Finite Group Databasebeta

← #11806085

Subgroups — #11806085

Order 1152.

2784 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic, complemented
2C22×#3752C211yesmaximal, characteristic, complemented
3C2×#64102C211yesmaximal, characteristic, complemented
4C2×#64091C211yesmaximal, characteristic
5C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
6C32×#385C211yesmaximal, characteristic, complemented
7#10592689C211yesmaximal, characteristic, complemented
8#10592688C211yesmaximal, characteristic, complemented
9#10592687C211yesmaximal, characteristic, complemented
10#10592657C211yesmaximal, characteristic, complemented
11C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
12#10592368C211yesmaximal, characteristic, complemented
13#10592365C211yesmaximal, characteristic, complemented
14#10592364C211yesmaximal, characteristic, complemented
15#10592364C211yesmaximal, characteristic, complemented
16#74596—34nomaximal
17C24×C3⋊D3C2211yescharacteristic
18C23×C32×C4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic
24C22×C4×C3⋊D3C2211yescharacteristic
25C22×C4×C3⋊D3C2211yescharacteristic, complemented
26C2×C32×C4⋊C4C2211yescharacteristic, complemented
27C2×C32×C4⋊C4C2211yescharacteristic, complemented
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C4×#638—24no—
32C2×#3752—24no—
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3752C2211yescharacteristic
36C2×#3752C2211yescharacteristic
37C2×#3752C2211yescharacteristic
38C2×#3752C2211yescharacteristic
39C2×#3752C2211yescharacteristic
40C2×#3752C2211yescharacteristic
41C2×#3752C2211yescharacteristic, complemented
42C2×#3752C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic, complemented
44C2×#3750C2211yescharacteristic, complemented
45C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
46C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
47C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
48#64102—24no—
49#64091C418yescomplemented
50C22⋊C4×C3⋊D3—24no—
51C32×#95C2211yescharacteristic, complemented
52C32×#95C2211yescharacteristic, complemented
53#63658C2211yescharacteristic, complemented
54#63658C2211yescharacteristic, complemented
55#63658C2211yescharacteristic, complemented
56#63658C2211yescharacteristic, complemented
57C2×C4×#67—34no—
58C22×(C2×D3)⋊C4—34no—
59C2×#893—34no—
60C2×#882—34no—
61C2×D3×C22⋊C4—34no—
62C3×#385D314yescomplemented
63#4990—34no—
64#4989—34no—
65#4988—34no—
66#4958—34no—
67Dic3×C22⋊C4—34no—
68#4669—34no—
69#4666—34no—
70#4665—34no—
71#4665—34no—
72C24×C32C2311yescharacteristic
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⋊D3C2×C414yescomplemented
80C23×C3⋊D3C2311yescharacteristic
81C23×C3⋊D3C2311yescharacteristic
82C23×C3⋊D3C2311yescharacteristic
83C22×C32×C4—22no—
84C22×C32×C4—22no—
85C22×C32×C4—41no—
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C2×#638—22no—
