Finite Group Databasebeta

← #11792243

Subgroups — #11792243

Order 1152.

961 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64158C211yesmaximal, characteristic, complemented
2C3×#5833C211yesmaximal, characteristic, complemented
3C2×#63825C211yesmaximal, characteristic, complemented
4C2×C3×#837C211yesmaximal, characteristic, complemented
5#10591320C211yesmaximal, characteristic, complemented
6C2×#63569C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#71879—31nomaximal
9#70392—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13#64158—22no—
14#64158—22no—
15C2×#3755—21no—
16C2×#3753—21no—
17C2×#3748C2211yescharacteristic
18C3×#946—21no—
19C3×#939—22no—
20C3×#938—21no—
21C3×#930—21no—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C3×#924—21no—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×#3722—22no—
27C2×#3717—21no—
28#63825—22no—
29#63825—22no—
30C2×#3714—21no—
31C3×#837—22no—
32#63569—22no—
33C3×#537—31no—
34#5833D311yescharacteristic, complemented
35C2×#949—31no—
36C2×#949—31no—
37C2×#949—31no—
38C2×#949—61no—
39C2×#908—31no—
40C2×C3×#104—31no—
41C2×#837—31no—
42C2×#837D311yescharacteristic, complemented
43#4988—31no—
44#4939—31no—
45C2×#805—31no—
46#4554—31no—
47#4530—31no—
48C23×C3⋊D3—21no—
49C32×#41—21no—
50C32×#41—21no—
51C32×#41—21no—
52C32×#41—21no—
53C2×C32×Q8D411yescharacteristic
54C2×C32×D4—21no—
55C2×C32×D4D411yescharacteristic
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)D412yescomplemented
64C2×C3×#67—21no—
65C2×C3×#67—22no—
66C22×C3×Dic3—21no—
67C22×C3×Dic3D412yes—
68C3×#235—21no—
69C3×#235—21no—
70C3×#235—21no—
71C3×#235—21no—
72C2×C3×D12D411yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×Dic6D411yescharacteristic
75#3755—24no—
76#3753—24no—
77#3748—21no—
78#3748D412yescomplemented
79C2×C3⋊(C3⋊C8)—21no—
80C3×#217—22no—
81C3×(C2×D3)⋊C4—22no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3—21no—
84C3×Dic3⋊C4—22no—
85C3×C4×Dic3—21no—
86C3×C4×Dic3—21no—
87C3×#208—21no—
88C3×#208D412yescomplemented
89C2×C3×C3⋊C8—21no—
90#3722—44no—
91#3717—24no—
92#3714—24no—
93#2006—91noSylow
94C2×C3×#41—21no—
95C2×C3×#41—31no—
96C2×C3×#41C2×D311yescharacteristic
97C2×C3×#41C2×D311yescharacteristic
98C2×#235C2×D311yescharacteristic
99C22×D12—31no—
100C22×D12—31no—
101C22×D12—61no—
102C2×C3×M16—31no—
103C3×C22⋊Q8—61no—
104C3×C22⋊Q8—61no—
105C3×#121—61no—
106C3×#121—62no—
107C3×#121—61no—
108C2×C3×C4⋊C4—31no—
109C2×C3×C42—31no—
110#949—62no—
111#949—62no—
112#949—62no—
113#949—62no—
114#949—62no—
115#949—64no—
116#949—64no—
117#949—62no—
118#946—21no—
119C2×#215—61no—
120C2×#215—62no—
121C2×#215—61no—
122C2×#215—61no—
123#939—22no—
124#938—21no—
125C2×#213—61no—
126C2×#213—62no—
127C2×#213—61no—
