Finite Group Databasebeta

← C2×#10594910 #11900776

Subgroups — C2×#10594910 #11900776

Order 1152.

3669 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×#3804C212yesmaximal, complemented
2C2×#64139C211yesmaximal, characteristic, complemented
3C2×C3×#930C211yesmaximal, characteristic, complemented
4C22×C3×C4×Dic3C211yesmaximal, characteristic, complemented
5C2×#63978C212yesmaximal, complemented
6C2×#63918C211yesmaximal, characteristic, complemented
7C2×#63911C211yesmaximal, characteristic, complemented
8C2×#63894C211yesmaximal, characteristic, complemented
9#10594910C2116yesmaximal, direct product factor
10C2×Dic3×D12C211yesmaximal, characteristic, complemented
11C2×#63880C212yesmaximal, complemented
12C2×#63852C212yesmaximal, complemented
13C2×#5596—31nomaximal
14C2×#5477—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#638C2212yes—
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C3×#67C2212yes—
19C23×C3×Dic3C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×#627C2212yes—
23C22×#626C2212yes—
24C22×#626C2212yes—
25C22×#624C2212yes—
26C2×#3804—216no—
27C2×#3804C22116yescomplemented
28C22×D3×Dic3C2212yes—
29#64139C2218yescomplemented
30C2×#3752C2212yes—
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C3×#930C2218yescomplemented
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2218yescomplemented
40#63978C22116yescomplemented
41C2×Dic3⋊Dic3C2212yes—
42C2×#3722C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44#63918C2218yescomplemented
45#63911C2218yescomplemented
46#63894C2218yescomplemented
47Dic3×D12C2218yescomplemented
48#63880C22116yescomplemented
49#63852C22116yescomplemented
50C22×#237—32no—
51C22×#235—32no—
52C2×C3×#121—31no—
53C22×C3×C42—31no—
54C2×#940—31no—
55C2×#939—32no—
56C2×D4×Dic3—31no—
57C2×#930—31no—
58C2×#930—31no—
59C2×#930—32no—
60C2×#930—61no—
61C2×#930D311yescharacteristic, complemented
62C22×C4×Dic3D311yescharacteristic, complemented
63#5596—316no—
64C2×#893—31no—
65C2×#888—31no—
66C2×#885—32no—
67C2×#67⋊C4—32no—
68#5477—316no—
69C2×#875—32no—
70C2×#874—31no—
71C2×C4×D12—31no—
72C2×C4×D12—32no—
73C2×C4×D12—31no—
74C2×#869—31no—
75C24×C32C2311yescharacteristic
76C23×C3⋊D3C2312yes—
77C23×C3×D3C2312yes—
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×#67—28no—
88C2×C3×#67C2318yes—
89C22×C3×Dic3—24no—
90C22×C3×Dic3D418yescomplemented
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2314yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2314yes—
97C22×C3×Dic3C2311yescharacteristic
98C2×C3×D12—24no—
99C2×C3×D12C2314yes—
100C2×#627—28no—
101C2×#627C2318yes—
102C2×#626—28no—
103C2×#626—28no—
104C2×#626C2318yes—
105C2×#626C2318yes—
106C2×#624—28no—
107C2×#624C2318yes—
108#3804—264no—
