Finite Group Databasebeta

← #11872827

Subgroups — #11872827

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 751 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5545C211yesmaximal, characteristic
2#10593862C211yesmaximal, characteristic, complemented
3#10592708C211yesmaximal, characteristic, complemented
4C3×#5019C211yesmaximal, characteristic, complemented
5#10591458C211yesmaximal, characteristic
6#10591458C211yesmaximal, characteristic
7#10591440C211yesmaximal, characteristic, complemented
8Dic3×#214C211yesmaximal, characteristic, complemented
9#10590521C211yesmaximal, characteristic, complemented
10#10590519C211yesmaximal, characteristic, complemented
11#10590478C211yesmaximal, characteristic, complemented
12#10590475C211yesmaximal, characteristic, complemented
13#10590363C211yesmaximal, characteristic, complemented
14#10590271C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#82545—31nomaximal
17#80413—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20#64079C2211yescharacteristic, complemented
21C3×D4×Dic3C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C3×C4×#67—21no—
25C2×C3×(C2×D3)⋊C4—21no—
26C3×#893C2211yescharacteristic
27C3×#892C2211yescharacteristic
28C3×#67⋊C4—21no—
29C3×D3×C22⋊C4—21no—
30C3×C4×D12C2211yescharacteristic
31C3×#872C2211yescharacteristic
32C3×#869C2211yescharacteristic, complemented
33#63858—21no—
34#63858—21no—
35#63856C2211yescharacteristic
36#63856C2211yescharacteristic
37#63847—21no—
38#63847—21no—
39Dic3×Dic6C2211yescharacteristic, complemented
40Dic3×Dic6C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43#63659C2211yescharacteristic
44#63659C2211yescharacteristic
45#63635C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
48C3×#810C2211yescharacteristic, complemented
49C3×#810C2211yescharacteristic, complemented
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63565C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#518—31no—
62#5731—31no—
63#5545D311yescharacteristic
64#5518—31no—
65C3×#461—31no—
66#5218—31no—
67#5218—31no—
68#5169—31no—
69#5169—31no—
70#5164—31no—
71Dic3×SD16—31no—
72#5083—31no—
73#5019—31no—
74#5019D311yescharacteristic, complemented
75#5018—31no—
76#5018—31no—
77C4×#214—31no—
78C4×#214—31no—
79#5009—31no—
80#5009—31no—
81#5009—31no—
82#5009—61no—
83#5000—31no—
84#4996—31no—
85#4996—31no—
86#4847—31no—
87#4840—31no—
88#4817—31no—
89#4815—31no—
90#4814—31no—
91#4788—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C3×D3×D4—22no—
98C3×D3×D4—22no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106C32×C22⋊C4—21no—
107C32×C42C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111#3750—21no—
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#217—21no—
115C3×#214—22no—
116C3×#214—22no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4D411yescharacteristic
126C3×Dic3⋊C4D411yescharacteristic
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139#3715—22no—
140#3715—22no—
141#3123—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C3×C4⋊Q8—31no—
147C3×C4×D4—21no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150C3×C4×D4—31no—
151C3×C4×D4—61no—
152C3×C4×D4—61no—
153C3×C4×D4C2×D311yescharacteristic
154C3×C4×D4C2×D311yescharacteristic
155C3×#117—31no—
156C3×#117—31no—
157C2×C3×C22⋊C4—61no—
158C2×C3×C22⋊C4—61no—
159#946—31no—
160#946—31no—
161Q8×Dic3—31no—
162Q8×Dic3—31no—
163C2×#215—31no—
164C2×#215—31no—
165D4×Dic3C2×D311yescharacteristic
166C2×#214—31no—
167C2×#214—31no—
168C2×#214C2×D311yescharacteristic
169C2×#214C2×D311yescharacteristic
170C4×#67—21no—
