Finite Group Databasebeta

← #11872752

Subgroups — #11872752

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596016C211yesmaximal, characteristic, complemented
2#10593984C211yesmaximal, characteristic, complemented
3C3×#5014C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591486C211yesmaximal, characteristic, complemented
6#10591479C211yesmaximal, characteristic, complemented
7#10591456C211yesmaximal, characteristic, complemented
8#10591456C211yesmaximal, characteristic, complemented
9#10590551C211yesmaximal, characteristic, complemented
10#10590513C211yesmaximal, characteristic, complemented
11#10590512C211yesmaximal, characteristic, complemented
12#10590435C211yesmaximal, characteristic, complemented
13#10590346C211yesmaximal, characteristic, complemented
14C4×#3714C211yesmaximal, characteristic, complemented
15#10590298C211yesmaximal, characteristic, complemented
16#79874—31nomaximal
17#79596—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21C4×#638—21no—
22C2×#3752—21no—
23#64102C2211yescharacteristic
24#64101C2211yescharacteristic
25#64090—21no—
26C22⋊C4×C3⋊D3—21no—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28#64081C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic, complemented
32C3×C4×D12C2211yescharacteristic, complemented
33#63916C2211yescharacteristic
34#63916C2211yescharacteristic
35#63914C2211yescharacteristic, complemented
36#63906—21no—
37#63906—21no—
38#63905—21no—
39#63905—21no—
40#63872C2211yescharacteristic, complemented
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#832C2211yescharacteristic
44C3×#832C2211yescharacteristic
45C3×#809C2211yescharacteristic, complemented
46C3×#809C2211yescharacteristic, complemented
47C3×#808C2211yescharacteristic, complemented
48C3×#807C2211yescharacteristic, complemented
49C3×#803C2211yescharacteristic, complemented
50C3×C4×C3⋊C8C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63572C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60#63557C2211yescharacteristic
61#5562—31no—
62#5562—31no—
63#5545—31no—
64#5545—31no—
65#5545—61no—
66C3×#442—31no—
67C3×C4×D8—31no—
68#5156—31no—
69#5156—31no—
70#5150—31no—
71#5150—31no—
72#5014—31no—
73#5014D311yescharacteristic, complemented
74C4×#213—31no—
75C4×#213D311yescharacteristic, complemented
76#4891—31no—
77#4885—31no—
78#4871—31no—
79#4866—31no—
80#4786—31no—
81#4786—31no—
82#4784—31no—
83#4779—31no—
84#4773—31no—
85#4773—31no—
86#4766—31no—
87#4763—31no—
88#4711—31no—
89#4709—31no—
90C4×D24—31no—
91#4690—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#638—21no—
96C22×C3⋊Dic3—21no—
97D4×C3⋊D3—22no—
98D4×C3⋊D3—22no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#625—21no—
110C2×#625—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C42C2311yescharacteristic
114#3757—21no—
115#3752—21no—
116#3752—21no—
117#3752—21no—
118#3752D411yescharacteristic
119#3752D411yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750D411yescharacteristic
122#3750D411yescharacteristic
123C4×C3⋊Dic3—21no—
124C4×C3⋊Dic3C2311yescharacteristic
125C3×#213—22no—
126C3×#213—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3714—22no—
140#3714—22no—
141#3122—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×D3×D4—61no—
145C2×C3×D8—31no—
146C2×C3×D8—31no—
147C3×C4×D4—21no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150C3×C4×D4C2×D311yescharacteristic
151C3×C4×D4C2×D311yescharacteristic
152#940—31no—
153#940—31no—
154#938—31no—
155#938—31no—
156D4×Dic3—31no—
157D4×Dic3—31no—
158D4×Dic3—61no—
159C2×#213—31no—
160C2×#213—31no—
161C2×#213C2×D311yescharacteristic
162C2×#213C2×D311yescharacteristic
163#930—61no—
164#930—61no—
165#929—61no—
166#929—61no—
167C4×#67—61no—
168C4×#67—61no—
169C4×#67—62no—
170C2×(C2×D3)⋊C4—61no—
171C2×(C2×D3)⋊C4—61no—
172C2×(C2×D3)⋊C4—62no—
173C2×D24—31no—
174C2×D24—31no—
175#895—31no—
176#895—31no—
177#893—31no—
178#893—31no—
