Finite Group Databasebeta

← D3×#5126 #11857362

Subgroups — D3×#5126 #11857362

Order 1152.

2111 conjugacy classes of subgroups.

The subgroup lattice has 739 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D32C211yesmaximal, characteristic
2C2×C3×D3×M16C211yesmaximal, characteristic, complemented
3C2×D3×#208C211yesmaximal, characteristic, complemented
4#10592825C211yesmaximal, characteristic, complemented
5C3×#5126C211yesmaximal, characteristic, complemented
6#10591074C211yesmaximal, characteristic, complemented
7#10591069C211yesmaximal, characteristic, complemented
8#10590936C214yesmaximal, complemented
9D3×(C2×D3)⋊C8C214yesmaximal, complemented
10C2×#5126—31nomaximal
11D3×#407—31nomaximal
12C23×D32C411yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×#624C411yescharacteristic
17C22×D3×Dic3C411yescharacteristic
18C22×D3×Dic3C411yescharacteristic
19C2×C4×D32—24no—
20C2×C4×D32—24no—
21C2×C4×D32C412yes—
22C2×C4×D32C412yes—
23C2×C4×D32C2212yes—
24C2×C4×D32C2212yes—
25C2×C32×M16C2211yescharacteristic, complemented
26C2×#3748C2211yescharacteristic, complemented
27C2×C3×#208C2211yescharacteristic, complemented
28C2×C3×#208C2211yescharacteristic, complemented
29C3×D3×M16—24no—
30C2×C3×ΓL(1,𝔽25)C2212yescomplemented
31C2×C3×D3×C8C2212yescomplemented
32C2×#3711C2212yescomplemented
33D3×#208—24no—
34C2×D3×C3⋊C8C2212yescomplemented
35#63647C2214yescomplemented
36C3×(C2×D3)⋊C8C2214yescomplemented
37#63557C2214yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C23×C4×D3—31no—
40C23×C4×D3—31no—
41C22×C3×M16—31no—
42C22×#208—31no—
43C2×D3×M16—31no—
44C2×D3×M16D311yescharacteristic, complemented
45C3×#407—31no—
46#5207—31no—
47#5126—31no—
48#5126—31no—
49#5126—31no—
50#5126—31no—
51#5126—31no—
52#5126—34no—
53#5126—61no—
54#5126D311yescharacteristic, direct product factor
55C2×(C2×D3)⋊C8—34no—
56#4726—34no—
57D3×C22⋊C8—34no—
58C23×C3⋊D3C2×C411yescharacteristic
59C23×C3×D3C2×C411yescharacteristic
60C23×C3×D3C2×C411yescharacteristic
61C22×D32—24no—
62C22×D32—28no—
63C22×D32C2×C412yes—
64C22×D32C2×C412yes—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2×C411yescharacteristic
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3C2×C412yes—
70C2×C4×C3⋊D3C2312yes—
71C22×C3×Dic3C2×C411yescharacteristic
72C22×C3×Dic3C2×C411yescharacteristic
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3C2×C412yes—
76C2×C3×C4×D3C2×C411yescharacteristic
77C2×C3×C4×D3C2×C411yescharacteristic
78C2×C3×C4×D3D414yes—
