Finite Group Databasebeta

← #11886793

Subgroups — #11886793

Order 1152.

984 conjugacy classes of subgroups.

The subgroup lattice has 973 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5836C211yesmaximal, characteristic, complemented
2C3×#5835C211yesmaximal, characteristic, complemented
3#10595467C211yesmaximal, characteristic, complemented
4#10595466C211yesmaximal, characteristic, complemented
5#10592941C211yesmaximal, characteristic, complemented
6#10591684C211yesmaximal, characteristic, complemented
7#10591682C211yesmaximal, characteristic, complemented
8#10591679C211yesmaximal, characteristic, complemented
9#10591673C211yesmaximal, characteristic, complemented
10#10591673C211yesmaximal, characteristic, complemented
11#10591664C211yesmaximal, characteristic, complemented
12#10591524C211yesmaximal, characteristic, complemented
13#10591506C211yesmaximal, characteristic, complemented
14#10591505C211yesmaximal, characteristic, complemented
15#10591474C211yesmaximal, characteristic, complemented
16#84012—31nomaximal
17#84011—31nomaximal
18C32×H(5,𝔽2)C2211yescharacteristic
19C3×#1010C2211yescharacteristic, complemented
20C3×#1009C2211yescharacteristic
21#64298C2211yescharacteristic, complemented
22#64160C2211yescharacteristic
23#64160C2211yescharacteristic, complemented
24#64145C2211yescharacteristic, complemented
25C3×#951—21no—
26C3×#951C2211yescharacteristic
27C3×#950—21no—
28C3×#950—21no—
29C3×#950C2211yescharacteristic
30C3×#950C2211yescharacteristic
31C3×#949—21no—
32C3×#949C2211yescharacteristic
33C3×#948C2211yescharacteristic
34C3×#948C2211yescharacteristic, complemented
35C2×C3×#214—21no—
36C2×C3×#214C2211yescharacteristic, complemented
37C3×#932—21no—
38C3×#932—21no—
39C3×#932C2211yescharacteristic
40C3×#932C2211yescharacteristic, complemented
41C2×C3×#213—21no—
42C2×C3×#213C2211yescharacteristic
43#63947—21no—
44#63946—21no—
45#63943—21no—
46D3×#216—21no—
47#63933—21no—
48#63932—21no—
49#63929—21no—
50D3×#214—21no—
51#63863C2211yescharacteristic, complemented
52C2×#3719C2211yescharacteristic, complemented
53C2×#3716C2211yescharacteristic, complemented
54#63827C2211yescharacteristic, complemented
55#63823C2211yescharacteristic, complemented
56#63814C2211yescharacteristic, complemented
57#63814C2211yescharacteristic, complemented
58#63664C2211yescharacteristic
59#63664C2211yescharacteristic, complemented
60#63660C2211yescharacteristic, complemented
61#63577C2211yescharacteristic, complemented
62#63577C2211yescharacteristic, complemented
63#63568C2211yescharacteristic, complemented
64#63568C2211yescharacteristic, complemented
65#63561C2211yescharacteristic, complemented
66#63560C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68#63553C2211yescharacteristic, complemented
69C3×#577—31no—
70C3×#576—31no—
71#5838—31no—
72#5836—31no—
73#5836D311yescharacteristic, complemented
74#5835D311yescharacteristic, complemented
75#5771—31no—
