Finite Group Databasebeta

← C2×#10593901 #11902615

Subgroups — C2×#10593901 #11902615

Order 1152.

3453 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C2×C3×#875C211yesmaximal, characteristic, complemented
5C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
6C2×#63916C211yesmaximal, characteristic, complemented
7C2×#63910C212yesmaximal, complemented
8C2×#63893C212yesmaximal, complemented
9C2×#63880C212yesmaximal, complemented
10C2×#63871C211yesmaximal, characteristic, complemented
11C2×#63852C212yesmaximal, complemented
12#10593901C2116yesmaximal, direct product factor
13C2×#5677—31nomaximal
14C2×#5576—31nomaximal
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C3×D12C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#627C2212yes—
22C22×#626C2212yes—
23C22×#626C2212yes—
24C22×#624C2212yes—
25C22×D3×Dic3C2212yes—
26C2×#3797—28no—
27C2×#3797C2218yescomplemented
28C2×#3796—28no—
29C2×#3796C2218yescomplemented
30C2×C32×C42C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
34C4×C4⋊(C3⋊D3)C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2212yes—
36C2×C3×(C2×D3)⋊C4C2212yes—
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×Dic3⋊C4C2212yes—
39C2×C3×C4×Dic3C2212yes—
40C3×#875C2218yescomplemented
41C3×C4×Dic6C2218yescomplemented
42C2×Dic3⋊Dic3C2212yes—
43C2×#3722C2212yes—
44C2×(C2×D3)⋊Dic3C2212yes—
45#63916C2218yescomplemented
46#63910C22116yescomplemented
47#63893C22116yescomplemented
48#63880C22116yescomplemented
49#63871C2218yescomplemented
50#63852C22116yescomplemented
51C22×#239—31no—
52C22×D3×Q8—31no—
53C22×D3×Q8—31no—
54C22×#237—31no—
55C2×C3×#124—31no—
56C2×C3×C4×Q8—31no—
57C2×#946—31no—
58C2×#938—31no—
59#5677—316no—
60#5576—316no—
61C2×#897—31no—
62C2×#897—32no—
63C2×#895—31no—
64C2×#895—32no—
65C2×#885—32no—
66C2×#884—32no—
67C2×#67⋊C4—32no—
68C2×#878—32no—
69C2×#875—32no—
70C2×#875D311yescharacteristic, complemented
71C2×C4×D12—31no—
72C2×C4×D12—31no—
73C2×C4×D12—32no—
74C2×C4×D12—61no—
75C2×C4×Dic6D311yescharacteristic, complemented
76C23×C3⋊D3C2311yescharacteristic
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2311yescharacteristic
84C2×C4⋊(C3⋊D3)—24no—
85C2×C4⋊(C3⋊D3)C2314yes—
86C2×C4×C3⋊D3—24no—
87C2×C4×C3⋊D3—24no—
88C2×C4×C3⋊D3C2314yes—
89C2×C4×C3⋊D3C2314yes—
90C22×C3×Dic3C2312yes—
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2312yes—
93C2×C3×D12—24no—
94C2×C3×D12C2314yes—
95C2×C3×Dic6—24no—
96C2×C3×Dic6D418yescomplemented
97C2×C3×Dic6C2314yes—
98C2×C3×Dic6C2314yes—
99C2×#627—28no—
100C2×#627C2318yes—
101C2×#626—28no—
102C2×#626—28no—
103C2×#626C2318yes—
104C2×#626C2318yes—
105C2×#624—28no—
