Finite Group Databasebeta

← #11803310

Subgroups — #11803310

Order 1152.

1947 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64091C211yesmaximal, characteristic
2C22×#3722C211yesmaximal, characteristic, complemented
3C2×#63952C211yesmaximal, characteristic, complemented
4C3×#4950C211yesmaximal, characteristic, complemented
5C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
6#10591714C211yesmaximal, characteristic, complemented
7#10591711C211yesmaximal, characteristic, complemented
8#10591380C212yesmaximal, complemented
9#10591320C212yesmaximal, complemented
10#10591266C212yesmaximal, complemented
11#10591202C212yesmaximal, complemented
12#74592—31nomaximal
13#73569—31nomaximal
14C24×C3⋊D3C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×C4⋊(C3⋊D3)C2212yes—
17C23×C3×Dic3C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C22×#624C2211yescharacteristic, complemented
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×#3752C2212yes—
22#64091C418yescomplemented
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×C4⋊Dic3C2212yescomplemented
26C2×C3×C4×Dic3C2212yescomplemented
27C2×#3724C2211yescharacteristic, complemented
28C2×#3722—24no—
29C2×#3722C2212yes—
30C2×#3722C2212yes—
31C2×#3722C2212yes—
32C2×#3722C2212yes—
33C2×#3722C2211yescharacteristic, complemented
34C2×#3722C2212yescomplemented
35C2×Dic32C2211yescharacteristic, complemented
36#63952—24no—
37C3×C3⋊#95C2212yescomplemented
38C3×C3⋊#95C2212yescomplemented
39#63579C2212yescomplemented
40C2×C4×#67—31no—
41C22×(C2×D3)⋊C4—31no—
42C22×(C2×D3)⋊C4—31no—
43C2×#882—31no—
44C2×#882—31no—
45C2×#882—61no—
46C2×#67⋊C4—31no—
47C3×#385—31no—
48C3×C4×C22⋊C4—31no—
49#5213—31no—
50#4990—32no—
51#4988—32no—
52#4958—31no—
53#4955—31no—
54#4955—31no—
55#4950D311yescharacteristic, complemented
56Dic3×C22⋊C4D311yescharacteristic, complemented
57#4940—32no—
58#4939—32no—
59#4670—32no—
60#4669—32no—
61#4665—32no—
62#4665—32no—
63C24×C32C2311yescharacteristic
64C23×C3⋊D3—22no—
65C23×C3⋊D3—22no—
66C23×C3⋊D3—42no—
67C23×C3⋊D3—42no—
68C23×C3⋊D3C2×C414yescomplemented
69C23×C3⋊D3C2311yescharacteristic
70C23×C3⋊D3C2312yes—
71C22×C32×C4C2312yes—
72C2×#638—22no—
73C2×#638—22no—
74C2×#638C2×C414yes—
75C22×C3⋊Dic3C2311yescharacteristic
76C2×C4⋊(C3⋊D3)—42no—
77C2×C4⋊(C3⋊D3)—42no—
78C2×C4⋊(C3⋊D3)C2×C418yescomplemented
79C22×C3×Dic3—22no—
80C22×C3×Dic3—42no—
81C22×C3×Dic3—42no—
82C22×C3×Dic3D414yescomplemented
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C2×#624—22no—
90C2×#624—42no—
91C32×C22⋊C4C2×C414yescomplemented
92#3752C2×C418yescomplemented
93C3×#217—22no—
94C3×#217—22no—
95C3×C4⋊Dic3—42no—
