Finite Group Databasebeta

← #11887416

Subgroups — #11887416

Order 1152.

902 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
1C3×#5618C211yesmaximal, characteristic, complemented
2#10594886C211yesmaximal, characteristic, complemented
3#10592740C211yesmaximal, characteristic, complemented
4C3×#5036C211yesmaximal, characteristic, complemented
5#10591519C211yesmaximal, characteristic, complemented
6#10591498C211yesmaximal, characteristic, complemented
7#10591468C211yesmaximal, characteristic, complemented
8Dic3×#213C211yesmaximal, characteristic, complemented
9#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#10591135C211yesmaximal, characteristic, complemented
11C2×#63562C211yesmaximal, characteristic, complemented
12#10590608C211yesmaximal, characteristic, complemented
13#10590533C211yesmaximal, characteristic, complemented
14#10590505C211yesmaximal, characteristic, complemented
15#10590469C211yesmaximal, characteristic, complemented
16#83614—31nomaximal
17#80015—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C32×#121C2211yescharacteristic
21C2×#3754C2211yescharacteristic, complemented
22#64133C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×#939—21no—
25C3×#938C2211yescharacteristic, complemented
26C3×D4×Dic3—21no—
27C3×D4×Dic3C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×C4×#67C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C3×#892C2211yescharacteristic, complemented
33C3×#890C2211yescharacteristic, complemented
34C3×#886—21no—
35C3×#879—21no—
36#63976—21no—
37D3×#217—21no—
38#63908C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40#63885—21no—
41#63884—21no—
42#63860C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45#63637C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic
50#63575C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63567C2211yescharacteristic, complemented
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#553—31no—
62#5806—31no—
63#5618D311yescharacteristic, complemented
64#5550—31no—
65C3×#447—31no—
66C2×#832—31no—
67#5158—31no—
68#5157—31no—
69#5153—31no—
70Dic3×D8—31no—
71#5068—31no—
72#5066—31no—
73#5041—31no—
74#5041—31no—
75#5041—61no—
76#5038—31no—
77#5037—31no—
78#5036D311yescharacteristic, complemented
79#5016—31no—
80C4×#213—31no—
81D4×C3⋊C8—31no—
82#5003—31no—
83#5002—31no—
84#4970—31no—
85C2×#809—31no—
86#4784—31no—
87#4772—31no—
88#4768—31no—
89#4766—31no—
90#67⋊C8—31no—
91#4722—31no—
92C23×C3×D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67D411yescharacteristic
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C2×C3×D12—22no—
102C2×C3×D12—21no—
103C2×C3×D12—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×#625—21no—
108C2×#625—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3795—22no—
112#3795—41no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115#3757—21no—
116#3754—41no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C2×C3⋊(C3⋊C8)—41no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—21no—
123C3×#217—21no—
124C3×#217D411yescharacteristic
125C3×#213—22no—
126C3×#213—41no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#235—31no—
148C22×D12C2×D311yescharacteristic
149C2×C3×D8—31no—
150C2×C3×D8—31no—
151C3×#126—61no—
152C3×#125—31no—
153C3×#123—61no—
154C3×#121—21no—
155C3×#121—31no—
156C3×#121—61no—
157C3×#121C2×D311yescharacteristic
158C3×#121C2×D311yescharacteristic
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×C4×D4—61no—
162C3×#117—31no—
163C2×C3×C4⋊C4—31no—
164#953—61no—
165C2×#217—61no—
166#939—21no—
167#939—61no—
168#938—31no—
169#938C2×D311yescharacteristic, complemented
170#937—61no—
171#936—31no—
172#935—61no—
173D4×Dic3—21no—
174D4×Dic3—31no—
175D4×Dic3C2×D311yescharacteristic, complemented
176C2×#214—31no—
177C2×#214—31no—
178C2×#214—61no—
179C2×#213C2×D311yescharacteristic
180C2×#213C2×D311yescharacteristic
181#930—31no—
182C4×#67C2×D311yescharacteristic
183C2×C4⋊Dic3C2×D311yescharacteristic
184#924—31no—
185#924—31no—
186#924—61no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8—31no—
189C22×C3⋊C8—31no—
190C22×C3⋊C8—61no—
191C2×D3×C8—31no—
192#894—61no—
193#892C2×D311yescharacteristic, complemented
194#890C2×D311yescharacteristic, complemented
195#886—21no—
196#884—61no—
197D3×C22⋊C4—61no—
198#879—21no—
199#875—31no—
200C4×D12—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×C22⋊C8—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—61no—
211#830—31no—
212#830C2×D311yescharacteristic
213(C2×D3)⋊C8—31no—
214#818—31no—
215#818—31no—
216#816—31no—
217#816—31no—
218Dic3⋊C8—31no—
219C8×Dic3—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—61no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809C2×D311yescharacteristic
230#809C2×D311yescharacteristic
231#808—31no—
