Finite Group Databasebeta

← #11824552

Subgroups — #11824552

Order 1152.

2172 conjugacy classes of subgroups.

The subgroup lattice has 741 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic, complemented
2C2×#64093C211yesmaximal, characteristic, complemented
3C2×#64093C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
5C32×#388C211yesmaximal, characteristic, complemented
6#10592681C211yesmaximal, characteristic, complemented
7#10592660C211yesmaximal, characteristic, complemented
8#10592659C211yesmaximal, characteristic, complemented
9#10592655C211yesmaximal, characteristic, complemented
10#10592655C211yesmaximal, characteristic, complemented
11#10592639C211yesmaximal, characteristic, complemented
12#10592374C211yesmaximal, characteristic, complemented
13#10592364C211yesmaximal, characteristic, complemented
14#10592364C211yesmaximal, characteristic, complemented
15C3⋊D3×#95C211yesmaximal, characteristic, complemented
16#75882—34nomaximal
17C22×#638C2211yescharacteristic
18C22×#638C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic
24C22×C4×C3⋊D3C2211yescharacteristic
25C22×C4×C3⋊D3C2211yescharacteristic
26C22×C4×C3⋊D3C2211yescharacteristic
27C2×C32×C4⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×C32×C42C2211yescharacteristic
32C2×#3757C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3752C2211yescharacteristic
36C2×#3752C2211yescharacteristic
37C2×#3752C2211yescharacteristic
38C2×#3752C2211yescharacteristic
39C2×#3752C2211yescharacteristic
40C2×#3752C2211yescharacteristic
41C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
42C2×#3750C2211yescharacteristic
43C2×#3750C2211yescharacteristic
44#64104—24no—
45#64093—24no—
46#64093—24no—
47C4×C4⋊(C3⋊D3)—24no—
48C32×#95C2211yescharacteristic
49C32×#95C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53#63658C2211yescharacteristic
54#63658C2211yescharacteristic
55#63658C2211yescharacteristic
56C2×#895—34no—
57C2×#884—34no—
58C2×#884—34no—
59C2×C4×D12—34no—
60C3×#388D314yescomplemented
61#4982—34no—
62#4961—34no—
63#4960—34no—
64#4956—34no—
65#4956—34no—
66#4940—34no—
67#4675—34no—
68#4665—34no—
69#4665—34no—
70D3×#95—34no—
71C24×C32C2311yescharacteristic
72C23×C3⋊D3C2311yescharacteristic
73C23×C3⋊D3C2311yescharacteristic
74C23×C3⋊D3C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C2×#638—22no—
82C2×#638—22no—
83C2×#638—22no—
84C2×#638—22no—
85C2×#638—22no—
86C2×#638—22no—
87C2×#638—41no—
88C2×#638—41no—
89C2×#638—41no—
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)—22no—
99C2×C4⋊(C3⋊D3)—22no—
100C2×C4⋊(C3⋊D3)—22no—
101C2×C4⋊(C3⋊D3)—22no—
102C2×C4⋊(C3⋊D3)—41no—
103C2×C4⋊(C3⋊D3)D414yescomplemented
104C2×C4×C3⋊D3—22no—
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—
111C2×C4×C3⋊D3—41no—
112C2×C4×C3⋊D3—41no—
113C2×C4×C3⋊D3—41no—