79C2×C3×C4×D3D414yes—
80C2×C3×C4×D3C2312yes—
81C2×C3×C4×D3C2311yescharacteristic
82C2×C3×C4×D3C2311yescharacteristic
83C2×#624—24no—
84C2×#624C2×C412yes—
85C2×#624C2×C412yes—
86C2×D3×Dic3—24no—
87C2×D3×Dic3—24no—
88C2×D3×Dic3C2×C412yes—
89C2×D3×Dic3C2×C412yes—
90C2×D3×Dic3C2×C412yes—
91C2×D3×Dic3C2×C412yes—
92C4×D32—28no—
93C4×D32—28no—
94C4×D32—24no—
95C4×D32—24no—
96C4×D32—24no—
97C4×D32—24no—
98C32×M16—22no—
99C2×C32×C8C2312yescomplemented
100#3748—22no—
101C2×C3⋊(C3⋊C8)C2312yescomplemented
102C3×#208—22no—
103C3×#208—22no—
104C2×C3×C3⋊C8C2312yescomplemented
105C2×C3×C3⋊C8C2312yescomplemented
106C3×ΓL(1,𝔽25)—24no—
107C3×D3×C8—24no—
108#3711—24no—
109D3×C3⋊C8—24no—
110C2×#407—91noSylow
111C24×D3—31no—
112C24×D3—31no—
113C23×C3×C4—31no—
114C23×C3×C4—31no—
115C23×Dic3—31no—
116C23×Dic3—31no—
117C22×C4×D3—31no—
118C22×C4×D3—31no—
119C22×C4×D3—31no—
120C22×C4×D3—31no—
121C22×C4×D3—31no—
122C22×C4×D3—31no—
123C22×C4×D3—32no—
124C22×C4×D3—32no—
125C22×C4×D3—32no—
126C22×C4×D3—32no—
127C22×C4×D3—32no—
128C22×C4×D3—32no—
129C22×C4×D3—32no—
130C22×C4×D3—32no—
131C22×C4×D3—61no—
132C22×C4×D3—64no—
133C22×C4×D3—64no—
134C22×C4×D3—64no—
135C22×C4×D3—64no—
136C22×C4×D3C2×D311yescharacteristic
137C22×C4×D3C2×D311yescharacteristic
138C2×C3×M16—21no—
139C2×C3×M16—31no—
140C2×C3×M16—31no—
141C2×C3×M16—32no—
142C2×C3×M16—64no—
143C2×C3×M16C2×D311yescharacteristic, complemented
144C2×C3×M16C2×D311yescharacteristic, complemented
145C22×C3×C8—32no—
146C2×#208—31no—
147C2×#208—31no—
148C2×#208—32no—
149C2×#208—61no—
150C2×#208—64no—
151C2×#208C2×D311yescharacteristic, complemented
152C2×#208C2×D311yescharacteristic, complemented
153C22×C3⋊C8—32no—
154D3×M16—24no—
155D3×M16—64no—
156C2×ΓL(1,𝔽25)—32no—
157C2×ΓL(1,𝔽25)C2×D312yescomplemented
158C2×D3×C8—32no—
159C2×D3×C8C2×D312yescomplemented
160C3×C22⋊C8—34no—
161#830—34no—
162(C2×D3)⋊C8—34no—
163(C2×D3)⋊C8—34no—
164(C2×D3)⋊C8—34no—
165(C2×D3)⋊C8—34no—
166(C2×D3)⋊C8—34no—
167(C2×D3)⋊C8—64no—
168(C2×D3)⋊C8C2×D314yescomplemented
169C23×C32C22×C411yescharacteristic
170C22×C3⋊D3—22no—
171C22×C3⋊D3—24no—
172C22×C3⋊D3C22×C412yes—
173C22×C3×D3—22no—
174C22×C3×D3—24no—
175C22×C3×D3—24no—
176C22×C3×D3C22⋊C414yes—
177C22×C3×D3C22×C411yescharacteristic
178C22×C3×D3C22×C412yes—
179C22×C3×D3C22×C411yescharacteristic
180C2×D32—232no—
181C2×D32—24no—
182C2×D32—24no—
183C2×D32—24no—
184C2×D32—24no—
185C2×D32—24no—
186C2×D32M1618yescomplemented
187C2×C32×C4C22×C411yescharacteristic
