Finite Group Databasebeta

← #11860689

Subgroups — #11860689

Order 1152.

1122 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5545C211yesmaximal, characteristic, complemented
2C2×D3×#213C211yesmaximal, characteristic
3#10593994C211yesmaximal, characteristic, complemented
4#10592713C211yesmaximal, characteristic, complemented
5C3×C4×#213C211yesmaximal, characteristic, complemented
6Dic3×#213C211yesmaximal, characteristic, complemented
7#10591421C211yesmaximal, characteristic, complemented
8#10591404C211yesmaximal, characteristic, complemented
9#10590592C211yesmaximal, characteristic, complemented
10#10590571C211yesmaximal, characteristic, complemented
11#10590456C211yesmaximal, characteristic, complemented
12#10590455C211yesmaximal, characteristic, complemented
13C4×#3714C211yesmaximal, characteristic, complemented
14#10590344C211yesmaximal, characteristic, complemented
15#10590318C211yesmaximal, characteristic, complemented
16#82538—31nomaximal
17#79588—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic, complemented
21C2×#3753C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic, complemented
24C2×C3×#213C2211yescharacteristic
25C3×C4×#67—21no—
26C2×C3×(C2×D3)⋊C4—21no—
27C3×#893C2211yescharacteristic, complemented
28C3×#892C2211yescharacteristic
29C3×#67⋊C4—21no—
30C3×D3×C22⋊C4—21no—
31C3×C4×D12C2211yescharacteristic, complemented
32C3×C4×D12C2211yescharacteristic, complemented
33C3×#872C2211yescharacteristic
34D3×#213C418yescomplemented
35#63921—21no—
36D3×(C2×D3)⋊C4—21no—
37#63904—21no—
38#63894C2211yescharacteristic, complemented
39Dic3×D12C2211yescharacteristic, complemented
40#63881—21no—
41#63841C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C2×#3713C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63659C2211yescharacteristic, complemented
47#63636C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49#63630C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53C3×C4×C3⋊C8C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C3×#518—31no—
63C22×#213—31no—
64C2×D3×D8—31no—
65#5545—31no—
66#5545D311yescharacteristic, complemented
67#5521—31no—
68C3×C4×D8—31no—
69#5215—31no—
70Dic3×D8—31no—
71#5014—31no—
72#5014—31no—
73#5014—31no—
74#5014—31no—
75#5014—31no—
76#5014—31no—
77#5014—61no—
78C4×#213—31no—
79C4×#213—31no—
80C4×#213—31no—
81C4×#213D311yescharacteristic, complemented
82#5001—31no—
83#4998—31no—
84#4997—31no—
85#4880—31no—
86#4872—31no—
87#4785—31no—
88#4785—31no—
89#4770—31no—
90#4770—31no—
91C4×D24—31no—
92#4689—31no—
93C23×C3×D3—21no—
94C22×D32—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×D3×D4—22no—
102C3×D3×D4C2×C414yescomplemented
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×#626—21no—
110C2×#624—21no—
111C2×D3×Dic3—21no—
112D3×D12—22no—
113D3×D12C2×C414yescomplemented
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C42C2311yescharacteristic
117#3753C2×C414yescomplemented
118#3752—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—21no—
123C3×#213C2×C414yescomplemented
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3714C2×C414yescomplemented
143#3713C2×C414yescomplemented
144#3711—22no—
145D3×C3⋊C8C2×C414yescomplemented
146#2948—91noSylow
147C22×C3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4C2×D311yescharacteristic
150C22×D12—31no—
151C2×C3×D8—31no—
152C3×C4×D4—21no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157C3×C4×D4—61no—
