Finite Group Databasebeta

← D3×#4898 #11867865

Subgroups — D3×#4898 #11867865

Order 1152.

988 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#909C211yesmaximal, characteristic, complemented
2D3×#908C211yesmaximal, characteristic
3C2×D3×#204C211yesmaximal, characteristic, complemented
4D3×#901C211yesmaximal, characteristic, complemented
5#10592597C211yesmaximal, characteristic, complemented
6C3×#4898C211yesmaximal, characteristic, complemented
7C3×D3×#108C211yesmaximal, characteristic, complemented
8D3×#824C211yesmaximal, characteristic, complemented
9D3×#823C211yesmaximal, characteristic, complemented
10#10590990C211yesmaximal, characteristic, complemented
11#10590989C211yesmaximal, characteristic, complemented
12#10590986C211yesmaximal, characteristic, complemented
13#10590985C211yesmaximal, characteristic, complemented
14#10590931C211yesmaximal, characteristic, complemented
15#10590928C211yesmaximal, characteristic, complemented
16D3×#471—31nomaximal
17C2×#4898—31nomaximal
18D3×#235C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21#64118C2211yescharacteristic, complemented
22#64117C2211yescharacteristic
23C2×#3744C2211yescharacteristic, complemented
24#64110C2211yescharacteristic, complemented
25C3×#909C2211yescharacteristic, complemented
26C3×#908C2211yescharacteristic
27C3×D3×M16C2211yescharacteristic
28C3×D3×M16C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic, complemented
30C3×#901C2211yescharacteristic, complemented
31C2×C3×D3×C8C2211yescharacteristic
32#63833C2211yescharacteristic, complemented
33C2×#3717C2211yescharacteristic, complemented
34#63831C2211yescharacteristic, complemented
35#63830C2211yescharacteristic
36C2×#3716C2211yescharacteristic, complemented
37#63825C2211yescharacteristic
38#63817C2211yescharacteristic, complemented
39#63814C2211yescharacteristic, complemented
40D3×#208C2211yescharacteristic
41#63804—21no—
42#63803—21no—
43#63801—21no—
44#63800—21no—
45D3×Dic12—21no—
46#63795—21no—
47#63794—21no—
48D3×D24—21no—
49D3×#204—21no—
50D3×#204—21no—
51D3×#204—21no—
52D3×#204—21no—
53D3×#204—21no—
54D3×#204—21no—
55D3×ΓL(1,𝔽25)—21no—
56D32×C8—21no—
57C32×#108C2211yescharacteristic, complemented
58#63651C2211yescharacteristic, complemented
59#63650C2211yescharacteristic, complemented
60C3×#824C2211yescharacteristic, complemented
61C3×#823C2211yescharacteristic, complemented
62C3×#822C2211yescharacteristic, complemented
63C3×#822C2211yescharacteristic, complemented
64C3×#819C2211yescharacteristic, complemented
65#63561C2211yescharacteristic, complemented
66#63560C2211yescharacteristic, complemented
67#63559C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69D3×#137—31no—
70D3×AGL(1,ℤ/8)—31no—
71C2×D3×SD16—31no—
72D3×#131—31no—
73C2×#909—31no—
74C2×#908—31no—
75C22×#204—31no—
76C2×#901—31no—
77C3×#471—31no—
78C2×C3×#108—31no—
79#5203—31no—
80#5200—31no—
81#5177—31no—
82#5141—31no—
83C2×#824—31no—
84C2×#823—31no—
85#4898—31no—
86#4898—31no—
87#4898—31no—
88#4898—31no—
