Finite Group Databasebeta

← #11810290

Subgroups — #11810290

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×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C22×#3752C211yesmaximal, characteristic, complemented
4C2×#64095C211yesmaximal, characteristic, complemented
5C32×#386C211yesmaximal, characteristic, complemented
6#10592911C211yesmaximal, characteristic, complemented
7#10592660C211yesmaximal, characteristic, complemented
8#10592660C211yesmaximal, characteristic, complemented
9#10592657C211yesmaximal, characteristic, complemented
10#10592654C211yesmaximal, characteristic, complemented
11#10592649C211yesmaximal, characteristic, complemented
12#10592376C211yesmaximal, characteristic, complemented
13#10592373C211yesmaximal, characteristic, complemented
14#10592369C211yesmaximal, characteristic, complemented
15#10592369C211yesmaximal, characteristic, complemented
16#74891—34nomaximal
17C24×C3⋊D3C2211yescharacteristic
18C22×C32×D4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic
23C23×C3⋊Dic3C2211yescharacteristic, complemented
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic, complemented
26C2×C32×C22⋊C4C2211yescharacteristic, complemented
27C2×#3757C2211yescharacteristic
28C2×#3757C2211yescharacteristic
29C2×#3757C2211yescharacteristic, complemented
30#64146—24no—
31D4×C3⋊Dic3—24no—
32C2×#3752—24no—
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3752C2211yescharacteristic
36C2×#3752C2211yescharacteristic
37C2×#3752C2211yescharacteristic
38C2×#3752C2211yescharacteristic
39C2×#3752C2211yescharacteristic
40C2×#3752C2211yescharacteristic
41C2×#3752C2211yescharacteristic
42C2×#3752C2211yescharacteristic
43C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
49#64095—24no—
50C32×#95C2211yescharacteristic, complemented
51C32×#95C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53#63658C2211yescharacteristic, complemented
54#63658C2211yescharacteristic, complemented
55#63658C2211yescharacteristic, complemented
56C2×#937—34no—
57C2×D4×Dic3—34no—
58C22×(C2×D3)⋊C4—34no—
59C2×#886—34no—
60C3×#386D314yescomplemented
61#5212—34no—
62#4961—34no—
63#4961—34no—
64#4958—34no—
65#4955—34no—
66#4950—34no—
67#4677—34no—
68#4674—34no—
69#4670—34no—
70#4670—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×D4D414yes—
85C22×C32×C4—22no—
86C22×C32×C4—22no—
87C22×C32×C4—41no—
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C2×#638—22no—
94C2×#638—22no—
95C2×#638—22no—
96C2×#638—22no—
97C2×#638—41no—
98C2×#638—41no—
99C22×C3⋊Dic3—22no—
100C22×C3⋊Dic3—22no—
101C22×C3⋊Dic3—22no—
102C22×C3⋊Dic3—22no—
103C22×C3⋊Dic3—41no—
104C22×C3⋊Dic3—41no—
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C32×C22⋊C4—22no—
112C32×C22⋊C4—22no—
113C32×C22⋊C4—41no—
114#3757—22no—
115#3757—22no—
116#3757—22no—
117#3752—22no—
118#3752—22no—
119#3752—22no—
120#3752—22no—
121#3752—22no—
122#3752—22no—
123#3752—22no—
124#3752—41no—
125#3752—41no—
126#3752D414yescomplemented
127C4⋊(C3⋊Dic3)—22no—
128C4⋊(C3⋊Dic3)—22no—
129C4⋊(C3⋊Dic3)—22no—
130C4⋊(C3⋊Dic3)—41no—
