Finite Group Databasebeta

← C2×#10594255 #11899892

Subgroups — C2×#10594255 #11899892

Order 1152.

5393 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3811C211yesmaximal, characteristic
2C23×#624C211yesmaximal, characteristic, complemented
3C22×C4×D32C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
5C2×C3×#67⋊C4C212yesmaximal, complemented
6C2×Dic3×#67C212yesmaximal, complemented
7C2×#63921C211yesmaximal, characteristic, complemented
8C2×#63904C212yesmaximal, complemented
9C2×#63883C211yesmaximal, characteristic, complemented
10C2×C4×#624C211yesmaximal, characteristic, complemented
11C2×#63880C212yesmaximal, complemented
12#10594255C2116yesmaximal, direct product factor
13C2×C4×D3×D4—32nomaximal
14C24×C3⋊D3C2211yescharacteristic
15C23×D32C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C3×#67C2212yes—
19C23×C3×Dic3C2212yescomplemented
20C22×C3×C4×D3C2212yescomplemented
21C2×#3811C4116yescomplemented
22C2×#3811C2218yes—
23C22×#626C2212yes—
24C22×#624—28no—
25C22×#624C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×#624C2211yescharacteristic
28C22×#624C2218yescomplemented
29C22×#624C2212yescomplemented
30C22×D3×Dic3C2212yescomplemented
31C2×C4×D32—28no—
32C2×C4×D32C2218yescomplemented
33C2×C32×C22⋊C4C2211yescharacteristic, complemented
34C2×#3757C2211yescharacteristic, complemented
35C2×#3752C2211yescharacteristic, complemented
36C2×#3752C2211yescharacteristic, complemented
37C22⋊C4×C3⋊D3C2218yescomplemented
38C2×C3×(C2×D3)⋊C4C2212yescomplemented
39C2×C3×Dic3⋊C4C2212yescomplemented
40C2×C3×C4×Dic3C2212yescomplemented
41C3×#67⋊C4C22116yescomplemented
42Dic3×#67C22116yescomplemented
43C2×Dic3⋊Dic3C2212yescomplemented
44C2×(C2×D3)⋊Dic3C2212yescomplemented
45C2×Dic32C2212yescomplemented
46#63921C2218yescomplemented
47#63904C22116yescomplemented
48#63883C2218yescomplemented
49C4×#624C2218yescomplemented
50#63880C22116yescomplemented
51C22×D3×D4—32no—
52C23×C4×D3—32no—
53C23×C4×D3—32no—
54C2×C3×C4×D4—32no—
55C2×D4×Dic3—32no—
56C2×C4×#67—32no—
57C2×C4×#67—32no—
58C4×D3×D4—332no—
59C2×#893—32no—
60C2×D3×C4⋊C4—32no—
61C2×#67⋊C4—32no—
62C2×#67⋊C4D312yescomplemented
63C2×D3×C22⋊C4—32no—
64C2×D3×C22⋊C4—32no—
65C2×D3×C22⋊C4—61no—
66C2×C4×D12—32no—
67C2×C42×D3—32no—
68C24×C32C2311yescharacteristic
69C23×C3⋊D3—24no—
70C23×C3⋊D3—24no—
71C23×C3⋊D3C2×C418yescomplemented
72C23×C3⋊D3C2311yescharacteristic
73C23×C3⋊D3C2314yes—
74C23×C3⋊D3C2311yescharacteristic
75C23×C3×D3C2312yes—
76C22×D32—24no—
77C22×D32—24no—
78C22×D32C2×C418yescomplemented
79C22×D32C2314yes—
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2311yescharacteristic
84C2×C4×C3⋊D3—24no—
85C2×C4×C3⋊D3—24no—
86C2×C4×C3⋊D3C2314yes—