179#893—61no—
180#892—31no—
181#892—31no—
182#892—61no—
183#890—31no—
184#890—31no—
185#884—61no—
186#884—61no—
187#883—61no—
188#883—61no—
189#67⋊C4—61no—
190#67⋊C4—61no—
191#67⋊C4—62no—
192D3×C22⋊C4—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—62no—
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—61no—
198C4×D12C2×D311yescharacteristic, complemented
199C4×D12C2×D311yescharacteristic, complemented
200#872—31no—
201#872—31no—
202#872—61no—
203C3×#107—31no—
204C3×#106—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#97—31no—
210C3×C4×C8—31no—
211#832—31no—
212#832—31no—
213#832C2×D311yescharacteristic
214#832C2×D311yescharacteristic
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223#818—31no—
224#817—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229#809—31no—
230#809—31no—
231#809C2×D311yescharacteristic, complemented
232#809C2×D311yescharacteristic, complemented
233#808—31no—
234#808C2×D311yescharacteristic, complemented
235#807—31no—
236#807C2×D311yescharacteristic, complemented
237#803C2×D311yescharacteristic, complemented
238C4×C3⋊C8C2×D311yescharacteristic, complemented
239C23×C32—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—24no—
242C22×C3⋊D3—81no—
243C22×C3⋊D3—81no—
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C32×D4—21no—
248C32×D4#4112yes—
249C2×C32×C4—21no—
250C2×C32×C4—81no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254#638—24no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—81no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C2×C3⋊Dic3C2×D411yescharacteristic
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)#4112yes—
262C4×C3⋊D3—21no—
263C4×C3⋊D3—21no—
264C4×C3⋊D3—81no—
265C4×C3⋊D3—81no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×C4×D3—81no—
273C3×C4×D3—81no—
274#626—81no—
275#626—81no—
276#625—81no—
277#625—81no—
278C3×C3⋊C8—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#540—91no—
283#518—91no—
284#482—91no—
285#482—91no—
286#478—91no—
287#478—91no—
288#459—91no—
289#459—91no—
290#447—91no—
291#447—91no—
292#442—31no—
293#442—91no—
294C4×D8—31no—
295C4×D8—91no—
296#433—91no—
297C23×D3—61no—
298C23×D3—61no—
299C23×D3—62no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C22×C3×C4—22no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—62no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—62no—
322D3×D4—62no—
323D3×D4—62no—
324D3×D4—64no—
325D3×D4—64no—
326D3×D4—62no—
327D3×D4—62no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12C22×D311yescharacteristic
334C2×D12C22×D311yescharacteristic
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—62no—
343C2×C4×D3—62no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C3×D8—62no—
347C3×D8—62no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C22⋊C4—22no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C42—21no—
363C3×C42C22×D311yescharacteristic
364C3×C42C22×D311yescharacteristic
365#217—61no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—62no—
370#213—22no—
371#213—22no—
372#213—62no—
373#213—62no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
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—61no—
388(C2×D3)⋊C4—62no—
389(C2×D3)⋊C4—62no—
390(C2×D3)⋊C4—62no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393C4⋊Dic3—31no—
394C4⋊Dic3—31no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3C22×D311yescharacteristic
399C4⋊Dic3C22×D311yescharacteristic
400Dic3⋊C4—31no—
401Dic3⋊C4—31no—
402Dic3⋊C4—31no—
403Dic3⋊C4—31no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408C4×Dic3—31no—
409C4×Dic3—31no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413C4×Dic3—62no—
414C2×C3⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418D24—62no—
419D24—62no—
420C22×C32—22no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32C22×D411yescharacteristic
424C2×C3⋊D3—21no—
425C2×C3⋊D3—22no—
426C2×C3⋊D3—21no—
