Finite Group Databasebeta

← C2×#10594915 #11902672

Subgroups — C2×#10594915 #11902672

Order 1152.

3561 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#634C211yesmaximal, characteristic, complemented
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×C3×C4×#67C211yesmaximal, characteristic
4C2×C3×#924C211yesmaximal, characteristic, complemented
5C2×#63982C212yesmaximal, complemented
6C2×#67⋊Dic3C212yesmaximal
7#10594915C2116yesmaximal, direct product factor
8C2×#63896C212yesmaximal, complemented
9C2×#63866C211yesmaximal, characteristic, complemented
10C2×#63857C211yesmaximal, characteristic, complemented
11C2×#63844C211yesmaximal, characteristic, complemented
12C2×#63840C212yesmaximal, complemented
13C2×#5632—31nomaximal
14C2×D4×Dic6—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C23×C3⋊Dic3C2212yes—
17C22×#634—28no—
18C22×#634C2211yescharacteristic
19C22×#634C2212yes—
20C22×#634C2211yescharacteristic
21C22×#634C2218yescomplemented
22C22×C3×#67C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C22×#627C2212yes—
26C22×D3×Dic3C2212yes—
27C2×D3×Dic6—28no—
28C2×D3×Dic6C2218yescomplemented
29C2×C3×#217C2212yes—
30C2×C3×#217C2211yescharacteristic
31C3×C4×#67C2218yes—
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C3×#924C2218yescomplemented
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38#63982C22116yescomplemented
39#67⋊Dic3C22116yes—
40C2×#3724C2212yes—
41C2×Dic3⋊Dic3C2212yes—
42C2×Dic3⋊Dic3C2212yes—
43C2×Dic3⋊Dic3C2212yes—
44C2×(C2×D3)⋊Dic3C2212yes—
45C2×Dic32C2212yes—
46#63896C22116yescomplemented
47#63866C2218yescomplemented
48#63857C2218yescomplemented
49#63844C2218yescomplemented
50#63840C22116yescomplemented
51C22×D3×Q8—31no—
52C23×Dic6—31no—
53C23×Dic6—31no—
54C23×Dic6—31no—
55C23×Dic6—61no—
56C2×C3×C22⋊Q8—31no—
57C2×C3×C4×D4—31no—
58C2×#944—31no—
59C2×D4×Dic3—32no—
60C2×C4×#67D311yescharacteristic
61C2×#924—31no—
62C2×#924D311yescharacteristic, complemented
63#5632—316no—
64D4×Dic6—316no—
65C2×#897—31no—
66C2×#896—32no—
67C2×#888—32no—
68C2×#888—32no—
69C2×#887—31no—
70C2×#67⋊C4—32no—
71C2×#878—32no—
72C2×#878—32no—
73C2×#878—32no—
74C2×#869—31no—
75C2×C4×Dic6—31no—
76C24×C32C2311yescharacteristic
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×#634—24no—
87C2×#634—28no—
88C2×#634—232no—
89C2×#634D418yescomplemented
90C2×#634C2318yes—
91C2×#634C2314yes—
92C2×#634C2314yes—
93C2×C3×#67Q818yescomplemented
94C2×C3×#67C2314yes—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2312yes—
97C22×C3×Dic3C2312yes—
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C2×C3×C4×D3—24no—
101C2×C3×C4×D3C2314yes—
102C2×C3×Dic6—24no—
103C2×C3×Dic6C2314yes—