89#4898—31no—
90#4898—31no—
91#4898—31no—
92#4898—31no—
93#4898—61no—
94#4898D311yescharacteristic, direct product factor
95D3×#108D311yescharacteristic, complemented
96#4754—31no—
97D3×#101—31no—
98#4748—31no—
99D3×#100—31no—
100C22×D32—21no—
101#3828C2311yescharacteristic
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×#634C2311yescharacteristic
104C3×#235C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108D3×#67—21no—
109C2×#627—21no—
110C2×#626—21no—
111#3804—21no—
112C2×D3×Dic3—21no—
113D3×D12—21no—
114D3×D12—21no—
115D3×D12—21no—
116D3×D12—21no—
117D3×D12D411yescharacteristic
118C4×D32—21no—
119#3799D411yescharacteristic
120#3798—21no—
121#3795D411yescharacteristic
122D3×Dic6—21no—
123D3×Dic6—21no—
124D3×Dic6—21no—
125D3×Dic6—21no—
126D3×Dic6D411yescharacteristic
127C32×M16C2311yescharacteristic
128C32×M16C2311yescharacteristic
129C2×C32×C8C2311yescharacteristic
130#3748C2311yescharacteristic
131#3746—21no—
132#3745—21no—
133#3744—21no—
134#3744—21no—
135#3744—21no—
136#3744—21no—
137#3743—21no—
138C8×C3⋊D3—21no—
139C3×#208C2311yescharacteristic
140C3×#208C2311yescharacteristic
141C3×#208C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×Dic12—21no—
144C3×D24—21no—
145C3×#204—21no—
146C3×#204—21no—
147C3×#204—21no—
148C3×#204—21no—
149C3×ΓL(1,𝔽25)—21no—
150C3×ΓL(1,𝔽25)—21no—
151C3×ΓL(1,𝔽25)—21no—
152C3×D3×C8—21no—
153C3×D3×C8—21no—
154C3×D3×C8—21no—
155C3×D3×C8D411yescharacteristic
156C3×D3×C8D411yescharacteristic
157C3×D3×C8D411yescharacteristic
158C3×D3×C8D411yescharacteristic
159#3719—21no—
160#3719—21no—
161#3717—21no—
162#3717—21no—
163#3717—21no—
164#3717—21no—
165#3716—21no—
166#3716—21no—
167#3716—21no—
168#3716—21no—
169#3714—21no—
170#3714—21no—
171#3712—21no—
172#3711—21no—
173#3711—21no—
174#3710—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177C2×#471—91noSylow
178D3×#41—31no—
179C2×D3×Q8—31no—
180C2×D3×D4—31no—
181C2×#235—31no—
182C22×D12—31no—
183C22×Dic6—31no—
184C3×#137—31no—
185C3×AGL(1,ℤ/8)—31no—
186C2×C3×SD16—31no—
187C3×#131—31no—
188C2×C3×M16—31no—
189C2×C3×M16—31no—
190C22×C3×C8—31no—
191#951—31no—
192#949—31no—
193#948—31no—
194#942—31no—
195C2×#215—31no—
196C2×#214—31no—
197#932—31no—
198C2×#208—31no—
199#918—61no—
200D3×Q16—61no—
201#915—61no—
202#914—61no—
203D3×SD16—61no—
204D3×SD16—61no—
205D3×SD16—61no—
206D3×SD16—61no—
207D3×SD16—61no—
208D3×SD16—61no—
209#911—61no—
210D3×D8—61no—
211#909—31no—
212#909—31no—
213#909—31no—
214#909—31no—
215#909—61no—
216#909—61no—
217#909—61no—
218#909C2×D311yescharacteristic, complemented
219#908—31no—
220#908—31no—
221#908—31no—
222#908—31no—
223#908—61no—
224#908—61no—
225#908—61no—
226#908C2×D311yescharacteristic
227#907—31no—
228#907—61no—
229D3×M16—31no—
230D3×M16—61no—
231D3×M16C2×D311yescharacteristic
232D3×M16C2×D311yescharacteristic
233C2×Dic12—61no—
234C2×D24—61no—
235C2×#204—31no—
236C2×#204—31no—
237C2×#204—31no—
238C2×#204—31no—
239C2×#204—61no—
240C2×#204—61no—
241C2×#204—61no—
242C2×#204—61no—
243C2×#204—61no—