93C2×#638—22no—
94C2×#638C2×C414yescomplemented
95C22×C3⋊Dic3—22no—
96C22×C3⋊Dic3—22no—
97C22×C3⋊Dic3—41no—
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C2×C4⋊(C3⋊D3)—22no—
104C2×C4⋊(C3⋊D3)—22no—
105C2×C4⋊(C3⋊D3)—41no—
106C2×C4⋊(C3⋊D3)—41no—
107C2×C4⋊(C3⋊D3)C2×C414yescomplemented
108C2×C4⋊(C3⋊D3)C2×C414yescomplemented
109C2×C4×C3⋊D3—22no—
110C2×C4×C3⋊D3—22no—
111C2×C4×C3⋊D3—22no—
112C2×C4×C3⋊D3—22no—
113C2×C4×C3⋊D3—22no—
114C2×C4×C3⋊D3—22no—
115C2×C4×C3⋊D3—41no—
116C2×C4×C3⋊D3—41no—
117C2×C4×C3⋊D3—41no—
118C32×C4⋊C4—22no—
119C32×C4⋊C4—41no—
120C32×C22⋊C4—22no—
121C32×C22⋊C4C2×C414yescomplemented
122#3757D414yescomplemented
123#3752—22no—
124#3752—22no—
125#3752—22no—
126#3752—22no—
127#3752—22no—
128#3752—22no—
129#3752—22no—
130#3752—41no—
131#3752C2×C414yescomplemented
132#3752C2×C414yescomplemented
133#3752D414yescomplemented
134#3750—22no—
135C4×C3⋊Dic3—22no—
136C4×C3⋊Dic3—22no—
137C4×C3⋊Dic3—41no—
138#2358—91noSylow
139C24×D3—34no—
140C23×C3×C4C2×D314yes—
141C22×#67—34no—
142C23×Dic3—34no—
143C22×D12—34no—
144C22×D12—34no—
145C22×C4×D3—34no—
146C22×C4×D3—34no—
147C22×C4×D3—34no—
148C2×C3×C4⋊C4C2×D314yescomplemented
149C2×C3×C4⋊C4C2×D314yescomplemented
150C2×C3×C22⋊C4C2×D314yes—
151C2×C3×C22⋊C4C2×D314yes—
152C2×#217—34no—
153C4×#67—616no—
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—34no—
160C2×(C2×D3)⋊C4—34no—
161C2×(C2×D3)⋊C4—34no—
162C2×(C2×D3)⋊C4—34no—
163C2×(C2×D3)⋊C4—34no—
164C2×(C2×D3)⋊C4—34no—
165C2×(C2×D3)⋊C4—616no—
166C2×Dic3⋊C4—34no—
167C2×C4×Dic3—34no—
168C2×C4×Dic3—34no—
169C2×C4×Dic3—34no—
170#893—616no—
171#882—332no—
172D3×C22⋊C4—616no—
173C3×#95C2×D314yescomplemented
174C3×#95C2×D314yescomplemented
175C3⋊#95—34no—
176C3⋊#95—34no—
177C3⋊#95—34no—
178C3⋊#95—34no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—21no—
182C23×C32—21no—
183C23×C32C22×C412yes—
184C23×C32C2×D412yes—
185C23×C32#4112yes—
186C23×C32C2411yescharacteristic
187C22×C3⋊D3—21no—
188C22×C3⋊D3—21no—
189C22×C3⋊D3—21no—
190C22×C3⋊D3—21no—
191C22×C3⋊D3—28no—
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—21no—
202C22×C3⋊D3—21no—
203C22×C3⋊D3—21no—
204C22×C3⋊D3—28no—
205C22×C3⋊D3—44no—
206C22×C3⋊D3—44no—
207C22×C3⋊D3—44no—
208C22×C3⋊D3—44no—
209C22×C3⋊D3—44no—
210C22×C3⋊D3C22×C412yes—
211C22×C3⋊D3C22×C412yes—
212C22×C3⋊D3C22×C412yes—
213C22×C3⋊D3C2×D412yes—
214C22×C3⋊D3#4112yes—
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×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—44no—
231C2×C32×C4C22×C412yes—
232C2×C32×C4C22×C412yes—
233C2×C32×C4C2×D412yes—
234#638—28no—
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—21no—
246C2×C3⋊Dic3—44no—
247C2×C3⋊Dic3C22×C412yes—
248C2×C3⋊Dic3C2×D412yes—
249C2×C3⋊Dic3C2×D412yes—
250C2×C3⋊Dic3C2×D412yes—
251C4⋊(C3⋊D3)—28no—
252C4⋊(C3⋊D3)—44no—
253C4×C3⋊D3—44no—
254C4×C3⋊D3—44no—
255C4×C3⋊D3—44no—
256C2×#120—91no—
