Finite Group Databasebeta

← C2×#10594907 #11902532

Subgroups — C2×#10594907 #11902532

Order 1152.

3473 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3805C212yesmaximal, complemented
2C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
3C2×C3×#930C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic, complemented
5C2×#63962C212yesmaximal, complemented
6C2×#63918C211yesmaximal, characteristic, complemented
7C2×#63908C211yesmaximal, characteristic, complemented
8C2×#63893C212yesmaximal, complemented
9C2×Dic3×D12C211yesmaximal, characteristic, complemented
10#10594907C2116yesmaximal, direct product factor
11C2×#63891C212yesmaximal, complemented
12C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
13C2×#5611—31nomaximal
14C2×#5555—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C23×C3⋊Dic3C2212yes—
17C22×C3×#67C2212yes—
18C22×C3×#67C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#627C2212yes—
22C22×#625C2212yes—
23C2×#3805—216no—
24C2×#3805C22116yescomplemented
25C22×D3×Dic3C2212yes—
26C22×D3×Dic3C2212yes—
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2212yes—
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×C4⋊(C3⋊Dic3)C2218yescomplemented
31C2×C3×#217C2211yescharacteristic
32C3×#930C2218yescomplemented
33C3×C4×#67C2218yescomplemented
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2212yes—
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2212yes—
40C2×Dic3⋊Dic3C2212yes—
41#63962C22116yescomplemented
42C2×(C2×D3)⋊Dic3C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44#63918C2218yescomplemented
45#63908C2218yescomplemented
46#63893C22116yescomplemented
47Dic3×D12C2218yescomplemented
48#63891C22116yescomplemented
49D3×C4⋊Dic3C2218yescomplemented
50C22×#237—32no—
51C22×#237—32no—
52C2×C3×#121—31no—
53C2×C3×C4×D4—31no—
54C2×#938—31no—
55C2×#935—32no—
56C2×D4×Dic3—31no—
57C2×#930—31no—
58C2×#930D311yescharacteristic, complemented
59C2×C4×#67D311yescharacteristic, complemented
60C22×C4⋊Dic3—31no—
61C22×C4⋊Dic3—31no—
62C22×C4⋊Dic3—31no—
63C22×C4⋊Dic3—61no—
64#5611—316no—
65#5555—316no—
66C2×#897—32no—
67C2×D3×C4⋊C4—31no—
68C2×#888—31no—
69C2×#886—32no—
70C2×#886—32no—
71C2×#883—32no—
72C2×#878—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
82C22×C3⋊Dic3—28no—
83C22×C3⋊Dic3C2312yes—
84C22×C3⋊Dic3C2318yes—
85C22×C3⋊Dic3C2312yes—
86C2×C3×#67—28no—
87C2×C3×#67D418yescomplemented
88C2×C3×#67C2318yes—
89C2×C3×#67C2314yes—
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2312yes—
93C22×C3×Dic3C2311yescharacteristic
94C2×C3×D12—24no—
95C2×C3×D12C2314yes—
96C2×C3×C4×D3—24no—
97C2×C3×C4×D3C2314yes—
