Finite Group Databasebeta

← #13155433

Subgroups — #13155433

Order 1728.

908 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#3828C211yesmaximal, characteristic
2C3×#63855C211yesmaximal, characteristic, complemented
3C3×D3×#208C211yesmaximal, characteristic, complemented
4#11722077C211yesmaximal, characteristic, complemented
5#11722048C211yesmaximal, characteristic, complemented
6#11722047C211yesmaximal, characteristic, complemented
7C3×#63570C211yesmaximal, characteristic, complemented
8#10591113—31nomaximal
9#10591005—31nomaximal
10#10590392—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
22C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
23C3×#3748C2211yescharacteristic, complemented
24C32×C4×Dic3C2211yescharacteristic, complemented
25C32×#208C2211yescharacteristic, complemented
26C3×Dic3⋊Dic3—21no—
27C3×(C2×D3)⋊Dic3—21no—
28C3×#3711—21no—
29C3×D3×C3⋊C8—21no—
30C2×#3828—31no—
31D3×#235—31no—
32D3×#235—31no—
33D3×#235—61no—
34C3×#926—31no—
35C2×C3×#208—31no—
36C3×D3×M16—31no—
37C3×#872—31no—
38#63855D311yescharacteristic, 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, complemented
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
59C4×C3⋊(C3⋊D3)—21no—
60#6308C2×C411yescharacteristic
61C3×#638—21no—
62C2×C3×C3⋊Dic3—21no—
63C3×C4⋊(C3⋊D3)C2×C411yescharacteristic
64C3×C4×C3⋊D3—21no—
65C3×#634C2×C411yescharacteristic
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×C3⋊(C3⋊C8)—21no—
80C32×C3⋊C8—21no—
81#5139—91no—
82#5005—91no—
83#4821—91no—
84C22×C32×C4—31no—
85C2×#638—61no—
86#3828—31no—
87#3828—31no—
88#3828—31no—
89#3828—31no—
90#3828—31no—
91#3828—61no—
92#3828—61no—
93#3828—61no—
94#3828—61no—
95#3828—61no—
96#3828—121no—
97#3828C2×D311yescharacteristic
98C2×C4⋊(C3⋊D3)—31no—
99C2×C4×C3⋊D3—61no—
100C2×#634—31no—
101C3×#235—31no—
102C3×#235—31no—
103C3×#235—61no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2×D311yescharacteristic
106C2×C3×C4×D3C2×D311yescharacteristic
107D3×#67—62no—
108D3×#67—61no—
109D3×#67—61no—
110#3804—62no—
111#3804—61no—
112#3804—61no—
113D3×D12—31no—
114D3×D12—31no—
115D3×D12—61no—
116C4×D32—62no—
117C4×D32—61no—
118C4×D32—61no—
119#3799—31no—
120#3799—31no—
121#3799—61no—
122#3798—62no—
123#3798—61no—
124#3798—61no—
125#3795—31no—
126#3795—31no—
127#3795—61no—
128D3×Dic6—31no—
129D3×Dic6—31no—
130D3×Dic6—61no—
131C32×M16—31no—
132C32×C42—31no—
133C4×C3⋊Dic3C2×D311yescharacteristic, complemented
134#3748C2×D311yescharacteristic, complemented
135C3×#217—61no—
136C3×(C2×D3)⋊C4—61no—
137C3×C4⋊Dic3—61no—
138C3×Dic3⋊C4—61no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3—31no—
141C3×C4×Dic3—31no—
142C3×C4×Dic3—61no—
143C3×C4×Dic3C2×D311yescharacteristic, complemented
