Finite Group Databasebeta

← C2×#10594329 #11902609

Subgroups — C2×#10594329 #11902609

Order 1152.

3453 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic, complemented
2C22×#3797C211yesmaximal, characteristic, complemented
3C2×#64104C211yesmaximal, characteristic, complemented
4C2×C3×#897C211yesmaximal, characteristic, complemented
5C2×C3×#887C211yesmaximal, characteristic, complemented
6C2×#63910C212yesmaximal, complemented
7C2×C4×#626C211yesmaximal, characteristic, complemented
8C2×#63895C212yesmaximal, complemented
9C2×#63894C212yesmaximal, complemented
10C2×#63864C211yesmaximal, characteristic, complemented
11C2×#63852C212yesmaximal, complemented
12#10594329C2116yesmaximal, direct product factor
13C2×#5633—31nomaximal
14C2×#5576—31nomaximal
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4⋊(C3⋊D3)C2212yes—
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#627C2212yes—
22C22×#626C2212yes—
23C22×#626C2211yescharacteristic
24C22×#624C2212yes—
25C22×#624C2212yes—
26C2×#3799—28no—
27C2×#3799C2218yescomplemented
28C2×#3797—28no—
29C2×#3797C2218yescomplemented
30C2×C32×C4⋊C4C2211yescharacteristic
31C2×#3752C2212yes—
32#64104C2218yescomplemented
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×C4⋊Dic3C2212yes—
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×C4×Dic3C2212yes—
37C2×C3×C4×Dic3C2211yescharacteristic
38C3×#897C2218yescomplemented
39C3×#887C2218yescomplemented
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×#3722C2212yes—
42C2×#3722C2212yes—
43C2×#3722C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45#63910C22116yescomplemented
46C4×#626C2218yescomplemented
47#63895C22116yescomplemented
48#63894C22116yescomplemented
49#63864C2218yescomplemented
50#63852C22116yescomplemented
51C22×#239—31no—
52C22×D3×Q8—31no—
53C22×D3×Q8—31no—
54C22×#235—31no—
55C2×C3×C22⋊Q8—31no—
56C2×C3×C4×Q8—31no—
57C2×#947—31no—
58C2×C4×#67—31no—
59#5633—316no—
60#5576—316no—
61C2×#897—32no—
62C2×#897D311yescharacteristic, complemented
63C2×#896—32no—
64C2×#895—31no—
65C2×#895—31no—
66C2×#895—32no—
67C2×#895—61no—
68C2×#893—32no—
69C2×#887D311yescharacteristic, complemented
70C2×#885—32no—
71C2×#884—32no—
72C2×#875—31no—
73C2×#875—32no—
74C2×C4×D12—31no—
75C2×C4×D12—32no—
76C23×C3⋊D3C2312yes—
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3C2311yescharacteristic
79C22×C32×C4C2312yes—
80C22×C32×C4C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C2×C4⋊(C3⋊D3)—28no—
83C2×C4⋊(C3⋊D3)—24no—
84C2×C4⋊(C3⋊D3)C2314yes—
85C2×C4⋊(C3⋊D3)C2318yes—
86C2×C4×C3⋊D3—24no—
87C2×C4×C3⋊D3C2314yes—
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2312yes—
93C2×C3×C4×D3—24no—
94C2×C3×C4×D3C2314yes—