244C2×#204—61no—
245C2×#204—61no—
246C2×#204C2×D311yescharacteristic, complemented
247#901—31no—
248#901—31no—
249#901—31no—
250#901—31no—
251#901—61no—
252#901—61no—
253#901—61no—
254#901—61no—
255#901C2×D311yescharacteristic, complemented
256C2×ΓL(1,𝔽25)—61no—
257C2×D3×C8—61no—
258C2×D3×C8—61no—
259C2×D3×C8C2×D311yescharacteristic
260C3×#108—21no—
261C3×#108—31no—
262C3×#108—31no—
263C3×#108—31no—
264C3×#108C2×D311yescharacteristic, complemented
265C3×#108C2×D311yescharacteristic, complemented
266C3×#101—31no—
267C3×#100—31no—
268#836—31no—
269#833—31no—
270#824—31no—
271#824—31no—
272#824—31no—
273#824—31no—
274#824—31no—
275#824—61no—
276#824C2×D311yescharacteristic, complemented
277#823—31no—
278#823—31no—
279#823—31no—
280#823—31no—
281#823—31no—
282#823—61no—
283#823C2×D311yescharacteristic, complemented
284#822C2×D311yescharacteristic, complemented
285#822C2×D311yescharacteristic, complemented
286#819C2×D311yescharacteristic, complemented
287C22×C3⋊D3—21no—
288C22×C3×D3—21no—
289C22×C3×D3#4111yescharacteristic
290C2×D32—21no—
291C2×D32—41no—
292C2×D32—41no—
293C2×D32—82no—
294C2×C32×C4C2411yescharacteristic
295#638—21no—
296C2×C3⋊Dic3—21no—
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)—21no—
299C4⋊(C3⋊D3)C2×D411yescharacteristic
300C4×C3⋊D3—21no—
301#634—21no—
302#634—21no—
303#634C2×D411yescharacteristic
304C3×#67—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3#4111yescharacteristic
307C3×D12—21no—
308C3×D12—21no—
309C3×D12C2×D411yescharacteristic
310C3×C4×D3—21no—
311C3×C4×D3C2×D411yescharacteristic
312C3×C4×D3C2×D411yescharacteristic
313C3×C4×D3C2×D411yescharacteristic
314C3×C4×D3C2×D411yescharacteristic
315C3×Dic6—21no—
316C3×Dic6—21no—
317C3×Dic6C2×D411yescharacteristic
318#627—21no—
319#627—41no—
320#627—41no—
321#626—21no—
322#626—21no—
323#626—41no—
324#626—41no—
325#625—21no—
326#624—21no—
327D3×Dic3—21no—
328D3×Dic3—21no—
329D3×Dic3—41no—
330D3×Dic3—41no—
331C32×C8—21no—
332C32×C8—21no—
333C32×C8C2×D411yescharacteristic
334C32×C8C2×D411yescharacteristic
335C3⋊(C3⋊C8)—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C3×C3⋊C8—21no—
339C3×C3⋊C8C2×D411yescharacteristic
340C3×C3⋊C8C2×D411yescharacteristic
341C2×#137—91no—
342C2×AGL(1,ℤ/8)—91no—
343C22×SD16—91no—
344C2×#131—91no—
345#471—31no—
346#471—91no—
347#471—91no—
348#471—91no—
349#471—91no—
350#471—91no—
351#471—91no—
352#471—91no—
353C2×#108—31no—
354C2×#101—91no—
355C2×#100—91no—
356C23×D3—61no—
357C23×D3—61no—
358C3×#41—31no—
359C2×C3×Q8—31no—
360C2×C3×D4—31no—
361C22×C3×C4—31no—
362C2×#67—61no—
363C2×#67—61no—
364C22×Dic3—61no—
365#239—31no—
366D3×Q8—31no—
367D3×Q8—61no—
368D3×Q8—61no—
369D3×Q8—61no—
370D3×Q8—61no—
371#237—31no—
372#237—61no—
373D3×D4—31no—
374D3×D4—61no—
375D3×D4—61no—
376D3×D4—61no—
377D3×D4—61no—
378D3×D4—61no—
379#235—31no—
380#235—31no—
381#235—31no—
382#235—31no—
383#235—61no—
384#235—61no—
385#235—61no—
386#235—61no—
387#235C22×D311yescharacteristic
388C2×D12—31no—
389C2×D12—31no—
390C2×D12—31no—