96C3×C4×Dic3—42no—
97#3724—22no—
98#3722—22no—
99#3722—24no—
100#3722—24no—
101#3722—42no—
102#3722—42no—
103#3722—42no—
104Dic32—22no—
105#2321—91noSylow
106C24×D3—31no—
107C24×D3—31no—
108C24×D3—61no—
109C23×C3×C4—31no—
110C23×C3×C4—31no—
111C22×#67—31no—
112C22×#67—31no—
113C22×#67—61no—
114C23×Dic3C2×D311yescharacteristic
115C23×Dic3C2×D311yescharacteristic
116C22×D12—32no—
117C22×D12—32no—
118C22×D12—62no—
119C22×C4×D3—31no—
120C22×C4×D3—31no—
121C2×C3×C4⋊C4—32no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—31no—
124C2×C3×C22⋊C4—31no—
125C2×C3×C22⋊C4C2×D311yescharacteristic
126C2×C3×C22⋊C4C2×D311yescharacteristic
127C2×C3×C42—32no—
128C2×#217C2×D311yescharacteristic
129C2×#217C2×D311yescharacteristic
130C4×#67—64no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—31no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—31no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—62no—
146C2×(C2×D3)⋊C4—64no—
147C2×(C2×D3)⋊C4—64no—
148C2×C4⋊Dic3C2×D312yescomplemented
149C2×Dic3⋊C4—31no—
150C2×Dic3⋊C4—31no—
151C2×C4×Dic3—31no—
152C2×C4×Dic3—31no—
153C2×C4×Dic3C2×D312yescomplemented
154#882—38no—
155#882—38no—
156#882—68no—
157#67⋊C4—64no—
158C3×#95—32no—
159C3×#95—32no—
160C3⋊#95—32no—
161C3⋊#95—32no—
162C3⋊#95C2×D312yescomplemented
163C3⋊#95C2×D312yescomplemented
164C23×C32—22no—
165C23×C32—22no—
166C23×C32C22×C412yes—
167C23×C32C2×D412yes—
168C23×C32#4112yes—
169C23×C32C2411yescharacteristic
170C22×C3⋊D3—22no—
171C22×C3⋊D3—22no—
172C22×C3⋊D3—28no—
173C22×C3⋊D3—22no—
174C22×C3⋊D3—21no—
175C22×C3⋊D3—22no—
176C22×C3⋊D3—21no—
177C22×C3⋊D3—22no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3—22no—
180C22×C3⋊D3—22no—
181C22×C3⋊D3—48no—
182C22×C3⋊D3—44no—
183C22×C3⋊D3—44no—
184C22×C3⋊D3—48no—
185C22×C3⋊D3C22×C414yes—
186C22×C3⋊D3C22×C412yes—
187C2×C32×C4—22no—
188C2×C32×C4—22no—
189C2×C32×C4C22×C414yes—
190#638—28no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3C22×C412yes—
194C4⋊(C3⋊D3)—48no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—44no—
208C2×C3×Dic3—44no—
209C2×C3×Dic3C2×D412yes—
210C2×C3×Dic3C2×D412yes—
211#624—44no—
212C2×#120—91no—
213C2×C4×D4—91no—
214C22×C22⋊C4—91no—
215#390—92no—
216#388—92no—
217#388—92no—
218#386—92no—
219#386—91no—
220#385—31no—
221#379—91no—
222C4×C22⋊C4—31no—
223C24×C3—21no—
224C24×C3C22×D311yescharacteristic
225C24×C3C22×D311yescharacteristic
226C23×D3—32no—
227C23×D3—32no—
228C23×D3—31no—
229C23×D3—31no—
230C23×D3—34no—
231C23×D3—34no—
232C23×D3—62no—
233C23×D3—64no—
234C23×D3—61no—
235C23×D3—62no—
236C23×D3—62no—
237C23×D3—62no—
238C23×D3—62no—
239C23×D3—122no—
240C23×D3—122no—
241C23×D3—122no—
