Finite Group Databasebeta

← #11836026

Subgroups — #11836026

Order 1152.

2796 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic, complemented
2C2×#64146C211yesmaximal, characteristic, complemented
3C2×#64104C211yesmaximal, characteristic, complemented
4C2×#64093C211yesmaximal, characteristic, complemented
5C2×#64091C211yesmaximal, characteristic, complemented
6C2×#64091C211yesmaximal, characteristic, complemented
7C32×#394C211yesmaximal, characteristic, complemented
8#10592689C211yesmaximal, characteristic, complemented
9#10592659C211yesmaximal, characteristic, complemented
10#10592659C211yesmaximal, characteristic, complemented
11#10592659C211yesmaximal, characteristic, complemented
12#10592658C211yesmaximal, characteristic, complemented
13#10592655C211yesmaximal, characteristic, complemented
14#10592370C211yesmaximal, characteristic, complemented
15#10592368C211yesmaximal, characteristic, complemented
16#77128—34nomaximal
17C24×C3⋊D3C2211yescharacteristic
18C22×C32×D4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic
23C22×#638C2211yescharacteristic, complemented
24C22×#638C2211yescharacteristic, complemented
25C22×C4⋊(C3⋊D3)C2211yescharacteristic
26C22×C4⋊(C3⋊D3)C2211yescharacteristic
27C22×C4⋊(C3⋊D3)C2211yescharacteristic
28C22×C4⋊(C3⋊D3)C2211yescharacteristic
29C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
30C22×C4×C3⋊D3C2211yescharacteristic, complemented
31C2×C32×C4⋊C4C2211yescharacteristic, complemented
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×C32×C22⋊C4C2211yescharacteristic
34C2×C32×C22⋊C4C2211yescharacteristic, complemented
35C2×C32×C22⋊C4C2211yescharacteristic, complemented
36C2×#3757C2211yescharacteristic
37#64149—24no—
38#64146—24no—
39C2×#3752C2211yescharacteristic
40C2×#3752C2211yescharacteristic
41C2×#3752C2211yescharacteristic
42C2×#3752C2211yescharacteristic
43C2×#3752C2211yescharacteristic
44C2×#3752C2211yescharacteristic
45C2×#3752C2211yescharacteristic, complemented
46C2×#3752C2211yescharacteristic, complemented
47C2×#3752C2211yescharacteristic, complemented
48C2×#3750C2211yescharacteristic, complemented
49C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
50#64104—24no—
51#64093—24no—
52#64091—24no—
53#64091—24no—
54C32×#95C2211yescharacteristic, complemented
55#63658C2211yescharacteristic, complemented
56#63658C2211yescharacteristic, complemented
57#63658C2211yescharacteristic, complemented
58C2×#940—34no—
59C2×#937—34no—
60C2×#895—34no—
61C2×#884—34no—
62C2×#882—34no—
63C2×#882—34no—
64C3×#394D314yescomplemented
65#4990—34no—
66#4960—34no—
