Finite Group Databasebeta

← #11889096

Subgroups — #11889096

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×#67C211yesmaximal, characteristic
2#10594853C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C3×#5218C211yesmaximal, characteristic, complemented
5#10591502C211yesmaximal, characteristic, complemented
6#10591477C211yesmaximal, characteristic, complemented
7#10591458C211yesmaximal, characteristic, complemented
8#10591440C211yesmaximal, characteristic, complemented
9#10591438C211yesmaximal, characteristic, complemented
10#10591423C211yesmaximal, characteristic, complemented
11#10591421C211yesmaximal, characteristic, complemented
12#10591411C211yesmaximal, characteristic, complemented
13#10591179C211yesmaximal, characteristic, complemented
14#10591158C211yesmaximal, characteristic, complemented
15#10591094C211yesmaximal, characteristic, complemented
16#83484—31nomaximal
17#80160—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×C3×#67—21no—
20C2×C3×D3×D4C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C3×#953—21no—
24C3×#940C2211yescharacteristic
25C3×#939—21no—
26C3×#938C2211yescharacteristic
27C3×#937—21no—
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic, complemented
31C3×#930C2211yescharacteristic
32C3×C4×#67C2211yescharacteristic
33C3×#924C2211yescharacteristic, complemented
34#63962—21no—
35#63957—21no—
36#63869C2211yescharacteristic, complemented
37#63861—21no—
38#63856C2211yescharacteristic, complemented
39#63845—21no—
40Dic3×Dic6C2211yescharacteristic, complemented
41#63841C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic, complemented
43C2×#3711C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63659C2211yescharacteristic, complemented
47#63659C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic, complemented
50C3×#830C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×D42—31no—
62D4×#67D311yescharacteristic
63#5642—31no—
64#5541—31no—
65C3×#450—31no—
66#5218—31no—
67#5218D311yescharacteristic, complemented
68#5215—31no—
69C2×#832—31no—
70C2×#832—31no—
71C2×#832—61no—
72#5174—31no—
73#5169—31no—
74#5164—31no—
75#5163—31no—
76#5075—31no—
77#5071—31no—
78#5048—31no—
79#5042—31no—
80#5041—31no—
81#5035—31no—
82#5033—31no—
83#5018—31no—
84#5011—31no—
85#5009—31no—
86#4784—31no—
87#4770—31no—
88#4766—31no—
89#4764—31no—
90#4736—31no—
91#4730—31no—
92C24×C32—21no—
93C23×C3×D3—21no—
94C2×C32×D4—22no—
95C2×C32×D4—21no—
96C2×C32×D4—41no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C3⋊Dic3—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—44no—
107C2×C3×#67D411yescharacteristic
108C22×C3×Dic3—21no—
109C3×D3×D4—22no—
110C3×D3×D4—41no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)—41no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#217D411yescharacteristic
124C3×#214—22no—
125C3×#214—41no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142Dic32—21no—
143#3715—41no—
144#3711—41no—
145#3310—91noSylow
146C22×C3×D4—21no—
147C22×C3×D4—31no—
148C22×C3×D4—61no—
149C22×C3×D4C2×D311yescharacteristic
150C22×C3×D4C2×D311yescharacteristic
151C22×#67—21no—
152C2×D3×D4C2×D311yescharacteristic
153C2×C3×SD16—31no—
154C2×C3×SD16—31no—
155C3×#127—31no—
156C3×C22⋊Q8—31no—
157C3×#121—31no—
158C3×#121—31no—
159C3×#121—61no—
160C3×#120—61no—
161C3×#120—61no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164#953—21no—
165#946—31no—
166Q8×Dic3—31no—
167C2×#215—31no—
168#940C2×D311yescharacteristic
169#939—21no—
170#938C2×D311yescharacteristic
171#937—21no—
172#935—61no—
173D4×Dic3C2×D311yescharacteristic
174C2×#214—31no—
175C2×#214C2×D311yescharacteristic
176C2×#214C2×D311yescharacteristic, complemented
177#930C2×D311yescharacteristic
178C4×#67C2×D311yescharacteristic
179#926—31no—
180C2×C4⋊Dic3—31no—
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—61no—
183#924—31no—
184#924C2×D311yescharacteristic, complemented