391C2×D12—61no—
392C2×D12—61no—
393C2×D12—61no—
394C2×D12—61no—
395C2×D12—61no—
396C2×D12—61no—
397C2×D12C22×D311yescharacteristic
398C2×C4×D3—61no—
399C2×C4×D3—61no—
400C2×C4×D3—61no—
401C2×C4×D3C22×D311yescharacteristic
402C2×Dic6—31no—
403C2×Dic6—31no—
404C2×Dic6—31no—
405C2×Dic6—61no—
406C2×Dic6—61no—
407C2×Dic6—61no—
408C2×Dic6—61no—
409C2×Dic6—61no—
410C2×Dic6—61no—
411C2×Dic6—61no—
412C2×Dic6C22×D311yescharacteristic
413C3×Q16—61no—
414C3×SD16—61no—
415C3×SD16—61no—
416C3×SD16—61no—
417C3×SD16—61no—
418C3×D8—61no—
419C3×M16—21no—
420C3×M16—21no—
421C3×M16—31no—
422C3×M16—31no—
423C3×M16—31no—
424C3×M16—61no—
425C3×M16—61no—
426C3×M16—61no—
427C3×M16C22×D311yescharacteristic
428C3×M16C22×D311yescharacteristic
429C3×M16C22×D311yescharacteristic
430C3×M16C22×D311yescharacteristic
431C2×C3×C8—21no—
432C2×C3×C8—31no—
433C2×C3×C8—31no—
434C2×C3×C8—31no—
435C2×C3×C8—31no—
436C2×C3×C8—31no—
437C2×C3×C8—61no—
438C2×C3×C8—61no—
439C2×C3×C8—61no—
440C2×C3×C8C22×D311yescharacteristic
441C2×C3×C8C22×D311yescharacteristic
442#216—61no—
443#216—61no—
444#215—61no—
445#215—61no—
446#215—61no—
447#215—61no—
448#214—61no—
449#214—61no—
450#214—61no—
451#214—61no—
452#213—61no—
453#213—61no—
454#208—31no—
455#208—31no—
456#208—61no—
457#208—61no—
458#208—61no—
459#208C22×D311yescharacteristic
460#208C22×D311yescharacteristic
461#208C22×D311yescharacteristic
462C2×C3⋊C8—61no—
463C2×C3⋊C8—61no—
464C2×C3⋊C8C22×D311yescharacteristic
465Dic12—21no—
466Dic12—61no—
467Dic12—61no—
468Dic12—61no—
469Dic12—61no—
470Dic12—121no—
471D24—21no—
472D24—61no—
473D24—61no—
474D24—61no—
475D24—61no—
476D24—121no—
477#204—21no—
478#204—21no—
479#204—21no—
480#204—21no—
481#204—61no—
482#204—61no—
483#204—61no—
484#204—61no—
485#204—61no—
486#204—61no—
487#204—61no—
488#204—61no—
489#204—61no—
490#204—61no—
491#204—61no—
492#204—61no—
493#204—61no—
494#204—61no—
495#204—61no—
496#204—61no—
497#204—121no—
498#204—121no—
499#204—121no—
500#204—121no—
501ΓL(1,𝔽25)—21no—
502ΓL(1,𝔽25)—21no—
503ΓL(1,𝔽25)—21no—
504ΓL(1,𝔽25)—61no—
505ΓL(1,𝔽25)—61no—
506ΓL(1,𝔽25)—61no—
507ΓL(1,𝔽25)—61no—
508ΓL(1,𝔽25)—61no—
509ΓL(1,𝔽25)—61no—
510ΓL(1,𝔽25)—121no—
511D3×C8—21no—
512D3×C8—21no—
513D3×C8—21no—
514D3×C8—61no—
515D3×C8—61no—
516D3×C8—61no—
517D3×C8—61no—
518D3×C8—61no—
519D3×C8—61no—
520D3×C8—121no—
521D3×C8D1211yescharacteristic
522D3×C8D1211yescharacteristic
523D3×C8D1211yescharacteristic
524D3×C8D1211yescharacteristic
525C22×C32C2×#4111yescharacteristic
526C2×C3⋊D3—21no—
527C2×C3⋊D3—41no—
528C2×C3⋊D3—81no—
529C2×C3×D3—22no—
530C2×C3×D3—21no—
531C2×C3×D3—41no—
532C2×C3×D3—81no—
533C2×C3×D3#12111yescharacteristic
534C2×C3×D3#12111yescharacteristic
535D32—42no—
536D32—82no—
537D32—82no—
538C32×C4C22×D411yescharacteristic
539C32×C4C22×D411yescharacteristic
540C3⋊Dic3—21no—
541C3⋊Dic3—41no—
542C3×Dic3—21no—
543C3×Dic3—41no—
544C3×Dic3#12111yescharacteristic
545C3×Dic3#12111yescharacteristic
546C2×#41—91no—
547C22×Q8—91no—
548C22×D4—91no—
549#137—31no—
