Finite Group Databasebeta

← #10847393

Subgroups — #10847393

Order 768.

1194 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5622C211yesmaximal, characteristic, complemented
2C2×#5114C211yesmaximal, characteristic
3C2×#5048C211yesmaximal, characteristic
4#73999C211yesmaximal, characteristic
5C3×#1892C211yesmaximal, characteristic, complemented
6C2×#4550C211yesmaximal, characteristic, complemented
7#70282C211yesmaximal, characteristic, complemented
8#70246C211yesmaximal, characteristic, complemented
9#70240C211yesmaximal, characteristic, complemented
10#70238C211yesmaximal, characteristic, complemented
11#69514C211yesmaximal, characteristic, complemented
12#68909C211yesmaximal, characteristic, complemented
13#68907C211yesmaximal, characteristic, complemented
14#68898C211yesmaximal, characteristic, complemented
15#68827C211yesmaximal, characteristic, complemented
16#25497—31nomaximal, Sylow
17C23×C3×C8C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×Q8×Dic3C2211yescharacteristic
20C2×#944C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#924C2211yescharacteristic
24C22×C4×Dic3C2211yescharacteristic
25C23×C3⋊C8C2211yescharacteristic
26C22×#204C2211yescharacteristic
27#5622—24no—
28#5622—24no—
29C2×#889—21no—
30C2×#888C2211yescharacteristic
31C2×#887—21no—
32C2×#887C2211yescharacteristic
33C2×#886—21no—
34C2×#878—21no—
35C2×#877—21no—
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C3×#380C2211yescharacteristic
39C2×#835C2211yescharacteristic
40#5114—24no—
41C2×#821C2211yescharacteristic
42C2×#817C2211yescharacteristic
43C2×#816C2211yescharacteristic
44#5048—24no—
45#4988C2211yescharacteristic
46#4988C2211yescharacteristic
47#4984C2211yescharacteristic
48#4984C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#808C2211yescharacteristic
53#4958—21no—
54#4670—21no—
55#4670—21no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#533—31no—
65C2×#465—31no—
66C2×#465—31no—
67#2854—31no—
68#2058—31no—
69#2043—31no—
70#2023—31no—
71#2013—31no—
72#1892—31no—
73#1892D311yescharacteristic, complemented
74#1880—31no—
75#1880—31no—
76#1865—31no—
77#1865—31no—
78C2×#336—31no—
79C22×C3×Q8C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C23×Dic3D411yescharacteristic
83C23×Dic3D411yescharacteristic
84C22×D12C2311yescharacteristic
85C22×Dic6—21no—
86C22×Dic6C2311yescharacteristic
87C22×C3×C8—22no—
88C22×C3×C8—22no—
89C22×C3×C8—41no—
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×C22⋊Q8—22no—
93C3×C22⋊Q8D414yes—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×#217—21no—
101Q8×Dic3—22no—
102Q8×Dic3—22no—
103#944—22no—
104#944—22no—
105C2×#215—22no—
106C2×#215—22no—
107C2×#215—41no—
108#930—22no—
109#930—22no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×C4⋊Dic3—21no—
116C2×C4⋊Dic3—21no—
117C2×C4⋊Dic3—21no—
118C2×C4⋊Dic3C2311yescharacteristic
119C2×C4⋊Dic3C2311yescharacteristic
120#924—22no—
121#924D414yes—
122C2×Dic3⋊C4—21no—
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×C4×Dic3—22no—
128C2×C4×Dic3—22no—
129C2×C4×Dic3—21no—
130C2×C4×Dic3—21no—
131C2×C4×Dic3D411yescharacteristic
132C2×C4×Dic3D411yescharacteristic
133C2×C4×Dic3C2311yescharacteristic
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8—22no—
136C22×C3⋊C8—22no—
137C22×C3⋊C8—41no—
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C2×#204—22no—
141C2×#204—22no—
142C2×#204—41no—