87C2×C4×C3⋊D3C2314yes—
88C2×C3×#67C2×C4116yescomplemented
89C2×C3×#67C2318yes—
90C22×C3×Dic3—28no—
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2312yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2318yescomplemented
95C2×C3×C4×D3—28no—
96C2×C3×C4×D3C2318yescomplemented
97#3811C2×C4164yescomplemented
98C2×#626C2×C4116yescomplemented
99C2×#626C2318yes—
100C2×#624—24no—
101C2×#624—28no—
102C2×#624—232no—
103C2×#624C2×C418yescomplemented
104C2×#624D418yescomplemented
105C2×#624C2314yes—
106C2×#624C2314yes—
107C2×#624C2314yes—
108C2×#624C2318yescomplemented
109C2×D3×Dic3—28no—
110C2×D3×Dic3C2318yescomplemented
111C4×D32—232no—
112C32×C22⋊C4C2314yescomplemented
113#3757C2314yescomplemented
114#3752C2314yescomplemented
115#3752C2314yescomplemented
116C3×(C2×D3)⋊C4C2318yescomplemented
117C3×Dic3⋊C4C2318yescomplemented
118C3×C4×Dic3C2318yescomplemented
119Dic3⋊Dic3C2318yescomplemented
120(C2×D3)⋊Dic3C2318yescomplemented
121Dic32C2318yescomplemented
122C22×C4×D4—91noSylow
123C24×D3—32no—
124C24×D3—32no—
125C24×D3—61no—
126C22×C3×D4—32no—
127C23×C3×C4—32no—
128C23×C3×C4—32no—
129C22×#67—32no—
130C22×#67C2×D312yes—
131C23×Dic3—32no—
132C23×Dic3C2×D312yescomplemented
133C2×D3×D4—332no—
134C2×D3×D4—316no—
135C22×D12—32no—
136C22×C4×D3—32no—
137C22×C4×D3—32no—
138C22×C4×D3—32no—
139C22×C4×D3—32no—
140C22×C4×D3—32no—
141C22×C4×D3—32no—
142C22×C4×D3—32no—
143C22×C4×D3—32no—
144C22×C4×D3—316no—
145C22×C4×D3—316no—
146C22×C4×D3—61no—
147C22×C4×D3—61no—
148C22×C4×D3—616no—
149C22×C4×D3—616no—
150C22×C4×D3C2×D312yescomplemented
151C3×C4×D4—316no—
152C2×C3×C4⋊C4—32no—
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—32no—
155C2×C3×C22⋊C4C2×D312yescomplemented
156C2×C3×C42—32no—
157C2×#217—32no—
158C2×#217—32no—
159C2×#217—61no—
160D4×Dic3—316no—
161C4×#67—316no—
162C4×#67—316no—
163C2×(C2×D3)⋊C4—32no—
164C2×(C2×D3)⋊C4—32no—
165C2×(C2×D3)⋊C4—32no—
166C2×(C2×D3)⋊C4—61no—
167C2×(C2×D3)⋊C4—61no—
168C2×(C2×D3)⋊C4C2×D312yescomplemented
169C2×C4⋊Dic3—32no—
170C2×Dic3⋊C4—32no—
171C2×Dic3⋊C4C2×D312yescomplemented
172C2×C4×Dic3—32no—
173C2×C4×Dic3—32no—
174C2×C4×Dic3C2×D312yescomplemented
175#893—316no—
176D3×C4⋊C4—316no—
177#67⋊C4—316no—
178#67⋊C4C2×D3116yescomplemented
179D3×C22⋊C4—316no—
180D3×C22⋊C4—316no—
181D3×C22⋊C4—68no—
182C4×D12—316no—
183C42×D3—316no—
184C23×C32—22no—
185C23×C32—22no—
186C23×C32C22×C414yescomplemented
187C23×C32C2412yes—
188C23×C32C2411yescharacteristic
189C22×C3⋊D3—22no—
190C22×C3⋊D3—22no—
191C22×C3⋊D3—232no—
192C22×C3⋊D3—28no—
193C22×C3⋊D3—28no—
194C22×C3⋊D3C22×C414yes—
195C22×C3⋊D3C22×C4116yescomplemented
196C22×C3⋊D3C22×C414yescomplemented
197C22×C3⋊D3C2×D414yes—
198C22×C3⋊D3#4114yes—
