Finite Group Databasebeta

← D3×#4666 #11800697

Subgroups — D3×#4666 #11800697

Order 1152.

2849 conjugacy classes of subgroups.

The subgroup lattice has 729 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D32C211yesmaximal, characteristic
2C2×D3×(C2×D3)⋊C4C212yesmaximal
3C2×C4×D3×Dic3C212yesmaximal, complemented
4#10592365C211yesmaximal, characteristic, complemented
5C3×#4666C211yesmaximal, characteristic, complemented
6C3×D3×#95C211yesmaximal, characteristic, complemented
7#10591368C212yesmaximal, complemented
8D3×C3⋊#95C211yesmaximal, characteristic, complemented
9#10591260C211yesmaximal, characteristic, complemented
10#10591237C211yesmaximal, characteristic, complemented
11#10591233C212yesmaximal, complemented
12C4×D3×C22⋊C4—31nomaximal
13C2×#4666—31nomaximal
14C23×D32C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×C4×D3C2212yes—
19C22×#624C2211yescharacteristic
20C22×D3×Dic3C2212yes—
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C4×D32—28no—
24C2×C4×D32C418yescomplemented
25C2×#3752C2212yes—
26C2×C4×C3⋊Dic3C2212yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×C4×Dic3C2212yescomplemented
29C2×#3722C2212yes—
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×Dic32C2212yescomplemented
32C2×Dic32C2212yescomplemented
33D3×(C2×D3)⋊C4C4116yescomplemented
34C4×D3×Dic3—28no—
35C32×#95C2211yescharacteristic, complemented
36#63658C2211yescharacteristic, complemented
37C3×C3⋊#95C2212yescomplemented
38C3×C3⋊#95C2211yescharacteristic, complemented
39C3×C3⋊#95C2211yescharacteristic, complemented
40#63579C2212yescomplemented
41C23×C4×D3—31no—
42C23×C4×D3—31no—
43C22×(C2×D3)⋊C4—32no—
44C22×C4×Dic3—32no—
45C2×D3×C22⋊C4—32no—
46C2×C42×D3—32no—
47C3×C4×C22⋊C4—31no—
48C2×C3×#95—31no—
49C4×#217—31no—
50C2×C3⋊#95—31no—
51Dic3×C22⋊C4—32no—
52C4×(C2×D3)⋊C4—32no—
53#4666—31no—
54#4666—32no—
55#4666—32no—
56#4666—31no—
57#4666—31no—
58#4666—31no—
59#4666—31no—
60#4666—61no—
61#4666D311yescharacteristic, direct product factor
62D3×#95—31no—
63D3×#95D311yescharacteristic, complemented
64C23×C3⋊D3C2311yescharacteristic
65C23×C3×D3C2311yescharacteristic
66C23×C3×D3C2311yescharacteristic
67C22×D32—24no—
68C22×D32—22no—
69C22×D32—22no—
70C22×D32C2×C414yes—
71C22×D32C2×C418yes—
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2312yes—
74C22×C3⋊Dic3C2312yes—
75C22×C3⋊Dic3C2311yescharacteristic
76C2×C4×C3⋊D3—24no—
77C2×C4×C3⋊D3C2×C414yescomplemented
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2311yescharacteristic