143#889—28no—
144#888—22no—
145#888—22no—
146#887—28no—
147#887—22no—
148#887—22no—
149#886—44no—
150#878—28no—
151#877—28no—
152C3×#103—22no—
153C3×#103—41no—
154C3×#95—21no—
155#835—22no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158#821—22no—
159#817—22no—
160#816—22no—
161#810—22no—
162#810—41no—
163#809—22no—
164#808—22no—
165C22×SD16—31no—
166C22×SD16—31no—
167C23×C8—31no—
168C23×C8C2×D311yescharacteristic
169#533—64no—
170#533—64no—
171C2×C4⋊Q8—31no—
172C2×C4⋊Q8—31no—
173C2×#125—61no—
174C2×#123—61no—
175C2×C22⋊Q8—31no—
176C2×C22⋊Q8—61no—
177C2×C22⋊Q8C2×D311yescharacteristic
178C2×#121—31no—
179C2×C4×Q8—31no—
180C2×C4×Q8—31no—
181C2×C4×Q8—61no—
182C2×#117—61no—
183C22×C42—31no—
184#465—64no—
185#465—64no—
186C2×#106—31no—
187C2×#106—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#103C2×D311yescharacteristic
193C2×#103C2×D311yescharacteristic
194C2×#102—31no—
195C2×#102—31no—
196#390—31no—
197#390—31no—
198#389—31no—
199#389—31no—
200#388—61no—
201#388—61no—
202#386—61no—
203#380C2×D311yescharacteristic
204#340—31no—
205#340—31no—
206#340C2×D311yescharacteristic
207#340C2×D311yescharacteristic
208#336—31no—
209#336—31no—
210#336—31no—
211#336—31no—
212C24×C3C2×D411yescharacteristic
213C23×D3—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8C2×D412yes—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4C2×D412yes—
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2×D412yes—
231C22×C3×C4C2411yescharacteristic
232C2×#67—42no—
233C2×#67—42no—
234C2×#67—42no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—22no—
241C22×Dic3—21no—
242C22×Dic3—41no—
243C22×Dic3SD1614yescomplemented
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246C22×Dic3C2×D411yescharacteristic
247C22×Dic3C2×D411yescharacteristic
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×Dic6—21no—
255C2×Dic6—21no—
256C2×Dic6—21no—
257C2×Dic6—21no—
258C2×Dic6—24no—
259C2×Dic6—21no—
260C2×Dic6—42no—
261C2×Dic6—42no—
262C2×Dic6C2×D412yes—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—44no—
269C2×C3×C8#4112yes—
270C3×C4⋊C4—24no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4C2×D412yes—
277C3×C22⋊C4—24no—
278C3×C22⋊C4—42no—
279#217—24no—
280#215—44no—
281(C2×D3)⋊C4—42no—
282(C2×D3)⋊C4—42no—
283(C2×D3)⋊C4—42no—
284(C2×D3)⋊C4—42no—
285(C2×D3)⋊C4—42no—
286C4⋊Dic3—24no—
287C4⋊Dic3—21no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—42no—
291C4⋊Dic3—42no—
292C4⋊Dic3C2×D412yes—
293Dic3⋊C4—24no—
294Dic3⋊C4—24no—
295Dic3⋊C4—24no—
296Dic3⋊C4—24no—
297Dic3⋊C4—24no—
298C4×Dic3—24no—
299C4×Dic3—24no—
300C4×Dic3—22no—
301C4×Dic3—22no—
302C4×Dic3—21no—
303C4×Dic3—21no—
304C4×Dic3—21no—
305C4×Dic3—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—44no—
312C2×C3⋊C8#4112yes—
313#204—44no—
314C22×Q8—31no—
315C22×Q8—61no—
316C22×Q8C22×D311yescharacteristic
317C22×D4—31no—
318C22×D4—61no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4C22×D311yescharacteristic
322C2×SD16—62no—
323C2×SD16—62no—
324C2×SD16—62no—
325C2×SD16—62no—
326C2×SD16—121no—
327C2×SD16—121no—
328C22×C8—22no—
329C22×C8—22no—
330C22×C8—31no—
331C22×C8—31no—
332C22×C8—41no—
333C22×C8—62no—
334C22×C8—62no—
335C22×C8—121no—
336C22×C8C22×D311yescharacteristic
337C22×C8C22×D311yescharacteristic
338C4⋊Q8—62no—
339C4⋊Q8—62no—
340C4⋊Q8—62no—
341C4⋊Q8—62no—
342#125—68no—
343#123—124no—
344C22⋊Q8—22no—
345C22⋊Q8—34no—
346C22⋊Q8—68no—