98C2×#627—28no—
99C2×#627C2318yes—
100C2×#625—28no—
101C2×#625C2318yes—
102#3805—264no—
103C2×D3×Dic3—28no—
104C2×D3×Dic3—28no—
105C2×D3×Dic3C2318yes—
106C2×D3×Dic3C2318yes—
107C4⋊(C3⋊Dic3)C2314yes—
108C4⋊(C3⋊Dic3)C2318yes—
109C4⋊(C3⋊Dic3)C2314yes—
110C3×#217C2314yes—
111C3×(C2×D3)⋊C4C2314yes—
112C3×(C2×D3)⋊C4C2318yes—
113C3×C4⋊Dic3C2314yes—
114C3×Dic3⋊C4C2314yes—
115C3×C4×Dic3C2314yes—
116Dic3⋊Dic3C2318yes—
117Dic3⋊Dic3C2318yes—
118(C2×D3)⋊Dic3C2318yes—
119(C2×D3)⋊Dic3C2318yes—
120C2×#547—91noSylow
121C22×C3×D4—31no—
122C22×C3×D4—32no—
123C22×C3×D4—31no—
124C23×C3×C4—21no—
125C23×C3×C4—31no—
126C23×C3×C4C2×D311yescharacteristic
127C23×C3×C4C2×D311yescharacteristic
128C22×#67—32no—
129C22×#67—32no—
130C22×#67C2×D312yes—
131C22×#67C2×D311yescharacteristic
132C23×Dic3—32no—
133C23×Dic3—32no—
134C23×Dic3—32no—
135C23×Dic3—32no—
136C23×Dic3—62no—
137C2×#237—316no—
138C2×#237—316no—
139C2×#237—616no—
140C2×#237—616no—
141C22×D12C2×D311yescharacteristic
142C22×C4×D3—32no—
143C22×C4×D3—32no—
144C22×C4×D3C2×D311yescharacteristic
145C22×Dic6—32no—
146C22×Dic6—32no—
147C3×#121—38no—
148C3×C4×D4—38no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C22⋊C4—31no—
152C2×C3×C22⋊C4—32no—
153C2×C3×C22⋊C4—31no—
154C2×C3×C42—31no—
155C2×#217—32no—
156C2×#217—32no—
157C2×#217C2×D311yescharacteristic
158#938—38no—
159#935—316no—
160D4×Dic3—38no—
161#930—38no—
162#930C2×D318yescomplemented
163C4×#67C2×D318yescomplemented
164C2×(C2×D3)⋊C4—32no—
165C2×(C2×D3)⋊C4—32no—
166C2×(C2×D3)⋊C4C2×D311yescharacteristic
167C2×(C2×D3)⋊C4C2×D312yes—
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—32no—
171C2×C4⋊Dic3—32no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—38no—
175C2×C4⋊Dic3—38no—
176C2×C4⋊Dic3—32no—
177C2×C4⋊Dic3—32no—
178C2×C4⋊Dic3—38no—
179C2×C4⋊Dic3—61no—
180C2×C4⋊Dic3—61no—
181C2×C4⋊Dic3—62no—
182C2×C4⋊Dic3—68no—
183C2×C4⋊Dic3C2×D311yescharacteristic
184C2×Dic3⋊C4—32no—
185C2×Dic3⋊C4—32no—
186C2×Dic3⋊C4C2×D311yescharacteristic
187C2×C4×Dic3C2×D311yescharacteristic
188#897—316no—
189D3×C4⋊C4—38no—
190#888—38no—
191#886—316no—
192#886—316no—
193#883—316no—
194#878—316no—
195C4×D12—38no—
196#869—38no—
197C23×C32—22no—
198C23×C32—22no—
199C23×C32C2×D414yes—
200C23×C32C2412yes—
201C23×C32C2411yescharacteristic
202C22×C3×D3—22no—
203C22×C3×D3—22no—
204C22×C3×D3—24no—
205C22×C3×D3—24no—
206C22×C3×D3—24no—
207C22×C3×D3C2×D414yes—
208C22×C3×D3C2414yes—
209C22×C3×D3C2412yes—
210C2×C32×C4—22no—
211C2×C32×C4—28no—
212C2×C32×C4#4114yescomplemented
213C2×C32×C4C2412yes—
214C2×C32×C4C2412yes—
215C2×C3⋊Dic3—24no—
216C2×C3⋊Dic3—216no—
217C2×C3⋊Dic3—24no—
218C2×C3⋊Dic3C2414yes—