82C2×C3×C4×D3—24no—
83C2×C3×C4×D3—24no—
84C2×C3×C4×D3—24no—
85C2×C3×C4×D3—24no—
86C2×C3×C4×D3C2×C414yes—
87C2×C3×C4×D3C2×C414yescomplemented
88C2×C3×C4×D3C2×C418yescomplemented
89C2×#624—24no—
90C2×#624C2×C414yescomplemented
91C2×D3×Dic3—24no—
92C2×D3×Dic3—24no—
93C2×D3×Dic3—24no—
94C2×D3×Dic3C2×C414yes—
95C2×D3×Dic3C2×C414yescomplemented
96C2×D3×Dic3C2×C418yescomplemented
97C2×D3×Dic3D418yes—
98C4×D32—232no—
99#3752C2×C418yescomplemented
100C4×C3⋊Dic3—24no—
101C3×(C2×D3)⋊C4C2×C418yescomplemented
102C3×C4×Dic3—24no—
103#3722C2×C418yescomplemented
104(C2×D3)⋊Dic3C2×C418yescomplemented
105Dic32—24no—
106Dic32—24no—
107C2×C4×C22⋊C4—91noSylow
108C24×D3—31no—
109C24×D3—31no—
110C23×C3×C4—31no—
111C23×C3×C4—31no—
112C23×C3×C4—32no—
113C23×Dic3—31no—
114C23×Dic3—31no—
115C23×Dic3—32no—
116C22×C4×D3—31no—
117C22×C4×D3—32no—
118C22×C4×D3—31no—
119C22×C4×D3—31no—
120C22×C4×D3—31no—
121C22×C4×D3—31no—
122C22×C4×D3—31no—
123C22×C4×D3—38no—
124C22×C4×D3—38no—
125C22×C4×D3—61no—
126C22×C4×D3—68no—
127C22×C4×D3—68no—
128C22×C4×D3C2×D311yescharacteristic
129C22×C4×D3C2×D312yes—
130C22×C4×D3C2×D311yescharacteristic
131C2×C3×C22⋊C4—32no—
132C2×C3×C42—32no—
133C2×#217—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—316no—
140C2×(C2×D3)⋊C4—62no—
141C2×(C2×D3)⋊C4C2×D312yes—
142C2×C4×Dic3—32no—
143C2×C4×Dic3—32no—
144C2×C4×Dic3—32no—
145C2×C4×Dic3—32no—
146C2×C4×Dic3—32no—
147C2×C4×Dic3—32no—
148C2×C4×Dic3—62no—
149C2×C4×Dic3—68no—
150C2×C4×Dic3C2×D312yescomplemented
151D3×C22⋊C4—316no—
152C42×D3—68no—
153C3×#95—21no—
154C3×#95—31no—
155C3×#95—32no—
156C3×#95—31no—
157C3×#95C2×D311yescharacteristic, complemented
158C3×#95C2×D311yescharacteristic, complemented
159C3⋊#95—31no—
160C3⋊#95—31no—
161C3⋊#95—32no—
162C3⋊#95—32no—
163C3⋊#95—61no—
164C3⋊#95C2×D311yescharacteristic, complemented
165C3⋊#95C2×D312yescomplemented
166C3⋊#95C2×D311yescharacteristic, complemented
167C23×C32C2411yescharacteristic
168C22×C3⋊D3—22no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3—21no—
171C22×C3⋊D3C22×C414yes—
172C22×C3⋊D3C22×C412yes—
173C22×C3×D3—22no—
174C22×C3×D3—21no—
175C22×C3×D3—21no—
176C22×C3×D3C22×C414yes—
177C22×C3×D3C22×C412yes—
178C22×C3×D3C22×C412yes—
179C22×C3×D3C22×C414yes—
180C22×C3×D3C2×D414yes—
181C22×C3×D3#4112yes—
182C22×C3×D3#4112yes—
183C2×D32—28no—
184C2×D32—28no—
185C2×D32—216no—
186C2×D32—216no—
187C2×D32C42116yescomplemented
188C2×C32×C4—22no—
189C2×C32×C4—22no—
190C2×C32×C4—22no—