131C4⋊(C3⋊Dic3)—41no—
132C4×C3⋊Dic3—22no—
133#2418—91noSylow
134C24×D3—34no—
135C22×C3×D4C2×D314yes—
136C23×C3×C4C2×D314yes—
137C22×#67—34no—
138C22×#67—34no—
139C23×Dic3—34no—
140C23×Dic3—34no—
141C2×C3×C22⋊C4C2×D314yes—
142C2×C3×C22⋊C4C2×D314yescomplemented
143C2×C3×C22⋊C4C2×D314yescomplemented
144C2×#217—34no—
145C2×#217—34no—
146C2×#217—34no—
147#937—616no—
148D4×Dic3—616no—
149C2×(C2×D3)⋊C4—34no—
150C2×(C2×D3)⋊C4—34no—
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×(C2×D3)⋊C4—616no—
160C2×C4⋊Dic3—34no—
161C2×C4⋊Dic3—34no—
162C2×C4⋊Dic3—34no—
163C2×C4⋊Dic3—34no—
164C2×C4⋊Dic3—34no—
165C2×C4×Dic3—34no—
166#886—616no—
167C3×#95C2×D314yescomplemented
168C3×#95C2×D314yescomplemented
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×C32C2×D412yes—
184C23×C32C2×D412yes—
185C23×C32#4112yes—
186C23×C32#4112yes—
187C23×C32C2411yescharacteristic
188C22×C3⋊D3—28no—
189C22×C3⋊D3—21no—
190C22×C3⋊D3—21no—
191C22×C3⋊D3—21no—
192C22×C3⋊D3—21no—
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—21no—
200C22×C3⋊D3—21no—
201C22×C3⋊D3—44no—
202C22×C3⋊D3—44no—
203C22×C3⋊D3—44no—
204C22×C3⋊D3—44no—
205C22×C3⋊D3—44no—
206C22×C3⋊D3—44no—
207C22×C3⋊D3C2×D412yes—
208C22×C3⋊D3#4112yes—
209C32×D4—28no—
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—44no—
224C2×C32×C4C2×D412yes—
225C2×C32×C4C2×D412yes—
226#638—44no—
227#638—44no—
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—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—44no—
246C2×C3⋊Dic3—44no—
247C2×C3⋊Dic3C2×D412yes—
248C2×#123—91no—
249C2×#120—91no—
250C2×C4×D4—91no—
251C22×C22⋊C4—91no—
252#399—91no—
253#397—91no—
254#394—91no—
255#394—91no—
256#388—91no—
257#388—91no—
258#386—91no—
259#386C3⋊D311yescharacteristic, complemented
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×D4D12116yes—
277C22×C3×C4—28no—
278C22×C3×C4—28no—
279C22×C3×C4—44no—
280C22×C3×C4C22×D314yes—
281C22×C3×C4C22×D314yes—
282C22×C3×C4C22×D314yes—
283C22×C3×C4C22×D314yes—
284C22×C3×C4C22×D314yes—
285C2×#67—68no—
286C2×#67—68no—
287C2×#67—68no—
288C2×#67—68no—
289C2×#67—124no—
290C2×#67—124no—
291C22×Dic3—34no—
292C22×Dic3—34no—
293C22×Dic3—34no—
294C22×Dic3—34no—
295C22×Dic3—34no—
296C22×Dic3—34no—
297C22×Dic3—68no—
298C22×Dic3—68no—
299C22×Dic3—68no—
300C22×Dic3—68no—
301C22×Dic3—124no—
302C22×Dic3—124no—
303C3×C22⋊C4—28no—
304C3×C22⋊C4—28no—
305C3×C22⋊C4—44no—
306#217—68no—
307#217—68no—
308#217—68no—
309(C2×D3)⋊C4—316no—
310(C2×D3)⋊C4—68no—
311(C2×D3)⋊C4—68no—
312(C2×D3)⋊C4—68no—
313(C2×D3)⋊C4—68no—
314(C2×D3)⋊C4—68no—
315(C2×D3)⋊C4—68no—
316(C2×D3)⋊C4—68no—
317(C2×D3)⋊C4—124no—
318(C2×D3)⋊C4—124no—
319C4⋊Dic3—68no—
320C4⋊Dic3—68no—
321C4⋊Dic3—68no—
322C4⋊Dic3—124no—
323C4⋊Dic3—124no—
324C4×Dic3—68no—
325C22×C32—22no—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—22no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—41no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32#12314yescomplemented
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—416no—
353C2×C3⋊D3—41no—
354C2×C3⋊D3—41no—
355C2×C3⋊D3—41no—