171C2×(C2×D3)⋊C4—21no—
172#924—31no—
173#924—31no—
174#898—61no—
175#898—61no—
176#893C2×D311yescharacteristic
177#892C2×D311yescharacteristic
178#889—61no—
179#889—61no—
180#889—61no—
181#889—61no—
182#67⋊C4—21no—
183D3×C22⋊C4—21no—
184#879—61no—
185#879—61no—
186C4×D12C2×D311yescharacteristic
187#872C2×D311yescharacteristic
188#870—31no—
189#870—31no—
190#870—61no—
191#869C2×D311yescharacteristic, complemented
192C4×Dic6—31no—
193C4×Dic6—31no—
194C3×C4⋊C8—31no—
195C3×#103—31no—
196C3×#103—31no—
197#835—31no—
198#835—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—61no—
206#832—61no—
207#830—31no—
208#830—31no—
209#821—31no—
210#821—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213#818—31no—
214#817—31no—
215#815—31no—
216C8×Dic3—31no—
217#810—31no—
218#810—31no—
219#810C2×D311yescharacteristic, complemented
220#810C2×D311yescharacteristic, complemented
221#808—31no—
222#808—31no—
223#808—31no—
224#808—61no—
225#807—31no—
226#807—31no—
227#807—31no—
228#807—61no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3—24no—
238C22×C3×D3—81no—
239C22×C3×D3—81no—
240C22×C3×D3C2×D411yescharacteristic
241C32×D4—21no—
242C32×D4#4112yes—
243C2×C32×C4—21no—
244C2×C32×C4—81no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C3×#67—24no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—81no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12#4112yes—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—81no—
263C3×C4×D3—81no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—91no—
273#518—31no—
274#485—91no—
275#485—91no—
276#478—91no—
277#478—91no—
278#461—31no—
279#461—91no—
280#450—91no—
281#450—91no—
282#440—91no—
283#440—91no—
284C4×SD16—91no—
285C4×SD16—91no—
286#433—91no—
287C24×C3—61no—
288C23×D3—21no—
289C2×C3×Q8—31no—
290C2×C3×Q8—31no—
291C2×C3×D4—21no—
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C2×C3×D4—62no—
295C2×C3×D4—62no—
296C2×C3×D4C22×D311yescharacteristic
297C2×C3×D4C22×D311yescharacteristic
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—31no—
301C22×C3×C4—41no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C2×#67—21no—
306C22×Dic3—21no—
307D3×D4—22no—
308D3×D4—22no—
309C2×D12C22×D311yescharacteristic
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3C22×D311yescharacteristic
313C2×Dic6C22×D311yescharacteristic
314C2×Dic6C22×D311yescharacteristic
315C3×SD16—62no—
316C3×SD16—62no—
317C2×C3×C8—31no—
318C2×C3×C8—31no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4C22×D311yescharacteristic
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C22⋊C4—21no—
328C3×C22⋊C4—21no—
329C3×C22⋊C4—31no—
330C3×C22⋊C4—31no—
331C3×C22⋊C4—41no—
332C3×C22⋊C4—61no—
333C3×C22⋊C4—61no—
334C3×C22⋊C4—61no—
335C3×C22⋊C4—61no—
336C3×C42—21no—
337C3×C42—31no—
338C3×C42—61no—
339C3×C42C22×D311yescharacteristic
340C3×C42C22×D311yescharacteristic
341#217—21no—
342#217—61no—
343#217—61no—
344#215—62no—
345#215—62no—
346#214—22no—
347#214—22no—
348#214—62no—
349#214—62no—
350(C2×D3)⋊C4—21no—
351(C2×D3)⋊C4—21no—
352(C2×D3)⋊C4—21no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4#6711yescharacteristic
356(C2×D3)⋊C4#6711yescharacteristic
357C4⋊Dic3—21no—
358C4⋊Dic3—21no—
359C4⋊Dic3—31no—
360C4⋊Dic3—31no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3C22×D311yescharacteristic
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—121no—
379Dic3⋊C4—121no—
380Dic3⋊C4#6711yescharacteristic
381Dic3⋊C4#6711yescharacteristic
382C4×Dic3—21no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3C22×D311yescharacteristic
