Finite Group Databasebeta

← C2×#10594523 #11901165

Subgroups — C2×#10594523 #11901165

Order 1152.

3493 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3C2×#64104C211yesmaximal, characteristic, complemented
4C2×C3×#897C211yesmaximal, characteristic, complemented
5C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
6C2×#63910C212yesmaximal, complemented
7C2×#63909C211yesmaximal, characteristic, complemented
8C2×#63909C212yesmaximal, complemented
9C2×#63906C212yesmaximal, complemented
10C2×#63895C212yesmaximal, complemented
11C2×#63871C211yesmaximal, characteristic, complemented
12#10594523C2116yesmaximal, direct product factor
13C2×#5629—31nomaximal
14C2×#5510—31nomaximal
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4⋊(C3⋊D3)C2212yes—
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2212yes—
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C22×#627C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2212yes—
26C22×#626C2212yes—
27C22×#625C2211yescharacteristic
28C22×#624C2212yes—
29C2×#3799—28no—
30C2×#3799C2218yescomplemented
31C2×#3798—28no—
32C2×#3798C2218yescomplemented
33C2×C32×C4⋊C4C2211yescharacteristic
34C2×#3752C2212yes—
35#64104C2218yescomplemented
36C2×C3×(C2×D3)⋊C4C2212yes—
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×C4⋊Dic3C2212yes—
39C2×C3×Dic3⋊C4C2212yes—
40C3×#897C2218yescomplemented
41C3×D3×C4⋊C4C2218yescomplemented
42C2×Dic3⋊Dic3C2212yes—
43C2×#3722C2212yes—
44C2×#3722C2212yes—
45#63910C22116yescomplemented
46#63909C2218yescomplemented
47#63909C22116yescomplemented
48#63906C22116yescomplemented
49#63895C22116yescomplemented
50#63871C2218yescomplemented
51C22×#239—31no—
52C22×#235—31no—
53C22×#235—31no—
54C22×#235—31no—
55C2×C3×C22⋊Q8—31no—
56C22×C3×C4⋊C4—31no—
57C2×#946—31no—
58C2×#930—32no—
59C2×#930—32no—
60C2×#930—31no—
61#5629—316no—
62#5510—316no—
63C2×#897—31no—
64C2×#897—32no—
65C2×#897D311yescharacteristic, complemented
66C2×#896—32no—
67C2×#895—31no—
68C2×#895—32no—
69C2×#895—31no—
70C2×#895—31no—
71C2×#895—32no—
72C2×#895—61no—
73C2×D3×C4⋊C4D311yescharacteristic, complemented
74C2×#884—32no—
75C2×#884—32no—
76C23×C3⋊D3C2312yes—
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3C2311yescharacteristic
79C23×C3×D3C2311yescharacteristic
80C22×C32×C4C2312yes—
81C22×C32×C4C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C2×C4⋊(C3⋊D3)—24no—
84C2×C4⋊(C3⋊D3)—44no—
85C2×C4⋊(C3⋊D3)C2314yes—
86C2×C4⋊(C3⋊D3)C2318yes—
87C2×C4×C3⋊D3—24no—
88C2×C4×C3⋊D3C2314yes—
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2311yescharacteristic
93C2×C3×C4×D3—24no—
94C2×C3×C4×D3—44no—
95C2×C3×C4×D3D418yescomplemented
96C2×C3×C4×D3C2314yes—
97C2×C3×C4×D3C2318yes—
98C2×C3×C4×D3C2314yes—
99C2×C3×Dic6—24no—
100C2×C3×Dic6C2314yes—