76#5770—31no—
77#5245—31no—
78#5242—31no—
79#5242—31no—
80#5242—31no—
81#5242—61no—
82#5204—31no—
83#5202—31no—
84#5201—31no—
85#5201—31no—
86#5201—31no—
87#5200—31no—
88#5200—31no—
89#5199—31no—
90#5196—31no—
91#5196—31no—
92#5177—31no—
93#5168—31no—
94#5160—31no—
95#5155—31no—
96#5144—31no—
97#5144—31no—
98#5143—31no—
99#5141—31no—
100C32×#41—21no—
101C32×#41—21no—
102C32×#41C2311yescharacteristic
103C32×#41C2311yescharacteristic
104C2×C32×D4—21no—
105C2×C32×D4—21no—
106C2×C32×D4—41no—
107C2×C32×D4C2311yescharacteristic
108C2×#634C2311yescharacteristic
109C3×#239—21no—
110C3×D3×Q8—21no—
111C3×#237—21no—
112C3×#237—41no—
113C3×D3×D4—21no—
114C3×D3×D4—41no—
115C3×#235—21no—
116C3×#235—21no—
117C3×#235C2311yescharacteristic
118C3×#235C2311yescharacteristic
119C2×C3×D12—21no—
120C2×C3×D12C2311yescharacteristic
121C2×C3×Dic6—21no—
122C2×C3×Dic6C2311yescharacteristic
123#3805—41no—
124#3795—21no—
125#3795—21no—
126D3×Dic6—21no—
127D3×Dic6—21no—
128#3757—41no—
129#3756—21no—
130#3756—21no—
131#3754—21no—
132#3754—21no—
133C4×C3⋊Dic3C2311yescharacteristic
134#3748C2311yescharacteristic
135#3748C2311yescharacteristic
136C3×#216—21no—
137C3×#216D411yescharacteristic
138C3×#216D411yescharacteristic
139C3×#215—21no—
140C3×#215D411yescharacteristic
141C3×#215D411yescharacteristic
142C3×#214—21no—
143C3×#214—21no—
144C3×#214—21no—
145C3×#214—21no—
146C3×#214—21no—
147C3×#214D411yescharacteristic
148C3×#214D411yescharacteristic
149C3×#213—21no—
150C3×#213—21no—
151C3×#213—21no—
152C3×#213—21no—
153C3×#213—21no—
154C3×#213D411yescharacteristic
155C3×#213D411yescharacteristic
156C3×#208—21no—
157C3×#208—21no—
158C3×#208C2311yescharacteristic
159C3×#208C2311yescharacteristic
160C2×C3×C3⋊C8—21no—
161C2×C3×C3⋊C8—21no—
162C2×C3×C3⋊C8C2311yescharacteristic
163C2×C3×C3⋊C8C2311yescharacteristic
164(C2×D3)⋊Dic3—41no—
165#3719—21no—
166#3719—21no—
167#3718—21no—
168#3716—21no—
169#3716—21no—
170#3715—21no—
171#3715—21no—
172#3713—21no—
173#3711—21no—
174#3711—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3290—91noSylow
178C3×2−1+4—31no—
179C3×H(5,𝔽2)—21no—
180C3×H(5,𝔽2)—31no—
181C3×H(5,𝔽2)C2×D311yescharacteristic
182C3×H(5,𝔽2)C2×D311yescharacteristic
183#1010—31no—
184#1010—31no—
185#1010C2×D311yescharacteristic, complemented
186#1009C2×D311yescharacteristic
187C3×#137—31no—
188C3×#137—61no—
189C3×AGL(1,ℤ/8)—31no—
190C3×AGL(1,ℤ/8)—31no—
191C3×AGL(1,ℤ/8)—31no—
192C3×AGL(1,ℤ/8)—61no—
193C3×AGL(1,ℤ/8)—61no—
194C3×AGL(1,ℤ/8)—61no—
195C3×#135—31no—
196C3×#135—31no—
197C3×#135—61no—
198C3×#135—61no—
199C2×C3×SD16—31no—
200C2×C3×SD16—61no—
201C2×C3×D8—31no—
202C2×C3×D8—61no—
203C3×#131—31no—
204C3×#131—31no—
205#951—21no—
206#951—31no—
207#951—31no—
208#951—31no—
209#951—31no—
210#951—31no—
211#951—61no—
212#951—61no—
213#951—61no—
214#951—61no—
215#951C2×D311yescharacteristic
216#950—21no—
217#950—21no—
218#950—61no—
219#950—61no—
220#950C2×D311yescharacteristic
221#950C2×D311yescharacteristic