144C3×C4×Dic3C2×D311yescharacteristic, complemented
145C3×#208—21no—
146C3×#208—31no—
147C3×#208—31no—
148C3×#208—61no—
149C3×#208—61no—
150C3×#208C2×D311yescharacteristic, complemented
151C3×#208C2×D311yescharacteristic, complemented
152C2×C3×C3⋊C8—61no—
153C3×ΓL(1,𝔽25)—61no—
154C3×D3×C8—61no—
155Dic3⋊Dic3—21no—
156(C2×D3)⋊Dic3—21no—
157#3711—21no—
158D3×C3⋊C8—21no—
159C22×C33C2×D411yescharacteristic
160C2×C3⋊(C3⋊D3)—21no—
161C2×C3×C3⋊D3—21no—
162C2×C32×D3—41no—
163C2×C32×D3C22⋊C411yescharacteristic
164C2×C32×D3C22⋊C411yescharacteristic
165D3×C3⋊D3—42no—
166C33×C4C22×C411yescharacteristic
167C33×C4C2×D411yescharacteristic
168C3⋊(C3⋊Dic3)—21no—
169C3×C3⋊Dic3—21no—
170C3×C3⋊Dic3—41no—
171C32×Dic3—41no—
172C32×Dic3C22⋊C411yescharacteristic
173C32×Dic3C22⋊C411yescharacteristic
174D3×#41—91no—
175C2×#235—91no—
176C2×#235—91no—
177C2×#235—181no—
178C2×C3×M16—91no—
179C3×#117—91no—
180#926—31no—
181C2×#208—31no—
182D3×M16—31no—
183#872—31no—
184C3×#104—91no—
185#837—91no—
186#825—31no—
187#825—91no—
188#825—91no—
189#825—91no—
190#825—91no—
191#825—181no—
192#805—31no—
193#805—91no—
194#805—91no—
195#805—91no—
196#805—91no—
197#805—181no—
198C23×C32—31no—
199C22×C3⋊D3—61no—
200C22×C3×D3—21no—
201C22×C3×D3D1211yescharacteristic
202C22×C3×D3#6711yescharacteristic
203C2×D32—62no—
204C2×D32—61no—
205C2×D32—61no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—31no—
210C2×C32×C4—31no—
211C2×C32×C4—31no—
212C2×C32×C4—31no—
213C2×C32×C4—31no—
214C2×C32×C4—41no—
215C2×C32×C4—61no—
216C2×C32×C4C22×D311yescharacteristic
217C2×C32×C4C22×D311yescharacteristic
218C2×C32×C4C22×D311yescharacteristic
219#638—21no—
220#638—61no—
221#638—61no—
222#638—61no—
223#638—62no—
224#638—61no—
225#638—61no—
226#638—121no—
227#638—121no—
228#638—122no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—61no—
231C4⋊(C3⋊D3)—31no—
232C4⋊(C3⋊D3)—31no—
233C4⋊(C3⋊D3)—31no—
234C4⋊(C3⋊D3)—61no—
235C4⋊(C3⋊D3)—61no—
236C4⋊(C3⋊D3)—61no—
237C4⋊(C3⋊D3)—61no—
238C4⋊(C3⋊D3)—121no—
239C4⋊(C3⋊D3)C4×D311yescharacteristic
240C4×C3⋊D3—21no—
241C4×C3⋊D3—61no—
242C4×C3⋊D3—61no—
243C4×C3⋊D3—61no—
244C4×C3⋊D3—62no—
245C4×C3⋊D3—61no—
246C4×C3⋊D3—61no—
247C4×C3⋊D3—121no—
248C4×C3⋊D3—121no—
249C4×C3⋊D3—122no—
250#634—31no—
251#634—31no—
252#634—31no—
253#634—61no—
254#634—61no—
255#634—61no—
256#634—61no—
257#634—121no—
258#634C4×D311yescharacteristic
259C3×#67—62no—
260C3×#67—61no—
261C3×#67—61no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—41no—
266C2×C3×Dic3—61no—
267C2×C3×Dic3—61no—
268C2×C3×Dic3—121no—
269C2×C3×Dic3D1211yescharacteristic
270C2×C3×Dic3#6711yescharacteristic
271C3×D12—31no—
272C3×D12—31no—
273C3×D12—61no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—62no—
279C3×C4×D3—61no—