101C2×#627—24no—
102C2×#627C2314yes—
103C2×#626—24no—
104C2×#626—28no—
105C2×#626—24no—
106C2×#626—44no—
107C2×#626C2314yes—
108C2×#626C2314yes—
109C2×#626C2318yes—
110C2×#626C2318yes—
111C2×#625—24no—
112C2×#625C2314yes—
113C2×#624—28no—
114C2×#624C2318yes—
115#3799—232no—
116#3798—232no—
117C32×C4⋊C4C2314yes—
118#3752C2318yes—
119C3×(C2×D3)⋊C4C2318yes—
120C3×C4⋊Dic3C2314yes—
121C3×C4⋊Dic3C2318yes—
122C3×Dic3⋊C4C2318yes—
123Dic3⋊Dic3C2318yes—
124#3722C2318yes—
125#3722C2318yes—
126C2×#537—91noSylow
127C22×C3×Q8—31no—
128C23×C3×C4—31no—
129C23×C3×C4—31no—
130C23×C3×C4—32no—
131C22×#67—31no—
132C22×#67—31no—
133C22×#67—31no—
134C22×#67—32no—
135C22×#67—31no—
136C22×#67—32no—
137C2×#239—38no—
138C2×#239—68no—
139C2×#235—38no—
140C2×#235—38no—
141C2×#235—38no—
142C2×#235—68no—
143C2×#235—68no—
144C2×#235—68no—
145C22×D12—31no—
146C22×D12—31no—
147C22×D12—32no—
148C22×D12—31no—
149C22×D12—31no—
150C22×D12—32no—
151C22×D12—32no—
152C22×D12—32no—
153C22×D12—61no—
154C22×D12—62no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3—32no—
158C22×C4×D3—32no—
159C22×C4×D3—61no—
160C22×C4×D3C2×D311yescharacteristic
161C22×C4×D3C2×D312yes—
162C22×C4×D3C2×D311yescharacteristic
163C22×Dic6—31no—
164C22×Dic6—31no—
165C22×Dic6C2×D311yescharacteristic
166C3×C22⋊Q8—38no—
167C2×C3×C4⋊C4—21no—
168C2×C3×C4⋊C4—32no—
169C2×C3×C4⋊C4—32no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C4⋊C4—38no—
172C2×C3×C4⋊C4C2×D311yescharacteristic
173C2×C3×C4⋊C4C2×D311yescharacteristic
174C2×C3×C22⋊C4—32no—
175#946—38no—
176#930—316no—
177#930—316no—
178#930—38no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—32no—
183C2×(C2×D3)⋊C4—32no—
184C2×(C2×D3)⋊C4—32no—
185C2×(C2×D3)⋊C4—62no—
186C2×(C2×D3)⋊C4C2×D312yes—
187C2×C4⋊Dic3—32no—
188C2×C4⋊Dic3C2×D311yescharacteristic
189C2×C4⋊Dic3C2×D312yes—
190C2×Dic3⋊C4—32no—
191C2×Dic3⋊C4C2×D312yes—
192#897—38no—
193#897—316no—
194#897C2×D318yescomplemented
195#896—316no—
196#895—38no—
197#895—316no—
198#895—38no—
199#895—38no—
200#895—316no—
201#895—68no—
202D3×C4⋊C4C2×D318yescomplemented
203#884—316no—
204#884—316no—
205C23×C32C2411yescharacteristic
206C22×C3⋊D3—22no—
207C22×C3⋊D3—24no—
208C22×C3⋊D3—22no—
209C22×C3⋊D3—24no—
210C22×C3⋊D3—22no—
211C22×C3⋊D3—24no—
212C22×C3⋊D3C2412yes—
213C22×C3⋊D3C2414yes—
214C22×C3×D3—22no—
215C22×C3×D3—22no—
216C22×C3×D3—22no—
217C22×C3×D3—22no—
218C22×C3×D3—22no—
219C22×C3×D3C2×D414yes—
220C22×C3×D3C2412yes—
221C22×C3×D3C2412yes—
222C2×C32×C4—24no—
223C2×C32×C4C2×D414yes—
224C2×C32×C4C2414yes—
225C2×C32×C4C2412yes—
226C2×C3⋊Dic3—22no—
227C2×C3⋊Dic3C2412yes—
228C4⋊(C3⋊D3)—28no—
229C4⋊(C3⋊D3)—48no—
230C4×C3⋊D3—28no—
231C2×C3×Dic3—24no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—24no—
234C2×C3×Dic3C2×D414yes—
235C2×C3×Dic3C2414yes—
