Finite Group Databasebeta

← C2×#10594906 #11902534

Subgroups — C2×#10594906 #11902534

Order 1152.

3477 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C212yesmaximal, complemented
2C2×#64139C211yesmaximal, characteristic, complemented
3C2×C3×C4×#67C211yesmaximal, characteristic, complemented
4C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C2×#63966C212yesmaximal, complemented
6C2×#63918C211yesmaximal, characteristic, complemented
7C2×#63909C211yesmaximal, characteristic, complemented
8C2×#63895C212yesmaximal, complemented
9C2×#63894C211yesmaximal, characteristic, complemented
10#10594906C2116yesmaximal, direct product factor
11C2×#63890C212yesmaximal, complemented
12C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
13C2×#5555—31nomaximal
14C2×#5507—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#638C2212yes—
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2212yes—
20C22×C3×C4×D3C2211yescharacteristic
21C22×#627C2212yes—
22C22×#626C2212yes—
23C22×#624C2212yes—
24C2×#3804—216no—
25C2×#3804C22116yescomplemented
26C22×D3×Dic3C2212yes—
27#64139C2218yescomplemented
28C2×#3752C2212yes—
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C3×C4×#67C2218yescomplemented
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×C4⋊Dic3C2212yes—
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×C4⋊Dic3C2218yescomplemented
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39#63966C22116yescomplemented
40C2×Dic3⋊Dic3C2212yes—
41C2×Dic3⋊Dic3C2212yes—
42C2×#3722C2212yes—
43C2×#3722C2212yes—
44#63918C2218yescomplemented
45#63909C2218yescomplemented
46#63895C22116yescomplemented
47#63894C2218yescomplemented
48#63890C22116yescomplemented
49D3×C4⋊Dic3C2218yescomplemented
50C22×#237—32no—
51C22×#235—32no—
52C2×C3×C4×D4—31no—
53C22×C3×C4⋊C4—31no—
54C2×#930—31no—
55C2×#930—31no—
56C2×#930—31no—
57C2×#930—61no—
58C2×#929—32no—
59C2×C4×#67D311yescharacteristic, complemented
60C22×C4⋊Dic3—31no—
61C22×C4⋊Dic3D311yescharacteristic, complemented
62#5555—316no—
63C2×#897—32no—
64C2×#896—32no—
65#5507—316no—
66C2×#895—31no—
67C2×#894—32no—
68C2×#893—31no—
69C2×D3×C4⋊C4—31no—
70C2×#888—31no—
71C2×#886—32no—
72C2×#886—32no—
73C2×C4×D12—31no—
74C2×#869—31no—
75C24×C32C2311yescharacteristic
76C23×C3⋊D3C2312yes—
77C23×C3×D3C2311yescharacteristic
78C22×C32×C4—24no—
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2314yes—
81C22×C32×C4C2311yescharacteristic
82C2×#638—28no—
83C2×#638C2318yes—
84C22×C3⋊Dic3C2312yes—
85C2×C4⋊(C3⋊D3)—24no—
86C2×C4⋊(C3⋊D3)C2314yes—
87C2×C3×#67D418yescomplemented
88C2×C3×#67C2314yes—
89C22×C3×Dic3—28no—
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2312yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2318yes—
