Finite Group Databasebeta

← #11887107

Subgroups — #11887107

Order 1152.

1018 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5635C211yesmaximal, characteristic, complemented
2#10595074C211yesmaximal, characteristic
3#10592745C211yesmaximal, characteristic, complemented
4C3×#5048C211yesmaximal, characteristic, complemented
5#10591651C211yesmaximal, characteristic, complemented
6#10591617C211yesmaximal, characteristic, complemented
7#10591585C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9C3⋊C8×#67C211yesmaximal, characteristic, complemented
10C2×#63564C211yesmaximal, characteristic, complemented
11#10591091C211yesmaximal, characteristic, complemented
12D3×#809C211yesmaximal, characteristic, complemented
13#10590548C211yesmaximal, characteristic, complemented
14#10590466C211yesmaximal, characteristic, complemented
15#10590423C211yesmaximal, characteristic, complemented
16#83634—31nomaximal
17#80680—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3811—21no—
20C2×D3×D12C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic
23C2×#3755C2211yescharacteristic, complemented
24C3×#946C2211yescharacteristic, complemented
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic, complemented
27C3×#930C2211yescharacteristic
28C3×C4×#67C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
30C22×C3×C3⋊C8C2211yescharacteristic, complemented
31C3×#897—21no—
32C3×D3×C4⋊C4C2211yescharacteristic, complemented
33C3×#889—21no—
34C3×#888C2211yescharacteristic, complemented
35C3×#67⋊C4—21no—
36C3×#878—21no—
37#63981—21no—
38#63923—21no—
39#63911C2211yescharacteristic
40#63910—21no—
41#63909C2211yescharacteristic
42#63894C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63657C2211yescharacteristic, complemented
45#63636C2211yescharacteristic
46#63636C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50#63574C2211yescharacteristic, complemented
51#63574C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63564C2211yescharacteristic
54#63564C2211yescharacteristic
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#554—31no—
62#5635D311yescharacteristic, complemented
63#5609—31no—
64D4×D12—31no—
65C3×#465—31no—
66#5169—31no—
67#5163—31no—
68C2×#821—31no—
69C8×#67—31no—
70#5088—31no—
71#5084—31no—
72#5048—31no—
73#5048D311yescharacteristic, complemented
74#5046—31no—
75#5046—31no—
76#5046—31no—
77#5046—61no—
78#5034—31no—
79#5027—31no—
80C4×#215—31no—
81D4×C3⋊C8—31no—
82#4968—31no—
83#4968—31no—
84C2×#809—31no—
85C2×#809—31no—
86#4870—31no—
87#4863—31no—
88#4807—31no—
89#4788—31no—
90D3×#102—31no—
91#4760—31no—
92C23×C3⋊D3—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)—41no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108#3811—44no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#624—21no—
114D3×D12—22no—
115D3×D12—41no—
116C32×C4⋊C4—21no—
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119#3755—22no—
120#3755—41no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#217D411yescharacteristic
124C3×#215—41no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4D411yescharacteristic
137C3×C4×Dic3—21no—
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8—41no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142#3722—21no—
143#3722—21no—
144D3×C3⋊C8—41no—