236C2×C3×Dic3C2412yes—
237C2×C3×Dic3C2414yes—
238C2×C3×Dic3C2412yes—
239C3×C4×D3—28no—
240C3×C4×D3—48no—
241C3×C4×D3C2×D4116yescomplemented
242C3×Dic6—28no—
243#627—28no—
244#626—28no—
245#626—216no—
246#626—28no—
247#626—48no—
248#625—28no—
249#624—216no—
250C22×#41—91no—
251C22×#41—91no—
252#537—916no—
253C2×C22⋊Q8—31no—
254C2×C22⋊Q8—92no—
255C2×C22⋊Q8—91no—
256C2×#121—92no—
257C2×#121—92no—
258C2×#121—91no—
259C2×#121—92no—
260C2×#121—91no—
261C22×C4⋊C4—31no—
262C24×C3—31no—
263C24×C3—31no—
264C23×D3—32no—
265C23×D3—31no—
266C23×D3—32no—
267C23×D3—31no—
268C23×D3—61no—
269C23×D3—62no—
270C23×D3C22×D311yescharacteristic
271C23×D3C22×D311yescharacteristic
272C2×C3×Q8—34no—
273C2×C3×Q8—64no—
274C22×C3×C4—21no—
275C22×C3×C4—22no—
276C22×C3×C4—31no—
277C22×C3×C4—38no—
278C22×C3×C4—34no—
279C22×C3×C4—32no—
280C22×C3×C4—32no—
281C22×C3×C4—31no—
282C22×C3×C4—34no—
283C22×C3×C4—38no—
284C22×C3×C4—64no—
285C22×C3×C4—124no—
286C22×C3×C4C22×D312yes—
287C22×C3×C4C22×D312yes—
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C2×#67—34no—
291C2×#67—34no—
292C2×#67—34no—
293C2×#67—38no—
294C2×#67—34no—
295C2×#67—38no—
296C2×#67—68no—
297C2×#67—64no—
298C2×#67—64no—
299C2×#67—64no—
300C2×#67—64no—
301C2×#67—124no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—61no—
305C22×Dic3C22×D312yes—
306C22×Dic3C22×D312yes—
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309#239—632no—
310#235—632no—
311#235—632no—
312#235—632no—
313C2×D12—38no—
314C2×D12—34no—
315C2×D12—34no—
316C2×D12—34no—
317C2×D12—34no—
318C2×D12—38no—
319C2×D12—38no—
320C2×D12—38no—
321C2×D12—64no—
322C2×D12—68no—
323C2×D12—64no—
324C2×D12—64no—
325C2×D12—68no—
326C2×D12—64no—
327C2×D12—64no—
328C2×D12—124no—
329C2×D12—124no—
330C2×D12—124no—
331C2×D12—128no—
332C2×D12—124no—
333C2×C4×D3—24no—
334C2×C4×D3—34no—
335C2×C4×D3—34no—
336C2×C4×D3—38no—
337C2×C4×D3—38no—
338C2×C4×D3—44no—
339C2×C4×D3—64no—
340C2×C4×D3—68no—
341C2×C4×D3—64no—
342C2×C4×D3—64no—
343C2×C4×D3—68no—
344C2×C4×D3—124no—
345C2×C4×D3D1218yescomplemented
346C2×C4×D3C22×D314yes—
347C2×C4×D3C22×D318yes—
348C2×C4×D3C22×D314yes—
349C2×Dic6—24no—
350C2×Dic6—34no—
351C2×Dic6—34no—
352C2×Dic6—64no—
353C2×Dic6—64no—
354C2×Dic6C22×D314yes—
355C3×C4⋊C4—24no—
356C3×C4⋊C4—38no—
357C3×C4⋊C4—38no—
358C3×C4⋊C4—34no—
359C3×C4⋊C4C22×D314yes—
360C3×C4⋊C4C22×D314yes—
361C3×C22⋊C4—38no—
362(C2×D3)⋊C4—38no—
363(C2×D3)⋊C4—38no—
364(C2×D3)⋊C4—38no—
365(C2×D3)⋊C4—38no—
366(C2×D3)⋊C4—38no—
367(C2×D3)⋊C4—38no—
368(C2×D3)⋊C4—68no—
369(C2×D3)⋊C4C22×D318yes—
370C4⋊Dic3—38no—
371C4⋊Dic3C22×D314yes—
372C4⋊Dic3C22×D318yes—
373Dic3⋊C4—38no—
374Dic3⋊C4C22×D318yes—
375C22×C32C22×D412yes—
376C22×C32H(5,𝔽2)12yes—
377C22×C322−1+412yes—
378C22×C32C2511yescharacteristic
379C2×C3⋊D3—22no—
