Finite Group Databasebeta

← #11886908

Subgroups — #11886908

Order 1152.

1006 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5774C211yesmaximal, characteristic, complemented
2#10595456C211yesmaximal, characteristic, complemented
3#10595444C211yesmaximal, characteristic, complemented
4#10595097C211yesmaximal, characteristic, complemented
5#10592898C211yesmaximal, characteristic, complemented
6C3×#5198C211yesmaximal, characteristic, complemented
7#10591675C211yesmaximal, characteristic, complemented
8#10591666C211yesmaximal, characteristic, complemented
9#10591509C211yesmaximal, characteristic, complemented
10#10591505C211yesmaximal, characteristic, complemented
11#10591482C211yesmaximal, characteristic, complemented
12#10591013C211yesmaximal, characteristic, complemented
13#10590997C211yesmaximal, characteristic, complemented
14#10590982C211yesmaximal, characteristic, complemented
15#10590975C211yesmaximal, characteristic, complemented
16#84010—31nomaximal
17#80282—31nomaximal
18C3×#1009C2211yescharacteristic, complemented
19C3×#1009C2211yescharacteristic, complemented
20C3×#1004C2211yescharacteristic, complemented
21#64308C2211yescharacteristic, complemented
22C32×AGL(1,ℤ/8)C2211yescharacteristic, complemented
23#64158C2211yescharacteristic, complemented
24#64157C2211yescharacteristic, complemented
25C2×#3753C2211yescharacteristic, complemented
26C3×#950C2211yescharacteristic
27C3×#940C2211yescharacteristic, complemented
28C3×#932C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic, complemented
30C3×#916—21no—
31C3×#914—21no—
32C3×#911—21no—
33C3×D3×D8—21no—
34C3×#908C2211yescharacteristic, complemented
35C3×#907C2211yescharacteristic, complemented
36#63949—21no—
37#63939—21no—
38#63935—21no—
39#63934—21no—
40#63934—21no—
41#63925—21no—
42D3×#213—21no—
43D3×#213—21no—
44#63911C2211yescharacteristic, complemented
45#63825C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic, complemented
47#63823—21no—
48#63823—21no—
49#63823C2211yescharacteristic, complemented
50#63823C2211yescharacteristic, complemented
51#63823C2211yescharacteristic, complemented
52#63822—21no—
53#63822C2211yescharacteristic
54C2×#3713—21no—
55C2×#3713C2211yescharacteristic, complemented
56#63815C2211yescharacteristic, complemented
57#63814C2211yescharacteristic, complemented
58#63660C2211yescharacteristic, complemented
59#63650C2211yescharacteristic, complemented
60#63649C2211yescharacteristic, complemented
61C3×#837C2211yescharacteristic, complemented
62C3×#825C2211yescharacteristic, complemented
63C3×#823C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63569C2211yescharacteristic, complemented
66#63569C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68Dic3×C3⋊C8C2211yescharacteristic, complemented
