Finite Group Databasebeta

← #11871305

Subgroups — #11871305

Order 1152.

1030 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#893C211yesmaximal, characteristic, complemented
2#10594367C211yesmaximal, characteristic, complemented
3#10592569C211yesmaximal, characteristic, complemented
4C3×#4869C211yesmaximal, characteristic, complemented
5C3×#4863C211yesmaximal, characteristic, complemented
6#10590944C211yesmaximal, characteristic, complemented
7#10590749C211yesmaximal, characteristic, complemented
8#10590746C211yesmaximal, characteristic, complemented
9#10590660C211yesmaximal, characteristic, complemented
10#10590595C211yesmaximal, characteristic, complemented
11#10590589C211yesmaximal, characteristic, complemented
12#10590551C211yesmaximal, characteristic, complemented
13#10590500C211yesmaximal, characteristic, complemented
14#10590472C211yesmaximal, characteristic, complemented
15#10590455C211yesmaximal, characteristic, complemented
16#81310—31nomaximal
17#79869—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×C4×D32—21no—
20C2×#3795—21no—
21#64102C2211yescharacteristic
22#64097C2211yescharacteristic, complemented
23C2×C3×D24C2211yescharacteristic
24C3×#895C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#893C2211yescharacteristic, complemented
27C3×D3×C4⋊C4C2211yescharacteristic
28D3×(C2×D3)⋊C4—21no—
29#63914C2211yescharacteristic, complemented
30#63913—21no—
31#63908C2211yescharacteristic
32#63904—21no—
33#63898C2211yescharacteristic
34#63894C2211yescharacteristic
35Dic3×D12C2211yescharacteristic, complemented
36#63885—21no—
37#63881—21no—
38#63879—21no—
39C4×D3×Dic3C2211yescharacteristic
40C2×#3714C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C32×#106C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45#63641C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47#63635C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#815C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5596—31no—
62#5548—31no—
63C4×D3×D4—31no—
64C2×#893—31no—
65C3×#481—31no—
66C3×#442—31no—
67#5156—31no—
68#5150—31no—
69#5036—31no—
70#5014—31no—
71#5014—31no—
72#4968—31no—
73#4870—31no—
74#4870—31no—
75#4870—31no—
76#4870—61no—
77#4869—31no—
78#4869D311yescharacteristic, complemented
79#4863D311yescharacteristic, complemented
80#4786—31no—
81#4786—31no—
82#4786—31no—
83#4785—31no—
84#4785—31no—
85#4777—31no—
86#4773—31no—
87#4761—31no—
88#4732—31no—
89#4719—31no—
90#4711—31no—
91#4705—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634—21no—
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×#626—21no—
105C2×#625—21no—
106C2×#625—21no—
107C2×#625—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3D411yescharacteristic
112C2×D3×Dic3D411yescharacteristic
113D3×D12—22no—
114D3×D12—22no—
115C4×D32—44no—
116#3795—44no—
117C2×C32×C8C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119C32×C4⋊C4C2311yescharacteristic
120#3752—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×D24—22no—
134#3722—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32D411yescharacteristic
139Dic32D411yescharacteristic
140#3714—22no—
141#3714—22no—
142#3713—22no—
143#3109—91noSylow
144C2×#237—61no—
145C2×D3×D4—31no—
146C2×#235—61no—
147C22×D12—31no—
148C22×C4×D3—61no—
149C22×C4×D3—61no—
150C2×C3×D8—31no—
151C3×#121—31no—
152C3×C4×D4—31no—
153C3×C4×D4—31no—
154C2×C3×C4⋊C4—31no—
155#940—31no—
156#940—31no—
157#939—61no—
158#938—31no—
159D4×Dic3—31no—
160D4×Dic3—31no—
161C2×#213—31no—
162C2×#213—31no—
163C2×#213—31no—
164C2×#213—31no—
165#930—31no—
166C4×#67—61no—
167C4×#67—61no—
168C2×(C2×D3)⋊C4—61no—
169C2×C4×Dic3—31no—
170C2×D24—31no—
171C2×D24—31no—
172C2×D24C2×D311yescharacteristic
173#895C2×D311yescharacteristic