145#3295—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—61no—
148C2×D3×D4—61no—
149C22×D12—31no—
150C22×D12—31no—
151C22×D12—31no—
152C22×D12—61no—
153C2×C3×SD16—31no—
154C22×C3×C8—31no—
155C3×C4⋊Q8—31no—
156C3×#125—61no—
157C3×C22⋊Q8—21no—
158C3×C22⋊Q8—31no—
159C3×C22⋊Q8—61no—
160C3×C22⋊Q8—61no—
161C3×C22⋊Q8C2×D311yescharacteristic, complemented
162C3×C22⋊Q8C2×D311yescharacteristic, complemented
163C3×#121—31no—
164C3×C4×Q8—31no—
165C3×C4×D4—31no—
166C3×C4×D4—61no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—31no—
169#946C2×D311yescharacteristic, complemented
170Q8×Dic3C2×D311yescharacteristic, complemented
171C2×#215—31no—
172C2×#215—31no—
173C2×#215—31no—
174C2×#215—31no—
175C2×#215—61no—
176C2×#215—61no—
177C2×#215C2×D311yescharacteristic, complemented
178#940—31no—
179#937—61no—
180#930—31no—
181#930C2×D311yescharacteristic
182C4×#67C2×D311yescharacteristic
183C2×C4⋊Dic3C2×D311yescharacteristic, complemented
184C22×C3⋊C8—31no—
185C22×C3⋊C8C2×D311yescharacteristic, complemented
186C2×D3×C8—31no—
187#897—21no—
188#895—31no—
189#895—61no—
190#893—31no—
191D3×C4⋊C4C2×D311yescharacteristic, complemented
192#889—21no—
193#888C2×D311yescharacteristic, complemented
194#884—61no—
195#882—61no—
196#882—61no—
197#882—61no—
198#67⋊C4—21no—
199#878—21no—
200#874—31no—
201C4×D12—31no—
202C3×#106—31no—
203C3×#103—31no—
204C3×#102—31no—
205#835C2×D311yescharacteristic, complemented
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#821—31no—
215#821—31no—
216(C2×D3)⋊C8—31no—
217Dic3⋊C8—31no—
218C8×Dic3—31no—
219#809—31no—
220#809—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#809—61no—
231#809C2×D311yescharacteristic, complemented
232#808—31no—
233#808—31no—
234#808—31no—
235#808—31no—
236#808C2×D311yescharacteristic, complemented
237C4⋊(C3⋊C8)—31no—
238C4×C3⋊C8—31no—
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×D3—21no—
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
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)—42no—
262C4⋊(C3⋊D3)#4112yes—
263C3×#67—42no—
264C3×#67SD1614yescomplemented
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—81no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—81no—
277C3×Dic6—81no—
278#626—42no—
279#626—42no—
280#626—42no—
281#626—81no—
282#624—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—31no—
294#465—91no—
295#460—91no—
296#450—91no—
297#450—91no—
298C4×SD16—91no—
299C8×D4—91no—
300C2×#102—91no—
301C2×#102—91no—
302C23×D3—61no—
303C23×D3—61no—
304C23×D3—61no—
305C23×D3—61no—
306C23×D3—121no—
307C2×C3×Q8—21no—
308C2×C3×Q8—61no—
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—61no—
314C22×C3×C4—21no—
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C2×#67—21no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67#6711yescharacteristic
326C22×Dic3—21no—
327D3×D4—62no—
328D3×D4—121no—
329D3×D4—124no—
330D3×D4—124no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—31no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—62no—
338C2×D12—62no—
339C2×D12—62no—
340C2×D12—61no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12—61no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—122no—
347C2×D12—121no—
348C2×D12—121no—
349C2×D12—121no—
350C2×D12—121no—
351C2×D12—122no—
352C2×D12C22×D311yescharacteristic