95C22×C3×Dic3C2311yescharacteristic
96C2×C3×C4×D3—24no—
97C2×C3×C4×D3C2314yes—
98C2×#627—28no—
99C2×#627C2318yes—
100C2×#626—28no—
101C2×#626C2318yes—
102C2×#624—28no—
103C2×#624C2318yes—
104#3804—264no—
105C2×D3×Dic3—28no—
106C2×D3×Dic3C2318yes—
107#3752C2318yes—
108C4⋊(C3⋊Dic3)C2314yes—
109C3×#217C2314yes—
110C3×(C2×D3)⋊C4C2314yes—
111C3×C4⋊Dic3C2314yes—
112C3×C4⋊Dic3C2318yes—
113C3×C4⋊Dic3C2314yes—
114C3×Dic3⋊C4C2314yes—
115C3×C4×Dic3C2314yes—
116Dic3⋊Dic3C2318yes—
117Dic3⋊Dic3C2318yes—
118#3722C2318yes—
119#3722C2318yes—
120C2×#547—91noSylow
121C22×C3×D4—31no—
122C23×C3×C4—21no—
123C23×C3×C4—32no—
124C23×C3×C4—31no—
125C23×C3×C4C2×D311yescharacteristic
126C23×C3×C4C2×D311yescharacteristic
127C22×#67—32no—
128C22×#67—32no—
129C22×#67—32no—
130C22×#67—62no—
131C22×#67C2×D311yescharacteristic
132C23×Dic3—32no—
133C23×Dic3C2×D312yes—
134C2×#237—316no—
135C2×#237—616no—
136C2×#235—316no—
137C2×#235—616no—
138C22×D12—32no—
139C22×D12—31no—
140C22×D12—31no—
141C22×D12—61no—
142C22×C4×D3—32no—
143C22×C4×D3—32no—
144C22×C4×D3—32no—
145C22×C4×D3C2×D311yescharacteristic
146C22×Dic6—32no—
147C22×Dic6—32no—
148C3×C4×D4—38no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—32no—
153C2×C3×C4⋊C4—38no—
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C42—31no—
157C2×#217C2×D311yescharacteristic
158#930—38no—
159#930—38no—
160#930—38no—
161#930—68no—
162#929—316no—
163C4×#67C2×D318yescomplemented
164C2×(C2×D3)⋊C4—32no—
165C2×(C2×D3)⋊C4—32no—
166C2×(C2×D3)⋊C4—32no—
167C2×(C2×D3)⋊C4—32no—
168C2×(C2×D3)⋊C4—32no—
169C2×(C2×D3)⋊C4—32no—
170C2×(C2×D3)⋊C4—62no—
171C2×(C2×D3)⋊C4C2×D311yescharacteristic
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—32no—
175C2×C4⋊Dic3—32no—
176C2×C4⋊Dic3—38no—
177C2×C4⋊Dic3—61no—
178C2×C4⋊Dic3C2×D311yescharacteristic
179C2×C4⋊Dic3C2×D311yescharacteristic
180C2×C4⋊Dic3C2×D312yes—
181C2×C4⋊Dic3C2×D318yescomplemented
182C2×Dic3⋊C4—32no—
183C2×Dic3⋊C4—32no—
184C2×Dic3⋊C4C2×D311yescharacteristic
185C2×C4×Dic3C2×D311yescharacteristic
186#897—316no—
187#896—316no—
188#895—38no—
189#894—316no—
190#893—38no—
191D3×C4⋊C4—38no—
192#888—38no—
193#886—316no—
194#886—316no—
195C4×D12—38no—
196#869—38no—
197C23×C32—22no—
198C23×C32—22no—
199C23×C32C2×D414yes—
200C23×C32C2412yes—
201C23×C32C2411yescharacteristic
202C22×C3⋊D3—24no—
203C22×C3⋊D3—24no—
204C22×C3⋊D3—24no—
205C22×C3⋊D3C2414yes—
206C22×C3×D3—22no—
207C22×C3×D3—22no—
208C22×C3×D3C2×D414yes—
209C22×C3×D3C2412yes—
210C2×C32×C4—22no—
211C2×C32×C4—28no—
212C2×C32×C4#4114yescomplemented
213C2×C32×C4C2412yes—
214C2×C32×C4C2412yes—
215#638—216no—
216C2×C3⋊Dic3—24no—
217C2×C3⋊Dic3C2414yes—
218C4⋊(C3⋊D3)—28no—
219C3×#67C2×D4116yescomplemented
220C2×C3×Dic3—24no—