280C3×C4×D3—61no—
281C3×C4×D3C4×D311yescharacteristic
282C3×C4×D3C4×D311yescharacteristic
283C3×C4×D3C4×D311yescharacteristic
284C3×C4×D3C4×D311yescharacteristic
285C3×C4×D3D1211yescharacteristic
286C3×C4×D3D1211yescharacteristic
287C3×C4×D3#6711yescharacteristic
288C3×C4×D3#6711yescharacteristic
289C3×Dic6—31no—
290C3×Dic6—31no—
291C3×Dic6—61no—
292#627—62no—
293#627—61no—
294#627—61no—
295#626—62no—
296#626—62no—
297#626—61no—
298#626—61no—
299#626—61no—
300#626—61no—
301#625—62no—
302#625—61no—
303#625—61no—
304#624—62no—
305#624—61no—
306#624—61no—
307D3×Dic3—62no—
308D3×Dic3—62no—
309D3×Dic3—61no—
310D3×Dic3—61no—
311D3×Dic3—61no—
312D3×Dic3—61no—
313C32×C8—61no—
314C3⋊(C3⋊C8)—21no—
315C3×C3⋊C8—21no—
316C3×C3⋊C8—21no—
317C3×C3⋊C8—41no—
318C3×C3⋊C8—61no—
319C3×C3⋊C8—61no—
320C3×C3⋊C8—121no—
321#421—271noSylow
322C2×C33—21no—
323C2×C33C2×C22⋊C411yescharacteristic
324C3⋊(C3⋊D3)—41no—
325C3×C3⋊D3—41no—
326C32×D3—21no—
327C32×D3—21no—
328C3×#41—91no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C2×#67—181no—
333C2×#67—181no—
334C2×#67—182no—
335#239—91no—
336D3×Q8—91no—
337#237—91no—
338#237—181no—
339D3×D4—91no—
340D3×D4—181no—
341#235—31no—
342#235—31no—
343#235—61no—
344#235—91no—
345#235—91no—
346#235—91no—
347#235—91no—
348#235—91no—
349#235—91no—
350#235—91no—
351#235—181no—
352#235—181no—
353#235—181no—
354#235—181no—
355#235—181no—
356#235—181no—
357#235—181no—
358#235—182no—
359#235—181no—
360#235—181no—
361#235—182no—
362#235—181no—
363#235—361no—
364C2×D12—91no—
365C2×D12—91no—
366C2×D12—181no—
367C2×C4×D3—181no—
368C2×C4×D3—181no—
369C2×C4×D3—182no—
370C2×C4×D3—181no—
371C2×C4×D3D3211yescharacteristic
372C2×Dic6—91no—
373C2×Dic6—91no—
374C2×Dic6—181no—
375C3×M16—31no—
376C3×M16—31no—
377C3×M16—61no—
378C3×M16—91no—
379C3×M16—181no—
380C2×C3×C8—181no—
381C3×C4⋊C4—181no—
382C3×C22⋊C4—181no—
383C3×C42—31no—
384C3×C42—31no—
385C3×C42—61no—
386C3×C42—91no—
387#217—61no—
388(C2×D3)⋊C4—61no—
389C4⋊Dic3—61no—
390Dic3⋊C4—61no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—61no—
394C4×Dic3D3211yescharacteristic, complemented
395#208—31no—
396#208—31no—
397#208—61no—
398#208—61no—
399#208D3211yescharacteristic, complemented
400C2×C3⋊C8—61no—
401ΓL(1,𝔽25)—61no—
402D3×C8—61no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—31no—
407C22×C32—31no—
408C22×C32—41no—
409C22×C32—121no—
410C22×C32C2×D1211yescharacteristic
411C22×C32D3×D411yescharacteristic
412C22×C32C2×#6711yescharacteristic
413C2×C3⋊D3—21no—
414C2×C3⋊D3—61no—
415C2×C3⋊D3—62no—
416C2×C3⋊D3—61no—
417C2×C3⋊D3—61no—
418C2×C3⋊D3—121no—
419C2×C3⋊D3—121no—
420C2×C3⋊D3—122no—
421C2×C3⋊D3—122no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—42no—
427C2×C3×D3—62no—
428C2×C3×D3—61no—