219C2×C3⋊Dic3C2414yes—
220C3×#67—216no—
221C3×#67C2×D4116yescomplemented
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×Dic3C2412yes—
230C3×D12—28no—
231C3×C4×D3—28no—
232#627—216no—
233#625—216no—
234D3×Dic3—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—31no—
243C2×#121—91no—
244C2×C4×D4—31no—
245C2×C4×D4—91no—
246C22×C4⋊C4—91no—
247C22×C4⋊C4—91no—
248C24×C3—21no—
249C24×C3—31no—
250C24×C3—32no—
251C24×C3C22×D311yescharacteristic
252C24×C3C22×D311yescharacteristic
253C23×D3C22×D312yes—
254C23×D3C22×D311yescharacteristic
255C2×C3×D4—38no—
256C2×C3×D4—34no—
257C2×C3×D4—38no—
258C2×C3×D4—34no—
259C2×C3×D4—68no—
260C2×C3×D4—64no—
261C22×C3×C4—28no—
262C22×C3×C4—24no—
263C22×C3×C4—24no—
264C22×C3×C4—24no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—31no—
268C22×C3×C4—32no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—34no—
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—28no—
280C2×#67—38no—
281C2×#67—38no—
282C2×#67—68no—
283C2×#67—68no—
284C2×#67D1218yescomplemented
285C2×#67C22×D318yes—
286C2×#67C22×D314yes—
287C22×Dic3—38no—
288C22×Dic3—32no—
289C22×Dic3—32no—
290C22×Dic3—32no—
291C22×Dic3—32no—
292C22×Dic3—38no—
293C22×Dic3—38no—
294C22×Dic3—38no—
295C22×Dic3—68no—
296C22×Dic3—62no—
297C22×Dic3—62no—
298C22×Dic3—68no—
299C22×Dic3—68no—
300C22×Dic3—68no—
301C22×Dic3—68no—
302C22×Dic3—128no—
303C22×Dic3C22×D311yescharacteristic
304C22×Dic3C22×D311yescharacteristic
305C22×Dic3C22×D312yes—
306C22×Dic3C22×D311yescharacteristic
307#237—664no—
308#237—664no—
309C2×D12—24no—
310C2×D12C22×D314yes—
311C2×C4×D3—24no—
312C2×C4×D3—38no—
313C2×C4×D3—38no—
314C2×C4×D3—68no—
315C2×C4×D3—68no—
316C2×C4×D3C22×D314yes—
317C2×Dic6—38no—
318C2×Dic6—38no—
319C2×Dic6—68no—
320C2×Dic6—68no—
321C3×C4⋊C4—34no—
322C3×C4⋊C4—34no—
323C3×C22⋊C4—34no—
324C3×C22⋊C4—38no—
325C3×C22⋊C4—34no—
326C3×C42—34no—
327#217—38no—
328#217—38no—
329#217C22×D314yes—
330(C2×D3)⋊C4—38no—
331(C2×D3)⋊C4—38no—
332(C2×D3)⋊C4C22×D314yes—
333(C2×D3)⋊C4C22×D318yes—
334C4⋊Dic3—34no—
335C4⋊Dic3—34no—
336C4⋊Dic3—38no—
337C4⋊Dic3—38no—
338C4⋊Dic3—34no—
339C4⋊Dic3—34no—
340C4⋊Dic3—38no—
341C4⋊Dic3—38no—
342C4⋊Dic3—64no—
343C4⋊Dic3—64no—
344C4⋊Dic3—68no—
345C4⋊Dic3C22×D314yes—
346Dic3⋊C4—38no—
347Dic3⋊C4—38no—
348Dic3⋊C4C22×D314yes—
349C4×Dic3C22×D314yes—
350C22×C32—28no—
351C22×C32—22no—
352C22×C32—22no—
353C22×C32C22×D414yes—
354C22×C32C22×D412yes—
355C22×C32C2×#4112yes—
356C22×C322−1+412yes—
357C22×C32C2511yescharacteristic
358C2×C3×D3—28no—
359C2×C3×D3—22no—
360C2×C3×D3—22no—
361C2×C3×D3—24no—
362C2×C3×D3—24no—
363C2×C3×D3—24no—
364C2×C3×D3—48no—