353C2×C4×D3—21no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3C22×D311yescharacteristic
357C2×Dic6—21no—
358C3×SD16—121no—
359C2×C3×C8—31no—
360C2×C3×C8—31no—
361C2×C3×C8—121no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—41no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4C22×D311yescharacteristic
376C3×C4⋊C4C22×D311yescharacteristic
377C3×C22⋊C4—21no—
378C3×C22⋊C4—21no—
379C3×C22⋊C4—31no—
380C3×C22⋊C4—31no—
381C3×C22⋊C4—41no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C42—31no—
385C3×C42—61no—
386#217#6711yescharacteristic
387#215—41no—
388#215—62no—
389#215—62no—
390#215—122no—
391#215—121no—
392#215—121no—
393#215—122no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4#6711yescharacteristic
401C4⋊Dic3—21no—
402C4⋊Dic3—21no—
403C4⋊Dic3C22×D311yescharacteristic
404C4⋊Dic3C22×D311yescharacteristic
405C4⋊Dic3C22×D311yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—21no—
408Dic3⋊C4—21no—
409Dic3⋊C4#6711yescharacteristic
410C4×Dic3—21no—
411C4×Dic3C22×D311yescharacteristic
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—41no—
417C2×C3⋊C8—61no—
418C2×C3⋊C8—61no—
419C2×C3⋊C8—121no—
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422D3×C8—121no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32C2×SD1612yes—
426C22×C32C22×D411yescharacteristic
427C2×C3⋊D3—22no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3—41no—
432C2×C3⋊D3—41no—
433C2×C3⋊D3—84no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3C2×SD1612yes—
440D32—84no—
441C32×C4—21no—
442C32×C4—41no—
443C32×C4—41no—
444C32×C4C2×#4111yescharacteristic
445C32×C4H(5,𝔽2)11yescharacteristic
446C3×Dic3—21no—
447C3×Dic3—21no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C3×Dic3C2×SD1612yes—
452C22×D4—91no—
453C22×D4—91no—
454C22×D4—181no—
455C2×SD16—31no—
456C2×SD16—91no—
457C2×SD16—91no—
458C22×C8—31no—
459C22×C8—91no—
460C4⋊Q8—31no—
461#127—91no—
462#125—61no—
463C22⋊Q8—31no—
464C22⋊Q8—61no—
465C22⋊Q8—61no—
466C22⋊Q8D3211yescharacteristic, complemented
467#121—31no—
468#121—91no—
469#121—181no—
470#120—181no—
471#120—181no—
472C4×Q8—31no—
473C4×D4—31no—
474C4×D4—61no—
475C4×D4—91no—
476C2×C4⋊C4—31no—
477C2×C4⋊C4—31no—
478#106—31no—
479#106—91no—
480#106—91no—
481C4⋊C8—91no—
482#103—31no—
483#102—31no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490#102—91no—
491#102—91no—
492C22⋊C8—91no—
493C22⋊C8—91no—
494C4×C8—91no—
495C23×C3—21no—
496C23×C3—31no—
497C23×C3—61no—
498C23×C3D3×D411yescharacteristic
499C23×C3C2×#6711yescharacteristic
500C22×D3—21no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—121no—
506C22×D3—121no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—124no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—122no—
516C22×D3—242no—
517C22×D3—241no—
518C22×D3—241no—
519C22×D3—241no—
520C22×D3—241no—
521C22×D3—242no—
522C22×D3C2×#6711yescharacteristic
523C3×Q8—21no—
524C3×Q8—21no—
525C3×Q8—21no—
526C3×Q8—21no—
527C3×Q8—41no—
528C3×Q8—41no—
529C3×Q8—241no—
530C3×D4—34no—
531C3×D4—61no—
532C3×D4—61no—
533C3×D4—122no—
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—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—31no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—241no—
557C2×C3×C4—241no—
558C2×C3×C4D3×D411yescharacteristic