95C2×C3×Dic6—24no—
96C2×C3×Dic6D418yescomplemented
97C2×C3×Dic6C2314yes—
98C2×C3×Dic6C2314yes—
99C2×#627—28no—
100C2×#627C2318yes—
101C2×#626—24no—
102C2×#626—28no—
103C2×#626C2318yes—
104C2×#626C2314yes—
105C2×#624—28no—
106C2×#624—28no—
107C2×#624C2318yes—
108C2×#624C2318yes—
109#3799—232no—
110#3797—232no—
111C32×C4⋊C4C2314yes—
112#3752C2318yes—
113C3×(C2×D3)⋊C4C2318yes—
114C3×C4⋊Dic3C2318yes—
115C3×Dic3⋊C4C2318yes—
116C3×C4×Dic3C2318yes—
117C3×C4×Dic3C2314yes—
118Dic3⋊Dic3C2314yes—
119#3722C2318yes—
120#3722C2318yes—
121#3722C2314yes—
122(C2×D3)⋊Dic3C2314yes—
123C2×#548—91noSylow
124C22×C3×Q8—31no—
125C22×C3×Q8—31no—
126C23×C3×C4—31no—
127C22×#67—32no—
128C22×#67—31no—
129C2×#239—38no—
130C2×#239—68no—
131C2×D3×Q8—38no—
132C2×D3×Q8—38no—
133C2×D3×Q8—68no—
134C2×D3×Q8—68no—
135C2×#235—38no—
136C2×#235—68no—
137C22×D12—32no—
138C22×D12—31no—
139C22×D12—31no—
140C22×D12—31no—
141C22×D12—32no—
142C22×D12—32no—
143C22×D12—62no—
144C22×D12—61no—
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C22×C4×D3—32no—
148C22×C4×D3—32no—
149C22×C4×D3—32no—
150C22×C4×D3—32no—
151C22×C4×D3—61no—
152C22×C4×D3C2×D311yescharacteristic
153C22×Dic6—32no—
154C22×Dic6—32no—
155C22×Dic6C2×D311yescharacteristic
156C22×Dic6C2×D311yescharacteristic
157C3×C22⋊Q8—38no—
158C3×C4×Q8—38no—
159C2×C3×C4⋊C4—21no—
160C2×C3×C4⋊C4—32no—
161C2×C3×C4⋊C4—32no—
162C2×C3×C4⋊C4C2×D311yescharacteristic
163C2×C3×C4⋊C4C2×D311yescharacteristic
164C2×C3×C22⋊C4—32no—
165C2×C3×C42—32no—
166C2×C3×C42—31no—
167C2×#217—31no—
168#947—38no—
169C4×#67—38no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—32no—
172C2×(C2×D3)⋊C4—32no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—32no—
175C2×(C2×D3)⋊C4—32no—
176C2×(C2×D3)⋊C4—32no—
177C2×(C2×D3)⋊C4—32no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—62no—
180C2×(C2×D3)⋊C4C2×D312yes—
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3C2×D312yes—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4C2×D312yes—
185C2×C4×Dic3C2×D312yes—
186C2×C4×Dic3C2×D311yescharacteristic
187#897—316no—
188#897C2×D318yescomplemented
189#896—316no—
190#895—38no—
191#895—38no—
192#895—316no—
193#895—68no—
194#893—316no—
195#887C2×D318yescomplemented
196#885—316no—
197#884—316no—
198#875—38no—
199#875—316no—
200C4×D12—38no—
201C4×D12—316no—
202C23×C32C2411yescharacteristic
203C22×C3⋊D3—22no—
204C22×C3⋊D3—22no—
205C22×C3⋊D3—24no—
206C22×C3⋊D3—24no—
207C22×C3⋊D3—24no—
208C22×C3⋊D3#4114yescomplemented
209C22×C3⋊D3C2414yes—
210C22×C3⋊D3C2412yes—
211C22×C3×D3—22no—
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3C2412yes—
215C2×C32×C4—24no—
216C2×C32×C4C2×D414yes—
217C2×C32×C4C2414yes—
218C2×C32×C4C2412yes—