232#808—31no—
233#808—61no—
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—42no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256#634—21no—
257#634—21no—
258C3×#67—22no—
259C3×#67—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—81no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—42no—
271C3×D12#4112yes—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274#625—42no—
275#625—81no—
276D3×Dic3—42no—
277D3×Dic3—81no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—31no—
283#546—91no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—31no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C24×C3—61no—
298C23×D3—21no—
299C2×C3×D4—21no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—41no—
306C2×C3×D4—62no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—121no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—21no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C2×#67—21no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67#6711yescharacteristic
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328#237—62no—
329#237—121no—
330#235—62no—
331#235—121no—
332C2×D12—22no—
333C2×D12—21no—
334C2×D12—41no—
335C2×D12C22×D311yescharacteristic
336C2×D12C22×D311yescharacteristic
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3C22×D311yescharacteristic
340C2×Dic6—31no—
341C2×Dic6—31no—
342C2×Dic6—61no—
343C3×D8—62no—
344C3×D8—121no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—41no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—31no—
365C3×C42—61no—
366#217—21no—
367#217—21no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—121no—
375#217#6711yescharacteristic
376#214—121no—
377#214—121no—
378#214—122no—
379#213—22no—
380#213—41no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4#6711yescharacteristic
387C4⋊Dic3—21no—
388C4⋊Dic3—21no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—121no—
398Dic3⋊C4#6711yescharacteristic
399C4×Dic3—21no—
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8—121no—
410C2×C3⋊C8—122no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413D3×C8—121no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32#13512yes—
420C22×C32C22×D411yescharacteristic
421C2×C3×D3—22no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—84no—
431C32×C4—21no—
432C32×C4—41no—
433C32×C4C2×#4111yescharacteristic
434C32×C4H(5,𝔽2)11yescharacteristic
435C3⋊Dic3—41no—
436C3⋊Dic3—41no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—91no—
443C22×D4—31no—
444C2×SD16—91no—
445C2×D8—31no—
446C2×D8—31no—
447C22×C8—91no—
448C22×C8—91no—
449#126—61no—
450#125—31no—
451#124—91no—
452#123—61no—
453#123—181no—
454C22⋊Q8—91no—
455#121—31no—
456#121—61no—
457#121—91no—
458#121—181no—
459#121D3211yescharacteristic
460#120—181no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—61no—
464C4×D4—91no—
465#117—31no—
466C2×C4⋊C4—31no—
467C2×C22⋊C4—181no—
468#107—91no—
469#107—91no—
470#106—91no—
471C4⋊C8—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482C22⋊C8—31no—
483C22⋊C8—91no—
484C4×C8—91no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—31no—
489C23×C3—41no—
490C23×C3—61no—
491C23×C3—61no—
492C23×C3—122no—
493C23×C3—122no—
494C23×C3—241no—
495C23×C3D3×D411yescharacteristic
496C23×C3C2×#6711yescharacteristic
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—42no—
500C22×D3—42no—
501C22×D3—81no—
502C22×D3C2×#6711yescharacteristic
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—32no—
508C3×D4—41no—
509C3×D4—41no—
510C3×D4—42no—
511C3×D4—42no—
512C3×D4—62no—
513C3×D4—61no—
514C3×D4—61no—
515C3×D4—61no—
516C3×D4—82no—
517C3×D4—122no—
518C3×D4—241no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—241no—
538C2×C3×C4—241no—
539C2×C3×C4D3×D411yescharacteristic
540C2×C3×C4C2×#6711yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543#67—22no—
544#67—81no—
545#67—122no—
546#67—122no—
547#67—241no—
548#67—241no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—81no—
556C2×Dic3—81no—
557C2×Dic3—121no—
558C2×Dic3—121no—
559C2×Dic3—122no—
560C2×Dic3—241no—
561C2×Dic3C2×#6711yescharacteristic
562C2×Dic3C2×#6711yescharacteristic
563C2×Dic3C2×#6711yescharacteristic
564D12—21no—
565D12—21no—
566D12—21no—
567D12—42no—
568D12#23712yes—
569C4×D3—21no—
570C4×D3—21no—
571C4×D3—122no—
572C4×D3—241no—
573Dic6—61no—
574Dic6—61no—
575Dic6—61no—
576Dic6—61no—
577Dic6—121no—
578Dic6—121no—
579C3×C8—61no—
580C3×C8—61no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C3⋊C8—62no—
584C3⋊C8—61no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—61no—
588C3⋊C8—121no—
589C2×C32—22no—
590C2×C32—81no—
591C2×C32#54611yescharacteristic
592C2×C32C2×#13511yescharacteristic
593C2×C32#57611yescharacteristic
594C3×D3—41no—
595C3×D3—42no—
596C3×D3—81no—
597C24—61no—