109C2×D3×Dic3—28no—
110C2×D3×Dic3C2318yes—
111#3752C2318yes—
112C4⋊(C3⋊Dic3)C2314yes—
113C3×(C2×D3)⋊C4C2318yes—
114C3×C4⋊Dic3C2314yes—
115C3×C4×Dic3C2314yes—
116C3×C4×Dic3C2314yes—
117C3×C4×Dic3C2314yes—
118C3×C4×Dic3C2314yes—
119Dic3⋊Dic3C2318yes—
120#3722C2318yes—
121(C2×D3)⋊Dic3C2318yes—
122C2×#532—91noSylow
123C22×C3×D4—32no—
124C22×C3×D4—31no—
125C23×C3×C4—21no—
126C23×C3×C4—31no—
127C23×C3×C4—31no—
128C23×C3×C4C2×D311yescharacteristic
129C23×C3×C4C2×D311yescharacteristic
130C22×#67—32no—
131C22×#67—32no—
132C22×#67—32no—
133C22×#67—32no—
134C22×#67—62no—
135C22×#67C2×D312yes—
136C23×Dic3—32no—
137C23×Dic3C2×D311yescharacteristic
138C23×Dic3C2×D311yescharacteristic
139C2×#237—316no—
140C2×#237—616no—
141C2×#235—316no—
142C2×#235—616no—
143C22×D12—32no—
144C22×D12—32no—
145C22×D12—31no—
146C22×D12—31no—
147C22×D12—61no—
148C22×D12C2×D311yescharacteristic
149C22×C4×D3—32no—
150C22×C4×D3—32no—
151C22×C4×D3—32no—
152C22×Dic6—32no—
153C22×Dic6—32no—
154C3×#121—38no—
155C2×C3×C4⋊C4—31no—
156C2×C3×C22⋊C4—32no—
157C2×C3×C42—31no—
158C2×C3×C42—31no—
159C2×C3×C42—31no—
160C2×C3×C42—31no—
161C2×C3×C42—38no—
162C2×#217—32no—
163#940—38no—
164#939—316no—
165D4×Dic3—38no—
166#930—38no—
167#930—38no—
168#930—316no—
169#930—68no—
170#930C2×D318yescomplemented
171C2×(C2×D3)⋊C4—32no—
172C2×(C2×D3)⋊C4—32no—
173C2×(C2×D3)⋊C4—32no—
174C2×(C2×D3)⋊C4—32no—
175C2×(C2×D3)⋊C4—32no—
176C2×(C2×D3)⋊C4—62no—
177C2×(C2×D3)⋊C4C2×D312yes—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3—32no—
181C2×C4⋊Dic3—61no—
182C2×C4⋊Dic3C2×D311yescharacteristic
183C2×Dic3⋊C4—32no—
184C2×C4×Dic3C2×D311yescharacteristic
185C2×C4×Dic3C2×D311yescharacteristic
186C2×C4×Dic3C2×D311yescharacteristic
187C2×C4×Dic3C2×D311yescharacteristic
188C2×C4×Dic3C2×D318yescomplemented
189#893—38no—
190#888—38no—
191#885—316no—
192#67⋊C4—316no—
193#875—316no—
194#874—38no—
195C4×D12—38no—
196C4×D12—316no—
197C4×D12—38no—
198#869—38no—
199C23×C32—22no—
200C23×C32—22no—
201C23×C32C2×D414yes—
202C23×C32C2412yes—
203C23×C32C2411yescharacteristic
204C22×C3⋊D3—24no—
205C22×C3⋊D3—24no—
206C22×C3⋊D3—24no—
207C22×C3⋊D3C2414yes—
208C22×C3×D3—24no—
209C22×C3×D3—24no—
210C22×C3×D3—24no—
211C22×C3×D3C2414yes—
212C2×C32×C4—22no—
213C2×C32×C4—28no—
214C2×C32×C4#4114yescomplemented
215C2×C32×C4C2412yes—
216C2×C32×C4C2412yes—
217#638—216no—
218C2×C3⋊Dic3—24no—
219C2×C3⋊Dic3C2414yes—
220C4⋊(C3⋊D3)—28no—
221C3×#67—216no—
222C2×C3×Dic3—24no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—28no—
225C2×C3×Dic3C2×D414yes—
226C2×C3×Dic3C2×D414yes—
227C2×C3×Dic3C2×D4116yescomplemented
228C2×C3×Dic3#4114yescomplemented
229C2×C3×Dic3C2412yes—
230C2×C3×Dic3C2414yes—
231C2×C3×Dic3C2412yes—
232C2×C3×Dic3C2412yes—
233C2×C3×Dic3C2412yes—