257C2×C4×D4—91no—
258C2×C4×D4—91no—
259C22×C22⋊C4—91no—
260C22×C22⋊C4—91no—
261#390—91no—
262#388—91no—
263#388—91no—
264#386—91no—
265#386—91no—
266#386—91no—
267#385—91no—
268#385C3⋊D311yescharacteristic, complemented
269C4×C22⋊C4—91no—
270C4×C22⋊C4—91no—
271C24×C3C22×D314yes—
272C23×D3—34no—
273C23×D3—34no—
274C23×D3—34no—
275C23×D3—316no—
276C23×D3—68no—
277C23×D3—68no—
278C23×D3—68no—
279C23×D3—68no—
280C23×D3—124no—
281C23×D3—124no—
282C22×C3×C4—28no—
283C22×C3×C4—28no—
284C22×C3×C4—44no—
285C22×C3×C4C22×D314yes—
286C22×C3×C4C22×D314yes—
287C22×C3×C4C22×D314yes—
288C22×C3×C4C22×D314yes—
289C22×C3×C4C22×D314yes—
290C22×C3×C4C22×D314yes—
291C2×#67—316no—
292C2×#67—68no—
293C2×#67—68no—
294C22×Dic3—34no—
295C22×Dic3—34no—
296C22×Dic3—34no—
297C22×Dic3—34no—
298C22×Dic3—34no—
299C22×Dic3—68no—
300C22×Dic3—68no—
301C22×Dic3—124no—
302C2×D12—316no—
303C2×D12—316no—
304C2×D12—68no—
305C2×D12—68no—
306C2×D12—124no—
307C2×D12—124no—
308C2×C4×D3—68no—
309C2×C4×D3—68no—
310C2×C4×D3—68no—
311C2×C4×D3—68no—
312C2×C4×D3—68no—
313C2×C4×D3—68no—
314C2×C4×D3—124no—
315C2×C4×D3—124no—
316C2×C4×D3—124no—
317C3×C4⋊C4—28no—
318C3×C4⋊C4—44no—
319C3×C22⋊C4—28no—
320C3×C22⋊C4C4×D3116yescomplemented
321#217—316no—
322(C2×D3)⋊C4—316no—
323(C2×D3)⋊C4—316no—
324(C2×D3)⋊C4—316no—
325(C2×D3)⋊C4—68no—
326(C2×D3)⋊C4—68no—
327(C2×D3)⋊C4—68no—
328(C2×D3)⋊C4—68no—
329(C2×D3)⋊C4—68no—
330(C2×D3)⋊C4—68no—
331(C2×D3)⋊C4—68no—
332(C2×D3)⋊C4—124no—
333Dic3⋊C4—68no—
334C4×Dic3—68no—
335C4×Dic3—68no—
336C4×Dic3—124no—
337C22×C32—22no—
338C22×C32—22no—
339C22×C32—22no—
340C22×C32—22no—
341C22×C32—22no—
342C22×C32—22no—
343C22×C32C4×D414yescomplemented
344C22×C32C23×C411yescharacteristic
345C22×C32C22×D411yescharacteristic
346C22×C32C22×D411yescharacteristic
347C22×C32C2×#4111yescharacteristic
348C22×C32C2×#4111yescharacteristic
349C22×C32H(5,𝔽2)11yescharacteristic
350C22×C32H(5,𝔽2)11yescharacteristic
351C2×C3⋊D3—22no—
352C2×C3⋊D3—22no—
353C2×C3⋊D3—22no—
354C2×C3⋊D3—22no—
355C2×C3⋊D3—22no—
356C2×C3⋊D3—22no—
357C2×C3⋊D3—22no—
358C2×C3⋊D3—22no—
359C2×C3⋊D3—22no—
360C2×C3⋊D3—22no—
361C2×C3⋊D3—22no—
362C2×C3⋊D3—22no—
363C2×C3⋊D3—416no—
364C2×C3⋊D3—41no—
365C2×C3⋊D3—41no—
366C2×C3⋊D3—41no—
367C2×C3⋊D3—41no—
368C2×C3⋊D3—41no—
369C2×C3⋊D3—41no—
370C2×C3⋊D3—41no—
371C2×C3⋊D3—41no—
372C2×C3⋊D3C4×D414yescomplemented
373C32×C4—22no—
374C32×C4—22no—
375C32×C4—22no—
376C32×C4—41no—
377C32×C4—41no—
378C32×C4—41no—
379C3⋊Dic3—22no—
380C3⋊Dic3—22no—
381C3⋊Dic3—22no—
382C3⋊Dic3—22no—
383C3⋊Dic3—41no—
384C25—91no—
385C22×D4—91no—
386C22×D4—91no—
387C22×D4—91no—
388C23×C4—91no—
389C23×C4—91no—
390C23×C4—91no—
391C23×C4—91no—
392C23×C4C2×C3⋊D311yescharacteristic
393#120—98no—
394C4×D4—184no—
395C4×D4—184no—
396C2×C4⋊C4—91no—
397C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
398C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
