Finite Group Databasebeta

← #11810281

Subgroups — #11810281

Order 1152.

2400 conjugacy classes of subgroups.

The subgroup lattice has 753 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64146C211yesmaximal, characteristic
2C2×#64095C211yesmaximal, characteristic, complemented
3C2×#64090C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
5C32×#394C211yesmaximal, characteristic, complemented
6#10592919C211yesmaximal, characteristic, complemented
7#10592689C211yesmaximal, characteristic, complemented
8#10592686C211yesmaximal, characteristic, complemented
9#10592658C211yesmaximal, characteristic, complemented
10#10592655C211yesmaximal, characteristic, complemented
11#10592654C211yesmaximal, characteristic, complemented
12#10592650C211yesmaximal, characteristic, complemented
13#10592648C211yesmaximal, characteristic, complemented
14#10592374C211yesmaximal, characteristic, complemented
15#10592367C211yesmaximal, characteristic, complemented
16#77112—34nomaximal
17C24×C3⋊D3C2211yescharacteristic
18C22×C32×D4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic, complemented
22C22×C4×C3⋊D3C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic, complemented
28C2×C32×C22⋊C4C2211yescharacteristic, complemented
29C2×#3757C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×#3757C2211yescharacteristic
32C2×#3757C2211yescharacteristic, complemented
33#64146—24no—
34C2×#3752C2211yescharacteristic
35C2×#3752C2211yescharacteristic
36C2×#3752C2211yescharacteristic
37C2×#3752C2211yescharacteristic
38C2×#3752C2211yescharacteristic
39C2×#3752C2211yescharacteristic
40C2×#3752C2211yescharacteristic
41C2×#3752C2211yescharacteristic
42C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44C2×#3750C2211yescharacteristic, complemented
45C2×#3750C2211yescharacteristic, complemented
46C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
47#64095—24no—
48#64090—24no—
49C22⋊C4×C3⋊D3—24no—
50C32×#95C2211yescharacteristic, complemented
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53#63658C2211yescharacteristic, complemented
54#63658C2211yescharacteristic, complemented
55#63658C2211yescharacteristic, complemented
56C2×#937—34no—
57C2×#886—34no—
58C2×#67⋊C4—34no—
59C2×D3×C22⋊C4—34no—
60C3×#394D314yescomplemented
61#5220—34no—
62#4990—34no—
63#4987—34no—
64#4959—34no—
65#4956—34no—
66#4955—34no—
67#4951—34no—
68#4949—34no—
69#4675—34no—
70#4668—34no—
71C24×C32C2311yescharacteristic
72C24×C32C2311yescharacteristic
73C23×C3⋊D3—22no—
74C23×C3⋊D3—22no—
75C23×C3⋊D3—22no—
76C23×C3⋊D3—22no—
77C23×C3⋊D3—22no—
78C23×C3⋊D3—41no—
79C23×C3⋊D3—41no—
80C23×C3⋊D3C2311yescharacteristic