242C23×D3—122no—
243C23×D3—122no—
244C23×D3—122no—
245C23×D3—124no—
246C23×D3—124no—
247C22×C3×C4—22no—
248C22×C3×C4—31no—
249C22×C3×C4—31no—
250C22×C3×C4—34no—
251C22×C3×C4—32no—
252C22×C3×C4—32no—
253C22×C3×C4—31no—
254C22×C3×C4—31no—
255C22×C3×C4—62no—
256C22×C3×C4—122no—
257C22×C3×C4—122no—
258C22×C3×C4C22×D312yes—
259C22×C3×C4C22×D312yes—
260C2×#67—34no—
261C2×#67—34no—
262C2×#67—64no—
263C2×#67—62no—
264C2×#67—62no—
265C2×#67—62no—
266C2×#67—62no—
267C2×#67—122no—
268C2×#67—122no—
269C22×Dic3—22no—
270C22×Dic3—31no—
271C22×Dic3—31no—
272C22×Dic3—42no—
273C22×Dic3—42no—
274C22×Dic3—61no—
275C22×Dic3D1214yescomplemented
276C22×Dic3C22×D312yes—
277C22×Dic3C22×D312yes—
278C22×Dic3C22×D311yescharacteristic
279C22×Dic3C22×D311yescharacteristic
280C22×Dic3C22×D311yescharacteristic
281C22×Dic3C22×D311yescharacteristic
282C2×D12—38no—
283C2×D12—38no—
284C2×D12—68no—
285C2×D12—122no—
286C2×D12—122no—
287C2×D12—122no—
288C2×D12—122no—
289C2×D12—124no—
290C2×D12—124no—
291C2×C4×D3—62no—
292C2×C4×D3—62no—
293C2×C4×D3—122no—
294C2×C4×D3—122no—
295C3×C4⋊C4—122no—
296C3×C22⋊C4—24no—
297C3×C22⋊C4—62no—
298C3×C22⋊C4—62no—
299C3×C22⋊C4C4×D314yescomplemented
300C3×C22⋊C4C4×D314yescomplemented
301C3×C42—122no—
302#217—22no—
303#217—22no—
304(C2×D3)⋊C4—38no—
305(C2×D3)⋊C4—38no—
306(C2×D3)⋊C4—68no—
307(C2×D3)⋊C4—64no—
308(C2×D3)⋊C4—64no—
309(C2×D3)⋊C4—62no—
310(C2×D3)⋊C4—62no—
311(C2×D3)⋊C4—64no—
312(C2×D3)⋊C4—64no—
313(C2×D3)⋊C4—122no—
314(C2×D3)⋊C4—122no—
315(C2×D3)⋊C4—122no—
316(C2×D3)⋊C4—122no—
317(C2×D3)⋊C4—122no—
318(C2×D3)⋊C4—122no—
319C4⋊Dic3—42no—
320Dic3⋊C4—62no—
321Dic3⋊C4—62no—
322C4×Dic3—42no—
323C4×Dic3—62no—
324C4×Dic3—62no—
325C22×C32—24no—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—24no—
329C22×C32C4×D414yes—
330C22×C32C23×C411yescharacteristic
331C22×C32C22×D411yescharacteristic
332C22×C32C2×#4111yescharacteristic
333C22×C32H(5,𝔽2)12yes—
334C22×C32H(5,𝔽2)12yes—
335C2×C3⋊D3—24no—
336C2×C3⋊D3—22no—
337C2×C3⋊D3—24no—
338C2×C3⋊D3—24no—
339C2×C3⋊D3—24no—
340C2×C3⋊D3—416no—
341C2×C3⋊D3—42no—
342C2×C3⋊D3—42no—
343C2×C3⋊D3—42no—
344C2×C3⋊D3—42no—
345C2×C3⋊D3—41no—
346C2×C3⋊D3—41no—
347C2×C3⋊D3—42no—
348C32×C4—24no—
349C3⋊Dic3—22no—
350C3×Dic3—22no—
351C3×Dic3—22no—
352C3×Dic3—41no—
353C3×Dic3—41no—
354C3×Dic3—42no—
355C3×Dic3—42no—
356C25—91no—
357C22×D4—91no—
358C22×D4—92no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—91no—
362#120—98no—
363C4×D4—184no—
364C2×C4⋊C4—32no—
365C2×C4⋊C4—91no—
366C2×C22⋊C4—31no—
367C2×C22⋊C4—31no—
368C2×C22⋊C4—92no—
369C2×C22⋊C4—92no—
370C2×C22⋊C4—92no—
371C2×C22⋊C4—91no—
372C2×C22⋊C4—92no—
373C2×C22⋊C4—92no—