128C2×#213—61no—
129#930—21no—
130C2×(C2×D3)⋊C4—62no—
131C2×(C2×D3)⋊C4—62no—
132C2×C4⋊Dic3C2×D311yescharacteristic
133#924—21no—
134C2×C4×Dic3C2×D311yescharacteristic
135C2×#208—31no—
136C2×#208—31no—
137C2×#208—61no—
138C2×#208C2×D311yescharacteristic
139#908—62no—
140#908—62no—
141C2×D24—61no—
142C2×#204—61no—
143C3×#104—62no—
144#837—22no—
145#837—62no—
146#805—62no—
147C23×C32—21no—
148C23×C32C2×D411yescharacteristic
149C22×C3⋊D3—22no—
150C22×C3⋊D3—41no—
151C22×C3⋊D3—41no—
152C22×C3⋊D3—42no—
153C22×C3⋊D3—42no—
154C22×C3×D3—21no—
155C32×Q8—21no—
156C32×Q8—21no—
157C32×D4—21no—
158C32×D4—21no—
159C32×D4—41no—
160C32×D4—41no—
161C2×C32×C4—21no—
162C2×C32×C4—41no—
163C2×C32×C4—41no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4#4111yescharacteristic
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—22no—
172C4⋊(C3⋊D3)—41no—
173C4⋊(C3⋊D3)—41no—
174C3×#67—41no—
175C3×#67—41no—
176C3×#67—82no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—41no—
181C2×C3×Dic3—41no—
182C2×C3×Dic3—42no—
183C3×D12—21no—
184C3×D12—21no—
185C3×C4×D3—41no—
186C3×C4×D3—41no—
187C3×Dic6—21no—
188C3×Dic6—21no—
189C3⋊(C3⋊C8)—22no—
190C3×C3⋊C8—22no—
191C2×AGL(1,ℤ/8)—91no—
192C2×AGL(1,ℤ/8)—91no—
193#537—31no—
194C2×#104—31no—
195C2×#104—91no—
196#390—91no—
197#343—91no—
198C23×D3—61no—
199C23×D3—61no—
200C23×D3—121no—
201C3×#41—22no—
202C3×#41—22no—
203C3×#41—21no—
204C3×#41—21no—
205C3×#41—21no—
206C3×#41—21no—
207C3×#41—21no—
208C3×#41—21no—
209C3×#41—21no—
210C3×#41—21no—
211C3×#41—41no—
212C3×#41—41no—
213C3×#41—61no—
214C3×#41—61no—
215C3×#41—61no—
216C3×#41—61no—
217C2×C3×Q8—21no—
218C2×C3×Q8—31no—
219C2×C3×Q8D1211yescharacteristic
220C2×C3×Q8#6711yescharacteristic
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—31no—
225C2×C3×D4—41no—
226C2×C3×D4—61no—
227C2×C3×D4—62no—
228C2×C3×D4D1211yescharacteristic
229C2×C3×D4#6711yescharacteristic
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—32no—
234C22×C3×C4—41no—
235C22×C3×C4—61no—
236C22×C3×C4—61no—
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C2×#67—21no—
240C2×#67—22no—
241C22×Dic3—21no—
242C22×Dic3#6712yes—
243#235—21no—
244#235—21no—
245#235—21no—
246#235—21no—
247C2×D12—32no—
248C2×D12—32no—
249C2×D12—62no—
250C2×D12—62no—
251C2×D12—62no—
252C2×D12—61no—
253C2×D12—61no—
254C2×D12—61no—
255C2×D12—61no—
256C2×D12—61no—
257C2×D12—61no—
258C2×D12—61no—
259C2×D12—61no—
260C2×D12—61no—
261C2×D12—61no—
262C2×D12—121no—
263C2×D12—121no—
264C2×D12—121no—
265C2×D12#6711yescharacteristic
266C2×C4×D3—21no—
267C2×Dic6#6711yescharacteristic
268C3×M16—32no—
269C3×M16—61no—
270C2×C3×C8—61no—
271C3×C4⋊C4—62no—
272C3×C4⋊C4—61no—
273C3×C4⋊C4—61no—
274C3×C22⋊C4—62no—
275C3×C22⋊C4—62no—
276C3×C42—61no—