221C2×C3×Dic3—216no—
222C2×C3×Dic3—24no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3C2×D414yes—
226C2×C3×Dic3C2412yes—
227C2×C3×Dic3C2412yes—
228C2×C3×Dic3C2414yes—
229C2×C3×Dic3C2414yes—
230C2×C3×Dic3C2412yes—
231C3×C4×D3—28no—
232#627—216no—
233#626—216no—
234#624—216no—
235D3×Dic3—216no—
236C22×#41—92no—
237#547—916no—
238C2×C4⋊Q8—91no—
239C2×#123—92no—
240C2×#123—92no—
241C2×C22⋊Q8—92no—
242C2×#121—91no—
243C2×#121—91no—
244C2×C4×D4—31no—
245C2×C4×D4—91no—
246C22×C4⋊C4—31no—
247C22×C4⋊C4—91no—
248C24×C3—21no—
249C24×C3—31no—
250C24×C3C22×D311yescharacteristic
251C24×C3C22×D311yescharacteristic
252C23×D3—32no—
253C23×D3—32no—
254C23×D3—62no—
255C23×D3C22×D311yescharacteristic
256C2×C3×D4—38no—
257C2×C3×D4—34no—
258C22×C3×C4—24no—
259C22×C3×C4—24no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—24no—
263C22×C3×C4—31no—
264C22×C3×C4—32no—
265C22×C3×C4—32no—
266C22×C3×C4—31no—
267C22×C3×C4—31no—
268C22×C3×C4—38no—
269C22×C3×C4—34no—
270C22×C3×C4—44no—
271C22×C3×C4—68no—
272C22×C3×C4—64no—
273C22×C3×C4C22×D311yescharacteristic
274C22×C3×C4C22×D311yescharacteristic
275C22×C3×C4C22×D314yes—
276C22×C3×C4C22×D314yes—
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C2×#67—38no—
280C2×#67—38no—
281C2×#67—38no—
282C2×#67—68no—
283C2×#67—68no—
284C2×#67—68no—
285C2×#67—68no—
286C2×#67—128no—
287C2×#67D1218yescomplemented
288C2×#67C22×D314yes—
289C22×Dic3—28no—
290C22×Dic3—32no—
291C22×Dic3—32no—
292C22×Dic3—38no—
293C22×Dic3—62no—
294C22×Dic3—68no—
295C22×Dic3C22×D318yes—
296C22×Dic3C22×D311yescharacteristic
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D312yes—
299C22×Dic3C22×D312yes—
300C22×Dic3C22×D311yescharacteristic
301#237—664no—
302#235—664no—
303C2×D12—38no—
304C2×D12—34no—
305C2×D12—34no—
306C2×D12—64no—
307C2×D12—68no—
308C2×D12—64no—
309C2×D12—64no—
310C2×D12—124no—
311C2×C4×D3—24no—
312C2×C4×D3—38no—
313C2×C4×D3—38no—
314C2×C4×D3—38no—
315C2×C4×D3—68no—
316C2×C4×D3—68no—
317C2×C4×D3—68no—
318C2×C4×D3C22×D314yes—
319C2×Dic6—38no—
320C2×Dic6—38no—
321C2×Dic6—68no—
322C2×Dic6—68no—
323C3×C4⋊C4—34no—
324C3×C4⋊C4—34no—
325C3×C4⋊C4—38no—
326C3×C4⋊C4—34no—
327C3×C22⋊C4—34no—
328C3×C22⋊C4—34no—
329C3×C42—34no—
330#217C22×D314yes—
331(C2×D3)⋊C4—38no—
332(C2×D3)⋊C4—38no—
333(C2×D3)⋊C4—38no—
334(C2×D3)⋊C4—38no—
335(C2×D3)⋊C4—38no—
336(C2×D3)⋊C4—38no—
337(C2×D3)⋊C4—68no—
338(C2×D3)⋊C4C22×D314yes—
339C4⋊Dic3—34no—
340C4⋊Dic3—34no—
341C4⋊Dic3—38no—
342C4⋊Dic3—38no—
343C4⋊Dic3—64no—
344C4⋊Dic3C22×D314yes—
345C4⋊Dic3C22×D314yes—
346C4⋊Dic3C22×D318yes—
347Dic3⋊C4—38no—
348Dic3⋊C4—38no—
349Dic3⋊C4C22×D314yes—
350C4×Dic3C22×D314yes—
351C22×C32—28no—
352C22×C32—22no—
353C22×C32—22no—
354C22×C32C22×D414yes—
355C22×C32C22×D412yes—