199C22×C3⋊D3C2412yes—
200C22×C3⋊D3C2412yes—
201C22×C3×D3—24no—
202C22×C3×D3—24no—
203C22×C3×D3C22×C418yescomplemented
204C22×C3×D3C2414yes—
205C2×D32—232no—
206C2×D32—28no—
207C2×D32—28no—
208C2×D32C22×C4116yescomplemented
209C2×C32×C4—22no—
210C2×C32×C4—22no—
211C2×C32×C4C2412yes—
212C2×C32×C4C2412yes—
213C2×C3⋊Dic3—22no—
214C2×C3⋊Dic3—22no—
215C2×C3⋊Dic3C2412yes—
216C2×C3⋊Dic3C2412yes—
217C4×C3⋊D3—28no—
218C4×C3⋊D3—28no—
219C3×#67C22×C4132yescomplemented
220C2×C3×Dic3—24no—
221C2×C3×Dic3—216no—
222C2×C3×Dic3C22×C418yescomplemented
223C2×C3×Dic3C2×D418yescomplemented
224C2×C3×Dic3C2414yes—
225C2×C3×Dic3C2414yes—
226C2×C3×Dic3C2414yes—
227C3×C4×D3—216no—
228#626C22×C4132yescomplemented
229#624—28no—
230#624—216no—
231#624C22×C4116yescomplemented
232#624C2×D4116yescomplemented
233D3×Dic3—216no—
234C23×D4—91no—
235C24×C4—91no—
236C24×C4—91no—
237C2×C4×D4—32no—
238C2×C4×D4—92no—
239C2×C4×D4—92no—
240C2×C4×D4—916no—
241C2×C4×D4—92no—
242C22×C4⋊C4—91no—
243C22×C22⋊C4—91no—
244C22×C22⋊C4—91no—
245C22×C42—91no—
246C24×C3—21no—
247C24×C3—32no—
248C24×C3C22×D312yes—
249C23×D3—32no—
250C23×D3—316no—
251C23×D3—38no—
252C23×D3—32no—
253C23×D3—316no—
254C23×D3—38no—
255C23×D3—61no—
256C23×D3—68no—
257C23×D3—64no—
258C23×D3—61no—
259C23×D3—68no—
260C23×D3—68no—
261C23×D3—68no—
262C23×D3—68no—
263C23×D3—124no—
264C23×D3—124no—
265C23×D3C22×D312yes—
266C2×C3×D4—316no—
267C2×C3×D4—38no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—32no—
271C22×C3×C4—32no—
272C22×C3×C4—32no—
273C22×C3×C4—38no—
274C22×C3×C4—38no—
275C22×C3×C4—68no—
276C22×C3×C4—68no—
277C22×C3×C4C22×D312yes—
278C22×C3×C4C22×D312yes—
279C2×#67—316no—
280C2×#67—38no—
281C2×#67C4×D3116yescomplemented
282C2×#67C22×D318yes—
283C22×Dic3—28no—
284C22×Dic3—32no—
285C22×Dic3—32no—
286C22×Dic3—38no—
287C22×Dic3—61no—
288C22×Dic3—61no—
289C22×Dic3—68no—
290C22×Dic3C22×D312yes—
291C22×Dic3C22×D312yes—
292C22×Dic3C22×D312yes—
293C22×Dic3C22×D318yescomplemented
294D3×D4—3128no—
295C2×D12—316no—
296C2×D12—38no—
297C2×C4×D3—28no—
298C2×C4×D3—316no—
299C2×C4×D3—316no—
300C2×C4×D3—38no—
301C2×C4×D3—38no—
302C2×C4×D3—38no—
303C2×C4×D3—38no—
304C2×C4×D3—38no—
305C2×C4×D3—38no—
306C2×C4×D3—38no—
307C2×C4×D3—38no—
308C2×C4×D3—64no—
309C2×C4×D3—64no—
310C2×C4×D3—664no—
311C2×C4×D3—664no—
312C2×C4×D3—68no—
313C2×C4×D3—68no—
314C2×C4×D3—68no—
315C2×C4×D3—68no—
316C2×C4×D3—68no—
317C2×C4×D3—68no—
318C2×C4×D3—124no—
319C2×C4×D3—124no—
320C2×C4×D3C22×D318yescomplemented
321C3×C4⋊C4—38no—
322C3×C22⋊C4—24no—
323C3×C22⋊C4—38no—
324C3×C22⋊C4C22×D318yescomplemented
325C3×C42—38no—
326#217—38no—
327#217—38no—
328#217—64no—
329(C2×D3)⋊C4—38no—
330(C2×D3)⋊C4—38no—
331(C2×D3)⋊C4—38no—