67#4960—34no—
68#4960—34no—
69#4959—34no—
70#4956—34no—
71#4671—34no—
72#4669—34no—
73C24×C32C2311yescharacteristic
74C24×C32C2311yescharacteristic
75C23×C3⋊D3—22no—
76C23×C3⋊D3—22no—
77C23×C3⋊D3—22no—
78C23×C3⋊D3—41no—
79C23×C3⋊D3—41no—
80C23×C3⋊D3—41no—
81C23×C3⋊D3—41no—
82C23×C3⋊D3C2311yescharacteristic
83C23×C3⋊D3C2311yescharacteristic
84C23×C3⋊D3C2311yescharacteristic
85C23×C3⋊D3C2311yescharacteristic
86C2×C32×D4—22no—
87C2×C32×D4—22no—
88C2×C32×D4—41no—
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638—22no—
95C2×#638—22no—
96C2×#638—22no—
97C2×#638—22no—
98C2×#638—22no—
99C2×#638—22no—
100C2×#638—22no—
101C2×#638—22no—
102C2×#638—41no—
103C2×#638—41no—
104C2×#638—41no—
105C2×#638—41no—
106C2×#638—41no—
107C2×#638—41no—
108C2×#638—41no—
109C2×#638—41no—
110C2×#638—41no—
111C2×#638D414yescomplemented
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C2×C4⋊(C3⋊D3)—22no—
117C2×C4⋊(C3⋊D3)—22no—
118C2×C4⋊(C3⋊D3)—22no—
119C2×C4⋊(C3⋊D3)—22no—
120C2×C4⋊(C3⋊D3)—22no—
121C2×C4⋊(C3⋊D3)—22no—
122C2×C4⋊(C3⋊D3)—22no—
123C2×C4⋊(C3⋊D3)—22no—
124C2×C4⋊(C3⋊D3)—22no—
125C2×C4⋊(C3⋊D3)—41no—
126C2×C4⋊(C3⋊D3)—41no—
127C2×C4⋊(C3⋊D3)—41no—
128C2×C4⋊(C3⋊D3)—41no—
129C2×C4⋊(C3⋊D3)—41no—
130C2×C4⋊(C3⋊D3)—41no—
131C2×C4×C3⋊D3—22no—
132C2×C4×C3⋊D3—22no—
133C2×C4×C3⋊D3—41no—
134C32×C4⋊C4—22no—
135C32×C22⋊C4—22no—
136C32×C22⋊C4—22no—
137C32×C22⋊C4—22no—
138C32×C22⋊C4—41no—
139#3757—22no—
140#3752—22no—
141#3752—22no—
142#3752—22no—
143#3752—22no—
144#3752—22no—
145#3752—41no—
146#3752—41no—
147#3752D414yescomplemented
148#3752D414yescomplemented
149#3750—22no—
150C4×C3⋊Dic3—22no—
151#2669—91noSylow
152C24×D3—34no—
153C22×C3×D4C2×D314yes—
154C22×#67—34no—
155C22×#67—34no—
156C22×#67—34no—
157C22×#67—34no—
158C22×#67—34no—
159C22×#67—34no—
160C22×D12—34no—
161C22×D12—34no—
162C22×D12—34no—
163C22×D12—34no—
164C22×D12—34no—
165C22×C4×D3—34no—
166C2×C3×C4⋊C4C2×D314yescomplemented
167C2×C3×C22⋊C4C2×D314yes—
168C2×C3×C22⋊C4C2×D314yes—
169C2×C3×C22⋊C4C2×D314yescomplemented
170C2×C3×C22⋊C4C2×D314yescomplemented
171C2×#217—34no—
172#940—616no—
173#937—616no—
174C2×(C2×D3)⋊C4—34no—
175C2×(C2×D3)⋊C4—34no—
176C2×(C2×D3)⋊C4—34no—
177C2×(C2×D3)⋊C4—34no—
178C2×(C2×D3)⋊C4—34no—
179C2×(C2×D3)⋊C4—34no—
180C2×(C2×D3)⋊C4—34no—
181C2×(C2×D3)⋊C4—34no—
182C2×(C2×D3)⋊C4—34no—
183C2×Dic3⋊C4—34no—
184C2×C4×Dic3—34no—
185#895—616no—
186#884—616no—
187#882—616no—
188#882—616no—
189C3×#95C2×D314yescomplemented
190C3⋊#95—34no—
191C3⋊#95—34no—
192C3⋊#95—34no—
193C23×C32—21no—
194C23×C32—21no—
195C23×C32—21no—
196C23×C32—21no—
197C23×C32—21no—
198C23×C32—21no—