69C3×#576—31no—
70#5835—31no—
71#5835—31no—
72#5835—31no—
73#5835—31no—
74#5774—31no—
75#5774D311yescharacteristic, complemented
76#5769—31no—
77C3×#453—31no—
78#5241—31no—
79#5241—31no—
80#5199—31no—
81#5199—31no—
82#5199—31no—
83#5199—31no—
84#5199—61no—
85#5198—31no—
86#5198D311yescharacteristic, complemented
87#5196—31no—
88#5160—31no—
89#5151—31no—
90#5144—31no—
91#5142—31no—
92#5077—31no—
93#5073—31no—
94#4824—31no—
95#4824—31no—
96#4822—31no—
97#4822—31no—
98#4749—31no—
99#4749—31no—
100C32×#41C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C3×#67—41no—
104C2×C3×#67—41no—
105C3×#239—21no—
106C3×#239—21no—
107C3×#237—21no—
108C3×#237—21no—
109C3×D3×D4—21no—
110C3×D3×D4—21no—
111C3×D3×D4—21no—
112C3×D3×D4—21no—
113C3×D3×D4—41no—
114C3×D3×D4—41no—
115C3×#235—21no—
116C3×#235—21no—
117C3×#235C2311yescharacteristic
118C3×#235C2311yescharacteristic
119C3×#235C2311yescharacteristic
120C2×C3×D12—21no—
121C2×C3×D12—21no—
122C2×C3×D12C2311yescharacteristic
123C2×C3×D12C2311yescharacteristic
124#3811—41no—
125C2×#626—41no—
126D3×D12—21no—
127D3×D12—21no—
128#3799—21no—
129#3799—21no—
130C32×SD16—21no—
131C32×D8—21no—
132C32×M16C2311yescharacteristic
133#3755—21no—
134#3753—21no—
135#3753—21no—
136#3753—21no—
137#3748—21no—
138#3748C2311yescharacteristic
139#3748C2311yescharacteristic
140C2×C3⋊(C3⋊C8)—21no—
141C2×C3⋊(C3⋊C8)C2311yescharacteristic
142C3×#216D411yescharacteristic, complemented
143C3×#215D411yescharacteristic, complemented
144C3×#214—21no—
145C3×#214D411yescharacteristic, complemented
146C3×#213—21no—
147C3×#213—21no—
148C3×#213—21no—
149C3×#213D411yescharacteristic, complemented
150C3×C4×Dic3C2311yescharacteristic
151C3×#208C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×D24—21no—
154C3×#204—21no—
155C3×ΓL(1,𝔽25)—21no—
156C3×D3×C8—21no—
157#3718D411yescharacteristic, complemented
158#3717—21no—
159#3715—21no—
160#3715—21no—
161#3715—21no—
162#3715D411yescharacteristic, complemented
163#3715D411yescharacteristic, complemented
164#3714—21no—
165#3714—21no—
166#3714—21no—
167#3713—21no—
168#3713—21no—
169#3713—21no—
170#3713—21no—
171#3713—21no—
172#3713D411yescharacteristic, complemented
173#3711—21no—
174#3711—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3292—91noSylow
178C3×H(5,𝔽2)—31no—
179C3×H(5,𝔽2)—31no—
180C3×H(5,𝔽2)—31no—
181#1009—31no—
182#1009—31no—
183#1009C2×D311yescharacteristic, complemented
184#1009C2×D311yescharacteristic, complemented
185#1004C2×D311yescharacteristic, complemented
186C3×AGL(1,ℤ/8)—21no—
187C3×AGL(1,ℤ/8)—31no—
188C3×AGL(1,ℤ/8)—31no—
189C3×AGL(1,ℤ/8)—61no—
190C3×AGL(1,ℤ/8)—61no—
191C3×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