427C2×C3⋊D3—21no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—84no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C32×C4—21no—
438C32×C4—21no—
439C32×C4—41no—
440C32×C4C2×#4111yescharacteristic
441C32×C4C2×#4111yescharacteristic
442C3⋊Dic3—21no—
443C3⋊Dic3—21no—
444C3⋊Dic3—21no—
445C3⋊Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C22×D4—91no—
449C2×D8—31no—
450C2×D8—31no—
451C2×D8—91no—
452C2×D8—91no—
453#127—91no—
454#125—91no—
455#123—181no—
456#123—181no—
457#121—91no—
458#121—91no—
459#121—181no—
460#121—181no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—91no—
464C4×D4—91no—
465C4×D4—91no—
466C4×D4—181no—
467C4×D4—181no—
468C4×D4D3211yescharacteristic
469#117—91no—
470#117—91no—
471C2×C22⋊C4—181no—
472C2×C22⋊C4—181no—
473#107—31no—
474#107—91no—
475#106—31no—
476#106—91no—
477C4⋊C8—91no—
478C4⋊C8—91no—
479#102—31no—
480#102—31no—
481#102—31no—
482#102—31no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487C22⋊C8—91no—
488C22⋊C8—91no—
489#97—31no—
490C4×C8—31no—
491C23×C3—22no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—61no—
495C23×C3—61no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—31no—
499C22×D3—31no—
500C22×D3—61no—
501C22×D3—62no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—68no—
505C22×D3—64no—
506C22×D3—64no—
507C22×D3—241no—
508C22×D3—241no—
509C22×D3—241no—
510C22×D3—241no—
511C22×D3—242no—
512C22×D3—242no—
513C3×D4—22no—
514C3×D4—21no—
515C3×D4—21no—
516C3×D4—22no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—61no—
521C3×D4#23512yes—
522C3×D4#23512yes—
523C2×C3×C4—22no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—81no—
532C2×C3×C4—81no—
533C2×C3×C4—82no—
534C2×C3×C4—241no—
535C2×C3×C4—241no—
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4D3×D411yescharacteristic
539C2×C3×C4D3×D411yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542#67—68no—
543#67—64no—
544#67—64no—
545#67—241no—
546#67—241no—
547#67—241no—
548#67—241no—
549#67—241no—
550#67—241no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—62no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—241no—
566C2×Dic3—241no—
567C2×Dic3—242no—
568D12—21no—
569D12—21no—
570D12—21no—
571D12—21no—
572D12—32no—
573D12—32no—
574D12—62no—
575D12—62no—
576D12—61no—
577D12—61no—
578D12—241no—
579D12—241no—
580C4×D3—62no—
581C4×D3—62no—
582C4×D3—61no—
583C4×D3—61no—
584C4×D3—61no—
585C4×D3—61no—
586C4×D3—81no—
587C4×D3—81no—
588C4×D3—241no—
589C4×D3—241no—
590C4×D3—241no—
591C4×D3—241no—
592C4×D3—242no—
593C4×D3—242no—
594C3×C8—61no—
595C3×C8—61no—
596C3×C8—61no—
597C3×C8—61no—
598C3⋊C8—21no—
599C3⋊C8—21no—
600C3⋊C8—21no—
601C3⋊C8—21no—
602C2×C32—42no—
603C2×C32#52511yescharacteristic
604C2×C32#57611yescharacteristic
605C2×C32#57611yescharacteristic
606C3⋊D3—41no—
607C3⋊D3—42no—
608C3×D3—81no—
609C3×D3—81no—
610C24—181no—
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—91no—
614C2×D4—181no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4—181no—
618C2×D4—181no—
619C2×D4—182no—
620C2×D4—182no—
621C2×D4C2×D3211yescharacteristic
622C22×C4—21no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—91no—
626C22×C4—181no—
627C22×C4—181no—
628C22×C4—181no—
629D8—62no—
630D8—62no—
631D8—182no—
632D8—182no—
633C2×C8—31no—
634C2×C8—31no—
635C2×C8—31no—
636C2×C8—31no—
637C4⋊C4—31no—
638C4⋊C4—31no—
639C4⋊C4—91no—
640C4⋊C4—91no—
641C4⋊C4—91no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C4⋊C4C2×D3211yescharacteristic
645C22⋊C4—21no—
646C22⋊C4—61no—
647C22⋊C4—61no—
648C22⋊C4—91no—
649C22⋊C4—91no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C22⋊C4—181no—
656C42—91no—
657C42—181no—
658C42C2×D3211yescharacteristic
659C22×C3—24no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—21no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3C2×D3×D411yescharacteristic
676C22×C3C2×D3×D411yescharacteristic
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—62no—