191C2×C32×C4C22×C412yes—
192C2×C32×C4C22×C414yescomplemented
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3C22×C412yes—
196C2×C3⋊Dic3C22×C414yescomplemented
197C2×C3⋊Dic3C2×D414yes—
198C4×C3⋊D3—28no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3C22×C412yes—
205C2×C3×Dic3C22×C412yes—
206C2×C3×Dic3C22×C414yescomplemented
207C2×C3×Dic3C22×C414yescomplemented
208C2×C3×Dic3C2×D414yes—
209C3×C4×D3—28no—
210C3×C4×D3—216no—
211C3×C4×D3—28no—
212#624—28no—
213D3×Dic3—216no—
214D3×Dic3—28no—
215D3×Dic3C22⋊C4116yescomplemented
216C24×C4—91no—
217C22×C22⋊C4—92no—
218C22×C42—92no—
219C4×C22⋊C4—31no—
220C4×C22⋊C4—91no—
221C4×C22⋊C4—92no—
222C4×C22⋊C4—92no—
223C4×C22⋊C4—91no—
224C4×C22⋊C4—91no—
225C2×#95—31no—
226C2×#95—91no—
227C24×C3—31no—
228C24×C3—31no—
229C23×D3—31no—
230C23×D3—31no—
231C23×D3—38no—
232C23×D3—38no—
233C23×D3—34no—
234C23×D3—34no—
235C23×D3—61no—
236C23×D3—64no—
237C23×D3—62no—
238C23×D3—62no—
239C23×D3—64no—
240C23×D3—62no—
241C23×D3—62no—
242C23×D3C22×D311yescharacteristic
243C23×D3C22×D311yescharacteristic
244C22×C3×C4—21no—
245C22×C3×C4—22no—
246C22×C3×C4—31no—
247C22×C3×C4—31no—
248C22×C3×C4—32no—
249C22×C3×C4—32no—
250C22×C3×C4—34no—
251C22×C3×C4—34no—
252C22×C3×C4—38no—
253C22×C3×C4—64no—
254C22×C3×C4—64no—
255C22×C3×C4—64no—
256C22×C3×C4—64no—
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C22×D311yescharacteristic
259C22×C3×C4C22×D312yes—
260C22×C3×C4C22×D312yes—
261C22×Dic3—31no—
262C22×Dic3—31no—
263C22×Dic3—34no—
264C22×Dic3—38no—
265C22×Dic3—32no—
266C22×Dic3—32no—
267C22×Dic3—34no—
268C22×Dic3—38no—
269C22×Dic3—61no—
270C22×Dic3—62no—
271C22×Dic3—64no—
272C22×Dic3—64no—
273C22×Dic3—64no—
274C22×Dic3C22×D311yescharacteristic
275C22×Dic3C22×D312yes—
276C22×Dic3C22×D312yes—
277C22×Dic3C22×D311yescharacteristic
278C2×C4×D3—24no—
279C2×C4×D3—24no—
280C2×C4×D3—24no—
281C2×C4×D3—24no—
282C2×C4×D3—34no—
283C2×C4×D3—38no—
284C2×C4×D3—38no—
285C2×C4×D3—34no—
286C2×C4×D3—34no—
287C2×C4×D3—34no—
288C2×C4×D3—34no—
289C2×C4×D3—34no—
290C2×C4×D3—64no—
291C2×C4×D3—632no—
292C2×C4×D3—632no—
293C2×C4×D3—64no—
294C2×C4×D3—64no—
295C2×C4×D3—64no—
296C2×C4×D3—64no—
297C2×C4×D3—64no—
298C2×C4×D3—64no—
299C2×C4×D3—64no—
300C2×C4×D3—124no—
301C2×C4×D3C4×D314yes—
302C2×C4×D3C4×D314yescomplemented
303C2×C4×D3C4×D318yescomplemented
304C3×C22⋊C4—38no—
305C3×C42—64no—
306#217—38no—
307(C2×D3)⋊C4—38no—
308(C2×D3)⋊C4—38no—
309(C2×D3)⋊C4—38no—
310(C2×D3)⋊C4—38no—
311(C2×D3)⋊C4—38no—
312(C2×D3)⋊C4—68no—
