Finite Group Databasebeta

← D3×#63570 #13155423

Subgroups — D3×#63570 #13155423

Order 1728.

972 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#3828C211yesmaximal, characteristic
2C3×C4×D3×Dic3C211yesmaximal, characteristic, complemented
3C3×D3×#208C211yesmaximal, characteristic, complemented
4#11722077C211yesmaximal, characteristic, complemented
5#11722048C211yesmaximal, characteristic, complemented
6#11722047C211yesmaximal, characteristic, complemented
7C3×#63570C211yesmaximal, characteristic, complemented
8C2×#63570—31nomaximal
9D3×#825—31nomaximal
10D3×#805—31nomaximal
11#89076C2211yescharacteristic
12C3×#3828C2211yescharacteristic
13C2×C32×C4×D3C2211yescharacteristic
14D3×#638—21no—
15#89031—21no—
16D3×C4⋊(C3⋊D3)C411yescharacteristic, complemented
17C4×D3×C3⋊D3—21no—
18#89022C411yescharacteristic, complemented
19#89021C411yescharacteristic, complemented
20#89020—21no—
21D3×#634C411yescharacteristic, complemented
22C2×C3×D3×Dic3—21no—
23C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
24C3×#3748C2211yescharacteristic, complemented
25C32×C4×Dic3C2211yescharacteristic, complemented
26C32×#208C2211yescharacteristic, complemented
27C3×Dic32—21no—
28C3×#3711—21no—
29C3×D3×C3⋊C8—21no—
30C2×#3828—31no—
31D3×#235—31no—
32D3×#235—31no—
33D3×#235—61no—
34C2×C3×C4×Dic3—31no—
35C2×C3×#208—31no—
36C3×D3×M16—31no—
37C3×C42×D3—31no—
38C4×D3×Dic3D311yescharacteristic, complemented
39D3×#208D311yescharacteristic, complemented
40#63652—31no—
41#63632—31no—
42C3×#825—31no—
43C3×#805—31no—
44#63570—31no—
45#63570—31no—
46#63570—31no—
47#63570—31no—
48#63570—31no—
49#63570—61no—
50#63570—61no—
51#63570D311yescharacteristic, direct product factor
52#63569—31no—
53#63568—31no—
54C22×C32×D3D411yescharacteristic
55C2×D3×C3⋊D3—21no—
56C2×C33×C4C2311yescharacteristic
57#6312—21no—
58C4⋊(C3⋊(C3⋊D3))C2×C411yescharacteristic, complemented
59C4×C3⋊(C3⋊D3)—21no—
60#6308C2×C411yescharacteristic, complemented
61C3×#638—21no—
62C2×C3×C3⋊Dic3—21no—
63C3×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
64C3×C4×C3⋊D3—21no—
65C3×#634C2×C411yescharacteristic, complemented
66C2×C32×Dic3—21no—
67C2×C32×Dic3D411yescharacteristic
68C32×C4×D3C2×C411yescharacteristic
69C32×C4×D3C2×C411yescharacteristic
70C32×C4×D3D411yescharacteristic
71C32×C4×D3D411yescharacteristic
72#6293—21no—
73#6292—21no—
74#6291—21no—
75#6290—21no—
76#6289—21no—
77Dic3×C3⋊D3—21no—
78D3×C3⋊Dic3—21no—
79C3×D3×Dic3—24no—
80C3×C3⋊(C3⋊C8)—21no—
81C32×C3⋊C8—21no—
82C2×#825—91no—
83C2×#805—91no—
84D3×#104—91no—
85C22×C32×C4—31no—
86C2×#638—61no—
87#3828—31no—
88#3828—31no—
89#3828—31no—
90#3828—31no—
91#3828—31no—
92#3828—61no—
93#3828—61no—
94#3828—61no—
95#3828—61no—
96#3828—61no—
97#3828—121no—
98#3828C2×D311yescharacteristic
99C2×C4⋊(C3⋊D3)—31no—
100C2×C4×C3⋊D3—61no—
101C2×#634—31no—
102C22×C3×Dic3—61no—
103C3×#235—31no—
104C3×#235—31no—
105C3×#235—61no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—61no—
108C2×C3×C4×D3C2×D311yescharacteristic
