Finite Group Databasebeta

← #11810311

Subgroups — #11810311

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×#64092C211yesmaximal, characteristic, complemented
2C2×#64091C211yesmaximal, characteristic
3C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
5C32×#388C211yesmaximal, characteristic, complemented
6#10592690C211yesmaximal, characteristic, complemented
7#10592686C211yesmaximal, characteristic, complemented
8#10592660C211yesmaximal, characteristic, complemented
9#10592654C211yesmaximal, characteristic, complemented
10#10592652C211yesmaximal, characteristic, complemented
11#10592639C211yesmaximal, characteristic, complemented
12#10592376C211yesmaximal, characteristic, complemented
13#10592367C211yesmaximal, characteristic, complemented
14#10592364C211yesmaximal, characteristic, complemented
15#10592364C211yesmaximal, characteristic, complemented
16#75844—34nomaximal
17C24×C3⋊D3C2211yescharacteristic
18C22×#638C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C2×C32×C4⋊C4C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C42C2211yescharacteristic, complemented
29C2×#3757C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3752C2211yescharacteristic
36C2×#3752C2211yescharacteristic
37C2×#3752C2211yescharacteristic
38C2×#3752C2211yescharacteristic
39C2×#3752C2211yescharacteristic, complemented
40C2×#3752C2211yescharacteristic, complemented
41C2×#3752C2211yescharacteristic, complemented
42C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45C2×#3750C2211yescharacteristic, complemented
46#64092—24no—
47#64091—24no—
48C22⋊C4×C3⋊D3—24no—
49C4×C4⋊(C3⋊D3)—24no—
50C32×#95C2211yescharacteristic, complemented
51C32×#95C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53#63658C2211yescharacteristic, complemented
54#63658C2211yescharacteristic, complemented
55#63658C2211yescharacteristic, complemented
56C2×#883—34no—
57C2×#882—34no—
58C2×D3×C22⋊C4—34no—
59C2×C4×D12—34no—
60C3×#388D314yescomplemented
61#4991—34no—
62#4987—34no—
63#4961—34no—
64#4955—34no—
65#4953—34no—
66#4940—34no—
67#4677—34no—
68#4668—34no—
69#4665—34no—
70#4665—34no—
71C24×C32C2311yescharacteristic
72C23×C3⋊D3—22no—
73C23×C3⋊D3—22no—
74C23×C3⋊D3—22no—
75C23×C3⋊D3—22no—
76C23×C3⋊D3—22no—
77C23×C3⋊D3—41no—
78C23×C3⋊D3—41no—
79C23×C3⋊D3C2311yescharacteristic
80C23×C3⋊D3C2311yescharacteristic
81C23×C3⋊D3C2311yescharacteristic
82C22×C32×C4C2311yescharacteristic
83C22×C32×C4C2311yescharacteristic
84C22×C32×C4C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C2×#638—22no—
89C2×#638—22no—
90C2×#638—41no—
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)—22no—
99C2×C4⋊(C3⋊D3)—22no—
100C2×C4⋊(C3⋊D3)—41no—
101C2×C4⋊(C3⋊D3)D414yes—
102C2×C4×C3⋊D3—22no—
103C2×C4×C3⋊D3—22no—
104C2×C4×C3⋊D3—22no—
105C2×C4×C3⋊D3—22no—
106C2×C4×C3⋊D3—22no—
107C2×C4×C3⋊D3—22no—
108C2×C4×C3⋊D3—41no—
109C2×C4×C3⋊D3—41no—
110C2×C4×C3⋊D3—41no—
111C32×C4⋊C4—41no—
112C32×C22⋊C4—22no—
113C32×C22⋊C4—41no—
114C32×C22⋊C4D414yescomplemented
115C32×C42—22no—
116#3757—22no—
117#3757—22no—
118#3752—22no—
119#3752—22no—
120#3752—22no—
121#3752—22no—
122#3752—22no—
123#3752—22no—
124#3752—22no—
125#3752—22no—