313(C2×D3)⋊C4C4×D318yescomplemented
314C4×Dic3—24no—
315C4×Dic3—64no—
316C4×Dic3—64no—
317C4×Dic3—64no—
318C4×Dic3—64no—
319C4×Dic3—64no—
320C4×Dic3—64no—
321C4×Dic3—124no—
322C22×C32C23×C411yescharacteristic
323C22×C32C23×C412yes—
324C22×C32C22×D412yes—
325C22×C32C2×#4111yescharacteristic
326C22×C32C2×#4111yescharacteristic
327C2×C3⋊D3—22no—
328C2×C3⋊D3—22no—
329C2×C3⋊D3—24no—
330C2×C3⋊D3—24no—
331C2×C3⋊D3C2×C4214yescomplemented
332C2×C3×D3—22no—
333C2×C3×D3—22no—
334C2×C3×D3—24no—
335C2×C3×D3—24no—
336C2×C3×D3C2×C4214yes—
337C2×C3×D3C2×C4214yescomplemented
338C2×C3×D3C2×C22⋊C414yes—
339C2×C3×D3#11714yes—
340C2×C3×D3C4×D418yes—
341C2×C3×D3C4×D418yes—
342D32—232no—
343C32×C4—22no—
344C32×C4—24no—
345C3⋊Dic3—24no—
346C3⋊Dic3C2×C22⋊C414yescomplemented
347C3×Dic3—22no—
348C3×Dic3—24no—
349C3×Dic3—24no—
350C3×Dic3C2×C22⋊C414yescomplemented
351C25—91no—
352C23×C4—32no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—91no—
356C23×C4—98no—
357C23×C4—91no—
358C23×C4—92no—
359C23×C4—91no—
360C23×C4—91no—
361C23×C4—188no—
362C2×C22⋊C4—32no—
363C2×C22⋊C4—916no—
364C2×C22⋊C4—92no—
365C2×C22⋊C4—92no—
366C2×C22⋊C4—92no—
367C2×C42—32no—
368C2×C42—92no—
369C2×C42—92no—
370C2×C42—92no—
371C2×C42—188no—
372#95—32no—
373#95—31no—
374#95—31no—
375#95—92no—
376#95—91no—
377#95D3211yescharacteristic, complemented
378C23×C3—21no—
379C23×C3—32no—
380C23×C3—34no—
381C23×C3—34no—
382C23×C3—32no—
383C23×C3—32no—
384C23×C3—34no—
385C23×C3—32no—
386C23×C3—62no—
387C23×C3—61no—
388C23×C3—61no—
389C23×C3C23×D311yescharacteristic
390C23×C3C23×D311yescharacteristic
391C22×D3—22no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—34no—
395C22×D3—34no—
396C22×D3—32no—
397C22×D3—32no—
398C22×D3—316no—
399C22×D3—316no—
400C22×D3—64no—
401C22×D3—62no—
402C22×D3—68no—
403C22×D3—68no—
404C22×D3—616no—
405C22×D3—616no—
406C22×D3—62no—
407C22×D3—62no—
408C22×D3—61no—
409C22×D3—61no—
410C22×D3—61no—
411C22×D3—61no—
412C22×D3—68no—
413C22×D3—616no—
414C22×D3—68no—
415C22×D3—616no—
416C22×D3—122no—
417C22×D3—121no—
418C22×D3—121no—
419C22×D3C2×C4×D314yes—
420C22×D3C2×C4×D312yes—
421C22×D3C2×C4×D312yes—
422C22×D3C2×C4×D314yes—
423C22×D3D3×D414yes—
424C22×D3#23712yes—
425C22×D3#23912yes—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—24no—
434C2×C3×C4—32no—
435C2×C3×C4—34no—
436C2×C3×C4—32no—
437C2×C3×C4—34no—
438C2×C3×C4—34no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—42no—
442C2×C3×C4—68no—
443C2×C3×C4—68no—
444C2×C3×C4—616no—
