Finite Group Databasebeta

← #11887034

Subgroups — #11887034

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5609C211yesmaximal, characteristic, complemented
2#10594907C211yesmaximal, characteristic, complemented
3#10592732C211yesmaximal, characteristic, complemented
4C3×#5038C211yesmaximal, characteristic, complemented
5#10591487C211yesmaximal, characteristic, complemented
6#10591447C211yesmaximal, characteristic, complemented
7#10591428C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10591160C211yesmaximal, characteristic, complemented
10C3⋊C8×#67C211yesmaximal, characteristic, complemented
11C2×#63563C211yesmaximal, characteristic, complemented
12#10590555C211yesmaximal, characteristic, complemented
13#10590499C211yesmaximal, characteristic, complemented
14#10590452C211yesmaximal, characteristic, complemented
15#10590438C211yesmaximal, characteristic, complemented
16#83482—31nomaximal
17#80731—31nomaximal
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C2×#3805—21no—
22C32×#121C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
24C3×#940C2211yescharacteristic
25C3×#937—21no—
26C2×C3×#213C2211yescharacteristic, complemented
27C3×#930C2211yescharacteristic, complemented
28C3×C4×#67C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic
31C3×#893C2211yescharacteristic
32C3×#884—21no—
33C3×#882—21no—
34#63962—21no—
35#63918C2211yescharacteristic, complemented
36#63908C2211yescharacteristic, complemented
37#63893—21no—
38Dic3×D12C2211yescharacteristic, complemented
39#63891—21no—
40D3×C4⋊Dic3C2211yescharacteristic, complemented
41C2×#3713C2211yescharacteristic
42C2×#3713C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45#63659C2211yescharacteristic, complemented
46#63657C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#809C2211yescharacteristic, 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
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×D42—31no—
62#5611—31no—
63#5609D311yescharacteristic, complemented
64#5555—31no—
65C3×#466—31no—
66#5217—31no—
67#5217—31no—
68C2×#832—31no—
69C2×#832—31no—
70#5156—31no—
71#5150—31no—
72C2×#821—31no—
73C8×#67—31no—
74#5072—31no—
75#5070—31no—
76#5038—31no—
77#5038D311yescharacteristic, complemented
78#5036—31no—
79#5033—31no—
80#5033—31no—
81#5033—31no—
82#5033—61no—
83C4×#213—31no—
84D4×C3⋊C8—31no—
85#5007—31no—
86#4890—31no—
87#4882—31no—
88#4775—31no—
89D3×#102—31no—
90#4760—31no—
91#4756—31no—
92C23×C3×D3—21no—
93C23×C3×D3—21no—
94C2×C32×D4—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C3⋊Dic3—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C3×D3×D4—22no—
104C3×D3×D4—41no—
105C3×D3×D4—44no—
106C2×C3×D12—22no—
107C2×C3×D12—21no—
108C2×C3×D12—21no—
109C2×C3×D12—41no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×#627—21no—
116C2×#625—21no—
117#3805—44no—
118C2×D3×Dic3—21no—
119C2×D3×Dic3—21no—
120C32×C4⋊C4C2311yescharacteristic
121C32×C22⋊C4—21no—
122C4⋊(C3⋊Dic3)—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#217D411yescharacteristic
128C3×#213—41no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4D411yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8—41no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3713—22no—
144#3713—41no—
145D3×C3⋊C8—41no—
146#3294—91noSylow
147C22×C3×D4—31no—
148C22×C3×D4—31no—
149C22×C3×D4—61no—
150C2×#237—61no—
151C2×#237—61no—
152C2×D3×D4—21no—
153C2×D3×D4C2×D311yescharacteristic
154C22×D12C2×D311yescharacteristic
