Finite Group Databasebeta

← #11889140

Subgroups — #11889140

Order 1152.

953 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5609C211yesmaximal, characteristic
2#10594942C211yesmaximal, characteristic, complemented
3#10592734C211yesmaximal, characteristic, complemented
4C3×#5042C211yesmaximal, characteristic, complemented
5#10591477C211yesmaximal, characteristic, complemented
6#10591458C211yesmaximal, characteristic, complemented
7#10591438C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10591169C211yesmaximal, characteristic, complemented
10#10591147C211yesmaximal, characteristic, complemented
11#10591086C211yesmaximal, characteristic, complemented
12#10590542C211yesmaximal, characteristic, complemented
13#10590514C211yesmaximal, characteristic, complemented
14#10590478C211yesmaximal, characteristic, complemented
15#10590438C211yesmaximal, characteristic, complemented
16#83484—31nomaximal
17#80821—31nomaximal
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C32×#121C2211yescharacteristic
22#64135C2211yescharacteristic, complemented
23C3×#940C2211yescharacteristic
24C3×#937—21no—
25C2×C3×#214C2211yescharacteristic, complemented
26C3×C4×#67C2211yescharacteristic
27C3×#924C2211yescharacteristic, complemented
28C2×C3×#208C2211yescharacteristic, complemented
29C3×#895C2211yescharacteristic
30C3×#893C2211yescharacteristic
31C3×#884—21no—
32C3×#882—21no—
33#63969—21no—
34#63956—21no—
35D3×C4⋊Dic3C2211yescharacteristic, complemented
36#63878—21no—
37#63870—21no—
38#63869C2211yescharacteristic, complemented
39#63856C2211yescharacteristic, complemented
40Dic3×Dic6C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic
42C2×#3715C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45#63659C2211yescharacteristic, complemented
46#63657C2211yescharacteristic, complemented
47#63635C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#810C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63563C2211yescharacteristic
54#63563C2211yescharacteristic
55#63563C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×D42—31no—
62#5639—31no—
63#5609D311yescharacteristic
64#5541—31no—
65C3×#468—31no—
66#5218—31no—
67#5218—31no—
68#5215—31no—
69C2×#832—31no—
70#5169—31no—
71#5163—31no—
72#5131—31no—
73#5127—31no—
74#5075—31no—
75#5071—31no—
76#5046—31no—
77#5042D311yescharacteristic, complemented
78#5041—31no—
79#5035—31no—
80#5035—31no—
81#5035—61no—
82#5033—31no—
83#5018—31no—
84#5011—31no—
85#5009—31no—
86#4891—31no—
87#4882—31no—
88#4817—31no—
89#4807—31no—
90D3×#102—31no—
91#4764—31no—
92C23×C3×D3—21no—
93C23×C3×D3—21no—
94C2×C32×D4—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67D411yescharacteristic
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C3×D3×D4—44no—
104C2×C3×D12—22no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12—41no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×D3×Dic3—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116#3757—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4×C3⋊Dic3—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—21no—
123C3×#217D411yescharacteristic
124C3×#214—41no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C3×#208—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3715—22no—
143#3715—41no—
144D3×C3⋊C8—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×C3×D4—31no—
148C22×C3×D4—61no—
149C2×D3×D4—21no—
150C2×D3×D4C2×D311yescharacteristic
151C22×D12C2×D311yescharacteristic
152C2×C3×SD16—31no—
153C2×C3×M16—31no—
154C3×#127—31no—
155C3×C22⋊Q8—31no—
156C3×#121—21no—
157C3×#121—31no—
158C3×#121—61no—
159C3×#121C2×D311yescharacteristic
160C3×#121C2×D311yescharacteristic
161C3×#120—61no—
162C3×#120—61no—
163C3×C4×D4—31no—
164C3×C4×D4—31no—
165#946—31no—
166Q8×Dic3—31no—
167C2×#215—31no—
168C2×#215—31no—
169#940C2×D311yescharacteristic
170#937—21no—
171#935—61no—
172C2×#214—31no—