192C3×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
193C3×#135—31no—
194C3×#135—61no—
195C2×C3×D8—31no—
196C2×C3×D8—61no—
197C3×#131—31no—
198C3×#127—31no—
199#950—31no—
200#950—31no—
201#950—61no—
202#950—61no—
203#950—61no—
204#950—61no—
205#950C2×D311yescharacteristic
206#949—31no—
207#949—31no—
208#949—31no—
209#949—31no—
210#949—31no—
211#949—31no—
212#949—61no—
213#949—61no—
214#949—61no—
215#949—61no—
216#949—61no—
217#948—31no—
218#948—31no—
219#948—31no—
220#948—31no—
221#948—61no—
222#940—31no—
223#940C2×D311yescharacteristic, complemented
224#932—31no—
225#932—31no—
226#932—31no—
227#932—61no—
228#932—61no—
229#932—61no—
230#932—61no—
231#932C2×D311yescharacteristic, complemented
232C2×#213—31no—
233C2×#213—31no—
234C2×#213—31no—
235C2×#213—31no—
236C2×#213—31no—
237C2×#213—61no—
238C2×#213—61no—
239C2×#213—61no—
240C2×#213—61no—
241C2×#213—61no—
242C2×#213C2×D311yescharacteristic, complemented
243#919—61no—
244#916—21no—
245#916—61no—
246#914—21no—
247#914—61no—
248#914—61no—
249#914—61no—
250#911—21no—
251#911—61no—
252D3×D8—21no—
253D3×D8—61no—
254D3×D8—61no—
255#908—31no—
256#908C2×D311yescharacteristic, complemented
257#907—31no—
258#907C2×D311yescharacteristic, complemented
259C2×D24—31no—
260#901—31no—
261#874—31no—
262C3×#104—31no—
263C3×#104—31no—
264C3×#100—31no—
265#837—31no—
266#837—31no—
267#837C2×D311yescharacteristic, complemented
268#833—31no—
269#833—31no—
270#833—31no—
271#833—61no—
272#825C2×D311yescharacteristic, complemented
273#823—31no—
274#823—31no—
275#823—31no—
276#823—61no—
277#823C2×D311yescharacteristic, complemented
278#822—31no—
279#822—31no—
280#822—31no—
281#822—61no—
282#819—31no—
283C8×Dic3—31no—
284#805—31no—
285#805—31no—
286C4×C3⋊C8—31no—
287C23×C32—21no—
288C22×C3⋊D3—21no—
289C22×C3×D3—21no—
290C22×C3×D3—21no—
291C22×C3×D3—41no—
292C22×C3×D3—41no—
293C22×C3×D3—41no—
294C2×D32—41no—
295C32×Q8C2×D411yescharacteristic
296C32×D4—21no—
297C32×D4—21no—
298C32×D4—21no—
299C32×D4C2×D411yescharacteristic
300C2×C32×C4—21no—
301C2×C32×C4C2411yescharacteristic
302C4⋊(C3⋊D3)—21no—
303C4⋊(C3⋊D3)—21no—
304C3×#67—21no—
305C3×#67—21no—
306C3×#67—21no—
307C3×#67—41no—
308C3×#67—41no—
309C3×#67—41no—
310C3×#67—41no—
311C3×#67—82no—
312C2×C3×Dic3—21no—
313C2×C3×Dic3—41no—
314C3×D12—21no—
315C3×D12—21no—
316C3×D12—21no—
317C3×D12—21no—
318C3×D12—41no—
319C3×D12—41no—
320C3×D12C2×D411yescharacteristic
321C3×D12C2×D411yescharacteristic
322C3×D12C2×D411yescharacteristic
323C3×C4×D3—21no—
324C3×C4×D3—21no—
325C3×C4×D3—21no—
326C3×C4×D3—41no—
327C3×C4×D3—41no—
328C3×Dic6C2×D411yescharacteristic
329C3×Dic6C2×D411yescharacteristic
330C3×Dic6C2×D411yescharacteristic
331#626—41no—
332#626—41no—
333#626—82no—
334#624—41no—
335C32×C8—21no—
336C3⋊(C3⋊C8)—21no—