399C2×C22⋊C4—91no—
400C2×C22⋊C4—91no—
401C2×C22⋊C4—91no—
402C2×C22⋊C4—91no—
403C2×C22⋊C4—91no—
404C2×C22⋊C4—91no—
405C2×C22⋊C4—91no—
406C2×C22⋊C4—91no—
407C2×C22⋊C4—91no—
408C2×C22⋊C4—91no—
409C2×C22⋊C4—91no—
410C2×C22⋊C4—91no—
411C2×C22⋊C4—184no—
412C2×C22⋊C4—184no—
413C2×C22⋊C4C2×C3⋊D311yescharacteristic
414C2×C22⋊C4C2×C3⋊D311yescharacteristic
415C2×C42—91no—
416C2×C42—91no—
417C2×C42—91no—
418#95—91no—
419#95—91no—
420#95—91no—
421#95—91no—
422#95C2×C3⋊D311yescharacteristic, complemented
423#95C2×C3⋊D311yescharacteristic, complemented
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—24no—
428C23×C3C2×C4×D318yes—
429C23×C3D3×D418yes—
430C23×C3#23918yes—
431C23×C3C23×D314yes—
432C22×D3—38no—
433C22×D3—38no—
434C22×D3—38no—
435C22×D3—38no—
436C22×D3—38no—
437C22×D3—632no—
438C22×D3—64no—
439C22×D3—64no—
440C22×D3—64no—
441C22×D3—64no—
442C22×D3—632no—
443C22×D3—64no—
444C22×D3—64no—
445C22×D3—64no—
446C22×D3—64no—
447C22×D3—64no—
448C22×D3—64no—
449C22×D3—64no—
450C22×D3—64no—
451C22×D3—64no—
452C22×D3—64no—
453C22×D3—64no—
454C22×D3—64no—
455C22×D3—1216no—
456C22×D3—1216no—
457C22×D3—1216no—
458C22×D3—1216no—
459C22×D3—1216no—
460C2×C3×C4—24no—
461C2×C3×C4—24no—
462C2×C3×C4—24no—
463C2×C3×C4—24no—
464C2×C3×C4—24no—
465C2×C3×C4—24no—
466C2×C3×C4—24no—
467C2×C3×C4—24no—
468C2×C3×C4—24no—
469C2×C3×C4—24no—
470C2×C3×C4—24no—
471C2×C3×C4—24no—
472C2×C3×C4—24no—
473C2×C3×C4—24no—
474C2×C3×C4—24no—
475C2×C3×C4—416no—
476C2×C3×C4C2×C4×D318yes—
477C2×C3×C4C2×C4×D318yes—
478C2×C3×C4D3×D418yes—
479#67—632no—
480C2×Dic3—38no—
481C2×Dic3—38no—
482C2×Dic3—38no—
483C2×Dic3—38no—
484C2×Dic3—64no—
485C2×Dic3—64no—
486C2×Dic3—64no—
487C2×Dic3—64no—
488C2×Dic3—64no—
489C2×Dic3—64no—
490C2×Dic3—64no—
491C2×Dic3—64no—
492C2×Dic3—64no—
493C2×Dic3—64no—
494C2×Dic3—64no—
495C2×Dic3—1216no—
496D12—632no—
497D12—1216no—
498C4×D3—1216no—
499C4×D3—1216no—
500C4×D3—1216no—
501C2×C32—24no—
502C2×C32C2×C4×D411yescharacteristic
503C2×C32C2×C4×D411yescharacteristic
504C2×C32#51811yescharacteristic
505C2×C32D4211yescharacteristic
506C2×C32#54611yescharacteristic
507C2×C32#54611yescharacteristic
508C2×C32#55111yescharacteristic
509C3⋊D3—24no—
510C3⋊D3—42no—
511C3⋊D3—42no—
512C24—91no—
513C24—91no—
514C24—91no—
515C24—94no—
516C24—182no—
517C24—182no—
518C24—182no—
519C24—182no—
520C24—361no—
521C24—361no—
522C24C22×C3⋊D311yescharacteristic
523C2×D4—94no—
524C2×D4—94no—
525C2×D4—94no—
526C2×D4—182no—
527C2×D4—182no—
528C2×D4—182no—
529C2×D4—182no—
530C2×D4—361no—
531C2×D4—361no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—41no—
535C22×C4—91no—
536C22×C4—91no—
537C22×C4—91no—
538C22×C4—91no—
539C22×C4—91no—
540C22×C4—182no—
541C22×C4—182no—
542C22×C4—182no—
543C22×C4—182no—
544C22×C4—182no—
545C22×C4—182no—
546C22×C4—182no—
547C22×C4—182no—
548C22×C4—361no—
549C22×C4—361no—