174#893—31no—
175#893—31no—
176#893—31no—
177#893—31no—
178#893—61no—
179#893—61no—
180#893—61no—
181#893C2×D311yescharacteristic
182#893C2×D311yescharacteristic, complemented
183D3×C4⋊C4C2×D311yescharacteristic
184#888—31no—
185#888—31no—
186#888—61no—
187#885—61no—
188#885—61no—
189#884—61no—
190#67⋊C4—61no—
191#67⋊C4—61no—
192D3×C22⋊C4—61no—
193C4×D12—31no—
194C4×D12—31no—
195C42×D3—31no—
196C3×#106—21no—
197C3×#106—31no—
198C3×#106C2×D311yescharacteristic, complemented
199C3×#106C2×D311yescharacteristic, complemented
200C3×#102—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205C3×#97—31no—
206#832—31no—
207#832—31no—
208#830—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—61no—
213#821C2×D311yescharacteristic, complemented
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8C2×D311yescharacteristic
216#817—31no—
217#815—31no—
218#815C2×D311yescharacteristic, complemented
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8—31no—
222Dic3⋊C8—31no—
223Dic3⋊C8—61no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—61no—
228#809C2×D311yescharacteristic
229#809C2×D311yescharacteristic, complemented
230#809C2×D311yescharacteristic, complemented
231#808—31no—
232#808—31no—
233#808—31no—
234#808—61no—
235#808C2×D311yescharacteristic, complemented
236#803—31no—
237C22×C3⋊D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—24no—
243C2×D32—42no—
244C2×D32—42no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)#4112yescomplemented
253C4×C3⋊D3—42no—
254#634—42no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—42no—
265C3×D12#4112yescomplemented
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—42no—
269C3×C4×D3—42no—
270C3×C4×D3—42no—
271#626—24no—
272#625—42no—
273#625—42no—
274#625—42no—
275#624—42no—
276D3×Dic3—22no—
277D3×Dic3—22no—
278D3×Dic3—42no—
279D3×Dic3—42no—
280C32×C8—21no—
281C3⋊(C3⋊C8)—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284#532—91no—
285C2×C4×D4—91no—
286#481—31no—
287#481—91no—
288#476—91no—
289#476—91no—
290#459—91no—
291#459—91no—
292#447—91no—
293#447—91no—
294#442—31no—
295#442—91no—
296#442—91no—
297#442—91no—
298#432—91no—
299C23×D3—61no—
300C23×D3—61no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—61no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320#237—124no—
321D3×D4—62no—
322D3×D4—62no—
323#235—124no—
324C2×D12—21no—
325C2×D12—31no—
326C2×D12—31no—
327C2×D12—61no—
328C2×D12—62no—
329C2×D12—61no—
330C2×D12—62no—
331C2×D12C22×D311yescharacteristic
332C2×D12C22×D311yescharacteristic
333C2×D12C22×D311yescharacteristic
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×C4×D3—21no—
337C2×C4×D3—31no—
338C2×C4×D3—31no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—121no—
346C2×C4×D3—124no—
347C2×C4×D3—124no—
348C2×C4×D3C22×D311yescharacteristic
349C2×Dic6—61no—
350C2×Dic6—61no—
351C2×Dic6—121no—
352C3×D8—62no—
353C2×C3×C8—21no—
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C42—31no—
370#217—61no—
371#217—61no—
372#217—61no—
373#213—62no—
374#213—62no—
375#213—62no—
376#213—62no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—121no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—121no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—61no—
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409D24—22no—
410D24—62no—
411D24—62no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—22no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—22no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3AGL(1,ℤ/8)12yes—
428D32—48no—
429C32×C4—41no—
430C32×C4—41no—
431C32×C4C2×#4111yescharacteristic
432C32×C4C2×#4111yescharacteristic
433C3⋊Dic3—21no—
434C3⋊Dic3—41no—
435C3⋊Dic3AGL(1,ℤ/8)12yes—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C2×#41—181no—