114C2×C4×C3⋊D3—41no—
115C2×C4×C3⋊D3D414yescomplemented
116C32×C4⋊C4—22no—
117C32×C22⋊C4—22no—
118C32×C22⋊C4—22no—
119C32×C22⋊C4—22no—
120C32×C42—22no—
121#3757—41no—
122#3752—22no—
123#3752—22no—
124#3752—22no—
125#3752—22no—
126#3752—22no—
127#3752—22no—
128#3752—22no—
129#3752—41no—
130C4⋊(C3⋊Dic3)—22no—
131#3750—22no—
132#3750—22no—
133#2543—91noSylow
134C22×#67—34no—
135C22×#67—34no—
136C22×#67—34no—
137C22×D12—34no—
138C22×D12—34no—
139C22×D12—34no—
140C22×C4×D3—34no—
141C22×C4×D3—34no—
142C22×C4×D3—34no—
143C22×C4×D3—34no—
144C2×C3×C4⋊C4C2×D314yes—
145C2×C3×C22⋊C4C2×D314yes—
146C2×C3×C22⋊C4C2×D314yes—
147C2×C3×C22⋊C4C2×D314yes—
148C2×C3×C42C2×D314yes—
149C2×#217—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×C4⋊Dic3—34no—
159C2×Dic3⋊C4—34no—
160C2×Dic3⋊C4—34no—
161#895—616no—
162#884—616no—
163#884—616no—
164C4×D12—616no—
165C3×#95C2×D314yes—
166C3×#95C2×D314yes—
167C3⋊#95—34no—
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×C32C2411yescharacteristic
181C22×C3⋊D3—21no—
182C22×C3⋊D3—21no—
183C22×C3⋊D3—21no—
184C22×C3⋊D3—21no—
185C22×C3⋊D3—21no—
186C22×C3⋊D3—21no—
187C22×C3⋊D3—21no—
188C22×C3⋊D3—21no—
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⋊D3C2×D412yes—
199C22×C3⋊D3C2×D412yes—
200C22×C3⋊D3C2×D412yes—
201C22×C3⋊D3#4112yes—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
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×C4C2×D412yes—
218C2×C32×C4C2×D412yes—
219C2×C32×C4#4112yes—
220#638—44no—
221#638—44no—
222#638—44no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
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⋊Dic3C2×D412yes—
237C2×C3⋊Dic3#4112yes—
238C4⋊(C3⋊D3)—28no—
239C4⋊(C3⋊D3)—44no—
240C4⋊(C3⋊D3)—44no—
241C4×C3⋊D3—44no—
242C4×C3⋊D3—44no—
243C4×C3⋊D3—44no—
244C4×C3⋊D3—44no—
245C2×#121—91no—
246C2×#121—91no—
247C2×#121—91no—
248C2×C4×D4—91no—
249#398—91no—
250#397—91no—
251#394—91no—
252#392—91no—
253#388—91no—
254#388C3⋊D311yescharacteristic, complemented
255#386—91no—
256#386—91no—
257#386—91no—
258#386—91no—
259C2×#95—91no—
260C24×C3C22×D314yes—
261C23×D3—34no—
262C23×D3—34no—
263C23×D3—34no—
264C22×C3×C4C22×D314yes—
265C22×C3×C4C22×D314yes—
266C22×C3×C4C22×D314yes—
267C22×C3×C4C22×D314yes—
268C22×C3×C4C22×D314yes—
269C22×C3×C4C22×D314yes—
270C2×#67—68no—
271C2×#67—68no—
272C2×#67—68no—
273C2×#67—68no—
274C2×#67—68no—
275C2×#67—68no—
276C2×#67—124no—
277C2×#67—124no—
278C2×#67—124no—
279C22×Dic3—34no—
280C22×Dic3—34no—
281C22×Dic3—34no—
282C22×Dic3—34no—
283C22×Dic3—34no—
284C2×D12—316no—
285C2×D12—68no—
286C2×D12—68no—
287C2×D12—68no—
288C2×D12—68no—
289C2×D12—68no—
290C2×D12—68no—
291C2×D12—68no—
292C2×D12—124no—
293C2×C4×D3—316no—
294C2×C4×D3—68no—
295C2×C4×D3—68no—
296C2×C4×D3—68no—
297C2×C4×D3—68no—
298C2×C4×D3—68no—
299C2×C4×D3—124no—
300C2×C4×D3—124no—
301C2×C4×D3—124no—