188C2×C32×C4C2×D412yes—
189C2×C32×C4C2×D412yes—
190C2×C32×C4C2411yescharacteristic
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3C22×C412yes—
193C4×C3⋊D3—24no—
194C4×C3⋊D3—22no—
195C4×C3⋊D3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3C22⋊C414yes—
198C2×C3×Dic3C22×C412yes—
199C2×C3×Dic3C22×C411yescharacteristic
200C2×C3×Dic3C22×C411yescharacteristic
201C3×C4×D3—24no—
202C3×C4×D3—22no—
203C3×C4×D3—22no—
204C3×C4×D3C22⋊C414yes—
205C3×C4×D3C22⋊C414yes—
206C3×C4×D3C2×D412yes—
207C3×C4×D3C2×D412yes—
208C3×C4×D3C2×D412yes—
209C3×C4×D3C2×D412yes—
210#624—24no—
211#624—24no—
212D3×Dic3—24no—
213D3×Dic3—24no—
214D3×Dic3—24no—
215D3×Dic3—24no—
216C32×C8—22no—
217C3⋊(C3⋊C8)—22no—
218C3×C3⋊C8—22no—
219C3×C3⋊C8—22no—
220C24×C4—91no—
221C22×M16—31no—
222C22×M16—91no—
223#407—31no—
224#407—94no—
225#407—91no—
226#407—91no—
227#407—91no—
228C2×C22⋊C8—94no—
229C24×C3—31no—
230C24×C3—31no—
231C23×D3—32no—
232C23×D3—32no—
233C23×D3—31no—
234C23×D3—31no—
235C23×D3—32no—
236C23×D3—32no—
237C23×D3—61no—
238C23×D3—68no—
239C23×D3—68no—
240C23×D3—64no—
241C23×D3—64no—
242C23×D3C4×D311yescharacteristic
243C23×D3C4×D311yescharacteristic
244C22×C3×C4—21no—
245C22×C3×C4—31no—
246C22×C3×C4—31no—
247C22×C3×C4—31no—
248C22×C3×C4—34no—
249C22×C3×C4—34no—
250C22×C3×C4—31no—
251C22×C3×C4—31no—
252C22×C3×C4—31no—
253C22×C3×C4—32no—
254C22×C3×C4—32no—
255C22×C3×C4—62no—
256C22×C3×C4—62no—
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C22×D311yescharacteristic
259C22×Dic3—31no—
260C22×Dic3—31no—
261C22×Dic3—32no—
262C22×Dic3—32no—
263C22×Dic3—32no—
264C22×Dic3—32no—
265C22×Dic3—61no—
266C22×Dic3—64no—
267C22×Dic3—64no—
268C22×Dic3C4×D311yescharacteristic
269C22×Dic3C4×D311yescharacteristic
270C2×C4×D3—22no—
271C2×C4×D3—22no—
272C2×C4×D3—32no—
273C2×C4×D3—32no—
274C2×C4×D3—32no—
275C2×C4×D3—32no—
276C2×C4×D3—32no—
277C2×C4×D3—32no—
278C2×C4×D3—32no—
279C2×C4×D3—32no—
280C2×C4×D3—32no—
281C2×C4×D3—32no—
282C2×C4×D3—32no—
283C2×C4×D3—32no—
284C2×C4×D3—62no—
285C2×C4×D3—62no—
286C2×C4×D3—68no—
287C2×C4×D3—68no—
288C2×C4×D3—64no—
289C2×C4×D3—64no—
290C2×C4×D3—64no—
291C2×C4×D3—64no—
292C2×C4×D3—64no—
293C2×C4×D3—64no—
294C2×C4×D3—64no—
295C2×C4×D3—62no—
296C2×C4×D3—62no—
297C2×C4×D3—62no—
298C2×C4×D3—62no—
299C2×C4×D3—64no—
300C2×C4×D3—68no—
301C2×C4×D3—68no—
302C2×C4×D3—64no—
303C2×C4×D3—64no—
304C2×C4×D3—64no—
305C2×C4×D3—64no—
306C2×C4×D3—122no—
307C2×C4×D3—122no—
308C2×C4×D3C4×D312yes—