126#3752—22no—
127#3752—41no—
128#3752—41no—
129C4⋊(C3⋊Dic3)—22no—
130C4⋊(C3⋊Dic3)—22no—
131C4⋊(C3⋊Dic3)—41no—
132#3750—22no—
133#2418—91noSylow
134C24×D3—34no—
135C22×#67—34no—
136C22×D12—34no—
137C22×D12—34no—
138C22×C4×D3—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×D314yes—
145C2×C3×C42C2×D314yescomplemented
146C2×#217—34no—
147C2×#217—34no—
148C2×(C2×D3)⋊C4—34no—
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×C4⋊Dic3—34no—
160C2×C4⋊Dic3—34no—
161C2×C4⋊Dic3—34no—
162C2×Dic3⋊C4—34no—
163#883—616no—
164#882—616no—
165D3×C22⋊C4—616no—
166C4×D12—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×C32C2×D412yes—
180C23×C32C2411yescharacteristic
181C22×C3⋊D3—21no—
182C22×C3⋊D3—21no—
183C22×C3⋊D3—21no—
184C22×C3⋊D3—21no—
185C22×C3⋊D3—28no—
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⋊D3—44no—
199C22×C3⋊D3—44no—
200C22×C3⋊D3—44no—
201C22×C3⋊D3—44no—
202C22×C3⋊D3—44no—
203C22×C3⋊D3—44no—
204C22×C3⋊D3C2×D412yes—
205C22×C3⋊D3C2×D412yes—
206C22×C3⋊D3#4112yes—
207C22×C3⋊D3#4112yes—
208C22×C3⋊D3#4112yes—
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×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—
225C2×C32×C4C2×D412yes—
226C2×C32×C4C2×D412yes—
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—
243C4⋊(C3⋊D3)—28no—
244C4⋊(C3⋊D3)—44no—
245C4×C3⋊D3—44no—
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#394—91no—
256#388—91no—
257#388C3⋊D311yescharacteristic, complemented
258#386—91no—
259#386—91no—
260#385—91no—
261#380—91no—
262#379—91no—
263C24×C3C22×D314yes—
264C23×D3—34no—
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—
274C22×C3×C4C22×D314yes—
275C22×C3×C4C22×D314yes—
276C22×C3×C4C22×D314yes—
277C22×C3×C4C22×D314yes—
278C22×C3×C4C22×D314yes—
279C22×C3×C4C22×D314yes—
280C2×#67—68no—
281C2×#67—68no—
282C2×#67—124no—
283C22×Dic3—34no—
284C22×Dic3—34no—
285C22×Dic3—34no—
286C22×Dic3—34no—
287C22×Dic3—34no—
288C2×D12—316no—
289C2×D12—68no—
290C2×D12—68no—
291C2×D12—68no—
292C2×D12—68no—
293C2×D12—124no—
294C2×C4×D3—68no—
295C2×C4×D3—68no—
296C2×C4×D3—68no—
297C2×C4×D3—68no—
298C2×C4×D3—68no—
299C2×C4×D3—68no—
300C2×C4×D3—124no—
301C2×C4×D3—124no—
302C2×C4×D3—124no—
303C3×C4⋊C4—44no—
304C3×C22⋊C4—28no—
305C3×C22⋊C4—44no—
306C3×C22⋊C4D12116yescomplemented
307C3×C42—28no—
308#217—68no—
309#217—68no—
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—68no—
318(C2×D3)⋊C4—68no—
319(C2×D3)⋊C4—124no—
320(C2×D3)⋊C4—124no—
321C4⋊Dic3—68no—
322C4⋊Dic3—68no—
323C4⋊Dic3—124no—
324Dic3⋊C4—68no—
325C22×C32—22no—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—41no—
329C22×C32—41no—
330C22×C32—41no—
331C22×C32—41no—
332C22×C32C22×D411yescharacteristic
333C22×C32C22×D411yescharacteristic
334C22×C32C2×#4111yescharacteristic
335C22×C32C2×#4111yescharacteristic
336C22×C32C2×#4111yescharacteristic
337C22×C32H(5,𝔽2)11yescharacteristic
338C22×C32H(5,𝔽2)11yescharacteristic
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—22no—
346C2×C3⋊D3—22no—
347C2×C3⋊D3—22no—
348C2×C3⋊D3—22no—
349C2×C3⋊D3—22no—
350C2×C3⋊D3—22no—
351C2×C3⋊D3—416no—
352C2×C3⋊D3—41no—
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#12314yescomplemented