81C23×C3⋊D3C2311yescharacteristic
82C2×C32×D4—22no—
83C2×C32×D4—22no—
84C2×C32×D4—41no—
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C2×#638—22no—
91C2×#638—22no—
92C2×#638—22no—
93C2×#638—22no—
94C2×#638—41no—
95C2×#638D414yes—
96C22×C3⋊Dic3—22no—
97C22×C3⋊Dic3—22no—
98C22×C3⋊Dic3—41no—
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C2×C4×C3⋊D3—22no—
106C2×C4×C3⋊D3—22no—
107C2×C4×C3⋊D3—22no—
108C2×C4×C3⋊D3—22no—
109C2×C4×C3⋊D3—41no—
110C2×C4×C3⋊D3—41no—
111C32×C4⋊C4—41no—
112C32×C22⋊C4—22no—
113C32×C22⋊C4—22no—
114C32×C22⋊C4—22no—
115C32×C22⋊C4—22no—
116#3757—22no—
117#3757—22no—
118#3757—41no—
119#3757—41no—
120#3752—22no—
121#3752—22no—
122#3752—22no—
123#3752—22no—
124#3752—22no—
125#3752—22no—
126#3752—41no—
127#3752D414yescomplemented
128C4⋊(C3⋊Dic3)—22no—
129C4⋊(C3⋊Dic3)—22no—
130#3750—22no—
131#3750—41no—
132C4×C3⋊Dic3—22no—
133#2418—91noSylow
134C24×D3—34no—
135C22×C3×D4C2×D314yes—
136C22×#67—34no—
137C22×#67—34no—
138C23×Dic3—34no—
139C22×C4×D3—34no—
140C22×C4×D3—34no—
141C2×C3×C4⋊C4C2×D314yescomplemented
142C2×C3×C22⋊C4C2×D314yes—
143C2×C3×C22⋊C4C2×D314yes—
144C2×C3×C22⋊C4C2×D314yescomplemented
145C2×C3×C22⋊C4C2×D314yescomplemented
146C2×#217—34no—
147C2×#217—34no—
148C2×#217—34no—
149C2×#217—34no—
150#937—616no—
151C2×(C2×D3)⋊C4—34no—
152C2×(C2×D3)⋊C4—34no—
153C2×(C2×D3)⋊C4—34no—
154C2×(C2×D3)⋊C4—34no—
155C2×(C2×D3)⋊C4—34no—
156C2×(C2×D3)⋊C4—34no—
157C2×(C2×D3)⋊C4—34no—
158C2×(C2×D3)⋊C4—34no—
159C2×C4⋊Dic3—34no—
160C2×C4⋊Dic3—34no—
161C2×Dic3⋊C4—34no—
162C2×Dic3⋊C4—34no—
163C2×C4×Dic3—34no—
164#886—616no—
165#67⋊C4—616no—
166D3×C22⋊C4—616no—
167C3×#95C2×D314yescomplemented
168C3⋊#95—34no—
169C3⋊#95—34no—
170C3⋊#95—34no—
171C3⋊#95—34no—
172C3⋊#95—34no—
173C23×C32—21no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—21no—
177C23×C32—21no—
178C23×C32—21no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—21no—
182C23×C32—21no—
183C23×C32—21no—
184C23×C32—21no—
185C23×C32C2×D412yes—
186C23×C32#4112yes—
187C23×C32C2411yescharacteristic
188C22×C3⋊D3—21no—
189C22×C3⋊D3—21no—
190C22×C3⋊D3—21no—
191C22×C3⋊D3—21no—
192C22×C3⋊D3—28no—
193C22×C3⋊D3—21no—
194C22×C3⋊D3—21no—
195C22×C3⋊D3—21no—
196C22×C3⋊D3—21no—
197C22×C3⋊D3—21no—
198C22×C3⋊D3—21no—
199C22×C3⋊D3—44no—
200C22×C3⋊D3—44no—
201C22×C3⋊D3—44no—
202C22×C3⋊D3—44no—
203C22×C3⋊D3—44no—
204C22×C3⋊D3—44no—
205C22×C3⋊D3C2×D412yes—
206C22×C3⋊D3C2×D412yes—
207C22×C3⋊D3#4112yes—
208C22×C3⋊D3#4112yes—
209C32×D4—44no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4C2×D412yes—
225#638—28no—
226#638—44no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—44no—