158C3×C4×D4—61no—
159C3×C4×D4C2×D311yescharacteristic, complemented
160C3×C4×D4C2×D311yescharacteristic, complemented
161C3×#117—31no—
162C3×#117—31no—
163C2×C3×C22⋊C4—61no—
164C2×C3×C22⋊C4—61no—
165D4×Dic3—31no—
166D4×Dic3C2×D311yescharacteristic, complemented
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—38no—
172C2×#213—31no—
173C2×#213—61no—
174C2×#213C2×D311yescharacteristic
175C4×#67—21no—
176C4×#67—61no—
177C2×(C2×D3)⋊C4—21no—
178C2×(C2×D3)⋊C4—61no—
179#926—31no—
180C2×#208—31no—
181C22×C3⋊C8—31no—
182D3×D8—38no—
183C2×D24—31no—
184C2×ΓL(1,𝔽25)—31no—
185C2×D3×C8—31no—
186#893—31no—
187#893—61no—
188#893—61no—
189#893C2×D311yescharacteristic, complemented
190#892—31no—
191#892C2×D311yescharacteristic
192#67⋊C4—21no—
193#67⋊C4—61no—
194D3×C22⋊C4—21no—
195D3×C22⋊C4—61no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198C4×D12—31no—
199C4×D12—31no—
200C4×D12—31no—
201C4×D12—31no—
202C4×D12—61no—
203C4×D12C2×D311yescharacteristic, complemented
204C4×D12C2×D311yescharacteristic, complemented
205#872C2×D311yescharacteristic
206C3×#107—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×C4×C8—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—61no—
216#832C2×D311yescharacteristic, complemented
217#821—31no—
218#821—31no—
219#818—31no—
220#815—31no—
221C8×Dic3—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—61no—
228#809C2×D311yescharacteristic, complemented
229#808—31no—
230#808—31no—
231#808—31no—
232#808—31no—
233#808—61no—
234#807—31no—
235#807C2×D311yescharacteristic, complemented
236#803—31no—
237#803—31no—
238#803—31no—
239#803—61no—
240C4×C3⋊C8—31no—
241C4×C3⋊C8C2×D311yescharacteristic, complemented
242C23×C32—21no—
243C22×C3⋊D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—24no—
247C22×C3×D3—81no—
248C22×C3×D3—81no—
249C22×C3×D3C2×D411yescharacteristic
250C2×D32—24no—
251C2×D32—81no—
252C2×D32—81no—
253C32×D4—21no—
254C32×D4C22×C412yes—
255C2×C32×C4—21no—
256C2×C32×C4—81no—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2411yescharacteristic
260C2×C3⋊Dic3—21no—
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)C22×C412yes—
263C4×C3⋊D3—81no—
264C3×#67—24no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—81no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C3×D12—21no—
272C3×D12—21no—
273C3×D12C22×C412yes—
274C3×D12C22×C412yes—
275C3×C4×D3—81no—
276C3×C4×D3—81no—
277C3×C4×D3—81no—
278C3×C4×D3C22×C412yes—
279C3×C4×D3#4112yes—
280#626—24no—
281#624—81no—
282D3×Dic3—81no—
283C3⋊(C3⋊C8)—21no—
284C3⋊(C3⋊C8)C22×C412yes—
285C3×C3⋊C8—21no—
286C3×C3⋊C8C22×C412yes—
287C22×D8—91no—
288#518—31no—
289#518—91no—
290#442—91no—
291#442—91no—
292#442—91no—
293#442—91no—
294C4×D8—31no—
295C4×D8—91no—
296C4×D8—91no—
297C4×D8—91no—
298#427—91no—
299#418—91no—
300#418—91no—
301#405—91no—
302C24×C3—61no—
303C23×D3—21no—
304C23×D3—61no—
305C23×D3—61no—
306C2×C3×D4—21no—
307C2×C3×D4—34no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—62no—
311C2×C3×D4—61no—
312C2×C3×D4C22×D311yescharacteristic
313C2×C3×D4C22×D311yescharacteristic
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—31no—
317C22×C3×C4—41no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C2×#67—21no—
323C2×#67—61no—
324C22×Dic3—21no—
325C22×Dic3—61no—
326D3×D4—22no—
327D3×D4—34no—
328D3×D4—62no—
329D3×D4C4×D314yescomplemented
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—34no—