173C2×#214—31no—
174C2×#214C2×D311yescharacteristic, complemented
175C4×#67C2×D311yescharacteristic
176#926—31no—
177#926—31no—
178#926—61no—
179C2×C4⋊Dic3—31no—
180#924—31no—
181#924C2×D311yescharacteristic, complemented
182C2×#208C2×D311yescharacteristic, complemented
183C22×C3⋊C8—31no—
184C2×D3×C8—31no—
185#895C2×D311yescharacteristic
186#893C2×D311yescharacteristic
187#892—61no—
188D3×C4⋊C4—31no—
189#890—31no—
190#889—61no—
191#889—61no—
192#884—21no—
193#883—61no—
194#882—21no—
195#879—61no—
196#879—61no—
197#877—61no—
198#870—31no—
199C4×Dic6—31no—
200C3×#107—31no—
201C3×#103—31no—
202C3×#102—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832—61no—
215#832C2×D311yescharacteristic, complemented
216#830—31no—
217#830—31no—
218#830—31no—
219#830—61no—
220#821—31no—
221#821—31no—
222#821—31no—
223#821—31no—
224(C2×D3)⋊C8—31no—
225#815—31no—
226Dic3⋊C8—31no—
227#810C2×D311yescharacteristic, complemented
228#809—31no—
229#809—31no—
230#808—31no—
231#808—31no—
232#808—61no—
233#807—31no—
234#807—31no—
235#807—61no—
236#807C2×D311yescharacteristic, complemented
237C4⋊(C3⋊C8)—31no—
238#803—31no—
239C23×C32—21no—
240C23×C32C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—42no—
246C22×C3×D3—42no—
247C22×C3×D3—81no—
248C22×C3×D3—81no—
249C22×C3×D3C2×D411yescharacteristic
250C32×D4—21no—
251C32×D4—21no—
252C32×D4—42no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2411yescharacteristic
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C3×#67—22no—
261C3×#67—42no—
262C3×#67—42no—
263C3×#67—81no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—42no—
273C3×D12—42no—
274C3×D12#4112yes—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—42no—
278C3×Dic6—21no—
279C3×Dic6—21no—
280D3×Dic3—42no—
281C3⋊(C3⋊C8)—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—31no—
287#490—91no—
288#482—91no—
289#480—91no—
290#478—91no—
291#468—31no—
292#465—91no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C24×C3—61no—
301C24×C3—61no—
302C23×D3—21no—
303C23×D3—21no—
304C2×C3×Q8—31no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C2×C3×D4—41no—
312C2×C3×D4—62no—
313C2×C3×D4—61no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C2×C3×D4—61no—
317C2×C3×D4—62no—
318C2×C3×D4—61no—
319C2×C3×D4—121no—
320C2×C3×D4—121no—
321C2×C3×D4—124no—
322C2×C3×D4C22×D311yescharacteristic
323C2×C3×D4C22×D311yescharacteristic
324C22×C3×C4—21no—
325C22×C3×C4—31no—
326C22×C3×C4—61no—
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C2×#67—21no—
330C2×#67—21no—
331C2×#67—21no—
332C2×#67#6711yescharacteristic
333C22×Dic3—61no—
334D3×D4—22no—
335D3×D4—41no—
336D3×D4—44no—
337C2×D12—22no—
338C2×D12—21no—
339C2×D12—21no—
340C2×D12—41no—
341C2×D12C22×D311yescharacteristic
342C2×D12C22×D311yescharacteristic
343C2×C4×D3—21no—
344C2×C4×D3—61no—
345C2×C4×D3C22×D311yescharacteristic
346C2×Dic6C22×D311yescharacteristic
347C3×SD16—121no—
348C3×M16—121no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—41no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C42—31no—
366#217—21no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—121no—
371#217#6711yescharacteristic
372#215—62no—
373#215—121no—
374#214—41no—
375#214—62no—
376#214—121no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4#6711yescharacteristic
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4#6711yescharacteristic
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—121no—
405C4×Dic3C22×D311yescharacteristic
406#208—41no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8—121no—
414C2×C3⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416D3×C8—121no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32C22×D411yescharacteristic
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—22no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—84no—
433C2×C3×D3—84no—
434C2×C3×D3AGL(1,ℤ/8)12yes—
435C32×C4—21no—