441C22×D4—91no—
442C23×C4—181no—
443C2×D8—31no—
444C2×D8—91no—
445C2×D8—91no—
446C2×D8—91no—
447C4⋊Q8—91no—
448#127—91no—
449#124—181no—
450#121—31no—
451#121—91no—
452#121—181no—
453C4×D4—31no—
454C4×D4—31no—
455C4×D4—91no—
456C4×D4—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—181no—
460C4×D4—181no—
461C4×D4—181no—
462C2×C4⋊C4—31no—
463C2×C22⋊C4—181no—
464C2×C42—91no—
465#106—31no—
466#106—91no—
467#106—91no—
468#106D3211yescharacteristic, complemented
469C4⋊C8—91no—
470C4⋊C8—91no—
471#102—31no—
472#102—31no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8—91no—
481#97—31no—
482#97—91no—
483C23×C3—31no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3—61no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—21no—
490C22×D3—64no—
491C22×D3—64no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—121no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3D3×D411yescharacteristic
500C3×D4—32no—
501C3×D4—61no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—122no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—122no—
521C2×C3×C4—122no—
522C2×C3×C4—122no—
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525#67—64no—
526#67—122no—
527#67—122no—
528#67—122no—
529#67—122no—
530#67—122no—
531#67—122no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—62no—
540C2×Dic3—62no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—121no—
544C2×Dic3—122no—
545C2×Dic3—122no—
546C2×Dic3D3×D411yescharacteristic
547C2×Dic3D3×D411yescharacteristic
548C2×Dic3D3×D411yescharacteristic
549D12—21no—
550D12—21no—
551D12—21no—
552D12—21no—
553D12—21no—
554D12—32no—
555D12—32no—
556D12—42no—
557D12—62no—
558D12—64no—
559D12—61no—
560D12—61no—
561D12—121no—
562D12#23512yescomplemented
563C4×D3—21no—
564C4×D3—21no—
565C4×D3—42no—
566C4×D3—42no—
567C4×D3—42no—
568C4×D3—62no—
569C4×D3—62no—
570C4×D3—122no—
571C4×D3—122no—
572C4×D3—122no—
573C4×D3—122no—
574C4×D3—122no—
575C4×D3—122no—
576C4×D3—242no—
577Dic6—122no—
578Dic6—122no—
579Dic6—242no—
580C3×C8—21no—
581C3×C8—21no—
582C3×C8—41no—
583C3×C8—61no—
584C3×C8—61no—
585C3⋊C8—21no—
586C3⋊C8—21no—
587C3⋊C8—61no—
588C3⋊C8—61no—
589C3⋊C8—121no—
590C2×C32#52511yescharacteristic
591C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
592C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
593C3⋊D3—42no—
594C3×D3—22no—
595C3×D3—42no—
596C3×D3—81no—
597C3×D3—81no—
598C24—181no—
599#41—364no—
600C2×Q8—181no—
601C2×D4—31no—
602C2×D4—31no—
603C2×D4—31no—
604C2×D4—61no—
605C2×D4—91no—
606C2×D4—181no—
607C2×D4—182no—
608C2×D4—182no—
609C2×D4—181no—
610C2×D4—181no—
611C2×D4—181no—
612C22×C4—31no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4—181no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—364no—
623D8—62no—
624D8—182no—
625D8—182no—
626D8—182no—
627C2×C8—31no—
628C2×C8—31no—
629C2×C8—91no—
630C2×C8C2×D3211yescharacteristic
631C4⋊C4—31no—
632C4⋊C4—61no—
633C4⋊C4—91no—
634C4⋊C4—181no—
635C4⋊C4C2×D3211yescharacteristic
636C4⋊C4C2×D3211yescharacteristic
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C42—31no—
646C42—91no—
647C42—91no—
648C42—91no—
649C22×C3—21no—
650C22×C3—32no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—62no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3C2×D3×D411yescharacteristic
663C22×C3C2×D3×D411yescharacteristic
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—22no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—62no—
676C2×D3—62no—
677C2×D3—122no—
678C2×D3—128no—
679C2×D3—128no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—241no—
685C2×D3—241no—
686C2×D3#91412yes—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—61no—
694C3×C4—61no—
695C3×C4—61no—