104C2×#627—28no—
105C2×#627C2318yes—
106C2×D3×Dic3—28no—
107C2×D3×Dic3C2318yes—
108D3×Dic6—232no—
109C3×#217C2318yes—
110C3×#217C2314yes—
111C3×(C2×D3)⋊C4C2314yes—
112C3×C4⋊Dic3C2314yes—
113C3×Dic3⋊C4C2318yes—
114C3×Dic3⋊C4C2314yes—
115C3×C4×Dic3C2314yes—
116#3724C2318yes—
117Dic3⋊Dic3C2318yes—
118Dic3⋊Dic3C2318yes—
119Dic3⋊Dic3C2318yes—
120(C2×D3)⋊Dic3C2318yes—
121Dic32C2318yes—
122C2×D4×Q8—91noSylow
123C22×C3×Q8—31no—
124C22×C3×D4—31no—
125C23×C3×C4—21no—
126C23×C3×C4—31no—
127C23×C3×C4C2×D311yescharacteristic
128C23×C3×C4C2×D311yescharacteristic
129C22×#67C2×D311yescharacteristic
130C23×Dic3—32no—
131C23×Dic3—32no—
132C23×Dic3—32no—
133C23×Dic3—62no—
134C2×D3×Q8—38no—
135C2×D3×Q8—68no—
136C22×C4×D3—32no—
137C22×C4×D3C2×D311yescharacteristic
138C22×Dic6—31no—
139C22×Dic6—31no—
140C22×Dic6—38no—
141C22×Dic6—31no—
142C22×Dic6—32no—
143C22×Dic6—32no—
144C22×Dic6—31no—
145C22×Dic6—38no—
146C22×Dic6—32no—
147C22×Dic6—32no—
148C22×Dic6—38no—
149C22×Dic6—61no—
150C22×Dic6—61no—
151C22×Dic6—62no—
152C22×Dic6—68no—
153C22×Dic6—68no—
154C22×Dic6—68no—
155C22×Dic6—68no—
156C22×Dic6—616no—
157C22×Dic6C2×D311yescharacteristic
158C3×C22⋊Q8—38no—
159C3×C4×D4—38no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—32no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—32no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C42—31no—
167C2×#217—32no—
168C2×#217C2×D311yescharacteristic
169C2×#217C2×D312yes—
170#944—38no—
171D4×Dic3—316no—
172C4×#67C2×D318yes—
173C2×(C2×D3)⋊C4—32no—
174C2×(C2×D3)⋊C4C2×D311yescharacteristic
175C2×C4⋊Dic3—32no—
176C2×C4⋊Dic3—32no—
177C2×C4⋊Dic3—32no—
178C2×C4⋊Dic3C2×D311yescharacteristic
179#924—38no—
180#924C2×D318yescomplemented
181C2×Dic3⋊C4—32no—
182C2×Dic3⋊C4—32no—
183C2×Dic3⋊C4—32no—
184C2×Dic3⋊C4—32no—
185C2×Dic3⋊C4—32no—
186C2×Dic3⋊C4C2×D312yes—
187C2×Dic3⋊C4C2×D311yescharacteristic
188C2×C4×Dic3—32no—
189C2×C4×Dic3—32no—
190C2×C4×Dic3C2×D311yescharacteristic
191#897—38no—
192#896—316no—
193#888—316no—
194#888—316no—
195#887—38no—
196#67⋊C4—316no—
197#878—316no—
198#878—316no—
199#878—316no—
200#869—38no—
201C4×Dic6—38no—
202C23×C32—22no—
203C23×C32—22no—
204C23×C32C2×Q814yescomplemented
205C23×C32C2412yes—
206C23×C32C2411yescharacteristic
207C22×C3×D3—22no—
208C22×C3×D3—22no—
209C22×C3×D3C2×Q814yescomplemented
210C22×C3×D3C2412yes—
211C2×C32×C4—22no—
212C2×C32×C4—28no—
213C2×C32×C4C2×D414yes—
214C2×C32×C4C2412yes—
215C2×C32×C4C2412yes—
216C2×C3⋊Dic3—24no—
217C2×C3⋊Dic3—216no—
218C2×C3⋊Dic3C2×D418yes—
219C2×C3⋊Dic3C2414yes—
220C2×C3⋊Dic3C2414yes—
221#634—28no—
222#634—216no—
223#634C2×D4116yescomplemented
224C3×#67C2×Q8116yescomplemented