380C2×C3⋊D3—24no—
381C2×C3⋊D3—22no—
382C2×C3⋊D3—24no—
383C2×C3⋊D3—22no—
384C2×C3⋊D3—24no—
385C2×C3⋊D3—44no—
386C2×C3⋊D3—48no—
387C2×C3×D3—28no—
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—22no—
393C2×C3×D3—44no—
394C2×C3×D3C22×D414yes—
395C32×C4—24no—
396C32×C4C22×D414yes—
397C3⋊Dic3—22no—
398C3×Dic3—24no—
399C3×Dic3—22no—
400C3×Dic3—24no—
401C3×Dic3C22×D414yes—
402C2×#41—98no—
403C2×#41—98no—
404C2×#41—188no—
405C2×#41—188no—
406C22×Q8—31no—
407C22×Q8—91no—
408C22×D4—91no—
409C22×D4—92no—
410C22×D4—91no—
411C22×D4—92no—
412C22×D4—91no—
413C22×D4—91no—
414C22×D4—92no—
415C23×C4—31no—
416C23×C4—31no—
417C23×C4—32no—
418C23×C4—92no—
419C23×C4—91no—
420C22⋊Q8—38no—
421C22⋊Q8—916no—
422C22⋊Q8—98no—
423#121—916no—
424#121—916no—
425#121—98no—
426#121—916no—
427#121—98no—
428C2×C4⋊C4—32no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—32no—
431C2×C4⋊C4—38no—
432C2×C4⋊C4—92no—
433C2×C4⋊C4D3211yescharacteristic
434C2×C22⋊C4—32no—
435C2×C22⋊C4—92no—
436C2×C22⋊C4—92no—
437C2×C22⋊C4—92no—
438C23×C3—21no—
439C23×C3—34no—
440C23×C3—32no—
441C23×C3—32no—
442C23×C3—62no—
443C23×C3—62no—
444C23×C3—62no—
445C23×C3—62no—
446C23×C3—62no—
447C23×C3C23×D311yescharacteristic
448C23×C3C23×D311yescharacteristic
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—34no—
455C22×D3—32no—
456C22×D3—32no—
457C22×D3—34no—
458C22×D3—62no—
459C22×D3—64no—
460C22×D3—64no—
461C22×D3—64no—
462C22×D3—62no—
463C22×D3—64no—
464C22×D3—62no—
465C22×D3—62no—
466C22×D3—64no—
467C22×D3—62no—
468C22×D3—64no—
469C22×D3—62no—
470C22×D3—64no—
471C22×D3—62no—
472C22×D3—64no—
473C22×D3—122no—
474C22×D3—122no—
475C22×D3—124no—
476C22×D3—124no—
477C22×D3—124no—
478C22×D3C2×D1214yes—
479C22×D3C23×D312yes—
480C22×D3C23×D312yes—
481C3×Q8—68no—
482C2×C3×C4—24no—
483C2×C3×C4—24no—
484C2×C3×C4—22no—
485C2×C3×C4—24no—
486C2×C3×C4—24no—
487C2×C3×C4—34no—
488C2×C3×C4—32no—
489C2×C3×C4—316no—
490C2×C3×C4—34no—
491C2×C3×C4—34no—
492C2×C3×C4—32no—
493C2×C3×C4—44no—
494C2×C3×C4—62no—
495C2×C3×C4—64no—
496C2×C3×C4—64no—
497C2×C3×C4—68no—
498C2×C3×C4—128no—
499C2×C3×C4C2×D1214yes—
500C2×C3×C4D3×D414yes—
501C2×C3×C4C23×D314yes—
502C2×C3×C4C23×D314yes—
503C2×C3×C4C23×D312yes—
504C2×C3×C4C23×D312yes—
505#67—616no—
506#67—68no—
507#67—68no—
508#67—68no—
509#67—68no—
510#67—128no—
511C2×Dic3—24no—
512C2×Dic3—22no—
513C2×Dic3—24no—
514C2×Dic3—32no—
515C2×Dic3—32no—
516C2×Dic3—62no—
517C2×Dic3—62no—
518C2×Dic3—62no—
519C2×Dic3—122no—
520C2×Dic3C2×D1214yes—
521C2×Dic3C23×D314yes—
522C2×Dic3C23×D314yes—
523C2×Dic3C23×D312yes—
524C2×Dic3C23×D312yes—
525D12—68no—
526D12—68no—
527D12—616no—
528D12—68no—
529D12—68no—
530D12—128no—
531D12—128no—
532D12—128no—
533D12—1216no—
534D12—128no—
535C4×D3—28no—
536C4×D3—48no—
537C4×D3—616no—
538C4×D3—68no—