429C2×C3×D3—61no—
430C2×C3×D3(C2×D3)⋊C411yescharacteristic
431C2×C3×D3(C2×D3)⋊C411yescharacteristic
432C2×C3×D3(C2×D3)⋊C411yescharacteristic
433C2×C3×D3(C2×D3)⋊C411yescharacteristic
434D32—124no—
435D32—122no—
436D32—122no—
437C32×C4—21no—
438C32×C4—21no—
439C32×C4—21no—
440C32×C4—21no—
441C32×C4—21no—
442C32×C4—21no—
443C32×C4—31no—
444C32×C4—31no—
445C32×C4—41no—
446C32×C4—41no—
447C32×C4—121no—
448C32×C4C2×C4×D311yescharacteristic
449C32×C4C2×C4×D311yescharacteristic
450C32×C4C2×C4×D311yescharacteristic
451C32×C4C2×D1211yescharacteristic
452C32×C4D3×D411yescharacteristic
453C32×C4C2×#6711yescharacteristic
454C3⋊Dic3—21no—
455C3⋊Dic3—41no—
456C3⋊Dic3—61no—
457C3⋊Dic3—62no—
458C3⋊Dic3—61no—
459C3⋊Dic3—61no—
460C3⋊Dic3—121no—
461C3⋊Dic3—121no—
462C3⋊Dic3—122no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3—42no—
468C3×Dic3—62no—
469C3×Dic3—61no—
470C3×Dic3—61no—
471C3×Dic3—121no—
472C3×Dic3—121no—
473C3×Dic3—122no—
474C3×Dic3(C2×D3)⋊C411yescharacteristic
475C3×Dic3(C2×D3)⋊C411yescharacteristic
476C3×Dic3(C2×D3)⋊C411yescharacteristic
477C3×Dic3(C2×D3)⋊C411yescharacteristic
478C2×#41—271no—
479C2×M16—91no—
480#117—91no—
481#104—91no—
482#104—271no—
483#104—271no—
484#104—271no—
485C33#42111yescharacteristic, complemented, Sylow
486C23×C3—31no—
487C23×C3—31no—
488C23×C3—61no—
489C22×D3—181no—
490C22×D3—181no—
491C22×D3—182no—
492C22×D3—181no—
493C22×D3#62611yescharacteristic
494C3×Q8—91no—
495C3×D4—91no—
496C3×D4—181no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
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—41no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—121no—
519C2×C3×C4—181no—
520C2×C3×C4—181no—
521C2×C3×C4C2×D3211yescharacteristic
522C2×C3×C4C2×D3211yescharacteristic
523C2×C3×C4C2×D3211yescharacteristic
524#67—62no—
525#67—61no—
526#67—61no—
527#67—181no—
528#67—181no—
529#67—182no—
530#67—181no—
531#67—181no—
532#67—182no—
533#67—182no—
534#67—181no—
535#67—181no—
536#67—181no—
537#67—181no—
538#67—181no—
539#67—361no—
540#67—361no—
541#67—362no—
542C2×Dic3—21no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—121no—
546C2×Dic3—181no—
547C2×Dic3—181no—
548C2×Dic3—182no—
549C2×Dic3—181no—
550C2×Dic3#62611yescharacteristic
551D12—31no—
552D12—31no—
553D12—61no—
554D12—91no—
555D12—91no—
556D12—91no—
557D12—181no—
558D12—181no—
559D12—181no—
560D12—181no—
561D12—181no—
562D12—182no—
563D12—181no—
564D12—361no—
565C4×D3—62no—
566C4×D3—61no—
567C4×D3—61no—
568C4×D3—181no—
569C4×D3—181no—
570C4×D3—182no—
571C4×D3—182no—
572C4×D3—181no—
573C4×D3—181no—
574C4×D3—182no—
575C4×D3—181no—
576C4×D3—181no—
577C4×D3—181no—
578C4×D3—181no—
579C4×D3—181no—
580C4×D3—361no—
581C4×D3—361no—
582C4×D3—362no—
583C4×D3#62411yescharacteristic