225C2×C3×Dic3—24no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—24no—
229C2×C3×Dic3C2×Q814yescomplemented
230C2×C3×Dic3C2414yes—
231C2×C3×Dic3C2412yes—
232C2×C3×Dic3C2414yes—
233C2×C3×Dic3C2412yes—
234C2×C3×Dic3C2412yes—
235C3×C4×D3—28no—
236C3×Dic6—28no—
237#627—216no—
238D3×Dic3—216no—
239C23×Q8—91no—
240C23×Q8—91no—
241D4×Q8—916no—
242C2×C4⋊Q8—91no—
243C2×C4⋊Q8—92no—
244C2×C22⋊Q8—31no—
245C2×C22⋊Q8—92no—
246C2×C22⋊Q8—92no—
247C2×C22⋊Q8—91no—
248C2×C4×Q8—91no—
249C2×C4×D4—31no—
250C2×C4×D4—92no—
251C24×C3—21no—
252C24×C3—31no—
253C24×C3C22×D311yescharacteristic
254C24×C3C22×D311yescharacteristic
255C23×D3C22×D311yescharacteristic
256C2×C3×Q8—34no—
257C2×C3×Q8—64no—
258C2×C3×D4—38no—
259C2×C3×D4—34no—
260C22×C3×C4—28no—
261C22×C3×C4—24no—
262C22×C3×C4—24no—
263C22×C3×C4—24no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—31no—
267C22×C3×C4—32no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—32no—
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×#67Dic618yescomplemented
280C2×#67C22×D314yes—
281C22×Dic3—32no—
282C22×Dic3—32no—
283C22×Dic3—38no—
284C22×Dic3—38no—
285C22×Dic3—32no—
286C22×Dic3—32no—
287C22×Dic3—38no—
288C22×Dic3—62no—
289C22×Dic3—68no—
290C22×Dic3—62no—
291C22×Dic3—68no—
292C22×Dic3—68no—
293C22×Dic3—68no—
294C22×Dic3—616no—
295C22×Dic3C22×D312yes—
296C22×Dic3C22×D311yescharacteristic
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D312yes—
299C22×Dic3C22×D311yescharacteristic
300D3×Q8—632no—
301C2×C4×D3—24no—
302C2×C4×D3—38no—
303C2×C4×D3—68no—
304C2×C4×D3C22×D314yes—
305C2×Dic6—24no—
306C2×Dic6—38no—
307C2×Dic6—38no—
308C2×Dic6—34no—
309C2×Dic6—34no—
310C2×Dic6—34no—
311C2×Dic6—38no—
312C2×Dic6—38no—
313C2×Dic6—34no—
314C2×Dic6—38no—
315C2×Dic6—38no—
316C2×Dic6—68no—
317C2×Dic6—64no—
318C2×Dic6—68no—
319C2×Dic6—64no—
320C2×Dic6—632no—
321C2×Dic6—632no—
322C2×Dic6—632no—
323C2×Dic6—68no—
324C2×Dic6—68no—
325C2×Dic6—68no—
326C2×Dic6—68no—
327C2×Dic6—616no—
328C2×Dic6—664no—
329C2×Dic6—68no—
330C2×Dic6—64no—
331C2×Dic6—64no—
332C2×Dic6C22×D314yes—
333C3×C4⋊C4—34no—
334C3×C4⋊C4—34no—
335C3×C4⋊C4—38no—
336C3×C22⋊C4—34no—
337C3×C22⋊C4—38no—
338C3×C22⋊C4—34no—
339C3×C42—34no—
340#217—38no—
341#217C22×D314yes—
342#217C22×D318yes—
343(C2×D3)⋊C4—38no—
344(C2×D3)⋊C4C22×D314yes—
345C4⋊Dic3—38no—
346C4⋊Dic3—38no—
347C4⋊Dic3—38no—
348C4⋊Dic3C22×D314yes—
349Dic3⋊C4—38no—
350Dic3⋊C4—38no—
351Dic3⋊C4—38no—
352Dic3⋊C4—38no—
353Dic3⋊C4—38no—
354Dic3⋊C4C22×D318yes—
355Dic3⋊C4C22×D314yes—
356C4×Dic3—38no—
357C4×Dic3—38no—
358C4×Dic3C22×D314yes—
359C22×C32—28no—
360C22×C32—22no—
361C22×C32—22no—
362C22×C32C22×D412yes—
363C22×C32C22×Q812yes—
364C22×C32C22×Q814yescomplemented