109C2×C3×C4×D3C2×D311yescharacteristic
110D3×#67—62no—
111D3×#67—61no—
112D3×#67—61no—
113#3804—62no—
114#3804—61no—
115#3804—61no—
116C2×D3×Dic3—21no—
117D3×D12—31no—
118D3×D12—31no—
119D3×D12—61no—
120C4×D32—62no—
121C4×D32—61no—
122C4×D32—61no—
123#3799—31no—
124#3799—31no—
125#3799—61no—
126#3798—62no—
127#3798—61no—
128#3798—61no—
129#3795—31no—
130#3795—31no—
131#3795—61no—
132D3×Dic6—31no—
133D3×Dic6—31no—
134D3×Dic6—61no—
135C32×M16—31no—
136C32×C42—31no—
137C4×C3⋊Dic3C2×D311yescharacteristic, complemented
138#3748C2×D311yescharacteristic, complemented
139C3×C4×Dic3—21no—
140C3×C4×Dic3—31no—
141C3×C4×Dic3—31no—
142C3×C4×Dic3—61no—
143C3×C4×Dic3—61no—
144C3×C4×Dic3—61no—
145C3×C4×Dic3C2×D311yescharacteristic, complemented
146C3×C4×Dic3C2×D311yescharacteristic, complemented
147C3×#208—21no—
148C3×#208—31no—
149C3×#208—31no—
150C3×#208—61no—
151C3×#208—61no—
152C3×#208C2×D311yescharacteristic, complemented
153C3×#208C2×D311yescharacteristic, complemented
154C2×C3×C3⋊C8—61no—
155C3×ΓL(1,𝔽25)—61no—
156C3×D3×C8—61no—
157Dic32—21no—
158#3711—21no—
159D3×C3⋊C8—21no—
160C22×C33C2×D411yescharacteristic
161C2×C3⋊(C3⋊D3)—21no—
162C2×C3×C3⋊D3—21no—
163C2×C32×D3—22no—
164C2×C32×D3C22⋊C411yescharacteristic
165C2×C32×D3C22⋊C411yescharacteristic
166D3×C3⋊D3—42no—
167C33×C4C22×C411yescharacteristic
168C33×C4C2×D411yescharacteristic
169C3⋊(C3⋊Dic3)—21no—
170C3×C3⋊Dic3—22no—
171C3×C3⋊Dic3—21no—
172C32×Dic3—22no—
173C32×Dic3C22⋊C411yescharacteristic
174C32×Dic3C22⋊C411yescharacteristic
175D3×#41—91no—
176C2×#235—91no—
177C2×#235—91no—
178C2×#235—181no—
179C2×C3×M16—91no—
180C2×C3×C42—91no—
181C2×C4×Dic3—31no—
182C2×#208—31no—
183D3×M16—31no—
184C42×D3—31no—
185C3×#104—91no—
186#837—91no—
187#825—31no—
188#825—91no—
189#825—91no—
190#825—91no—
191#825—91no—
192#825—181no—
193#805—31no—
194#805—91no—
195#805—91no—
196#805—91no—
197#805—91no—
198#805—181no—
199C23×C32—31no—
200C22×C3⋊D3—61no—
201C22×C3×D3—21no—
202C22×C3×D3D1211yescharacteristic
203C22×C3×D3#6711yescharacteristic
204C2×D32—62no—
205C2×D32—61no—
206C2×D32—61no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—31no—
211C2×C32×C4—31no—
212C2×C32×C4—31no—
213C2×C32×C4—31no—
214C2×C32×C4—31no—
215C2×C32×C4—41no—
216C2×C32×C4—61no—
217C2×C32×C4C22×D311yescharacteristic
218C2×C32×C4C22×D311yescharacteristic
219C2×C32×C4C22×D311yescharacteristic
220#638—21no—
221#638—61no—
222#638—61no—
223#638—61no—
224#638—62no—
225#638—61no—
226#638—61no—
227#638—121no—
228#638—121no—
229#638—122no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—61no—
232C4⋊(C3⋊D3)—31no—
233C4⋊(C3⋊D3)—31no—
234C4⋊(C3⋊D3)—31no—
235C4⋊(C3⋊D3)—61no—
236C4⋊(C3⋊D3)—61no—
237C4⋊(C3⋊D3)—61no—
238C4⋊(C3⋊D3)—61no—
239C4⋊(C3⋊D3)—121no—
240C4⋊(C3⋊D3)C4×D311yescharacteristic, complemented
241C4×C3⋊D3—21no—
242C4×C3⋊D3—61no—
243C4×C3⋊D3—61no—
244C4×C3⋊D3—61no—
245C4×C3⋊D3—62no—
246C4×C3⋊D3—61no—
247C4×C3⋊D3—61no—
248C4×C3⋊D3—121no—
249C4×C3⋊D3—121no—
250C4×C3⋊D3—122no—
251#634—31no—
252#634—31no—
253#634—31no—
254#634—61no—