550#137—91no—
551#137—91no—
552#137—91no—
553#137—181no—
554#137—181no—
555AGL(1,ℤ/8)—31no—
556AGL(1,ℤ/8)—91no—
557AGL(1,ℤ/8)—91no—
558AGL(1,ℤ/8)—91no—
559AGL(1,ℤ/8)—181no—
560AGL(1,ℤ/8)—181no—
561C2×Q16—181no—
562C2×SD16—31no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×SD16—181no—
567C2×SD16—181no—
568C2×SD16—181no—
569C2×SD16—181no—
570C2×SD16—181no—
571C2×SD16—181no—
572C2×D8—181no—
573#131—31no—
574#131—91no—
575#131—91no—
576#131—91no—
577#131—181no—
578#131—181no—
579C2×M16—31no—
580C2×M16—31no—
581C2×M16—91no—
582C2×M16—181no—
583C22×C8—31no—
584C22×C8—181no—
585#108—31no—
586#108—31no—
587#108—31no—
588#108D3211yescharacteristic, complemented
589#101—31no—
590#101—91no—
591#101—91no—
592#101—91no—
593#100—31no—
594#100—91no—
595#100—91no—
596#100—91no—
597C23×C3—31no—
598C23×C3—61no—
599C22×D3—21no—
600C22×D3—61no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—121no—
605C22×D3—121no—
606C22×D3—121no—
607C22×D3—121no—
608C22×D3—121no—
609C22×D3—242no—
610C22×D3—242no—
611C22×D3#23911yescharacteristic
612C3×Q8—31no—
613C3×Q8—61no—
614C3×Q8—61no—
615C3×D4—31no—
616C3×D4—61no—
617C3×D4—61no—
618C3×D4—61no—
619C2×C3×C4—21no—
620C2×C3×C4—31no—
621C2×C3×C4—31no—
622C2×C3×C4—31no—
623C2×C3×C4—31no—
624C2×C3×C4—31no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4C23×D311yescharacteristic
628C2×C3×C4C23×D311yescharacteristic
629#67—21no—
630#67—61no—
631#67—61no—
632#67—61no—
633#67—61no—
634#67—61no—
635#67—61no—
636#67—121no—
637#67—121no—
638#67—121no—
639C2×Dic3—21no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—61no—
644C2×Dic3—121no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3#23911yescharacteristic
648D12—21no—
649D12—21no—
650D12—31no—
651D12—31no—
652D12—61no—
653D12—61no—
654D12—61no—
655D12—61no—
656D12—61no—
657D12—61no—
658D12—61no—
659D12—121no—
660D12—121no—
661D12—121no—
662D12—121no—
663D12D3×D411yescharacteristic
664C4×D3—21no—
665C4×D3—61no—
666C4×D3—61no—
667C4×D3—61no—
668C4×D3—61no—
669C4×D3—61no—
670C4×D3—61no—
671C4×D3—121no—
672C4×D3—121no—
673C4×D3—121no—
674C4×D3C2×D1211yescharacteristic
675C4×D3C2×D1211yescharacteristic
676C4×D3D3×D411yescharacteristic
677C4×D3D3×D411yescharacteristic
678Dic6—21no—
679Dic6—21no—
680Dic6—31no—
681Dic6—31no—
682Dic6—61no—
683Dic6—61no—
684Dic6—61no—
685Dic6—61no—
686Dic6—61no—
687Dic6—61no—
688Dic6—61no—
689Dic6—121no—
690Dic6—121no—
691Dic6—121no—
692Dic6—121no—
693Dic6—121no—
694Dic6—121no—
695Dic6D3×D411yescharacteristic
696C3×C8—21no—
697C3×C8—21no—
698C3×C8—21no—
699C3×C8—21no—
700C3×C8—21no—
701C3×C8—21no—
702C3×C8—31no—
703C3×C8—31no—
704C3×C8—41no—
705C3×C8—41no—
706C3×C8—61no—
707C3×C8—61no—
708C3×C8—61no—
709C3×C8C2×D1211yescharacteristic
710C3×C8C2×D1211yescharacteristic
711C3×C8D3×D411yescharacteristic
712C3×C8D3×D411yescharacteristic
713C3⋊C8—21no—
714C3⋊C8—21no—
715C3⋊C8—21no—
716C3⋊C8—61no—
717C3⋊C8—61no—
718C3⋊C8—121no—
719C3⋊C8C2×D1211yescharacteristic
720C3⋊C8C2×D1211yescharacteristic
721C2×C32—21no—