365C22×C322−1+412yes—
366C22×C32C2511yescharacteristic
367C2×C3×D3—28no—
368C2×C3×D3—22no—
369C2×C3×D3—22no—
370C2×C3×D3C22×Q814yescomplemented
371C32×C4—22no—
372C32×C4C22×D414yes—
373C3⋊Dic3—24no—
374C3⋊Dic3C22×D418yes—
375C3×Dic3—24no—
376C3×Dic3—22no—
377C3×Dic3—24no—
378C3×Dic3—22no—
379C3×Dic3C22×Q814yescomplemented
380C22×Q8—31no—
381C22×Q8—92no—
382C22×Q8—98no—
383C22×Q8—91no—
384C22×Q8—92no—
385C22×Q8—91no—
386C22×Q8—98no—
387C22×Q8—188no—
388C22×Q8—188no—
389C22×D4—31no—
390C23×C4—31no—
391C23×C4—92no—
392C23×C4—92no—
393C23×C4D3211yescharacteristic
394C4⋊Q8—98no—
395C4⋊Q8—916no—
396C22⋊Q8—38no—
397C22⋊Q8—916no—
398C22⋊Q8—916no—
399C22⋊Q8—98no—
400C4×Q8—98no—
401C4×D4—38no—
402C4×D4—916no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—92no—
407C2×C4⋊C4—92no—
408C2×C4⋊C4—92no—
409C2×C4⋊C4—92no—
410C2×C22⋊C4—31no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—31no—
413C2×C22⋊C4—92no—
414C2×C42—31no—
415C2×C42—92no—
416C23×C3—24no—
417C23×C3—24no—
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—32no—
427C23×C3—62no—
428C23×C3—62no—
429C23×C3C2×Dic614yescomplemented
430C23×C3D3×Q814yescomplemented
431C23×C3C23×D312yes—
432C23×C3C23×D312yes—
433C23×C3C23×D311yescharacteristic
434C23×C3C23×D311yescharacteristic
435C22×D3—22no—
436C22×D3—22no—
437C22×D3C2×Dic614yescomplemented
438C22×D3C23×D312yes—
439C3×Q8—68no—
440C3×D4—316no—
441C2×C3×C4—24no—
442C2×C3×C4—216no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—28no—
446C2×C3×C4—28no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—24no—
450C2×C3×C4—34no—
451C2×C3×C4—32no—
452C2×C3×C4—34no—
453C2×C3×C4—32no—
454C2×C3×C4—32no—
455C2×C3×C4—34no—
456C2×C3×C4—62no—
457C2×C3×C4—64no—
458C2×C3×C4—62no—
459C2×C3×C4—64no—
460C2×C3×C4—68no—
461C2×C3×C4D3×D414yes—
462C2×C3×C4D3×D414yes—
463C2×C3×C4C23×D312yes—
464C2×C3×C4C23×D312yes—
465C2×C3×C4C23×D312yes—
466C2×C3×C4C23×D312yes—
467#67C2×Dic6116yescomplemented
468C2×Dic3—24no—
469C2×Dic3—22no—
470C2×Dic3—24no—
471C2×Dic3—22no—
472C2×Dic3—38no—
473C2×Dic3—38no—
474C2×Dic3—34no—
475C2×Dic3—34no—
476C2×Dic3—34no—
477C2×Dic3—34no—
478C2×Dic3—68no—
479C2×Dic3—64no—
480C2×Dic3—64no—
481C2×Dic3—616no—
482C2×Dic3—616no—
483C2×Dic3—616no—
484C2×Dic3—632no—
485C2×Dic3—68no—
486C2×Dic3—64no—
487C2×Dic3—64no—
488C2×Dic3C2×Dic614yescomplemented
489C2×Dic3C23×D314yes—
490C2×Dic3C23×D312yes—
491C2×Dic3C23×D312yes—
492C2×Dic3C23×D314yes—
493C2×Dic3C23×D312yes—
494C4×D3—28no—
495C4×D3—616no—
496Dic6—28no—
497Dic6—316no—
498Dic6—316no—
499Dic6—616no—
500Dic6—616no—
501Dic6—616no—
502Dic6—616no—
503Dic6—616no—
504Dic6—632no—
505Dic6—616no—
506Dic6—68no—
507Dic6—68no—