550C22×C4—361no—
551C22×C4—361no—
552C22×C4C22×C3⋊D311yescharacteristic
553C22×C4C22×C3⋊D311yescharacteristic
554C22×C4C22×C3⋊D311yescharacteristic
555C22×C4C22×C3⋊D311yescharacteristic
556C22×C4C22×C3⋊D311yescharacteristic
557C22×C4C22×C3⋊D311yescharacteristic
558C4⋊C4—22no—
559C4⋊C4—41no—
560C4⋊C4—182no—
561C22⋊C4—22no—
562C22⋊C4—94no—
563C22⋊C4—94no—
564C22⋊C4—94no—
565C22⋊C4—94no—
566C22⋊C4—182no—
567C22⋊C4—182no—
568C22⋊C4—182no—
569C22⋊C4—182no—
570C22⋊C4—182no—
571C22⋊C4—182no—
572C22⋊C4—182no—
573C22⋊C4—361no—
574C22⋊C4C4×C3⋊D314yescomplemented
575C42—182no—
576C42—182no—
577C42—361no—
578C22×C3—28no—
579C22×C3—28no—
580C22×C3—28no—
581C22×C3—28no—
582C22×C3—28no—
583C22×C3—28no—
584C22×C3#893116yescomplemented
585C22×C3C22×C4×D314yes—
586C22×C3C2×D3×D414yes—
587C22×C3C2×D3×D414yes—
588C22×C3#100414yes—
589C22×C3C2×#23914yes—
590C22×C3D3×#4114yes—
591C22×C3#100914yes—
592C2×D3—316no—
593C2×D3—68no—
594C2×D3—68no—
595C2×D3—68no—
596C2×D3—68no—
597C2×D3—68no—
598C2×D3—68no—
599C2×D3—68no—
600C2×D3—68no—
601C2×D3—68no—
602C2×D3—68no—
603C2×D3—68no—
604C2×D3—68no—
605C2×D3—1264no—
606C2×D3—124no—
607C2×D3—124no—
608C2×D3—124no—
609C2×D3—124no—
610C2×D3—124no—
611C2×D3—124no—
612C2×D3—124no—
613C2×D3—124no—
614C3×C4—28no—
615C3×C4—28no—
616C3×C4—28no—
617C3×C4—44no—
618C3×C4—44no—
619C3×C4—44no—
620Dic3—68no—
621Dic3—68no—
622Dic3—68no—
623Dic3—68no—
624Dic3—124no—
625C32#235811yescharacteristic, complemented, Sylow
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—92no—
631C23—92no—
632C23—92no—
633C23—92no—
634C23—92no—
635C23—188no—
636C23—181no—
637C23—181no—
638C23—181no—
639C23—181no—
640C23—188no—
641C23—181no—
642C23—181no—
643C23—181no—
644C23—181no—
645C23—181no—
646C23—181no—
647C23—181no—
648C23—181no—
649C23—181no—
650C23—181no—
651C23—181no—
652C23—181no—
653C23—364no—
654C23—364no—
655C23—364no—
656C23—364no—
657C23—364no—
658C23C2×C4×C3⋊D312yes—
659C23D4×C3⋊D312yes—
660C23#383212yes—
661C23C23×C3⋊D311yescharacteristic
662D4—188no—
663D4—188no—
664D4—364no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—44no—
681C2×C4—92no—
682C2×C4—92no—
683C2×C4—92no—
684C2×C4—92no—
685C2×C4—181no—
686C2×C4—181no—
687C2×C4—181no—
688C2×C4—181no—
689C2×C4—181no—
690C2×C4—181no—
691C2×C4—181no—
692C2×C4—181no—
693C2×C4—181no—
694C2×C4—181no—
695C2×C4—181no—
696C2×C4—364no—
697C2×C4—364no—
698C2×C4—364no—
699C2×C4—364no—
700C2×C4C2×C4×C3⋊D312yes—
701C2×C4C2×C4×C3⋊D312yes—
702C2×C4D4×C3⋊D312yes—
703C2×C3—216no—
704C2×C3C2×#89314yes—
705C2×C3C4×D3×D414yes—
706C2×C3#554514yes—
707C2×C3#559014yes—
708C2×C3#563014yes—
709C2×C3#563714yes—
710C2×C3#565414yes—
711D3—616no—
712D3—128no—
713D3—128no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—94no—
721C22—182no—
722C22—182no—
723C22—182no—
724C22—182no—
725C22—182no—
726C22—182no—
727C22—182no—
728C22—182no—
729C22—182no—
