Finite Group Databasebeta

← #11887109

Subgroups — #11887109

Order 1152.

986 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5635C211yesmaximal, characteristic, complemented
2D12×#67C211yesmaximal, characteristic
3#10592747C211yesmaximal, characteristic, complemented
4C3×#5046C211yesmaximal, characteristic, complemented
5#10591651C211yesmaximal, characteristic, complemented
6#10591634C211yesmaximal, characteristic, complemented
7#10591617C211yesmaximal, characteristic, complemented
8Dic3×#215C211yesmaximal, characteristic, complemented
9#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#10591125C211yesmaximal, characteristic, complemented
11C2×#63562C211yesmaximal, characteristic, complemented
12D3×#809C211yesmaximal, characteristic, complemented
13#10590548C211yesmaximal, characteristic, complemented
14#10590500C211yesmaximal, characteristic, complemented
15#10590465C211yesmaximal, characteristic, complemented
16#83634—31nomaximal
17#80158—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic, complemented
23#64139C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
25C3×#946C2211yescharacteristic, complemented
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic, complemented
29C3×C4×#67C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
31C3×#897—21no—
32C3×D3×C4⋊C4C2211yescharacteristic, complemented
33C3×#889—21no—
34C3×#888C2211yescharacteristic, complemented
35C3×#67⋊C4—21no—
36C3×#878—21no—
37#63977—21no—
38#63922—21no—
39#63911C2211yescharacteristic
40#63908C2211yescharacteristic
41Dic3×D12C2211yescharacteristic
42#63886—21no—
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63636C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic, complemented
50#63573C2211yescharacteristic, complemented
51#63573C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63564C2211yescharacteristic, complemented
54#63564C2211yescharacteristic, complemented
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#554—31no—
62D4×#67—31no—
63#5635D311yescharacteristic, complemented
64D4×D12—31no—
65C3×#450—31no—
66C2×#832—31no—
67#5171—31no—
68#5169—31no—
69#5163—31no—
70Dic3×SD16—31no—
71#5088—31no—
72#5084—31no—
73#5048—31no—
74#5048—31no—
75#5048—31no—
76#5048—61no—
77#5046—31no—
78#5046D311yescharacteristic, complemented
79#5027—31no—
80C4×#215—31no—
81D4×C3⋊C8—31no—
82#4968—31no—
83#4968—31no—
84C2×#809—31no—
85C2×#809—31no—
86#4777—31no—
87D3×#102—31no—
88#4761—31no—
89#4760—31no—
90#4735—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67D411yescharacteristic
99C22×C3×Dic3—21no—
100C2×C3×D12—22no—
101C2×C3×D12—21no—
102C2×C3×D12—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108D3×#67—44no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#625—21no—
113C2×D3×Dic3—21no—
114D3×D12—22no—
115D3×D12—41no—
116C32×C4⋊C4—21no—
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119#3755—41no—
120#3752—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)—41no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#217D411yescharacteristic
126C3×#215—22no—
127C3×#215—41no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4D411yescharacteristic
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144D3×C3⋊C8—41no—
145#3295—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12C2×D311yescharacteristic
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C3×C4⋊Q8—31no—
155C3×#125—61no—
156C3×C22⋊Q8—21no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—61no—
159C3×C22⋊Q8—61no—
160C3×C22⋊Q8C2×D311yescharacteristic, complemented
161C3×C22⋊Q8C2×D311yescharacteristic, complemented
162C3×C4×Q8—31no—
163C3×C4×D4—31no—
164C3×C4×D4—61no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167#953—61no—
168#946C2×D311yescharacteristic, complemented
169Q8×Dic3C2×D311yescharacteristic, complemented
170C2×#215—31no—
171C2×#215—31no—
172C2×#215—61no—
173C2×#215C2×D311yescharacteristic
174C2×#215C2×D311yescharacteristic, complemented
175#940—31no—
176#939—61no—
177#938—31no—
178#937—61no—
179D4×Dic3—31no—
180#930—31no—