696C3×C4—81no—
697C3×C4—81no—
698C3×C4—121no—
699C3×C4C2×#23511yescharacteristic
700C3×C4D3×#4111yescharacteristic
701C3×C4D3×#4111yescharacteristic
702C3×C4D3×#4111yescharacteristic
703Dic3—21no—
704Dic3—21no—
705Dic3—21no—
706Dic3—32no—
707Dic3—32no—
708Dic3—41no—
709Dic3—62no—
710Dic3—61no—
711Dic3—61no—
712Dic3—121no—
713Dic3—121no—
714Dic3—121no—
715Dic3—241no—
716C32#310911yescharacteristic, complemented, Sylow
717C23—31no—
718C23—61no—
719C23—61no—
720C23—61no—
721C23—184no—
722C23—181no—
723C23—362no—
724C23—362no—
725Q8—362no—
726D4—32no—
727D4—61no—
728D4—61no—
729D4—61no—
730D4—61no—
731D4—61no—
732D4—92no—
733D4—122no—
734D4—184no—
735D4—181no—
736D4—362no—
737D4—362no—
738D4—362no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—91no—
748C2×C4—91no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4—182no—
753C2×C4—182no—
754C2×C4—181no—
755C2×C4—362no—
756C2×C4—362no—
757C2×C4—362no—
758C2×C4—362no—
759C2×C4C22×D3211yescharacteristic
760C8—21no—
761C8—61no—
762C8—61no—
763C8—181no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—62no—
768C2×C3—122no—
769C2×C3—241no—
770C2×C3—241no—
771C2×C3#554711yescharacteristic
772C2×C3#565611yescharacteristic
773C2×C3C2×#91411yescharacteristic
774C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
775C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
776C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
777D3—22no—
778D3—42no—
779D3—81no—
780D3—81no—
781D3—122no—
782D3—122no—
783D3—242no—
784C22—32no—
785C22—61no—
786C22—61no—
787C22—62no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—182no—
797C22—368no—
798C22—361no—
799C22—361no—
800C22D32×D411yescharacteristic
801C4—41no—
802C4—41no—
803C4—61no—
804C4—61no—
805C4—61no—
806C4—92no—
807C4—121no—
808C4—181no—
809C4—361no—
810C4D3×#23511yescharacteristic
811C4#6431911yescharacteristic
812C3—21no—
813C3#7986911yescharacteristic, complemented
814C3#8131011yescharacteristic, complemented
815C2—62no—
816C2—122no—
817C2—241no—
818C2—241no—
819C2—362no—
820C2#1059461411yescharacteristic
821C2D3×#91411yescharacteristic
822C2#1059474011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
hypercenter#106D32
hypocenterC32#3109
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. D3×#893C2semidirect
2. #10594367C2semidirect
3. #10592569C2semidirect
4. C3×#4869C2semidirect
5. C3×#4863C2semidirect
6. #10590944C2semidirect
7. #10590749C2semidirect
8. #10590746C2semidirect
9. #10590660C2semidirect
10. #10590595C2semidirect
11. #10590589C2semidirect
12. #10590551C2semidirect
13. #10590500C2semidirect
14. #10590472C2semidirect
15. #10590455C2semidirect
22. #64097C22semidirect
26. C3×#893C22semidirect
29. #63914C22semidirect
35. Dic3×D12C22semidirect
43. C32×#106C22semidirect
45. #63641C22semidirect
47. #63635C22semidirect
48. C3×#821C22semidirect
50. C3×#815C22semidirect
52. C3×#809C22semidirect
53. C3×#809C22semidirect
54. C3×#808C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
58. #63562C22semidirect
60. #63554C22semidirect
78. #4869D3semidirect
79. #4863D3semidirect
182. #893C2×D3semidirect
198. C3×#106C2×D3semidirect
199. C3×#106C2×D3semidirect
213. #821C2×D3semidirect
218. #815C2×D3semidirect
229. #809C2×D3semidirect
230. #809C2×D3semidirect
235. #808C2×D3semidirect
252. C4⋊(C3⋊D3)#41semidirect
265. C3×D12#41semidirect
468. #106D32semidirect
562. D12#235semidirect
716. C32#3109semidirect
813. C3#79869semidirect
814. C3#81310semidirect

Maximal subgroups

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

subgroupindex
D3×#8932
#105943672
#105925692
C3×#48692
C3×#48632
#105909442
#105907492
#105907462
#105906602
#105905952
#105905892
#105905512
#105905002
#105904722
#105904552
#813103
#798693