Finite Group Databasebeta

← C2×#10595222 #11900090

Subgroups — C2×#10595222 #11900090

Order 1152.

3493 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic
2C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×#67⋊Dic3C212yesmaximal, complemented
5C2×Dic3×#67C212yesmaximal, complemented
6C22×Dic3⋊Dic3C212yesmaximal, complemented
7C2×#63955C212yesmaximal, complemented
8#10595222C2116yesmaximal, direct product factor
9C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
10C2×#63855C211yesmaximal, characteristic, complemented
11C2×#63843C211yesmaximal, characteristic, complemented
12C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
13C2×#5827—31nomaximal
14C2×#5546—31nomaximal
15C22×C32×D4C2211yescharacteristic
16C23×C3⋊Dic3C2212yes—
17C22×C3×#67C2212yes—
18C23×C3×Dic3C2212yes—
19C23×C3×Dic3C2212yes—
20C2×C3×#237C4116yescomplemented
21C2×C3×#237C2218yes—
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C22×D3×Dic3C2212yes—
25C2×#3757C2212yes—
26D4×C3⋊Dic3C2218yescomplemented
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×C3×#217C2212yes—
30C3×D4×Dic3C2218yescomplemented
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33#67⋊Dic3C22116yescomplemented
34Dic3×#67C22116yescomplemented
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2212yes—
40C2×Dic3⋊Dic3C22116yescomplemented
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43#63955C22116yescomplemented
44C2×Dic32C2212yes—
45C2×Dic32C2212yes—
46D3×C4⋊Dic3C2218yescomplemented
47#63855C2218yescomplemented
48#63843C2218yescomplemented
49Dic3×Dic6C2218yescomplemented
50C22×C3×#41—31no—
51C22×#237D311yescharacteristic
52C2×C3×C4×D4—31no—
53#5827—316no—
54C2×Q8×Dic3—31no—
55C2×Q8×Dic3—31no—
56C2×D4×Dic3—31no—
57C2×D4×Dic3—31no—
58C2×D4×Dic3—32no—
59C2×D4×Dic3—32no—
60C2×D4×Dic3—61no—
61C2×D4×Dic3D311yescharacteristic, complemented
62C2×C4×#67—32no—
63C2×#926—32no—
64C2×#926—31no—
65C22×C4⋊Dic3—32no—
66C22×C4⋊Dic3—31no—
67C22×Dic3⋊C4—32no—
68#5546—316no—
69C2×D3×C4⋊C4—31no—
70C2×#887—31no—
71C2×#67⋊C4—32no—
72C2×#877—32no—
73C2×#872—31no—
74C2×C4×Dic6—31no—
75C24×C32C2312yes—
76C23×C3×D3C2311yescharacteristic
77C2×C32×D4C2×C418yescomplemented
78C2×C32×D4C2314yes—
79C22×C32×C4C2311yescharacteristic
80C22×C3⋊Dic3—44no—
81C22×C3⋊Dic3C2312yes—
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2311yescharacteristic
84C22×C3⋊Dic3C2318yes—
85C2×C3×#67C2×C4116yescomplemented
86C2×C3×#67C2318yes—
87C22×C3×Dic3—44no—
88C22×C3×Dic3C2×C4116yescomplemented
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2318yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2318yes—
96C3×#237C2×C4164yescomplemented
97C2×C3×C4×D3C2×C418yescomplemented
98C2×C3×C4×D3C2314yes—
99C2×C3×Dic6C2×C418yescomplemented