365C2×C3×D3C22×D414yes—
366C32×C4—22no—
367C32×C4C2×#4114yescomplemented
368C3⋊Dic3—24no—
369C3⋊Dic3—24no—
370C3×Dic3—24no—
371C3×Dic3—22no—
372C3×Dic3—22no—
373C3×Dic3C22×D414yes—
374C2×#41—916no—
375C2×#41—1816no—
376C22×Q8—92no—
377C22×D4—31no—
378C22×D4—32no—
379C22×D4—31no—
380C22×D4—92no—
381C23×C4—31no—
382C23×C4—92no—
383C23×C4—92no—
384C23×C4—92no—
385C23×C4D3211yescharacteristic
386C4⋊Q8—98no—
387#123—916no—
388#123—916no—
389C22⋊Q8—916no—
390#121—38no—
391#121—98no—
392C4×D4—38no—
393C4×D4—98no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—98no—
397C2×C4⋊C4—92no—
398C2×C4⋊C4—92no—
399C2×C4⋊C4—91no—
400C2×C4⋊C4—91no—
401C2×C4⋊C4—92no—
402C2×C4⋊C4—98no—
403C2×C22⋊C4—31no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—92no—
407C2×C22⋊C4—92no—
408C2×C42—31no—
409C23×C3—24no—
410C23×C3—24no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—21no—
417C23×C3—24no—
418C23×C3—34no—
419C23×C3—32no—
420C23×C3—34no—
421C23×C3—62no—
422C23×C3—62no—
423C23×C3—64no—
424C23×C3—64no—
425C23×C3—64no—
426C23×C3C2×D1214yes—
427C23×C3D3×D414yes—
428C23×C3C23×D312yes—
429C23×C3C23×D312yes—
430C23×C3C23×D311yescharacteristic
431C23×C3C23×D311yescharacteristic
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—24no—
435C22×D3—24no—
436C22×D3—24no—
437C22×D3C2×D1214yes—
438C22×D3C23×D314yes—
439C22×D3C23×D312yes—
440C3×D4—316no—
441C3×D4—616no—
442C3×D4—68no—
443C2×C3×C4—24no—
444C2×C3×C4—216no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—28no—
448C2×C3×C4—28no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—24no—
452C2×C3×C4—34no—
453C2×C3×C4—32no—
454C2×C3×C4—34no—
455C2×C3×C4—32no—
456C2×C3×C4—32no—
457C2×C3×C4—64no—
458C2×C3×C4—62no—
459C2×C3×C4—62no—
460C2×C3×C4—68no—
461C2×C3×C4#23714yescomplemented
462C2×C3×C4#23714yescomplemented
463C2×C3×C4C23×D312yes—
464C2×C3×C4C23×D312yes—
465C2×C3×C4C23×D312yes—
466C2×C3×C4C23×D312yes—
467#67—216no—
468#67—616no—
469#67—616no—
470#67C2×D12116yescomplemented
471C2×Dic3—24no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—34no—
475C2×Dic3—34no—
476C2×Dic3—34no—
477C2×Dic3—34no—
478C2×Dic3—64no—
479C2×Dic3—64no—
480C2×Dic3—616no—
481C2×Dic3—64no—
482C2×Dic3—64no—
483C2×Dic3—616no—
484C2×Dic3—64no—
485C2×Dic3—64no—
486C2×Dic3—616no—
487C2×Dic3—616no—
488C2×Dic3—124no—
489C2×Dic3—124no—
490C2×Dic3—1216no—
491C2×Dic3C2×D1214yes—
492C2×Dic3C23×D312yes—
493C2×Dic3C23×D312yes—
494C2×Dic3C23×D314yes—
495C2×Dic3C23×D312yes—
496D12—28no—
497C4×D3—28no—
498C4×D3—616no—
499C4×D3—616no—
500Dic6—616no—
501Dic6—616no—
502C2×C32—24no—
503C2×C32#54714yescomplemented
504C2×C32C23×D411yescharacteristic