374C2×C22⋊C4—92no—
375C2×C22⋊C4—184no—
376C2×C22⋊C4D3211yescharacteristic
377C2×C42—32no—
378C2×C42—91no—
379#95—32no—
380#95—32no—
381#95—92no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—21no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3C2×C4×D312yes—
393C23×C3C2×C4×D312yes—
394C23×C3C2×D1212yes—
395C23×C3#23512yes—
396C23×C3D3×D412yes—
397C23×C3#23912yes—
398C23×C3C23×D311yescharacteristic
399C23×C3C23×D311yescharacteristic
400C22×D3—34no—
401C22×D3—34no—
402C22×D3—32no—
403C22×D3—32no—
404C22×D3—64no—
405C22×D3—62no—
406C22×D3—64no—
407C22×D3—64no—
408C22×D3—68no—
409C22×D3—68no—
410C22×D3—62no—
411C22×D3—61no—
412C22×D3—61no—
413C22×D3—62no—
414C22×D3—62no—
415C22×D3—61no—
416C22×D3—62no—
417C22×D3—62no—
418C22×D3—62no—
419C22×D3—62no—
420C22×D3—62no—
421C22×D3—62no—
422C22×D3—61no—
423C22×D3—62no—
424C22×D3—62no—
425C22×D3—62no—
426C22×D3—62no—
427C22×D3—62no—
428C22×D3—62no—
429C22×D3—62no—
430C22×D3—122no—
431C22×D3—122no—
432C22×D3—122no—
433C22×D3—122no—
434C22×D3—128no—
435C22×D3—122no—
436C22×D3—122no—
437C22×D3—121no—
438C22×D3—121no—
439C22×D3—128no—
440C22×D3—128no—
441C22×D3—1216no—
442C22×D3—128no—
443C22×D3—124no—
444C22×D3—124no—
445C22×D3—124no—
446C22×D3—128no—
447C22×D3—124no—
448C22×D3—128no—
449C22×D3—1216no—
450C22×D3—128no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—24no—
456C2×C3×C4—32no—
457C2×C3×C4—32no—
458C2×C3×C4—42no—
459C2×C3×C4—42no—
460C2×C3×C4—62no—
461C2×C3×C4—62no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—62no—
465C2×C3×C4—62no—
466C2×C3×C4—62no—
467C2×C3×C4—62no—
468C2×C3×C4—62no—
469C2×C3×C4—62no—
470C2×C3×C4—62no—
471C2×C3×C4—62no—
472C2×C3×C4—124no—
473C2×C3×C4—124no—
474C2×C3×C4C2×C4×D314yes—
475C2×C3×C4C2×C4×D314yes—
476#67—68no—
477#67—68no—
478#67—128no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—32no—
492C2×Dic3—32no—
493C2×Dic3—44no—
494C2×Dic3—44no—
495C2×Dic3—62no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—121no—
501C2×Dic3—121no—
502C2×Dic3C2×D1212yes—
503C2×Dic3C2×D1212yes—
504D12—128no—
505D12—128no—
506D12—1216no—
507C4×D3—124no—
508C4×D3—124no—
509C2×C32—24no—
510C2×C32C2×C4×D411yescharacteristic
511C2×C32#51812yes—
512C2×C32#53411yescharacteristic
513C2×C32#53511yescharacteristic
514C2×C32#53812yes—
515C3⋊D3—44no—
516C3⋊D3—42no—
517C24—92no—
518C24—91no—
519C24—94no—
520C24—182no—
521C24—182no—
522C24—362no—
523C24—362no—
524C24C2×D3211yescharacteristic
525C2×D4—94no—
526C2×D4—98no—
527C2×D4—182no—
528C2×D4—182no—
529C2×D4—362no—
530C2×D4—362no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—34no—
534C22×C4—31no—
535C22×C4—32no—