234C3×D12—28no—
235#627—216no—
236#626—216no—
237#626—216no—
238#624—216no—
239D3×Dic3—216no—
240C22×#41—92no—
241#532—916no—
242C2×C4⋊Q8—91no—
243C2×#127—91no—
244C2×#124—92no—
245C2×#121—31no—
246C2×#121—92no—
247C2×#121—91no—
248C2×C4×D4—92no—
249C2×C4×D4—91no—
250C2×C4×D4—91no—
251C22×C42—31no—
252C24×C3—21no—
253C24×C3—32no—
254C24×C3C22×D311yescharacteristic
255C24×C3C22×D311yescharacteristic
256C23×D3—32no—
257C23×D3—32no—
258C23×D3—62no—
259C23×D3C22×D312yes—
260C2×C3×D4—38no—
261C2×C3×D4—34no—
262C2×C3×D4—68no—
263C2×C3×D4—64no—
264C22×C3×C4—24no—
265C22×C3×C4—24no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—24no—
269C22×C3×C4—38no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—34no—
274C22×C3×C4—32no—
275C22×C3×C4—31no—
276C22×C3×C4—34no—
277C22×C3×C4—44no—
278C22×C3×C4—64no—
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D314yes—
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D314yes—
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D311yescharacteristic
285C2×#67—28no—
286C2×#67—38no—
287C2×#67—38no—
288C2×#67—38no—
289C2×#67—38no—
290C2×#67—68no—
291C2×#67—68no—
292C2×#67—68no—
293C2×#67—68no—
294C2×#67—68no—
295C2×#67—128no—
296C2×#67C22×D318yes—
297C22×Dic3—24no—
298C22×Dic3—32no—
299C22×Dic3—32no—
300C22×Dic3—38no—
301C22×Dic3—62no—
302C22×Dic3—68no—
303C22×Dic3D1218yescomplemented
304C22×Dic3C22×D311yescharacteristic
305C22×Dic3C22×D314yes—
306C22×Dic3C22×D312yes—
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D314yes—
310C22×Dic3C22×D311yescharacteristic
311#237—664no—
312#235—664no—
313C2×D12—24no—
314C2×D12—38no—
315C2×D12—38no—
316C2×D12—34no—
317C2×D12—34no—
318C2×D12—64no—
319C2×D12—68no—
320C2×D12—68no—
321C2×D12—64no—
322C2×D12—64no—
323C2×D12—124no—
324C2×D12C22×D314yes—
325C2×C4×D3—38no—
326C2×C4×D3—38no—
327C2×C4×D3—38no—
328C2×C4×D3—68no—
329C2×C4×D3—68no—
330C2×C4×D3—68no—
331C2×Dic6—38no—
332C2×Dic6—38no—
333C2×Dic6—68no—
334C2×Dic6—68no—
335C3×C4⋊C4—34no—
336C3×C22⋊C4—38no—
337C3×C42—34no—
338C3×C42—34no—
339C3×C42—34no—
340C3×C42—34no—
341#217—38no—
342(C2×D3)⋊C4—38no—
343(C2×D3)⋊C4—38no—
344(C2×D3)⋊C4—38no—
345(C2×D3)⋊C4—38no—
346(C2×D3)⋊C4—38no—
347(C2×D3)⋊C4—68no—
348(C2×D3)⋊C4C22×D318yes—
349C4⋊Dic3—34no—
350C4⋊Dic3—34no—
351C4⋊Dic3—38no—
352C4⋊Dic3—64no—
353C4⋊Dic3C22×D314yes—
354Dic3⋊C4—38no—
355C4×Dic3C22×D314yes—
356C4×Dic3C22×D314yes—
357C4×Dic3C22×D314yes—
358C4×Dic3C22×D314yes—
359C22×C32—28no—
360C22×C32—22no—
361C22×C32—22no—
362C22×C32C22×D414yes—
363C22×C32C22×D412yes—
364C22×C32C2×#4112yes—
365C22×C32C2×#4112yes—
366C22×C32C2511yescharacteristic
367C2×C3⋊D3—24no—
368C2×C3⋊D3—24no—
369C2×C3⋊D3—24no—
370C2×C3⋊D3—48no—
371C2×C3×D3—24no—
372C2×C3×D3—24no—
373C2×C3×D3—24no—