106C2×#624C2318yes—
107C2×D3×Dic3—28no—
108C2×D3×Dic3C2318yes—
109#3797—232no—
110#3796—232no—
111C32×C42C2314yes—
112#3752C2314yes—
113#3752C2314yes—
114C4⋊(C3⋊Dic3)C2314yes—
115C3×(C2×D3)⋊C4C2318yes—
116C3×(C2×D3)⋊C4C2318yes—
117C3×C4⋊Dic3C2314yes—
118C3×Dic3⋊C4C2318yes—
119C3×C4×Dic3C2318yes—
120Dic3⋊Dic3C2318yes—
121#3722C2318yes—
122(C2×D3)⋊Dic3C2318yes—
123C2×#548—91noSylow
124C22×C3×Q8—31no—
125C22×C3×Q8—31no—
126C22×C3×D4—31no—
127C22×#67—32no—
128C22×#67—32no—
129C23×Dic3—32no—
130C2×#239—38no—
131C2×#239—68no—
132C2×D3×Q8—38no—
133C2×D3×Q8—38no—
134C2×D3×Q8—68no—
135C2×D3×Q8—68no—
136C2×#237—38no—
137C2×#237—68no—
138C22×D12—32no—
139C22×D12—32no—
140C22×D12—31no—
141C22×D12—31no—
142C22×D12—61no—
143C22×D12C2×D311yescharacteristic
144C22×C4×D3—32no—
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—32no—
150C22×C4×D3—32no—
151C22×C4×D3—61no—
152C22×C4×D3—61no—
153C22×Dic6—32no—
154C22×Dic6—32no—
155C22×Dic6C2×D311yescharacteristic
156C22×Dic6C2×D311yescharacteristic
157C3×#124—38no—
158C3×C4×Q8—38no—
159C2×C3×C4⋊C4—32no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C22⋊C4—32no—
162C2×C3×C22⋊C4—32no—
163C2×C3×C42—21no—
164C2×C3×C42—32no—
165C2×C3×C42C2×D311yescharacteristic
166C2×C3×C42C2×D311yescharacteristic
167C2×#217—32no—
168#946—38no—
169#938—38no—
170C2×(C2×D3)⋊C4—32no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—32no—
176C2×(C2×D3)⋊C4—32no—
177C2×(C2×D3)⋊C4—61no—
178C2×(C2×D3)⋊C4—61no—
179C2×(C2×D3)⋊C4C2×D312yes—
180C2×(C2×D3)⋊C4C2×D312yes—
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—32no—
184C2×C4⋊Dic3—61no—
185C2×C4⋊Dic3C2×D311yescharacteristic
186C2×Dic3⋊C4—32no—
187C2×Dic3⋊C4C2×D312yes—
188C2×C4×Dic3C2×D312yes—
189#897—38no—
190#897—316no—
191#895—38no—
192#895—316no—
193#885—316no—
194#884—316no—
195#67⋊C4—316no—
196#878—316no—
197#875—316no—
198#875C2×D318yescomplemented
199C4×D12—38no—
200C4×D12—38no—
201C4×D12—316no—
202C4×D12—68no—
203C4×Dic6C2×D318yescomplemented
204C23×C32C2411yescharacteristic
205C22×C3⋊D3—22no—
206C22×C3⋊D3—22no—
207C22×C3⋊D3—22no—
208C22×C3⋊D3—22no—
209C22×C3⋊D3—22no—
210C22×C3⋊D3#4114yescomplemented
211C22×C3⋊D3C2412yes—
212C22×C3⋊D3C2412yes—
213C22×C3×D3—24no—
214C22×C3×D3—24no—
215C22×C3×D3—24no—
216C22×C3×D3C2414yes—
217C2×C32×C4—22no—
218C2×C32×C4—22no—
219C2×C32×C4C2×D414yes—
220C2×C32×C4C2412yes—
221C2×C32×C4C2412yes—
222C2×C32×C4C2412yes—
223C2×C3⋊Dic3—22no—
224C2×C3⋊Dic3—22no—
225C2×C3⋊Dic3C2412yes—
226C2×C3⋊Dic3C2412yes—
227C4⋊(C3⋊D3)—28no—
228C4×C3⋊D3—28no—
229C4×C3⋊D3—28no—
230C2×C3×Dic3—24no—
231C2×C3×Dic3—24no—
232C2×C3×Dic3C2×D418yes—