277C3×C42—61no—
278#217—22no—
279#215—64no—
280#215—68no—
281#215—64no—
282#215—64no—
283#213—64no—
284#213—68no—
285#213—64no—
286#213—64no—
287(C2×D3)⋊C4—22no—
288(C2×D3)⋊C4—124no—
289(C2×D3)⋊C4—124no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292Dic3⋊C4—22no—
293C4×Dic3—21no—
294C4×Dic3—21no—
295#208—21no—
296#208—32no—
297#208—32no—
298#208—62no—
299#208—62no—
300#208—61no—
301#208—61no—
302#208#6712yescomplemented
303C2×C3⋊C8—21no—
304C2×C3⋊C8—62no—
305C2×C3⋊C8—61no—
306C2×C3⋊C8—61no—
307D24—64no—
308#204—64no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—41no—
312C22×C32—41no—
313C22×C32—41no—
314C22×C32#12011yescharacteristic
315C22×C32#12111yescharacteristic
316C22×C32#12711yescharacteristic
317C2×C3⋊D3—42no—
318C2×C3⋊D3—44no—
319C2×C3⋊D3—82no—
320C2×C3⋊D3—81no—
321C2×C3⋊D3—81no—
322C2×C3×D3—41no—
323C2×C3×D3—41no—
324C2×C3×D3—41no—
325C32×C4—41no—
326C32×C4#12011yescharacteristic
327C32×C4#12011yescharacteristic
328C32×C4#12111yescharacteristic
329C32×C4#12111yescharacteristic
330C3×Dic3—42no—
331C3×Dic3—41no—
332C3×Dic3—42no—
333C2×#41—31no—
334C2×#41D3211yescharacteristic
335C22×D4—91no—
336AGL(1,ℤ/8)—182no—
337AGL(1,ℤ/8)—182no—
338AGL(1,ℤ/8)—182no—
339AGL(1,ℤ/8)—182no—
340C2×SD16—181no—
341C2×SD16—181no—
342C2×D8—181no—
343C2×D8—181no—
344C2×M16—31no—
345C2×M16—91no—
346C22⋊Q8—61no—
347C22⋊Q8—61no—
348#121—61no—
349#121—62no—
350#121—61no—
351C2×C4⋊C4—31no—
352C2×C22⋊C4—182no—
353C2×C42—31no—
354#104—62no—
355#104—182no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—41no—
360C23×C3—61no—
361C23×C3D3×D411yescharacteristic
362C23×C3C2×#6711yescharacteristic
363C22×D3—21no—
364C22×D3—62no—
365C22×D3—62no—
366C22×D3—122no—
367C22×D3—122no—
368C22×D3—122no—
369C22×D3—122no—
370C22×D3—122no—
371C22×D3—122no—
372C22×D3—122no—
373C22×D3—121no—
374C22×D3—121no—
375C22×D3—121no—
376C22×D3—121no—
377C22×D3—242no—
378C22×D3—242no—
379C3×Q8—22no—
380C3×Q8—21no—
381C3×Q8—21no—
382C3×Q8—21no—
383C3×Q8—21no—
384C3×Q8—41no—
385C3×Q8—61no—
386C3×Q8—61no—
387C3×D4—22no—
388C3×D4—21no—
389C3×D4—21no—
390C3×D4—21no—
391C3×D4—21no—
392C3×D4—41no—
393C3×D4—42no—
394C3×D4—42no—
395C3×D4—41no—
396C3×D4—41no—
397C3×D4—41no—
398C3×D4—41no—
399C3×D4—61no—
400C3×D4—61no—
401C3×D4—121no—
402C3×D4—121no—
403C3×D4—242no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—41no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—61no—
422C2×C3×C4—121no—
423C2×C3×C4—121no—
424C2×C3×C4—121no—
425C2×C3×C4—121no—
426C2×C3×C4—122no—
427C2×C3×C4C2×D1211yescharacteristic
428C2×C3×C4#23511yescharacteristic
429C2×C3×C4D3×D411yescharacteristic
430C2×C3×C4D3×D411yescharacteristic
431C2×C3×C4D3×D411yescharacteristic
432C2×C3×C4D3×D411yescharacteristic