309C2×C4×D3C4×D311yescharacteristic
310C2×C4×D3C4×D311yescharacteristic
311C2×C4×D3D1214yes—
312C2×C4×D3#6714yes—
313C2×C4×D3C22×D312yes—
314C2×C4×D3C22×D311yescharacteristic
315C2×C4×D3C22×D311yescharacteristic
316C3×M16—22no—
317C3×M16—22no—
318C3×M16—42no—
319C3×M16—64no—
320C3×M16—62no—
321C3×M16—62no—
322C2×C3×C8—22no—
323C2×C3×C8—32no—
324C2×C3×C8—32no—
325C2×C3×C8—64no—
326C2×C3×C8C22×D312yescomplemented
327C2×C3×C8C22×D312yescomplemented
328#208—22no—
329#208—22no—
330#208—64no—
331#208—62no—
332#208—62no—
333#208—122no—
334C2×C3⋊C8—32no—
335C2×C3⋊C8—32no—
336C2×C3⋊C8—62no—
337C2×C3⋊C8—64no—
338C2×C3⋊C8C22×D312yescomplemented
339C2×C3⋊C8C22×D312yescomplemented
340ΓL(1,𝔽25)—24no—
341ΓL(1,𝔽25)—64no—
342D3×C8—24no—
343D3×C8—64no—
344C22×C32—22no—
345C22×C32C2×C22⋊C412yes—
346C22×C32C23×C411yescharacteristic
347C2×C3⋊D3—28no—
348C2×C3⋊D3—22no—
349C2×C3⋊D3—22no—
350C2×C3⋊D3C2×M1614yescomplemented
351C2×C3×D3—28no—
352C2×C3×D3—22no—
353C2×C3×D3—22no—
354C2×C3×D3—22no—
355C2×C3×D3—28no—
356C2×C3×D3C2×C22⋊C412yes—
357C2×C3×D3C2×C22⋊C412yes—
358C2×C3×D3C2×M1614yes—
359C2×C3×D3C2×M1614yescomplemented
360D32—216no—
361D32—216no—
362C32×C4C2×C22⋊C412yes—
363C32×C4C22×D411yescharacteristic
364C32×C4C22×D411yescharacteristic
365C3⋊Dic3—22no—
366C3×Dic3—22no—
367C3×Dic3C2×C22⋊C412yes—
368C3×Dic3C2×C22⋊C412yes—
369C25—91no—
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—92no—
373C23×C4—92no—
374C23×C4—91no—
375C23×C4—92no—
376C23×C4—92no—
377C23×C4—91no—
378C23×C4—91no—
379C23×C4—91no—
380C23×C4—184no—
381C23×C4—184no—
382C2×M16—31no—
383C2×M16—31no—
384C2×M16—32no—
385C2×M16—64no—
386C2×M16—92no—
387C2×M16—91no—
388C2×M16—184no—
389C2×M16D3211yescharacteristic, complemented
390C22×C8—32no—
391C22×C8—92no—
392C22⋊C8—34no—
393C22⋊C8—94no—
394C22⋊C8—94no—
395C22⋊C8—94no—
396C23×C3—21no—
397C23×C3—31no—
398C23×C3—34no—
399C23×C3—31no—
400C23×C3—32no—
401C23×C3—64no—
402C23×C3—64no—
403C23×C3—62no—
404C23×C3C2×C4×D311yescharacteristic
405C23×C3C2×C4×D311yescharacteristic
406C22×D3—22no—
407C22×D3—24no—
408C22×D3—24no—
409C22×D3—32no—
410C22×D3—32no—
411C22×D3—38no—
412C22×D3—38no—
413C22×D3—62no—
414C22×D3—64no—
415C22×D3—64no—
416C22×D3—64no—
417C22×D3—64no—
418C22×D3—64no—
419C22×D3—64no—
420C22×D3—632no—
421C22×D3—632no—
422C22×D3—64no—
423C22×D3—64no—
424C22×D3—62no—
425C22×D3—62no—
426C22×D3—64no—
427C22×D3—64no—
428C22×D3—64no—
429C22×D3—64no—
430C22×D3—124no—
431C22×D3—122no—
432C22×D3(C2×D3)⋊C414yes—