233C2×C3×Dic3C2414yes—
234C2×C3×Dic3C2414yes—
235C2×C3×Dic3C2414yes—
236C3×D12—28no—
237C3×Dic6—28no—
238C3×Dic6C2×D4116yescomplemented
239#627—216no—
240#626—216no—
241#626—216no—
242#624—216no—
243D3×Dic3—216no—
244C22×#41—91no—
245C23×Q8—91no—
246#548—916no—
247C2×#124—31no—
248C2×#124—92no—
249C2×C22⋊Q8—92no—
250C2×C22⋊Q8—91no—
251C2×#121—92no—
252C2×#121—91no—
253C2×C4×Q8—31no—
254C2×C4×D4—92no—
255C2×C4×D4—91no—
256C24×C3—32no—
257C23×D3—31no—
258C23×D3—31no—
259C23×D3—31no—
260C23×D3—31no—
261C23×D3—61no—
262C23×D3—61no—
263C23×D3C22×D312yes—
264C2×C3×Q8—38no—
265C2×C3×Q8—34no—
266C2×C3×Q8—34no—
267C2×C3×Q8—64no—
268C2×C3×D4—34no—
269C2×C3×D4—64no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—32no—
274C22×C3×C4—32no—
275C22×C3×C4—32no—
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C2×#67—38no—
283C2×#67—38no—
284C2×#67—68no—
285C2×#67—68no—
286C22×Dic3—31no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—38no—
291C22×Dic3—61no—
292C22×Dic3—61no—
293C22×Dic3—68no—
294C22×Dic3C22×D312yes—
295C22×Dic3C22×D312yes—
296C22×Dic3C22×D312yes—
297#239—632no—
298D3×Q8—632no—
299D3×Q8—632no—
300#237—632no—
301C2×D12—24no—
302C2×D12—38no—
303C2×D12—38no—
304C2×D12—34no—
305C2×D12—34no—
306C2×D12—64no—
307C2×D12—64no—
308C2×D12—64no—
309C2×D12—68no—
310C2×D12—68no—
311C2×D12—68no—
312C2×D12C22×D314yes—
313C2×C4×D3—38no—
314C2×C4×D3—34no—
315C2×C4×D3—34no—
316C2×C4×D3—34no—
317C2×C4×D3—34no—
318C2×C4×D3—38no—
319C2×C4×D3—38no—
320C2×C4×D3—64no—
321C2×C4×D3—64no—
322C2×C4×D3—68no—
323C2×C4×D3—68no—
324C2×C4×D3—64no—
325C2×C4×D3—64no—
326C2×C4×D3—64no—
327C2×C4×D3—64no—
328C2×C4×D3—68no—
329C2×C4×D3—124no—
330C2×C4×D3—124no—
331C2×Dic6—24no—
332C2×Dic6—38no—
333C2×Dic6—38no—
334C2×Dic6—68no—
335C2×Dic6—68no—
336C2×Dic6D1218yescomplemented
337C2×Dic6C22×D314yes—
338C2×Dic6C22×D314yes—
339C3×C4⋊C4—38no—
340C3×C4⋊C4—34no—
341C3×C22⋊C4—38no—
342C3×C22⋊C4—38no—
343C3×C42—24no—
344C3×C42—38no—
345C3×C42C22×D314yes—
346C3×C42C22×D314yes—
347#217—38no—
348(C2×D3)⋊C4—38no—
349(C2×D3)⋊C4—34no—
350(C2×D3)⋊C4—34no—
351(C2×D3)⋊C4—34no—
352(C2×D3)⋊C4—34no—
353(C2×D3)⋊C4—38no—
354(C2×D3)⋊C4—38no—
355(C2×D3)⋊C4—64no—
356(C2×D3)⋊C4—64no—
357(C2×D3)⋊C4C22×D318yes—
358(C2×D3)⋊C4C22×D318yes—
359C4⋊Dic3—34no—
360C4⋊Dic3—34no—
361C4⋊Dic3—38no—
362C4⋊Dic3—64no—
363C4⋊Dic3C22×D314yes—
364Dic3⋊C4—38no—
365Dic3⋊C4C22×D318yes—
366C4×Dic3C22×D318yes—
367C22×C32C22×D412yes—
368C22×C32C2×#4112yes—
369C22×C322−1+412yes—
370C22×C32C2511yescharacteristic
371C2×C3⋊D3—22no—
372C2×C3⋊D3—28no—
373C2×C3⋊D3—22no—
374C2×C3⋊D3—22no—
375C2×C3⋊D3—22no—
376C2×C3⋊D3—22no—
377C2×C3⋊D3—44no—