100C2×C3×Dic6C2314yes—
101C2×D3×Dic3—44no—
102C2×D3×Dic3C2318yes—
103#3757C2318yes—
104C4⋊(C3⋊Dic3)C2314yes—
105C4×C3⋊Dic3C2314yes—
106C3×#217C2318yes—
107C3×C4⋊Dic3C2314yes—
108C3×C4×Dic3C2314yes—
109Dic3⋊Dic3C2318yes—
110Dic3⋊Dic3C2318yes—
111Dic3⋊Dic3C2314yes—
112Dic3⋊Dic3C2314yes—
113Dic3⋊Dic3C2318yes—
114(C2×D3)⋊Dic3C2314yes—
115(C2×D3)⋊Dic3C2314yes—
116Dic32C2318yes—
117Dic32C2318yes—
118C2×#520—91noSylow
119C2×C3×#41—316no—
120C2×C3×#41—38no—
121C22×C3×Q8—31no—
122C22×C3×D4—21no—
123C22×C3×D4—32no—
124C22×C3×D4C2×D311yescharacteristic
125C22×C3×D4C2×D311yescharacteristic
126C23×C3×C4—32no—
127C23×C3×C4—31no—
128C23×C3×C4—32no—
129C22×#67C2×D312yes—
130C23×Dic3—32no—
131C23×Dic3—32no—
132C23×Dic3—32no—
133C23×Dic3—62no—
134C23×Dic3C2×D312yes—
135C23×Dic3C2×D312yes—
136C2×#237Dic3116yescomplemented
137C2×#237C2×D318yes—
138C22×C4×D3—32no—
139C22×C4×D3C2×D311yescharacteristic
140C22×Dic6C2×D311yescharacteristic
141C3×C4×D4—38no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C22⋊C4—32no—
144C2×C3×C42—31no—
145C2×#217—32no—
146C2×#217—32no—
147C2×#217—31no—
148C2×#217—31no—
149C2×#217—62no—
150C2×#217C2×D312yes—
151Q8×Dic3—38no—
152Q8×Dic3—38no—
153D4×Dic3—38no—
154D4×Dic3—38no—
155D4×Dic3—316no—
156D4×Dic3—316no—
157D4×Dic3—68no—
158D4×Dic3C2×D318yescomplemented
159C4×#67—316no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162#926—316no—
163#926—38no—
164C2×C4⋊Dic3—31no—
165C2×C4⋊Dic3—31no—
166C2×C4⋊Dic3—32no—
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3—32no—
169C2×C4⋊Dic3—32no—
170C2×C4⋊Dic3—316no—
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—38no—
173C2×C4⋊Dic3—61no—
174C2×C4⋊Dic3C2×D311yescharacteristic
175C2×Dic3⋊C4—32no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—32no—
179C2×Dic3⋊C4—32no—
180C2×Dic3⋊C4—316no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3—31no—
183C2×C4×Dic3—32no—
184C2×C4×Dic3—32no—
185C2×C4×Dic3—32no—
186C2×C4×Dic3—32no—
187C2×C4×Dic3—61no—
188C2×C4×Dic3C2×D311yescharacteristic
189D3×C4⋊C4—38no—
190#887—38no—
191#67⋊C4—316no—
192#877—316no—
193#872—38no—
194C4×Dic6—38no—
195C23×C32—24no—
196C23×C32—24no—
197C23×C32C22×C418yes—
198C23×C32C2414yes—
199C23×C32C2411yescharacteristic
200C22×C3×D3—22no—
201C22×C3×D3—22no—
202C22×C3×D3C22×C414yes—
203C22×C3×D3C2412yes—
204C32×D4C22×C4116yescomplemented
205C2×C32×C4C22×C414yes—
206C2×C32×C4C2412yes—
207C2×C3⋊Dic3—22no—
208C2×C3⋊Dic3—24no—
209C2×C3⋊Dic3—22no—
210C2×C3⋊Dic3—48no—
211C2×C3⋊Dic3C2412yes—
212C2×C3⋊Dic3C2414yes—
213C2×C3⋊Dic3C2412yes—
214C3×#67C22×C4132yescomplemented
215C2×C3×Dic3—24no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—48no—
219C2×C3×Dic3C22×C418yes—
220C2×C3×Dic3C22×C414yes—
221C2×C3×Dic3C22×C4132yescomplemented
