Finite Group Databasebeta

← #11887014

Subgroups — #11887014

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×#5507C211yesmaximal, characteristic, complemented
2D12×#67C211yesmaximal, characteristic, complemented
3#10592666C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5#10591164C211yesmaximal, characteristic, complemented
6#10591160C211yesmaximal, characteristic, complemented
7C3⋊C8×#67C211yesmaximal, characteristic, complemented
8#10590595C211yesmaximal, characteristic, complemented
9D3×#809C211yesmaximal, characteristic, complemented
10#10590548C211yesmaximal, characteristic, complemented
11#10590547C211yesmaximal, characteristic, complemented
12#10590499C211yesmaximal, characteristic, complemented
13#10590498C211yesmaximal, characteristic, complemented
14#10590463C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#83525—31nomaximal
17#78757—31nomaximal
18C2×C3×#235—21no—
19C22×C3×D12C2211yescharacteristic
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic, complemented
23#64139C2211yescharacteristic
24C3×#930C2211yescharacteristic, complemented
25C3×#929—21no—
26C3×C4×#67C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic, complemented
28C3×#896—21no—
29C3×#895C2211yescharacteristic, complemented
30C3×#894—21no—
31C3×#893C2211yescharacteristic, complemented
32C3×D3×C4⋊C4C2211yescharacteristic, complemented
33C3×#888C2211yescharacteristic, complemented
34#63977—21no—
35#63922—21no—
36#63911C2211yescharacteristic
37#63908C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39#63886—21no—
40C2×#3714C2211yescharacteristic, complemented
41C2×#3713C2211yescharacteristic
42C2×#3713C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63657C2211yescharacteristic, complemented
45#63636C2211yescharacteristic, complemented
46#63636C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#809C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#547—31no—
62D4×#67—31no—
63D4×D12—31no—
64#5507D311yescharacteristic, complemented
65C2×C3×#102—31no—
66#5217—31no—
67#5115—31no—
68C8×#67—31no—
69#5088—31no—
70#5087—31no—
71#5038—31no—
72#5038—31no—
73#5036—31no—
74#5036—31no—
75#5015—31no—
76C4×#213—31no—
77D4×C3⋊C8—31no—
78#4967—31no—
79#4967—31no—
80#4967—31no—
81#4967—61no—
82C2×#809—31no—
83C2×#809D311yescharacteristic, complemented
84#4786—31no—
85#4775—31no—
86#4774—31no—
87#4773—31no—
88D3×#102—31no—
89#4760—31no—
90#4759—31no—
91#4756—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C22×C32×C4—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67D411yescharacteristic
100C3×#235—44no—
101C2×C3×D12—22no—
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6—21no—
112D3×#67—44no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#625—21no—
117C2×D3×Dic3—21no—
118D3×D12—22no—
119D3×D12—41no—
120C32×C4⋊C4—21no—
121C32×C4⋊C4C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3752—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#217D411yescharacteristic
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4D411yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4D411yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8—41no—
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142#3714—41no—
143#3713—22no—
144#3713—41no—
145D3×C3⋊C8—41no—
146#3294—91noSylow
147C2×C3×#41—61no—
148C22×C3×D4—31no—
149C22×#67—61no—
150C2×D3×D4—31no—
151C2×D3×D4—61no—
152C2×#235—21no—
153C22×D12—31no—
154C22×D12C2×D311yescharacteristic
155C22×C3×C8—31no—
156C3×C4⋊Q8—31no—
157C3×#123—61no—
158C3×#123—61no—
159C3×C22⋊Q8—61no—
160C3×#121—31no—
161C3×#121—31no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C2×C3×C4⋊C4—21no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
167C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
168#953—61no—
169#940—31no—
170#939—61no—
171#938—31no—
172#937—61no—
173D4×Dic3—31no—
174C2×#213—31no—
175C2×#213—31no—
176C2×#213—31no—
177C2×#213—31no—
178C2×#213—31no—
179#930—31no—
180#930—31no—
181#930—31no—
182#930—61no—
183#930C2×D311yescharacteristic, complemented
184#929—21no—
185C4×#67C2×D311yescharacteristic
186C22×C3⋊C8—31no—
187C22×C3⋊C8C2×D311yescharacteristic, complemented