337C3⋊(C3⋊C8)—21no—
338C3⋊(C3⋊C8)C2×D411yescharacteristic
339C3⋊(C3⋊C8)C2×D411yescharacteristic
340C3×C3⋊C8—21no—
341C3×C3⋊C8C2×D411yescharacteristic
342C3×C3⋊C8C2×D411yescharacteristic
343#576—31no—
344#576—91no—
345#576—91no—
346#576—91no—
347#493—91no—
348#472—91no—
349#472—91no—
350#472—91no—
351#472—91no—
352#453—31no—
353#453—91no—
354#453—91no—
355#453—91no—
356#443—91no—
357#443—91no—
358C3×#41—21no—
359C3×#41—31no—
360C3×#41—31no—
361C3×#41—31no—
362C3×#41—61no—
363C3×#41—61no—
364C3×#41—61no—
365C3×#41—61no—
366C3×#41—61no—
367C3×#41—61no—
368C3×#41C22×D311yescharacteristic
369C3×#41C22×D311yescharacteristic
370C2×C3×D4—21no—
371C2×C3×D4—31no—
372C2×C3×D4—31no—
373C2×C3×D4—61no—
374C2×C3×D4—61no—
375C2×C3×D4—61no—
376C2×C3×D4—61no—
377C2×C3×D4—61no—
378C2×C3×D4—61no—
379C2×C3×D4—121no—
380C2×C3×D4—121no—
381C2×C3×D4—121no—
382C2×C3×D4—121no—
383C2×C3×D4C22×D311yescharacteristic
384C2×C3×D4C22×D311yescharacteristic
385C2×#67—41no—
386C2×#67—41no—
387C2×#67—121no—
388#239—21no—
389#239—21no—
390#239—61no—
391#239—61no—
392#237—21no—
393#237—21no—
394D3×D4—21no—
395D3×D4—21no—
396D3×D4—21no—
397D3×D4—21no—
398D3×D4—41no—
399D3×D4—41no—
400D3×D4—61no—
401D3×D4—61no—
402D3×D4—121no—
403D3×D4—121no—
404#235—21no—
405#235—21no—
406#235—61no—
407#235—61no—
408#235C22×D311yescharacteristic
409#235C22×D311yescharacteristic
410#235C22×D311yescharacteristic
411C2×D12—21no—
412C2×D12—21no—
413C2×D12—31no—
414C2×D12—31no—
415C2×D12—61no—
416C2×D12—61no—
417C2×D12—61no—
418C2×D12—121no—
419C2×D12C22×D311yescharacteristic
420C2×D12C22×D311yescharacteristic
421C3×Q16—31no—
422C3×SD16—21no—
423C3×SD16—21no—
424C3×SD16—31no—
425C3×SD16—31no—
426C3×SD16—41no—
427C3×SD16—61no—
428C3×SD16—61no—
429C3×D8—21no—
430C3×D8—21no—
431C3×D8—31no—
432C3×D8—41no—
433C3×D8—61no—
434C3×D8—61no—
435C3×D8—61no—
436C3×D8—61no—
437C3×M16—21no—
438C3×M16—31no—
439C3×M16—61no—
440C3×M16C22×D311yescharacteristic
441C3×M16C22×D311yescharacteristic
442C2×C3×C8—31no—
443C2×C3×C8—61no—
444C3×C42—31no—
445#216—31no—
446#216—31no—
447#216#6711yescharacteristic, complemented
448#215—31no—
449#215—31no—
450#215—61no—
451#215—61no—
452#215—61no—
453#215—61no—
454#215—61no—
455#215—61no—
456#215—121no—
457#215#6711yescharacteristic, complemented
458#214—21no—
459#214—31no—
460#214—31no—
461#214—61no—
462#214—61no—
463#214—61no—
464#214#6711yescharacteristic, complemented
465#213—21no—
466#213—21no—
467#213—21no—
468#213—31no—
469#213—31no—
470#213—61no—
471#213—61no—
472#213—61no—
473#213—61no—
474#213—61no—
475#213—61no—
476#213—61no—
477#213—61no—
478#213—61no—
479#213—61no—
480#213—61no—
481#213—61no—
482#213—61no—
483#213—61no—
484#213—61no—
485#213—61no—
486#213—61no—
487#213—61no—