356C22×C32C2×#4112yes—
357C22×C322−1+412yes—
358C22×C32C2511yescharacteristic
359C2×C3⋊D3—24no—
360C2×C3⋊D3—24no—
361C2×C3⋊D3—24no—
362C2×C3⋊D3—48no—
363C2×C3×D3—28no—
364C2×C3×D3—22no—
365C2×C3×D3—22no—
366C2×C3×D3C22×D414yes—
367C32×C4—22no—
368C32×C4C2×#4114yescomplemented
369C3⋊Dic3—24no—
370C3×Dic3—24no—
371C3×Dic3—24no—
372C3×Dic3—22no—
373C3×Dic3—22no—
374C3×Dic3C22×D414yes—
375C2×#41—916no—
376C2×#41—1816no—
377C22×Q8—92no—
378C22×D4—31no—
379C22×D4—92no—
380C22×D4—92no—
381C22×D4—91no—
382C23×C4—32no—
383C23×C4—31no—
384C23×C4—92no—
385C23×C4—92no—
386C23×C4D3211yescharacteristic
387C4⋊Q8—98no—
388#123—916no—
389#123—916no—
390C22⋊Q8—916no—
391#121—98no—
392#121—98no—
393C4×D4—38no—
394C4×D4—98no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—38no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—98no—
401C2×C4⋊C4—92no—
402C2×C4⋊C4—92no—
403C2×C4⋊C4—91no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—92no—
407C2×C22⋊C4—92no—
408C2×C22⋊C4—92no—
409C2×C42—31no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—21no—
416C23×C3—24no—
417C23×C3—34no—
418C23×C3—32no—
419C23×C3—42no—
420C23×C3—42no—
421C23×C3—62no—
422C23×C3—62no—
423C23×C3C2×D1214yes—
424C23×C3D3×D414yes—
425C23×C3C23×D312yes—
426C23×C3C23×D312yes—
427C23×C3C23×D311yescharacteristic
428C23×C3C23×D311yescharacteristic
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—34no—
432C22×D3—34no—
433C22×D3—64no—
434C22×D3—64no—
435C22×D3—64no—
436C22×D3—64no—
437C22×D3—64no—
438C22×D3—64no—
439C22×D3—64no—
440C22×D3—124no—
441C22×D3—124no—
442C22×D3—124no—
443C22×D3C2×D1214yes—
444C22×D3C23×D312yes—
445C3×D4—316no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—28no—
449C2×C3×C4—28no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—24no—
453C2×C3×C4—34no—
454C2×C3×C4—32no—
455C2×C3×C4—34no—
456C2×C3×C4—34no—
457C2×C3×C4—32no—
458C2×C3×C4—32no—
459C2×C3×C4—48no—
460C2×C3×C4—42no—
461C2×C3×C4—64no—
462C2×C3×C4—64no—
463C2×C3×C4—616no—
464C2×C3×C4—62no—
465C2×C3×C4—62no—
466C2×C3×C4—68no—
467C2×C3×C4#23514yescomplemented
468C2×C3×C4#23714yescomplemented
469C2×C3×C4C23×D312yes—
470C2×C3×C4C23×D312yes—
471C2×C3×C4C23×D312yes—
472C2×C3×C4C23×D312yes—
473#67—616no—
474#67—616no—
475#67—616no—
476#67—1216no—
477#67C2×D12116yescomplemented
478C2×Dic3—24no—
479C2×Dic3—24no—
480C2×Dic3—216no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—34no—
484C2×Dic3—34no—
485C2×Dic3—64no—
486C2×Dic3—616no—
487C2×Dic3—64no—
488C2×Dic3—64no—
489C2×Dic3—124no—
490C2×Dic3C2×D1214yes—
491C2×Dic3C23×D312yes—
492C2×Dic3C23×D312yes—
493C2×Dic3C23×D314yes—
494C2×Dic3C23×D314yes—
495C2×Dic3C23×D312yes—
496D12—616no—
497D12—68no—
498D12—68no—
499D12—128no—
500C4×D3—28no—
501C4×D3—616no—