188C2×D24—31no—
189C2×D3×C8—31no—
190#896—21no—
191#895—61no—
192#895C2×D311yescharacteristic, complemented
193#894—21no—
194#893C2×D311yescharacteristic, complemented
195D3×C4⋊C4C2×D311yescharacteristic, complemented
196#888C2×D311yescharacteristic, complemented
197#882—61no—
198#882—61no—
199#874—31no—
200C4×D12—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#830—31no—
209#830—31no—
210#830—31no—
211#830—61no—
212#821—31no—
213#821—31no—
214(C2×D3)⋊C8—31no—
215#818—31no—
216Dic3⋊C8—31no—
217C8×Dic3—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—61no—
226#809—61no—
227#809C2×D311yescharacteristic
228#809C2×D311yescharacteristic
229#809C2×D311yescharacteristic, complemented
230#809C2×D311yescharacteristic, complemented
231#807—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235#807—31no—
236#807—61no—
237#807—61no—
238C4⋊(C3⋊C8)—31no—
239C4×C3⋊C8—31no—
240C23×C32C2×D411yescharacteristic
241C22×C3⋊D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—42no—
246C22×C3×D3—42no—
247C22×C3×D3—81no—
248C22×C3×D3C2×D411yescharacteristic
249C2×D32—42no—
250C2×D32—42no—
251C2×D32—81no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—42no—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259#638—42no—
260C2×C3⋊Dic3—21no—
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)—21no—
263C3×#67—42no—
264C3×#67D814yescomplemented
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—21no—
273C3×D12—21no—
274C3×D12—42no—
275C3×D12—42no—
276C3×D12#4112yescomplemented
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×C4×D3—42no—
280C3×C4×D3—42no—
281C3×Dic6—42no—
282#626—42no—
283#626—42no—
284#626—81no—
285#625—42no—
286D3×Dic3—42no—
287C3⋊(C3⋊C8)—21no—
288C3⋊(C3⋊C8)—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291#547—31no—
292D42—91no—
293#486—91no—
294#480—91no—
295#480—91no—
296#474—91no—
297#466—91no—
298#466—91no—
299#459—91no—
300#447—91no—
301#447—91no—
302C4×D8—91no—
303C8×D4—91no—
304C2×#102—31no—
305C2×#102—91no—
306C24×C3—61no—
307C23×D3—21no—
308C23×D3—61no—
309C23×D3—61no—
310C3×#41—124no—
311C2×C3×Q8—61no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C2×C3×D4—62no—
317C2×C3×D4—61no—
318C2×C3×D4—61no—
319C2×C3×D4—61no—
320C2×C3×D4—121no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—31no—
325C22×C3×C4—41no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C2×#67—21no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—121no—
339C2×#67—124no—
340C2×#67#6711yescharacteristic
341C22×Dic3—61no—
342D3×D4—62no—
343D3×D4—121no—
344D3×D4—124no—
345#235—44no—
346C2×D12—22no—
347C2×D12—21no—
348C2×D12—21no—
349C2×D12—31no—
350C2×D12—31no—
351C2×D12—41no—
352C2×D12—61no—
353C2×D12—62no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—121no—
358C2×D12C22×D311yescharacteristic
359C2×D12C22×D311yescharacteristic
360C2×D12C22×D311yescharacteristic
361C2×C4×D3—21no—
362C2×C4×D3—21no—
363C2×C4×D3—61no—
364C2×C4×D3C22×D311yescharacteristic
365C2×Dic6—21no—
366C2×C3×C8—31no—
367C2×C3×C8—31no—
368C2×C3×C8—121no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4—21no—
372C3×C4⋊C4—21no—
373C3×C4⋊C4—31no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—41no—
376C3×C4⋊C4—61no—
377C3×C4⋊C4—61no—
378C3×C4⋊C4C22×D311yescharacteristic
379C3×C4⋊C4C22×D311yescharacteristic
380C3×C4⋊C4C22×D311yescharacteristic
381C3×C4⋊C4C22×D311yescharacteristic
382C3×C22⋊C4—31no—
383C3×C22⋊C4—31no—
384C3×C22⋊C4—61no—
385C3×C22⋊C4—61no—
386C3×C22⋊C4—61no—
387C3×C42—31no—
388#217—61no—
389#217—61no—
390#217#6711yescharacteristic
391#213—62no—
392#213—62no—
393#213—121no—
394#213—121no—
395#213—121no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—121no—
404(C2×D3)⋊C4#6711yescharacteristic
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—61no—
408C4⋊Dic3C22×D311yescharacteristic
409Dic3⋊C4—21no—
410Dic3⋊C4—21no—
411Dic3⋊C4#6711yescharacteristic
412C4×Dic3C22×D311yescharacteristic
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—41no—
418C2×C3⋊C8—61no—
419C2×C3⋊C8—61no—
420C2×C3⋊C8—121no—
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423D24—121no—
424D3×C8—121no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32C2×D812yes—