222#949—21no—
223#949—31no—
224#949C2×D311yescharacteristic
225#948—31no—
226#948—31no—
227#948C2×D311yescharacteristic
228#948C2×D311yescharacteristic, complemented
229#947—31no—
230C2×#216—31no—
231C2×#216—61no—
232#942—31no—
233#942—61no—
234#936—31no—
235#936—31no—
236#936—31no—
237#936—61no—
238C2×#214—21no—
239C2×#214—31no—
240C2×#214—61no—
241C2×#214C2×D311yescharacteristic, complemented
242#932—21no—
243#932—21no—
244#932—31no—
245#932—61no—
246#932C2×D311yescharacteristic
247#932C2×D311yescharacteristic, complemented
248C2×#213—21no—
249C2×#213C2×D311yescharacteristic
250#918—61no—
251D3×Q16—61no—
252#916—61no—
253#915—61no—
254#915—61no—
255D3×SD16—61no—
256#912—61no—
257#911—61no—
258C2×Dic12—31no—
259C2×#204—31no—
260#901—31no—
261#901—31no—
262#837—31no—
263#837—31no—
264#837—31no—
265#837—31no—
266#837—31no—
267#837—31no—
268#837—61no—
269#837—61no—
270#836—31no—
271#833—31no—
272#833—31no—
273#833—31no—
274#833—61no—
275#825—31no—
276#825—31no—
277#824—31no—
278#824—31no—
279#824—31no—
280#823—31no—
281#822—31no—
282#822—31no—
283#819—31no—
284#819—31no—
285C8×Dic3—31no—
286C8×Dic3—31no—
287C23×C32—21no—
288C23×C32—41no—
289C22×C3×D3—21no—
290C22×C3×D3—41no—
291C32×Q8C2×D411yescharacteristic
292C32×Q8C2×D411yescharacteristic
293C32×D4—21no—
294C32×D4—21no—
295C32×D4—21no—
296C32×D4—21no—
297C32×D4—41no—
298C32×D4—41no—
299C32×D4C2×D411yescharacteristic
300C32×D4C2×D411yescharacteristic
301C2×C32×C4—21no—
302C2×C32×C4—21no—
303C2×C32×C4—41no—
304C2×C32×C4C2411yescharacteristic
305C2×C3⋊Dic3—21no—
306C2×C3⋊Dic3—21no—
307#634—21no—
308#634—21no—
309C3×#67—21no—
310C3×#67—21no—
311C3×#67—41no—
312C3×#67—41no—
313C2×C3×Dic3—21no—
314C2×C3×Dic3—41no—
315C3×D12—21no—
316C3×D12—21no—
317C3×D12—41no—
318C3×D12C2×D411yescharacteristic
319C3×D12C2×D411yescharacteristic
320C3×C4×D3—21no—
321C3×C4×D3—21no—
322C3×C4×D3—41no—
323C3×C4×D3—41no—
324C3×Dic6—21no—
325C3×Dic6—21no—
326C3×Dic6—41no—
327C3×Dic6C2×D411yescharacteristic
328C3×Dic6C2×D411yescharacteristic
329#627—41no—
330#625—41no—
331D3×Dic3—41no—
332D3×Dic3—41no—
333C3⋊(C3⋊C8)—21no—
334C3⋊(C3⋊C8)—21no—
335C3×C3⋊C8—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8C2×D411yescharacteristic
338C3×C3⋊C8C2×D411yescharacteristic
339C3×C3⋊C8C2×D411yescharacteristic
340C3×C3⋊C8C2×D411yescharacteristic
341#578—91no—
342#577—31no—
343#577—91no—
344#576—31no—
345#495—91no—
346#473—91no—
347#472—91no—
348#471—91no—
349#471—91no—
350#455—91no—
351#455—91no—
352#454—91no—
353#454—91no—
354#443—91no—
355#443—91no—
356C3×#41—21no—
357C3×#41—21no—
358C3×#41—21no—
359C3×#41—21no—
360C3×#41—21no—
361C3×#41—21no—
362C3×#41—31no—
363C3×#41—31no—
364C3×#41—41no—
365C3×#41—41no—
366C3×#41—61no—
367C3×#41—61no—
368C3×#41—61no—
369C3×#41—61no—
370C3×#41—121no—
371C3×#41C22×D311yescharacteristic
372C3×#41C22×D311yescharacteristic
373C3×#41C22×D311yescharacteristic
374C3×#41C22×D311yescharacteristic