433C22×D3C2×C4×D312yes—
434C22×D3C2×C4×D311yescharacteristic
435C22×D3C2×C4×D311yescharacteristic
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—34no—
441C2×C3×C4—31no—
442C2×C3×C4—31no—
443C2×C3×C4—34no—
444C2×C3×C4—34no—
445C2×C3×C4—32no—
446C2×C3×C4—32no—
447C2×C3×C4—32no—
448C2×C3×C4—32no—
449C2×C3×C4—32no—
450C2×C3×C4—62no—
451C2×C3×C4—64no—
452C2×C3×C4—62no—
453C2×C3×C4—62no—
454C2×C3×C4C2×C4×D311yescharacteristic
455C2×C3×C4C2×C4×D311yescharacteristic
456C2×C3×C4C2×D1212yes—
457C2×C3×C4D3×D412yes—
458C2×C3×C4D3×D412yes—
459C2×C3×C4C2×#6712yes—
460C2×C3×C4C23×D311yescharacteristic
461C2×C3×C4C23×D311yescharacteristic
462C2×Dic3—22no—
463C2×Dic3—32no—
464C2×Dic3—32no—
465C2×Dic3—62no—
466C2×Dic3—64no—
467C2×Dic3—64no—
468C2×Dic3—62no—
469C2×Dic3—62no—
470C2×Dic3—64no—
471C2×Dic3—64no—
472C2×Dic3—122no—
473C2×Dic3(C2×D3)⋊C414yes—
474C2×Dic3C2×C4×D312yes—
475C2×Dic3C2×C4×D311yescharacteristic
476C2×Dic3C2×C4×D311yescharacteristic
477C4×D3—24no—
478C4×D3—22no—
479C4×D3—22no—
480C4×D3—64no—
481C4×D3—64no—
482C4×D3—64no—
483C4×D3—64no—
484C4×D3—64no—
485C4×D3—64no—
486C4×D3—64no—
487C4×D3—64no—
488C4×D3—62no—
489C4×D3—62no—
490C4×D3—62no—
491C4×D3—62no—
492C4×D3—64no—
493C4×D3—64no—
494C4×D3—122no—
495C4×D3—122no—
496C4×D3—124no—
497C4×D3(C2×D3)⋊C414yes—
498C4×D3(C2×D3)⋊C414yes—
499C4×D3C2×D1212yes—
500C4×D3C2×D1212yes—
501C4×D3C2×#6712yes—
502C4×D3C2×#6712yes—
503C3×C8—22no—
504C3×C8—22no—
505C3×C8—42no—
506C3×C8—62no—
507C3×C8—62no—
508C3⋊C8—22no—
509C3⋊C8—22no—
510C3⋊C8—62no—
511C3⋊C8—62no—
512C3⋊C8—122no—
513C2×C32—22no—
514C2×C32C22×C22⋊C411yescharacteristic
515C2×C32C22×M1612yes—
516C3⋊D3—24no—
517C3×D3—22no—
518C3×D3—24no—
519C3×D3#40714yescomplemented
520C24—31no—
521C24—31no—
522C24—92no—
523C24—92no—
524C24—91no—
525C24—184no—
526C24—188no—
527C22×C4—31no—
528C22×C4—31no—
529C22×C4—31no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—34no—
533C22×C4—34no—
534C22×C4—31no—
535C22×C4—32no—
536C22×C4—32no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—92no—
540C22×C4—92no—
541C22×C4—92no—
542C22×C4—92no—
543C22×C4—92no—
544C22×C4—92no—
545C22×C4—91no—
546C22×C4—92no—
547C22×C4—92no—
548C22×C4—184no—
549C22×C4—184no—
550C22×C4—184no—
551C22×C4—184no—
552C22×C4—184no—
553C22×C4—188no—
554C22×C4—188no—
555C22×C4—184no—
556C22×C4—184no—
557C22×C4—182no—
558C22×C4—182no—
559C22×C4C2×D3211yescharacteristic
560M16—22no—
561M16—64no—
562M16—62no—
563M16—62no—