436C32×C4—41no—
437C32×C4C2×#4111yescharacteristic
438C32×C4H(5,𝔽2)11yescharacteristic
439C3⋊Dic3—41no—
440C3⋊Dic3—41no—
441C3×Dic3—21no—
442C3×Dic3—21no—
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C22×D4—31no—
447C22×D4—31no—
448C22×D4—61no—
449C2×SD16—31no—
450C2×SD16—91no—
451C2×SD16—91no—
452C2×M16—31no—
453C22×C8—91no—
454#127—31no—
455#126—181no—
456#125—91no—
457#125—181no—
458#123—181no—
459C22⋊Q8—31no—
460C22⋊Q8—91no—
461#121—31no—
462#121—61no—
463#121D3211yescharacteristic
464#120—61no—
465#120—61no—
466C4×Q8—91no—
467C4×D4—31no—
468C4×D4—31no—
469#117—91no—
470#117—181no—
471C2×C4⋊C4—91no—
472#107—31no—
473#107—91no—
474#106—91no—
475C4⋊C8—91no—
476#103—31no—
477#102—31no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486C22⋊C8—91no—
487C22⋊C8—91no—
488#97—91no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—31no—
493C23×C3—41no—
494C23×C3—61no—
495C23×C3—61no—
496C23×C3—122no—
497C23×C3—122no—
498C23×C3—122no—
499C23×C3—122no—
500C23×C3—241no—
501C23×C3—241no—
502C23×C3D3×D411yescharacteristic
503C23×C3C2×#6711yescharacteristic
504C22×D3—21no—
505C22×D3—21no—
506C22×D3—42no—
507C22×D3—42no—
508C22×D3—42no—
509C22×D3—42no—
510C22×D3—81no—
511C22×D3—81no—
512C22×D3C2×#6711yescharacteristic
513C3×Q8—61no—
514C3×Q8—61no—
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—21no—
519C3×D4—32no—
520C3×D4—41no—
521C3×D4—41no—
522C3×D4—42no—
523C3×D4—42no—
524C3×D4—62no—
525C3×D4—61no—
526C3×D4—61no—
527C3×D4—61no—
528C3×D4—82no—
529C3×D4—122no—
530C3×D4—122no—
531C3×D4—122no—
532C3×D4—122no—
533C3×D4—241no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—122no—
553C2×C3×C4D3×D411yescharacteristic
554C2×C3×C4C2×#6711yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556C2×C3×C4C23×D311yescharacteristic
557#67—22no—
558#67—42no—
559#67—42no—
560#67—81no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—121no—
568C2×Dic3—121no—
569C2×Dic3—122no—
570C2×Dic3C2×#6711yescharacteristic
571C2×Dic3C2×#6711yescharacteristic
572C2×Dic3C2×#6711yescharacteristic
573D12—21no—
574D12—21no—
575D12—21no—
576D12—42no—
577D12—42no—
578D12#23712yes—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—42no—
582C4×D3—122no—
583Dic6—21no—
584Dic6—21no—
585C3×C8—61no—
586C3×C8—61no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C3⋊C8—61no—
590C3⋊C8—61no—
591C3⋊C8—61no—
592C3⋊C8—61no—
593C3⋊C8—121no—
594C3⋊C8—121no—
595C2×C32—41no—
596C2×C32—81no—
597C2×C32#54611yescharacteristic
598C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
599C2×C32#57711yescharacteristic
600C3×D3—22no—
601C3×D3—42no—
602C3×D3—81no—
603C24—61no—
604C24—61no—
605C2×Q8—31no—
606C2×D4—21no—
607C2×D4—31no—
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—62no—
611C2×D4—61no—
612C2×D4—61no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—62no—
616C2×D4—61no—
617C2×D4—121no—
618C2×D4—121no—
619C2×D4—124no—
620C2×D4C2×D3211yescharacteristic
621C22×C4—31no—
622C22×C4—61no—
623C22×C4—181no—
624C22×C4C2×D3211yescharacteristic
625SD16—121no—
626SD16—182no—
627SD16—361no—
628M16—121no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—91no—
632C2×C8—91no—
633C2×C8—361no—
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—91no—
638C4⋊C4—91no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C4⋊C4C2×D3211yescharacteristic
645C22⋊C4—21no—
646C22⋊C4—31no—
647C22⋊C4—31no—
648C22⋊C4—61no—
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C42—31no—
654C42—181no—
655C42—181no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—32no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—62no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—244no—
685C22×C3—244no—
686C22×C3C2×D3×D411yescharacteristic
687C22×C3C22×#6711yescharacteristic
688C2×D3—21no—
689C2×D3—21no—
690C2×D3—22no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—84no—
697C2×D3—84no—