181#930—31no—
182#930—31no—
183#930—61no—
184C4×#67C2×D311yescharacteristic
185C2×C4⋊Dic3C2×D311yescharacteristic, complemented
186C22×C3⋊C8—31no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8—31no—
189C22×C3⋊C8—61no—
190C2×D3×C8—31no—
191#897—21no—
192#895—61no—
193D3×C4⋊C4C2×D311yescharacteristic, complemented
194#889—21no—
195#888C2×D311yescharacteristic, complemented
196#882—61no—
197#882—61no—
198#67⋊C4—21no—
199#878—21no—
200#874—31no—
201C4×D12—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205#835—31no—
206#835—31no—
207#835—61no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#830—31no—
213#830C2×D311yescharacteristic, complemented
214#821—31no—
215#821—31no—
216(C2×D3)⋊C8—31no—
217#817—31no—
218#817—31no—
219Dic3⋊C8—31no—
220C8×Dic3—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—61no—
230#809C2×D311yescharacteristic
231#809C2×D311yescharacteristic, complemented
232#808—31no—
233#808—31no—
234#808—31no—
235#808—31no—
236#808—61no—
237C4⋊(C3⋊C8)—31no—
238C4×C3⋊C8—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—81no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C32×Q8—21no—
251C32×Q8—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2411yescharacteristic
258#638—42no—
259C2×C3⋊Dic3—21no—
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)—21no—
262C3×#67SD1614yescomplemented
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—81no—
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#4112yes—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—81no—
277C3×Dic6—81no—
278#626—42no—
279#626—42no—
280#626—81no—
281#625—42no—
282D3×Dic3—42no—
283C3⋊(C3⋊C8)—21no—
284C3⋊(C3⋊C8)—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287#554—31no—
288D42—91no—
289#486—91no—
290#481—91no—
291#481—91no—
292#476—91no—
293#465—91no—
294#465—91no—
295#460—91no—
296#450—31no—
297#450—91no—
298C4×SD16—91no—
299C8×D4—91no—
300C2×#102—91no—
301C2×#102—91no—
302C24×C3—61no—
303C23×D3—21no—
304C23×D3—61no—
305C23×D3—61no—
306C2×C3×Q8—21no—
307C2×C3×Q8—61no—
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×D4—31no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—62no—
314C2×C3×D4—61no—
315C2×C3×D4—121no—
316C22×C3×C4—21no—
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—121no—
330C2×#67—124no—
331C2×#67#6711yescharacteristic
332C22×Dic3—21no—
333C22×Dic3—61no—
334D3×D4—62no—
335D3×D4—121no—
336D3×D4—124no—
337C2×D12—22no—
338C2×D12—21no—
339C2×D12—31no—
340C2×D12—31no—
341C2×D12—41no—
342C2×D12—61no—
343C2×D12—62no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—61no—
347C2×D12—121no—
348C2×D12C22×D311yescharacteristic
349C2×D12C22×D311yescharacteristic
350C2×C4×D3—21no—
351C2×C4×D3—61no—
352C2×C4×D3C22×D311yescharacteristic
353C2×Dic6—21no—
354C3×SD16—62no—
355C3×SD16—121no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—41no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—41no—
377C3×C22⋊C4—61no—
378C3×C42—31no—
379C3×C42—61no—
380#217—61no—
381#217—61no—
382#217#6711yescharacteristic
383#215—22no—
384#215—41no—
385#215—121no—
386#215—121no—
387#215—122no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—121no—
394(C2×D3)⋊C4#6711yescharacteristic
395C4⋊Dic3—21no—
396C4⋊Dic3—21no—
397C4⋊Dic3—31no—
398C4⋊Dic3—31no—
399C4⋊Dic3—61no—
400C4⋊Dic3C22×D311yescharacteristic
401C4⋊Dic3C22×D311yescharacteristic
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405Dic3⋊C4#6711yescharacteristic
406C4×Dic3—21no—
407C4×Dic3C22×D311yescharacteristic
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—121no—
417C2×C3⋊C8—122no—
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420D3×C8—121no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32C2×SD1612yes—
424C22×C32C22×D411yescharacteristic
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—22no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—84no—
437C2×C3×D3C2×SD1612yes—
438D32—84no—
439C32×C4—21no—
440C32×C4—41no—
441C32×C4—41no—
442C32×C4C2×#4111yescharacteristic
443C32×C4H(5,𝔽2)11yescharacteristic