375C2×C3×Q8—31no—
376C2×C3×Q8—61no—
377C2×C3×Q8—61no—
378C2×C3×D4—21no—
379C2×C3×D4—21no—
380C2×C3×D4—21no—
381C2×C3×D4—21no—
382C2×C3×D4—21no—
383C2×C3×D4—31no—
384C2×C3×D4—41no—
385C2×C3×D4—41no—
386C2×C3×D4—41no—
387C2×C3×D4—41no—
388C2×C3×D4—42no—
389C2×C3×D4—61no—
390C2×C3×D4—61no—
391C2×C3×D4—121no—
392C2×C3×D4C22×D311yescharacteristic
393C2×C3×D4C22×D311yescharacteristic
394#239—21no—
395D3×Q8—21no—
396D3×Q8—61no—
397D3×Q8—61no—
398#237—21no—
399#237—41no—
400#237—61no—
401#237—61no—
402#237—121no—
403#237—121no—
404D3×D4—21no—
405D3×D4—41no—
406#235—21no—
407#235—21no—
408#235—61no—
409#235—61no—
410#235C22×D311yescharacteristic
411#235C22×D311yescharacteristic
412C2×D12—21no—
413C2×D12C22×D311yescharacteristic
414C2×Dic6—21no—
415C2×Dic6—31no—
416C2×Dic6—31no—
417C2×Dic6—61no—
418C2×Dic6—61no—
419C2×Dic6—61no—
420C2×Dic6C22×D311yescharacteristic
421C3×Q16—31no—
422C3×Q16—31no—
423C3×Q16—61no—
424C3×SD16—31no—
425C3×SD16—31no—
426C3×SD16—31no—
427C3×SD16—31no—
428C3×SD16—61no—
429C3×SD16—61no—
430C3×SD16—61no—
431C3×SD16—61no—
432C3×SD16—61no—
433C3×SD16—61no—
434C3×D8—31no—
435C3×D8—31no—
436C3×D8—61no—
437C3×D8—61no—
438C3×D8—61no—
439C3×D8—61no—
440C3×D8—61no—
441C3×M16—31no—
442C3×M16—31no—
443C3×M16—61no—
444C3×M16—61no—
445C2×C3×C8—31no—
446C2×C3×C8—31no—
447C2×C3×C8—61no—
448C2×C3×C8—61no—
449#217—121no—
450#217—121no—
451#217—121no—
452#217—122no—
453#216—21no—
454#216—61no—
455#216—61no—
456#216—61no—
457#216—61no—
458#216—61no—
459#216—61no—
460#216—61no—
461#216—61no—
462#216—121no—
463#216—121no—
464#216#6711yescharacteristic
465#216#6711yescharacteristic
466#215—21no—
467#215—61no—
468#215—61no—
469#215#6711yescharacteristic
470#215#6711yescharacteristic
471#214—21no—
472#214—21no—
473#214—21no—
474#214—21no—
475#214—21no—
476#214—61no—
477#214—61no—
478#214—61no—
479#214—61no—
480#214—61no—
481#214—61no—
482#214—61no—
483#214—61no—
484#214—121no—
485#214—121no—
486#214#6711yescharacteristic
487#214#6711yescharacteristic
488#213—21no—
489#213—21no—
490#213—21no—
491#213—21no—
492#213—21no—
493#213—61no—
494#213—61no—
495#213#6711yescharacteristic
496#213#6711yescharacteristic
497(C2×D3)⋊C4—121no—
498C4×Dic3—31no—
499C4×Dic3—31no—
500C4×Dic3—61no—
501#208—21no—
502#208—21no—
503#208—31no—
504#208—31no—
505#208—31no—
506#208—31no—
507#208—61no—
508#208—61no—
509#208—61no—
510#208—61no—
511#208C22×D311yescharacteristic
512#208C22×D311yescharacteristic
513C2×C3⋊C8—21no—
514C2×C3⋊C8—21no—
515C2×C3⋊C8—61no—
516C2×C3⋊C8—61no—
517C2×C3⋊C8C22×D311yescharacteristic
518C2×C3⋊C8C22×D311yescharacteristic
519Dic12—61no—
520Dic12—61no—
521#204—61no—
522#204—61no—
523ΓL(1,𝔽25)—61no—
524ΓL(1,𝔽25)—61no—
525D3×C8—61no—
526D3×C8—61no—
527C22×C32—21no—
528C22×C32—21no—
529C22×C32—41no—
530C22×C32—81no—
531C22×C32—161no—
532C22×C32H(5,𝔽2)11yescharacteristic
533C2×C3×D3—21no—
534C2×C3×D3—21no—
535C2×C3×D3—41no—
536C2×C3×D3—81no—
537C2×C3×D3—161no—