332(C2×D3)⋊C4—64no—
333(C2×D3)⋊C4—64no—
334(C2×D3)⋊C4C22×D318yescomplemented
335C4⋊Dic3—38no—
336Dic3⋊C4—38no—
337Dic3⋊C4C22×D318yescomplemented
338C4×Dic3—38no—
339C4×Dic3—38no—
340C4×Dic3C22×D318yescomplemented
341C22×C32—28no—
342C22×C32—22no—
343C22×C32—22no—
344C22×C32C23×C412yes—
345C22×C32C23×C414yescomplemented
346C22×C32C22×D412yes—
347C22×C32C2×#4112yes—
348C22×C32C2511yescharacteristic
349C2×C3⋊D3—28no—
350C2×C3⋊D3—22no—
351C2×C3⋊D3—22no—
352C2×C3⋊D3—232no—
353C2×C3⋊D3C4×D4116yescomplemented
354C2×C3⋊D3C23×C414yes—
355C2×C3⋊D3C23×C414yescomplemented
356C2×C3⋊D3C22×D414yes—
357C2×C3⋊D3C2×#4114yes—
358C2×C3×D3—216no—
359C2×C3×D3—24no—
360C2×C3×D3—24no—
361C2×C3×D3C23×C418yescomplemented
362D32—232no—
363C32×C4—22no—
364C32×C4—22no—
365C3⋊Dic3—22no—
366C3⋊Dic3—22no—
367C3×Dic3—24no—
368C3×Dic3C23×C418yescomplemented
369C3×Dic3C22×D418yescomplemented
370C25—91no—
371C25—91no—
372C22×D4—32no—
373C22×D4—92no—
374C22×D4—98no—
375C22×D4—916no—
376C23×C4—32no—
377C23×C4—32no—
378C23×C4—91no—
379C23×C4—91no—
380C23×C4—91no—
381C23×C4—92no—
382C23×C4—98no—
383C23×C4—98no—
384C23×C4—92no—
385C23×C4—91no—
386C23×C4—91no—
387C23×C4—188no—
388C23×C4—188no—
389C4×D4—316no—
390C4×D4—916no—
391C4×D4—916no—
392C4×D4—916no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—98no—
395C2×C4⋊C4—92no—
396C2×C22⋊C4—32no—
397C2×C22⋊C4—98no—
398C2×C22⋊C4—92no—
399C2×C22⋊C4—91no—
400C2×C22⋊C4—91no—
401C2×C22⋊C4—91no—
402C2×C22⋊C4—98no—
403C2×C22⋊C4D3211yescharacteristic, complemented
404C2×C42—32no—
405C2×C42—98no—
406C2×C42—92no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—22no—
410C23×C3—21no—
411C23×C3—24no—
412C23×C3—38no—
413C23×C3—34no—
414C23×C3—42no—
415C23×C3—42no—
416C23×C3—64no—
417C23×C3—64no—
418C23×C3C2×C4×D318yescomplemented
419C23×C3C23×D314yes—
420C23×C3C23×D312yes—
421C22×D3—24no—
422C22×D3—24no—
423C22×D3—38no—
424C22×D3—38no—
425C22×D3—38no—
426C22×D3—34no—
427C22×D3—38no—
428C22×D3—332no—
429C22×D3—34no—
430C22×D3—332no—
431C22×D3—64no—
432C22×D3—64no—
433C22×D3—64no—
434C22×D3—62no—
435C22×D3—64no—
436C22×D3—616no—
437C22×D3—62no—
438C22×D3—616no—
439C22×D3—616no—
440C22×D3—664no—
441C22×D3—616no—
442C22×D3—616no—
443C22×D3—664no—
444C22×D3—64no—
445C22×D3—64no—
446C22×D3—128no—
447C22×D3—128no—
448C22×D3—1232no—
449C22×D3—122no—
450C22×D3—122no—
451C22×D3C2×C4×D318yescomplemented
452C22×D3C23×D314yes—
453C3×D4—332no—
454C2×C3×C4—24no—
455C2×C3×C4—24no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—38no—
459C2×C3×C4—38no—
460C2×C3×C4—34no—
461C2×C3×C4—34no—
462C2×C3×C4—34no—
463C2×C3×C4—42no—
464C2×C3×C4—42no—
465C2×C3×C4—616no—
466C2×C3×C4—616no—
467C2×C3×C4—64no—
468C2×C3×C4C23×D314yes—