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8C22×D311yescharacteristic
395C2×C3⋊C8C22×D311yescharacteristic
396C22×C32—22no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32C22×D411yescharacteristic
400C2×C3×D3—21no—
401C2×C3×D3—22no—
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—84no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—41no—
410C32×C4C2×#4111yescharacteristic
411C32×C4C2×#4111yescharacteristic
412C3⋊Dic3—41no—
413C3⋊Dic3—41no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C22×D4—31no—
421C2×SD16—31no—
422C2×SD16—31no—
423C2×SD16—91no—
424C2×SD16—91no—
425C4⋊Q8—31no—
426#126—181no—
427#126—181no—
428#125—91no—
429#125—181no—
430#125—181no—
431C22⋊Q8—91no—
432C22⋊Q8—91no—
433C4×Q8—91no—
434C4×Q8—91no—
435C4×D4—31no—
436C4×D4—31no—
437C4×D4—31no—
438C4×D4—61no—
439C4×D4—61no—
440C4×D4D3211yescharacteristic
441#117—31no—
442#117—31no—
443C2×C22⋊C4—61no—
444C2×C22⋊C4—61no—
445#107—91no—
446#107—91no—
447#106—91no—
448#106—91no—
449C4⋊C8—31no—
450C4⋊C8—91no—
451#103—31no—
452#103—31no—
453#103—91no—
454#103—91no—
455#102—91no—
456#102—91no—
457#102—91no—
458#102—91no—
459C22⋊C8—91no—
460C22⋊C8—91no—
461#97—91no—
462C4×C8—91no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—31no—
466C23×C3—41no—
467C23×C3—64no—
468C23×C3—61no—
469C23×C3—241no—
470C23×C3—241no—
471C22×D3—21no—
472C22×D3—24no—
473C22×D3—81no—
474C22×D3—81no—
475C22×D3C2×#6711yescharacteristic
476C3×Q8—61no—
477C3×Q8—61no—
478C3×Q8—61no—
479C3×Q8—61no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—22no—
483C3×D4—32no—
484C3×D4—41no—
485C3×D4—64no—
486C3×D4—61no—
487C3×D4#23512yes—
488C3×D4#23712yes—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—41no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—81no—
504C2×C3×C4—81no—
505C2×C3×C4—82no—
506C2×C3×C4—241no—
507C2×C3×C4—241no—
508C2×C3×C4—241no—
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4C2×#6711yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—24no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—81no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3C2×#6711yescharacteristic
527C2×Dic3C2×#6711yescharacteristic
528C2×Dic3C2×#6711yescharacteristic
529D12—21no—
530D12#23512yes—
531C4×D3—21no—
532C4×D3—21no—
533C4×D3—81no—
534C4×D3—81no—
535Dic6—21no—
536Dic6—21no—
537Dic6—21no—
538Dic6—21no—
539C3×C8—61no—
540C3×C8—61no—
541C3⋊C8—21no—
542C3⋊C8—21no—
543C3⋊C8—61no—
544C3⋊C8—61no—
545C3⋊C8—61no—
546C3⋊C8—61no—
547C3⋊C8—121no—
548C3⋊C8—121no—
549C2×C32—42no—
550C2×C32#52511yescharacteristic
551C2×C32#57711yescharacteristic
552C2×C32#57711yescharacteristic
553C3×D3—41no—
554C3×D3—42no—
555C24—61no—
556C2×Q8—31no—
557C2×Q8—31no—
558C2×D4—31no—
559C2×D4—61no—
560C2×D4—62no—
561C2×D4—62no—
562C2×D4C2×D3211yescharacteristic
563C22×C4—21no—
564C22×C4—31no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568SD16—62no—
569SD16—62no—
570SD16—182no—
571SD16—182no—
572C2×C8—31no—
573C2×C8—31no—
574C2×C8—91no—
575C2×C8—91no—
576C4⋊C4—31no—
577C4⋊C4—31no—
578C4⋊C4—31no—
579C4⋊C4—61no—
580C4⋊C4—61no—
581C4⋊C4—91no—
582C4⋊C4—91no—
583C4⋊C4—181no—
584C4⋊C4—181no—
585C4⋊C4—181no—
586C4⋊C4—181no—
587C4⋊C4—181no—
588C4⋊C4—181no—
589C4⋊C4C2×D3211yescharacteristic
590C22⋊C4—21no—
591C22⋊C4—31no—
592C22⋊C4—31no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—181no—
598C22⋊C4—181no—
599C42—31no—
600C42—61no—
601C42—181no—
602C42—181no—
603C42C2×D3211yescharacteristic
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—21no—
607C22×C3—42no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—61no—