698C2×D3#93212yes—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—61no—
707C3×C4—61no—
708C3×C4—61no—
709C3×C4—81no—
710C3×C4—121no—
711C3×C4—121no—
712C3×C4C2×#23711yescharacteristic
713C3×C4#100411yescharacteristic
714C3×C4#100411yescharacteristic
715C3×C4D3×#4111yescharacteristic
716Dic3—21no—
717Dic3—21no—
718Dic3—21no—
719Dic3—41no—
720Dic3—41no—
721Dic3—121no—
722Dic3—121no—
723Dic3—121no—
724Dic3—121no—
725Dic3—241no—
726Dic3—241no—
727C32#331011yescharacteristic, complemented, Sylow
728C23—21no—
729C23—31no—
730C23—61no—
731C23—61no—
732C23—122no—
733C23—122no—
734C23—122no—
735C23—122no—
736C23—241no—
737C23—241no—
738C23D3×#6711yescharacteristic
739Q8—61no—
740Q8—61no—
741D4—21no—
742D4—21no—
743D4—32no—
744D4—42no—
745D4—62no—
746D4—61no—
747D4—61no—
748D4—61no—
749D4—122no—
750D4—122no—
751D4—122no—
752D4—122no—
753D4—241no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—31no—
758C2×C4—31no—
759C2×C4—31no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—122no—
765C2×C4—181no—
766C2×C4—181no—
767C2×C4—362no—
768C2×C4D3×#6711yescharacteristic
769C2×C4C22×D3211yescharacteristic
770C8—61no—
771C8—61no—
772C8—181no—
773C8—181no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—41no—
778C2×C3—41no—
779C2×C3—62no—
780C2×C3—81no—
781C2×C3—81no—
782C2×C3—81no—
783C2×C3—122no—
784C2×C3—161no—
785C2×C3—241no—
786C2×C3#561011yescharacteristic
787C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
788C2×C3#577811yescharacteristic
789C2×C3C2×#93211yescharacteristic
790C2×C3#580611yescharacteristic
791C2×C3#583611yescharacteristic
792D3—22no—
793D3—42no—
794D3—81no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—32no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—61no—
803C22—61no—
804C22—62no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—244no—
811C22—244no—
812C22C2×D3×#6711yescharacteristic
813C4—21no—
814C4—41no—
815C4—61no—
816C4—61no—
817C4—61no—
818C4—121no—
819C4—121no—
820C4—361no—
821C4—361no—
822C4D3×#23711yescharacteristic
823C4#6431311yescharacteristic
824C3—21no—
825C3#8082111yescharacteristic, complemented
826C3#8348411yescharacteristic, complemented
827C2—41no—
828C2—62no—
829C2—81no—
830C2—122no—
831C2—241no—
832C2D3×#93211yescharacteristic
833C2#1059515011yescharacteristic
834C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×#5609C2
hypercenter#121D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10594942C2semidirect
3. #10592734C2semidirect
4. C3×#5042C2semidirect
5. #10591477C2semidirect
6. #10591458C2semidirect
7. #10591438C2semidirect
8. D3×#832C2semidirect
9. #10591169C2semidirect
10. #10591147C2semidirect
11. #10591086C2semidirect
12. #10590542C2semidirect
13. #10590514C2semidirect
14. #10590478C2semidirect
15. #10590438C2semidirect
22. #64135C22semidirect
25. C2×C3×#214C22semidirect
27. C3×#924C22semidirect
28. C2×C3×#208C22semidirect
35. D3×C4⋊Dic3C22semidirect
38. #63869C22semidirect
39. #63856C22semidirect
40. Dic3×Dic6C22semidirect
42. C2×#3715C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63659C22semidirect
45. #63659C22semidirect
46. #63657C22semidirect
47. #63635C22semidirect
48. #63634C22semidirect
49. C3×#832C22semidirect
50. C3×#810C22semidirect
51. C3×#807C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
55. #63563C22semidirect
56. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
77. #5042D3semidirect
174. C2×#214C2×D3semidirect
181. #924C2×D3semidirect
182. C2×#208C2×D3semidirect
215. #832C2×D3semidirect
227. #810C2×D3semidirect
236. #807C2×D3semidirect
727. C32#3310semidirect
825. C3#80821semidirect
826. C3#83484semidirect

Maximal subgroups

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

subgroupindex
C3×#56092
#105949422
#105927342
C3×#50422
#105914772
#105914582
#105914382
D3×#8322
#105911692
#105911472
#105910862
#105905422
#105905142
#105904782
#105904382
#834843
#808213