199C23×C32—21no—
200C23×C32—21no—
201C23×C32—21no—
202C23×C32—21no—
203C23×C32—21no—
204C23×C32—21no—
205C23×C32—21no—
206C23×C32C2×D412yes—
207C23×C32C2411yescharacteristic
208C22×C3⋊D3—21no—
209C22×C3⋊D3—21no—
210C22×C3⋊D3—21no—
211C22×C3⋊D3—21no—
212C22×C3⋊D3—21no—
213C22×C3⋊D3—21no—
214C22×C3⋊D3—21no—
215C22×C3⋊D3—21no—
216C22×C3⋊D3—21no—
217C22×C3⋊D3—21no—
218C22×C3⋊D3—21no—
219C22×C3⋊D3—21no—
220C22×C3⋊D3—21no—
221C22×C3⋊D3—21no—
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3—21no—
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—44no—
234C22×C3⋊D3—44no—
235C22×C3⋊D3—44no—
236C22×C3⋊D3—44no—
237C22×C3⋊D3—44no—
238C22×C3⋊D3—44no—
239C22×C3⋊D3—44no—
240C22×C3⋊D3C2×D412yes—
241C22×C3⋊D3C2×D412yes—
242C22×C3⋊D3C2×D412yes—
243C32×D4—44no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C2×D412yes—
258C2×C32×C4C2×D412yes—
259#638—44no—
260#638—44no—
261#638—44no—
262#638—44no—
263#638—44no—
264#638—44no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3C2×D412yes—
275C2×C3⋊Dic3C2×D412yes—
276C2×C3⋊Dic3C2×D412yes—
277C4⋊(C3⋊D3)—44no—
278C4⋊(C3⋊D3)—44no—
279C4⋊(C3⋊D3)—44no—
280C4⋊(C3⋊D3)—44no—
281C4⋊(C3⋊D3)—44no—
282C4×C3⋊D3—44no—
283C2×#127—91no—
284C2×#121—91no—
285C2×#121—91no—
286C2×#120—91no—
287C2×#120—91no—
288C2×#120—91no—
289#394—91no—
290#394C3⋊D311yescharacteristic, complemented
291#392—91no—
292#392—91no—
293#392—91no—
294#392—91no—
295#388—91no—
296#388—91no—
297#386—91no—
298C24×C3C22×D314yes—
299C24×C3C22×D314yes—
300C23×D3—34no—
301C23×D3—34no—
302C23×D3—34no—
303C23×D3—34no—
304C23×D3—68no—
305C23×D3—68no—
306C23×D3—68no—
307C23×D3—124no—
308C23×D3—124no—
309C23×D3—124no—
310C23×D3—124no—
311C2×C3×D4—28no—
312C2×C3×D4—28no—
313C2×C3×D4—44no—
314C22×C3×C4C22×D314yes—
315C22×C3×C4C22×D314yes—
316C22×C3×C4C22×D314yes—
317C22×C3×C4C22×D314yes—
318C22×C3×C4C22×D314yes—
319C2×#67—316no—
320C2×#67—68no—
321C2×#67—68no—
322C2×#67—68no—
323C2×#67—68no—
324C2×#67—68no—
325C2×#67—68no—
326C2×#67—68no—
327C2×#67—68no—
328C2×#67—124no—
329C2×#67—124no—
330C2×#67—124no—
331C2×#67—124no—
332C2×#67—124no—
333C2×#67—124no—
334C2×#67—124no—
335C2×#67—124no—
336C2×#67—124no—
337C22×Dic3—34no—
338C22×Dic3—34no—
339C22×Dic3—34no—
340C22×Dic3—34no—
341C2×D12—68no—
342C2×D12—68no—
343C2×D12—68no—
344C2×D12—68no—
345C2×D12—68no—
346C2×D12—68no—
347C2×D12—68no—
348C2×D12—68no—
349C2×D12—68no—
350C2×D12—124no—
351C2×D12—124no—
352C2×D12—124no—
353C2×D12—124no—
354C2×D12—124no—
355C2×D12—124no—
356C2×C4×D3—68no—
357C2×C4×D3—68no—
358C2×C4×D3—124no—
359C3×C4⋊C4—28no—
360C3×C22⋊C4—28no—
361C3×C22⋊C4—28no—