155C2×C3×D8—31no—
156C22×C3×C8—31no—
157C3×#127—31no—
158C3×#121—21no—
159C3×#121—31no—
160C3×#121—31no—
161C3×#121—61no—
162C3×#121C2×D311yescharacteristic
163C3×#121C2×D311yescharacteristic
164C3×#120—61no—
165C3×#120—61no—
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168#940C2×D311yescharacteristic
169#938—31no—
170#937—21no—
171#935—61no—
172D4×Dic3—31no—
173C2×#213—31no—
174C2×#213—31no—
175C2×#213—31no—
176C2×#213—31no—
177C2×#213C2×D311yescharacteristic, complemented
178#930—31no—
179#930C2×D311yescharacteristic, complemented
180C4×#67C2×D311yescharacteristic
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—61no—
185C22×C3⋊C8—31no—
186C22×C3⋊C8C2×D311yescharacteristic, complemented
187C2×D3×C8—31no—
188#897—61no—
189#895C2×D311yescharacteristic
190#893C2×D311yescharacteristic
191D3×C4⋊C4—31no—
192#888—31no—
193#886—61no—
194#886—61no—
195#884—21no—
196#883—61no—
197#882—21no—
198#878—61no—
199C4×D12—31no—
200#869—31no—
201C3×#107—31no—
202C3×#102—31no—
203C3×#102—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—31no—
214#832—61no—
215#832—61no—
216#832C2×D311yescharacteristic, complemented
217#830—31no—
218#830—31no—
219#830—31no—
220#830—61no—
221#821—31no—
222#821—31no—
223#821—31no—
224#821—31no—
225(C2×D3)⋊C8—31no—
226Dic3⋊C8—31no—
227C8×Dic3—31no—
228#809—31no—
229#809—31no—
230#809C2×D311yescharacteristic, complemented
231#807—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235#807—61no—
236#807—61no—
237#807C2×D311yescharacteristic, complemented
238C4⋊(C3⋊C8)—31no—
239C4×C3⋊C8—31no—
240C23×C32—21no—
241C23×C32C2×D411yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—42no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3—42no—
249C22×C3×D3—81no—
250C22×C3×D3—81no—
251C22×C3×D3C2×D411yescharacteristic
252C32×D4—21no—
253C32×D4—21no—
254C32×D4—42no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2411yescharacteristic
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—42no—
263C3×#67—42no—
264C3×#67—42no—
265C3×#67—42no—
266C3×#67—81no—
267C3×#67D814yescomplemented
268C2×C3×Dic3—21no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—42no—
278C3×D12—42no—
279C3×D12#4112yescomplemented
280C3×C4×D3—21no—
281C3×C4×D3—21no—
282C3×C4×D3—42no—
283#627—42no—
284#625—42no—
285D3×Dic3—42no—
286D3×Dic3—42no—
287C3⋊(C3⋊C8)—21no—
288C3⋊(C3⋊C8)—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291#547—91no—
292D42—31no—
293#486—91no—
294#480—91no—
295#480—91no—
296#474—91no—
297#466—31no—
298#466—91no—
299#459—91no—
300#447—91no—
301#447—91no—
302C4×D8—91no—
303C8×D4—91no—
304C2×#102—91no—
305C2×#102—91no—
306C24×C3—61no—
307C24×C3—61no—
308C23×D3—21no—
309C23×D3—21no—
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—21no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C2×C3×D4—31no—
317C2×C3×D4—41no—
318C2×C3×D4—62no—
319C2×C3×D4—61no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4—61no—
323C2×C3×D4—62no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C2×C3×D4—121no—
327C2×C3×D4—121no—
328C2×C3×D4—124no—
329C2×C3×D4C22×D311yescharacteristic
330C2×C3×D4C22×D311yescharacteristic
331C22×C3×C4—21no—
332C22×C3×C4—31no—
333C22×C3×C4—61no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—21no—
339C2×#67—21no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67#6711yescharacteristic
343C22×Dic3—61no—
344C22×Dic3—61no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347C22×Dic3—121no—