508C2×C32—24no—
509C2×C32D4×Q814yescomplemented
510C2×C32C23×D411yescharacteristic
511C2×C32C23×Q811yescharacteristic
512C2×C32C2×2−1+411yescharacteristic
513C3×D3—24no—
514C24—31no—
515C24C2×D3211yescharacteristic
516C2×Q8—34no—
517C2×Q8—64no—
518C2×Q8—98no—
519C2×Q8—94no—
520C2×Q8—98no—
521C2×Q8—94no—
522C2×Q8—98no—
523C2×Q8—188no—
524C2×Q8—1832no—
525C2×Q8—188no—
526C2×Q8—1832no—
527C2×Q8—184no—
528C2×D4—34no—
529C2×D4—38no—
530C22×C4—24no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—32no—
534C22×C4—31no—
535C22×C4—32no—
536C22×C4—34no—
537C22×C4—64no—
538C22×C4—98no—
539C22×C4—92no—
540C22×C4—98no—
541C22×C4—92no—
542C22×C4—188no—
543C22×C4—188no—
544C22×C4C2×D3214yes—
545C22×C4C2×D3211yescharacteristic
546C22×C4C2×D3211yescharacteristic
547C4⋊C4—34no—
548C4⋊C4—34no—
549C4⋊C4—38no—
550C4⋊C4—98no—
551C4⋊C4—98no—
552C4⋊C4—98no—
553C4⋊C4—98no—
554C22⋊C4—34no—
555C22⋊C4—38no—
556C22⋊C4—34no—
557C22⋊C4—98no—
558C42—34no—
559C42—98no—
560C22×C3—24no—
561C22×C3—24no—
562C22×C3—216no—
563C22×C3—28no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—28no—
569C22×C3—22no—
570C22×C3—24no—
571C22×C3—22no—
572C22×C3—22no—
573C22×C3—21no—
574C22×C3—34no—
575C22×C3—68no—
576C22×C3—62no—
577C22×C3—62no—
578C22×C3C22×Dic612yes—
579C22×C3C22×Dic614yescomplemented
580C22×C3C2×D3×D412yes—
581C22×C3C2×D3×D412yes—
582C22×C3C2×D3×Q812yes—
583C22×C3C2×D3×Q814yescomplemented
584C22×C3#101012yes—
585C22×C3#101012yes—
586C22×C3C24×D311yescharacteristic
587C22×C3C24×D311yescharacteristic
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—28no—
591C2×D3C22×Dic614yescomplemented
592C3×C4—24no—
593C3×C4—22no—
594C3×C4—22no—
595C3×C4—24no—
596C3×C4—34no—
597C3×C4—62no—
598C3×C4—64no—
599C3×C4—62no—
600C3×C4—64no—
601C3×C4C2×D3×D414yes—
602C3×C4C2×D3×D414yes—
603Dic3—24no—
604Dic3—22no—
605Dic3—24no—
606Dic3—22no—
607Dic3—38no—
608Dic3—38no—
609Dic3—68no—
610Dic3—68no—
611Dic3—64no—
612Dic3—64no—
613Dic3C22×Dic614yescomplemented
614C32C2×D4×Q811yescharacteristic, complemented, Sylow
615C23—22no—
616C23—22no—
617C23—34no—
618C23—32no—
619C23—62no—
620C23—62no—
621C23D3×Dic614yescomplemented
622C23C22×D3212yes—
623C23C22×D3211yescharacteristic
624Q8—68no—
625Q8—916no—
626Q8—1816no—
627Q8—1816no—
628Q8—188no—
629D4—316no—
630C2×C4—22no—
631C2×C4—28no—
632C2×C4—34no—
633C2×C4—32no—
634C2×C4—32no—
635C2×C4—34no—
636C2×C4—32no—
637C2×C4—34no—
638C2×C4—62no—
639C2×C4—64no—
640C2×C4—62no—
641C2×C4—64no—
642C2×C4—68no—
643C2×C4—98no—
644C2×C4—94no—
645C2×C4—94no—
646C2×C4—1816no—
647C2×C4—1816no—
648C2×C4—184no—
649C2×C4#381114yes—
650C2×C4C22×D3212yes—
651C2×C4C22×D3212yes—
652C2×C3—28no—
653C2×C3—24no—