333C2×D12—61no—
334C2×D12—62no—
335C2×D12—61no—
336C2×D12C22×D311yescharacteristic
337C2×D12C22×D311yescharacteristic
338C2×C4×D3—21no—
339C2×C4×D3—21no—
340C2×C4×D3—21no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—121no—
347C2×C4×D3C22×D311yescharacteristic
348C3×D8—34no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—41no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C42—21no—
369C3×C42—31no—
370C3×C42—61no—
371C3×C42C22×D311yescharacteristic
372C3×C42C22×D311yescharacteristic
373#217—21no—
374#217—61no—
375#217—61no—
376#213—34no—
377#213—34no—
378#213—34no—
379#213—34no—
380#213—34no—
381#213—64no—
382#213C4×D314yescomplemented
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
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
395(C2×D3)⋊C4#6711yescharacteristic
396C4⋊Dic3—31no—
397C4⋊Dic3—31no—
398C4⋊Dic3—61no—
399C4⋊Dic3C22×D311yescharacteristic
400C4⋊Dic3C22×D311yescharacteristic
401Dic3⋊C4#6711yescharacteristic
402Dic3⋊C4#6711yescharacteristic
403C4×Dic3—21no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3C22×D311yescharacteristic
407#208—62no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—34no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—61no—
414C2×C3⋊C8—61no—
415C2×C3⋊C8C22×D311yescharacteristic
416C2×C3⋊C8C22×D311yescharacteristic
417D24—34no—
418ΓL(1,𝔽25)—62no—
419D3×C8—34no—
420C22×C32—22no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32C22×D411yescharacteristic
424C2×C3⋊D3—22no—
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—84no—
436C2×C3×D3C4×D412yes—
437D32—84no—
438C32×C4—21no—
439C32×C4—21no—
440C32×C4—41no—
441C32×C4C23×C411yescharacteristic
442C32×C4C2×#4111yescharacteristic
443C3⋊Dic3—41no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C3×Dic3C4×D412yes—
449C22×D4—31no—
450C22×D4—91no—
451C2×D8—31no—
452C2×D8—91no—
453C2×D8—98no—
454C2×D8—91no—
455C2×D8—91no—
456C2×M16—91no—
457C22×C8—91no—
458C4×D4—31no—
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—61no—
463C4×D4—61no—
464C4×D4—91no—
465C4×D4—91no—
466C4×D4—91no—
467C4×D4—181no—
468C4×D4—181no—
469C4×D4D3211yescharacteristic, complemented
470#117—31no—
471#117—31no—
472#117—91no—
473C2×C22⋊C4—61no—
474C2×C22⋊C4—61no—
475C2×C22⋊C4—181no—
476C2×C22⋊C4—181no—
477#107—31no—
478#107—91no—
479#106—91no—
480#106—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#97—91no—
490#97—91no—
491C4×C8—31no—
492C4×C8—91no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—31no—
496C23×C3—41no—
497C23×C3—64no—
498C23×C3—61no—
499C23×C3—61no—
500C23×C3—241no—
501C23×C3—241no—
502C22×D3—21no—
503C22×D3—21no—
504C22×D3—24no—
505C22×D3—64no—
506C22×D3—61no—
507C22×D3—61no—
508C22×D3—64no—
509C22×D3—81no—
510C22×D3—81no—
511C22×D3—121no—
512C22×D3—241no—
513C22×D3—241no—
514C22×D3—241no—
515C22×D3—241no—
516C22×D3C2×#6711yescharacteristic
517C3×D4—21no—
518C3×D4—21no—
519C3×D4—22no—
520C3×D4—32no—
521C3×D4—32no—
522C3×D4—41no—
523C3×D4—64no—
524C3×D4—61no—
525C3×D4—61no—
526C3×D4C2×C4×D312yes—
527C3×D4C2×C4×D312yes—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—31no—
534C2×C3×C4—32no—
535C2×C3×C4—32no—
536C2×C3×C4—31no—
537C2×C3×C4—31no—
538C2×C3×C4—41no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—81no—
542C2×C3×C4—81no—
543C2×C3×C4—82no—
544C2×C3×C4—241no—
545C2×C3×C4—241no—
546C2×C3×C4—241no—
547C2×C3×C4—241no—