222C2×C3×Dic3C2412yes—
223C2×C3×Dic3C2414yes—
224C2×C3×Dic3C2412yes—
225C2×C3×Dic3C2414yes—
226C2×C3×Dic3C2412yes—
227C3×C4×D3C22×C4116yescomplemented
228C3×Dic6C22×C4116yescomplemented
229D3×Dic3—48no—
230C22×#41—31no—
231#520—916no—
232C2×C4×Q8—91no—
233C2×C4×Q8—91no—
234C2×C4×D4—31no—
235C2×C4×D4—92no—
236C2×C4×D4—92no—
237C2×C4×D4—91no—
238C2×#117—91no—
239C2×#117—92no—
240C22×C4⋊C4—91no—
241C22×C4⋊C4—92no—
242C24×C3—22no—
243C24×C3—31no—
244C24×C3C22×D312yes—
245C24×C3C22×D312yes—
246C23×D3C22×D311yescharacteristic
247C3×#41—364no—
248C2×C3×Q8—38no—
249C2×C3×Q8—34no—
250C2×C3×D4—28no—
251C2×C3×D4—24no—
252C2×C3×D4—316no—
253C2×C3×D4—38no—
254C2×C3×D4C4×D318yescomplemented
255C2×C3×D4C2×Dic318yescomplemented
256C2×C3×D4C22×D314yes—
257C2×C3×D4C22×D314yes—
258C22×C3×C4—21no—
259C22×C3×C4—316no—
260C22×C3×C4—32no—
261C22×C3×C4—31no—
262C22×C3×C4—38no—
263C22×C3×C4—38no—
264C22×C3×C4—34no—
265C22×C3×C4—31no—
266C22×C3×C4—32no—
267C22×C3×C4—31no—
268C22×C3×C4—38no—
269C22×C3×C4—124no—
270C22×C3×C4C22×D311yescharacteristic
271C22×C3×C4C22×D311yescharacteristic
272C2×#67C2×Dic3116yescomplemented
273C2×#67C22×D318yes—
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—31no—
277C22×Dic3—32no—
278C22×Dic3—31no—
279C22×Dic3—32no—
280C22×Dic3—38no—
281C22×Dic3—38no—
282C22×Dic3—38no—
283C22×Dic3—44no—
284C22×Dic3—61no—
285C22×Dic3—61no—
286C22×Dic3—62no—
287C22×Dic3—68no—
288C22×Dic3—124no—
289C22×Dic3—124no—
290C22×Dic3—124no—
291C22×Dic3—128no—
292C22×Dic3C2×Dic3116yescomplemented
293C22×Dic3C22×D311yescharacteristic
294C22×Dic3C22×D312yes—
295C22×Dic3C22×D311yescharacteristic
296C22×Dic3C22×D318yes—
297C22×Dic3C22×D312yes—
298C22×Dic3C22×D311yescharacteristic
299C22×Dic3C22×D318yes—
300#237C2×Dic3164yescomplemented
301C2×C4×D3—38no—
302C2×C4×D3—124no—
303C2×C4×D3C2×Dic318yescomplemented
304C2×C4×D3C22×D314yes—
305C2×Dic6C2×Dic318yescomplemented
306C2×Dic6C22×D314yes—
307C3×C4⋊C4—34no—
308C3×C22⋊C4—38no—
309C3×C42—34no—
310#217—38no—
311#217—38no—
312#217—34no—
313#217—34no—
314#217—68no—
315#217C22×D318yes—
316(C2×D3)⋊C4—34no—
317(C2×D3)⋊C4—34no—
318C4⋊Dic3—34no—
319C4⋊Dic3—34no—
320C4⋊Dic3—38no—
321C4⋊Dic3—34no—
322C4⋊Dic3—38no—
323C4⋊Dic3—38no—
324C4⋊Dic3—34no—
325C4⋊Dic3—64no—
326C4⋊Dic3C22×D314yes—
327Dic3⋊C4—38no—
328Dic3⋊C4—34no—
329Dic3⋊C4—34no—
330Dic3⋊C4—38no—
331Dic3⋊C4—38no—
332C4×Dic3—34no—
333C4×Dic3—34no—
334C4×Dic3—38no—
335C4×Dic3—38no—
336C4×Dic3—38no—
337C4×Dic3—38no—
338C4×Dic3—64no—
339C4×Dic3C22×D314yes—
340C22×C32—216no—
341C22×C32—24no—
342C22×C32—24no—
343C22×C32C23×C418yes—
344C22×C32C23×C412yes—
345C22×C32H(5,𝔽2)12yes—
346C22×C322−1+412yes—
347C22×C32C2511yescharacteristic
348C2×C3×D3—28no—
349C2×C3×D3—22no—