219C2×C3⋊Dic3—22no—
220C2×C3⋊Dic3C2412yes—
221C4⋊(C3⋊D3)—216no—
222C4⋊(C3⋊D3)—28no—
223C4×C3⋊D3—28no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—24no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3C2×D418yes—
229C2×C3×Dic3C2412yes—
230C2×C3×Dic3C2412yes—
231C2×C3×Dic3C2414yes—
232C2×C3×Dic3C2412yes—
233C2×C3×Dic3C2414yes—
234C3×C4×D3—28no—
235C3×Dic6—28no—
236C3×Dic6C2×D4116yescomplemented
237#627—216no—
238#626—28no—
239#626—216no—
240#624—216no—
241#624—216no—
242C22×#41—91no—
243C23×Q8—91no—
244#548—916no—
245C2×#124—92no—
246C2×#124—91no—
247C2×C22⋊Q8—31no—
248C2×C22⋊Q8—92no—
249C2×#121—92no—
250C2×#121—91no—
251C2×C4×Q8—31no—
252C2×C4×D4—92no—
253C2×C4×D4—91no—
254C24×C3—31no—
255C23×D3—31no—
256C23×D3—31no—
257C23×D3—32no—
258C23×D3—32no—
259C23×D3—61no—
260C23×D3—62no—
261C23×D3C22×D311yescharacteristic
262C2×C3×Q8—38no—
263C2×C3×Q8—34no—
264C2×C3×Q8—34no—
265C2×C3×Q8—64no—
266C22×C3×C4—21no—
267C22×C3×C4—22no—
268C22×C3×C4—32no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—32no—
273C22×C3×C4—34no—
274C22×C3×C4—64no—
275C22×C3×C4C22×D312yes—
276C22×C3×C4C22×D312yes—
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C2×#67—34no—
280C2×#67—38no—
281C2×#67—64no—
282C2×#67—68no—
283C22×Dic3—31no—
284C22×Dic3—31no—
285C22×Dic3—61no—
286C22×Dic3C22×D311yescharacteristic
287C22×Dic3C22×D311yescharacteristic
288C22×Dic3C22×D311yescharacteristic
289C22×Dic3C22×D312yes—
290C22×Dic3C22×D312yes—
291#239—632no—
292D3×Q8—632no—
293D3×Q8—632no—
294#235—632no—
295C2×D12—34no—
296C2×D12—38no—
297C2×D12—38no—
298C2×D12—34no—
299C2×D12—38no—
300C2×D12—34no—
301C2×D12—68no—
302C2×D12—64no—
303C2×D12—68no—
304C2×D12—68no—
305C2×D12—68no—
306C2×D12—64no—
307C2×D12—64no—
308C2×D12—64no—
309C2×D12—124no—
310C2×D12—128no—
311C2×C4×D3—24no—
312C2×C4×D3—34no—
313C2×C4×D3—34no—
314C2×C4×D3—38no—
315C2×C4×D3—38no—
316C2×C4×D3—38no—
317C2×C4×D3—38no—
318C2×C4×D3—64no—
319C2×C4×D3—68no—
320C2×C4×D3—68no—
321C2×C4×D3—64no—
322C2×C4×D3—64no—
323C2×C4×D3—68no—
324C2×C4×D3—68no—
325C2×C4×D3—124no—
326C2×C4×D3C22×D314yes—
327C2×Dic6—24no—
328C2×Dic6—38no—
329C2×Dic6—38no—
330C2×Dic6—68no—
331C2×Dic6—68no—
332C2×Dic6D1218yescomplemented
333C2×Dic6C22×D314yes—
334C2×Dic6C22×D314yes—
335C3×C4⋊C4—24no—
336C3×C4⋊C4—38no—
337C3×C4⋊C4—38no—
338C3×C4⋊C4C22×D314yes—
339C3×C4⋊C4C22×D314yes—
340C3×C22⋊C4—38no—
341C3×C42—38no—
342C3×C42—34no—
343#217—34no—
344(C2×D3)⋊C4—34no—
345(C2×D3)⋊C4—38no—
346(C2×D3)⋊C4—38no—
347(C2×D3)⋊C4—34no—
348(C2×D3)⋊C4—38no—
349(C2×D3)⋊C4—38no—
350(C2×D3)⋊C4—38no—
351(C2×D3)⋊C4—38no—
352(C2×D3)⋊C4—34no—
353(C2×D3)⋊C4—68no—
354(C2×D3)⋊C4C22×D318yes—
355C4⋊Dic3—34no—
356C4⋊Dic3C22×D318yes—