348#237—124no—
349#237—124no—
350D3×D4—22no—
351D3×D4—41no—
352D3×D4—44no—
353C2×D12—22no—
354C2×D12—21no—
355C2×D12—21no—
356C2×D12—41no—
357C2×D12C22×D311yescharacteristic
358C2×D12C22×D311yescharacteristic
359C2×D12C22×D311yescharacteristic
360C2×C4×D3—21no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3C22×D311yescharacteristic
364C2×Dic6—61no—
365C2×Dic6—61no—
366C3×D8—121no—
367C2×C3×C8—31no—
368C2×C3×C8—31no—
369C2×C3×C8—121no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—31no—
373C3×C4⋊C4C22×D311yescharacteristic
374C3×C4⋊C4C22×D311yescharacteristic
375C3×C22⋊C4—21no—
376C3×C22⋊C4—21no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—41no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C42—31no—
384#217—61no—
385#217—61no—
386#217#6711yescharacteristic
387#213—41no—
388#213—62no—
389#213—62no—
390#213—121no—
391#213—121no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4#6711yescharacteristic
398C4⋊Dic3—31no—
399C4⋊Dic3—31no—
400C4⋊Dic3—31no—
401C4⋊Dic3—31no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3—61no—
408C4⋊Dic3—121no—
409C4⋊Dic3C22×D311yescharacteristic
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4#6711yescharacteristic
413C4×Dic3C22×D311yescharacteristic
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—41no—
419C2×C3⋊C8—61no—
420C2×C3⋊C8—61no—
421C2×C3⋊C8—121no—
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424D3×C8—121no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32C2×D812yes—
431C22×C32C22×D411yescharacteristic
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—22no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—84no—
444C2×C3×D3—84no—
445C2×C3×D3C2×D812yes—
446C32×C4—21no—
447C32×C4—41no—
448C32×C4C2×#4111yescharacteristic
449C32×C4H(5,𝔽2)11yescharacteristic
450C3⋊Dic3—41no—
451C3⋊Dic3—41no—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—41no—
455C3×Dic3C2×D812yes—
456C2×#41—181no—
457C22×D4—31no—
458C22×D4—31no—
459C22×D4—61no—
460C2×D8—31no—
461C2×D8—91no—
462C2×D8—91no—
463C22×C8—31no—
464C22×C8—91no—
465C4⋊Q8—91no—
466#127—31no—
467#123—181no—
468#123—181no—
469C22⋊Q8—181no—
470#121—31no—
471#121—31no—
472#121—61no—
473#121—91no—
474#121D3211yescharacteristic
475#120—61no—
476#120—61no—
477C4×D4—31no—
478C4×D4—31no—
479C4×D4—91no—
480C2×C4⋊C4—91no—
481C2×C4⋊C4—91no—
482#107—31no—
483#107—91no—
484#107—91no—
485C4⋊C8—91no—
486#102—31no—
487#102—31no—
488#102—91no—
489#102—91no—
490#102—91no—
491#102—91no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496C22⋊C8—91no—
497C22⋊C8—91no—
498C4×C8—91no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—31no—
503C23×C3—41no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3—61no—
507C23×C3—122no—
508C23×C3—122no—
509C23×C3—122no—
510C23×C3—122no—
511C23×C3—241no—
512C23×C3—241no—
513C23×C3D3×D411yescharacteristic
514C23×C3C2×#6711yescharacteristic
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—42no—
519C22×D3—42no—
520C22×D3—42no—
521C22×D3—42no—
522C22×D3—81no—
523C22×D3—81no—
524C22×D3C2×#6711yescharacteristic
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—34no—
530C3×D4—32no—
531C3×D4—41no—
532C3×D4—41no—
533C3×D4—42no—
534C3×D4—42no—
535C3×D4—61no—
536C3×D4—61no—
537C3×D4—61no—
538C3×D4—61no—
539C3×D4—61no—
540C3×D4—82no—
541C3×D4—122no—
542C3×D4—122no—
543C3×D4—122no—
544C3×D4—122no—
545C3×D4—122no—
546C3×D4—241no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—31no—