255#634—61no—
256#634—61no—
257#634—61no—
258#634—121no—
259#634C4×D311yescharacteristic, complemented
260C3×#67—62no—
261C3×#67—61no—
262C3×#67—61no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—41no—
267C2×C3×Dic3—64no—
268C2×C3×Dic3—61no—
269C2×C3×Dic3—61no—
270C2×C3×Dic3—121no—
271C2×C3×Dic3D1211yescharacteristic
272C2×C3×Dic3#6711yescharacteristic
273C3×D12—31no—
274C3×D12—31no—
275C3×D12—61no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×C4×D3—21no—
280C3×C4×D3—62no—
281C3×C4×D3—64no—
282C3×C4×D3—61no—
283C3×C4×D3—61no—
284C3×C4×D3C4×D311yescharacteristic
285C3×C4×D3C4×D311yescharacteristic
286C3×C4×D3C4×D311yescharacteristic
287C3×C4×D3C4×D311yescharacteristic
288C3×C4×D3D1211yescharacteristic
289C3×C4×D3D1211yescharacteristic
290C3×C4×D3#6711yescharacteristic
291C3×C4×D3#6711yescharacteristic
292C3×Dic6—31no—
293C3×Dic6—31no—
294C3×Dic6—61no—
295#627—62no—
296#627—61no—
297#627—61no—
298#626—62no—
299#626—62no—
300#626—61no—
301#626—61no—
302#626—61no—
303#626—61no—
304#625—62no—
305#625—61no—
306#625—61no—
307#624—62no—
308#624—61no—
309#624—61no—
310D3×Dic3—24no—
311D3×Dic3—62no—
312D3×Dic3—62no—
313D3×Dic3—61no—
314D3×Dic3—61no—
315D3×Dic3—61no—
316D3×Dic3—61no—
317C32×C8—61no—
318C3⋊(C3⋊C8)—21no—
319C3×C3⋊C8—21no—
320C3×C3⋊C8—21no—
321C3×C3⋊C8—41no—
322C3×C3⋊C8—61no—
323C3×C3⋊C8—61no—
324C3×C3⋊C8—121no—
325C2×#104—271noSylow
326C2×C33—21no—
327C2×C33C2×C22⋊C411yescharacteristic
328C3⋊(C3⋊D3)—41no—
329C3×C3⋊D3—41no—
330C32×D3—21no—
331C32×D3#10412yescomplemented
332C3×#41—91no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—61no—
336C22×C3×C4—181no—
337C2×#67—181no—
338C2×#67—181no—
339C2×#67—182no—
340C22×Dic3—61no—
341#239—91no—
342D3×Q8—91no—
343#237—91no—
344#237—181no—
345D3×D4—91no—
346D3×D4—181no—
347#235—31no—
348#235—31no—
349#235—61no—
350#235—91no—
351#235—91no—
352#235—91no—
353#235—91no—
354#235—91no—
355#235—91no—
356#235—91no—
357#235—181no—
358#235—181no—
359#235—181no—
360#235—181no—
361#235—181no—
362#235—181no—
363#235—181no—
364#235—182no—
365#235—181no—
366#235—181no—
367#235—182no—
368#235—181no—
369#235—361no—
370C2×D12—91no—
371C2×D12—91no—
372C2×D12—181no—
373C2×C4×D3—61no—
374C2×C4×D3—181no—
375C2×C4×D3—181no—
376C2×C4×D3—182no—
377C2×C4×D3—181no—
378C2×C4×D3D3211yescharacteristic
379C2×Dic6—91no—
380C2×Dic6—91no—
381C2×Dic6—181no—
382C3×M16—31no—
383C3×M16—31no—
384C3×M16—61no—
385C3×M16—91no—
386C3×M16—181no—
387C2×C3×C8—181no—
388C3×C42—31no—
389C3×C42—31no—
390C3×C42—61no—
391C3×C42—91no—
392C3×C42—181no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3D3211yescharacteristic, complemented
399#208—31no—
400#208—31no—
401#208—61no—
402#208—61no—
403#208D3211yescharacteristic, complemented
404C2×C3⋊C8—61no—
405ΓL(1,𝔽25)—61no—
406D3×C8—61no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—31no—
411C22×C32—31no—
412C22×C32—41no—
413C22×C32—62no—
414C22×C32C2×D1211yescharacteristic
415C22×C32D3×D411yescharacteristic
416C22×C32C2×#6711yescharacteristic