538C32×C4—21no—
539C32×C4—21no—
540C32×C4C22×D411yescharacteristic
541C32×C4C22×D411yescharacteristic
542C3⋊Dic3—41no—
543C3⋊Dic3—41no—
544C3×Dic3—21no—
545C3×Dic3—21no—
546C3×Dic3—41no—
5472−1+4—31no—
5482−1+4—91no—
549H(5,𝔽2)—31no—
550H(5,𝔽2)D3211yescharacteristic
551#137—31no—
552#137—61no—
553#137—91no—
554#137—91no—
555#137—91no—
556#137—181no—
557#137—181no—
558#137—181no—
559AGL(1,ℤ/8)—31no—
560AGL(1,ℤ/8)—31no—
561AGL(1,ℤ/8)—31no—
562AGL(1,ℤ/8)—61no—
563AGL(1,ℤ/8)—61no—
564AGL(1,ℤ/8)—61no—
565AGL(1,ℤ/8)—91no—
566AGL(1,ℤ/8)—181no—
567#135—31no—
568#135—31no—
569#135—61no—
570#135—61no—
571#135—181no—
572#135—181no—
573C2×Q16—91no—
574C2×Q16—181no—
575C2×SD16—31no—
576C2×SD16—61no—
577C2×SD16—91no—
578C2×SD16—181no—
579C2×D8—31no—
580C2×D8—61no—
581#131—31no—
582#131—31no—
583#131—91no—
584#131—91no—
585#124—91no—
586#124—91no—
587#108—91no—
588#108—91no—
589#104—91no—
590#104—91no—
591#104—91no—
592#104—91no—
593#101—91no—
594#101—91no—
595#100—91no—
596#100—91no—
597C4×C8—91no—
598C23×C3—22no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—41no—
602C23×C3—41no—
603C23×C3—42no—
604C23×C3—61no—
605C23×C3—121no—
606C22×D3—21no—
607C22×D3—41no—
608C3×Q8—21no—
609C3×Q8—21no—
610C3×Q8—31no—
611C3×Q8—31no—
612C3×Q8—61no—
613C3×Q8—61no—
614C3×Q8—121no—
615C3×Q8D3×D411yescharacteristic
616C3×Q8D3×D411yescharacteristic
617C3×Q8C2×#6711yescharacteristic
618C3×Q8C2×#6711yescharacteristic
619C3×D4—21no—
620C3×D4—21no—
621C3×D4—21no—
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—21no—
627C3×D4—21no—
628C3×D4—21no—
629C3×D4—31no—
630C3×D4—31no—
631C3×D4—41no—
632C3×D4—41no—
633C3×D4—41no—
634C3×D4—41no—
635C3×D4—41no—
636C3×D4—41no—
637C3×D4—41no—
638C3×D4—41no—
639C3×D4—42no—
640C3×D4—42no—
641C3×D4—61no—
642C3×D4—61no—
643C3×D4—61no—
644C3×D4—61no—
645C3×D4—121no—
646C3×D4—121no—
647C3×D4—121no—
648C3×D4D3×D411yescharacteristic
649C3×D4D3×D411yescharacteristic
650C3×D4C2×#6711yescharacteristic
651C3×D4C2×#6711yescharacteristic
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—42no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—121no—
666C2×C3×C4—121no—
667C2×C3×C4—121no—
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D311yescharacteristic
670#67—21no—
671#67—21no—
672#67—41no—
673#67—41no—
674#67—121no—
675#67—121no—
676C2×Dic3—21no—
677C2×Dic3—41no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—61no—
682C2×Dic3—121no—
683C2×Dic3—121no—
684C2×Dic3—121no—
685C2×Dic3—121no—
686D12—21no—
687D12—21no—
688D12—41no—
689D12C2×#6711yescharacteristic
690D12C2×#6711yescharacteristic
691C4×D3—21no—
692C4×D3—21no—
693C4×D3—41no—
694C4×D3—41no—
695C4×D3—121no—
696C4×D3—121no—
697Dic6—21no—
698Dic6—21no—
699Dic6—41no—
700Dic6—61no—
701Dic6—61no—
702Dic6—61no—
703Dic6—61no—
704Dic6—121no—
705Dic6—121no—
706Dic6—121no—
707Dic6—121no—
708Dic6C2×#6711yescharacteristic
709Dic6C2×#6711yescharacteristic
710C3×C8—31no—
711C3×C8—31no—
712C3×C8—31no—