374C2×C3×D3—48no—
375C32×C4—22no—
376C32×C4C2×#4114yescomplemented
377C3⋊Dic3—24no—
378C3×Dic3—24no—
379C3×Dic3—22no—
380C3×Dic3C22×D414yes—
381C3×Dic3C22×D414yes—
382C3×Dic3C2×#4114yescomplemented
383C2×#41—916no—
384C2×#41—1816no—
385C22×Q8—92no—
386C22×D4—32no—
387C22×D4—31no—
388C22×D4—92no—
389C22×D4—92no—
390C22×D4—92no—
391C22×D4—91no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—92no—
395C23×C4—92no—
396C23×C4D3211yescharacteristic
397C4⋊Q8—98no—
398#127—98no—
399#124—916no—
400#121—38no—
401#121—916no—
402#121—98no—
403C4×D4—916no—
404C4×D4—98no—
405C4×D4—98no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—92no—
408C2×C4⋊C4—91no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—92no—
411C2×C22⋊C4—92no—
412C2×C22⋊C4—92no—
413C2×C42—31no—
414C2×C42—31no—
415C2×C42—31no—
416C2×C42—31no—
417C2×C42—38no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—21no—
424C23×C3—24no—
425C23×C3—34no—
426C23×C3—42no—
427C23×C3—42no—
428C23×C3—64no—
429C23×C3—64no—
430C23×C3—64no—
431C23×C3C2×D1214yes—
432C23×C3D3×D414yes—
433C23×C3C23×D312yes—
434C23×C3C23×D312yes—
435C23×C3C23×D311yescharacteristic
436C23×C3C23×D311yescharacteristic
437C22×D3—24no—
438C22×D3—24no—
439C22×D3—24no—
440C22×D3—34no—
441C22×D3—34no—
442C22×D3—64no—
443C22×D3—64no—
444C22×D3—64no—
445C22×D3—64no—
446C22×D3—64no—
447C22×D3—64no—
448C22×D3—64no—
449C22×D3—124no—
450C22×D3—124no—
451C22×D3—124no—
452C22×D3C23×D314yes—
453C3×D4—616no—
454C3×D4—68no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—28no—
458C2×C3×C4—28no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—24no—
462C2×C3×C4—34no—
463C2×C3×C4—34no—
464C2×C3×C4—316no—
465C2×C3×C4—34no—
466C2×C3×C4—32no—
467C2×C3×C4—32no—
468C2×C3×C4—32no—
469C2×C3×C4—34no—
470C2×C3×C4—32no—
471C2×C3×C4—48no—
472C2×C3×C4—42no—
473C2×C3×C4—68no—
474C2×C3×C4—64no—
475C2×C3×C4—62no—
476C2×C3×C4#23514yescomplemented
477C2×C3×C4#23714yescomplemented
478C2×C3×C4C23×D312yes—
479C2×C3×C4C23×D312yes—
480C2×C3×C4C23×D312yes—
481C2×C3×C4C23×D312yes—
482#67—216no—
483#67—616no—
484#67—616no—
485#67—616no—
486#67—616no—
487#67—1216no—
488C2×Dic3—22no—
489C2×Dic3—24no—
490C2×Dic3—28no—
491C2×Dic3—34no—
492C2×Dic3—34no—
493C2×Dic3—64no—
494C2×Dic3—64no—
495C2×Dic3—64no—
496C2×Dic3—616no—
497C2×Dic3—124no—
498C2×Dic3C2×D1214yes—
499C2×Dic3C2×D1214yes—
500C2×Dic3C2×D12116yescomplemented
501C2×Dic3#23514yescomplemented
502C2×Dic3C23×D312yes—
503C2×Dic3C23×D314yes—
504C2×Dic3C23×D312yes—
505C2×Dic3C23×D312yes—
506C2×Dic3C23×D312yes—
507D12—28no—
508D12—616no—
509D12—616no—
510D12—68no—
511D12—68no—
512D12—128no—
513C4×D3—616no—
514C4×D3—616no—
515C4×D3—616no—
516Dic6—616no—
517Dic6—616no—
518C2×C32—24no—
519C2×C32#53214yescomplemented