185C2×#208—31no—
186C22×C3⋊C8—31no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8—61no—
189C2×ΓL(1,𝔽25)—31no—
190#898—61no—
191#892—31no—
192#890—31no—
193#890—61no—
194#889—61no—
195#886—61no—
196#879—61no—
197#877—61no—
198#877—61no—
199#870—31no—
200C4×Dic6—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×C22⋊C8—31no—
204#835—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—31no—
215#832—31no—
216#832—61no—
217#832—61no—
218#832—61no—
219#832—61no—
220#832C2×D311yescharacteristic
221#832C2×D311yescharacteristic, complemented
222#830—31no—
223#830C2×D311yescharacteristic, complemented
224#821—31no—
225#821—31no—
226(C2×D3)⋊C8—31no—
227#818—31no—
228#818—31no—
229#815—31no—
230Dic3⋊C8—31no—
231#810—31no—
232#809—31no—
233#808—31no—
234#808—31no—
235#807—31no—
236#807—31no—
237C4⋊(C3⋊C8)—31no—
238#803—31no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—42no—
242C23×C32—42no—
243C23×C32—81no—
244C23×C32C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3—81no—
249C22×C3×D3C2×D411yescharacteristic
250C32×D4—21no—
251C32×D4—21no—
252C32×D4—21no—
253C32×D4—42no—
254C32×D4#4112yes—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—42no—
262C3×#67—22no—
263C3×#67—42no—
264C3×#67—42no—
265C3×#67—42no—
266C3×#67—42no—
267C3×#67—81no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—42no—
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—21no—
276C3×D12—21no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×Dic6—21no—
280C3×Dic6—21no—
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—91no—
292#465—91no—
293#460—91no—
294#450—31no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C24×C3—21no—
301C24×C3—21no—
302C24×C3—41no—
303C24×C3—61no—
304C23×D3—21no—
305C2×C3×Q8—31no—
306C2×C3×D4—24no—
307C2×C3×D4—22no—
308C2×C3×D4—22no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—21no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C2×C3×D4—41no—
316C2×C3×D4—41no—
317C2×C3×D4—41no—
318C2×C3×D4—42no—
319C2×C3×D4—61no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4—62no—
323C2×C3×D4—61no—
324C2×C3×D4—61no—
325C2×C3×D4—121no—
326C2×C3×D4—124no—
327C2×C3×D4C22×D311yescharacteristic
328C2×C3×D4C22×D311yescharacteristic
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—21no—
341C2×#67—44no—
342C2×#67#6711yescharacteristic
343C22×Dic3—21no—
344C22×Dic3—61no—
345C22×Dic3—61no—
346C22×Dic3—121no—
347D3×D4—22no—
348D3×D4—41no—
349C2×D12C22×D311yescharacteristic
350C2×C4×D3C22×D311yescharacteristic
351C2×Dic6C22×D311yescharacteristic
352C3×SD16—62no—
353C3×SD16—121no—
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—61no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—31no—
367#217—21no—
368#217—21no—
369#217—21no—
370#217—61no—
371#217—61no—
372#217#6711yescharacteristic
373#215—121no—
374#214—22no—
375#214—41no—
376#214—121no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—61no—
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⋊Dic3—61no—
391C4⋊Dic3—121no—
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4#6711yescharacteristic
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3C22×D311yescharacteristic
407#208—121no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8—61no—
414C2×C3⋊C8—121no—
415C2×C3⋊C8—121no—
416C2×C3⋊C8—122no—
417C2×C3⋊C8C22×D311yescharacteristic
418C2×C3⋊C8C22×D311yescharacteristic
419ΓL(1,𝔽25)—121no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—22no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32—84no—
429C22×C32AGL(1,ℤ/8)12yes—
430C22×C32C22×D411yescharacteristic
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—84no—
438C32×C4—21no—
439C32×C4C2×#4111yescharacteristic
440C32×C4H(5,𝔽2)11yescharacteristic
441C3⋊Dic3—41no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C22×D4—31no—
450C22×D4—61no—
451C22×D4D3211yescharacteristic
452C2×SD16—31no—
453C2×SD16—31no—