444C3⋊Dic3—41no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3C2×SD1612yes—
450C22×D4—31no—
451C22×D4—91no—
452C22×D4—181no—
453C2×SD16—31no—
454C2×SD16—31no—
455C2×SD16—91no—
456C22×C8—91no—
457C22×C8—91no—
458C4⋊Q8—31no—
459#127—91no—
460#125—61no—
461C22⋊Q8—31no—
462C22⋊Q8—61no—
463C22⋊Q8—61no—
464C22⋊Q8D3211yescharacteristic, complemented
465#121—91no—
466#121—91no—
467#121—181no—
468#120—181no—
469#120—181no—
470C4×Q8—31no—
471C4×D4—31no—
472C4×D4—61no—
473C4×D4—91no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—31no—
476#106—91no—
477#106—91no—
478#106—91no—
479C4⋊C8—91no—
480#103—91no—
481#102—31no—
482#102—31no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490C22⋊C8—31no—
491C22⋊C8—91no—
492C4×C8—91no—
493C23×C3—21no—
494C23×C3—31no—
495C23×C3—61no—
496C23×C3—61no—
497C23×C3—122no—
498C23×C3—122no—
499C23×C3—241no—
500C23×C3D3×D411yescharacteristic
501C23×C3C2×#6711yescharacteristic
502C22×D3—21no—
503C22×D3—21no—
504C22×D3—42no—
505C22×D3—42no—
506C22×D3—61no—
507C22×D3—61no—
508C22×D3—81no—
509C22×D3—121no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—241no—
515C22×D3—241no—
516C22×D3C2×#6711yescharacteristic
517C3×Q8—21no—
518C3×Q8—21no—
519C3×Q8—21no—
520C3×Q8—21no—
521C3×Q8—41no—
522C3×Q8—41no—
523C3×Q8—241no—
524C3×D4—34no—
525C3×D4—32no—
526C3×D4—61no—
527C3×D4—61no—
528C3×D4—61no—
529C3×D4—122no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
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—31no—
541C2×C3×C4—31no—
542C2×C3×C4—31no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—241no—
552C2×C3×C4—241no—
553C2×C3×C4D3×D411yescharacteristic
554C2×C3×C4C2×#6711yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556C2×C3×C4C23×D311yescharacteristic
557#67—122no—
558#67—122no—
559#67—122no—
560#67—122no—
561#67—122no—
562#67—122no—
563#67—242no—
564#67—241no—
565#67#21514yescomplemented
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—81no—
571C2×Dic3—121no—
572C2×Dic3—122no—
573C2×Dic3C2×#6711yescharacteristic
574C2×Dic3C2×#6711yescharacteristic
575C2×Dic3C2×#6711yescharacteristic
576D12—21no—
577D12—21no—
578D12—21no—
579D12—42no—
580D12—61no—
581D12—61no—
582D12—61no—
583D12—61no—
584D12—121no—
585D12—121no—
586D12—122no—
587D12—122no—
588D12—241no—
589D12#23712yes—
590C4×D3—21no—
591C4×D3—21no—
592C4×D3—81no—
593C4×D3—122no—
594Dic6—81no—
595C3×C8—61no—
596C3×C8—61no—
597C3⋊C8—21no—
598C3⋊C8—21no—
599C3⋊C8—62no—
600C3⋊C8—61no—
601C3⋊C8—61no—
602C3⋊C8—61no—
603C3⋊C8—61no—
604C3⋊C8—121no—
605C2×C32—22no—
606C2×C32#54611yescharacteristic
607C2×C32C22×SD1611yescharacteristic
608C2×C32#57611yescharacteristic
609C3⋊D3—81no—
610C3×D3—22no—
611C3×D3—42no—
612C3×D3—81no—
613C24—61no—
614C24—181no—
615C2×Q8—61no—
616C2×Q8C2×D3211yescharacteristic
617C2×D4—31no—
618C2×D4—31no—
619C2×D4—31no—
620C2×D4—62no—
621C2×D4—61no—
622C2×D4—91no—
623C2×D4—121no—
624C2×D4—181no—
625C2×D4—181no—
626C2×D4—181no—
627C2×D4—182no—
628C2×D4—181no—
629C2×D4—181no—
630C2×D4—361no—
631C2×D4—364no—
632C22×C4—31no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—181no—
636C22×C4C2×D3211yescharacteristic
637SD16—62no—
638SD16—121no—
639SD16—361no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—91no—
643C2×C8—91no—
644C2×C8—361no—
645C2×C8—361no—
646C4⋊C4—21no—
647C4⋊C4—31no—
648C4⋊C4—31no—
649C4⋊C4—31no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—61no—
653C4⋊C4—61no—
654C4⋊C4—61no—
655C4⋊C4—91no—
656C4⋊C4C2×D3211yescharacteristic
657C22⋊C4—21no—
658C22⋊C4—31no—
659C22⋊C4—31no—
660C22⋊C4—61no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C42—31no—
665C42—61no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—22no—
672C22×C3—32no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—62no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—244no—
684C22×C3D3×SD1612yes—
685C22×C3C2×#21512yes—
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—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—241no—
704C2×D3—241no—
705C2×D3—241no—
706C2×D3—244no—
707C2×D3—244no—