361C32×C4—22no—
362C32×C4—22no—
363C32×C4—22no—
364C32×C4—41no—
365C32×C4—41no—
366C32×C4—41no—
367C3⋊Dic3—41no—
368C3⋊Dic3—41no—
369C3⋊Dic3—41no—
370C3⋊Dic3—41no—
371C3⋊Dic3—41no—
372C25—91no—
373C22×D4—91no—
374C22×D4—91no—
375C22×D4—91no—
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—91no—
400C2×C22⋊C4—184no—
401C2×C22⋊C4C2×C3⋊D311yescharacteristic
402C2×C22⋊C4C2×C3⋊D311yescharacteristic
403C2×C22⋊C4C2×C3⋊D311yescharacteristic
404C2×C42C2×C3⋊D311yescharacteristic, complemented
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×C3C2×D1218yes—
418C23×C3C23×D314yes—
419C22×D3—38no—
420C22×D3—38no—
421C22×D3—38no—
422C22×D3—38no—
423C22×D3—38no—
424C22×D3—64no—
425C22×D3—64no—
426C22×D3—64no—
427C22×D3—64no—
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—
447C2×C3×C4—24no—
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×C4C2×D1218yes—
463C2×C3×C4C2×D1218yes—
464C2×C3×C4D3×D418yes—
465#67—1216no—
466C2×Dic3—64no—
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—
481D12—632no—
482D12—1216no—
483C4×D3—1216no—
484C4×D3—1216no—
485C4×D3—1216no—
486C2×C32—42no—
487C2×C32C2×#12311yescharacteristic
488C2×C32#52511yescharacteristic
489C2×C32#53811yescharacteristic
490C2×C32D4211yescharacteristic
491C2×C32#54611yescharacteristic
492C2×C32#54611yescharacteristic
493C2×C32#55111yescharacteristic
494C3⋊D3—24no—
495C3⋊D3—42no—
496C3⋊D3—42no—
497C24—91no—
498C24—91no—
499C24—91no—
500C24—182no—
501C24—182no—
502C24—182no—
503C24—182no—
504C24—182no—
505C24—361no—
506C24—361no—
507C24C22×C3⋊D311yescharacteristic
508C2×D4—94no—
509C2×D4—182no—
510C2×D4—182no—
511C2×D4—182no—
512C2×D4—182no—
513C2×D4—182no—
514C2×D4—182no—
515C2×D4—361no—
516C2×D4—361no—
517C22×C4—91no—
518C22×C4—91no—
519C22×C4—91no—
520C22×C4—91no—
521C22×C4—91no—
522C22×C4—182no—
523C22×C4—182no—
524C22×C4—182no—
525C22×C4—182no—
526C22×C4—182no—
527C22×C4—182no—
528C22×C4—361no—
529C22×C4—361no—
530C22×C4—361no—
531C22×C4C22×C3⋊D311yescharacteristic
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—41no—
544C22⋊C4—182no—
545C22⋊C4—182no—
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—361no—
556C22⋊C4—361no—
557C22⋊C4C4⋊(C3⋊D3)14yescomplemented
558C42—22no—
559C22×C3—28no—
560C22×C3—28no—
561C22×C3—28no—
562C22×C3—44no—
563C22×C3—44no—
564C22×C3—44no—
565C22×C3—44no—
566C22×C3C22×D1214yes—
567C22×C3C2×D3×D414yes—
568C22×C3#100414yes—
569C22×C3D3×#4114yes—
570C22×C3D3×#4114yes—
571C22×C3D3×#4114yes—
572C22×C3#100914yes—
573C2×D3—316no—
574C2×D3—68no—
575C2×D3—68no—
576C2×D3—68no—
577C2×D3—68no—
578C2×D3—68no—
579C2×D3—68no—
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—28no—
598C3×C4—44no—
599C3×C4—44no—
600C3×C4—44no—
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—92no—
614C23—92no—
615C23—92no—
616C23—92no—
617C23—92no—
618C23—188no—
619C23—181no—
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—181no—
633C23—181no—
634C23—181no—
635C23—364no—
636C23—364no—
637C23—364no—
638C23—364no—
639C23—364no—
640C23—364no—
641C23C2×C4⋊(C3⋊D3)12yes—
642C23C23×C3⋊D311yescharacteristic
643D4—188no—
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—21no—