417C2×C3⋊D3—21no—
418C2×C3⋊D3—61no—
419C2×C3⋊D3—62no—
420C2×C3⋊D3—61no—
421C2×C3⋊D3—61no—
422C2×C3⋊D3—121no—
423C2×C3⋊D3—121no—
424C2×C3⋊D3—122no—
425C2×C3⋊D3—122no—
426C2×C3×D3—22no—
427C2×C3×D3—22no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—42no—
431C2×C3×D3—62no—
432C2×C3×D3—61no—
433C2×C3×D3—61no—
434C2×C3×D3(C2×D3)⋊C411yescharacteristic
435C2×C3×D3(C2×D3)⋊C411yescharacteristic
436C2×C3×D3(C2×D3)⋊C411yescharacteristic
437C2×C3×D3(C2×D3)⋊C411yescharacteristic
438D32—124no—
439D32—122no—
440D32—122no—
441C32×C4—21no—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—31no—
448C32×C4—31no—
449C32×C4—41no—
450C32×C4—41no—
451C32×C4—62no—
452C32×C4C2×C4×D311yescharacteristic
453C32×C4C2×C4×D311yescharacteristic
454C32×C4C2×C4×D311yescharacteristic
455C32×C4C2×D1211yescharacteristic
456C32×C4D3×D411yescharacteristic
457C32×C4C2×#6711yescharacteristic
458C3⋊Dic3—21no—
459C3⋊Dic3—22no—
460C3⋊Dic3—61no—
461C3⋊Dic3—62no—
462C3⋊Dic3—61no—
463C3⋊Dic3—61no—
464C3⋊Dic3—121no—
465C3⋊Dic3—121no—
466C3⋊Dic3—122no—
467C3×Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—42no—
472C3×Dic3—62no—
473C3×Dic3—62no—
474C3×Dic3—62no—
475C3×Dic3—61no—
476C3×Dic3—61no—
477C3×Dic3—122no—
478C3×Dic3(C2×D3)⋊C411yescharacteristic
479C3×Dic3(C2×D3)⋊C411yescharacteristic
480C3×Dic3(C2×D3)⋊C411yescharacteristic
481C3×Dic3(C2×D3)⋊C411yescharacteristic
482C2×#41—271no—
483C2×M16—91no—
484C2×C42—91no—
485#104—91no—
486#104—271no—
487#104—271no—
488#104—271no—
489C33C2×#10411yescharacteristic, complemented, Sylow
490C23×C3—31no—
491C23×C3—31no—
492C23×C3—61no—
493C22×D3—181no—
494C22×D3—181no—
495C22×D3—182no—
496C22×D3—181no—
497C22×D3#62611yescharacteristic
498C3×Q8—91no—
499C3×D4—91no—
500C3×D4—181no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—41no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—121no—
523C2×C3×C4—184no—
524C2×C3×C4—181no—
525C2×C3×C4—181no—
526C2×C3×C4C2×D3211yescharacteristic
527C2×C3×C4C2×D3211yescharacteristic
528C2×C3×C4C2×D3211yescharacteristic
529#67—62no—
530#67—61no—
531#67—61no—
532#67—181no—
533#67—181no—
534#67—182no—
535#67—181no—
536#67—181no—
537#67—182no—
538#67—182no—
539#67—181no—
540#67—181no—
541#67—181no—
542#67—181no—
543#67—181no—
544#67—361no—
545#67—361no—
546#67—362no—
547C2×Dic3—21no—
548C2×Dic3—64no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—121no—
552C2×Dic3—181no—
553C2×Dic3—181no—
554C2×Dic3—182no—
555C2×Dic3—181no—
556C2×Dic3#62611yescharacteristic
557D12—31no—
558D12—31no—
559D12—61no—
560D12—91no—
561D12—91no—
562D12—91no—
563D12—181no—
564D12—181no—
565D12—181no—
566D12—181no—
567D12—181no—
568D12—182no—
569D12—181no—
570D12—361no—
571C4×D3—62no—
572C4×D3—64no—
573C4×D3—61no—
574C4×D3—61no—
575C4×D3—181no—
576C4×D3—181no—
577C4×D3—182no—
578C4×D3—182no—
579C4×D3—181no—
580C4×D3—181no—
581C4×D3—182no—
582C4×D3—181no—
583C4×D3—181no—
584C4×D3—181no—
585C4×D3—181no—
586C4×D3—181no—
587C4×D3—361no—
588C4×D3—361no—
589C4×D3—362no—
590C4×D3#62411yescharacteristic