445C2×C3×C4—62no—
446C2×C3×C4—62no—
447C2×C3×C4—62no—
448C2×C3×C4—62no—
449C2×C3×C4—62no—
450C2×C3×C4C2×C4×D312yes—
451C2×C3×C4C2×C4×D312yes—
452C2×C3×C4C2×C4×D314yescomplemented
453C2×C3×C4C2×C4×D314yescomplemented
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—32no—
460C2×Dic3—32no—
461C2×Dic3—34no—
462C2×Dic3—34no—
463C2×Dic3—316no—
464C2×Dic3—34no—
465C2×Dic3—34no—
466C2×Dic3—62no—
467C2×Dic3—64no—
468C2×Dic3—64no—
469C2×Dic3—68no—
470C2×Dic3—616no—
471C2×Dic3—62no—
472C2×Dic3—62no—
473C2×Dic3—62no—
474C2×Dic3—62no—
475C2×Dic3—122no—
476C2×Dic3—122no—
477C2×Dic3C2×C4×D312yes—
478C2×Dic3C2×C4×D312yes—
479C2×Dic3C2×C4×D314yescomplemented
480C2×Dic3C2×C4×D314yescomplemented
481C2×Dic3D3×D414yes—
482C4×D3—28no—
483C4×D3—216no—
484C4×D3—28no—
485C4×D3—316no—
486C4×D3—68no—
487C4×D3—68no—
488C4×D3—68no—
489C4×D3—68no—
490C4×D3—616no—
491C4×D3—68no—
492C4×D3—128no—
493C2×C32C22×C4211yescharacteristic
494C2×C32C22×C22⋊C411yescharacteristic
495C2×C32C2×#11711yescharacteristic
496C2×C32C2×C4×D412yes—
497C2×C32C2×C4×D412yes—
498C3⋊D3—24no—
499C3×D3—24no—
500C3×D3C4×C22⋊C418yescomplemented
501C24—31no—
502C24—31no—
503C24—98no—
504C24—94no—
505C24—91no—
506C24—184no—
507C24—182no—
508C24—182no—
509C22×C4—31no—
510C22×C4—31no—
511C22×C4—32no—
512C22×C4—32no—
513C22×C4—34no—
514C22×C4—34no—
515C22×C4—38no—
516C22×C4—64no—
517C22×C4—64no—
518C22×C4—64no—
519C22×C4—64no—
520C22×C4—94no—
521C22×C4—98no—
522C22×C4—94no—
523C22×C4—98no—
524C22×C4—94no—
525C22×C4—91no—
526C22×C4—92no—
527C22×C4—94no—
528C22×C4—184no—
529C22×C4—184no—
530C22×C4—1832no—
531C22×C4—184no—
532C22×C4—184no—
533C22×C4—184no—
534C22×C4C2×D3211yescharacteristic
535C22×C4C2×D3212yes—
536C22⋊C4—38no—
537C22⋊C4—98no—
538C22⋊C4—98no—
539C22⋊C4—98no—
540C42—64no—
541C42—184no—
542C42—184no—
543C42—184no—
544C22×C3—21no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—34no—
550C22×C3—34no—
551C22×C3—34no—
552C22×C3—38no—
553C22×C3—38no—
554C22×C3—34no—
555C22×C3—62no—
556C22×C3—64no—
557C22×C3—62no—
558C22×C3—64no—
559C22×C3C22×C4×D311yescharacteristic
560C22×C3C22×C4×D311yescharacteristic
561C22×C3C22×C4×D312yes—
562C22×C3C22×C4×D312yes—
563C22×C3C2×D3×D412yes—
564C22×C3C2×D3×D412yes—
565C22×C3C2×#23711yescharacteristic
566C22×C3C2×#23911yescharacteristic
567C22×C3D3×#4111yescharacteristic
568C22×C3D3×#4111yescharacteristic
569C2×D3—22no—
570C2×D3—22no—
571C2×D3—24no—
572C2×D3—24no—
573C2×D3—34no—
574C2×D3—34no—
575C2×D3—64no—
576C2×D3—632no—