613C22×C3—61no—
614C22×C3—61no—
615C22×C3—62no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3—121no—
619C22×C3—121no—
620C22×C3—244no—
621C22×C3C2×D3×D411yescharacteristic
622C22×C3C22×#6711yescharacteristic
623C2×D3—21no—
624C2×D3—22no—
625C2×D3—21no—
626C2×D3—21no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—84no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—61no—
641C3×C4—61no—
642C3×C4—61no—
643C3×C4—81no—
644C3×C4—121no—
645C3×C4—121no—
646C3×C4—121no—
647C3×C4C2×#23511yescharacteristic
648C3×C4C2×#23511yescharacteristic
649C3×C4C2×#23711yescharacteristic
650C3×C4D3×#4111yescharacteristic
651Dic3—21no—
652Dic3—21no—
653Dic3—21no—
654Dic3—41no—
655Dic3—41no—
656Dic3—41no—
657Dic3—121no—
658Dic3—121no—
659Dic3—121no—
660Dic3—121no—
661Dic3—241no—
662Dic3—241no—
663C32#312311yescharacteristic, complemented, Sylow
664C23—21no—
665C23—31no—
666C23—64no—
667C23—61no—
668C23—241no—
669C23—241no—
670Q8—61no—
671Q8—61no—
672Q8—61no—
673Q8—61no—
674D4—21no—
675D4—32no—
676D4—64no—
677D4—61no—
678D4#379512yes—
679C2×C4—21no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—81no—
689C2×C4—181no—
690C2×C4—181no—
691C2×C4—241no—
692C2×C4—241no—
693C2×C4—241no—
694C2×C4D3×#6711yescharacteristic
695C2×C4D3×#6711yescharacteristic
696C2×C4C22×D3211yescharacteristic
697C8—61no—
698C8—61no—
699C8—181no—
700C8—181no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—42no—
705C2×C3—42no—
706C2×C3—82no—
707C2×C3—121no—
708C2×C3—122no—
709C2×C3#560611yescharacteristic
710C2×C3#576211yescharacteristic
711C2×C3#577811yescharacteristic
712C2×C3#579111yescharacteristic
713C2×C3#583611yescharacteristic
714C2×C3#583611yescharacteristic
715D3—41no—
716D3—42no—
717C22—22no—
718C22—41no—
719C22—41no—
720C22—61no—
721C22—61no—
722C22—62no—
723C22—61no—
724C22—121no—
725C22—121no—
726C22—244no—
727C22C2×D3×#6711yescharacteristic
728C4—21no—
729C4—21no—
730C4—41no—
731C4—61no—
732C4—61no—
733C4—61no—
734C4—121no—
735C4—121no—
736C4—121no—
737C4—361no—
738C4—361no—
739C4C2×#379511yescharacteristic
740C4D3×#23511yescharacteristic
741C3—21no—
742C3#8041311yescharacteristic, complemented
743C3#8254511yescharacteristic, complemented
744C2—42no—
745C2—121no—
746C2—122no—
747C2#1059489211yescharacteristic
748C2#1059510511yescharacteristic
749C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC4×D4D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593862C2semidirect
3. #10592708C2semidirect
4. C3×#5019C2semidirect
7. #10591440C2semidirect
8. Dic3×#214C2semidirect
9. #10590521C2semidirect
10. #10590519C2semidirect
11. #10590478C2semidirect
12. #10590475C2semidirect
13. #10590363C2semidirect
14. #10590271C2semidirect
15. #10590253C2semidirect
20. #64079C22semidirect
32. C3×#869C22semidirect
39. Dic3×Dic6C22semidirect
40. Dic3×Dic6C22semidirect
45. #63635C22semidirect
46. #63634C22semidirect
47. C4⋊(C3⋊(C3⋊C8))C22semidirect
48. C3×#810C22semidirect
49. C3×#810C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
53. #63565C22semidirect
54. #63565C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
74. #5019D3semidirect
191. #869C2×D3semidirect
219. #810C2×D3semidirect
220. #810C2×D3semidirect
232. C4⋊(C3⋊C8)C2×D3semidirect
663. C32#3123semidirect
742. C3#80413semidirect
743. C3#82545semidirect

Maximal subgroups

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

subgroupindex
C3×#55452
#105938622
#105927082
C3×#50192
#105914582
#105914402
Dic3×#2142
#105905212
#105905192
#105904782
#105904752
#105903632
#105902712
#105902532
#825453
#804133