722C2×C32C2×#12111yescharacteristic
723C3⋊D3—41no—
724C3⋊D3—81no—
725C3×D3—21no—
726C3×D3—41no—
727C3×D3—81no—
728C3×D3#47112yescomplemented
729C24—181no—
730#41—31no—
731#41—91no—
732#41—91no—
733#41—91no—
734#41—181no—
735#41—181no—
736C2×Q8—31no—
737C2×Q8—91no—
738C2×Q8—91no—
739C2×Q8—181no—
740C2×Q8—181no—
741C2×Q8—181no—
742C2×Q8—181no—
743C2×Q8—181no—
744C2×D4—31no—
745C2×D4—91no—
746C2×D4—91no—
747C2×D4—181no—
748C2×D4—181no—
749C2×D4—181no—
750C2×D4—181no—
751C2×D4—181no—
752C2×D4—181no—
753C22×C4—31no—
754C22×C4—181no—
755C22×C4—181no—
756Q16—61no—
757Q16—181no—
758Q16—181no—
759Q16—181no—
760SD16—61no—
761SD16—61no—
762SD16—61no—
763SD16—61no—
764SD16—181no—
765SD16—181no—
766SD16—181no—
767SD16—181no—
768SD16—181no—
769SD16—181no—
770SD16—181no—
771SD16—181no—
772SD16—181no—
773SD16—181no—
774SD16—181no—
775SD16—181no—
776D8—61no—
777D8—181no—
778D8—181no—
779D8—181no—
780M16—31no—
781M16—31no—
782M16—31no—
783M16—61no—
784M16—61no—
785M16—61no—
786M16—91no—
787M16—181no—
788M16—181no—
789M16—181no—
790M16—181no—
791M16C2×D3211yescharacteristic
792M16C2×D3211yescharacteristic
793C2×C8—31no—
794C2×C8—31no—
795C2×C8—31no—
796C2×C8—31no—
797C2×C8—31no—
798C2×C8—61no—
799C2×C8—61no—
800C2×C8—61no—
801C2×C8—181no—
802C2×C8—181no—
803C2×C8—181no—
804C2×C8—181no—
805C2×C8C2×D3211yescharacteristic
806C22×C3—21no—
807C22×C3—31no—
808C22×C3—31no—
809C22×C3—62no—
810C22×C3—61no—
811C22×C3—121no—
812C22×C3—241no—
813C22×C3C2×#23911yescharacteristic
814C22×C3D3×#4111yescharacteristic
815C2×D3—22no—
816C2×D3—21no—
817C2×D3—41no—
818C2×D3—61no—
819C2×D3—61no—
820C2×D3—81no—
821C2×D3—121no—
822C2×D3—122no—
823C2×D3—122no—
824C2×D3—121no—
825C2×D3—121no—
826C2×D3—241no—
827C2×D3—242no—
828C2×D3—242no—
829C2×D3—242no—
830C2×D3—242no—
831C2×D3—241no—
832C2×D3—241no—
833C2×D3—481no—
834C2×D3#89511yescharacteristic
835C2×D3#89511yescharacteristic
836C3×C4—21no—
837C3×C4—21no—
838C3×C4—31no—
839C3×C4—31no—
840C3×C4—61no—
841C3×C4—121no—
842C3×C4C22×D1211yescharacteristic
843C3×C4C2×D3×D411yescharacteristic
844C3×C4C2×D3×D411yescharacteristic
845C3×C4C2×D3×D411yescharacteristic
846Dic3—21no—
847Dic3—41no—
848Dic3—61no—
849Dic3—61no—
850Dic3—121no—
851Dic3—121no—
852Dic3—121no—
853Dic3—241no—
854Dic3#89511yescharacteristic
855Dic3#89511yescharacteristic
856C32C2×#47111yescharacteristic, complemented, Sylow
857C23—31no—
858C23—61no—
859C23—181no—
860C23—181no—
861C23—361no—
862C23—361no—
863C23—722no—
864Q8—31no—
865Q8—61no—
866Q8—61no—
867Q8—91no—
868Q8—181no—
869Q8—181no—
870Q8—181no—
871Q8—361no—
872Q8—361no—
873D4—31no—
874D4—61no—
875D4—61no—
876D4—61no—
877D4—91no—
878D4—181no—
879D4—181no—
880D4—181no—
881D4—181no—
882D4—181no—
883D4—181no—
884D4—361no—
885D4—361no—
886C2×C4—31no—
887C2×C4—31no—
888C2×C4—31no—
889C2×C4—31no—
890C2×C4—31no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—181no—
894C2×C4—181no—
895C2×C4—181no—
896C2×C4—181no—
897C2×C4—181no—
898C2×C4—361no—
899C2×C4—361no—
900C2×C4C22×D3211yescharacteristic