598#41—182no—
599#41—361no—
600C2×Q8—91no—
601C2×D4—21no—
602C2×D4—31no—
603C2×D4—31no—
604C2×D4—31no—
605C2×D4—62no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—121no—
609C2×D4—181no—
610C2×D4—181no—
611C2×D4C2×D3211yescharacteristic
612C22×C4—31no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4C2×D3211yescharacteristic
618SD16—361no—
619D8—62no—
620D8—121no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—91no—
624C2×C8—91no—
625C2×C8—361no—
626C2×C8—361no—
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—91no—
634C4⋊C4—181no—
635C4⋊C4C2×D3211yescharacteristic
636C22⋊C4—21no—
637C22⋊C4—31no—
638C22⋊C4—31no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C42—31no—
648C42—61no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—22no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—62no—
666C22×C3—61no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—244no—
676C22×C3#91212yes—
677C22×C3#95012yes—
678C22×C3C2×D3×D411yescharacteristic
679C22×C3C22×#6711yescharacteristic
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—21no—
683C2×D3—22no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—84no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—61no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—81no—
701C3×C4—121no—
702C3×C4—121no—
703C3×C4C2×#23711yescharacteristic
704C3×C4#100411yescharacteristic
705C3×C4D3×#4111yescharacteristic
706C3×C4#100911yescharacteristic
707Dic3—21no—
708Dic3—21no—
709Dic3—21no—
710Dic3—41no—
711Dic3—41no—
712Dic3—121no—
713Dic3—121no—
714Dic3—121no—
715Dic3—121no—
716Dic3—241no—
717Dic3—241no—
718C32#329711yescharacteristic, complemented, Sylow
719C23—21no—
720C23—31no—
721C23—61no—
722C23—61no—
723C23—122no—
724C23—122no—
725C23—241no—
726C23D3×#6711yescharacteristic
727Q8—181no—
728Q8—181no—
729D4—21no—
730D4—21no—
731D4—32no—
732D4—42no—
733D4—62no—
734D4—61no—
735D4—61no—
736D4—61no—
737D4—122no—
738D4—241no—
739D4—362no—
740D4—721no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—31no—
745C2×C4—31no—
746C2×C4—31no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—181no—
752C2×C4—181no—
753C2×C4—241no—
754C2×C4—241no—
755C2×C4—362no—
756C2×C4—721no—
757C2×C4D3×#6711yescharacteristic
758C2×C4C22×D3211yescharacteristic
759C8—61no—
760C8—61no—
761C8—181no—
762C8—181no—
763C2×C3—22no—
764C2×C3—22no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—42no—
769C2×C3—81no—
770C2×C3—81no—
771C2×C3—121no—
772C2×C3—122no—
773C2×C3—161no—
774C2×C3—241no—
775C2×C3#559111yescharacteristic
776C2×C3C2×#91211yescharacteristic
777C2×C3#577411yescharacteristic
778C2×C3C2×#95011yescharacteristic
779C2×C3#582911yescharacteristic
780C2×C3#583511yescharacteristic
781D3—42no—
782D3—41no—
783D3—81no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—61no—
790C22—61no—
791C22—61no—
792C22—62no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—244no—
799C22#6393312yes—
800C22C2×D3×#6711yescharacteristic
801C4—21no—
802C4—41no—
803C4—61no—
804C4—61no—
805C4—61no—
806C4—121no—
807C4—121no—
808C4—361no—
809C4—361no—
810C4D3×#23711yescharacteristic
811C4#6431411yescharacteristic
812C3—21no—
813C3#8001511yescharacteristic, complemented
814C3#8361411yescharacteristic, complemented
815C2—22no—
816C2—81no—
817C2—121no—
818C2—122no—
819C2—241no—
820C2C2×#6393311yescharacteristic
821C2#1059530411yescharacteristic
822C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3297
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×#5618C2semidirect
2. #10594886C2semidirect
3. #10592740C2semidirect
4. C3×#5036C2semidirect
5. #10591519C2semidirect
6. #10591498C2semidirect
7. #10591468C2semidirect
8. Dic3×#213C2semidirect
9. #67⋊(C3⋊C8)C2semidirect
10. #10591135C2semidirect
11. C2×#63562C2semidirect
12. #10590608C2semidirect
13. #10590533C2semidirect
14. #10590505C2semidirect
15. #10590469C2semidirect
21. C2×#3754C22semidirect
25. C3×#938C22semidirect
27. C3×D4×Dic3C22semidirect
32. C3×#892C22semidirect
33. C3×#890C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63659C22semidirect
45. #63637C22semidirect
46. #63635C22semidirect
50. #63575C22semidirect
51. #63575C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63567C22semidirect
54. #63567C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
63. #5618D3semidirect
78. #5036D3semidirect
169. #938C2×D3semidirect
175. D4×Dic3C2×D3semidirect
193. #892C2×D3semidirect
194. #890C2×D3semidirect
718. C32#3297semidirect
813. C3#80015semidirect
814. C3#83614semidirect

Maximal subgroups

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

subgroupindex
C3×#56182
#105948862
#105927402
C3×#50362
#105915192
#105914982
#105914682
Dic3×#2132
#67⋊(C3⋊C8)2
#105911352
C2×#635622
#105906082
#105905332
#105905052
#105904692
#836143
#800153