350C2×C3×D3—22no—
351C2×C3×D3C23×C414yes—
352C32×C4C23×C414yes—
353C3⋊Dic3—22no—
354C3⋊Dic3—24no—
355C3⋊Dic3—22no—
356C3×Dic3—24no—
357C3×Dic3—22no—
358C3×Dic3—22no—
359C3×Dic3C23×C418yes—
360C3×Dic3C23×C414yes—
361C2×#41—316no—
362C2×#41—38no—
363C22×Q8—31no—
364C22×D4—32no—
365C22×D4D3211yescharacteristic
366C23×C4—32no—
367C23×C4—31no—
368C23×C4—32no—
369C23×C4—92no—
370C23×C4—92no—
371C4×Q8—98no—
372C4×Q8—98no—
373C4×D4—38no—
374C4×D4—916no—
375C4×D4—916no—
376C4×D4—98no—
377#117—98no—
378#117—916no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—98no—
381C2×C4⋊C4—91no—
382C2×C4⋊C4—92no—
383C2×C4⋊C4—92no—
384C2×C4⋊C4—92no—
385C2×C4⋊C4—916no—
386C2×C4⋊C4—91no—
387C2×C4⋊C4—91no—
388C2×C22⋊C4—32no—
389C2×C22⋊C4—91no—
390C2×C22⋊C4—91no—
391C2×C22⋊C4—92no—
392C2×C42—31no—
393C2×C42—92no—
394C2×C42—92no—
395C2×C42—91no—
396C23×C3—24no—
397C23×C3—24no—
398C23×C3—24no—
399C23×C3—24no—
400C23×C3—24no—
401C23×C3—21no—
402C23×C3—28no—
403C23×C3—34no—
404C23×C3—32no—
405C23×C3—44no—
406C23×C3—44no—
407C23×C3—62no—
408C23×C3—62no—
409C23×C3C2×C4×D318yes—
410C23×C3C22×Dic318yes—
411C23×C3C23×D314yes—
412C23×C3C23×D314yes—
413C23×C3C23×D311yescharacteristic
414C23×C3C23×D311yescharacteristic
415C22×D3—22no—
416C22×D3—22no—
417C22×D3C22×Dic314yes—
418C22×D3C23×D312yes—
419C3×Q8—316no—
420C3×D4—216no—
421C3×D4—332no—
422C3×D4C2×C4×D3116yescomplemented
423C3×D4C22×Dic3116yescomplemented
424C2×C3×C4—22no—
425C2×C3×C4—24no—
426C2×C3×C4—34no—
427C2×C3×C4—38no—
428C2×C3×C4—332no—
429C2×C3×C4—34no—
430C2×C3×C4—32no—
431C2×C3×C4—316no—
432C2×C3×C4—32no—
433C2×C3×C4—34no—
434C2×C3×C4—32no—
435C2×C3×C4—64no—
436C2×C3×C4—62no—
437C2×C3×C4—62no—
438C2×C3×C4—128no—
439C2×C3×C4C2×C4×D314yes—
440C2×C3×C4C22×Dic314yes—
441C2×C3×C4C23×D312yes—
442C2×C3×C4C23×D312yes—
443#67C22×Dic3132yescomplemented
444C2×Dic3—22no—
445C2×Dic3—24no—
446C2×Dic3—22no—
447C2×Dic3—32no—
448C2×Dic3—32no—
449C2×Dic3—32no—
450C2×Dic3—34no—
451C2×Dic3—34no—
452C2×Dic3—32no—
453C2×Dic3—48no—
454C2×Dic3—62no—
455C2×Dic3—62no—
456C2×Dic3—64no—
457C2×Dic3—64no—
458C2×Dic3—62no—
459C2×Dic3—64no—
460C2×Dic3—64no—
461C2×Dic3—62no—
462C2×Dic3—62no—
463C2×Dic3—62no—
464C2×Dic3—122no—
465C2×Dic3—124no—
466C2×Dic3—128no—
467C2×Dic3—128no—
468C2×Dic3—128no—
469C2×Dic3—1216no—
470C2×Dic3C22×Dic318yes—
471C2×Dic3C22×Dic314yes—
472C2×Dic3C22×Dic3132yescomplemented
473C2×Dic3C23×D312yes—
474C2×Dic3C23×D314yes—
475C2×Dic3C23×D312yes—
476C2×Dic3C23×D314yes—
477C2×Dic3C23×D312yes—
478C4×D3—128no—
479C4×D3C22×Dic3116yescomplemented
480Dic6C22×Dic3116yescomplemented
481C2×C32—28no—
482C2×C32#52014yescomplemented
483C2×C32C24×C411yescharacteristic
484C2×C32C2×H(5,𝔽2)11yescharacteristic
485C2×C32C2×2−1+411yescharacteristic