362C3×C22⋊C4—28no—
363C3×C22⋊C4—44no—
364#217—68no—
365(C2×D3)⋊C4—316no—
366(C2×D3)⋊C4—316no—
367(C2×D3)⋊C4—68no—
368(C2×D3)⋊C4—68no—
369(C2×D3)⋊C4—68no—
370(C2×D3)⋊C4—68no—
371(C2×D3)⋊C4—68no—
372(C2×D3)⋊C4—124no—
373(C2×D3)⋊C4—124no—
374Dic3⋊C4—68no—
375C4×Dic3—68no—
376C22×C32—22no—
377C22×C32—22no—
378C22×C32—22no—
379C22×C32—41no—
380C22×C32—41no—
381C22×C32—41no—
382C22×C32—41no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32—41no—
389C22×C32—41no—
390C22×C32C22×D411yescharacteristic
391C22×C32C22×D411yescharacteristic
392C22×C32C22×D411yescharacteristic
393C22×C32H(5,𝔽2)11yescharacteristic
394C22×C32H(5,𝔽2)11yescharacteristic
395C22×C32H(5,𝔽2)11yescharacteristic
396C22×C32H(5,𝔽2)11yescharacteristic
397C2×C3⋊D3—22no—
398C2×C3⋊D3—22no—
399C2×C3⋊D3—22no—
400C2×C3⋊D3—22no—
401C2×C3⋊D3—22no—
402C2×C3⋊D3—22no—
403C2×C3⋊D3—22no—
404C2×C3⋊D3—22no—
405C2×C3⋊D3—22no—
406C2×C3⋊D3—416no—
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C32×C4—22no—
427C32×C4—22no—
428C32×C4—41no—
429C32×C4—41no—
430C32×C4—41no—
431C3⋊Dic3—22no—
432C3⋊Dic3—22no—
433C3⋊Dic3—22no—
434C3⋊Dic3—41no—
435C25—91no—
436C22×D4—91no—
437C22×D4—91no—
438C22×D4—91no—
439C22×D4—91no—
440C22×D4—91no—
441C22×D4—91no—
442C22×D4—91no—
443C22×D4—91no—
444C22×D4—91no—
445C22×D4—91no—
446C22×D4—91no—
447C22×D4C2×C3⋊D311yescharacteristic
448C23×C4—91no—
449#127—184no—
450#121—184no—
451#121—184no—
452#120—184no—
453#120—184no—
454#120—184no—
455C2×C4⋊C4—91no—
456C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
457C2×C22⋊C4—91no—
458C2×C22⋊C4—91no—
459C2×C22⋊C4—91no—
460C2×C22⋊C4—91no—
461C2×C22⋊C4—91no—
462C2×C22⋊C4—91no—
463C2×C22⋊C4—91no—
464C2×C22⋊C4—91no—
465C2×C22⋊C4—91no—
466C2×C22⋊C4—91no—
467C2×C22⋊C4C2×C3⋊D311yescharacteristic
468C2×C22⋊C4C2×C3⋊D311yescharacteristic
469C2×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
470C2×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
471C2×C42—91no—
472#95—91no—
473#95—91no—
474#95—91no—
475#95C2×C3⋊D311yescharacteristic, complemented
476C23×C3—24no—
477C23×C3—24no—
478C23×C3—24no—
479C23×C3—24no—
480C23×C3—24no—
481C23×C3—24no—
482C23×C3—24no—
483C23×C3—24no—
484C23×C3—24no—
485C23×C3—24no—
486C23×C3—24no—
487C23×C3—24no—
488C23×C3—24no—
489C23×C3D3×D418yes—
490C23×C3C23×D314yes—
491C22×D3—38no—
492C22×D3—38no—
493C22×D3—38no—
494C22×D3—64no—
495C22×D3—64no—
496C22×D3—64no—
497C22×D3—64no—
498C22×D3—64no—
499C22×D3—64no—
500C22×D3—64no—
501C22×D3—64no—
502C22×D3—64no—
503C22×D3—64no—
504C22×D3—64no—
505C22×D3—64no—
506C22×D3—64no—
507C22×D3—64no—
508C22×D3—64no—
509C22×D3—64no—