548C2×C3×C4D3×D411yescharacteristic
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4C2×#6711yescharacteristic
551C2×C3×C4C2×#6711yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554#67—24no—
555#67—64no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—81no—
561C2×Dic3—121no—
562C2×Dic3—241no—
563C2×Dic3C2×#6711yescharacteristic
564C2×Dic3C2×#6711yescharacteristic
565C2×Dic3C2×#6711yescharacteristic
566D12—21no—
567D12—21no—
568D12—32no—
569D12—32no—
570D12—62no—
571D12—64no—
572D12—61no—
573D12—61no—
574D12—121no—
575D12C2×C4×D312yes—
576D12C2×C4×D312yes—
577C4×D3—81no—
578C4×D3—81no—
579C4×D3—81no—
580C4×D3—241no—
581C4×D3—241no—
582C4×D3—241no—
583C4×D3—241no—
584C4×D3—241no—
585C4×D3—242no—
586C4×D3C2×C4×D312yes—
587C4×D3#23512yes—
588C3×C8—32no—
589C3×C8—61no—
590C3⋊C8—21no—
591C3⋊C8—32no—
592C3⋊C8—32no—
593C3⋊C8—62no—
594C3⋊C8—61no—
595C3⋊C8—61no—
596C3⋊C8—121no—
597C3⋊C8C2×C4×D312yes—
598C2×C32—42no—
599C2×C32C2×C4×D411yescharacteristic
600C2×C32#57611yescharacteristic
601C2×C32#57611yescharacteristic
602C3⋊D3—42no—
603C3×D3—22no—
604C3×D3—42no—
605C3×D3—42no—
606C24—61no—
607C24—181no—
608C2×D4—34no—
609C2×D4—31no—
610C2×D4—31no—
611C2×D4—62no—
612C2×D4—61no—
613C2×D4—94no—
614C2×D4—91no—
615C2×D4—182no—
616C2×D4—181no—
617C2×D4C2×D3211yescharacteristic
618C22×C4—21no—
619C22×C4—31no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—181no—
625C22×C4—181no—
626C22×C4—181no—
627D8—34no—
628D8—94no—
629D8—94no—
630D8—94no—
631M16—182no—
632C2×C8—31no—
633C2×C8—31no—
634C2×C8—94no—
635C2×C8—91no—
636C2×C8—91no—
637C4⋊C4—31no—
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—31no—
641C4⋊C4—91no—
642C4⋊C4C2×D3211yescharacteristic
643C22⋊C4—21no—
644C22⋊C4—31no—
645C22⋊C4—31no—
646C22⋊C4—61no—
647C22⋊C4—61no—
648C22⋊C4—61no—
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C42—31no—
656C42—61no—
657C42—181no—
658C42C2×D3211yescharacteristic
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—21no—
662C22×C3—32no—
663C22×C3—42no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—62no—
671C22×C3—62no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—244no—
679C22×C3C2×D3×D411yescharacteristic
680C22×C3C22×#6711yescharacteristic
681C2×D3—21no—
682C2×D3—21no—
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—62no—
690C2×D3—62no—
691C2×D3—84no—
692C2×D3—122no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—241no—
698C2×D3—241no—
699C2×D3—244no—
700C2×D3—244no—
701C2×D3C4×#6712yes—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—32no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4—61no—
714C3×C4—61no—
715C3×C4—81no—
716C3×C4—121no—
717C3×C4—121no—
718C3×C4C22×C4×D311yescharacteristic
719C3×C4C22×C4×D311yescharacteristic
720C3×C4C2×#23511yescharacteristic
721C3×C4D3×#4111yescharacteristic
722Dic3—21no—
723Dic3—21no—
724Dic3—41no—
725Dic3—41no—
726Dic3—121no—
727Dic3—121no—
728Dic3—241no—
729Dic3C4×#6712yes—
730C32#294811yescharacteristic, complemented, Sylow
731C23—21no—
732C23—31no—
733C23—64no—
734C23—61no—
735C23—61no—
736C23—184no—
737C23—181no—
738C23—241no—
739C23—241no—
740C23—721no—
741C23—721no—
742D4—21no—
743D4—32no—
744D4—32no—
745D4—64no—
746D4—61no—
747D4—61no—
748D4—92no—
749D4—184no—
750D4—181no—
751D4C4×D3212yes—
752C2×C4—21no—
753C2×C4—31no—
754C2×C4—32no—
755C2×C4—32no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—81no—
761C2×C4—181no—