357Dic3⋊C4—34no—
358Dic3⋊C4C22×D318yes—
359C4×Dic3C22×D318yes—
360C4×Dic3C22×D314yes—
361C22×C32C22×D412yes—
362C22×C32C2×#4112yes—
363C22×C322−1+412yes—
364C22×C32C2511yescharacteristic
365C2×C3⋊D3—28no—
366C2×C3⋊D3—22no—
367C2×C3⋊D3—22no—
368C2×C3⋊D3—24no—
369C2×C3⋊D3—24no—
370C2×C3⋊D3—24no—
371C2×C3⋊D3—48no—
372C2×C3⋊D3C2×#4114yescomplemented
373C2×C3×D3—22no—
374C2×C3×D3—22no—
375C2×C3×D3—22no—
376C2×C3×D3—44no—
377C32×C4—24no—
378C32×C4C22×D414yes—
379C3⋊Dic3—22no—
380C3×Dic3—22no—
381C3×Dic3—24no—
382C3×Dic3—22no—
383C3×Dic3—22no—
384C3×Dic3C22×D418yes—
385C2×#41—98no—
386C2×#41—188no—
387C22×Q8—31no—
388C22×Q8—31no—
389C22×Q8—92no—
390C22×Q8—98no—
391C22×Q8—188no—
392C22×D4—91no—
393C22×D4—92no—
394C22×D4—92no—
395C22×D4—91no—
396C23×C4—31no—
397C23×C4—92no—
398C23×C4—92no—
399C23×C4—91no—
400#124—916no—
401#124—98no—
402C22⋊Q8—38no—
403C22⋊Q8—916no—
404#121—916no—
405#121—98no—
406C4×Q8—38no—
407C4×D4—916no—
408C4×D4—98no—
409C2×C4⋊C4—32no—
410C2×C4⋊C4—32no—
411C2×C4⋊C4—91no—
412C2×C4⋊C4D3211yescharacteristic
413C2×C22⋊C4—32no—
414C2×C22⋊C4—91no—
415C2×C22⋊C4—92no—
416C2×C22⋊C4—92no—
417C2×C22⋊C4—91no—
418C2×C22⋊C4—92no—
419C2×C42—32no—
420C2×C42—31no—
421C23×C3—21no—
422C23×C3—32no—
423C23×C3—62no—
424C23×C3—62no—
425C23×C3—62no—
426C23×C3C23×D311yescharacteristic
427C23×C3C23×D311yescharacteristic
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—34no—
432C22×D3—34no—
433C22×D3—32no—
434C22×D3—32no—
435C22×D3—34no—
436C22×D3—34no—
437C22×D3—64no—
438C22×D3—62no—
439C22×D3—64no—
440C22×D3—62no—
441C22×D3—62no—
442C22×D3—62no—
443C22×D3—62no—
444C22×D3—64no—
445C22×D3—64no—
446C22×D3—64no—
447C22×D3—64no—
448C22×D3—64no—
449C22×D3—64no—
450C22×D3—122no—
451C22×D3—122no—
452C22×D3—124no—
453C22×D3—124no—
454C22×D3—124no—
455C22×D3C23×D312yes—
456C3×Q8—316no—
457C3×Q8—68no—
458C2×C3×C4—24no—
459C2×C3×C4—24no—
460C2×C3×C4—22no—
461C2×C3×C4—24no—
462C2×C3×C4—24no—
463C2×C3×C4—38no—
464C2×C3×C4—34no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
467C2×C3×C4—32no—
468C2×C3×C4—34no—
469C2×C3×C4—44no—
470C2×C3×C4—64no—
471C2×C3×C4—62no—
472C2×C3×C4—62no—
473C2×C3×C4—62no—
474C2×C3×C4—68no—
475C2×C3×C4C2×D1214yes—
476C2×C3×C4D3×D414yes—
477C2×C3×C4C23×D314yes—
478C2×C3×C4C23×D314yes—
479C2×C3×C4C23×D312yes—
480C2×C3×C4C23×D312yes—
481#67—68no—
482#67—616no—
483C2×Dic3—24no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—32no—
488C2×Dic3—32no—
489C2×Dic3—62no—
490C2×Dic3—62no—
491C2×Dic3—62no—
492C2×Dic3—122no—
493C2×Dic3C2×D1218yes—
494C2×Dic3C23×D312yes—
495C2×Dic3C23×D312yes—
496C2×Dic3C23×D312yes—
497C2×Dic3C23×D314yes—
498C2×Dic3C23×D314yes—
499D12—616no—
500D12—616no—
501D12—616no—