244C2×C3⋊Dic3C2×D412yes—
245C2×C3⋊Dic3C2×D412yes—
246C4×C3⋊D3—44no—
247C4×C3⋊D3—44no—
248C2×#123—91no—
249C2×#120—91no—
250C2×C4×D4—91no—
251C22×C22⋊C4—91no—
252#399—91no—
253#397—91no—
254#394—91no—
255#394C3⋊D311yescharacteristic, complemented
256#388—91no—
257#388—91no—
258#386—91no—
259#386—91no—
260#385—91no—
261#380—91no—
262#379—91no—
263C24×C3C22×D314yes—
264C24×C3C22×D314yes—
265C23×D3—34no—
266C23×D3—34no—
267C23×D3—68no—
268C23×D3—68no—
269C23×D3—68no—
270C23×D3—68no—
271C23×D3—68no—
272C23×D3—124no—
273C23×D3—124no—
274C2×C3×D4—28no—
275C2×C3×D4—28no—
276C2×C3×D4—44no—
277C22×C3×C4C22×D314yes—
278C22×C3×C4C22×D314yes—
279C22×C3×C4C22×D314yes—
280C22×C3×C4C22×D314yes—
281C22×C3×C4C22×D314yes—
282C2×#67—316no—
283C2×#67—68no—
284C2×#67—68no—
285C2×#67—68no—
286C2×#67—68no—
287C2×#67—124no—
288C22×Dic3—34no—
289C22×Dic3—34no—
290C22×Dic3—34no—
291C22×Dic3—34no—
292C22×Dic3—34no—
293C22×Dic3—34no—
294C22×Dic3—68no—
295C22×Dic3—68no—
296C22×Dic3—124no—
297C2×C4×D3—68no—
298C2×C4×D3—68no—
299C2×C4×D3—68no—
300C2×C4×D3—68no—
301C2×C4×D3—124no—
302C2×C4×D3—124no—
303C3×C4⋊C4—44no—
304C3×C22⋊C4—28no—
305C3×C22⋊C4—28no—
306C3×C22⋊C4—28no—
307C3×C22⋊C4—28no—
308#217—68no—
309#217—68no—
310#217—124no—
311#217—124no—
312(C2×D3)⋊C4—316no—
313(C2×D3)⋊C4—68no—
314(C2×D3)⋊C4—68no—
315(C2×D3)⋊C4—68no—
316(C2×D3)⋊C4—68no—
317(C2×D3)⋊C4—68no—
318(C2×D3)⋊C4—68no—
319(C2×D3)⋊C4—124no—
320C4⋊Dic3—68no—
321C4⋊Dic3—68no—
322Dic3⋊C4—68no—
323Dic3⋊C4—124no—
324C4×Dic3—68no—
325C22×C32—22no—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—22no—
331C22×C32—41no—
332C22×C32—41no—
333C22×C32—41no—
334C22×C32—41no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32—41no—
339C22×C32C22×D411yescharacteristic
340C22×C32C22×D411yescharacteristic
341C22×C32C2×#4111yescharacteristic
342C22×C32C2×#4111yescharacteristic
343C22×C32C2×#4111yescharacteristic
344C22×C32H(5,𝔽2)11yescharacteristic
345C22×C32H(5,𝔽2)11yescharacteristic
346C2×C3⋊D3—22no—
347C2×C3⋊D3—22no—
348C2×C3⋊D3—22no—
349C2×C3⋊D3—22no—
350C2×C3⋊D3—22no—
351C2×C3⋊D3—22no—
352C2×C3⋊D3—22no—
353C2×C3⋊D3—22no—
354C2×C3⋊D3—22no—
355C2×C3⋊D3—416no—
356C2×C3⋊D3—41no—
357C2×C3⋊D3—41no—
358C2×C3⋊D3—41no—
359C2×C3⋊D3—41no—
360C2×C3⋊D3#12314yescomplemented
361C32×C4—22no—
362C32×C4—41no—
363C32×C4—41no—
364C32×C4—41no—
365C32×C4—41no—
366C3⋊Dic3—22no—
367C3⋊Dic3—22no—
368C3⋊Dic3—41no—
369C3⋊Dic3—41no—
370C3⋊Dic3—41no—
371C3⋊Dic3—41no—
372C25—91no—
373C22×D4—91no—
374C22×D4—91no—
375C22×D4C2×C3⋊D311yescharacteristic
376C23×C4—91no—
377C23×C4—91no—
378C23×C4—91no—
379#123—184no—
380#120—184no—
381C4×D4—184no—