502C4×D3—616no—
503C4×D3—616no—
504Dic6—616no—
505Dic6—616no—
506C2×C32—24no—
507C2×C32#54714yescomplemented
508C2×C32C23×D411yescharacteristic
509C2×C32C22×#4111yescharacteristic
510C2×C32C2×2−1+411yescharacteristic
511C3⋊D3—44no—
512C3×D3—24no—
513C24—31no—
514C24—92no—
515C24C2×D3211yescharacteristic
516#41—1864no—
517C2×Q8—98no—
518C2×Q8—188no—
519C2×D4—34no—
520C2×D4—38no—
521C2×D4—98no—
522C2×D4—98no—
523C2×D4—94no—
524C2×D4—188no—
525C2×D4—188no—
526C2×D4—184no—
527C22×C4—24no—
528C22×C4—31no—
529C22×C4—38no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—32no—
533C22×C4—32no—
534C22×C4—34no—
535C22×C4—68no—
536C22×C4—64no—
537C22×C4—98no—
538C22×C4—98no—
539C22×C4—92no—
540C22×C4—188no—
541C22×C4—188no—
542C22×C4C2×D3214yes—
543C22×C4C2×D3211yescharacteristic
544C22×C4C2×D3211yescharacteristic
545C4⋊C4—34no—
546C4⋊C4—34no—
547C4⋊C4—38no—
548C4⋊C4—34no—
549C4⋊C4—98no—
550C4⋊C4—98no—
551C4⋊C4—94no—
552C22⋊C4—34no—
553C22⋊C4—34no—
554C22⋊C4—98no—
555C22⋊C4—98no—
556C22⋊C4—98no—
557C42—34no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—28no—
563C22×C3—28no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—24no—
567C22×C3—22no—
568C22×C3—21no—
569C22×C3—34no—
570C22×C3—42no—
571C22×C3—42no—
572C22×C3—48no—
573C22×C3—62no—
574C22×C3—62no—
575C22×C3—68no—
576C22×C3C22×D1214yes—
577C22×C3C22×D1212yes—
578C22×C3C2×#23512yes—
579C22×C3C2×D3×D414yes—
580C22×C3C2×D3×D412yes—
581C22×C3C2×#23712yes—
582C22×C3#100712yes—
583C22×C3#101012yes—
584C22×C3C24×D311yescharacteristic
585C22×C3C24×D311yescharacteristic
586C2×D3—22no—
587C2×D3—22no—
588C2×D3—28no—
589C2×D3—64no—
590C2×D3—64no—
591C2×D3—64no—
592C2×D3—64no—
593C2×D3—64no—
594C2×D3—64no—
595C2×D3—124no—
596C2×D3—124no—
597C2×D3—124no—
598C2×D3—128no—
599C2×D3—128no—
600C2×D3—248no—
601C2×D3C22×D1214yes—
602C3×C4—22no—
603C3×C4—22no—
604C3×C4—24no—
605C3×C4—34no—
606C3×C4—42no—
607C3×C4—64no—
608C3×C4—64no—
609C3×C4—62no—
610C3×C4—62no—
611C3×C4C2×#23514yescomplemented
612C3×C4C2×#23714yescomplemented
613Dic3—24no—
614Dic3—24no—
615Dic3—22no—
616Dic3—22no—
617Dic3—64no—
618Dic3—64no—
619Dic3—124no—
620Dic3C22×D1214yes—
621C32C2×#54711yescharacteristic, complemented, Sylow
622C23—22no—
623C23—22no—
624C23—34no—
625C23—32no—
626C23—62no—
627C23—62no—
628C23—94no—
629C23—184no—
630C23—184no—
631C23—184no—
632C23D3×D1214yes—
633C23C22×D3212yes—
634C23C22×D3211yescharacteristic
635Q8—1816no—
636D4—316no—
637D4—1816no—
638D4—1816no—
639D4—188no—
640C2×C4—22no—
641C2×C4—28no—
642C2×C4—34no—
643C2×C4—32no—
644C2×C4—32no—
645C2×C4—32no—
646C2×C4—34no—
647C2×C4—34no—
648C2×C4—62no—
649C2×C4—64no—
650C2×C4—64no—
651C2×C4—616no—
652C2×C4—62no—
653C2×C4—68no—
654C2×C4—94no—
655C2×C4—1816no—