505C2×C32C22×#4111yescharacteristic
506C2×C32C2×2−1+411yescharacteristic
507C3×D3—24no—
508C3×D3—44no—
509C24—31no—
510C24—32no—
511C24C2×D3211yescharacteristic
512#41—1864no—
513C2×Q8—98no—
514C2×Q8—188no—
515C2×D4—34no—
516C2×D4—38no—
517C2×D4—38no—
518C2×D4—34no—
519C2×D4—68no—
520C2×D4—64no—
521C2×D4—98no—
522C2×D4—188no—
523C22×C4—24no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—32no—
528C22×C4—34no—
529C22×C4—64no—
530C22×C4—98no—
531C22×C4—98no—
532C22×C4—98no—
533C22×C4—92no—
534C22×C4—92no—
535C22×C4—188no—
536C22×C4—188no—
537C22×C4—188no—
538C22×C4C2×D3214yes—
539C22×C4C2×D3211yescharacteristic
540C22×C4C2×D3211yescharacteristic
541C4⋊C4—34no—
542C4⋊C4—34no—
543C4⋊C4—98no—
544C4⋊C4—98no—
545C4⋊C4—94no—
546C4⋊C4—94no—
547C4⋊C4—98no—
548C22⋊C4—34no—
549C22⋊C4—34no—
550C22⋊C4—38no—
551C22⋊C4—98no—
552C22⋊C4—98no—
553C42—34no—
554C22×C3—24no—
555C22×C3—24no—
556C22×C3—216no—
557C22×C3—22no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—28no—
562C22×C3—28no—
563C22×C3—22no—
564C22×C3—24no—
565C22×C3—22no—
566C22×C3—22no—
567C22×C3—21no—
568C22×C3—34no—
569C22×C3—62no—
570C22×C3—62no—
571C22×C3—68no—
572C22×C3—64no—
573C22×C3—64no—
574C22×C3—64no—
575C22×C3—128no—
576C22×C3C22×D1214yes—
577C22×C3C22×D1212yes—
578C22×C3C2×D3×D414yes—
579C22×C3C2×D3×D412yes—
580C22×C3C2×#23712yes—
581C22×C3C2×#23712yes—
582C22×C3#101012yes—
583C22×C3#101012yes—
584C22×C3C24×D311yescharacteristic
585C22×C3C24×D311yescharacteristic
586C2×D3—22no—
587C2×D3—22no—
588C2×D3—28no—
589C2×D3—24no—
590C2×D3—24no—
591C2×D3—24no—
592C2×D3—48no—
593C2×D3C22×D1214yes—
594C3×C4—24no—
595C3×C4—22no—
596C3×C4—22no—
597C3×C4—24no—
598C3×C4—34no—
599C3×C4—64no—
600C3×C4—62no—
601C3×C4—62no—
602C3×C4C2×#23714yescomplemented
603C3×C4C2×#23714yescomplemented
604Dic3—24no—
605Dic3—22no—
606Dic3—22no—
607Dic3—64no—
608Dic3—64no—
609Dic3—64no—
610Dic3—64no—
611Dic3—124no—
612Dic3—124no—
613Dic3C22×D1214yes—
614C32C2×#54711yescharacteristic, complemented, Sylow
615C23—22no—
616C23—22no—
617C23—34no—
618C23—32no—
619C23—34no—
620C23—62no—
621C23—62no—
622C23—64no—
623C23—64no—
624C23—64no—
625C23D3×D1214yes—
626C23C22×D3212yes—
627C23C22×D3211yescharacteristic
628Q8—1816no—
629D4—316no—
630D4—616no—
631D4—68no—
632D4—1816no—
633C2×C4—22no—
634C2×C4—28no—
635C2×C4—34no—
636C2×C4—32no—
637C2×C4—32no—
638C2×C4—32no—
639C2×C4—34no—
640C2×C4—62no—
641C2×C4—64no—
642C2×C4—62no—
643C2×C4—68no—
644C2×C4—94no—
645C2×C4—94no—
646C2×C4—1816no—
647C2×C4—1816no—
648C2×C4—184no—
649C2×C4—184no—
650C2×C4—1816no—
651C2×C4#380514yescomplemented
652C2×C4C22×D3212yes—
653C2×C4C22×D3212yes—