486C3×D3—24no—
487C24—31no—
488C24C2×D3212yes—
489#41—364no—
490C2×Q8—34no—
491C2×Q8—38no—
492C2×D4—38no—
493C2×D4—316no—
494C2×D4D3×Dic318yescomplemented
495C2×D4C2×D3214yes—
496C22×C4—38no—
497C22×C4—32no—
498C22×C4—31no—
499C22×C4—316no—
500C22×C4—34no—
501C22×C4—38no—
502C22×C4—31no—
503C22×C4—31no—
504C22×C4—32no—
505C22×C4—38no—
506C22×C4—98no—
507C22×C4—91no—
508C22×C4—91no—
509C22×C4—92no—
510C22×C4—98no—
511C22×C4—124no—
512C22×C4—364no—
513C22×C4—364no—
514C22×C4C2×D3211yescharacteristic
515C4⋊C4—34no—
516C4⋊C4—94no—
517C4⋊C4—98no—
518C4⋊C4—98no—
519C4⋊C4—98no—
520C4⋊C4—94no—
521C4⋊C4—94no—
522C22⋊C4—38no—
523C22⋊C4—94no—
524C22⋊C4—94no—
525C22⋊C4—98no—
526C42—34no—
527C42—98no—
528C42—98no—
529C42—94no—
530C22×C3—24no—
531C22×C3—24no—
532C22×C3—24no—
533C22×C3—24no—
534C22×C3—216no—
535C22×C3—216no—
536C22×C3—22no—
537C22×C3—22no—
538C22×C3—22no—
539C22×C3—28no—
540C22×C3—21no—
541C22×C3—34no—
542C22×C3—44no—
543C22×C3—44no—
544C22×C3—416no—
545C22×C3—62no—
546C22×C3—62no—
547C22×C3—68no—
548C22×C3C22×C4×D318yes—
549C22×C3C22×C4×D312yes—
550C22×C3#100412yes—
551C22×C3#100912yes—
552C22×C3#101012yes—
553C22×C3#101012yes—
554C22×C3C23×Dic318yes—
555C22×C3C23×Dic312yes—
556C22×C3C24×D311yescharacteristic
557C22×C3C24×D311yescharacteristic
558C2×D3—22no—
559C2×D3—22no—
560C2×D3—28no—
561C2×D3C23×Dic314yes—
562C3×C4—24no—
563C3×C4—34no—
564C3×C4—38no—
565C3×C4—64no—
566C3×C4—62no—
567C3×C4—62no—
568C3×C4C22×C4×D314yes—
569C3×C4C23×Dic314yes—
570Dic3—22no—
571Dic3—24no—
572Dic3—22no—
573Dic3—64no—
574Dic3—62no—
575Dic3—64no—
576Dic3—64no—
577Dic3—62no—
578Dic3—62no—
579Dic3—62no—
580Dic3—124no—
581Dic3—122no—
582Dic3C23×Dic318yes—
583Dic3C23×Dic314yes—
584C32C2×#52011yescharacteristic, complemented, Sylow
585C23—24no—
586C23—24no—
587C23—34no—
588C23—32no—
589C23—62no—
590C23—62no—
591C23C2×D3×Dic318yes—
592C23C22×D3214yes—
593C23C22×D3211yescharacteristic
594Q8—316no—
595D4—332no—
596D4C2×D3×Dic3116yescomplemented
597C2×C4—34no—
598C2×C4—38no—
599C2×C4—332no—
600C2×C4—34no—
601C2×C4—32no—
602C2×C4—316no—
603C2×C4—32no—
604C2×C4—32no—
605C2×C4—34no—
606C2×C4—62no—
607C2×C4—62no—
608C2×C4—64no—
609C2×C4—92no—
610C2×C4—92no—
611C2×C4—94no—
612C2×C4—128no—
613C2×C4—182no—
614C2×C4—182no—
615C2×C4—184no—
616C2×C4—368no—
617C2×C4—368no—
618C2×C4C2×D3×Dic314yes—
619C2×C4C22×D3212yes—
620C2×C3—28no—
621C2×C3—28no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—24no—
626C2×C3—48no—
627C2×C3—64no—
628C2×C3#554614yescomplemented
629C2×C3#582714yescomplemented
630C2×C3C23×C4×D311yescharacteristic
631C2×C3C2×#100411yescharacteristic
632C2×C3C2×#100911yescharacteristic
633C2×C3C2×#101011yescharacteristic
634C2×C3C2×#101011yescharacteristic
635C2×C3C24×Dic311yescharacteristic