302C2×C4×D3—124no—
303C2×C4×D3—124no—
304C2×C4×D3—124no—
305C3×C4⋊C4—28no—
306C3×C22⋊C4—28no—
307C3×C22⋊C4—28no—
308C3×C22⋊C4—28no—
309C3×C42—28no—
310#217—124no—
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—68no—
318(C2×D3)⋊C4—124no—
319C4⋊Dic3—68no—
320Dic3⋊C4—68no—
321Dic3⋊C4—68no—
322C22×C32—41no—
323C22×C32—41no—
324C22×C32—41no—
325C22×C32—41no—
326C22×C32—41no—
327C22×C32—41no—
328C22×C32—41no—
329C22×C32C22×D411yescharacteristic
330C22×C32C22×D411yescharacteristic
331C22×C32C2×#4111yescharacteristic
332C22×C32C2×#4111yescharacteristic
333C22×C32C2×#4111yescharacteristic
334C22×C32H(5,𝔽2)11yescharacteristic
335C22×C32H(5,𝔽2)11yescharacteristic
336C2×C3⋊D3—22no—
337C2×C3⋊D3—22no—
338C2×C3⋊D3—22no—
339C2×C3⋊D3—22no—
340C2×C3⋊D3—22no—
341C2×C3⋊D3—22no—
342C2×C3⋊D3—22no—
343C2×C3⋊D3—22no—
344C2×C3⋊D3—22no—
345C2×C3⋊D3—41no—
346C2×C3⋊D3—41no—
347C2×C3⋊D3—41no—
348C2×C3⋊D3—41no—
349C2×C3⋊D3—41no—
350C2×C3⋊D3—41no—
351C2×C3⋊D3—41no—
352C2×C3⋊D3—41no—
353C2×C3⋊D3—41no—
354C2×C3⋊D3—41no—
355C2×C3⋊D3—41no—
356C2×C3⋊D3#12114yes—
357C32×C4—22no—
358C32×C4—22no—
359C32×C4—22no—
360C32×C4—41no—
361C32×C4—41no—
362C32×C4—41no—
363C3⋊Dic3—22no—
364C3⋊Dic3—22no—
365C3⋊Dic3—41no—
366C3⋊Dic3—41no—
367C3⋊Dic3—41no—
368C22×D4—91no—
369C22×D4—91no—
370C22×D4—91no—
371C22×D4—91no—
372C22×D4—91no—
373C22×D4—91no—
374C23×C4—91no—
375C23×C4—91no—
376C23×C4—91no—
377C23×C4—91no—
378#121—184no—
379#121—184no—
380#121—184no—
381C4×D4—184no—
382C2×C4⋊C4—91no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4—91no—
385C2×C4⋊C4C2×C3⋊D311yescharacteristic
386C2×C22⋊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⋊C4C2×C3⋊D311yescharacteristic
396C2×C22⋊C4C2×C3⋊D311yescharacteristic
397C2×C22⋊C4C2×C3⋊D311yescharacteristic
398C2×C42C2×C3⋊D311yescharacteristic
399#95—91no—
400#95—91no—
401#95—91no—
402#95—91no—
403#95—91no—
404#95—91no—
405#95C2×C3⋊D311yescharacteristic
406#95C2×C3⋊D311yescharacteristic
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—24no—
410C23×C3—24no—
411C23×C3—24no—
412C23×C3—24no—
413C23×C3—24no—
414C23×C3C23×D314yes—
415C22×D3—38no—
416C22×D3—38no—
417C22×D3—38no—
418C22×D3—38no—
419C22×D3—64no—
420C22×D3—64no—
421C22×D3—64no—
422C22×D3—64no—
423C22×D3—64no—
424C22×D3—64no—
425C22×D3—64no—
426C22×D3—64no—
427C22×D3—64no—
428C22×D3—64no—
429C22×D3—64no—
430C22×D3—64no—
431C22×D3—64no—
432C22×D3—64no—
433C22×D3—64no—
434C22×D3—64no—
435C22×D3—64no—
436C2×C3×C4—24no—
437C2×C3×C4—24no—
438C2×C3×C4—24no—
439C2×C3×C4—24no—
440C2×C3×C4—24no—
441C2×C3×C4—24no—
442C2×C3×C4—24no—
443C2×C3×C4—24no—
444C2×C3×C4—24no—
445C2×C3×C4—24no—
446C2×C3×C4—24no—
447C2×C3×C4—24no—
448C2×C3×C4—24no—
449C2×C3×C4—24no—
450C2×C3×C4—24no—
451C2×C3×C4#23518yes—
452C2×C3×C4D3×D418yes—
453C2×C3×C4D3×D418yes—
454#67—1216no—
455#67—1216no—
456#67—1216no—