502D12—68no—
503D12—68no—
504D12—68no—
505D12—128no—
506D12—1216no—
507C4×D3—28no—
508C4×D3—616no—
509C4×D3—616no—
510C4×D3—68no—
511C4×D3—68no—
512C4×D3—616no—
513C4×D3—616no—
514C4×D3—128no—
515Dic6—28no—
516Dic6—616no—
517Dic6—616no—
518Dic6C2×D12116yescomplemented
519C2×C32#54814yescomplemented
520C2×C32C23×D411yescharacteristic
521C2×C32C22×#4111yescharacteristic
522C2×C32C2×2−1+411yescharacteristic
523C3⋊D3—24no—
524C3⋊D3—44no—
525C3×D3—42no—
526C24—31no—
527C24—91no—
528C24—92no—
529#41—1832no—
530C2×Q8—34no—
531C2×Q8—34no—
532C2×Q8—38no—
533C2×Q8—64no—
534C2×Q8—98no—
535C2×Q8—188no—
536C2×Q8—1832no—
537C2×D4—94no—
538C2×D4—98no—
539C2×D4—98no—
540C2×D4—94no—
541C2×D4—188no—
542C2×D4—188no—
543C2×D4—184no—
544C2×D4—184no—
545C22×C4—32no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—32no—
549C22×C4—31no—
550C22×C4—34no—
551C22×C4—64no—
552C22×C4—98no—
553C22×C4—98no—
554C22×C4—91no—
555C22×C4—94no—
556C22×C4—188no—
557C22×C4—188no—
558C22×C4—184no—
559C22×C4C2×D3212yes—
560C22×C4C2×D3211yescharacteristic
561C4⋊C4—38no—
562C4⋊C4—38no—
563C4⋊C4—94no—
564C4⋊C4C2×D3214yes—
565C22⋊C4—38no—
566C22⋊C4—94no—
567C22⋊C4—98no—
568C22⋊C4—98no—
569C22⋊C4—94no—
570C22⋊C4—98no—
571C42—38no—
572C42—34no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—21no—
577C22×C3—62no—
578C22×C3—62no—
579C22×C3—62no—
580C22×C3—124no—
581C22×C3C22×D1212yes—
582C22×C3C2×D3×D412yes—
583C22×C3#100712yes—
584C22×C3#100712yes—
585C22×C3D3×#4112yes—
586C22×C3D3×#4112yes—
587C22×C3C24×D311yescharacteristic
588C22×C3C24×D311yescharacteristic
589C2×D3—22no—
590C2×D3—22no—
591C2×D3—22no—
592C2×D3—34no—
593C2×D3—34no—
594C2×D3—44no—
595C2×D3—64no—
596C2×D3—68no—
597C2×D3—62no—
598C2×D3—62no—
599C2×D3—62no—
600C2×D3—62no—
601C2×D3—68no—
602C2×D3—64no—
603C2×D3—64no—
604C2×D3—64no—
605C2×D3—64no—
606C2×D3—64no—
607C2×D3—64no—
608C2×D3—122no—
609C2×D3—128no—
610C2×D3—122no—
611C2×D3—124no—
612C2×D3—124no—
613C2×D3—124no—
614C2×D3—128no—
615C2×D3—128no—
616C2×D3—248no—
617C3×C4—24no—
618C3×C4—24no—
619C3×C4—24no—
620C3×C4—38no—
621C3×C4—44no—
622C3×C4—64no—
623C3×C4—62no—
624C3×C4—62no—
625C3×C4—62no—
626C3×C4C22×D1214yes—
627C3×C4C2×D3×D414yes—
628Dic3—24no—
629Dic3—22no—
630Dic3—22no—
631Dic3—22no—
632Dic3—62no—
633Dic3—62no—
634Dic3—122no—
635Dic3C22×D1218yes—
636C32C2×#54811yescharacteristic, complemented, Sylow
637C23—32no—
638C23—62no—
639C23—62no—
640C23—62no—
641C23—94no—
642C23—92no—
643C23—94no—
644C23—182no—
645C23—182no—
646C23—184no—
647C23—184no—
648C23—184no—
649C23C22×D3211yescharacteristic
650Q8—316no—
651Q8—68no—
652Q8—1816no—
653D4—1816no—
654D4—1816no—
655D4—188no—
656D4—188no—
657C2×C4—24no—
658C2×C4—38no—