454C2×SD16—91no—
455C2×M16—91no—
456C22×C8—91no—
457#127—31no—
458#126—181no—
459#125—91no—
460#125—181no—
461#123—181no—
462C22⋊Q8—31no—
463C22⋊Q8—91no—
464#121—31no—
465#121—31no—
466#121—61no—
467#120—61no—
468#120—61no—
469C4×Q8—91no—
470C4×D4—31no—
471C4×D4—31no—
472#117—91no—
473#117—181no—
474C2×C4⋊C4—91no—
475#107—91no—
476#107—91no—
477#106—91no—
478C4⋊C8—91no—
479#103—91no—
480#102—31no—
481#102—31no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489C22⋊C8—31no—
490C22⋊C8—91no—
491#97—91no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—31no—
498C23×C3—41no—
499C23×C3—41no—
500C23×C3—42no—
501C23×C3—42no—
502C23×C3—44no—
503C23×C3—42no—
504C23×C3—42no—
505C23×C3—61no—
506C23×C3—82no—
507C23×C3—81no—
508C23×C3—81no—
509C23×C3—82no—
510C23×C3—122no—
511C23×C3—122no—
512C23×C3—241no—
513C23×C3D3×D411yescharacteristic
514C23×C3C2×#6711yescharacteristic
515C22×D3—21no—
516C22×D3—42no—
517C22×D3—42no—
518C22×D3—81no—
519C22×D3C2×#6711yescharacteristic
520C3×Q8—61no—
521C3×Q8—61no—
522C3×D4—22no—
523C3×D4—21no—
524C3×D4—21no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—22no—
530C3×D4—41no—
531C3×D4—41no—
532C3×D4—42no—
533C3×D4—42no—
534C3×D4—44no—
535C3×D4—62no—
536C3×D4—61no—
537C3×D4—61no—
538C3×D4—122no—
539C3×D4—122no—
540C3×D4—122no—
541C3×D4—122no—
542C3×D4—241no—
543C3×D4#23712yes—
544C3×D4#23712yes—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
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—31no—
554C2×C3×C4—31no—
555C2×C3×C4—31no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—122no—
562C2×C3×C4D3×D411yescharacteristic
563C2×C3×C4C2×#6711yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565C2×C3×C4C23×D311yescharacteristic
566#67—22no—
567#67—42no—
568#67—42no—
569#67—42no—
570#67—42no—
571#67—81no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—42no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—121no—
581C2×Dic3—121no—
582C2×Dic3—122no—
583C2×Dic3—122no—
584C2×Dic3—242no—
585C2×Dic3C2×#6711yescharacteristic
586C2×Dic3C2×#6711yescharacteristic
587C2×Dic3C2×#6711yescharacteristic
588D12—21no—
589D12—21no—
590C4×D3—21no—
591C4×D3—21no—
592Dic6—21no—
593Dic6—21no—
594C3×C8—61no—
595C3×C8—61no—
596C3⋊C8—21no—
597C3⋊C8—21no—
598C3⋊C8—61no—
599C3⋊C8—61no—
600C3⋊C8—61no—
601C3⋊C8—61no—
602C3⋊C8—121no—
603C3⋊C8—121no—
604C2×C32—22no—
605C2×C32—42no—
606C2×C32—81no—
607C2×C32#54611yescharacteristic
608C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
609C2×C32#57711yescharacteristic
610C3×D3—41no—
611C3×D3—81no—
612C24—21no—
613C24—61no—
614C2×Q8—31no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—31no—
618C2×D4—31no—
619C2×D4—41no—
620C2×D4—61no—
621C2×D4—61no—
622C2×D4—61no—
623C2×D4—62no—
624C2×D4—61no—
625C2×D4—61no—
626C2×D4—121no—
627C2×D4—124no—
628C2×D4C2×D3211yescharacteristic
629C2×D4C2×D3211yescharacteristic
630C22×C4—31no—
631C22×C4—61no—
632C22×C4—181no—
633C22×C4C2×D3211yescharacteristic
634SD16—62no—
635SD16—121no—
636SD16—361no—
637M16—361no—
638C2×C8—31no—
639C2×C8—31no—
640C2×C8—91no—
641C2×C8—91no—
642C2×C8—361no—
643C4⋊C4—31no—
644C4⋊C4—31no—
645C4⋊C4—31no—
646C4⋊C4—61no—
647C4⋊C4—91no—
648C4⋊C4—91no—
649C4⋊C4—181no—
650C4⋊C4—181no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C22⋊C4—31no—
655C22⋊C4—31no—
656C22⋊C4—61no—
657C22⋊C4—61no—
658C22⋊C4—61no—
659C22⋊C4—61no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C42—31no—
663C42—181no—
664C42—181no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—21no—
674C22×C3—22no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—61no—
690C22×C3—81no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3—84no—
695C22×C3—84no—
696C22×C3—88no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—244no—
701C22×C3#91412yes—
702C22×C3#93212yes—
703C22×C3C2×D3×D411yescharacteristic
704C22×C3C22×#6711yescharacteristic