356C2×C3⋊D3—41no—
357C2×C3⋊D3—41no—
358C2×C3⋊D3—41no—
359C2×C3⋊D3—41no—
360C2×C3⋊D3—41no—
361C32×C4—22no—
362C32×C4—22no—
363C32×C4—41no—
364C32×C4—41no—
365C32×C4—41no—
366C3⋊Dic3—22no—
367C3⋊Dic3—41no—
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×C4C2×C3⋊D311yescharacteristic
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⋊C4—91no—
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—91no—
400C2×C22⋊C4—184no—
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#95C2×C3⋊D311yescharacteristic, complemented
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×C3C2×D1218yes—
422C23×C3C2×D1218yes—
423C23×C3#23718yes—
424C23×C3#23718yes—
425C23×C3C23×D314yes—
426C22×D3—38no—
427C22×D3—38no—
428C22×D3—632no—
429C22×D3—64no—
430C22×D3—64no—
431C22×D3—64no—
432C22×D3—64no—
433C22×D3—64no—
434C22×D3—64no—
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—232no—
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—416no—
462C2×C3×C4C2×D1218yes—
463C2×C3×C4D3×D418yes—
464#67—1216no—
465#67—1216no—
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—64no—
484C2×Dic3—1216no—
485C2×Dic3—1216no—
486C2×C32—24no—
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—42no—
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—182no—
511C2×D4—182no—
512C2×D4—182no—
513C2×D4—182no—
514C2×D4—361no—
515C2×D4—361no—
516C2×D4C4⋊(C3⋊D3)14yes—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—41no—
520C22×C4—91no—
521C22×C4—91no—
522C22×C4—91no—
523C22×C4—91no—
524C22×C4—91no—
525C22×C4—91no—
526C22×C4—182no—
527C22×C4—182no—
528C22×C4—182no—
529C22×C4—182no—
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—182no—
538C4⋊C4—182no—
539C4⋊C4—182no—
540C4⋊C4—361no—
541C4⋊C4—361no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—41no—
545C22⋊C4—94no—
546C22⋊C4—182no—
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—182no—
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—28no—
566C22×C3—28no—
567C22×C3—28no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3#886116yescomplemented
573C22×C3C22×D1214yes—
574C22×C3C2×D3×D414yes—
575C22×C3C2×#23714yes—
576C22×C3C2×#23714yes—
577C22×C3#100414yes—
578C22×C3D3×#4114yes—
579C22×C3#100914yes—
580C2×D3—68no—
581C2×D3—68no—
582C2×D3—68no—
583C2×D3—68no—
584C2×D3—68no—
585C2×D3—68no—
586C2×D3—1264no—
587C2×D3—124no—
588C2×D3—124no—
589C2×D3—124no—
590C2×D3—124no—
591C2×D3—124no—
592C2×D3—124no—
593C2×D3—124no—
594C2×D3—124no—
595C3×C4—28no—
596C3×C4—28no—
597C3×C4—44no—
598C3×C4—44no—
599C3×C4—44no—
600Dic3—68no—
601Dic3—124no—
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—92no—
618C23—92no—
619C23—188no—
620C23—181no—
621C23—181no—
622C23—181no—
623C23—181no—
624C23—181no—
625C23—181no—
626C23—181no—
627C23—181no—
628C23—181no—
629C23—181no—
630C23—181no—
631C23—181no—
632C23—364no—
633C23—364no—
634C23—364no—
635C23—364no—
636C23—364no—
637C23—364no—
638C23C2×C4⋊(C3⋊D3)12yes—
639C23C2×C4⋊(C3⋊D3)12yes—
640C23#383012yes—
641C23#383012yes—
642C23C23×C3⋊D311yescharacteristic
643D4—28no—
644D4—364no—