564M16—184no—
565M16—182no—
566C2×C8—32no—
567C2×C8—32no—
568C2×C8—64no—
569C2×C8—92no—
570C2×C8—184no—
571C2×C8C2×D3212yescomplemented
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—21no—
575C22×C3—22no—
576C22×C3—32no—
577C22×C3—34no—
578C22×C3—32no—
579C22×C3—34no—
580C22×C3—42no—
581C22×C3—68no—
582C22×C3—68no—
583C22×C3—62no—
584C22×C3—62no—
585C22×C3—62no—
586C22×C3D3×C22⋊C412yes—
587C22×C3C2×(C2×D3)⋊C412yes—
588C22×C3C22×C4×D311yescharacteristic
589C22×C3C22×C4×D311yescharacteristic
590C2×D3—28no—
591C2×D3—22no—
592C2×D3—22no—
593C2×D3—22no—
594C2×D3—28no—
595C2×D3—34no—
596C2×D3—34no—
597C2×D3—64no—
598C2×D3—616no—
599C2×D3—616no—
600C2×D3—616no—
601C2×D3—68no—
602C2×D3—68no—
603C2×D3—62no—
604C2×D3—62no—
605C2×D3—62no—
606C2×D3—62no—
607C2×D3—616no—
608C2×D3—122no—
609C2×D3—122no—
610C2×D3—128no—
611C2×D3D3×M1614yes—
612C2×D3D3×M1614yescomplemented
613C2×D3C2×(C2×D3)⋊C412yes—
614C2×D3C2×(C2×D3)⋊C412yes—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—22no—
618C3×C4—32no—
619C3×C4—32no—
620C3×C4—62no—
621C3×C4D3×C22⋊C412yes—
622C3×C4C2×(C2×D3)⋊C412yes—
623C3×C4C22×D1211yescharacteristic
624C3×C4C2×D3×D411yescharacteristic
625C3×C4C2×D3×D411yescharacteristic
626C3×C4C22×#6711yescharacteristic
627Dic3—22no—
628Dic3—62no—
629Dic3—62no—
630Dic3—122no—
631Dic3C2×(C2×D3)⋊C412yes—
632Dic3C2×(C2×D3)⋊C412yes—
633C32C2×#40711yescharacteristic, complemented, Sylow
634C23—31no—
635C23—32no—
636C23—31no—
637C23—34no—
638C23—64no—
639C23—64no—
640C23—62no—
641C23—98no—
642C23—92no—
643C23—184no—
644C23—184no—
645C23—184no—
646C23—184no—
647C23—184no—
648C23—184no—
649C23—1832no—
650C23—182no—
651C23C4×D3211yescharacteristic
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—34no—
655C2×C4—32no—
656C2×C4—32no—
657C2×C4—32no—
658C2×C4—32no—
659C2×C4—34no—
660C2×C4—34no—
661C2×C4—32no—
662C2×C4—62no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—64no—
666C2×C4—92no—
667C2×C4—184no—
668C2×C4—184no—
669C2×C4—184no—
670C2×C4—184no—
671C2×C4—184no—
672C2×C4—184no—
673C2×C4—182no—
674C2×C4—182no—
675C2×C4—182no—
676C2×C4—184no—
677C2×C4C4×D3211yescharacteristic
678C2×C4D3×D1212yes—
679C2×C4D3×#6712yes—
680C2×C4C22×D3211yescharacteristic
681C8—22no—
682C8—62no—
683C8—62no—
684C8—182no—
685C2×C3—22no—
686C2×C3—22no—
687C2×C3—22no—
688C2×C3—21no—
689C2×C3—34no—
690C2×C3—42no—
691C2×C3—62no—
692C2×C3—64no—
693C2×C3C2×D3×C22⋊C411yescharacteristic
694C2×C3C2×D3×M1612yes—
695C2×C3C2×D3×M1612yes—