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—84no—
712C3×C4—22no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—61no—
718C3×C4—61no—
719C3×C4—61no—
720C3×C4—121no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4C2×#23711yescharacteristic
724C3×C4C2×#23711yescharacteristic
725C3×C4#100411yescharacteristic
726C3×C4#100411yescharacteristic
727Dic3—21no—
728Dic3—21no—
729Dic3—21no—
730Dic3—41no—
731Dic3—41no—
732Dic3—41no—
733Dic3—121no—
734Dic3—121no—
735Dic3—121no—
736Dic3—121no—
737Dic3—241no—
738Dic3—241no—
739C32#331011yescharacteristic, complemented, Sylow
740C23—21no—
741C23—21no—
742C23—31no—
743C23—42no—
744C23—42no—
745C23—61no—
746C23—81no—
747C23—122no—
748C23—122no—
749C23—241no—
750C23D3×#6711yescharacteristic
751Q8—61no—
752Q8—61no—
753D4—21no—
754D4—21no—
755D4—21no—
756D4—42no—
757D4—62no—
758D4—61no—
759D4—61no—
760D4—122no—
761D4—122no—
762D4—122no—
763D4—122no—
764D4—241no—
765D4#380512yes—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—31no—
769C2×C4—31no—
770C2×C4—31no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—122no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—362no—
780C2×C4D3×#6711yescharacteristic
781C2×C4C22×D3211yescharacteristic
782C8—61no—
783C8—61no—
784C8—181no—
785C8—181no—
786C2×C3—24no—
787C2×C3—22no—
788C2×C3—22no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—42no—
793C2×C3—42no—
794C2×C3—82no—
795C2×C3—82no—
796C2×C3—81no—
797C2×C3—81no—
798C2×C3—121no—
799C2×C3—241no—
800C2×C3#559111yescharacteristic
801C2×C3C2×#91411yescharacteristic
802C2×C3#577511yescharacteristic
803C2×C3C2×#93211yescharacteristic
804C2×C3#580611yescharacteristic
805C2×C3#583611yescharacteristic
806D3—41no—
807D3—81no—
808C22—21no—
809C22—21no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—61no—
817C22—61no—
818C22—61no—
819C22—84no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—244no—
824C22#6393412yes—
825C22C2×D3×#6711yescharacteristic
826C4—21no—
827C4—61no—
828C4—61no—
829C4—61no—
830C4—121no—
831C4—121no—
832C4—121no—
833C4—361no—
834C4—361no—
835C4C2×#380511yescharacteristic
836C4#6433011yescharacteristic
837C3—21no—
838C3#8016011yescharacteristic, complemented
839C3#8348411yescharacteristic, complemented
840C2—22no—
841C2—42no—
842C2—81no—
843C2—121no—
844C2—241no—
845C2#1059510611yescharacteristic
846C2C2×#6393411yescharacteristic
847C2#1059549411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC3×D4×#67C2
hypercenterC22×D4D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10594853C2semidirect
3. C2×#63659C2semidirect
4. C3×#5218C2semidirect
5. #10591502C2semidirect
6. #10591477C2semidirect
7. #10591458C2semidirect
8. #10591440C2semidirect
9. #10591438C2semidirect
10. #10591423C2semidirect
11. #10591421C2semidirect
12. #10591411C2semidirect
13. #10591179C2semidirect
14. #10591158C2semidirect
15. #10591094C2semidirect
21. C2×C4⋊(C3⋊Dic3)C22semidirect
22. C22×C3⋊(C3⋊C8)C22semidirect
30. C2×C3×#214C22semidirect
33. C3×#924C22semidirect
36. #63869C22semidirect
38. #63856C22semidirect
40. Dic3×Dic6C22semidirect
41. #63841C22semidirect
42. C2×#3715C22semidirect
43. C2×#3711C22semidirect
46. #63659C22semidirect
47. #63659C22semidirect
49. C3×#832C22semidirect
50. C3×#830C22semidirect
51. #63575C22semidirect
52. #63575C22semidirect
53. #63574C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63565C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
67. #5218D3semidirect
176. C2×#214C2×D3semidirect
184. #924C2×D3semidirect
221. #832C2×D3semidirect
223. #830C2×D3semidirect
739. C32#3310semidirect
838. C3#80160semidirect
839. C3#83484semidirect

Maximal subgroups

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

subgroupindex
C3×D4×#672
#105948532
C2×#636592
C3×#52182
#105915022
#105914772
#105914582
#105914402
#105914382
#105914232
#105914212
#105914112
#105911792
#105911582
#105910942
#834843
#801603