654C2×C3—28no—
655C2×C3—24no—
656C2×C3—24no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—24no—
660C2×C3—21no—
661C2×C3—64no—
662C2×C3—124no—
663C2×C3#555514yescomplemented
664C2×C3#561114yescomplemented
665C2×C3C23×D1211yescharacteristic
666C2×C3C22×D3×D411yescharacteristic
667C2×C3C22×#23711yescharacteristic
668C2×C3C22×#23711yescharacteristic
669C2×C3C2×#101011yescharacteristic
670C2×C3C2×#101011yescharacteristic
671D3—24no—
672D3—44no—
673C22—22no—
674C22—28no—
675C22—22no—
676C22—34no—
677C22—62no—
678C22—68no—
679C22—62no—
680C22—64no—
681C22—64no—
682C22—64no—
683C22—128no—
684C22#6429812yes—
685C22C2×D3×D1214yes—
686C22C2×D3×D1212yes—
687C22C2×#380512yes—
688C22C23×D3211yescharacteristic
689C4—22no—
690C4—34no—
691C4—62no—
692C4—64no—
693C4—62no—
694C4—184no—
695C4—184no—
696C4C2×#380514yescomplemented
697C3—21no—
698C3C2×#555511yescharacteristic, complemented
699C3C2×#561111yescharacteristic, complemented
700C2—24no—
701C2—64no—
702C2—124no—
703C2#1059490714yesdirect product factor
704C2C2×#6429811yescharacteristic
705C2C22×D3×D1211yescharacteristic
706C2C22×#380511yescharacteristic
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×#3805C2semidirect
2. C22×C4⋊(C3⋊Dic3)C2semidirect
3. C2×C3×#930C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C2×#63962C2semidirect
6. C2×#63918C2semidirect
7. C2×#63908C2semidirect
8. C2×#63893C2semidirect
9. C2×Dic3×D12C2semidirect
10. #10594907C2direct (N × H)
11. C2×#63891C2semidirect
12. C2×D3×C4⋊Dic3C2semidirect
24. C2×#3805C22semidirect
30. C2×C4⋊(C3⋊Dic3)C22semidirect
32. C3×#930C22semidirect
33. C3×C4×#67C22semidirect
41. #63962C22semidirect
44. #63918C22semidirect
45. #63908C22semidirect
46. #63893C22semidirect
47. Dic3×D12C22semidirect
48. #63891C22semidirect
49. D3×C4⋊Dic3C22semidirect
58. C2×#930D3semidirect
59. C2×C4×#67D3semidirect
87. C2×C3×#67D4semidirect
162. #930C2×D3semidirect
163. C4×#67C2×D3semidirect
212. C2×C32×C4#41semidirect
221. C3×#67C2×D4semidirect
284. C2×#67D12semidirect
367. C32×C4C2×#41semidirect
461. C2×C3×C4#237semidirect
462. C2×C3×C4#237semidirect
470. #67C2×D12semidirect
503. C2×C32#547semidirect
602. C3×C4C2×#237semidirect
603. C3×C4C2×#237semidirect
614. C32C2×#547semidirect
651. C2×C4#3805semidirect
663. C2×C3#5555semidirect
664. C2×C3#5611semidirect
696. C4C2×#3805semidirect
698. C3C2×#5555semidirect
699. C3C2×#5611semidirect
703. C2#10594907direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38052
C22×C4⋊(C3⋊Dic3)2
C2×C3×#9302
C2×C3×C4×#672
C2×#639622
C2×#639182
C2×#639082
C2×#638932
C2×Dic3×D122
#105949072
C2×#638912
C2×D3×C4⋊Dic32
C2×#56113
C2×#55553