382C2×C4⋊C4—91no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4—91no—
385C2×C4⋊C4—91no—
386C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
387C2×C22⋊C4—91no—
388C2×C22⋊C4—91no—
389C2×C22⋊C4—91no—
390C2×C22⋊C4—91no—
391C2×C22⋊C4—91no—
392C2×C22⋊C4—91no—
393C2×C22⋊C4—91no—
394C2×C22⋊C4—91no—
395C2×C22⋊C4—91no—
396C2×C22⋊C4—91no—
397C2×C22⋊C4—91no—
398C2×C22⋊C4—91no—
399C2×C22⋊C4—184no—
400C2×C22⋊C4C2×C3⋊D311yescharacteristic
401C2×C22⋊C4C2×C3⋊D311yescharacteristic
402C2×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
403C2×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
404C2×C42—91no—
405#95—91no—
406#95—91no—
407#95—91no—
408#95—91no—
409#95—91no—
410#95C2×C3⋊D311yescharacteristic, complemented
411C23×C3—24no—
412C23×C3—24no—
413C23×C3—24no—
414C23×C3—24no—
415C23×C3—24no—
416C23×C3—24no—
417C23×C3—24no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—24no—
422C23×C3—24no—
423C23×C3D3×D418yes—
424C23×C3#23718yes—
425C23×C3C23×D314yes—
426C22×D3—38no—
427C22×D3—38no—
428C22×D3—38no—
429C22×D3—38no—
430C22×D3—64no—
431C22×D3—64no—
432C22×D3—64no—
433C22×D3—64no—
434C22×D3—632no—
435C22×D3—64no—
436C22×D3—64no—
437C22×D3—64no—
438C22×D3—64no—
439C22×D3—64no—
440C22×D3—64no—
441C22×D3—1216no—
442C22×D3—1216no—
443C22×D3—1216no—
444C22×D3—1216no—
445C22×D3—1216no—
446C22×D3—1216no—
447C3×D4—416no—
448C2×C3×C4—24no—
449C2×C3×C4—24no—
450C2×C3×C4—24no—
451C2×C3×C4—24no—
452C2×C3×C4—24no—
453C2×C3×C4—24no—
454C2×C3×C4—24no—
455C2×C3×C4—24no—
456C2×C3×C4—24no—
457C2×C3×C4—24no—
458C2×C3×C4—24no—
459C2×C3×C4—24no—
460C2×C3×C4—24no—
461C2×C3×C4—24no—
462C2×C3×C4D3×D418yes—
463#67—632no—
464#67—1216no—
465C2×Dic3—38no—
466C2×Dic3—38no—
467C2×Dic3—64no—
468C2×Dic3—64no—
469C2×Dic3—64no—
470C2×Dic3—64no—
471C2×Dic3—64no—
472C2×Dic3—64no—
473C2×Dic3—64no—
474C2×Dic3—64no—
475C2×Dic3—64no—
476C2×Dic3—64no—
477C2×Dic3—64no—
478C2×Dic3—64no—
479C2×Dic3—64no—
480C2×Dic3—64no—
481C2×Dic3—64no—
482C2×Dic3—64no—
483C2×Dic3—1216no—
484C4×D3—1216no—
485C4×D3—1216no—
486C2×C32—42no—
487C2×C32—42no—
488C2×C32C2×#12311yescharacteristic
489C2×C32#52511yescharacteristic
490C2×C32#53811yescharacteristic
491C2×C32D4211yescharacteristic
492C2×C32#54611yescharacteristic
493C2×C32#54611yescharacteristic
494C2×C32#55111yescharacteristic
495C3⋊D3—24no—
496C3⋊D3—42no—
497C24—91no—
498C24—91no—
499C24—182no—
500C24—182no—
501C24—182no—
502C24—182no—
503C24—182no—
504C24—361no—
505C24—361no—
506C24C22×C3⋊D311yescharacteristic
507C24C22×C3⋊D311yescharacteristic
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—41no—
511C2×D4—94no—
512C2×D4—182no—
513C2×D4—182no—
514C2×D4—182no—