654C2×C3—24no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—24no—
658C2×C3—21no—
659C2×C3—64no—
660C2×C3D4×Dic614yescomplemented
661C2×C3#563214yescomplemented
662C2×C3C23×Dic611yescharacteristic
663C2×C3C22×D3×D411yescharacteristic
664C2×C3C22×D3×D411yescharacteristic
665C2×C3C22×D3×Q811yescharacteristic
666C2×C3C2×#101011yescharacteristic
667C2×C3C2×#101011yescharacteristic
668D3—24no—
669C22—22no—
670C22—28no—
671C22—22no—
672C22—34no—
673C22—62no—
674C22—68no—
675C22—62no—
676C22C2×D3×Dic612yes—
677C22C2×D3×Dic614yescomplemented
678C22#6429812yes—
679C22C2×#381112yes—
680C22C23×D3211yescharacteristic
681C4—22no—
682C4—34no—
683C4—62no—
684C4—64no—
685C4—62no—
686C4—64no—
687C4—98no—
688C4—184no—
689C4C2×#381114yes—
690C3—21no—
691C3C2×D4×Dic611yescharacteristic, complemented
692C3C2×#563211yescharacteristic, complemented
693C2—24no—
694C2—64no—
695C2#1059491514yesdirect product factor
696C2C22×D3×Dic611yescharacteristic
697C2C2×#6429811yescharacteristic
698C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32C2×D4×Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×#634C2semidirect
2. C22×D3×Dic6C2semidirect
4. C2×C3×#924C2semidirect
5. C2×#63982C2semidirect
7. #10594915C2direct (N × H)
8. C2×#63896C2semidirect
9. C2×#63866C2semidirect
10. C2×#63857C2semidirect
11. C2×#63844C2semidirect
12. C2×#63840C2semidirect
21. C22×#634C22semidirect
28. C2×D3×Dic6C22semidirect
34. C3×#924C22semidirect
38. #63982C22semidirect
46. #63896C22semidirect
47. #63866C22semidirect
48. #63857C22semidirect
49. #63844C22semidirect
50. #63840C22semidirect
62. C2×#924D3semidirect
89. C2×#634D4semidirect
93. C2×C3×#67Q8semidirect
180. #924C2×D3semidirect
204. C23×C32C2×Q8semidirect
209. C22×C3×D3C2×Q8semidirect
223. #634C2×D4semidirect
224. C3×#67C2×Q8semidirect
229. C2×C3×Dic3C2×Q8semidirect
279. C2×#67Dic6semidirect
364. C22×C32C22×Q8semidirect
370. C2×C3×D3C22×Q8semidirect
379. C3×Dic3C22×Q8semidirect
429. C23×C3C2×Dic6semidirect
430. C23×C3D3×Q8semidirect
437. C22×D3C2×Dic6semidirect
467. #67C2×Dic6semidirect
488. C2×Dic3C2×Dic6semidirect
509. C2×C32D4×Q8semidirect
579. C22×C3C22×Dic6semidirect
583. C22×C3C2×D3×Q8semidirect
591. C2×D3C22×Dic6semidirect
613. Dic3C22×Dic6semidirect
614. C32C2×D4×Q8semidirect
621. C23D3×Dic6semidirect
660. C2×C3D4×Dic6semidirect
661. C2×C3#5632semidirect
677. C22C2×D3×Dic6semidirect
691. C3C2×D4×Dic6semidirect
692. C3C2×#5632semidirect
695. C2#10594915direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6342
C22×D3×Dic62
C2×C3×C4×#672
C2×C3×#9242
C2×#639822
C2×#67⋊Dic32
#105949152
C2×#638962
C2×#638662
C2×#638572
C2×#638442
C2×#638402
C2×#56323
C2×D4×Dic63