457C2×Dic3—38no—
458C2×Dic3—38no—
459C2×Dic3—64no—
460C2×Dic3—64no—
461C2×Dic3—64no—
462C2×Dic3—64no—
463C2×Dic3—64no—
464C2×Dic3—64no—
465C2×Dic3—64no—
466C2×Dic3—64no—
467C2×Dic3—64no—
468C2×Dic3—64no—
469C2×Dic3—64no—
470C2×Dic3—64no—
471C2×Dic3—64no—
472D12—632no—
473D12—1216no—
474D12—1216no—
475C4×D3—1216no—
476C4×D3—1216no—
477C4×D3—1216no—
478C4×D3—1216no—
479C2×C32—81no—
480C2×C32C2×#12111yescharacteristic
481C2×C32#53211yescharacteristic
482C2×C32#53411yescharacteristic
483C2×C32#54611yescharacteristic
484C2×C32#54611yescharacteristic
485C2×C32#55311yescharacteristic
486C2×C32#55311yescharacteristic
487C3⋊D3—24no—
488C3⋊D3—42no—
489C3⋊D3—81no—
490C24—91no—
491C24—91no—
492C24—91no—
493C24C22×C3⋊D311yescharacteristic
494C2×D4—94no—
495C2×D4—182no—
496C2×D4—182no—
497C2×D4—182no—
498C2×D4—182no—
499C2×D4—182no—
500C2×D4—182no—
501C2×D4—182no—
502C2×D4—182no—
503C2×D4—182no—
504C2×D4—182no—
505C2×D4—182no—
506C2×D4—182no—
507C2×D4—182no—
508C2×D4—361no—
509C2×D4—361no—
510C2×D4—361no—
511C2×D4—361no—
512C22×C4—91no—
513C22×C4—91no—
514C22×C4—94no—
515C22×C4—91no—
516C22×C4—91no—
517C22×C4—91no—
518C22×C4—182no—
519C22×C4—182no—
520C22×C4—182no—
521C22×C4—182no—
522C22×C4—182no—
523C22×C4—361no—
524C22×C4—361no—
525C22×C4—361no—
526C22×C4—361no—
527C22×C4—361no—
528C22×C4—361no—
529C22×C4C22×C3⋊D311yescharacteristic
530C22×C4C22×C3⋊D311yescharacteristic
531C22×C4C22×C3⋊D311yescharacteristic
532C22×C4C22×C3⋊D311yescharacteristic
533C22×C4C22×C3⋊D311yescharacteristic
534C22×C4C22×C3⋊D311yescharacteristic
535C4⋊C4—22no—
536C4⋊C4—182no—
537C4⋊C4—182no—
538C4⋊C4—182no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—182no—
543C22⋊C4—182no—
544C22⋊C4—182no—
545C22⋊C4—182no—
546C22⋊C4—182no—
547C22⋊C4—182no—
548C22⋊C4—182no—
549C22⋊C4—361no—
550C22⋊C4—361no—
551C42—22no—
552C22×C3—44no—
553C22×C3—44no—
554C22×C3—44no—
555C22×C3—44no—
556C22×C3—44no—
557C22×C3—44no—
558C22×C3—44no—
559C22×C3C2×#23514yes—
560C22×C3C2×D3×D414yes—
561C22×C3C2×D3×D414yes—
562C22×C3D3×#4114yes—
563C22×C3D3×#4114yes—
564C22×C3#100914yes—
565C22×C3#100914yes—
566C2×D3—316no—
567C2×D3—68no—
568C2×D3—68no—
569C2×D3—68no—
570C2×D3—68no—
571C2×D3—68no—
572C2×D3—68no—
573C2×D3—68no—
574C2×D3—68no—
575C2×D3—68no—
576C2×D3—124no—
577C2×D3—124no—
578C2×D3—124no—
579C2×D3—124no—
580C2×D3—124no—
581C2×D3—124no—
582C2×D3—124no—
583C2×D3—124no—
584C2×D3—124no—
585C2×D3—124no—
586C2×D3—124no—
587C3×C4—28no—
588C3×C4—28no—
589C3×C4—28no—
590C3×C4—44no—
591C3×C4—44no—
592C3×C4—44no—
593Dic3—68no—
594Dic3—68no—
595Dic3—124no—
596Dic3—124no—
597Dic3—124no—
598C32#254311yescharacteristic, complemented, Sylow
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—92no—
607C23—92no—
608C23—92no—
609C23—92no—
610C23—181no—
611C23—181no—
612C23—181no—
613C23—181no—
614C23—181no—