515C2×D4—182no—
516C2×D4—361no—
517C22×C4—91no—
518C22×C4—91no—
519C22×C4—91no—
520C22×C4—91no—
521C22×C4—91no—
522C22×C4—91no—
523C22×C4—182no—
524C22×C4—182no—
525C22×C4—182no—
526C22×C4—182no—
527C22×C4—182no—
528C22×C4—182no—
529C22×C4—361no—
530C22×C4—361no—
531C22×C4—361no—
532C22×C4C22×C3⋊D311yescharacteristic
533C22×C4C22×C3⋊D311yescharacteristic
534C22×C4C22×C3⋊D311yescharacteristic
535C22×C4C22×C3⋊D311yescharacteristic
536C22×C4C22×C3⋊D311yescharacteristic
537C4⋊C4—41no—
538C4⋊C4—182no—
539C4⋊C4—182no—
540C4⋊C4—182no—
541C4⋊C4—361no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—94no—
547C22⋊C4—182no—
548C22⋊C4—182no—
549C22⋊C4—182no—
550C22⋊C4—182no—
551C22⋊C4—182no—
552C22⋊C4—182no—
553C22⋊C4—182no—
554C22⋊C4—182no—
555C22⋊C4—361no—
556C22⋊C4—361no—
557C22⋊C4—361no—
558C42—182no—
559C22×C3—28no—
560C22×C3—28no—
561C22×C3—28no—
562C22×C3—28no—
563C22×C3—28no—
564C22×C3—28no—
565C22×C3—44no—
566C22×C3—44no—
567C22×C3—44no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3C2×D3×D414yes—
574C22×C3C2×D3×D414yes—
575C22×C3C2×#23714yes—
576C22×C3#100414yes—
577C22×C3D3×#4114yes—
578C22×C3D3×#4114yes—
579C22×C3#100914yes—
580C2×D3—316no—
581C2×D3—68no—
582C2×D3—68no—
583C2×D3—68no—
584C2×D3—68no—
585C2×D3—68no—
586C2×D3—68no—
587C2×D3—68no—
588C2×D3—68no—
589C2×D3—68no—
590C2×D3—1264no—
591C2×D3—124no—
592C2×D3—124no—
593C2×D3—124no—
594C2×D3—124no—
595C3×C4—28no—
596C3×C4—44no—
597C3×C4—44no—
598C3×C4—44no—
599C3×C4—44no—
600Dic3—68no—
601Dic3—68no—
602Dic3—124no—
603Dic3—124no—
604Dic3—124no—
605Dic3—124no—
606C32#241811yescharacteristic, complemented, Sylow
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—92no—
620C23—92no—
621C23—92no—
622C23—92no—
623C23—188no—
624C23—181no—
625C23—181no—
626C23—181no—
627C23—181no—
628C23—181no—
629C23—181no—
630C23—181no—
631C23—181no—
632C23—181no—
633C23—181no—
634C23—364no—
635C23—364no—
636C23—364no—
637C23—364no—
638C23—364no—
639C23—364no—
640C23D4×C3⋊D312yes—
641C23#383012yes—
642C23C23×C3⋊D311yescharacteristic
643D4—44no—
644D4—188no—
645D4—364no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—92no—
661C2×C4—92no—
662C2×C4—181no—
663C2×C4—181no—
664C2×C4—181no—
665C2×C4—181no—
666C2×C4—181no—
667C2×C4—181no—
668C2×C4—181no—
669C2×C4—181no—
670C2×C4—181no—
671C2×C4—181no—
672C2×C4—181no—
673C2×C4—181no—
674C2×C4—181no—
675C2×C4—181no—
676C2×C4—181no—
677C2×C4—181no—
678C2×C4—364no—
679C2×C4—364no—
680C2×C4—364no—
681C2×C4D4×C3⋊D312yes—
682C2×C3—48no—
683C2×C3—48no—
684C2×C3#559114yes—
685C2×C3#560614yes—
686C2×C3#560914yes—
687C2×C3#561014yes—
688C2×C3D3×#12314yes—
689C2×C3#565814yes—