520C2×C32C23×D411yescharacteristic
521C2×C32C22×#4111yescharacteristic
522C2×C32C22×#4111yescharacteristic
523C3⋊D3—44no—
524C3×D3—44no—
525C24—32no—
526C24—92no—
527C24C2×D3211yescharacteristic
528#41—1864no—
529C2×Q8—98no—
530C2×Q8—188no—
531C2×D4—38no—
532C2×D4—34no—
533C2×D4—68no—
534C2×D4—64no—
535C2×D4—98no—
536C2×D4—98no—
537C2×D4—98no—
538C2×D4—94no—
539C2×D4—188no—
540C2×D4—188no—
541C2×D4—188no—
542C2×D4—184no—
543C22×C4—24no—
544C22×C4—34no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—38no—
549C22×C4—34no—
550C22×C4—31no—
551C22×C4—32no—
552C22×C4—64no—
553C22×C4—98no—
554C22×C4—98no—
555C22×C4—92no—
556C22×C4—188no—
557C22×C4—188no—
558C22×C4C2×D3214yes—
559C22×C4C2×D3211yescharacteristic
560C22×C4C2×D3211yescharacteristic
561C4⋊C4—34no—
562C4⋊C4—98no—
563C4⋊C4—94no—
564C22⋊C4—38no—
565C22⋊C4—98no—
566C22⋊C4—98no—
567C22⋊C4—98no—
568C42—34no—
569C42—34no—
570C42—34no—
571C42—34no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—28no—
577C22×C3—28no—
578C22×C3—22no—
579C22×C3—24no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—21no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—48no—
586C22×C3—64no—
587C22×C3—64no—
588C22×C3—64no—
589C22×C3—128no—
590C22×C3C22×D1214yes—
591C22×C3C22×D1212yes—
592C22×C3C2×#23512yes—
593C22×C3C2×#23512yes—
594C22×C3C2×D3×D414yes—
595C22×C3C2×D3×D412yes—
596C22×C3C2×#23712yes—
597C22×C3D3×#4112yes—
598C22×C3C24×D311yescharacteristic
599C22×C3C24×D311yescharacteristic
600C2×D3—24no—
601C2×D3—24no—
602C2×D3—24no—
603C2×D3—48no—
604C2×D3—64no—
605C2×D3—64no—
606C2×D3—64no—
607C2×D3—64no—
608C2×D3—64no—
609C2×D3—64no—
610C2×D3—124no—
611C2×D3—124no—
612C2×D3—124no—
613C2×D3—128no—
614C2×D3—128no—
615C2×D3—248no—
616C3×C4—22no—
617C3×C4—22no—
618C3×C4—24no—
619C3×C4—34no—
620C3×C4—34no—
621C3×C4—34no—
622C3×C4—42no—
623C3×C4—64no—
624C3×C4—62no—
625C3×C4C2×#23514yescomplemented
626C3×C4C2×#23714yescomplemented
627Dic3—22no—
628Dic3—24no—
629Dic3—64no—
630Dic3—64no—
631Dic3—124no—
632Dic3C22×D1214yes—
633Dic3C22×D1214yes—
634Dic3C2×#23514yescomplemented
635C32C2×#53211yescharacteristic, complemented, Sylow
636C23—22no—
637C23—22no—
638C23—34no—
639C23—64no—
640C23—64no—
641C23—64no—
642C23—94no—
643C23—184no—
644C23—184no—
645C23—184no—
646C23D3×D1214yes—
647C23C22×D3212yes—
648C23C22×D3211yescharacteristic
649Q8—1816no—
650D4—616no—
651D4—68no—
652D4—1816no—
653D4—1816no—
654D4—1816no—
655D4—188no—
656C2×C4—22no—
657C2×C4—28no—
658C2×C4—34no—
659C2×C4—34no—
660C2×C4—316no—
661C2×C4—34no—
662C2×C4—32no—
663C2×C4—32no—
664C2×C4—32no—
665C2×C4—32no—
666C2×C4—34no—
667C2×C4—68no—
668C2×C4—64no—
669C2×C4—62no—
670C2×C4—94no—
671C2×C4—1816no—
672C2×C4—1816no—
673C2×C4—184no—
674C2×C4#380414yescomplemented