536C22×C4—32no—
537C22×C4—31no—
538C22×C4—62no—
539C22×C4—91no—
540C22×C4—122no—
541C22×C4—122no—
542C22×C4—182no—
543C22×C4—362no—
544C22×C4C2×D3212yes—
545C4⋊C4—122no—
546C4⋊C4—182no—
547C22⋊C4—62no—
548C22⋊C4—62no—
549C22⋊C4—98no—
550C22⋊C4—184no—
551C22⋊C4—184no—
552C22⋊C4—182no—
553C22⋊C4—362no—
554C22⋊C4—362no—
555C22⋊C4—362no—
556C22⋊C4#62414yescomplemented
557C42—122no—
558C42—182no—
559C22×C3—24no—
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—22no—
563C22×C3—24no—
564C22×C3—24no—
565C22×C3—24no—
566C22×C3—22no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—21no—
572C22×C3—24no—
573C22×C3—42no—
574C22×C3—44no—
575C22×C3—44no—
576C22×C3—42no—
577C22×C3C4×D1214yes—
578C22×C3#89314yes—
579C22×C3C22×C4×D311yescharacteristic
580C22×C3C22×C4×D311yescharacteristic
581C22×C3C22×D1211yescharacteristic
582C22×C3C2×#23511yescharacteristic
583C22×C3C2×D3×D411yescharacteristic
584C22×C3#100412yes—
585C22×C3#100412yes—
586C22×C3C2×#23911yescharacteristic
587C22×C3#100912yes—
588C22×C3#100912yes—
589C2×D3—68no—
590C2×D3—62no—
591C2×D3—64no—
592C2×D3—62no—
593C2×D3—64no—
594C2×D3—64no—
595C2×D3—64no—
596C2×D3—64no—
597C2×D3—64no—
598C2×D3—64no—
599C2×D3—64no—
600C2×D3—124no—
601C2×D3—124no—
602C2×D3—124no—
603C2×D3—122no—
604C2×D3—1216no—
605C2×D3—1216no—
606C2×D3—124no—
607C2×D3—124no—
608C2×D3—124no—
609C2×D3—124no—
610C2×D3—1232no—
611C2×D3—122no—
612C2×D3—122no—
613C2×D3—122no—
614C2×D3—121no—
615C2×D3—122no—
616C2×D3—121no—
617C2×D3—122no—
618C2×D3—122no—
619C2×D3—121no—
620C2×D3—122no—
621C2×D3—122no—
622C2×D3—122no—
623C2×D3—122no—
624C2×D3—121no—
625C2×D3—241no—
626C2×D3—242no—
627C2×D3—241no—
628C3×C4—24no—
629C3×C4—24no—
630C3×C4—44no—
631C3×C4—62no—
632C3×C4—62no—
633C3×C4—122no—
634C3×C4—121no—
635C3×C4—122no—
636C3×C4—121no—
637Dic3—22no—
638Dic3—22no—
639Dic3—41no—
640Dic3—42no—
641Dic3—42no—
642Dic3—41no—
643Dic3—62no—
644Dic3—62no—
645Dic3—122no—
646C32#232111yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—94no—
650C23—92no—
651C23—181no—
652C23—182no—
653C23—182no—
654C23—181no—
655C23—182no—
656C23—182no—
657C23—182no—
658C23—182no—
659C23—182no—
660C23—182no—
661C23—188no—
662C23—368no—
663C23—364no—
664C23—368no—
665C23—364no—
666C23#379912yes—
667C23D3×D1212yes—
668C23C2×#62412yes—
669C23C22×D3211yescharacteristic
670D4—188no—
671D4—368no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—32no—
675C2×C4—32no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—92no—
689C2×C4—124no—
690C2×C4—124no—
691C2×C4—181no—
692C2×C4—181no—
693C2×C4—364no—
694C2×C4C2×#62414yes—
695C2×C3—24no—
696C2×C3—24no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—22no—