378C2×C3⋊D3C2×#4114yescomplemented
379C2×C3×D3—24no—
380C2×C3×D3—24no—
381C2×C3×D3—24no—
382C2×C3×D3—48no—
383C32×C4—22no—
384C32×C4—22no—
385C32×C4C22×D414yes—
386C3⋊Dic3—22no—
387C3⋊Dic3—22no—
388C3×Dic3—24no—
389C3×Dic3—24no—
390C3×Dic3C22×D418yes—
391C2×#41—98no—
392C2×#41—188no—
393C22×Q8—31no—
394C22×Q8—31no—
395C22×Q8—92no—
396C22×Q8—98no—
397C22×Q8—188no—
398C22×D4—31no—
399C22×D4—92no—
400C22×D4—92no—
401C22×D4—91no—
402C23×C4—92no—
403C23×C4—92no—
404C23×C4—91no—
405C23×C4—91no—
406#124—38no—
407#124—916no—
408C22⋊Q8—916no—
409C22⋊Q8—98no—
410#121—916no—
411#121—98no—
412C4×Q8—38no—
413C4×D4—916no—
414C4×D4—98no—
415C2×C4⋊C4—32no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—92no—
418C2×C4⋊C4—91no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—92no—
422C2×C22⋊C4—92no—
423C2×C22⋊C4—91no—
424C2×C22⋊C4—91no—
425C2×C42—32no—
426C2×C42D3211yescharacteristic
427C23×C3—21no—
428C23×C3—34no—
429C23×C3—64no—
430C23×C3—64no—
431C23×C3—64no—
432C23×C3C23×D311yescharacteristic
433C23×C3C23×D311yescharacteristic
434C22×D3—24no—
435C22×D3—24no—
436C22×D3—24no—
437C22×D3—34no—
438C22×D3—34no—
439C22×D3—32no—
440C22×D3—32no—
441C22×D3—32no—
442C22×D3—32no—
443C22×D3—64no—
444C22×D3—62no—
445C22×D3—62no—
446C22×D3—62no—
447C22×D3—62no—
448C22×D3—62no—
449C22×D3—62no—
450C22×D3—64no—
451C22×D3—62no—
452C22×D3—62no—
453C22×D3—62no—
454C22×D3—62no—
455C22×D3—62no—
456C22×D3—62no—
457C22×D3—122no—
458C22×D3—122no—
459C22×D3—122no—
460C22×D3—122no—
461C22×D3C23×D314yes—
462C3×Q8—316no—
463C3×Q8—68no—
464C3×D4—68no—
465C2×C3×C4—24no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—24no—
474C2×C3×C4—38no—
475C2×C3×C4—34no—
476C2×C3×C4—34no—
477C2×C3×C4—34no—
478C2×C3×C4—42no—
479C2×C3×C4—64no—
480C2×C3×C4—64no—
481C2×C3×C4C2×D1214yes—
482C2×C3×C4D3×D414yes—
483C2×C3×C4C23×D312yes—
484C2×C3×C4C23×D312yes—
485C2×C3×C4C23×D312yes—
486C2×C3×C4C23×D312yes—
487C2×C3×C4C23×D312yes—
488C2×C3×C4C23×D312yes—
489#67—616no—
490#67—616no—
491C2×Dic3—24no—
492C2×Dic3—24no—
493C2×Dic3—32no—
494C2×Dic3—32no—
495C2×Dic3—32no—
496C2×Dic3—32no—
497C2×Dic3—62no—
498C2×Dic3—62no—
499C2×Dic3—62no—
500C2×Dic3—62no—
501C2×Dic3—62no—
502C2×Dic3—62no—
503C2×Dic3—616no—
504C2×Dic3—122no—
505C2×Dic3—122no—
506C2×Dic3C2×D1218yes—
507C2×Dic3C23×D314yes—
508C2×Dic3C23×D314yes—
509C2×Dic3C23×D314yes—
510D12—28no—
511D12—68no—
512D12—68no—
513D12—616no—
514D12—616no—
515D12—616no—
516C4×D3—616no—
517C4×D3—616no—
518C4×D3—68no—
519C4×D3—68no—
520C4×D3—68no—
521C4×D3—68no—
522C4×D3—616no—
523C4×D3—128no—
524C4×D3—128no—
525Dic6—28no—
526Dic6—616no—
527Dic6—616no—