713C3×C8—31no—
714C3×C8—61no—
715C3×C8—61no—
716C3⋊C8—21no—
717C3⋊C8—21no—
718C3⋊C8—61no—
719C3⋊C8—61no—
720C3⋊C8—61no—
721C3⋊C8—61no—
722C3⋊C8—121no—
723C3⋊C8—121no—
724C3⋊C8C2×#6711yescharacteristic
725C3⋊C8C2×#6711yescharacteristic
726C3⋊C8C2×#6711yescharacteristic
727C3⋊C8C2×#6711yescharacteristic
728C2×C32—21no—
729C2×C32—41no—
730C2×C32—41no—
731C2×C32—81no—
732C2×C32D4211yescharacteristic
733C3×D3—41no—
734C3×D3—41no—
735C3×D3—81no—
736#41—21no—
737#41—21no—
738#41—31no—
739#41—31no—
740#41—61no—
741#41—61no—
742#41—61no—
743#41—61no—
744#41—121no—
745#41—181no—
746#41—181no—
747#41—361no—
748#41C2×D3211yescharacteristic
749#41C2×D3211yescharacteristic
750C2×Q8—31no—
751C2×Q8—61no—
752C2×Q8—61no—
753C2×Q8—91no—
754C2×Q8—181no—
755C2×Q8—181no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—31no—
759C2×D4—41no—
760C2×D4—61no—
761C2×D4—61no—
762C2×D4—121no—
763C2×D4C2×D3211yescharacteristic
764Q16—31no—
765Q16—31no—
766Q16—61no—
767Q16—181no—
768Q16—181no—
769Q16—181no—
770Q16—181no—
771Q16—181no—
772SD16—31no—
773SD16—31no—
774SD16—31no—
775SD16—31no—
776SD16—61no—
777SD16—61no—
778SD16—61no—
779SD16—61no—
780SD16—61no—
781SD16—61no—
782SD16—181no—
783SD16—181no—
784SD16—181no—
785SD16—181no—
786SD16—181no—
787SD16—181no—
788D8—31no—
789D8—31no—
790D8—61no—
791D8—61no—
792D8—61no—
793D8—61no—
794D8—61no—
795D8—181no—
796M16—31no—
797M16—31no—
798M16—61no—
799M16—61no—
800M16—91no—
801M16—91no—
802M16—181no—
803M16—181no—
804C2×C8—31no—
805C2×C8—31no—
806C2×C8—61no—
807C2×C8—61no—
808C2×C8—181no—
809C2×C8—181no—
810C22⋊C4—361no—
811C22⋊C4—361no—
812C42—91no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—42no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—61no—
824C22×C3—61no—
825C22×C3—81no—
826C22×C3—81no—
827C22×C3—82no—
828C22×C3—121no—
829C22×C3—161no—
830C22×C3—161no—
831C22×C3—162no—
832C22×C3—241no—
833C22×C3—481no—
834C22×C3#100411yescharacteristic
835C22×C3#100411yescharacteristic
836C2×D3—21no—
837C2×D3—21no—
838C2×D3—41no—
839C2×D3—81no—
840C2×D3—161no—
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—41no—
848C3×C4—41no—
849C3×C4—61no—
850C3×C4—61no—
851C3×C4—121no—
852C3×C4C2×D3×D411yescharacteristic
853C3×C4C2×D3×D411yescharacteristic
854C3×C4C22×#6711yescharacteristic
855C3×C4C22×#6711yescharacteristic
856Dic3—21no—
857Dic3—21no—
858Dic3—41no—
859Dic3—121no—
860Dic3—121no—
861Dic3—121no—
862Dic3—121no—
863Dic3—241no—
864Dic3—241no—
865C32#329011yescharacteristic, complemented, Sylow
866C23—21no—
867C23—41no—
868C23—61no—
869C23—121no—
870Q8—31no—
871Q8—31no—
872Q8—61no—
873Q8—61no—
874Q8—121no—
875Q8—181no—
876Q8—181no—
877Q8—361no—
878Q8D3×#6711yescharacteristic
879Q8D3×#6711yescharacteristic
880D4—21no—
881D4—21no—
882D4—21no—
883D4—21no—
884D4—31no—
885D4—31no—
886D4—41no—
887D4—41no—
888D4—61no—
889D4—61no—
890D4—61no—
891D4—61no—
892D4—121no—
893D4—121no—
894D4—121no—
895D4—361no—
896D4D3×#6711yescharacteristic