577C2×D3—62no—
578C2×D3—62no—
579C2×D3—64no—
580C2×D3—62no—
581C2×D3—64no—
582C2×D3—62no—
583C2×D3—64no—
584C2×D3—64no—
585C2×D3—632no—
586C2×D3—122no—
587C2×D3—122no—
588C2×D3—124no—
589C2×D3—124no—
590C2×D3C42×D314yes—
591C2×D3C42×D314yescomplemented
592C2×D3D3×C22⋊C414yes—
593C2×D3#67⋊C418yes—
594C2×D3#89214yes—
595C2×D3#89318yes—
596C3×C4—22no—
597C3×C4—22no—
598C3×C4—24no—
599C3×C4—24no—
600C3×C4—34no—
601C3×C4—42no—
602C3×C4—44no—
603C3×C4—62no—
604C3×C4—64no—
605C3×C4—64no—
606Dic3—22no—
607Dic3—24no—
608Dic3—24no—
609Dic3—34no—
610Dic3—34no—
611Dic3—64no—
612Dic3—64no—
613Dic3—64no—
614Dic3—124no—
615Dic3D3×C22⋊C414yescomplemented
616C32C2×C4×C22⋊C411yescharacteristic, complemented, Sylow
617C23—32no—
618C23—34no—
619C23—34no—
620C23—32no—
621C23—32no—
622C23—34no—
623C23—32no—
624C23—62no—
625C23—61no—
626C23—61no—
627C23—916no—
628C23—94no—
629C23—92no—
630C23—188no—
631C23—188no—
632C23—1816no—
633C23—1816no—
634C23—182no—
635C23—181no—
636C23—181no—
637C23C22×D3211yescharacteristic
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—32no—
642C2×C4—34no—
643C2×C4—34no—
644C2×C4—34no—
645C2×C4—32no—
646C2×C4—68no—
647C2×C4—68no—
648C2×C4—616no—
649C2×C4—62no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—62no—
653C2×C4—62no—
654C2×C4—916no—
655C2×C4—92no—
656C2×C4—94no—
657C2×C4—94no—
658C2×C4—188no—
659C2×C4—188no—
660C2×C4—188no—
661C2×C4—1816no—
662C2×C4—182no—
663C2×C4—182no—
664C2×C4C4×D3212yes—
665C2×C4C4×D3214yescomplemented
666C2×C3—21no—
667C2×C3—22no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—22no—
671C2×C3—38no—
672C2×C3—64no—
673C2×C3C2×C42×D311yescharacteristic
674C2×C3C2×C42×D311yescharacteristic
675C2×C3C2×D3×C22⋊C411yescharacteristic
676C2×C3C2×D3×C22⋊C411yescharacteristic
677C2×C3C2×#67⋊C412yes—
678C2×C3C2×#89211yescharacteristic
679C2×C3C2×#89312yes—
680C2×C3D3×#11711yescharacteristic
681C2×C3C4×D3×D412yes—
682C2×C3C4×D3×D412yes—
683D3—24no—
684D3—64no—
685D3—64no—
686D3—124no—
687D3#466618yesdirect product factor
688C22—34no—
689C22—38no—
690C22—34no—
691C22—34no—
692C22—38no—
693C22—34no—
694C22—62no—
695C22—64no—
696C22—62no—
697C22—64no—
698C22—94no—
699C22—1832no—
700C22—182no—
701C22—184no—
702C22—182no—
703C22—184no—
704C22C2×C4×D3211yescharacteristic
705C22C2×C4×D3212yes—
706C22D32×D412yes—
707C22D3×#23711yescharacteristic
708C22D3×#23911yescharacteristic
709C4—22no—
710C4—24no—
711C4—34no—
712C4—64no—
713C4—62no—
714C4—64no—
715C4—94no—
716C4—184no—