539C4×D3—68no—
540C4×D3—616no—
541C4×D3—128no—
542C4×D3C2×D12116yescomplemented
543Dic6—28no—
544Dic6—68no—
545Dic6—68no—
546C2×C32#53714yescomplemented
547C2×C32C23×D411yescharacteristic
548C2×C32C2×H(5,𝔽2)11yescharacteristic
549C2×C32C2×2−1+411yescharacteristic
550C3⋊D3—42no—
551C3⋊D3—44no—
552C3×D3—24no—
553C3×D3—42no—
554C24—31no—
555C24—31no—
556C24—91no—
557C24—92no—
558#41—1832no—
559#41—1832no—
560C2×Q8—34no—
561C2×Q8—64no—
562C2×Q8—94no—
563C2×Q8—184no—
564C2×D4—94no—
565C2×D4—98no—
566C2×D4—94no—
567C2×D4—98no—
568C2×D4—94no—
569C2×D4—94no—
570C2×D4—98no—
571C2×D4—184no—
572C2×D4—184no—
573C2×D4—188no—
574C2×D4—184no—
575C2×D4—184no—
576C2×D4—364no—
577C2×D4—364no—
578C22×C4—31no—
579C22×C4—34no—
580C22×C4—38no—
581C22×C4—32no—
582C22×C4—32no—
583C22×C4—31no—
584C22×C4—34no—
585C22×C4—38no—
586C22×C4—64no—
587C22×C4—98no—
588C22×C4—91no—
589C22×C4—94no—
590C22×C4—124no—
591C22×C4—188no—
592C22×C4—184no—
593C22×C4C2×D3212yes—
594C22×C4C2×D3211yescharacteristic
595C4⋊C4—38no—
596C4⋊C4—34no—
597C4⋊C4—38no—
598C4⋊C4—98no—
599C4⋊C4C2×D3214yes—
600C22⋊C4—38no—
601C22⋊C4—98no—
602C22⋊C4—98no—
603C22⋊C4—98no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—21no—
608C22×C3—34no—
609C22×C3—62no—
610C22×C3—62no—
611C22×C3—68no—
612C22×C3—62no—
613C22×C3—62no—
614C22×C3—62no—
615C22×C3—124no—
616C22×C3C22×D1212yes—
617C22×C3C2×D3×D412yes—
618C22×C3#100412yes—
619C22×C3#100712yes—
620C22×C3#100712yes—
621C22×C3#100912yes—
622C22×C3C24×D311yescharacteristic
623C22×C3C24×D311yescharacteristic
624C2×D3—22no—
625C2×D3—22no—
626C2×D3—28no—
627C2×D3—22no—
628C2×D3—22no—
629C2×D3—22no—
630C2×D3—44no—
631C2×D3—64no—
632C2×D3—64no—
633C2×D3—62no—
634C2×D3—64no—
635C2×D3—62no—
636C2×D3—62no—
637C2×D3—64no—
638C2×D3—62no—
639C2×D3—64no—
640C2×D3—62no—
641C2×D3—64no—
642C2×D3—62no—
643C2×D3—64no—
644C2×D3—122no—
645C2×D3—122no—
646C2×D3—124no—
647C2×D3—124no—
648C2×D3—124no—
649C2×D3—128no—
650C2×D3—124no—
651C2×D3—128no—
652C2×D3—124no—
653C2×D3—128no—
654C2×D3—248no—
655C2×D3C22×D1214yes—
656C3×C4—24no—
657C3×C4—24no—
658C3×C4—24no—
659C3×C4—34no—
660C3×C4—44no—
661C3×C4—62no—
662C3×C4—64no—
663C3×C4—64no—
664C3×C4C22×D1214yes—
665C3×C4C2×D3×D414yes—
666Dic3—24no—
667Dic3—22no—
668Dic3—24no—
669Dic3—62no—
670Dic3—62no—
671Dic3—122no—
672Dic3C22×D1214yes—
673C32C2×#53711yescharacteristic, complemented, Sylow
674C23—34no—
675C23—32no—
676C23—32no—
677C23—62no—
678C23—62no—
679C23—62no—
680C23—62no—
681C23—62no—
682C23—92no—
683C23—94no—
684C23—182no—
685C23—184no—
686C23—182no—
687C23—184no—
688C23—182no—
689C23—184no—
690C23C22×D3211yescharacteristic
691Q8—68no—
692Q8—188no—
693D4—188no—
694D4—188no—
695D4—1816no—
696D4—188no—
697D4—188no—
698D4—368no—
699D4—368no—
700C2×C4—24no—