469C2×C3×C4C23×D314yes—
470#67—332no—
471#67C2×C4×D3132yescomplemented
472C2×Dic3—24no—
473C2×Dic3—216no—
474C2×Dic3—34no—
475C2×Dic3—34no—
476C2×Dic3—62no—
477C2×Dic3—62no—
478C2×Dic3—64no—
479C2×Dic3—64no—
480C2×Dic3—616no—
481C2×Dic3—122no—
482C2×Dic3—122no—
483C2×Dic3C2×C4×D318yescomplemented
484C2×Dic3D3×D418yescomplemented
485C2×Dic3C23×D314yes—
486C2×Dic3C23×D314yes—
487C2×Dic3C23×D314yes—
488D12—332no—
489C4×D3—216no—
490C4×D3—332no—
491C4×D3—332no—
492C4×D3—616no—
493C4×D3—616no—
494C4×D3—616no—
495C4×D3—616no—
496C4×D3—616no—
497C4×D3—616no—
498C4×D3—128no—
499C4×D3—128no—
500C2×C32—24no—
501C2×C32C2×C4×D414yescomplemented
502C2×C32C24×C411yescharacteristic
503C2×C32C23×D411yescharacteristic
504C2×C32C22×#4111yescharacteristic
505C3⋊D3—24no—
506C3⋊D3C2×C4×D418yescomplemented
507C3×D3—28no—
508C24—32no—
509C24—94no—
510C24—98no—
511C24—91no—
512C24—94no—
513C24—91no—
514C24—98no—
515C24—184no—
516C24—184no—
517C24—184no—
518C24—184no—
519C24C2×D3211yescharacteristic
520C2×D4—38no—
521C2×D4—316no—
522C2×D4—98no—
523C2×D4—916no—
524C2×D4—964no—
525C22×C4—32no—
526C22×C4—32no—
527C22×C4—38no—
528C22×C4—32no—
529C22×C4—38no—
530C22×C4—68no—
531C22×C4—68no—
532C22×C4—94no—
533C22×C4—94no—
534C22×C4—98no—
535C22×C4—98no—
536C22×C4—94no—
537C22×C4—98no—
538C22×C4—98no—
539C22×C4—91no—
540C22×C4—91no—
541C22×C4—94no—
542C22×C4—94no—
543C22×C4—184no—
544C22×C4—184no—
545C22×C4—188no—
546C22×C4—188no—
547C22×C4—1832no—
548C22×C4—1832no—
549C22×C4—184no—
550C22×C4C2×D3211yescharacteristic
551C22×C4C2×D3211yescharacteristic
552C4⋊C4—38no—
553C4⋊C4—98no—
554C22⋊C4—38no—
555C22⋊C4—98no—
556C22⋊C4—94no—
557C22⋊C4—94no—
558C22⋊C4—94no—
559C22⋊C4C2×D3214yescomplemented
560C42—38no—
561C42—98no—
562C22×C3—24no—
563C22×C3—24no—
564C22×C3—216no—
565C22×C3—22no—
566C22×C3—24no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—21no—
570C22×C3—38no—
571C22×C3—42no—
572C22×C3—42no—
573C22×C3—48no—
574C22×C3—64no—
575C22×C3—64no—
576C22×C3—616no—
577C22×C3C22×C4×D314yes—
578C22×C3C22×C4×D318yescomplemented
579C22×C3C2×D3×D414yes—
580C22×C3D3×#4114yes—
581C22×C3C24×D312yes—
582C2×D3—24no—
583C2×D3—24no—
584C2×D3—216no—
585C2×D3—38no—
586C2×D3—38no—
587C2×D3—38no—
588C2×D3—332no—
589C2×D3—38no—
590C2×D3—64no—
591C2×D3—64no—
592C2×D3—64no—
593C2×D3—616no—
594C2×D3—64no—
595C2×D3—664no—
596C2×D3—664no—
597C2×D3—64no—
598C2×D3—64no—
599C2×D3—616no—
600C2×D3—1232no—
601C2×D3—122no—
602C2×D3—122no—
603C2×D3—128no—
604C2×D3C22×C4×D318yescomplemented
605C3×C4—24no—
606C3×C4—24no—
607C3×C4—38no—
608C3×C4—38no—
609C3×C4—42no—
610C3×C4—42no—
611C3×C4—64no—
612Dic3—24no—
613Dic3—64no—
614Dic3—64no—
615Dic3—122no—
616Dic3—122no—