528Dic6C2×D12116yescomplemented
529C2×C32#54814yescomplemented
530C2×C32C23×D411yescharacteristic
531C2×C32C22×#4111yescharacteristic
532C2×C32C2×2−1+411yescharacteristic
533C3⋊D3—24no—
534C3⋊D3—42no—
535C3×D3—44no—
536C24—32no—
537C24—91no—
538C24—91no—
539#41—1832no—
540C2×Q8—34no—
541C2×Q8—34no—
542C2×Q8—38no—
543C2×Q8—64no—
544C2×Q8—98no—
545C2×Q8—188no—
546C2×Q8—1832no—
547C2×D4—34no—
548C2×D4—64no—
549C2×D4—98no—
550C2×D4—98no—
551C2×D4—94no—
552C2×D4—184no—
553C2×D4—188no—
554C2×D4—188no—
555C22×C4—32no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—98no—
559C22×C4—98no—
560C22×C4—91no—
561C22×C4—91no—
562C22×C4—94no—
563C22×C4—94no—
564C22×C4—188no—
565C22×C4—188no—
566C22×C4—184no—
567C22×C4—184no—
568C22×C4C2×D3211yescharacteristic
569C22×C4C2×D3211yescharacteristic
570C22×C4C2×D3211yescharacteristic
571C4⋊C4—38no—
572C4⋊C4—34no—
573C4⋊C4—98no—
574C4⋊C4—94no—
575C22⋊C4—38no—
576C22⋊C4—38no—
577C22⋊C4—98no—
578C22⋊C4—98no—
579C22⋊C4—94no—
580C22⋊C4—94no—
581C42—38no—
582C42C2×D3214yes—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—21no—
587C22×C3—64no—
588C22×C3—64no—
589C22×C3—64no—
590C22×C3—128no—
591C22×C3C22×D1212yes—
592C22×C3C2×D3×D412yes—
593C22×C3#100712yes—
594C22×C3D3×#4112yes—
595C22×C3D3×#4112yes—
596C22×C3#101012yes—
597C22×C3C24×D311yescharacteristic
598C22×C3C24×D311yescharacteristic
599C2×D3—24no—
600C2×D3—24no—
601C2×D3—24no—
602C2×D3—34no—
603C2×D3—34no—
604C2×D3—48no—
605C2×D3—64no—
606C2×D3—68no—
607C2×D3—62no—
608C2×D3—62no—
609C2×D3—62no—
610C2×D3—62no—
611C2×D3—68no—
612C2×D3—64no—
613C2×D3—62no—
614C2×D3—62no—
615C2×D3—62no—
616C2×D3—62no—
617C2×D3—62no—
618C2×D3—62no—
619C2×D3—122no—
620C2×D3—122no—
621C2×D3—122no—
622C2×D3—128no—
623C2×D3—122no—
624C2×D3—128no—
625C2×D3—124no—
626C2×D3—124no—
627C3×C4—24no—
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—22no—
631C3×C4—22no—
632C3×C4—24no—
633C3×C4—38no—
634C3×C4—42no—
635C3×C4—64no—
636C3×C4—64no—
637C3×C4C22×D1214yes—
638C3×C4C2×D3×D414yes—
639Dic3—24no—
640Dic3—24no—
641Dic3—62no—
642Dic3—62no—
643Dic3—62no—
644Dic3—62no—
645Dic3—122no—
646Dic3—122no—
647Dic3C22×D1218yes—
648C32C2×#54811yescharacteristic, complemented, Sylow
649C23—34no—
650C23—64no—
651C23—64no—
652C23—64no—
653C23—94no—
654C23—92no—
655C23—92no—
656C23—182no—
657C23—182no—
658C23—182no—
659C23—182no—
660C23—182no—
661C23C22×D3211yescharacteristic
662Q8—316no—
663Q8—68no—
664Q8—1816no—
665D4—68no—
666D4—188no—
667D4—1816no—
668D4—1816no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—38no—
672C2×C4—34no—
673C2×C4—34no—
674C2×C4—34no—
675C2×C4—64no—
676C2×C4—64no—