488#213—61no—
489#213—121no—
490#213—121no—
491#213—121no—
492#213#6711yescharacteristic, complemented
493C4×Dic3C22×D311yescharacteristic
494#208—31no—
495#208—31no—
496#208—31no—
497#208—31no—
498#208—61no—
499#208—61no—
500#208—61no—
501#208—61no—
502#208—61no—
503#208—61no—
504#208—121no—
505#208C22×D311yescharacteristic
506C2×C3⋊C8—31no—
507C2×C3⋊C8—31no—
508C2×C3⋊C8—61no—
509C2×C3⋊C8—61no—
510C2×C3⋊C8—61no—
511C2×C3⋊C8—61no—
512C2×C3⋊C8—61no—
513C2×C3⋊C8—121no—
514C2×C3⋊C8C22×D311yescharacteristic
515D24—21no—
516D24—61no—
517D24—61no—
518D24—61no—
519#204—21no—
520#204—61no—
521ΓL(1,𝔽25)—21no—
522ΓL(1,𝔽25)—61no—
523ΓL(1,𝔽25)—61no—
524D3×C8—21no—
525D3×C8—61no—
526D3×C8—61no—
527C22×C32—21no—
528C22×C32—41no—
529C22×C32—81no—
530C22×C32H(5,𝔽2)11yescharacteristic
531C2×C3⋊D3—41no—
532C2×C3⋊D3—81no—
533C2×C3×D3—21no—
534C2×C3×D3—21no—
535C2×C3×D3—21no—
536C2×C3×D3—41no—
537C2×C3×D3—41no—
538C2×C3×D3—81no—
539C2×C3×D3—81no—
540C2×C3×D3—161no—
541C2×C3×D3—161no—
542C2×C3×D3—161no—
543D32—161no—
544C32×C4—21no—
545C32×C4C22×D411yescharacteristic
546C32×C4C22×D411yescharacteristic
547C3×Dic3—22no—
548C3×Dic3—21no—
549C3×Dic3—21no—
550C3×Dic3—21no—
551H(5,𝔽2)—31no—
552H(5,𝔽2)—31no—
553H(5,𝔽2)—31no—
554H(5,𝔽2)—91no—
555AGL(1,ℤ/8)—31no—
556AGL(1,ℤ/8)—31no—
557AGL(1,ℤ/8)—61no—
558AGL(1,ℤ/8)—61no—
559AGL(1,ℤ/8)—91no—
560AGL(1,ℤ/8)—91no—
561AGL(1,ℤ/8)—91no—
562AGL(1,ℤ/8)—91no—
563AGL(1,ℤ/8)—91no—
564AGL(1,ℤ/8)—181no—
565AGL(1,ℤ/8)—181no—
566AGL(1,ℤ/8)—181no—
567AGL(1,ℤ/8)—181no—
568AGL(1,ℤ/8)—181no—
569AGL(1,ℤ/8)—181no—
570AGL(1,ℤ/8)D3211yescharacteristic, complemented
571#135—31no—
572#135—61no—
573#135—91no—
574#135—181no—
575#135—181no—
576#135—181no—
577C2×D8—31no—
578C2×D8—61no—
579C2×D8—91no—
580C2×D8—91no—
581C2×D8—91no—
582C2×D8—181no—
583C2×D8—181no—
584C2×D8—181no—
585#131—31no—
586#131—91no—
587#131—91no—
588#131—91no—
589#127—31no—
590#127—91no—
591#108—91no—
592#108—91no—
593#104—31no—
594#104—31no—
595#104—91no—
596#104—91no—
597#100—31no—
598#100—91no—
599#100—91no—
600#100—91no—
601C4×C8—91no—
602C23×C3—21no—
603C23×C3—21no—
604C23×C3—41no—
605C23×C3—61no—
606C23×C3—61no—
607C23×C3—121no—
608C23×C3—121no—
609C23×C3—121no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—41no—
613C22×D3—41no—
614C22×D3—41no—
615C22×D3—61no—
616C22×D3—61no—
617C22×D3—121no—
618C22×D3—121no—
619C22×D3—121no—
620C3×Q8—21no—
621C3×Q8—31no—
622C3×Q8—31no—
623C3×Q8—31no—
624C3×Q8D3×D411yescharacteristic
625C3×Q8C2×#6711yescharacteristic
626C3×D4—21no—
627C3×D4—21no—
628C3×D4—21no—
629C3×D4—21no—
630C3×D4—21no—
631C3×D4—21no—
632C3×D4—21no—
633C3×D4—31no—
634C3×D4—31no—
635C3×D4—31no—
636C3×D4—41no—
637C3×D4—41no—
638C3×D4—41no—
639C3×D4—61no—
640C3×D4—61no—
641C3×D4—61no—