675C2×C4C22×D3212yes—
676C2×C4C22×D3212yes—
677C2×C3—24no—
678C2×C3—24no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—24no—
683C2×C3—44no—
684C2×C3—124no—
685C2×C3#547714yescomplemented
686C2×C3#559614yescomplemented
687C2×C3C23×D1211yescharacteristic
688C2×C3C22×#23511yescharacteristic
689C2×C3C22×#23511yescharacteristic
690C2×C3C22×D3×D411yescharacteristic
691C2×C3C22×#23711yescharacteristic
692C2×C3C2×D3×#4111yescharacteristic
693D3—44no—
694D3—124no—
695D3—124no—
696D3—244no—
697C22—22no—
698C22—22no—
699C22—28no—
700C22—64no—
701C22—64no—
702C22—64no—
703C22—128no—
704C22—184no—
705C22—184no—
706C22—184no—
707C22—368no—
708C22C2×D3×D1214yes—
709C22C2×D3×D1212yes—
710C22D3×#23512yes—
711C22C2×#380412yes—
712C22C23×D3211yescharacteristic
713C4—22no—
714C4—34no—
715C4—34no—
716C4—34no—
717C4—64no—
718C4—62no—
719C4—184no—
720C4C2×#380414yescomplemented
721C3—21no—
722C3C2×#547711yescharacteristic, complemented
723C3C2×#559611yescharacteristic, complemented
724C2—24no—
725C2—124no—
726C2—364no—
727C2#1059491014yesdirect product factor
728C2C22×D3×D1211yescharacteristic
729C2C2×D3×#23511yescharacteristic
730C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#532
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×#930C2semidirect
4. C22×C3×C4×Dic3C2semidirect
5. C2×#63978C2semidirect
6. C2×#63918C2semidirect
7. C2×#63911C2semidirect
8. C2×#63894C2semidirect
9. #10594910C2direct (N × H)
10. C2×Dic3×D12C2semidirect
11. C2×#63880C2semidirect
12. C2×#63852C2semidirect
27. C2×#3804C22semidirect
29. #64139C22semidirect
32. C3×#930C22semidirect
39. C2×C3×C4×Dic3C22semidirect
40. #63978C22semidirect
44. #63918C22semidirect
45. #63911C22semidirect
46. #63894C22semidirect
47. Dic3×D12C22semidirect
48. #63880C22semidirect
49. #63852C22semidirect
61. C2×#930D3semidirect
62. C22×C4×Dic3D3semidirect
90. C22×C3×Dic3D4semidirect
170. #930C2×D3semidirect
188. C2×C4×Dic3C2×D3semidirect
214. C2×C32×C4#41semidirect
227. C2×C3×Dic3C2×D4semidirect
228. C2×C3×Dic3#41semidirect
303. C22×Dic3D12semidirect
376. C32×C4C2×#41semidirect
382. C3×Dic3C2×#41semidirect
476. C2×C3×C4#235semidirect
477. C2×C3×C4#237semidirect
500. C2×Dic3C2×D12semidirect
501. C2×Dic3#235semidirect
519. C2×C32#532semidirect
625. C3×C4C2×#235semidirect
626. C3×C4C2×#237semidirect
634. Dic3C2×#235semidirect
635. C32C2×#532semidirect
674. C2×C4#3804semidirect
685. C2×C3#5477semidirect
686. C2×C3#5596semidirect
720. C4C2×#3804semidirect
722. C3C2×#5477semidirect
723. C3C2×#5596semidirect
727. C2#10594910direct (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×#9302
C22×C3×C4×Dic32
C2×#639782
C2×#639182
C2×#639112
C2×#638942
#105949102
C2×Dic3×D122
C2×#638802
C2×#638522
C2×#55963
C2×#54773