591C4×D3#62411yescharacteristic
592C4×D3#62611yescharacteristic
593C4×D3#62611yescharacteristic
594Dic6—31no—
595Dic6—31no—
596Dic6—61no—
597Dic6—91no—
598Dic6—91no—
599Dic6—91no—
600Dic6—181no—
601Dic6—181no—
602Dic6—181no—
603Dic6—181no—
604Dic6—181no—
605Dic6—182no—
606Dic6—181no—
607Dic6—361no—
608C3×C8—61no—
609C3×C8—61no—
610C3×C8—121no—
611C3×C8—181no—
612C3⋊C8—21no—
613C3⋊C8—61no—
614C3⋊C8—61no—
615C3⋊C8—121no—
616C2×C32—21no—
617C2×C32—21no—
618C2×C32—21no—
619C2×C32—21no—
620C2×C32—21no—
621C2×C32—21no—
622C2×C32—32no—
623C2×C32—41no—
624C2×C32—41no—
625C2×C32—41no—
626C2×C32—41no—
627C2×C32—61no—
628C2×C32—81no—
629C2×C32D3×C22⋊C411yescharacteristic
630C2×C32C2×(C2×D3)⋊C411yescharacteristic
631C2×C32C2×(C2×D3)⋊C411yescharacteristic
632C3⋊D3—41no—
633C3⋊D3—121no—
634C3⋊D3—122no—
635C3⋊D3—121no—
636C3⋊D3—121no—
637C3⋊D3—241no—
638C3⋊D3—241no—
639C3⋊D3—242no—
640C3×D3—21no—
641C3×D3—21no—
642C3×D3—22no—
643C3×D3—41no—
644C3×D3—122no—
645C3×D3—121no—
646C3×D3—121no—
647C3×D3#80512yescomplemented
648C3×D3#82512yescomplemented
649#41—91no—
650#41—271no—
651#41—271no—
652#41—271no—
653#41—541no—
654#41—541no—
655C2×Q8—271no—
656C2×D4—271no—
657C2×D4—541no—
658C22×C4—31no—
659C22×C4—181no—
660C22×C4—541no—
661M16—31no—
662M16—91no—
663M16—181no—
664C2×C8—181no—
665C42—31no—
666C42—91no—
667C42—181no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—31no—
672C22×C3—31no—
673C22×C3—31no—
674C22×C3—31no—
675C22×C3—41no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—62no—
679C22×C3—62no—
680C22×C3—122no—
681C22×C3—181no—
682C22×C3D3×D1211yescharacteristic
683C22×C3C2×#62611yescharacteristic
684C22×C3D3×#6711yescharacteristic
685C2×D3—22no—
686C2×D3—62no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—182no—
690C2×D3—181no—
691C2×D3—181no—
692C2×D3—181no—
693C2×D3—361no—
694C2×D3—361no—
695C2×D3—362no—
696C2×D3—362no—
697C2×D3—362no—
698C2×D3—364no—
699C2×D3—362no—
700C2×D3#372211yescharacteristic
701C2×D3#372211yescharacteristic
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—31no—
709C3×C4—31no—
710C3×C4—31no—
711C3×C4—31no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—61no—
715C3×C4—61no—
716C3×C4—62no—
717C3×C4—62no—
718C3×C4—122no—
719C3×C4—182no—
720C3×C4—181no—
721C3×C4C4×D3211yescharacteristic
722C3×C4C4×D3211yescharacteristic
723C3×C4D3×D1211yescharacteristic
724C3×C4C2×#62411yescharacteristic
725C3×C4C2×#62611yescharacteristic
726C3×C4D3×#6711yescharacteristic
727Dic3—22no—
728Dic3—62no—
729Dic3—62no—
730Dic3—62no—
731Dic3—61no—
732Dic3—61no—
733Dic3—122no—
734Dic3—182no—
735Dic3—181no—
736Dic3—181no—
737Dic3—181no—
738Dic3—361no—
739Dic3—361no—
740Dic3—362no—
741Dic3#372211yescharacteristic
742Dic3#372211yescharacteristic
743C32—21no—
744C32—21no—
745C32—21no—
746C32—41no—
747C32D3×#10411yescharacteristic, complemented
748C32C2×#80511yescharacteristic, complemented
749C32C2×#82511yescharacteristic, complemented
750C23—31no—
751C23—541no—
752Q8—91no—
753Q8—271no—
754Q8—541no—