559C2×C3×C4C2×#6711yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562#67—42no—
563#67—122no—
564#67—122no—
565#67—122no—
566#67—241no—
567#67#21514yescomplemented
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—81no—
572C2×Dic3C2×#6711yescharacteristic
573C2×Dic3C2×#6711yescharacteristic
574C2×Dic3C2×#6711yescharacteristic
575D12—21no—
576D12—21no—
577D12—32no—
578D12—32no—
579D12—62no—
580D12—62no—
581D12—61no—
582D12—61no—
583D12—61no—
584D12—61no—
585D12—61no—
586D12—61no—
587D12—121no—
588D12—121no—
589D12—122no—
590D12—122no—
591D12—122no—
592D12—124no—
593D12—122no—
594D12—122no—
595D12—241no—
596C4×D3—21no—
597C4×D3—21no—
598C4×D3—81no—
599C4×D3—122no—
600C4×D3—122no—
601Dic6—81no—
602C3×C8—61no—
603C3×C8—61no—
604C3⋊C8—21no—
605C3⋊C8—21no—
606C3⋊C8—61no—
607C3⋊C8—61no—
608C3⋊C8—61no—
609C3⋊C8—61no—
610C3⋊C8—121no—
611C3⋊C8—121no—
612C2×C32—22no—
613C2×C32#54611yescharacteristic
614C2×C32C22×SD1611yescharacteristic
615C2×C32#57611yescharacteristic
616C3⋊D3—42no—
617C3⋊D3—81no—
618C3×D3—22no—
619C3×D3—81no—
620C24—181no—
621C24—181no—
622C2×Q8—61no—
623C2×Q8C2×D3211yescharacteristic
624C2×D4—31no—
625C2×D4—31no—
626C2×D4—61no—
627C2×D4—91no—
628C2×D4—91no—
629C2×D4—182no—
630C2×D4—181no—
631C2×D4—181no—
632C2×D4—181no—
633C2×D4—182no—
634C2×D4—181no—
635C2×D4—181no—
636C2×D4—361no—
637C2×D4—361no—
638C2×D4—364no—
639C22×C4—31no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—181no—
643C22×C4C2×D3211yescharacteristic
644SD16—121no—
645SD16—182no—
646SD16—361no—
647C2×C8—31no—
648C2×C8—31no—
649C2×C8—91no—
650C2×C8—91no—
651C2×C8—121no—
652C2×C8—361no—
653C4⋊C4—21no—
654C4⋊C4—31no—
655C4⋊C4—31no—
656C4⋊C4—31no—
657C4⋊C4—31no—
658C4⋊C4—61no—
659C4⋊C4—61no—
660C4⋊C4—61no—
661C4⋊C4—61no—
662C4⋊C4—61no—
663C4⋊C4C2×D3211yescharacteristic
664C22⋊C4—21no—
665C22⋊C4—31no—
666C22⋊C4—31no—
667C22⋊C4—61no—
668C22⋊C4—61no—
669C22⋊C4—181no—
670C22⋊C4—181no—
671C42—31no—
672C42—61no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—22no—
679C22×C3—32no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3D3×SD1612yes—
688C22×C3C2×#21512yes—
689C22×C3C2×D3×D411yescharacteristic
690C22×C3C22×#6711yescharacteristic
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—62no—
697C2×D3—62no—
698C2×D3—122no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—122no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—241no—
711C2×D3—241no—
712C2×D3—241no—
713C2×D3—241no—
714C2×D3—244no—
715C2×D3—244no—
716C2×D3—244no—
717C2×D3—244no—
718C2×D3—248no—
719C2×D3C2×#21512yes—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—32no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—61no—
731C3×C4—61no—
732C3×C4—81no—
733C3×C4—81no—
734C3×C4—121no—
735C3×C4—121no—
736C3×C4—121no—
737C3×C4#100411yescharacteristic
738C3×C4D3×#4111yescharacteristic
739C3×C4D3×#4111yescharacteristic
740C3×C4#100911yescharacteristic
741Dic3—21no—
742Dic3—21no—
743Dic3—41no—
744Dic3—41no—
745Dic3—41no—
746Dic3C2×#21512yes—
747C32#329511yescharacteristic, complemented, Sylow
748C23—31no—
749C23—61no—
750C23—181no—
751C23—181no—
752C23—362no—
753C23—362no—
754C23—362no—
755C23—362no—
756C23—721no—
757C23—721no—
758C23D3×#6711yescharacteristic
759Q8—21no—
760Q8—21no—
761Q8—241no—
762D4—34no—
763D4—61no—
764D4—61no—
765D4—92no—
766D4—122no—