708C2×D3C2×#21512yes—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—32no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—61no—
720C3×C4—61no—
721C3×C4—81no—
722C3×C4—81no—
723C3×C4—121no—
724C3×C4—121no—
725C3×C4C2×#23711yescharacteristic
726C3×C4#100411yescharacteristic
727C3×C4D3×#4111yescharacteristic
728C3×C4#100911yescharacteristic
729Dic3—21no—
730Dic3—21no—
731Dic3—41no—
732Dic3—41no—
733Dic3—121no—
734Dic3—121no—
735Dic3—241no—
736Dic3C2×#21512yes—
737C32#329511yescharacteristic, complemented, Sylow
738C23—31no—
739C23—61no—
740C23—61no—
741C23—122no—
742C23—122no—
743C23—181no—
744C23—241no—
745C23—362no—
746C23—362no—
747C23—721no—
748C23D3×#6711yescharacteristic
749Q8—21no—
750Q8—21no—
751Q8—241no—
752D4—34no—
753D4—32no—
754D4—61no—
755D4—61no—
756D4—61no—
757D4—122no—
758D4—181no—
759D4—181no—
760D4—362no—
761D4—362no—
762D4—362no—
763D4—362no—
764D4—721no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—31no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—181no—
777C2×C4—241no—
778C2×C4—241no—
779C2×C4—362no—
780C2×C4D3×#6711yescharacteristic
781C2×C4C22×D3211yescharacteristic
782C8—61no—
783C8—61no—
784C8—181no—
785C8—181no—
786C2×C3—22no—
787C2×C3—22no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—42no—
792C2×C3—62no—
793C2×C3—122no—
794C2×C3—241no—
795C2×C3#559111yescharacteristic
796C2×C3C2×D3×SD1611yescharacteristic
797C2×C3#577411yescharacteristic
798C2×C3C22×#21511yescharacteristic
799C2×C3#582911yescharacteristic
800C2×C3#583511yescharacteristic
801D3—22no—
802D3—42no—
803D3—81no—
804D3—241no—
805D3—241no—
806D3—481no—
807C22—21no—
808C22—21no—
809C22—32no—
810C22—61no—
811C22—61no—
812C22—62no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—244no—
819C22—361no—
820C22—361no—
821C22—361no—
822C22—724no—
823C22D3×#21512yes—
824C22C2×D3×#6711yescharacteristic
825C4—21no—
826C4—32no—
827C4—41no—
828C4—41no—
829C4—61no—
830C4—61no—
831C4—121no—
832C4—121no—
833C4—361no—
834C4D3×#23711yescharacteristic
835C4#6431411yescharacteristic
836C3—21no—
837C3#8015811yescharacteristic, complemented
838C3#8363411yescharacteristic, complemented
839C2—22no—
840C2—62no—
841C2—122no—
842C2—241no—
843C2—721no—
844C2#1059530411yescharacteristic
845C2C2×D3×#21511yescharacteristic
846C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalD12×#67C2
hypercenterC22⋊Q8D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5635C2semidirect
3. #10592747C2semidirect
4. C3×#5046C2semidirect
5. #10591651C2semidirect
6. #10591634C2semidirect
7. #10591617C2semidirect
8. Dic3×#215C2semidirect
9. #67⋊(C3⋊C8)C2semidirect
10. #10591125C2semidirect
11. C2×#63562C2semidirect
12. D3×#809C2semidirect
13. #10590548C2semidirect
14. #10590500C2semidirect
15. #10590465C2semidirect
21. C32×C22⋊Q8C22semidirect
22. C2×#3755C22semidirect
24. C22×C3⋊(C3⋊C8)C22semidirect
25. C3×#946C22semidirect
26. C3×Q8×Dic3C22semidirect
28. C2×C3×#215C22semidirect
30. C2×C3×C4⋊Dic3C22semidirect
32. C3×D3×C4⋊C4C22semidirect
34. C3×#888C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63662C22semidirect
45. #63636C22semidirect
46. #63635C22semidirect
47. C3×#830C22semidirect
49. C3×#809C22semidirect
50. #63573C22semidirect
51. #63573C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63564C22semidirect
54. #63564C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
63. #5635D3semidirect
78. #5046D3semidirect
160. C3×C22⋊Q8C2×D3semidirect
161. C3×C22⋊Q8C2×D3semidirect
168. #946C2×D3semidirect
169. Q8×Dic3C2×D3semidirect
174. C2×#215C2×D3semidirect
185. C2×C4⋊Dic3C2×D3semidirect
193. D3×C4⋊C4C2×D3semidirect
195. #888C2×D3semidirect
213. #830C2×D3semidirect
231. #809C2×D3semidirect
262. C3×#67SD16semidirect
464. C22⋊Q8D32semidirect
565. #67#215semidirect
737. C32#3295semidirect
837. C3#80158semidirect
838. C3#83634semidirect

Maximal subgroups

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

subgroupindex
C3×#56352
D12×#672
#105927472
C3×#50462
#105916512
#105916342
#105916172
Dic3×#2152
#67⋊(C3⋊C8)2
#105911252
C2×#635622
D3×#8092
#105905482
#105905002
#105904652
#836343
#801583