642C3×D4—61no—
643C3×D4—61no—
644C3×D4—61no—
645C3×D4—61no—
646C3×D4—121no—
647C3×D4—121no—
648C3×D4—121no—
649C3×D4—121no—
650C3×D4—121no—
651C3×D4—121no—
652C3×D4—242no—
653C3×D4D3×D411yescharacteristic
654C3×D4C2×#6711yescharacteristic
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—41no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—121no—
664C2×C3×C4—121no—
665C2×C3×C4—121no—
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D311yescharacteristic
668#67—21no—
669#67—21no—
670#67—21no—
671#67—41no—
672#67—41no—
673#67—41no—
674#67—41no—
675#67—82no—
676#67—121no—
677#67—121no—
678#67—242no—
679C2×Dic3—21no—
680C2×Dic3—41no—
681D12—21no—
682D12—21no—
683D12—21no—
684D12—21no—
685D12—41no—
686D12—41no—
687D12—61no—
688D12—61no—
689D12—61no—
690D12—61no—
691D12—121no—
692D12—121no—
693D12—121no—
694D12—121no—
695D12—242no—
696D12D3×D411yescharacteristic
697D12D3×D411yescharacteristic
698D12C2×#6711yescharacteristic
699C4×D3—21no—
700C4×D3—21no—
701C4×D3—21no—
702C4×D3—41no—
703C4×D3—41no—
704C4×D3—121no—
705C4×D3—121no—
706Dic6D3×D411yescharacteristic
707Dic6D3×D411yescharacteristic
708Dic6C2×#6711yescharacteristic
709C3×C8—21no—
710C3×C8—21no—
711C3×C8—31no—
712C3×C8—31no—
713C3×C8—41no—
714C3×C8—61no—
715C3⋊C8—21no—
716C3⋊C8—31no—
717C3⋊C8—31no—
718C3⋊C8—31no—
719C3⋊C8—31no—
720C3⋊C8—61no—
721C3⋊C8—61no—
722C3⋊C8—61no—
723C3⋊C8—61no—
724C3⋊C8—61no—
725C3⋊C8—61no—
726C3⋊C8—121no—
727C3⋊C8—121no—
728C3⋊C8C2×#6711yescharacteristic
729C3⋊C8C2×#6711yescharacteristic
730C2×C32—21no—
731C2×C32—41no—
732C2×C32—81no—
733C2×C32D4211yescharacteristic
734C3⋊D3—81no—
735C3×D3—41no—
736C3×D3—41no—
737C3×D3—41no—
738C3×D3—81no—
739C3×D3—81no—
740#41—31no—
741#41—31no—
742#41—31no—
743#41—61no—
744#41—61no—
745#41—61no—
746#41—61no—
747#41—61no—
748#41—61no—
749#41—181no—
750#41—181no—
751#41C2×D3211yescharacteristic
752C2×D4—31no—
753C2×D4—31no—
754C2×D4—61no—
755C2×D4—61no—
756C2×D4—61no—
757C2×D4—61no—
758C2×D4—61no—
759C2×D4—61no—
760C2×D4—91no—
761C2×D4—121no—
762C2×D4—121no—
763C2×D4—121no—
764C2×D4—121no—
765C2×D4—181no—
766C2×D4—181no—
767C2×D4—361no—
768C2×D4—361no—
769C2×D4C2×D3211yescharacteristic
770Q16—31no—
771Q16—91no—
772SD16—21no—
773SD16—31no—
774SD16—31no—
775SD16—61no—
776SD16—61no—
777SD16—91no—
778SD16—91no—
779SD16—181no—
780SD16—181no—
781SD16—181no—
782SD16—181no—
783SD16—181no—
784D8—21no—
785D8—31no—
786D8—61no—
787D8—61no—
788D8—61no—
789D8—61no—
790D8—91no—
791D8—181no—
792D8—181no—
793D8—181no—
794D8—181no—
795D8—181no—
796D8—181no—
797D8—181no—
798D8—181no—
799D8—181no—
800D8—181no—
801D8—181no—
802M16—31no—
803M16—61no—
804M16—91no—
805M16—91no—
806M16—181no—
807M16—181no—
808M16—181no—
809M16C2×D3211yescharacteristic