615C23—181no—
616C23—181no—
617C23—181no—
618C23—181no—
619C23—181no—
620C23—181no—
621C23—181no—
622C23—181no—
623C23—181no—
624C23—181no—
625C23—181no—
626C23—181no—
627C23C23×C3⋊D311yescharacteristic
628D4—188no—
629D4—364no—
630D4—364no—
631D4—364no—
632D4—364no—
633D4—364no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—92no—
650C2×C4—92no—
651C2×C4—181no—
652C2×C4—181no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—181no—
656C2×C4—181no—
657C2×C4—181no—
658C2×C4—181no—
659C2×C4—181no—
660C2×C4—181no—
661C2×C4—181no—
662C2×C4—181no—
663C2×C4—181no—
664C2×C4—364no—
665C2×C4—364no—
666C2×C4—364no—
667C2×C4—364no—
668C2×C4#382812yes—
669C2×C4D4×C3⋊D312yes—
670C2×C4D4×C3⋊D312yes—
671C2×C3—84no—
672C2×C3#553014yes—
673C2×C3#554814yes—
674C2×C3#555014yes—
675C2×C3D3×#12114yes—
676C2×C3#565314yes—
677C2×C3#567614yes—
678C2×C3#570914yes—
679D3—616no—
680D3—128no—
681D3—244no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—94no—
690C22—182no—
691C22—182no—
692C22—182no—
693C22—182no—
694C22—182no—
695C22—182no—
696C22—182no—
697C22—182no—
698C22—182no—
699C22—361no—
700C22—361no—
701C22—361no—
702C22—361no—
703C22—361no—
704C22—361no—
705C22—361no—
706C22—361no—
707C22—361no—
708C22—361no—
709C22—361no—
710C22C2×#382811yescharacteristic
711C22C2×D4×C3⋊D311yescharacteristic
712C22C2×D4×C3⋊D311yescharacteristic
713C22#41×C3⋊D311yescharacteristic
714C22#41×C3⋊D311yescharacteristic
715C22#6436611yescharacteristic
716C22#6436611yescharacteristic
717C4—22no—
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—182no—
724C4—182no—
725C4—361no—
726C4—361no—
727C4—361no—
728C3#7588214yescomplemented
729C2—81no—
730C2—184no—
731C2—362no—
732C2—721no—
733C2#1059600111yescharacteristic
734C2#1059601911yescharacteristic
735C2#1059602111yescharacteristic
736C2C3⋊D3×#12111yescharacteristic
737C2#1059612411yescharacteristic
738C2#1059614711yescharacteristic
739C2#1059618011yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#388C2
hypercenter#388C3⋊D3
hypocenterC32#2543
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#64104C2semidirect
2. C2×#64093C2semidirect
3. C2×#64093C2semidirect
4. C2×C4×C4⋊(C3⋊D3)C2semidirect
5. C32×#388C2semidirect
6. #10592681C2semidirect
7. #10592660C2semidirect
8. #10592659C2semidirect
9. #10592655C2semidirect
10. #10592655C2semidirect
11. #10592639C2semidirect
12. #10592374C2semidirect
13. #10592364C2semidirect
14. #10592364C2semidirect
15. C3⋊D3×#95C2semidirect
60. C3×#388D3semidirect
103. C2×C4⋊(C3⋊D3)D4semidirect
115. C2×C4×C3⋊D3D4semidirect
254. #388C3⋊D3semidirect
598. C32#2543semidirect
728. C3#75882semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
C2×#640932
C2×C4×C4⋊(C3⋊D3)2
C32×#3882
#105926812
#105926602
#105926592
#105926552
#105926392
#105923742
#105923642
C3⋊D3×#952
#758823