584C4×D3#62411yescharacteristic
585C4×D3#62611yescharacteristic
586C4×D3#62611yescharacteristic
587Dic6—31no—
588Dic6—31no—
589Dic6—61no—
590Dic6—91no—
591Dic6—91no—
592Dic6—91no—
593Dic6—181no—
594Dic6—181no—
595Dic6—181no—
596Dic6—181no—
597Dic6—181no—
598Dic6—182no—
599Dic6—181no—
600Dic6—361no—
601C3×C8—61no—
602C3×C8—61no—
603C3×C8—121no—
604C3×C8—181no—
605C3⋊C8—21no—
606C3⋊C8—61no—
607C3⋊C8—61no—
608C3⋊C8—121no—
609C2×C32—21no—
610C2×C32—21no—
611C2×C32—21no—
612C2×C32—21no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—41no—
616C2×C32—41no—
617C2×C32—41no—
618C2×C32—41no—
619C2×C32—61no—
620C2×C32—61no—
621C2×C32—81no—
622C2×C32D3×C22⋊C411yescharacteristic
623C2×C32C2×(C2×D3)⋊C411yescharacteristic
624C2×C32C2×(C2×D3)⋊C411yescharacteristic
625C3⋊D3—41no—
626C3⋊D3—121no—
627C3⋊D3—122no—
628C3⋊D3—121no—
629C3⋊D3—121no—
630C3⋊D3—241no—
631C3⋊D3—241no—
632C3⋊D3—242no—
633C3×D3—22no—
634C3×D3—21no—
635C3×D3—21no—
636C3×D3—21no—
637C3×D3—21no—
638C3×D3—41no—
639C3×D3—122no—
640C3×D3—121no—
641C3×D3—121no—
642#41—91no—
643#41—271no—
644#41—271no—
645#41—271no—
646#41—541no—
647#41—541no—
648C2×Q8—271no—
649C2×D4—271no—
650C2×D4—541no—
651C22×C4—31no—
652C22×C4—541no—
653M16—31no—
654M16—91no—
655M16—181no—
656C2×C8—181no—
657C4⋊C4—181no—
658C22⋊C4—181no—
659C42—31no—
660C42—91no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—31no—
665C22×C3—31no—
666C22×C3—31no—
667C22×C3—31no—
668C22×C3—41no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—122no—
674C22×C3—181no—
675C22×C3D3×D1211yescharacteristic
676C22×C3C2×#62611yescharacteristic
677C22×C3D3×#6711yescharacteristic
678C2×D3—41no—
679C2×D3—62no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—182no—
683C2×D3—181no—
684C2×D3—181no—
685C2×D3—181no—
686C2×D3—361no—
687C2×D3—361no—
688C2×D3—362no—
689C2×D3—362no—
690C2×D3—364no—
691C2×D3—362no—
692C2×D3—362no—
693C2×D3#372211yescharacteristic
694C2×D3#372211yescharacteristic
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—31no—
702C3×C4—31no—
703C3×C4—31no—
704C3×C4—31no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—61no—
708C3×C4—61no—
709C3×C4—121no—
710C3×C4—121no—
711C3×C4—122no—
712C3×C4—181no—
713C3×C4—361no—
714C3×C4C4×D3211yescharacteristic
715C3×C4C4×D3211yescharacteristic
716C3×C4D3×D1211yescharacteristic
717C3×C4C2×#62411yescharacteristic
718C3×C4C2×#62611yescharacteristic
719C3×C4D3×#6711yescharacteristic
720Dic3—41no—
721Dic3—62no—
722Dic3—61no—
723Dic3—61no—
724Dic3—121no—
725Dic3—121no—
726Dic3—122no—
727Dic3—182no—
728Dic3—181no—
729Dic3—181no—
730Dic3—181no—
731Dic3—361no—
732Dic3—361no—
733Dic3—362no—
734Dic3#372211yescharacteristic
735Dic3#372211yescharacteristic
736C32—21no—
737C32—21no—