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—44no—
660C2×C4—92no—
661C2×C4—181no—
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×C4C2×C4⋊(C3⋊D3)12yes—
681C2×C4D4×C3⋊D312yes—
682C2×C3—216no—
683C2×C3—48no—
684C2×C3C2×#88614yes—
685C2×C3D4×D1214yes—
686C2×C3#555414yes—
687C2×C3#559114yes—
688C2×C3#560614yes—
689C2×C3#561714yes—
690C2×C3#565814yes—
691D3—128no—
692D3—128no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—182no—
707C22—182no—
708C22—182no—
709C22—182no—
710C22—182no—
711C22—182no—
712C22—3616no—
713C22—361no—
714C22—361no—
715C22—361no—
716C22—361no—
717C22—361no—
718C22—361no—
719C22—361no—
720C22—361no—
721C22#6409514yescomplemented
722C22C22×C4⋊(C3⋊D3)11yescharacteristic
723C22C2×D4×C3⋊D311yescharacteristic
724C22C2×#383011yescharacteristic
725C22C2×#383011yescharacteristic
726C22#6436111yescharacteristic
727C22#41×C3⋊D311yescharacteristic
728C22#6436611yescharacteristic
729C4—22no—
730C4—22no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—182no—
735C4—361no—
736C4—361no—
737C4—361no—
738C4—361no—
739C4—361no—
740C3#7489114yescomplemented
741C2—24no—
742C2—42no—
743C2—362no—
744C2—362no—
745C2C2×#6409511yescharacteristic
746C2D4×C4⋊(C3⋊D3)11yescharacteristic
747C2#1059602511yescharacteristic
748C2#1059606211yescharacteristic
749C2#1059607711yescharacteristic
750C2#1059608811yescharacteristic
751C2#1059612911yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#386C2
prime radicalC2×#64146C2
hypercenter#386C3⋊D3
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×D4×C3⋊Dic3C2semidirect
3. C22×#3752C2semidirect
4. C2×#64095C2semidirect
5. C32×#386C2semidirect
6. #10592911C2semidirect
7. #10592660C2semidirect
8. #10592660C2semidirect
9. #10592657C2semidirect
10. #10592654C2semidirect
11. #10592649C2semidirect
12. #10592376C2semidirect
13. #10592373C2semidirect
14. #10592369C2semidirect
15. #10592369C2semidirect
23. C23×C3⋊Dic3C22semidirect
25. C2×C32×C22⋊C4C22semidirect
26. C2×C32×C22⋊C4C22semidirect
29. C2×#3757C22semidirect
43. C2×C4⋊(C3⋊Dic3)C22semidirect
44. C2×C4⋊(C3⋊Dic3)C22semidirect
45. C2×C4⋊(C3⋊Dic3)C22semidirect
46. C2×C4⋊(C3⋊Dic3)C22semidirect
47. C2×C4⋊(C3⋊Dic3)C22semidirect
48. C2×C4×C3⋊Dic3C22semidirect
50. C32×#95C22semidirect
51. C32×#95C22semidirect
52. #63658C22semidirect
53. #63658C22semidirect
54. #63658C22semidirect
55. #63658C22semidirect
60. C3×#386D3semidirect
126. #3752D4semidirect
142. C2×C3×C22⋊C4C2×D3semidirect
143. C2×C3×C22⋊C4C2×D3semidirect
167. C3×#95C2×D3semidirect
168. C3×#95C2×D3semidirect
259. #386C3⋊D3semidirect
338. C22×C32#123semidirect
402. C2×C22⋊C4C2×C3⋊D3semidirect
403. C2×C22⋊C4C2×C3⋊D3semidirect
409. #95C2×C3⋊D3semidirect
410. #95C2×C3⋊D3semidirect
572. C22×C3#886semidirect
606. C32#2418semidirect
721. C22#64095semidirect
740. C3#74891semidirect

Maximal subgroups

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

subgroupindex
C2×#641462
C2×D4×C3⋊Dic32
C22×#37522
C2×#640952
C32×#3862
#105929112
#105926602
#105926572
#105926542
#105926492
#105923762
#105923732
#105923692
#748913