762C2×C4—241no—
763C2×C4—241no—
764C2×C4—241no—
765C2×C4—241no—
766C2×C4—721no—
767C2×C4—721no—
768C2×C4—721no—
769C2×C4D3×#6711yescharacteristic
770C2×C4D3×#6711yescharacteristic
771C2×C4C22×D3211yescharacteristic
772C8—32no—
773C8—61no—
774C8—92no—
775C8—181no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—42no—
780C2×C3—42no—
781C2×C3—62no—
782C2×C3—82no—
783C2×C3—122no—
784C2×C3—122no—
785C2×C3C4×D3×D411yescharacteristic
786C2×C3#575711yescharacteristic
787C2×C3#576911yescharacteristic
788C2×C3C2×C4×#6711yescharacteristic
789C2×C3#583511yescharacteristic
790C2×C3#583511yescharacteristic
791D3—22no—
792D3—42no—
793D3—42no—
794D3—122no—
795D3—122no—
796D3—242no—
797C22—22no—
798C22—32no—
799C22—41no—
800C22—41no—
801C22—61no—
802C22—61no—
803C22—62no—
804C22—62no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—182no—
810C22—244no—
811C22—361no—
812C22—361no—
813C22—724no—
814C22C2×D3×#6711yescharacteristic
815C4—21no—
816C4—21no—
817C4—32no—
818C4—41no—
819C4—61no—
820C4—61no—
821C4—121no—
822C4—121no—
823C4—361no—
824C4C2×C4×D3211yescharacteristic
825C4D3×#23511yescharacteristic
826C3—21no—
827C3#7958811yescharacteristic, complemented
828C3#8253811yescharacteristic, complemented
829C2—42no—
830C2—62no—
831C2—122no—
832C2—122no—
833C2—362no—
834C2C4×D3×#6711yescharacteristic
835C2#1059509611yescharacteristic
836C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×D3×#213C2
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5545C2semidirect
3. #10593994C2semidirect
4. #10592713C2semidirect
5. C3×C4×#213C2semidirect
6. Dic3×#213C2semidirect
7. #10591421C2semidirect
8. #10591404C2semidirect
9. #10590592C2semidirect
10. #10590571C2semidirect
11. #10590456C2semidirect
12. #10590455C2semidirect
13. C4×#3714C2semidirect
14. #10590344C2semidirect
15. #10590318C2semidirect
20. C32×C4×D4C22semidirect
22. C4×C4⋊(C3⋊D3)C22semidirect
23. C3×D4×Dic3C22semidirect
27. C3×#893C22semidirect
31. C3×C4×D12C22semidirect
32. C3×C4×D12C22semidirect
34. D3×#213C4semidirect
38. #63894C22semidirect
39. Dic3×D12C22semidirect
46. #63659C22semidirect
47. #63636C22semidirect
48. #63635C22semidirect
49. #63630C22semidirect
50. C3×#832C22semidirect
51. C3×#809C22semidirect
52. C3×#807C22semidirect
53. C3×C4×C3⋊C8C22semidirect
54. #63575C22semidirect
55. #63574C22semidirect
56. #63564C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. #63562C22semidirect
60. #63554C22semidirect
61. Dic3×C3⋊C8C22semidirect
66. #5545D3semidirect
81. C4×#213D3semidirect
102. C3×D3×D4C2×C4semidirect
113. D3×D12C2×C4semidirect
117. #3753C2×C4semidirect
123. C3×#213C2×C4semidirect
142. #3714C2×C4semidirect
143. #3713C2×C4semidirect
145. D3×C3⋊C8C2×C4semidirect
159. C3×C4×D4C2×D3semidirect
160. C3×C4×D4C2×D3semidirect
166. D4×Dic3C2×D3semidirect
189. #893C2×D3semidirect
203. C4×D12C2×D3semidirect
204. C4×D12C2×D3semidirect
216. #832C2×D3semidirect
228. #809C2×D3semidirect
235. #807C2×D3semidirect
241. C4×C3⋊C8C2×D3semidirect
329. D3×D4C4×D3semidirect
382. #213C4×D3semidirect
469. C4×D4D32semidirect
730. C32#2948semidirect
827. C3#79588semidirect
828. C3#82538semidirect

Maximal subgroups

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

subgroupindex
C3×#55452
C2×D3×#2132
#105939942
#105927132
C3×C4×#2132
Dic3×#2132
#105914212
#105914042
#105905922
#105905712
#105904562
#105904552
C4×#37142
#105903442
#105903182
#825383
#795883