897D4D3×#6711yescharacteristic
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—41no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—121no—
905C2×C4—121no—
906C2×C4—121no—
907C2×C4—181no—
908C2×C4—181no—
909C2×C4—361no—
910C2×C4—361no—
911C2×C4C22×D3211yescharacteristic
912C8—31no—
913C8—31no—
914C8—31no—
915C8—31no—
916C8—61no—
917C8—61no—
918C8—181no—
919C8—181no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—41no—
924C2×C3—41no—
925C2×C3—41no—
926C2×C3—41no—
927C2×C3—41no—
928C2×C3—81no—
929C2×C3—81no—
930C2×C3—82no—
931C2×C3—81no—
932C2×C3—81no—
933C2×C3—121no—
934C2×C3—121no—
935C2×C3—241no—
936C2×C3D4×#6711yescharacteristic
937C2×C3D4×#6711yescharacteristic
938D3—41no—
939D3—41no—
940D3—81no—
941C22—21no—
942C22—21no—
943C22—41no—
944C22—61no—
945C22—61no—
946C22—81no—
947C22—121no—
948C22—161no—
949C22—241no—
950C22—481no—
951C22#6433011yescharacteristic
952C4—21no—
953C4—21no—
954C4—61no—
955C4—61no—
956C4—121no—
957C4—361no—
958C4—361no—
959C4C2×D3×#6711yescharacteristic
960C4C2×D3×#6711yescharacteristic
961C3—21no—
962C3#8401111yescharacteristic, complemented
963C3#8401211yescharacteristic, complemented
964C2—21no—
965C2—41no—
966C2—41no—
967C2—81no—
968C2—121no—
969C2—121no—
970C2—241no—
971C2#67211yescharacteristic
subgroupG/H
centerC2#672
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×H(5,𝔽2)C22
socleC2×C32D42
hypercenterH(5,𝔽2)D32
hypocenterC32#3290
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C3×#5836C2semidirect
2. C3×#5835C2semidirect
3. #10595467C2semidirect
4. #10595466C2semidirect
5. #10592941C2semidirect
6. #10591684C2semidirect
7. #10591682C2semidirect
8. #10591679C2semidirect
9. #10591673C2semidirect
10. #10591673C2semidirect
11. #10591664C2semidirect
12. #10591524C2semidirect
13. #10591506C2semidirect
14. #10591505C2semidirect
15. #10591474C2semidirect
19. C3×#1010C22semidirect
21. #64298C22semidirect
23. #64160C22semidirect
24. #64145C22semidirect
34. C3×#948C22semidirect
36. C2×C3×#214C22semidirect
40. C3×#932C22semidirect
51. #63863C22semidirect
52. C2×#3719C22semidirect
53. C2×#3716C22semidirect
54. #63827C22semidirect
55. #63823C22semidirect
56. #63814C22semidirect
57. #63814C22semidirect
59. #63664C22semidirect
60. #63660C22semidirect
61. #63577C22semidirect
62. #63577C22semidirect
63. #63568C22semidirect
64. #63568C22semidirect
65. #63561C22semidirect
66. #63560C22semidirect
67. #63558C22semidirect
68. #63553C22semidirect
73. #5836D3semidirect
74. #5835D3semidirect
185. #1010C2×D3semidirect
228. #948C2×D3semidirect
241. C2×#214C2×D3semidirect
247. #932C2×D3semidirect
865. C32#3290semidirect
962. C3#84011semidirect
963. C3#84012semidirect

Maximal subgroups

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

subgroupindex
C3×#58362
C3×#58352
#105954672
#105954662
#105929412
#105916842
#105916822
#105916792
#105916732
#105916642
#105915242
#105915062
#105915052
#105914742
#840123
#840113