510C22×D3—64no—
511C22×D3—64no—
512C22×D3—64no—
513C22×D3—64no—
514C22×D3—64no—
515C22×D3—64no—
516C22×D3—64no—
517C22×D3—64no—
518C22×D3—64no—
519C22×D3—1216no—
520C22×D3—1216no—
521C22×D3—1216no—
522C22×D3—1216no—
523C22×D3—1216no—
524C22×D3—1216no—
525C22×D3—1216no—
526C3×D4—416no—
527C2×C3×C4—24no—
528C2×C3×C4—24no—
529C2×C3×C4—24no—
530C2×C3×C4—24no—
531C2×C3×C4—24no—
532C2×C3×C4—24no—
533C2×C3×C4—24no—
534C2×C3×C4—24no—
535C2×C3×C4—24no—
536C2×C3×C4—24no—
537C2×C3×C4—24no—
538C2×C3×C4—24no—
539C2×C3×C4—24no—
540C2×C3×C4D3×D418yes—
541C2×C3×C4D3×D418yes—
542#67—1216no—
543#67—1216no—
544#67—1216no—
545#67—1216no—
546#67—1216no—
547#67—1216no—
548C2×Dic3—38no—
549C2×Dic3—38no—
550C2×Dic3—38no—
551C2×Dic3—64no—
552C2×Dic3—64no—
553C2×Dic3—64no—
554C2×Dic3—64no—
555C2×Dic3—64no—
556C2×Dic3—64no—
557C2×Dic3—64no—
558C2×Dic3—64no—
559C2×Dic3—64no—
560D12—1216no—
561D12—1216no—
562D12—1216no—
563D12—1216no—
564D12—1216no—
565C4×D3—1216no—
566C2×C32—42no—
567C2×C32—81no—
568C2×C32#53411yescharacteristic
569C2×C32#53511yescharacteristic
570C2×C32#53511yescharacteristic
571C2×C32D4211yescharacteristic
572C2×C32D4211yescharacteristic
573C2×C32D4211yescharacteristic
574C2×C32#56011yescharacteristic
575C3⋊D3—42no—
576C3⋊D3—42no—
577C3⋊D3—42no—
578C3⋊D3—81no—
579C24—91no—
580C24—91no—
581C24—91no—
582C24—91no—
583C24—182no—
584C24—182no—
585C24—182no—
586C24—361no—
587C24—361no—
588C24—361no—
589C24—361no—
590C24C22×C3⋊D311yescharacteristic
591C24C22×C3⋊D311yescharacteristic
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—41no—
595C2×D4—94no—
596C2×D4—182no—
597C2×D4—182no—
598C2×D4—182no—
599C2×D4—182no—
600C2×D4—182no—
601C2×D4—182no—
602C2×D4—182no—
603C2×D4—182no—
604C2×D4—182no—
605C2×D4—182no—
606C2×D4—182no—
607C2×D4—182no—
608C2×D4—182no—
609C2×D4—182no—
610C2×D4—182no—
611C2×D4—182no—
612C2×D4—182no—
613C2×D4—361no—
614C2×D4—361no—
615C2×D4—361no—
616C2×D4—361no—
617C2×D4—361no—
618C2×D4—361no—
619C2×D4—361no—
620C2×D4—361no—
621C2×D4—361no—
622C2×D4—361no—
623C2×D4—361no—
624C2×D4—361no—
625C2×D4—361no—
626C2×D4—361no—
627C2×D4—361no—
628C22×C4—91no—
629C22×C4—91no—
630C22×C4—91no—
631C22×C4—91no—
632C22×C4—182no—
633C22×C4—182no—
634C22×C4—361no—
635C22×C4C22×C3⋊D311yescharacteristic
636C22×C4C22×C3⋊D311yescharacteristic
637C22×C4C22×C3⋊D311yescharacteristic
638C22×C4C22×C3⋊D311yescharacteristic
639C22×C4C22×C3⋊D311yescharacteristic
640C4⋊C4—22no—
641C4⋊C4—182no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—41no—
646C22⋊C4—94no—
647C22⋊C4—94no—
648C22⋊C4—182no—
649C22⋊C4—182no—