656C2×C4—1816no—
657C2×C4—184no—
658C2×C4#380414yescomplemented
659C2×C4C22×D3212yes—
660C2×C4C22×D3212yes—
661C2×C3—24no—
662C2×C3—24no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—24no—
666C2×C3—21no—
667C2×C3—44no—
668C2×C3—64no—
669C2×C3#550714yescomplemented
670C2×C3#555514yescomplemented
671C2×C3C23×D1211yescharacteristic
672C2×C3C22×#23511yescharacteristic
673C2×C3C22×D3×D411yescharacteristic
674C2×C3C22×#23711yescharacteristic
675C2×C3C2×#100711yescharacteristic
676C2×C3C2×#101011yescharacteristic
677D3—24no—
678D3—124no—
679D3—124no—
680D3—244no—
681C22—22no—
682C22—28no—
683C22—22no—
684C22—34no—
685C22—62no—
686C22—68no—
687C22—62no—
688C22—184no—
689C22—184no—
690C22—184no—
691C22—368no—
692C22#6429712yes—
693C22C2×D3×D1214yes—
694C22C2×D3×D1212yes—
695C22C2×#380412yes—
696C22C23×D3211yescharacteristic
697C4—22no—
698C4—34no—
699C4—62no—
700C4—64no—
701C4—64no—
702C4—62no—
703C4—184no—
704C4C2×#380414yescomplemented
705C3—21no—
706C3C2×#550711yescharacteristic, complemented
707C3C2×#555511yescharacteristic, complemented
708C2—24no—
709C2—64no—
710C2—364no—
711C2#1059490614yesdirect product factor
712C2C2×#6429711yescharacteristic
713C2C22×D3×D1211yescharacteristic
714C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3804C2semidirect
2. C2×#64139C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C22×C3×C4⋊Dic3C2semidirect
5. C2×#63966C2semidirect
6. C2×#63918C2semidirect
7. C2×#63909C2semidirect
8. C2×#63895C2semidirect
9. C2×#63894C2semidirect
10. #10594906C2direct (N × H)
11. C2×#63890C2semidirect
12. C2×D3×C4⋊Dic3C2semidirect
25. C2×#3804C22semidirect
27. #64139C22semidirect
31. C3×C4×#67C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
39. #63966C22semidirect
44. #63918C22semidirect
45. #63909C22semidirect
46. #63895C22semidirect
47. #63894C22semidirect
48. #63890C22semidirect
49. D3×C4⋊Dic3C22semidirect
59. C2×C4×#67D3semidirect
61. C22×C4⋊Dic3D3semidirect
87. C2×C3×#67D4semidirect
163. C4×#67C2×D3semidirect
181. C2×C4⋊Dic3C2×D3semidirect
212. C2×C32×C4#41semidirect
219. C3×#67C2×D4semidirect
287. C2×#67D12semidirect
368. C32×C4C2×#41semidirect
467. C2×C3×C4#235semidirect
468. C2×C3×C4#237semidirect
477. #67C2×D12semidirect
507. C2×C32#547semidirect
611. C3×C4C2×#235semidirect
612. C3×C4C2×#237semidirect
621. C32C2×#547semidirect
658. C2×C4#3804semidirect
669. C2×C3#5507semidirect
670. C2×C3#5555semidirect
704. C4C2×#3804semidirect
706. C3C2×#5507semidirect
707. C3C2×#5555semidirect
711. C2#10594906direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38042
C2×#641392
C2×C3×C4×#672
C22×C3×C4⋊Dic32
C2×#639662
C2×#639182
C2×#639092
C2×#638952
C2×#638942
#105949062
C2×#638902
C2×D3×C4⋊Dic32
C2×#55553
C2×#55073