433C2×C3×C4D3×D411yescharacteristic
434C2×C3×C4D3×D411yescharacteristic
435C2×C3×C4#23711yescharacteristic
436C2×C3×C4C2×#6711yescharacteristic
437C2×C3×C4C2×#6711yescharacteristic
438C2×C3×C4C2×#6711yescharacteristic
439#67—41no—
440#67—41no—
441#67—82no—
442C2×Dic3—22no—
443C2×Dic3—21no—
444C2×Dic3—22no—
445C2×Dic3—41no—
446C2×Dic3—41no—
447C2×Dic3—42no—
448D12—21no—
449D12—21no—
450D12—64no—
451D12—62no—
452D12—62no—
453D12—62no—
454D12—62no—
455D12—122no—
456D12—122no—
457D12—122no—
458D12—121no—
459D12—121no—
460D12—121no—
461D12—121no—
462C4×D3—41no—
463C4×D3—41no—
464Dic6—21no—
465Dic6—21no—
466C3×C8—62no—
467C3⋊C8—22no—
468C3⋊C8—64no—
469C3⋊C8—62no—
470C3⋊C8—62no—
471C2×C32—21no—
472C2×C32—21no—
473C2×C32—81no—
474C2×C32#39211yescharacteristic
475C2×C32#45311yescharacteristic
476C2×C32#45411yescharacteristic
477C3⋊D3—82no—
478C3×D3—81no—
479C24—181no—
480#41—21no—
481#41—21no—
482#41—21no—
483#41—21no—
484#41—61no—
485#41—61no—
486#41—61no—
487#41—61no—
488C2×Q8—31no—
489C2×Q8#62611yescharacteristic
490C2×D4—21no—
491C2×D4—31no—
492C2×D4—61no—
493C2×D4—62no—
494C2×D4—92no—
495C2×D4—181no—
496C2×D4—181no—
497C2×D4—181no—
498C2×D4—181no—
499C2×D4—181no—
500C2×D4#62611yescharacteristic
501C22×C4—21no—
502C22×C4—32no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4C2×D3211yescharacteristic
506SD16—184no—
507SD16—184no—
508D8—184no—
509D8—184no—
510M16—32no—
511M16—61no—
512M16—92no—
513M16—181no—
514C2×C8—61no—
515C2×C8—181no—
516C4⋊C4—62no—
517C4⋊C4—61no—
518C4⋊C4—61no—
519C22⋊C4—62no—
520C22⋊C4—62no—
521C22⋊C4—364no—
522C42—61no—
523C42—61no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—41no—
532C22×C3—41no—
533C22×C3—42no—
534C22×C3—41no—
535C22×C3—41no—
536C22×C3—41no—
537C22×C3—41no—
538C22×C3—41no—
539C22×C3—41no—
540C22×C3—81no—
541C22×C3—81no—
542C22×C3—121no—
543C22×C3—121no—
544C22×C3—121no—
545C22×C3#88211yescharacteristic
546C22×C3#88411yescharacteristic
547C22×C3#93811yescharacteristic
548C22×C3#94011yescharacteristic
549C22×C3#94011yescharacteristic
550C22×C3#95311yescharacteristic
551C2×D3—41no—
552C2×D3—41no—
553C2×D3—41no—
554C2×D3—124no—
555C2×D3—124no—
556C2×D3—124no—
557C2×D3—122no—
558C2×D3—122no—
559C2×D3—244no—
560C2×D3—242no—
561C2×D3—242no—
562C2×D3—242no—
563C2×D3—242no—
564C2×D3—244no—
565C2×D3—241no—
566C2×D3—241no—
567C2×D3—241no—
568C2×D3—241no—
569C3×C4—21no—
570C3×C4—21no—
571C3×C4—21no—
572C3×C4—21no—
573C3×C4—42no—
574C3×C4—41no—
575C3×C4—41no—
576C3×C4—122no—
577C3×C4—121no—
578C3×C4—122no—
579C3×C4#88211yescharacteristic
580C3×C4#88411yescharacteristic
581C3×C4#93011yescharacteristic
582C3×C4#93711yescharacteristic
583C3×C4#93711yescharacteristic
584C3×C4#93711yescharacteristic
585C3×C4#93911yescharacteristic