650C22⋊C4—182no—
651C22⋊C4—182no—
652C22⋊C4—182no—
653C22⋊C4—182no—
654C22⋊C4—361no—
655C22⋊C4—361no—
656C42—182no—
657C22×C3—28no—
658C22×C3—28no—
659C22×C3—28no—
660C22×C3—44no—
661C22×C3—44no—
662C22×C3—44no—
663C22×C3—44no—
664C22×C3—44no—
665C22×C3—44no—
666C22×C3—44no—
667C22×C3—44no—
668C22×C3—44no—
669C22×C3—44no—
670C22×C3—44no—
671C22×C3C2×D3×D414yes—
672C22×C3C2×D3×D414yes—
673C22×C3C2×D3×D414yes—
674C22×C3#100414yes—
675C22×C3#100914yes—
676C22×C3#100914yes—
677C22×C3#100914yes—
678C2×D3—68no—
679C2×D3—68no—
680C2×D3—68no—
681C2×D3—68no—
682C2×D3—68no—
683C2×D3—68no—
684C2×D3—68no—
685C2×D3—68no—
686C2×D3—68no—
687C2×D3—1264no—
688C2×D3—124no—
689C2×D3—124no—
690C2×D3—124no—
691C2×D3—124no—
692C2×D3—124no—
693C2×D3—124no—
694C2×D3—124no—
695C2×D3—124no—
696C2×D3—124no—
697C2×D3—124no—
698C2×D3—124no—
699C2×D3—124no—
700C2×D3—124no—
701C2×D3—124no—
702C2×D3—124no—
703C2×D3—124no—
704C2×D3—124no—
705C2×D3—124no—
706C2×D3—124no—
707C3×C4—28no—
708C3×C4—28no—
709C3×C4—44no—
710C3×C4—44no—
711C3×C4—44no—
712Dic3—68no—
713Dic3—68no—
714Dic3—68no—
715Dic3—124no—
716C32#266911yescharacteristic, complemented, Sylow
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—92no—
731C23—92no—
732C23—92no—
733C23—181no—
734C23—181no—
735C23—181no—
736C23—181no—
737C23—181no—
738C23—181no—
739C23—181no—
740C23—181no—
741C23—181no—
742C23—181no—
743C23—181no—
744C23—181no—
745C23—181no—
746C23—181no—
747C23—181no—
748C23—181no—
749C23—181no—
750C23—181no—
751C23—181no—
752C23—181no—
753C23—181no—
754C23—181no—
755C23—181no—
756C23—181no—
757C23—181no—
758C23—364no—
759C23—364no—
760C23—364no—
761C23—364no—
762C23—364no—
763C23—364no—
764C23—364no—
765C23D4×C3⋊D312yes—
766C23C23×C3⋊D311yescharacteristic
767D4—44no—
768D4—364no—
769D4—364no—
770D4—364no—
771D4—364no—
772D4—364no—
773D4—364no—
774D4—364no—
775D4—364no—
776D4—364no—
777D4—364no—
778D4—364no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—92no—
793C2×C4—92no—
794C2×C4—92no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4—181no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4—181no—
801C2×C4—181no—
802C2×C4—181no—
803C2×C4—181no—
804C2×C4—364no—
805C2×C4D4×C3⋊D312yes—
806C2×C4D4×C3⋊D312yes—
807C2×C3—48no—
808C2×C3—84no—
809C2×C3#559014yes—
810C2×C3#560714yes—
811C2×C3#560914yes—
812C2×C3#560914yes—
813C2×C3#565314yes—
814C2×C3#566614yes—
815C2×C3#567414yes—
816D3—128no—
817D3—128no—
818D3—128no—
819D3—244no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—182no—
835C22—182no—
836C22—182no—
837C22—182no—
838C22—182no—
839C22—182no—
840C22—182no—