701C2×C4—34no—
702C2×C4—32no—
703C2×C4—316no—
704C2×C4—34no—
705C2×C4—34no—
706C2×C4—32no—
707C2×C4—62no—
708C2×C4—64no—
709C2×C4—64no—
710C2×C4—68no—
711C2×C4—92no—
712C2×C4—128no—
713C2×C4—1816no—
714C2×C4—182no—
715C2×C4—188no—
716C2×C4D3×D1214yes—
717C2×C4C22×D3214yes—
718C2×C4C22×D3212yes—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—24no—
723C2×C3—64no—
724C2×C3—122no—
725C2×C3#551014yescomplemented
726C2×C3#562914yescomplemented
727C2×C3C23×D1211yescharacteristic
728C2×C3C22×D3×D411yescharacteristic
729C2×C3C2×#100411yescharacteristic
730C2×C3C2×#100711yescharacteristic
731C2×C3C2×#100711yescharacteristic
732C2×C3C2×#100911yescharacteristic
733D3—24no—
734D3—42no—
735D3—124no—
736D3—122no—
737D3—124no—
738D3—122no—
739D3—124no—
740D3—244no—
741C22—34no—
742C22—62no—
743C22—62no—
744C22—68no—
745C22—62no—
746C22—62no—
747C22—62no—
748C22—124no—
749C22—182no—
750C22—184no—
751C22—182no—
752C22—184no—
753C22—182no—
754C22—184no—
755C22—364no—
756C22—368no—
757C22C2×D3×D1212yes—
758C22#6431412yes—
759C22#6431612yes—
760C22C23×D3211yescharacteristic
761C4—24no—
762C4—34no—
763C4—62no—
764C4—64no—
765C4—64no—
766C4—182no—
767C4C2×D3×D1214yes—
768C3—21no—
769C3C2×#551011yescharacteristic, complemented
770C3C2×#562911yescharacteristic, complemented
771C2—64no—
772C2—122no—
773C2—362no—
774C2—364no—
775C2#1059452314yesdirect product factor
776C2C22×D3×D1211yescharacteristic
777C2C2×#6431411yescharacteristic
778C2C2×#6431611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#537
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3799C2semidirect
2. C22×#3798C2semidirect
3. C2×#64104C2semidirect
4. C2×C3×#897C2semidirect
5. C2×C3×D3×C4⋊C4C2semidirect
6. C2×#63910C2semidirect
7. C2×#63909C2semidirect
8. C2×#63909C2semidirect
9. C2×#63906C2semidirect
10. C2×#63895C2semidirect
11. C2×#63871C2semidirect
12. #10594523C2direct (N × H)
30. C2×#3799C22semidirect
32. C2×#3798C22semidirect
35. #64104C22semidirect
40. C3×#897C22semidirect
41. C3×D3×C4⋊C4C22semidirect
45. #63910C22semidirect
46. #63909C22semidirect
47. #63909C22semidirect
48. #63906C22semidirect
49. #63895C22semidirect
50. #63871C22semidirect
65. C2×#897D3semidirect
73. C2×D3×C4⋊C4D3semidirect
95. C2×C3×C4×D3D4semidirect
194. #897C2×D3semidirect
202. D3×C4⋊C4C2×D3semidirect
241. C3×C4×D3C2×D4semidirect
345. C2×C4×D3D12semidirect
542. C4×D3C2×D12semidirect
546. C2×C32#537semidirect
673. C32C2×#537semidirect
725. C2×C3#5510semidirect
726. C2×C3#5629semidirect
769. C3C2×#5510semidirect
770. C3C2×#5629semidirect
775. C2#10594523direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37992
C22×#37982
C2×#641042
C2×C3×#8972
C2×C3×D3×C4⋊C42
C2×#639102
C2×#639092
C2×#639062
C2×#638952
C2×#638712
#105945232
C2×#56293
C2×#55103