659C2×C4—34no—
660C2×C4—32no—
661C2×C4—32no—
662C2×C4—34no—
663C2×C4—32no—
664C2×C4—62no—
665C2×C4—64no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—68no—
669C2×C4—92no—
670C2×C4—1816no—
671C2×C4—1816no—
672C2×C4—182no—
673C2×C4—188no—
674C2×C4D3×D1214yes—
675C2×C4C22×D3214yes—
676C2×C4C22×D3212yes—
677C2×C3—24no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—122no—
682C2×C3#557614yescomplemented
683C2×C3#563314yescomplemented
684C2×C3C23×D1211yescharacteristic
685C2×C3C22×D3×D411yescharacteristic
686C2×C3C2×#100711yescharacteristic
687C2×C3C2×#100711yescharacteristic
688C2×C3C2×D3×#4111yescharacteristic
689C2×C3C2×D3×#4111yescharacteristic
690D3—42no—
691D3—64no—
692D3—64no—
693D3—124no—
694D3—124no—
695D3—124no—
696D3—244no—
697C22—62no—
698C22—62no—
699C22—62no—
700C22—94no—
701C22—124no—
702C22—188no—
703C22—182no—
704C22—182no—
705C22—184no—
706C22—184no—
707C22—184no—
708C22—368no—
709C22C2×D3×D1212yes—
710C22#6431212yes—
711C22#6431612yes—
712C22C23×D3211yescharacteristic
713C4—24no—
714C4—38no—
715C4—62no—
716C4—64no—
717C4—62no—
718C4—62no—
719C4—182no—
720C4C2×D3×D1214yes—
721C3—21no—
722C3C2×#557611yescharacteristic, complemented
723C3C2×#563311yescharacteristic, complemented
724C2—122no—
725C2—184no—
726C2—364no—
727C2#1059432914yesdirect product factor
728C2C22×D3×D1211yescharacteristic
729C2C2×#6431211yescharacteristic
730C2C2×#6431611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3799C2semidirect
2. C22×#3797C2semidirect
3. C2×#64104C2semidirect
4. C2×C3×#897C2semidirect
5. C2×C3×#887C2semidirect
6. C2×#63910C2semidirect
7. C2×C4×#626C2semidirect
8. C2×#63895C2semidirect
9. C2×#63894C2semidirect
10. C2×#63864C2semidirect
11. C2×#63852C2semidirect
12. #10594329C2direct (N × H)
27. C2×#3799C22semidirect
29. C2×#3797C22semidirect
32. #64104C22semidirect
38. C3×#897C22semidirect
39. C3×#887C22semidirect
45. #63910C22semidirect
46. C4×#626C22semidirect
47. #63895C22semidirect
48. #63894C22semidirect
49. #63864C22semidirect
50. #63852C22semidirect
62. C2×#897D3semidirect
69. C2×#887D3semidirect
96. C2×C3×Dic6D4semidirect
188. #897C2×D3semidirect
195. #887C2×D3semidirect
208. C22×C3⋊D3#41semidirect
236. C3×Dic6C2×D4semidirect
332. C2×Dic6D12semidirect
372. C2×C3⋊D3C2×#41semidirect
518. Dic6C2×D12semidirect
519. C2×C32#548semidirect
636. C32C2×#548semidirect
682. C2×C3#5576semidirect
683. C2×C3#5633semidirect
722. C3C2×#5576semidirect
723. C3C2×#5633semidirect
727. C2#10594329direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37992
C22×#37972
C2×#641042
C2×C3×#8972
C2×C3×#8872
C2×#639102
C2×C4×#6262
C2×#638952
C2×#638942
C2×#638642
C2×#638522
#105943292
C2×#56333
C2×#55763