347C22⋊Q8—62no—
348C22⋊Q8D1214yes—
349#121—62no—
350#121—62no—
351C4×Q8—62no—
352C4×Q8—68no—
353C4×Q8—62no—
354C4×Q8—62no—
355C4×Q8—62no—
356#117—68no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4C22×D311yescharacteristic
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C42—31no—
380C2×C42—31no—
381C2×C42—31no—
382C2×C42—31no—
383C2×C42—61no—
384C2×C42—61no—
385C2×C42—62no—
386C2×C42—62no—
387#106—62no—
388#106—62no—
389#103—22no—
390#103—41no—
391#103—62no—
392#103—62no—
393#103—62no—
394#103—121no—
395#102—62no—
396#102—62no—
397#95—21no—
398#95—61no—
399#95—61no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3#12012yes—
405C23×C3C2×SD1612yes—
406C23×C3#13712yes—
407C23×C3C22×D411yescharacteristic
408C22×D3—41no—
409C22×D3—41no—
410C22×D3—41no—
411C22×D3—41no—
412C22×D3—41no—
413C22×D3—41no—
414C22×D3—41no—
415C3×Q8—22no—
416C3×Q8—22no—
417C3×Q8—41no—
418C3×Q8—41no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4#12012yes—
438C2×C3×C4C22×D411yescharacteristic
439C2×C3×C4C22×D411yescharacteristic
440C2×C3×C4C2×#4111yescharacteristic
441C2×C3×C4C2×#4111yescharacteristic
442C2×C3×C4H(5,𝔽2)11yescharacteristic
443C2×C3×C42−1+411yescharacteristic
444#67—84no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—28no—
452C2×Dic3—21no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—44no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3C2×SD1612yes—
466C2×Dic3C2×SD1612yes—
467C2×Dic3#13512yes—
468D12—41no—
469D12—41no—
470D12—41no—
471D12—41no—
472Dic6—22no—
473Dic6—22no—
474Dic6—48no—
475Dic6—41no—
476Dic6—41no—
477C3×C8—22no—
478C3×C8—41no—
479C3⋊C8—22no—
480C3⋊C8—41no—
481C24—61no—
482C24D3×D411yescharacteristic
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—32no—
489C2×Q8—64no—
490C2×Q8—61no—
491C2×Q8—61no—
492C2×Q8—61no—
493C2×Q8—61no—
494C2×Q8—61no—
495C2×Q8—122no—
496C2×Q8—122no—
497C2×Q8C2×D1212yes—
498C2×D4—61no—
499C2×D4—61no—
500C2×D4—61no—
501C2×D4—61no—
502C2×D4—61no—
503C2×D4—61no—
504C2×D4—122no—
505C2×D4—122no—
506C2×D4—122no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—34no—
516C22×C4—31no—
517C22×C4—31no—
518C22×C4—31no—
519C22×C4—31no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—121no—
528C22×C4C2×D1212yes—
529C22×C4D3×D411yescharacteristic
530C22×C4D3×D412yes—
531C22×C4C23×D311yescharacteristic
532SD16—124no—
533SD16—124no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—32no—
540C2×C8—44no—
541C2×C8—61no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8—61no—
545C2×C8—61no—
546C2×C8—124no—
547C2×C8#23712yes—
548C4⋊C4—24no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—32no—
555C4⋊C4—64no—
556C4⋊C4—64no—
557C4⋊C4—64no—
558C4⋊C4—64no—
559C4⋊C4—64no—
560C4⋊C4—64no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—122no—
565C4⋊C4—122no—
566C4⋊C4C2×D1212yes—
567C22⋊C4—24no—
568C22⋊C4—42no—
569C22⋊C4—64no—
570C22⋊C4—122no—
571C22⋊C4—122no—
572C22⋊C4—122no—
573C22⋊C4—122no—
574C22⋊C4—122no—
575C42—64no—
576C42—64no—
577C42—62no—
578C42—62no—
579C42—61no—
580C42—61no—
581C42—61no—
582C42—61no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3#44814yes—
590C22×C3C2×#12011yescharacteristic
591C22×C3#53211yescharacteristic
592C22×C3#53711yescharacteristic
593C22×C3C22×SD1611yescharacteristic
594C22×C3C2×#13511yescharacteristic
595C22×C3C2×#13711yescharacteristic
596C22×C3#57511yescharacteristic