767D4—181no—
768D4—181no—
769D4—181no—
770D4—362no—
771D4—362no—
772D4—362no—
773D4—362no—
774D4—721no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—31no—
780C2×C4—31no—
781C2×C4—31no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—241no—
788C2×C4—241no—
789C2×C4—362no—
790C2×C4D3×#6711yescharacteristic
791C2×C4C22×D3211yescharacteristic
792C8—61no—
793C8—61no—
794C8—181no—
795C8—181no—
796C2×C3—22no—
797C2×C3—22no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—42no—
802C2×C3—62no—
803C2×C3—241no—
804C2×C3#561011yescharacteristic
805C2×C3C2×D3×SD1611yescharacteristic
806C2×C3#576911yescharacteristic
807C2×C3C22×#21511yescharacteristic
808C2×C3#582911yescharacteristic
809C2×C3#583511yescharacteristic
810D3—22no—
811D3—81no—
812D3—122no—
813D3—122no—
814D3—242no—
815D3—242no—
816D3—241no—
817D3—241no—
818C22—21no—
819C22—21no—
820C22—32no—
821C22—61no—
822C22—61no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22—182no—
827C22—361no—
828C22—361no—
829C22—361no—
830C22—361no—
831C22—361no—
832C22—724no—
833C22—724no—
834C22D3×#21512yes—
835C22C2×D3×#6711yescharacteristic
836C4—21no—
837C4—32no—
838C4—41no—
839C4—41no—
840C4—61no—
841C4—61no—
842C4—121no—
843C4—121no—
844C4—121no—
845C4#6431211yescharacteristic
846C4#6431411yescharacteristic
847C3—21no—
848C3#8068011yescharacteristic, complemented
849C3#8363411yescharacteristic, complemented
850C2—22no—
851C2—62no—
852C2—241no—
853C2—362no—
854C2—721no—
855C2#1059530511yescharacteristic
856C2C2×D3×#21511yescharacteristic
857C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10595074C2
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. #10592745C2semidirect
4. C3×#5048C2semidirect
5. #10591651C2semidirect
6. #10591617C2semidirect
7. #10591585C2semidirect
8. #10591536C2semidirect
9. C3⋊C8×#67C2semidirect
10. C2×#63564C2semidirect
11. #10591091C2semidirect
12. D3×#809C2semidirect
13. #10590548C2semidirect
14. #10590466C2semidirect
15. #10590423C2semidirect
21. C32×C22⋊Q8C22semidirect
23. C2×#3755C22semidirect
24. C3×#946C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C2×C3×#215C22semidirect
29. C2×C3×C4⋊Dic3C22semidirect
30. C22×C3×C3⋊C8C22semidirect
32. C3×D3×C4⋊C4C22semidirect
34. C3×#888C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63657C22semidirect
46. #63636C22semidirect
47. C3×#835C22semidirect
48. C3×#809C22semidirect
49. C3×#808C22semidirect
50. #63574C22semidirect
51. #63574C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5635D3semidirect
73. #5048D3semidirect
161. C3×C22⋊Q8C2×D3semidirect
162. C3×C22⋊Q8C2×D3semidirect
169. #946C2×D3semidirect
170. Q8×Dic3C2×D3semidirect
177. C2×#215C2×D3semidirect
183. C2×C4⋊Dic3C2×D3semidirect
185. C22×C3⋊C8C2×D3semidirect
191. D3×C4⋊C4C2×D3semidirect
193. #888C2×D3semidirect
205. #835C2×D3semidirect
231. #809C2×D3semidirect
236. #808C2×D3semidirect
264. C3×#67SD16semidirect
466. C22⋊Q8D32semidirect
567. #67#215semidirect
747. C32#3295semidirect
848. C3#80680semidirect
849. C3#83634semidirect

Maximal subgroups

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

subgroupindex
C3×#56352
#105950742
#105927452
C3×#50482
#105916512
#105916172
#105915852
#105915362
C3⋊C8×#672
C2×#635642
#105910912
D3×#8092
#105905482
#105904662
#105904232
#836343
#806803