901C8—21no—
902C8—21no—
903C8—31no—
904C8—31no—
905C8—61no—
906C8—61no—
907C8—61no—
908C8—181no—
909C8D3×D1211yescharacteristic
910C8D3×D1211yescharacteristic
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—32no—
915C2×C3—41no—
916C2×C3—61no—
917C2×C3—121no—
918C2×C3—241no—
919C2×C3C2×#89511yescharacteristic
920C2×C3D3×#12111yescharacteristic
921D3—21no—
922D3—41no—
923D3—81no—
924D3—121no—
925D3—121no—
926D3—241no—
927D3—241no—
928D3—241no—
929D3—481no—
930D3#489812yesdirect product factor
931C22—31no—
932C22—31no—
933C22—62no—
934C22—61no—
935C22—121no—
936C22—181no—
937C22—241no—
938C22—362no—
939C22—361no—
940C22—721no—
941C22—722no—
942C22—722no—
943C22D3×#23911yescharacteristic
944C4—31no—
945C4—31no—
946C4—61no—
947C4—121no—
948C4—181no—
949C4—361no—
950C4C2×D3×D1211yescharacteristic
951C4D32×D411yescharacteristic
952C3—21no—
953C3C2×#489811yescharacteristic, complemented
954C3D3×#47111yescharacteristic, complemented
955C2—21no—
956C2—32no—
957C2—61no—
958C2—121no—
959C2—241no—
960C2—361no—
961C2—721no—
962C2D3×#89511yescharacteristic
subgroupG/H
centerC2D3×#895
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#108C22
socleC2×C32C2×#121
prime radicalD3×#908C2
hypercenter#108D32
hypocenterC32C2×#471
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
1. D3×#909C2semidirect
3. C2×D3×#204C2semidirect
4. D3×#901C2semidirect
5. #10592597C2semidirect
6. C3×#4898C2semidirect
7. C3×D3×#108C2semidirect
8. D3×#824C2semidirect
9. D3×#823C2semidirect
10. #10590990C2semidirect
11. #10590989C2semidirect
12. #10590986C2semidirect
13. #10590985C2semidirect
14. #10590931C2semidirect
15. #10590928C2semidirect
21. #64118C22semidirect
23. C2×#3744C22semidirect
24. #64110C22semidirect
25. C3×#909C22semidirect
29. C2×C3×#204C22semidirect
30. C3×#901C22semidirect
32. #63833C22semidirect
33. C2×#3717C22semidirect
34. #63831C22semidirect
36. C2×#3716C22semidirect
38. #63817C22semidirect
39. #63814C22semidirect
57. C32×#108C22semidirect
58. #63651C22semidirect
59. #63650C22semidirect
60. C3×#824C22semidirect
61. C3×#823C22semidirect
62. C3×#822C22semidirect
63. C3×#822C22semidirect
64. C3×#819C22semidirect
65. #63561C22semidirect
66. #63560C22semidirect
67. #63559C22semidirect
68. #63558C22semidirect
94. #4898D3direct (N × H)
95. D3×#108D3semidirect
218. #909C2×D3semidirect
246. C2×#204C2×D3semidirect
255. #901C2×D3semidirect
264. C3×#108C2×D3semidirect
265. C3×#108C2×D3semidirect
276. #824C2×D3semidirect
283. #823C2×D3semidirect
284. #822C2×D3semidirect
285. #822C2×D3semidirect
286. #819C2×D3semidirect
588. #108D32semidirect
728. C3×D3#471semidirect
856. C32C2×#471semidirect
930. D3#4898direct (N × H)
953. C3C2×#4898semidirect
954. C3D3×#471semidirect

Maximal subgroups

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

subgroupindex
D3×#9092
D3×#9082
C2×D3×#2042
D3×#9012
#105925972
C3×#48982
C3×D3×#1082
D3×#8242
D3×#8232
#105909902
#105909892
#105909862
#105909852
#105909312
#105909282
D3×#4713
C2×#48983