690C2×C3#567814yes—
691D3—616no—
692D3—128no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—94no—
708C22—182no—
709C22—182no—
710C22—182no—
711C22—182no—
712C22—182no—
713C22—182no—
714C22—182no—
715C22—182no—
716C22—182no—
717C22—3616no—
718C22—361no—
719C22—361no—
720C22—361no—
721C22—361no—
722C22C2×D4×C3⋊D311yescharacteristic
723C22C2×D4×C3⋊D311yescharacteristic
724C22C2×#383011yescharacteristic
725C22#6436111yescharacteristic
726C22#41×C3⋊D311yescharacteristic
727C22#41×C3⋊D311yescharacteristic
728C22#6436611yescharacteristic
729C4—22no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—182no—
735C4—182no—
736C4—361no—
737C4—361no—
738C4—361no—
739C4—361no—
740C3#7711214yescomplemented
741C2—42no—
742C2—42no—
743C2—184no—
744C2—362no—
745C2#1059606211yescharacteristic
746C2#1059607711yescharacteristic
747C2#1059608011yescharacteristic
748C2#1059608111yescharacteristic
749C2C3⋊D3×#12311yescharacteristic
750C2#1059612911yescharacteristic
751C2#1059614911yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#394C2
prime radicalC2×#64146C2
hypercenter#394C3⋊D3
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#64095C2semidirect
3. C2×#64090C2semidirect
4. C2×C22⋊C4×C3⋊D3C2semidirect
5. C32×#394C2semidirect
6. #10592919C2semidirect
7. #10592689C2semidirect
8. #10592686C2semidirect
9. #10592658C2semidirect
10. #10592655C2semidirect
11. #10592654C2semidirect
12. #10592650C2semidirect
13. #10592648C2semidirect
14. #10592374C2semidirect
15. #10592367C2semidirect
21. C23×C3⋊Dic3C22semidirect
24. C2×C32×C4⋊C4C22semidirect
27. C2×C32×C22⋊C4C22semidirect
28. C2×C32×C22⋊C4C22semidirect
32. C2×#3757C22semidirect
42. C2×C4⋊(C3⋊Dic3)C22semidirect
43. C2×C4⋊(C3⋊Dic3)C22semidirect
44. C2×#3750C22semidirect
45. C2×#3750C22semidirect
46. C2×C4×C3⋊Dic3C22semidirect
50. C32×#95C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. #63658C22semidirect
54. #63658C22semidirect
55. #63658C22semidirect
60. C3×#394D3semidirect
127. #3752D4semidirect
141. C2×C3×C4⋊C4C2×D3semidirect
144. C2×C3×C22⋊C4C2×D3semidirect
145. C2×C3×C22⋊C4C2×D3semidirect
167. C3×#95C2×D3semidirect
255. #394C3⋊D3semidirect
360. C2×C3⋊D3#123semidirect
386. C2×C4⋊C4C2×C3⋊D3semidirect
402. C2×C22⋊C4C2×C3⋊D3semidirect
403. C2×C22⋊C4C2×C3⋊D3semidirect
410. #95C2×C3⋊D3semidirect
606. C32#2418semidirect
740. C3#77112semidirect

Maximal subgroups

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

subgroupindex
C2×#641462
C2×#640952
C2×#640902
C2×C22⋊C4×C3⋊D32
C32×#3942
#105929192
#105926892
#105926862
#105926582
#105926552
#105926542
#105926502
#105926482
#105923742
#105923672
#771123