738C32—21no—
739C32—41no—
740C32#482111yescharacteristic, complemented
741C32#500511yescharacteristic, complemented
742C32#513911yescharacteristic, complemented
743C23—31no—
744C23—541no—
745Q8—91no—
746Q8—271no—
747Q8—541no—
748D4—91no—
749D4—181no—
750D4—271no—
751D4—541no—
752D4—541no—
753D4—541no—
754D4—541no—
755C2×C4—31no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—31no—
759C2×C4—31no—
760C2×C4—61no—
761C2×C4—181no—
762C2×C4—181no—
763C2×C4—541no—
764C2×C4—541no—
765C2×C4—541no—
766C2×C4—541no—
767C2×C4D3311yescharacteristic
768C8—61no—
769C8—181no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—41no—
777C2×C3—41no—
778C2×C3—41no—
779C2×C3—41no—
780C2×C3—62no—
781C2×C3—61no—
782C2×C3—61no—
783C2×C3—61no—
784C2×C3—61no—
785C2×C3—81no—
786C2×C3—121no—
787C2×C3—361no—
788C2×C3D3×(C2×D3)⋊C411yescharacteristic
789C2×C3D3×(C2×D3)⋊C411yescharacteristic
790C2×C3C2×#372211yescharacteristic
791D3—21no—
792D3—21no—
793D3—122no—
794D3—121no—
795D3—121no—
796D3—362no—
797D3—361no—
798D3—361no—
799D3—361no—
800D3—721no—
801D3—721no—
802D3—722no—
803C22—31no—
804C22—31no—
805C22—121no—
806C22—181no—
807C22—541no—
808C22—1082no—
809C22D3×#62611yescharacteristic
810C4—31no—
811C4—31no—
812C4—121no—
813C4—181no—
814C4—361no—
815C4—541no—
816C4D3×#62411yescharacteristic
817C4D3×#62611yescharacteristic
818C3—21no—
819C3—21no—
820C3—21no—
821C3—41no—
822C3#1059039211yescharacteristic, complemented
823C3#1059100511yescharacteristic, complemented
824C3#1059111311yescharacteristic, complemented
825C2—21no—
826C2—61no—
827C2—61no—
828C2—361no—
829C2—1081no—
830C2D3×#372211yescharacteristic
subgroupG/H
centerC4D3×#626
commutatorC33×C4C22×C4
Frattini, hypercenterC2×C4D33
Fitting, cosocleC2×C33×C4C23
socleC2×C33C2×C22⋊C4
prime radicalD3×#3828C2
hypocenterC33#421
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×#63855C2semidirect
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
22. C3×C4×C3⋊Dic3C22semidirect
23. C3×#3748C22semidirect
24. C32×C4×Dic3C22semidirect
25. C32×#208C22semidirect
38. #63855D3semidirect
39. D3×#208D3semidirect
51. #63570D3semidirect
133. C4×C3⋊Dic3C2×D3semidirect
134. #3748C2×D3semidirect
143. C3×C4×Dic3C2×D3semidirect
144. C3×C4×Dic3C2×D3semidirect
150. C3×#208C2×D3semidirect
151. C3×#208C2×D3semidirect
394. C4×Dic3D32semidirect
399. #208D32semidirect
485. C33#421semidirect
740. C32#4821semidirect
741. C32#5005semidirect
742. C32#5139semidirect
822. C3#10590392semidirect
823. C3#10591005semidirect
824. C3#10591113semidirect

Maximal subgroups

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

subgroupindex
D3×#38282
C3×#638552
C3×D3×#2082
#117220772
#117220482
#117220472
C3×#635702
#105911133
#105910053
#105903923