700C2×C3—22no—
701C2×C3—21no—
702C2×C3—44no—
703C2×C3C2×C4×D1211yescharacteristic
704C2×C3#549311yescharacteristic
705C2×C3C2×#89311yescharacteristic
706C2×C3#552511yescharacteristic
707C2×C3#554512yes—
708C2×C3#554512yes—
709C2×C3#556012yes—
710C2×C3#559211yescharacteristic
711C2×C3#564412yes—
712C2×C3#565311yescharacteristic
713D3—128no—
714D3—124no—
715D3—122no—
716D3—124no—
717D3—122no—
718D3—242no—
719C22—22no—
720C22—24no—
721C22—24no—
722C22—22no—
723C22—182no—
724C22—184no—
725C22—184no—
726C22—184no—
727C22—184no—
728C22—3616no—
729C22—362no—
730C22—361no—
731C22—362no—
732C22—362no—
733C22—362no—
734C22—361no—
735C22—362no—
736C22#6389414yes—
737C22C2×#379911yescharacteristic
738C22C2×D3×D1211yescharacteristic
739C22#6431412yes—
740C22#6431412yes—
741C22C22×#62411yescharacteristic
742C4—24no—
743C4—62no—
744C4—62no—
745C4—122no—
746C4—121no—
747C4—122no—
748C4—121no—
749C4—182no—
750C3—21no—
751C3#7356911yescharacteristic, complemented
752C3#7459211yescharacteristic, complemented
753C2—24no—
754C2—364no—
755C2—362no—
756C2#1059408011yescharacteristic
757C2#1059424312yes—
758C2#1059429111yescharacteristic
759C2C2×#6389411yescharacteristic
760C2#1059522312yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#64091C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#3722C2semidirect
3. C2×#63952C2semidirect
4. C3×#4950C2semidirect
5. C3×Dic3×C22⋊C4C2semidirect
6. #10591714C2semidirect
7. #10591711C2semidirect
8. #10591380C2semidirect
9. #10591320C2semidirect
10. #10591266C2semidirect
11. #10591202C2semidirect
19. C22×#624C22semidirect
22. #64091C4semidirect
25. C2×C3×C4⋊Dic3C22semidirect
26. C2×C3×C4×Dic3C22semidirect
27. C2×#3724C22semidirect
33. C2×#3722C22semidirect
34. C2×#3722C22semidirect
35. C2×Dic32C22semidirect
37. C3×C3⋊#95C22semidirect
38. C3×C3⋊#95C22semidirect
39. #63579C22semidirect
55. #4950D3semidirect
56. Dic3×C22⋊C4D3semidirect
68. C23×C3⋊D3C2×C4semidirect
78. C2×C4⋊(C3⋊D3)C2×C4semidirect
82. C22×C3×Dic3D4semidirect
91. C32×C22⋊C4C2×C4semidirect
92. #3752C2×C4semidirect
148. C2×C4⋊Dic3C2×D3semidirect
153. C2×C4×Dic3C2×D3semidirect
162. C3⋊#95C2×D3semidirect
163. C3⋊#95C2×D3semidirect
275. C22×Dic3D12semidirect
299. C3×C22⋊C4C4×D3semidirect
300. C3×C22⋊C4C4×D3semidirect
556. C22⋊C4#624semidirect
646. C32#2321semidirect
751. C3#73569semidirect
752. C3#74592semidirect

Maximal subgroups

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

subgroupindex
C2×#640912
C22×#37222
C2×#639522
C3×#49502
C3×Dic3×C22⋊C42
#105917142
#105917112
#105913802
#105913202
#105912662
#105912022
#745923
#735693