617Dic3C22×C4×D318yescomplemented
618Dic3C2×D3×D418yescomplemented
619C32C22×C4×D411yescharacteristic, complemented, Sylow
620C23—22no—
621C23—22no—
622C23—38no—
623C23—34no—
624C23—64no—
625C23—64no—
626C23—916no—
627C23—94no—
628C23—94no—
629C23—94no—
630C23—92no—
631C23—94no—
632C23—916no—
633C23—92no—
634C23—188no—
635C23—188no—
636C23—1832no—
637C23—188no—
638C23—188no—
639C23—1832no—
640C23—182no—
641C23—182no—
642C23C4×D3214yescomplemented
643C23C22×D3212yes—
644C23C22×D3211yescharacteristic
645D4—332no—
646D4—932no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—38no—
650C2×C4—38no—
651C2×C4—34no—
652C2×C4—34no—
653C2×C4—34no—
654C2×C4—616no—
655C2×C4—616no—
656C2×C4—64no—
657C2×C4—916no—
658C2×C4—916no—
659C2×C4—92no—
660C2×C4—92no—
661C2×C4—188no—
662C2×C4—188no—
663C2×C4—1816no—
664C2×C4—1816no—
665C2×C4—188no—
666C2×C4—182no—
667C2×C4—182no—
668C2×C4C22×D3212yes—
669C2×C4C22×D3212yes—
670C2×C3—28no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—24no—
675C2×C3—44no—
676C2×C3—68no—
677C2×C3C4×D3×D418yescomplemented
678C2×C3C23×C4×D312yes—
679C2×C3C22×D3×D412yes—
680C2×C3C2×D3×#4112yes—
681D3—28no—
682D3—316no—
683D3—68no—
684D3—68no—
685D3—124no—
686C22—22no—
687C22—22no—
688C22—28no—
689C22—38no—
690C22—64no—
691C22—64no—
692C22—616no—
693C22—94no—
694C22—94no—
695C22—94no—
696C22—916no—
697C22—94no—
698C22—1832no—
699C22—1832no—
700C22—182no—
701C22—182no—
702C22—188no—
703C22C2×C4×D3212yes—
704C22C2×C4×D3214yescomplemented
705C22D32×D412yes—
706C22#6431212yes—
707C22C23×D3211yescharacteristic
708C4—22no—
709C4—22no—
710C4—38no—
711C4—38no—
712C4—64no—
713C4—182no—
714C4—182no—
715C3—21no—
716C3C2×C4×D3×D412yescomplemented
717C2—24no—
718C2—68no—
719C2—98no—
720C2—184no—
721C2#1059425514yesdirect product factor
722C2C22×C4×D3211yescharacteristic
723C2C2×D32×D411yescharacteristic
724C2C2×#6431211yescharacteristic
subgroupG/H
centerC23C22×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC22×#3811C2
cosocleC22×C32C25
hypercenterC2×C22⋊C4D32
hypocenterC32C22×C4×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×#624C2semidirect
3. C22×C4×D32C2semidirect
4. C2×C22⋊C4×C3⋊D3C2semidirect
5. C2×C3×#67⋊C4C2semidirect
6. C2×Dic3×#67C2semidirect
7. C2×#63921C2semidirect
8. C2×#63904C2semidirect
9. C2×#63883C2semidirect
10. C2×C4×#624C2semidirect
11. C2×#63880C2semidirect
12. #10594255C2direct (N × H)
19. C23×C3×Dic3C22semidirect
20. C22×C3×C4×D3C22semidirect
21. C2×#3811C4semidirect
28. C22×#624C22semidirect
29. C22×#624C22semidirect
30. C22×D3×Dic3C22semidirect
32. C2×C4×D32C22semidirect
33. C2×C32×C22⋊C4C22semidirect
34. C2×#3757C22semidirect
35. C2×#3752C22semidirect
36. C2×#3752C22semidirect