841C22—182no—
842C22—182no—
843C22—3616no—
844C22—361no—
845C22—361no—
846C22—361no—
847C22—361no—
848C22—361no—
849C22—361no—
850C22—361no—
851C22—361no—
852C22—361no—
853C22—361no—
854C22—361no—
855C22—361no—
856C22—361no—
857C22—361no—
858C22—361no—
859C22—361no—
860C22—361no—
861C22—361no—
862C22—361no—
863C22C2×D4×C3⋊D311yescharacteristic
864C22C2×D4×C3⋊D311yescharacteristic
865C22C2×D4×C3⋊D311yescharacteristic
866C22#6436111yescharacteristic
867C22#6436611yescharacteristic
868C22#6436611yescharacteristic
869C22#6436611yescharacteristic
870C4—22no—
871C4—22no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—182no—
876C4—182no—
877C4—182no—
878C4—361no—
879C3#7712814yescomplemented
880C2—42no—
881C2—81no—
882C2—362no—
883C2—362no—
884C2—362no—
885C2—721no—
886C2#1059606111yescharacteristic
887C2#1059607811yescharacteristic
888C2#1059608011yescharacteristic
889C2#1059608011yescharacteristic
890C2#1059612411yescharacteristic
891C2#1059613711yescharacteristic
892C2#1059614511yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#394C2
hypercenter#394C3⋊D3
hypocenterC32#2669
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#64149C2semidirect
2. C2×#64146C2semidirect
3. C2×#64104C2semidirect
4. C2×#64093C2semidirect
5. C2×#64091C2semidirect
6. C2×#64091C2semidirect
7. C32×#394C2semidirect
8. #10592689C2semidirect
9. #10592659C2semidirect
10. #10592659C2semidirect
11. #10592659C2semidirect
12. #10592658C2semidirect
13. #10592655C2semidirect
14. #10592370C2semidirect
15. #10592368C2semidirect
23. C22×#638C22semidirect
24. C22×#638C22semidirect
29. C22×C4⋊(C3⋊D3)C22semidirect
30. C22×C4×C3⋊D3C22semidirect
31. C2×C32×C4⋊C4C22semidirect
34. C2×C32×C22⋊C4C22semidirect
35. C2×C32×C22⋊C4C22semidirect
45. C2×#3752C22semidirect
46. C2×#3752C22semidirect
47. C2×#3752C22semidirect
48. C2×#3750C22semidirect
49. C2×C4×C3⋊Dic3C22semidirect
54. C32×#95C22semidirect
55. #63658C22semidirect
56. #63658C22semidirect
57. #63658C22semidirect
64. C3×#394D3semidirect
111. C2×#638D4semidirect
147. #3752D4semidirect
148. #3752D4semidirect
166. C2×C3×C4⋊C4C2×D3semidirect
169. C2×C3×C22⋊C4C2×D3semidirect
170. C2×C3×C22⋊C4C2×D3semidirect
189. C3×#95C2×D3semidirect
290. #394C3⋊D3semidirect
456. C2×C4⋊C4C2×C3⋊D3semidirect
469. C2×C22⋊C4C2×C3⋊D3semidirect
470. C2×C22⋊C4C2×C3⋊D3semidirect
475. #95C2×C3⋊D3semidirect
716. C32#2669semidirect
879. C3#77128semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
C2×#641462
C2×#641042
C2×#640932
C2×#640912
C32×#3942
#105926892
#105926592
#105926582
#105926552
#105923702
#105923682
#771283