810C2×C8—31no—
811C2×C8—61no—
812C2×C8—91no—
813C2×C8—181no—
814C2×C8—181no—
815C2×C8—181no—
816C42—31no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—61no—
824C22×C3—61no—
825C22×C3—61no—
826C22×C3—81no—
827C22×C3—81no—
828C22×C3—81no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—161no—
832C22×C3—241no—
833C22×C3—241no—
834C22×C3—481no—
835C22×C3—481no—
836C22×C3—481no—
837C22×C3#100411yescharacteristic
838C22×C3#100411yescharacteristic
839C2×D3—21no—
840C2×D3—21no—
841C2×D3—21no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—81no—
845C2×D3—81no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—161no—
849C2×D3—161no—
850C2×D3—161no—
851C2×D3—241no—
852C2×D3—241no—
853C2×D3—241no—
854C2×D3—481no—
855C2×D3—481no—
856C2×D3—481no—
857C3×C4—21no—
858C3×C4—21no—
859C3×C4—21no—
860C3×C4—21no—
861C3×C4—41no—
862C3×C4—62no—
863C3×C4—61no—
864C3×C4—61no—
865C3×C4—61no—
866C3×C4C2×D3×D411yescharacteristic
867C3×C4C2×D3×D411yescharacteristic
868C3×C4C2×D3×D411yescharacteristic
869C3×C4C22×#6711yescharacteristic
870Dic3—22no—
871Dic3—21no—
872Dic3—21no—
873Dic3—21no—
874C32#329211yescharacteristic, complemented, Sylow
875C23—21no—
876C23—61no—
877C23—61no—
878C23—121no—
879C23—121no—
880C23—121no—
881C23—181no—
882C23—361no—
883Q8—31no—
884Q8—31no—
885Q8—31no—
886Q8D3×#6711yescharacteristic
887D4—21no—
888D4—21no—
889D4—21no—
890D4—31no—
891D4—31no—
892D4—31no—
893D4—61no—
894D4—61no—
895D4—61no—
896D4—61no—
897D4—61no—
898D4—61no—
899D4—61no—
900D4—121no—
901D4—121no—
902D4—121no—
903D4—121no—
904D4—121no—
905D4—121no—
906D4—181no—
907D4—181no—
908D4—242no—
909D4—361no—
910D4—361no—
911D4—722no—
912D4D3×#6711yescharacteristic
913C2×C4—21no—
914C2×C4—61no—
915C2×C4—61no—
916C2×C4—61no—
917C2×C4—61no—
918C2×C4—121no—
919C2×C4—121no—
920C2×C4—121no—
921C2×C4—361no—
922C2×C4C22×D3211yescharacteristic
923C8—21no—
924C8—31no—
925C8—31no—
926C8—61no—
927C8—91no—
928C8—91no—
929C8—181no—
930C8—181no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—41no—
935C2×C3—41no—
936C2×C3—41no—
937C2×C3—81no—
938C2×C3—81no—
939C2×C3—81no—
940C2×C3—121no—
941C2×C3—121no—
942C2×C3—121no—
943C2×C3—161no—
944C2×C3—241no—
945C2×C3—241no—
946C2×C3#559011yescharacteristic
947C2×C3D4×#6711yescharacteristic
948D3—41no—
949D3—41no—
950D3—41no—
951D3—81no—
952D3—81no—
953D3—241no—
954D3—241no—
955D3—481no—
956C22—21no—
957C22—41no—
958C22—61no—
959C22—61no—
960C22—61no—
961C22—81no—
962C22—121no—
963C22—121no—
964C22—241no—
965C22—241no—
966C22—361no—
967C22—481no—
968C22—481no—
969C22—481no—
970C22—721no—
971C22—1441no—
972C22#6431311yescharacteristic
973C4—21no—
974C4—62no—
975C4—61no—
976C4—61no—
977C4—61no—
978C4D32×D411yescharacteristic
979C4C2×D3×#6711yescharacteristic