684C2×D3—64no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—122no—
696C2×D3—122no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—248no—
702C2×D3—244no—
703C2×D3—244no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—42no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—121no—
716C3×C4—121no—
717C3×C4C2×#23511yescharacteristic
718C3×C4C2×#23511yescharacteristic
719C3×C4D3×#4111yescharacteristic
720C3×C4D3×#4111yescharacteristic
721Dic3—41no—
722Dic3—41no—
723Dic3—62no—
724Dic3—61no—
725Dic3—61no—
726Dic3—61no—
727Dic3—61no—
728Dic3—61no—
729Dic3—61no—
730Dic3—121no—
731Dic3—121no—
732Dic3—122no—
733Dic3—121no—
734Dic3—121no—
735C32#312211yescharacteristic, complemented, Sylow
736C23—21no—
737C23—61no—
738C23—61no—
739C23—91no—
740C23—184no—
741C23—181no—
742C23—721no—
743C23—721no—
744D4—21no—
745D4—61no—
746D4—61no—
747D4—61no—
748D4—61no—
749D4—92no—
750D4—184no—
751D4—181no—
752D4—721no—
753D4—721no—
754D4—721no—
755D4—721no—
756D4#379812yes—
757C2×C4—21no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—81no—
761C2×C4—91no—
762C2×C4—91no—
763C2×C4—91no—
764C2×C4—181no—
765C2×C4—181no—
766C2×C4—181no—
767C2×C4—241no—
768C2×C4—241no—
769C2×C4—721no—
770C2×C4—721no—
771C2×C4—721no—
772C2×C4#381111yescharacteristic
773C2×C4#381111yescharacteristic
774C2×C4C22×D3211yescharacteristic
775C8—61no—
776C8—61no—
777C8—61no—
778C8—61no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—44no—
783C2×C3—42no—
784C2×C3—42no—
785C2×C3—241no—
786C2×C3—241no—
787C2×C3#554711yescharacteristic
788C2×C3#554711yescharacteristic
789C2×C3#575711yescharacteristic
790C2×C3#576911yescharacteristic
791C2×C3#577411yescharacteristic
792C2×C3#577411yescharacteristic
793D3—81no—
794D3—81no—
795D3—122no—
796D3—124no—
797D3—121no—
798D3—122no—
799D3—121no—
800D3—122no—
801C22—22no—
802C22—41no—
803C22—41no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—181no—
811C22—181no—
812C22—181no—
813C22—182no—
814C22—361no—
815C22—361no—
816C22—724no—
817C22C2×#381111yescharacteristic
818C4—21no—
819C4—21no—
820C4—41no—
821C4—121no—
822C4—121no—
823C4—181no—
824C4—181no—
825C4—181no—
826C4—361no—
827C4C2×#379811yescharacteristic
828C4#6430611yescharacteristic
829C3—21no—
830C3#7959611yescharacteristic, complemented
831C3#7987411yescharacteristic, complemented
832C2—42no—
833C2—241no—
834C2—241no—
835C2—361no—
836C2—362no—
837C2#1059501611yescharacteristic
838C2#1059510211yescharacteristic
839C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596016C2semidirect
2. #10593984C2semidirect
3. C3×#5014C2semidirect
4. C3×C4×#213C2semidirect
5. #10591486C2semidirect
6. #10591479C2semidirect
7. #10591456C2semidirect
8. #10591456C2semidirect
9. #10590551C2semidirect
10. #10590513C2semidirect
11. #10590512C2semidirect
12. #10590435C2semidirect
13. #10590346C2semidirect
14. C4×#3714C2semidirect
15. #10590298C2semidirect
31. C3×C4×D12C22semidirect
32. C3×C4×D12C22semidirect
35. #63914C22semidirect
40. #63872C22semidirect
45. C3×#809C22semidirect
46. C3×#809C22semidirect
47. C3×#808C22semidirect
48. C3×#807C22semidirect
49. C3×#803C22semidirect
50. C3×C4×C3⋊C8C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
53. #63572C22semidirect
54. #63572C22semidirect
57. #63563C22semidirect
58. #63563C22semidirect
73. #5014D3semidirect
75. C4×#213D3semidirect
198. C4×D12C2×D3semidirect
199. C4×D12C2×D3semidirect
231. #809C2×D3semidirect
232. #809C2×D3semidirect
234. #808C2×D3semidirect
236. #807C2×D3semidirect
237. #803C2×D3semidirect
238. C4×C3⋊C8C2×D3semidirect
735. C32#3122semidirect
830. C3#79596semidirect
831. C3#79874semidirect

Maximal subgroups

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

subgroupindex
#105960162
#105939842
C3×#50142
C3×C4×#2132
#105914862
#105914792
#105914562
#105905512
#105905132
#105905122
#105904352
#105903462
C4×#37142
#105902982
#798743
#795963