677C2×C4—92no—
678C2×C4—92no—
679C2×C4—1816no—
680C2×C4—1816no—
681C2×C4—182no—
682C2×C4—182no—
683C2×C4—188no—
684C2×C4—188no—
685C2×C4D3×D1214yes—
686C2×C4C22×D3212yes—
687C2×C4C22×D3212yes—
688C2×C4C22×D3212yes—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—24no—
693C2×C3—124no—
694C2×C3#557614yescomplemented
695C2×C3#567714yescomplemented
696C2×C3C23×D1211yescharacteristic
697C2×C3C22×D3×D411yescharacteristic
698C2×C3C2×#100711yescharacteristic
699C2×C3C2×D3×#4111yescharacteristic
700C2×C3C2×D3×#4111yescharacteristic
701C2×C3C2×#101011yescharacteristic
702D3—44no—
703D3—64no—
704D3—64no—
705D3—124no—
706D3—124no—
707D3—122no—
708D3—122no—
709C22—64no—
710C22—64no—
711C22—64no—
712C22—94no—
713C22—128no—
714C22—182no—
715C22—182no—
716C22—188no—
717C22—182no—
718C22—182no—
719C22—182no—
720C22—364no—
721C22#6429712yes—
722C22C2×D3×D1212yes—
723C22#6430612yes—
724C22C23×D3211yescharacteristic
725C4—22no—
726C4—22no—
727C4—38no—
728C4—64no—
729C4—64no—
730C4—182no—
731C4—182no—
732C4C2×D3×D1214yes—
733C3—21no—
734C3C2×#557611yescharacteristic, complemented
735C3C2×#567711yescharacteristic, complemented
736C2—124no—
737C2—184no—
738C2—362no—
739C2#1059390114yesdirect product factor
740C2C2×#6429711yescharacteristic
741C2C22×D3×D1211yescharacteristic
742C2C2×#6430611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×#3797C2semidirect
2. C22×#3796C2semidirect
3. C2×C4×C4⋊(C3⋊D3)C2semidirect
4. C2×C3×#875C2semidirect
5. C2×C3×C4×Dic6C2semidirect
6. C2×#63916C2semidirect
7. C2×#63910C2semidirect
8. C2×#63893C2semidirect
9. C2×#63880C2semidirect
10. C2×#63871C2semidirect
11. C2×#63852C2semidirect
12. #10593901C2direct (N × H)
27. C2×#3797C22semidirect
29. C2×#3796C22semidirect
34. C4×C4⋊(C3⋊D3)C22semidirect
40. C3×#875C22semidirect
41. C3×C4×Dic6C22semidirect
45. #63916C22semidirect
46. #63910C22semidirect
47. #63893C22semidirect
48. #63880C22semidirect
49. #63871C22semidirect
50. #63852C22semidirect
70. C2×#875D3semidirect
75. C2×C4×Dic6D3semidirect
96. C2×C3×Dic6D4semidirect
198. #875C2×D3semidirect
203. C4×Dic6C2×D3semidirect
210. C22×C3⋊D3#41semidirect
238. C3×Dic6C2×D4semidirect
336. C2×Dic6D12semidirect
378. C2×C3⋊D3C2×#41semidirect
528. Dic6C2×D12semidirect
529. C2×C32#548semidirect
648. C32C2×#548semidirect
694. C2×C3#5576semidirect
695. C2×C3#5677semidirect
734. C3C2×#5576semidirect
735. C3C2×#5677semidirect
739. C2#10593901direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C22×#37962
C2×C4×C4⋊(C3⋊D3)2
C2×C3×#8752
C2×C3×C4×Dic62
C2×#639162
C2×#639102
C2×#638932
C2×#638802
C2×#638712
C2×#638522
#105939012
C2×#56773
C2×#55763