755D4—91no—
756D4—181no—
757D4—271no—
758D4—541no—
759D4—541no—
760D4—541no—
761D4—541no—
762C2×C4—31no—
763C2×C4—31no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—31no—
767C2×C4—61no—
768C2×C4—184no—
769C2×C4—181no—
770C2×C4—181no—
771C2×C4—541no—
772C2×C4—541no—
773C2×C4—541no—
774C2×C4—541no—
775C2×C4D3311yescharacteristic
776C8—61no—
777C8—181no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—32no—
785C2×C3—32no—
786C2×C3—41no—
787C2×C3—41no—
788C2×C3—41no—
789C2×C3—41no—
790C2×C3—62no—
791C2×C3—61no—
792C2×C3—61no—
793C2×C3—81no—
794C2×C3—121no—
795C2×C3—361no—
796C2×C3D3×(C2×D3)⋊C411yescharacteristic
797C2×C3D3×(C2×D3)⋊C411yescharacteristic
798C2×C3C2×#372211yescharacteristic
799D3—21no—
800D3—122no—
801D3—121no—
802D3—121no—
803D3—362no—
804D3—361no—
805D3—361no—
806D3—361no—
807D3—721no—
808D3—721no—
809D3—722no—
810D3#6357012yesdirect product factor
811C22—31no—
812C22—31no—
813C22—62no—
814C22—181no—
815C22—541no—
816C22—1082no—
817C22D3×#62611yescharacteristic
818C4—31no—
819C4—31no—
820C4—62no—
821C4—182no—
822C4—181no—
823C4—541no—
824C4D3×#62411yescharacteristic
825C4D3×#62611yescharacteristic
826C3—21no—
827C3—21no—
828C3—21no—
829C3—41no—
830C3D3×#80511yescharacteristic, complemented
831C3D3×#82511yescharacteristic, complemented
832C3C2×#6357011yescharacteristic, complemented
833C2—21no—
834C2—32no—
835C2—61no—
836C2—361no—
837C2—1081no—
838C2D3×#372211yescharacteristic
subgroupG/H
centerC4D3×#626
commutatorC33×C4C22×C4
Frattini, hypercenterC2×C4D33
Fitting, cosocleC2×C33×C4C23
socleC2×C33C2×C22⋊C4
prime radicalD3×#3828C2
hypocenterC33C2×#104
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×D3×Dic3C2semidirect
3. C3×D3×#208C2semidirect
4. #11722077C2semidirect
5. #11722048C2semidirect
6. #11722047C2semidirect
7. C3×#63570C2semidirect
16. D3×C4⋊(C3⋊D3)C4semidirect
18. #89022C4semidirect
19. #89021C4semidirect
21. D3×#634C4semidirect
23. C3×C4×C3⋊Dic3C22semidirect
24. C3×#3748C22semidirect
25. C32×C4×Dic3C22semidirect
26. C32×#208C22semidirect
38. C4×D3×Dic3D3semidirect
39. D3×#208D3semidirect
51. #63570D3direct (N × H)
58. C4⋊(C3⋊(C3⋊D3))C2×C4semidirect
60. #6308C2×C4semidirect
63. C3×C4⋊(C3⋊D3)C2×C4semidirect
65. C3×#634C2×C4semidirect
137. C4×C3⋊Dic3C2×D3semidirect
138. #3748C2×D3semidirect
145. C3×C4×Dic3C2×D3semidirect
146. C3×C4×Dic3C2×D3semidirect
152. C3×#208C2×D3semidirect
153. C3×#208C2×D3semidirect
240. C4⋊(C3⋊D3)C4×D3semidirect
259. #634C4×D3semidirect
331. C32×D3#104semidirect
398. C4×Dic3D32semidirect
403. #208D32semidirect
489. C33C2×#104semidirect
647. C3×D3#805semidirect
648. C3×D3#825semidirect
747. C32D3×#104semidirect
748. C32C2×#805semidirect
749. C32C2×#825semidirect
810. D3#63570direct (N × H)
830. C3D3×#805semidirect
831. C3D3×#825semidirect
832. C3C2×#63570semidirect

Maximal subgroups

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

subgroupindex
D3×#38282
C3×C4×D3×Dic32
C3×D3×#2082
#117220772
#117220482
#117220472
C3×#635702
C2×#635703
D3×#8253
D3×#8053