37. C22⋊C4×C3⋊D3C22semidirect
38. C2×C3×(C2×D3)⋊C4C22semidirect
39. C2×C3×Dic3⋊C4C22semidirect
40. C2×C3×C4×Dic3C22semidirect
41. C3×#67⋊C4C22semidirect
42. Dic3×#67C22semidirect
43. C2×Dic3⋊Dic3C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. C2×Dic32C22semidirect
46. #63921C22semidirect
47. #63904C22semidirect
48. #63883C22semidirect
49. C4×#624C22semidirect
50. #63880C22semidirect
62. C2×#67⋊C4D3semidirect
71. C23×C3⋊D3C2×C4semidirect
78. C22×D32C2×C4semidirect
88. C2×C3×#67C2×C4semidirect
94. C22×C3×Dic3C23semidirect
96. C2×C3×C4×D3C23semidirect
97. #3811C2×C4semidirect
98. C2×#626C2×C4semidirect
103. C2×#624C2×C4semidirect
104. C2×#624D4semidirect
108. C2×#624C23semidirect
110. C2×D3×Dic3C23semidirect
112. C32×C22⋊C4C23semidirect
113. #3757C23semidirect
114. #3752C23semidirect
115. #3752C23semidirect
116. C3×(C2×D3)⋊C4C23semidirect
117. C3×Dic3⋊C4C23semidirect
118. C3×C4×Dic3C23semidirect
119. Dic3⋊Dic3C23semidirect
120. (C2×D3)⋊Dic3C23semidirect
121. Dic32C23semidirect
132. C23×Dic3C2×D3semidirect
150. C22×C4×D3C2×D3semidirect
155. C2×C3×C22⋊C4C2×D3semidirect
168. C2×(C2×D3)⋊C4C2×D3semidirect
171. C2×Dic3⋊C4C2×D3semidirect
174. C2×C4×Dic3C2×D3semidirect
178. #67⋊C4C2×D3semidirect
186. C23×C32C22×C4semidirect
195. C22×C3⋊D3C22×C4semidirect
196. C22×C3⋊D3C22×C4semidirect
203. C22×C3×D3C22×C4semidirect
208. C2×D32C22×C4semidirect
219. C3×#67C22×C4semidirect
222. C2×C3×Dic3C22×C4semidirect
223. C2×C3×Dic3C2×D4semidirect
228. #626C22×C4semidirect
231. #624C22×C4semidirect
232. #624C2×D4semidirect
281. C2×#67C4×D3semidirect
293. C22×Dic3C22×D3semidirect
320. C2×C4×D3C22×D3semidirect
324. C3×C22⋊C4C22×D3semidirect
334. (C2×D3)⋊C4C22×D3semidirect
337. Dic3⋊C4C22×D3semidirect
340. C4×Dic3C22×D3semidirect
345. C22×C32C23×C4semidirect
353. C2×C3⋊D3C4×D4semidirect
355. C2×C3⋊D3C23×C4semidirect
361. C2×C3×D3C23×C4semidirect
368. C3×Dic3C23×C4semidirect
369. C3×Dic3C22×D4semidirect
403. C2×C22⋊C4D32semidirect
418. C23×C3C2×C4×D3semidirect
451. C22×D3C2×C4×D3semidirect
471. #67C2×C4×D3semidirect
483. C2×Dic3C2×C4×D3semidirect
484. C2×Dic3D3×D4semidirect
501. C2×C32C2×C4×D4semidirect
506. C3⋊D3C2×C4×D4semidirect
559. C22⋊C4C2×D32semidirect
578. C22×C3C22×C4×D3semidirect
604. C2×D3C22×C4×D3semidirect
617. Dic3C22×C4×D3semidirect
618. Dic3C2×D3×D4semidirect
619. C32C22×C4×D4semidirect
642. C23C4×D32semidirect
677. C2×C3C4×D3×D4semidirect
704. C22C2×C4×D32semidirect
716. C3C2×C4×D3×D4semidirect
721. C2#10594255direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38112
C23×#6242
C22×C4×D322
C2×C22⋊C4×C3⋊D32
C2×C3×#67⋊C42
C2×Dic3×#672
C2×#639212
C2×#639042
C2×#638832
C2×C4×#6242
C2×#638802
#105942552
C2×C4×D3×D43