636D3—24no—
637C22—24no—
638C22—24no—
639C22—216no—
640C22—34no—
641C22—62no—
642C22—62no—
643C22—68no—
644C22#6430912yes—
645C22#6431412yes—
646C22C22×D3×Dic318yes—
647C22C22×D3×Dic312yes—
648C22C23×D3211yescharacteristic
649C4—34no—
650C4—38no—
651C4—62no—
652C4—62no—
653C4—64no—
654C4—182no—
655C4—182no—
656C4—184no—
657C4C22×D3×Dic314yes—
658C3—21no—
659C3C2×#554611yescharacteristic, complemented
660C3C2×#582711yescharacteristic, complemented
661C2—28no—
662C2—64no—
663C2#1059522214yesdirect product factor
664C2C2×#6430911yescharacteristic
665C2C2×#6431411yescharacteristic
666C2C23×D3×Dic311yescharacteristic
subgroupG/H
centerC23C22×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
prime radicalC22×C3×#237C2
cosocleC22×C32C25
hypercenterC22×D4D32
hypocenterC32C2×#520
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×D4×C3⋊Dic3C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C2×#67⋊Dic3C2semidirect
5. C2×Dic3×#67C2semidirect
6. C22×Dic3⋊Dic3C2semidirect
7. C2×#63955C2semidirect
8. #10595222C2direct (N × H)
9. C2×D3×C4⋊Dic3C2semidirect
10. C2×#63855C2semidirect
11. C2×#63843C2semidirect
12. C2×Dic3×Dic6C2semidirect
20. C2×C3×#237C4semidirect
26. D4×C3⋊Dic3C22semidirect
30. C3×D4×Dic3C22semidirect
33. #67⋊Dic3C22semidirect
34. Dic3×#67C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
43. #63955C22semidirect
46. D3×C4⋊Dic3C22semidirect
47. #63855C22semidirect
48. #63843C22semidirect
49. Dic3×Dic6C22semidirect
61. C2×D4×Dic3D3semidirect
77. C2×C32×D4C2×C4semidirect
85. C2×C3×#67C2×C4semidirect
88. C22×C3×Dic3C2×C4semidirect
96. C3×#237C2×C4semidirect
97. C2×C3×C4×D3C2×C4semidirect
99. C2×C3×Dic6C2×C4semidirect
136. C2×#237Dic3semidirect
158. D4×Dic3C2×D3semidirect
204. C32×D4C22×C4semidirect
214. C3×#67C22×C4semidirect
221. C2×C3×Dic3C22×C4semidirect
227. C3×C4×D3C22×C4semidirect
228. C3×Dic6C22×C4semidirect
254. C2×C3×D4C4×D3semidirect
255. C2×C3×D4C2×Dic3semidirect
272. C2×#67C2×Dic3semidirect
292. C22×Dic3C2×Dic3semidirect
300. #237C2×Dic3semidirect
303. C2×C4×D3C2×Dic3semidirect
305. C2×Dic6C2×Dic3semidirect
422. C3×D4C2×C4×D3semidirect
423. C3×D4C22×Dic3semidirect
443. #67C22×Dic3semidirect
472. C2×Dic3C22×Dic3semidirect
479. C4×D3C22×Dic3semidirect
480. Dic6C22×Dic3semidirect
482. C2×C32#520semidirect
494. C2×D4D3×Dic3semidirect
584. C32C2×#520semidirect
596. D4C2×D3×Dic3semidirect
628. C2×C3#5546semidirect
629. C2×C3#5827semidirect
659. C3C2×#5546semidirect
660. C3C2×#5827semidirect
663. C2#10595222direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×D4×C3⋊Dic32
C2×C3×D4×Dic32
C2×#67⋊Dic32
C2×Dic3×#672
C22×Dic3⋊Dic32
C2×#639552
#105952222
C2×D3×C4⋊Dic32
C2×#638552
C2×#638432
C2×Dic3×Dic62
C2×#58273
C2×#55463