—62no—
400C22×C32C22×D411yescharacteristic
401C2×C3⋊D3—22no—
402C2×C3⋊D3—41no—
403C2×C3⋊D3—41no—
404C2×C3×D3—22no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413D32—84no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—21no—
419C3⋊Dic3—21no—
420C3⋊Dic3—41no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C22×D4—91no—
427C2×SD16—31no—
428C2×SD16—91no—
429C2×D8—31no—
430C2×D8—91no—
431C4⋊Q8—91no—
432#126—181no—
433#124—31no—
434#124—181no—
435#123—181no—
436C22⋊Q8—31no—
437C22⋊Q8—181no—
438#121—91no—
439C4×Q8—91no—
440C4×D4—31no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—181no—
446C4×D4—181no—
447#117—31no—
448#117—91no—
449C2×C22⋊C4—181no—
450C2×C22⋊C4—181no—
451#107—31no—
452#107—91no—
453#106—31no—
454#106—91no—
455C4⋊C8—31no—
456C4⋊C8—91no—
457#103—31no—
458#103D3211yescharacteristic, complemented
459#102—31no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464#102—91no—
465C22⋊C8—31no—
466C22⋊C8—91no—
467#97—91no—
468C4×C8—91no—
469C23×C3—31no—
470C23×C3—61no—
471C23×C3—61no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—64no—
475C22×D3—64no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—121no—
479C22×D3—241no—
480C22×D3—241no—
481C22×D3—241no—
482C22×D3—241no—
483C22×D3D3×D411yescharacteristic
484C3×Q8—22no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—41no—
490C3×D4—32no—
491C3×D4—61no—
492C3×D4—61no—
493C3×D4—61no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—241no—
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—64no—
512#67—241no—
513#67—241no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—121no—
525C2×Dic3—241no—
526C2×Dic3—241no—
527C2×Dic3D3×D411yescharacteristic
528C2×Dic3D3×D411yescharacteristic
529C2×Dic3D3×D411yescharacteristic
530D12—21no—
531D12—21no—
532D12—21no—
533D12—32no—
534D12—32no—
535D12—62no—
536D12—64no—
537D12—61no—
538D12—61no—
539D12—121no—
540D12#23712yes—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—81no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—242no—
549C4×D3—241no—
550C4×D3—241no—
551Dic6—241no—
552Dic6—241no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—41no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—62no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C2×C32#52511yescharacteristic
564C2×C32#57611yescharacteristic
565C2×C32#57711yescharacteristic
566C3⋊D3—42no—
567C3×D3—41no—
568C3×D3—42no—
569C3×D3—81no—
570C24—181no—
571C2×Q8—181no—
572C2×Q8C2×D3211yescharacteristic
573C2×D4—31no—
574C2×D4—31no—
575C2×D4—91no—
576C2×D4—181no—
577C2×D4—182no—
578C2×D4—182no—
579C2×D4—181no—
580C22×C4—31no—
581C22×C4—61no—
582C22×C4—181no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4—181no—
586SD16—62no—
587SD16—182no—
588D8—62no—
589D8—182no—
590C2×C8—31no—
591C2×C8—31no—
592C2×C8—91no—
593C2×C8C2×D3211yescharacteristic
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4C2×D3211yescharacteristic
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—91no—
609C22⋊C4—91no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—31no—
616C42—61no—
617C42—91no—
618C42—181no—
619C22×C3—21no—
620C22×C3—62no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3C2×D3×D411yescharacteristic
630C22×C3C2×D3×D411yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—22no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—62no—
641C2×D3—62no—
642C2×D3—122no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—241no—
648C2×D3—241no—
649C2×D3—244no—
650C2×D3—244no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—42no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—81no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4C2×#23711yescharacteristic
665C3×C4D3×#4111yescharacteristic
666C3×C4D3×#4111yescharacteristic
667C3×C4D3×#4111yescharacteristic
668Dic3—21no—
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—41no—
673Dic3—62no—
674Dic3—61no—
675Dic3—61no—
676Dic3—61no—
677Dic3—61no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—241no—
682C32#311811yescharacteristic, complemented, Sylow
683C23—31no—
684C23—61no—
685C23—61no—
686C23—184no—
687C23—181no—
688C23—721no—
689C23—721no—
690Q8—21no—
691Q8—21no—
692Q8—721no—
693D4—32no—
694D4—61no—
695D4—61no—
696D4—61no—
697D4—92no—
698D4—184no—
699D4—181no—
700D4—721no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—181no—
713C2×C4—241no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4—721no—
717C2×C4—721no—
718C2×C4C22×D3211yescharacteristic
719C8—21no—
720C8—61no—
721C8—61no—
722C8—181no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—122no—
727C2×C3—121no—
728C2×C3—241no—
729C2×C3#560611yescharacteristic
730C2×C3#565611yescharacteristic
731C2×C3#576911yescharacteristic
732C2×C3#576911yescharacteristic
733C2×C3#577511yescharacteristic
734C2×C3#577811yescharacteristic
735D3—41no—
736D3—42no—
737D3—81no—
738D3—122no—
739D3—122no—
740D3—242no—
741C22—61no—
742C22—61no—
743C22—61no—
744C22—62no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—182no—
751C22—361no—
752C22—361no—
753C22—724no—
754C22D32×D411yescharacteristic
755C4—41no—
756C4—41no—
757C4—61no—
758C4—61no—
759C4—61no—
760C4—121no—
761C4—121no—
762C4—181no—
763C4—181no—
764C4—361no—
765C4#6430611yescharacteristic
766C4D3×#23711yescharacteristic
767C3—21no—
768C3#8050811yescharacteristic, complemented
769C3#8149611yescharacteristic, complemented
770C2—121no—
771C2—122no—
772C2—241no—
773C2—362no—
774C2#1059426711yescharacteristic
775C2#1059475411yescharacteristic
776C2#1059477111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10590944C2
hypercenter#103D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595396C2semidirect
2. #10594604C2semidirect
3. #10592487C2semidirect
4. C3×#4819C2semidirect
5. C3×#4814C2semidirect
6. #10591651C2semidirect
7. #10591572C2semidirect
8. #10591568C2semidirect
10. #10590777C2semidirect
11. #10590764C2semidirect
12. #10590698C2semidirect
13. #10590558C2semidirect
14. #10590505C2semidirect
15. #10590462C2semidirect
19. Q8×C3⋊Dic3C22semidirect
22. C3×#947C22semidirect
30. #63918C22semidirect
35. #63898C22semidirect
43. C32×#103C22semidirect
45. C8×C3⋊Dic3C22semidirect
46. #63635C22semidirect
47. C3×#835C22semidirect
49. C3×#818C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#809C22semidirect
52. C3×#808C22semidirect
53. #63575C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
58. #63562C22semidirect
60. #63555C22semidirect
82. #4819D3semidirect
84. #4814D3semidirect
150. #947C2×D3semidirect
200. C3×#103C2×D3semidirect
201. C3×#103C2×D3semidirect
204. #835C2×D3semidirect
217. #818C2×D3semidirect
221. Dic3⋊C8C2×D3semidirect
228. #809C2×D3semidirect
232. #808C2×D3semidirect
458. #103D32semidirect
682. C32#3118semidirect
768. C3#80508semidirect
769. C3#81496semidirect

Maximal subgroups

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

subgroupindex
#105953962
#105946042
#105924872
C3×#48192
C3×#48142
#105916512
#105915722
#105915682
#105909442
#105907772
#105907642
#105906982
#105905582
#105905052
#105904622
#814963
#805083