730C22—182no—
731C22—182no—
732C22—182no—
733C22—3616no—
734C22—361no—
735C22—361no—
736C22—361no—
737C22—361no—
738C22—361no—
739C22—361no—
740C22—361no—
741C22—361no—
742C22#6410214yescomplemented
743C22C22×C4×C3⋊D311yescharacteristic
744C22C2×D4×C3⋊D311yescharacteristic
745C22C2×D4×C3⋊D311yescharacteristic
746C22#6436111yescharacteristic
747C22C2×#383211yescharacteristic
748C22#41×C3⋊D311yescharacteristic
749C22#6436611yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—182no—
757C4—182no—
758C4—182no—
759C4—182no—
760C4—361no—
761C3#7459614yescomplemented
762C2—24no—
763C2—184no—
764C2—362no—
765C2—362no—
766C2C2×#6410211yescharacteristic
767C2C4×D4×C3⋊D311yescharacteristic
768C2#1059601611yescharacteristic
769C2#1059606111yescharacteristic
770C2#1059610111yescharacteristic
771C2#1059610811yescharacteristic
772C2#1059612511yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#385C2
socle, cosocleC23×C32C24
prime radicalC2×#64091C2
hypercenter#385C3⋊D3
hypocenterC32#2358
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×C4×#638C2semidirect
2. C22×#3752C2semidirect
3. C2×#64102C2semidirect
5. C2×C22⋊C4×C3⋊D3C2semidirect
6. C32×#385C2semidirect
7. #10592689C2semidirect
8. #10592688C2semidirect
9. #10592687C2semidirect
10. #10592657C2semidirect
11. C22⋊C4×C3⋊Dic3C2semidirect
12. #10592368C2semidirect
13. #10592365C2semidirect
14. #10592364C2semidirect
15. #10592364C2semidirect
25. C22×C4×C3⋊D3C22semidirect
26. C2×C32×C4⋊C4C22semidirect
27. C2×C32×C4⋊C4C22semidirect
41. C2×#3752C22semidirect
42. C2×#3752C22semidirect
43. C2×#3752C22semidirect
44. C2×#3750C22semidirect
45. C2×C4×C3⋊Dic3C22semidirect
46. C2×C4×C3⋊Dic3C22semidirect
47. C2×C4×C3⋊Dic3C22semidirect
49. #64091C4semidirect
51. C32×#95C22semidirect
52. C32×#95C22semidirect
53. #63658C22semidirect
54. #63658C22semidirect
55. #63658C22semidirect
56. #63658C22semidirect
62. C3×#385D3semidirect
79. C23×C3⋊D3C2×C4semidirect
94. C2×#638C2×C4semidirect
107. C2×C4⋊(C3⋊D3)C2×C4semidirect
108. C2×C4⋊(C3⋊D3)C2×C4semidirect
121. C32×C22⋊C4C2×C4semidirect
122. #3757D4semidirect
131. #3752C2×C4semidirect
132. #3752C2×C4semidirect
133. #3752D4semidirect
148. C2×C3×C4⋊C4C2×D3semidirect
149. C2×C3×C4⋊C4C2×D3semidirect
173. C3×#95C2×D3semidirect
174. C3×#95C2×D3semidirect
268. #385C3⋊D3semidirect
320. C3×C22⋊C4C4×D3semidirect
343. C22×C32C4×D4semidirect
372. C2×C3⋊D3C4×D4semidirect
397. C2×C4⋊C4C2×C3⋊D3semidirect
398. C2×C4⋊C4C2×C3⋊D3semidirect
422. #95C2×C3⋊D3semidirect
423. #95C2×C3⋊D3semidirect
574. C22⋊C4C4×C3⋊D3semidirect
584. C22×C3#893semidirect
625. C32#2358semidirect
742. C22#64102semidirect
761. C3#74596semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C22×#37522
C2×#641022
C2×#640912
C2×C22⋊C4×C3⋊D32
C32×#3852
#105926892
#105926882
#105926872
#105926572
C22⋊C4×C3⋊Dic32
#105923682
#105923652
#105923642
#745963