696C2×C3C22×(C2×D3)⋊C411yescharacteristic
697D3—24no—
698D3—22no—
699D3—64no—
700D3—64no—
701D3—124no—
702D3#512614yesdirect product factor
703C22—22no—
704C22—34no—
705C22—32no—
706C22—34no—
707C22—32no—
708C22—68no—
709C22—68no—
710C22—62no—
711C22—62no—
712C22—62no—
713C22—94no—
714C22—188no—
715C22—1816no—
716C22—1816no—
717C22—182no—
718C22—182no—
719C22D3×(C2×D3)⋊C412yes—
720C22C2×C4×D3211yescharacteristic
721C4—32no—
722C4—32no—
723C4—62no—
724C4—182no—
725C4D3×(C2×D3)⋊C412yes—
726C4C2×D3×D1211yescharacteristic
727C4C2×D3×#6711yescharacteristic
728C3—21no—
729C3D3×#40711yescharacteristic, complemented
730C3C2×#512611yescharacteristic, complemented
731C2—22no—
732C2—34no—
733C2—64no—
734C2—62no—
735C2—184no—
736C2D32×M1612yes—
737C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radicalC23×D32C4
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32C2×#407
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×M16C2semidirect
3. C2×D3×#208C2semidirect
4. #10592825C2semidirect
5. C3×#5126C2semidirect
6. #10591074C2semidirect
7. #10591069C2semidirect
8. #10590936C2semidirect
9. D3×(C2×D3)⋊C8C2semidirect
25. C2×C32×M16C22semidirect
26. C2×#3748C22semidirect
27. C2×C3×#208C22semidirect
28. C2×C3×#208C22semidirect
30. C2×C3×ΓL(1,𝔽25)C22semidirect
31. C2×C3×D3×C8C22semidirect
32. C2×#3711C22semidirect
34. C2×D3×C3⋊C8C22semidirect
35. #63647C22semidirect
36. C3×(C2×D3)⋊C8C22semidirect
37. #63557C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
44. C2×D3×M16D3semidirect
54. #5126D3direct (N × H)
99. C2×C32×C8C23semidirect
101. C2×C3⋊(C3⋊C8)C23semidirect
104. C2×C3×C3⋊C8C23semidirect
105. C2×C3×C3⋊C8C23semidirect
143. C2×C3×M16C2×D3semidirect
144. C2×C3×M16C2×D3semidirect
151. C2×#208C2×D3semidirect
152. C2×#208C2×D3semidirect
157. C2×ΓL(1,𝔽25)C2×D3semidirect
159. C2×D3×C8C2×D3semidirect
168. (C2×D3)⋊C8C2×D3semidirect
186. C2×D32M16semidirect
326. C2×C3×C8C22×D3semidirect
327. C2×C3×C8C22×D3semidirect
338. C2×C3⋊C8C22×D3semidirect
339. C2×C3⋊C8C22×D3semidirect
350. C2×C3⋊D3C2×M16semidirect
359. C2×C3×D3C2×M16semidirect
389. C2×M16D32semidirect
519. C3×D3#407semidirect
571. C2×C8C2×D32semidirect
612. C2×D3D3×M16semidirect
633. C32C2×#407semidirect
702. D3#5126direct (N × H)
729. C3D3×#407semidirect
730. C3C2×#5126semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D322
C2×C3×D3×M162
C2×D3×#2082
#105928252
C3×#51262
#105910742
#105910692
#105909362
D3×(C2×D3)⋊C82
C2×#51263
D3×#4073