980C3—21no—
981C3#8028211yescharacteristic, complemented
982C3#8401011yescharacteristic, complemented
983C2—21no—
984C2—41no—
985C2—81no—
986C2—121no—
987C2—121no—
988C2—121no—
989C2—241no—
990C2—241no—
991C2—721no—
992C2#1059528711yescharacteristic
subgroupG/H
centerC2#10595287
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×AGL(1,ℤ/8)C22
socleC2×C32D42
hypercenterAGL(1,ℤ/8)D32
hypocenterC32#3292
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C3×#5774C2semidirect
2. #10595456C2semidirect
3. #10595444C2semidirect
4. #10595097C2semidirect
5. #10592898C2semidirect
6. C3×#5198C2semidirect
7. #10591675C2semidirect
8. #10591666C2semidirect
9. #10591509C2semidirect
10. #10591505C2semidirect
11. #10591482C2semidirect
12. #10591013C2semidirect
13. #10590997C2semidirect
14. #10590982C2semidirect
15. #10590975C2semidirect
18. C3×#1009C22semidirect
19. C3×#1009C22semidirect
20. C3×#1004C22semidirect
21. #64308C22semidirect
22. C32×AGL(1,ℤ/8)C22semidirect
23. #64158C22semidirect
24. #64157C22semidirect
25. C2×#3753C22semidirect
27. C3×#940C22semidirect
28. C3×#932C22semidirect
29. C2×C3×#213C22semidirect
34. C3×#908C22semidirect
35. C3×#907C22semidirect
44. #63911C22semidirect
45. #63825C22semidirect
46. C2×#3714C22semidirect
49. #63823C22semidirect
50. #63823C22semidirect
51. #63823C22semidirect
55. C2×#3713C22semidirect
56. #63815C22semidirect
57. #63814C22semidirect
58. #63660C22semidirect
59. #63650C22semidirect
60. #63649C22semidirect
61. C3×#837C22semidirect
62. C3×#825C22semidirect
63. C3×#823C22semidirect
64. #63577C22semidirect
65. #63569C22semidirect
66. #63569C22semidirect
67. #63558C22semidirect
68. Dic3×C3⋊C8C22semidirect
75. #5774D3semidirect
86. #5198D3semidirect
142. C3×#216D4semidirect
143. C3×#215D4semidirect
145. C3×#214D4semidirect
149. C3×#213D4semidirect
157. #3718D4semidirect
162. #3715D4semidirect
163. #3715D4semidirect
172. #3713D4semidirect
183. #1009C2×D3semidirect
184. #1009C2×D3semidirect
185. #1004C2×D3semidirect
191. C3×AGL(1,ℤ/8)C2×D3semidirect
192. C3×AGL(1,ℤ/8)C2×D3semidirect
223. #940C2×D3semidirect
231. #932C2×D3semidirect
242. C2×#213C2×D3semidirect
256. #908C2×D3semidirect
258. #907C2×D3semidirect
267. #837C2×D3semidirect
272. #825C2×D3semidirect
277. #823C2×D3semidirect
447. #216#67semidirect
457. #215#67semidirect
464. #214#67semidirect
492. #213#67semidirect
570. AGL(1,ℤ/8)D32semidirect
874. C32#3292semidirect
981. C3#80282semidirect
982. C3#84010semidirect

Maximal subgroups

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

subgroupindex
C3×#57742
#105954562
#105954442
#105950972
#105928982
C3×#51982
#105916752
#105916662
#105915092
#105915052
#105914822
#105910132
#105909972
#105909822
#105909752
#840103
#802823