717C3—21no—
718C3C2×#466611yescharacteristic, complemented
719C3C4×D3×C22⋊C411yescharacteristic, complemented
720C2—38no—
721C2—64no—
722C2—184no—
723C2C42×D3211yescharacteristic
724C2D32×C22⋊C411yescharacteristic
725C2D3×#67⋊C412yes—
726C2D3×#89211yescharacteristic
727C2D3×#89312yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×D32C22
hypercenter#95D32
hypocenterC32C2×C4×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C2×C4×D3×Dic3C2semidirect
4. #10592365C2semidirect
5. C3×#4666C2semidirect
6. C3×D3×#95C2semidirect
7. #10591368C2semidirect
8. D3×C3⋊#95C2semidirect
9. #10591260C2semidirect
10. #10591237C2semidirect
11. #10591233C2semidirect
24. C2×C4×D32C4semidirect
26. C2×C4×C3⋊Dic3C22semidirect
28. C2×C3×C4×Dic3C22semidirect
31. C2×Dic32C22semidirect
32. C2×Dic32C22semidirect
33. D3×(C2×D3)⋊C4C4semidirect
35. C32×#95C22semidirect
36. #63658C22semidirect
37. C3×C3⋊#95C22semidirect
38. C3×C3⋊#95C22semidirect
39. C3×C3⋊#95C22semidirect
40. #63579C22semidirect
61. #4666D3direct (N × H)
63. D3×#95D3semidirect
77. C2×C4×C3⋊D3C2×C4semidirect
87. C2×C3×C4×D3C2×C4semidirect
88. C2×C3×C4×D3C2×C4semidirect
90. C2×#624C2×C4semidirect
95. C2×D3×Dic3C2×C4semidirect
96. C2×D3×Dic3C2×C4semidirect
99. #3752C2×C4semidirect
101. C3×(C2×D3)⋊C4C2×C4semidirect
103. #3722C2×C4semidirect
104. (C2×D3)⋊Dic3C2×C4semidirect
150. C2×C4×Dic3C2×D3semidirect
157. C3×#95C2×D3semidirect
158. C3×#95C2×D3semidirect
164. C3⋊#95C2×D3semidirect
165. C3⋊#95C2×D3semidirect
166. C3⋊#95C2×D3semidirect
187. C2×D32C42semidirect
192. C2×C32×C4C22×C4semidirect
196. C2×C3⋊Dic3C22×C4semidirect
206. C2×C3×Dic3C22×C4semidirect
207. C2×C3×Dic3C22×C4semidirect
215. D3×Dic3C22⋊C4semidirect
302. C2×C4×D3C4×D3semidirect
303. C2×C4×D3C4×D3semidirect
313. (C2×D3)⋊C4C4×D3semidirect
331. C2×C3⋊D3C2×C42semidirect
337. C2×C3×D3C2×C42semidirect
346. C3⋊Dic3C2×C22⋊C4semidirect
350. C3×Dic3C2×C22⋊C4semidirect
377. #95D32semidirect
452. C2×C3×C4C2×C4×D3semidirect
453. C2×C3×C4C2×C4×D3semidirect
479. C2×Dic3C2×C4×D3semidirect
480. C2×Dic3C2×C4×D3semidirect
500. C3×D3C4×C22⋊C4semidirect
591. C2×D3C42×D3semidirect
615. Dic3D3×C22⋊C4semidirect
616. C32C2×C4×C22⋊C4semidirect
665. C2×C4C4×D32semidirect
687. D3#4666direct (N × H)
718. C3C2×#4666semidirect
719. C3C4×D3×C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D322
C2×D3×(C2×D3)⋊C42
C2×C4×D3×Dic32
#105923652
C3×#46662
C3×D3×#952
#105913682
D3×C3⋊#952
#105912602
#105912372
#105912332
C4×D3×C22⋊C43
C2×#46663