428C22×C32C22×D411yescharacteristic
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3—41no—
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×D3C2×D812yes—
445D32—84no—
446C32×C4—21no—
447C32×C4—41no—
448C32×C4—41no—
449C32×C4C2×#4111yescharacteristic
450C32×C4H(5,𝔽2)11yescharacteristic
451C3⋊Dic3—41no—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—41no—
455C3×Dic3C2×D812yes—
456C2×#41—61no—
457C22×D4—31no—
458C22×D4—91no—
459C22×D4—181no—
460C2×D8—91no—
461C2×D8—91no—
462C2×D8—91no—
463C22×C8—31no—
464C22×C8—91no—
465C4⋊Q8—31no—
466#127—91no—
467#123—61no—
468#123—61no—
469C22⋊Q8—61no—
470#121—31no—
471#121—31no—
472#121—91no—
473#121—91no—
474#121—181no—
475#120—181no—
476#120—181no—
477C4×D4—31no—
478C4×D4—31no—
479C4×D4—91no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4D3211yescharacteristic, complemented
482#107—91no—
483#107—91no—
484#107—91no—
485C4⋊C8—91no—
486#102—31no—
487#102—31no—
488#102—31no—
489#102—31no—
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—31no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—122no—
505C23×C3—122no—
506C23×C3—241no—
507C23×C3D3×D411yescharacteristic
508C23×C3C2×#6711yescharacteristic
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—42no—
513C22×D3—42no—
514C22×D3—61no—
515C22×D3—61no—
516C22×D3—81no—
517C22×D3—121no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—122no—
522C22×D3—241no—
523C22×D3—241no—
524C22×D3C2×#6711yescharacteristic
525C3×Q8—122no—
526C3×D4—34no—
527C3×D4—32no—
528C3×D4—61no—
529C3×D4—61no—
530C3×D4—61no—
531C3×D4—61no—
532C3×D4—61no—
533C3×D4—122no—
534C3×D4—122no—
535C3×D4—122no—
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—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—42no—
554C2×C3×C4—42no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—82no—
559C2×C3×C4—122no—
560C2×C3×C4—122no—
561C2×C3×C4D3×D411yescharacteristic
562C2×C3×C4C2×#6711yescharacteristic
563C2×C3×C4C23×D311yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565#67—42no—
566#67—122no—
567#67—122no—
568#67—122no—
569#67—122no—
570#67—122no—
571#67—122no—
572#67—242no—
573#67—241no—
574#67#21314yescomplemented
575C2×Dic3—21no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—121no—
579C2×Dic3—122no—
580C2×Dic3C2×#6711yescharacteristic
581C2×Dic3C2×#6711yescharacteristic
582C2×Dic3C2×#6711yescharacteristic
583D12—21no—
584D12—21no—
585D12—21no—
586D12—21no—
587D12—21no—
588D12—42no—
589D12—42no—
590D12—61no—
591D12—61no—
592D12—61no—
593D12—61no—
594D12—121no—
595D12—121no—
596D12—122no—
597D12—122no—
598D12—241no—
599D12#23512yescomplemented
600C4×D3—21no—
601C4×D3—21no—
602C4×D3—42no—
603C4×D3—42no—
604C4×D3—122no—
605Dic6—42no—
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#54611yescharacteristic
618C2×C32C22×D811yescharacteristic
619C2×C32#57711yescharacteristic
620C3⋊D3—81no—
621C3×D3—22no—
622C3×D3—42no—
623C3×D3—81no—
624C3×D3—81no—
625C24—61no—
626C24—181no—
627#41—124no—
628C2×Q8—61no—
629C2×D4—31no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—31no—
633C2×D4—62no—
634C2×D4—61no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—91no—
638C2×D4—121no—
639C2×D4—181no—
640C2×D4—181no—
641C2×D4—181no—
642C2×D4—182no—
643C2×D4—181no—
644C2×D4—181no—
645C2×D4—361no—
646C2×D4—364no—
647C22×C4—21no—
648C22×C4—31no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—181no—
652C22×C4C2×D3211yescharacteristic
653D8—182no—
654D8—361no—
655D8—361no—
656C2×C8—31no—
657C2×C8—31no—
658C2×C8—91no—
659C2×C8—91no—
660C2×C8—121no—
661C2×C8—361no—
662C4⋊C4—21no—
663C4⋊C4—31no—
664C4⋊C4—31no—
665C4⋊C4—61no—
666C4⋊C4—61no—
667C4⋊C4—91no—
668C4⋊C4C2×D3211yescharacteristic
669C4⋊C4C2×D3211yescharacteristic
670C22⋊C4—31no—
671C22⋊C4—31no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—181no—
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—61no—
689C22×C3—61no—
690C22×C3—62no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—244no—
700C22×C3D3×D812yes—
701C22×C3C2×#21312yes—
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C22×#6711yescharacteristic