586C3×C4#93911yescharacteristic
587Dic3—42no—
588Dic3—41no—
589Dic3—42no—
590C32#200611yescharacteristic, complemented, Sylow
591C23—21no—
592C23—61no—
593C23—182no—
594C23—362no—
595C23—362no—
596C23—361no—
597C23—361no—
598C23D3×#6711yescharacteristic
599Q8—21no—
600Q8—21no—
601Q8—61no—
602Q8—61no—
603D4—21no—
604D4—21no—
605D4—41no—
606D4—41no—
607D4—61no—
608D4—61no—
609D4—121no—
610D4—121no—
611D4—182no—
612D4—182no—
613D4—242no—
614D4—361no—
615D4—361no—
616C2×C4—21no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—62no—
620C2×C4—62no—
621C2×C4—61no—
622C2×C4—121no—
623C2×C4—121no—
624C2×C4—121no—
625C2×C4—121no—
626C2×C4—122no—
627C2×C4#380411yescharacteristic
628C2×C4C2×#62611yescharacteristic
629C2×C4D3×#6711yescharacteristic
630C2×C4D3×#6711yescharacteristic
631C2×C4#381111yescharacteristic
632C2×C4#381111yescharacteristic
633C8—62no—
634C8—182no—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—41no—
643C2×C3—41no—
644C2×C3—82no—
645C2×C3—81no—
646C2×C3—81no—
647C2×C3—241no—
648C2×C3#482211yescharacteristic
649C2×C3#482711yescharacteristic
650C2×C3#496011yescharacteristic
651C2×C3#522311yescharacteristic
652C2×C3#524111yescharacteristic
653C2×C3#524511yescharacteristic
654D3—81no—
655D3—244no—
656D3—242no—
657D3—242no—
658C22—21no—
659C22—21no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—121no—
664C22—121no—
665C22—121no—
666C22—364no—
667C22—362no—
668C22—722no—
669C22—721no—
670C22—721no—
671C22#6395811yescharacteristic
672C22#6397711yescharacteristic
673C22#6397911yescharacteristic
674C4—41no—
675C4—122no—
676C4—122no—
677C4—121no—
678C4#6397111yescharacteristic
679C4#6397811yescharacteristic
680C4#6398111yescharacteristic
681C4#6398311yescharacteristic
682C3—21no—
683C3#7039211yescharacteristic, complemented
684C3#7187911yescharacteristic, complemented
685C2—21no—
686C2—21no—
687C2—81no—
688C2—241no—
689C2—722no—
690C2#1059166611yescharacteristic
691C2#1059168511yescharacteristic
692C2#1059172411yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32#120
hypercenterC2×#41D32
hypocenterC32#2006
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64158C2semidirect
2. C3×#5833C2semidirect
3. C2×#63825C2semidirect
4. C2×C3×#837C2semidirect
5. #10591320C2semidirect
6. C2×#63569C2semidirect
7. #10589167C2semidirect
34. #5833D3semidirect
42. C2×#837D3semidirect
63. C2×C4⋊(C3⋊D3)D4semidirect
78. #3748D4semidirect
88. C3×#208D4semidirect
302. #208#67semidirect
590. C32#2006semidirect
683. C3#70392semidirect
684. C3#71879semidirect

Maximal subgroups

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

subgroupindex
C2×#641582
C3×#58332
C2×#638252
C2×C3×#8372
#105913202
C2×#635692
#105891672
#718793
#703923