660C2×C4—21no—
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—364no—
677C2×C4—364no—
678C2×C4—364no—
679C2×C4C2×C4⋊(C3⋊D3)12yes—
680C2×C4C2×C4⋊(C3⋊D3)12yes—
681C2×C4D4×C3⋊D312yes—
682C2×C3—48no—
683C2×C3#552414yes—
684C2×C3D4×D1214yes—
685C2×C3#555414yes—
686C2×C3#561214yes—
687C2×C3D3×#12314yes—
688C2×C3#567814yes—
689C2×C3#570514yes—
690D3—616no—
691D3—128no—
692D3—128no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—94no—
701C22—182no—
702C22—182no—
703C22—182no—
704C22—182no—
705C22—182no—
706C22—182no—
707C22—182no—
708C22—182no—
709C22—182no—
710C22—182no—
711C22—182no—
712C22—182no—
713C22—3616no—
714C22—361no—
715C22—361no—
716C22—361no—
717C22—361no—
718C22—361no—
719C22—361no—
720C22—361no—
721C22—361no—
722C22C22×C4⋊(C3⋊D3)11yescharacteristic
723C22C2×D4×C3⋊D311yescharacteristic
724C22#6436111yescharacteristic
725C22#41×C3⋊D311yescharacteristic
726C22#41×C3⋊D311yescharacteristic
727C22#41×C3⋊D311yescharacteristic
728C22#6436611yescharacteristic
729C4—22no—
730C4—22no—
731C4—22no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—361no—
736C4—361no—
737C4—361no—
738C4—361no—
739C4—361no—
740C3#7584414yescomplemented
741C2—42no—
742C2—184no—
743C2—362no—
744C2—362no—
745C2#1059599511yescharacteristic
746C2D4×C4⋊(C3⋊D3)11yescharacteristic
747C2#1059602511yescharacteristic
748C2#1059608311yescharacteristic
749C2C3⋊D3×#12311yescharacteristic
750C2#1059614911yescharacteristic
751C2#1059617611yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#388C2
prime radicalC2×#64091C2
hypercenter#388C3⋊D3
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#64092C2semidirect
3. C2×C22⋊C4×C3⋊D3C2semidirect
4. C2×C4×C4⋊(C3⋊D3)C2semidirect
5. C32×#388C2semidirect
6. #10592690C2semidirect
7. #10592686C2semidirect
8. #10592660C2semidirect
9. #10592654C2semidirect
10. #10592652C2semidirect
11. #10592639C2semidirect
12. #10592376C2semidirect
13. #10592367C2semidirect
14. #10592364C2semidirect
15. #10592364C2semidirect
23. C22×C4×C3⋊D3C22semidirect
24. C2×C32×C4⋊C4C22semidirect
28. C2×C32×C42C22semidirect
39. C2×#3752C22semidirect
40. C2×#3752C22semidirect
41. C2×#3752C22semidirect
42. C2×C4⋊(C3⋊Dic3)C22semidirect
43. C2×C4⋊(C3⋊Dic3)C22semidirect
44. C2×C4⋊(C3⋊Dic3)C22semidirect
45. C2×#3750C22semidirect
50. C32×#95C22semidirect
51. C32×#95C22semidirect
52. #63658C22semidirect
53. #63658C22semidirect
54. #63658C22semidirect
55. #63658C22semidirect
60. C3×#388D3semidirect
114. C32×C22⋊C4D4semidirect
141. C2×C3×C4⋊C4C2×D3semidirect
145. C2×C3×C42C2×D3semidirect
167. C3×#95C2×D3semidirect
168. C3×#95C2×D3semidirect
257. #388C3⋊D3semidirect
306. C3×C22⋊C4D12semidirect
360. C2×C3⋊D3#123semidirect
386. C2×C4⋊C4C2×C3⋊D3semidirect
404. C2×C42C2×C3⋊D3semidirect
409. #95C2×C3⋊D3semidirect
410. #95C2×C3⋊D3semidirect
557. C22⋊C4C4⋊(C3⋊D3)semidirect
606. C32#2418semidirect
740. C3#75844semidirect

Maximal subgroups

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

subgroupindex
C2×#640922
C2×#640912
C2×C22⋊C4×C3⋊D32
C2×C4×C4⋊(C3⋊D3)2
C32×#3882
#105926902
#105926862
#105926602
#105926542
#105926522
#105926392
#105923762
#105923672
#105923642
#758443