556C2×C3×C4—31no—
557C2×C3×C4—31no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—122no—
565C2×C3×C4D3×D411yescharacteristic
566C2×C3×C4C2×#6711yescharacteristic
567C2×C3×C4C23×D311yescharacteristic
568C2×C3×C4C23×D311yescharacteristic
569#67—42no—
570#67—42no—
571#67—42no—
572#67—81no—
573#67—122no—
574#67—122no—
575#67#21314yescomplemented
576C2×Dic3—21no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—121no—
582C2×Dic3—121no—
583C2×Dic3—122no—
584C2×Dic3—122no—
585C2×Dic3—122no—
586C2×Dic3—122no—
587C2×Dic3—242no—
588C2×Dic3C2×#6711yescharacteristic
589C2×Dic3C2×#6711yescharacteristic
590C2×Dic3C2×#6711yescharacteristic
591D12—21no—
592D12—21no—
593D12—21no—
594D12—21no—
595D12—21no—
596D12—42no—
597D12—42no—
598D12#23712yescomplemented
599C4×D3—21no—
600C4×D3—21no—
601C4×D3—42no—
602C4×D3—122no—
603C4×D3—122no—
604Dic6—122no—
605Dic6—122no—
606C3×C8—61no—
607C3×C8—61no—
608C3⋊C8—21no—
609C3⋊C8—21no—
610C3⋊C8—61no—
611C3⋊C8—61no—
612C3⋊C8—61no—
613C3⋊C8—61no—
614C3⋊C8—121no—
615C3⋊C8—121no—
616C2×C32—22no—
617C2×C32—81no—
618C2×C32#54611yescharacteristic
619C2×C32C22×D811yescharacteristic
620C2×C32#57711yescharacteristic
621C3×D3—22no—
622C3×D3—42no—
623C3×D3—81no—
624C3×D3—81no—
625C24—61no—
626C24—61no—
627#41—364no—
628C2×Q8—181no—
629C2×D4—21no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—31no—
633C2×D4—31no—
634C2×D4—62no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—61no—
638C2×D4—61no—
639C2×D4—62no—
640C2×D4—61no—
641C2×D4—61no—
642C2×D4—121no—
643C2×D4—121no—
644C2×D4—124no—
645C2×D4—181no—
646C2×D4C2×D3211yescharacteristic
647C22×C4—31no—
648C22×C4—61no—
649C22×C4—181no—
650C22×C4—181no—
651C22×C4—181no—
652C22×C4C2×D3211yescharacteristic
653D8—121no—
654D8—182no—
655D8—361no—
656C2×C8—31no—
657C2×C8—31no—
658C2×C8—91no—
659C2×C8—91no—
660C2×C8—121no—
661C2×C8—361no—
662C4⋊C4—31no—
663C4⋊C4—31no—
664C4⋊C4—91no—
665C4⋊C4—91no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C4⋊C4C2×D3211yescharacteristic
670C22⋊C4—21no—
671C22⋊C4—31no—
672C22⋊C4—31no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C42—31no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—22no—
685C22×C3—32no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—62no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—81no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3—121no—
703C22×C3—121no—
704C22×C3—121no—
705C22×C3—121no—
706C22×C3—121no—
707C22×C3—121no—
708C22×C3—244no—
709C22×C3—244no—
710C22×C3D3×D812yes—
711C22×C3C2×#21312yes—
712C22×C3C2×D3×D411yescharacteristic
713C22×C3C22×#6711yescharacteristic
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—22no—
717C2×D3—41no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—84no—
726C2×D3—84no—
727C2×D3C2×#21312yes—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—32no—
733C3×C4—41no—
734C3×C4—41no—
735C3×C4—41no—
736C3×C4—61no—
737C3×C4—61no—
738C3×C4—81no—
739C3×C4—121no—
740C3×C4C2×#23711yescharacteristic
741C3×C4#100411yescharacteristic
742C3×C4#100411yescharacteristic
743C3×C4D3×#4111yescharacteristic
744Dic3—21no—
745Dic3—21no—
746Dic3—41no—
747Dic3—121no—
748Dic3—121no—
749Dic3—121no—
750Dic3—121no—
751Dic3—241no—
752Dic3—241no—
753Dic3C2×#21312yes—
754C32#329411yescharacteristic, complemented, Sylow
755C23—21no—
756C23—31no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—122no—
761C23—122no—
762C23—122no—
763C23—122no—
764C23—241no—
765C23—241no—
766C23D3×#6711yescharacteristic