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—22no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—84no—
716C2×D3—121no—
717C2×D3—121no—
718C2×D3—121no—
719C2×D3—121no—
720C2×D3—121no—
721C2×D3—121no—
722C2×D3—241no—
723C2×D3—241no—
724C2×D3—241no—
725C2×D3—244no—
726C2×D3—244no—
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—41no—
737C3×C4—41no—
738C3×C4—61no—
739C3×C4—61no—
740C3×C4—81no—
741C3×C4—81no—
742C3×C4—121no—
743C3×C4C2×#23511yescharacteristic
744C3×C4#100411yescharacteristic
745C3×C4D3×#4111yescharacteristic
746C3×C4#100911yescharacteristic
747Dic3—21no—
748Dic3—21no—
749Dic3—41no—
750Dic3—121no—
751Dic3—121no—
752Dic3—241no—
753Dic3C2×#21312yes—
754C32#329411yescharacteristic, complemented, Sylow
755C23—31no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—122no—
760C23—122no—
761C23—181no—
762C23—241no—
763C23—362no—
764C23—362no—
765C23—721no—
766C23D3×#6711yescharacteristic
767Q8—122no—
768D4—34no—
769D4—32no—
770D4—61no—
771D4—61no—
772D4—61no—
773D4—61no—
774D4—61no—
775D4—122no—
776D4—122no—
777D4—122no—
778D4—181no—
779D4—181no—
780D4—362no—
781D4—362no—
782D4—362no—
783D4—362no—
784D4—721no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—42no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—122no—
797C2×C4—122no—
798C2×C4—181no—
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—122no—
814C2×C3—241no—
815C2×C3—241no—
816C2×C3#549011yescharacteristic
817C2×C3C2×D3×D811yescharacteristic
818C2×C3#576211yescharacteristic
819C2×C3C22×#21311yescharacteristic
820C2×C3#582911yescharacteristic
821C2×C3#583711yescharacteristic
822D3—22no—
823D3—42no—
824D3—81no—
825D3—81no—
826D3—241no—
827D3—241no—
828D3—481no—
829C22—21no—
830C22—21no—
831C22—32no—
832C22—61no—
833C22—61no—
834C22—62no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—244no—
844C22—361no—
845C22—361no—
846C22—361no—
847C22—724no—
848C22D3×#21312yes—
849C22C2×D3×#6711yescharacteristic
850C4—21no—
851C4—32no—
852C4—41no—
853C4—41no—
854C4—61no—
855C4—61no—
856C4—121no—
857C4—361no—
858C4D3×#23511yescharacteristic
859C4#6430711yescharacteristic
860C3—21no—
861C3#7875711yescharacteristic, complemented
862C3#8352511yescharacteristic, complemented
863C2—22no—
864C2—62no—
865C2—122no—
866C2—241no—
867C2—241no—
868C2—721no—
869C2#1059506511yescharacteristic
870C2C2×D3×#21311yescharacteristic
871C2#1059531811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5507C2semidirect
2. D12×#67C2semidirect
3. #10592666C2semidirect
4. C2×C3×#809C2semidirect
5. #10591164C2semidirect
6. #10591160C2semidirect
7. C3⋊C8×#67C2semidirect
8. #10590595C2semidirect
9. D3×#809C2semidirect
10. #10590548C2semidirect
11. #10590547C2semidirect
12. #10590499C2semidirect
13. #10590498C2semidirect
14. #10590463C2semidirect
15. #10590452C2semidirect
22. C2×C32×C4⋊C4C22semidirect
24. C3×#930C22semidirect
27. C22×C3×C3⋊C8C22semidirect
29. C3×#895C22semidirect
31. C3×#893C22semidirect
32. C3×D3×C4⋊C4C22semidirect
33. C3×#888C22semidirect
40. C2×#3714C22semidirect
42. C2×#3713C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63657C22semidirect
45. #63636C22semidirect
46. #63636C22semidirect
47. #63634C22semidirect
48. #63634C22semidirect
51. C3×#809C22semidirect
52. C3×#809C22semidirect
53. #63575C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63564C22semidirect
56. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
64. #5507D3semidirect
83. C2×#809D3semidirect
166. C2×C3×C4⋊C4C2×D3semidirect
167. C2×C3×C4⋊C4C2×D3semidirect
183. #930C2×D3semidirect
187. C22×C3⋊C8C2×D3semidirect
192. #895C2×D3semidirect
194. #893C2×D3semidirect
195. D3×C4⋊C4C2×D3semidirect
196. #888C2×D3semidirect
229. #809C2×D3semidirect
230. #809C2×D3semidirect
264. C3×#67D8semidirect
276. C3×D12#41semidirect
481. C2×C4⋊C4D32semidirect
574. #67#213semidirect
599. D12#235semidirect
754. C32#3294semidirect
861. C3#78757semidirect
862. C3#83525semidirect

Maximal subgroups

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

subgroupindex
C3×#55072
D12×#672
#105926662
C2×C3×#8092
#105911642
#105911602
C3⋊C8×#672
#105905952
D3×#8092
#105905482
#105905472
#105904992
#105904982
#105904632
#105904522
#835253
#787573