597C2×D3—81no—
598C2×D3—81no—
599C2×D3—81no—
600C2×D3—81no—
601C2×D3—81no—
602C2×D3—81no—
603C2×D3—81no—
604C3×C4—22no—
605C3×C4—42no—
606C3×C4—42no—
607C3×C4—81no—
608C3×C4—81no—
609C3×C4#54611yescharacteristic
610C3×C4#54611yescharacteristic
611C3×C4#54711yescharacteristic
612C3×C4#54711yescharacteristic
613Dic3—22no—
614Dic3—22no—
615Dic3—22no—
616Dic3—42no—
617Dic3—42no—
618Dic3—41no—
619Dic3—81no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—121no—
625C23—121no—
626C23—121no—
627C23—121no—
628C23—121no—
629C23—121no—
630C23—121no—
631C23#88212yes—
632C23D3×SD1612yes—
633C23#91812yes—
634C23C2×D3×D411yescharacteristic
635Q8—22no—
636Q8—22no—
637Q8—41no—
638Q8—41no—
639Q8—62no—
640Q8—62no—
641Q8—128no—
642Q8—121no—
643Q8—121no—
644D4—121no—
645D4—121no—
646D4—121no—
647D4—121no—
648D4—244no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—32no—
658C2×C4—32no—
659C2×C4—32no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—68no—
677C2×C4—61no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—124no—
683C2×C4—121no—
684C2×C4—121no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4#88212yes—
691C2×C4C22×D1211yescharacteristic
692C2×C4C2×D3×D411yescharacteristic
693C2×C4C2×#23711yescharacteristic
694C2×C4#100411yescharacteristic
695C2×C4D3×#4111yescharacteristic
696C2×C4#101011yescharacteristic
697C8—22no—
698C8—41no—
699C8—62no—
700C8—121no—
701C2×C3—24no—
702C2×C3#243011yescharacteristic
703C2×C3C2×#44811yescharacteristic
704C2×C3#300211yescharacteristic
705C2×C3#316711yescharacteristic
706C2×C3#318111yescharacteristic
707C2×C3#324611yescharacteristic
708C2×C3#324811yescharacteristic
709D3—161no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—241no—
717C22—241no—
718C22—241no—
719C22—241no—
720C22—241no—
721C22—241no—
722C22—241no—
723C22#480614yes—
724C22C2×#88211yescharacteristic
725C22#559611yescharacteristic
726C22#559711yescharacteristic
727C22C2×D3×SD1611yescharacteristic
728C22C2×#91811yescharacteristic
729C22D3×#13511yescharacteristic
730C22#576811yescharacteristic
731C4—22no—
732C4—42no—
733C4—42no—
734C4—62no—
735C4—62no—
736C4—62no—
737C4—81no—
738C4—81no—
739C4—122no—
740C4—121no—
741C4—122no—
742C4—241no—
743C4#555411yescharacteristic
744C4#555511yescharacteristic
745C4#559111yescharacteristic
746C4#565511yescharacteristic
747C3#2549711yescharacteristic, complemented, Sylow
748C2—24no—
749C2—481no—
750C2#7469911yescharacteristic
751C2C2×#480611yescharacteristic
752C2#7883311yescharacteristic
753C2#8063211yescharacteristic
754C2#8064011yescharacteristic
755C2#8074511yescharacteristic
756C2#8074611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1892C2
socleC23×C3C22×D4
prime radicalC2×#930C22
hypercenter#1892D3
hypocenterC3#25497
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
1. C2×#5622C2semidirect
5. C3×#1892C2semidirect
6. C2×#4550C2semidirect
7. #70282C2semidirect
8. #70246C2semidirect
9. #70240C2semidirect
10. #70238C2semidirect
11. #69514C2semidirect
12. #68909C2semidirect
13. #68907C2semidirect
14. #68898C2semidirect
15. #68827C2semidirect
73. #1892D3semidirect
243. C22×Dic3SD16semidirect
747. C3#25497semidirect

Maximal subgroups

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

subgroupindex
C2×#56222
C2×#51142
C2×#50482
#739992
C3×#18922
C2×#45502
#702822
#702462
#702402
#702382
#695142
#689092
#689072
#688982
#688272
#254973