767Q8—362no—
768D4—21no—
769D4—21no—
770D4—34no—
771D4—32no—
772D4—42no—
773D4—61no—
774D4—61no—
775D4—61no—
776D4—61no—
777D4—61no—
778D4—122no—
779D4—122no—
780D4—122no—
781D4—122no—
782D4—122no—
783D4—241no—
784D4—362no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—31no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—122no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4—362no—
798C2×C4—362no—
799C2×C4—362no—
800C2×C4D3×#6711yescharacteristic
801C2×C4C22×D3211yescharacteristic
802C8—61no—
803C8—61no—
804C8—181no—
805C8—181no—
806C2×C3—22no—
807C2×C3—22no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—42no—
812C2×C3—62no—
813C2×C3—81no—
814C2×C3—81no—
815C2×C3—122no—
816C2×C3—161no—
817C2×C3—241no—
818C2×C3—241no—
819C2×C3#561011yescharacteristic
820C2×C3C2×D3×D811yescharacteristic
821C2×C3#577011yescharacteristic
822C2×C3C22×#21311yescharacteristic
823C2×C3#580611yescharacteristic
824C2×C3#583611yescharacteristic
825D3—22no—
826D3—42no—
827D3—81no—
828D3—81no—
829C22—21no—
830C22—21no—
831C22—32no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—61no—
836C22—61no—
837C22—62no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—121no—
846C22—244no—
847C22—244no—
848C22D3×#21312yes—
849C22C2×D3×#6711yescharacteristic
850C4—21no—
851C4—32no—
852C4—41no—
853C4—61no—
854C4—61no—
855C4—121no—
856C4—361no—
857C4—361no—
858C4D3×#23711yescharacteristic
859C4#6431311yescharacteristic
860C3—21no—
861C3#8073111yescharacteristic, complemented
862C3#8348211yescharacteristic, complemented
863C2—22no—
864C2—62no—
865C2—81no—
866C2—122no—
867C2—241no—
868C2—241no—
869C2C2×D3×#21311yescharacteristic
870C2#1059515011yescharacteristic
871C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3294
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
1. C3×#5609C2semidirect
2. #10594907C2semidirect
3. #10592732C2semidirect
4. C3×#5038C2semidirect
5. #10591487C2semidirect
6. #10591447C2semidirect
7. #10591428C2semidirect
8. D3×#832C2semidirect
9. #10591160C2semidirect
10. C3⋊C8×#67C2semidirect
11. C2×#63563C2semidirect
12. #10590555C2semidirect
13. #10590499C2semidirect
14. #10590452C2semidirect
15. #10590438C2semidirect
23. C2×C4⋊(C3⋊Dic3)C22semidirect
26. C2×C3×#213C22semidirect
27. C3×#930C22semidirect
29. C22×C3×C3⋊C8C22semidirect
35. #63918C22semidirect
36. #63908C22semidirect
38. Dic3×D12C22semidirect
40. D3×C4⋊Dic3C22semidirect
42. C2×#3713C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63659C22semidirect
45. #63659C22semidirect
46. #63657C22semidirect
47. #63634C22semidirect
48. #63634C22semidirect
49. C3×#832C22semidirect
50. C3×#809C22semidirect
51. C3×#807C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
55. #63563C22semidirect
56. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
63. #5609D3semidirect
77. #5038D3semidirect
177. C2×#213C2×D3semidirect
179. #930C2×D3semidirect
186. C22×C3⋊C8C2×D3semidirect
216. #832C2×D3semidirect
230. #809C2×D3semidirect
237. #807C2×D3semidirect
267. C3×#67D8semidirect
279. C3×D12#41semidirect
575. #67#213semidirect
598. D12#237semidirect
754. C32#3294semidirect
861. C3#80731semidirect
862. C3#83482semidirect

Maximal subgroups

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

subgroupindex
C3×#56092
#105949072
#105927322
C3×#50382
#105914872
#105914472
#105914282
D3×#8322
#105911602
C3⋊C8×#672
C2×#635632
#105905552
#105904992
#105904522
#105904382
#834823
#807313