Finite Group Databasebeta

← #13150707

Subgroups — #13150707

Order 1728.

1391 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#272C211yesmaximal, characteristic, complemented
2C2×#88649C211yesmaximal, characteristic, complemented
3#64139⋊C3C211yesmaximal, characteristic, complemented
4#64133⋊C3C211yesmaximal, characteristic, complemented
5#11721323C212yesmaximal, complemented
6#11721315C212yesmaximal, complemented
7#11721159C211yesmaximal, characteristic, complemented
8#11721124C212yesmaximal, complemented
9#11721104C212yesmaximal, complemented
10#11721094C211yesmaximal, characteristic, complemented
11#11721089C211yesmaximal, characteristic, complemented
12#10595005—31nomaximal
13#10594892—31nomaximal
14C23×#272C2211yescharacteristic
15C22×C4×H(3,𝔽3)C2211yescharacteristic
16C22×#1084C2211yescharacteristic
17C2×C4×#272—24no—
18C2×C4×#272C2211yescharacteristic
19C2×C4×#272C2211yescharacteristic
20C2×C4×#272C2211yescharacteristic
21C2×C4×#272C2211yescharacteristic
22C2×#638⋊C3C2212yes—
23C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
24C2×#634⋊C3C2211yescharacteristic, complemented
25C2×#6200C2212yes—
26C2×#6200C2212yes—
27C2×((C3⋊D3)⋊C3)⋊C4C2212yescomplemented
28#88649—24no—
29#3757⋊C3C2212yes—
30#3752⋊C3C2212yescomplemented
31C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
32C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
33#3750⋊C3C2212yescomplemented
34#88451C2212yes—
35#88451C2212yes—
36#88450C2212yescomplemented
37#88448C2212yescomplemented
38#88447C2212yescomplemented
39C22×C3×C4×D3—31no—
40C22×C3×C4×D3—31no—
41C22×C3×C4×D3—61no—
42C2×#3799—31no—
43C2×#3795—31no—
44#64139D311yescharacteristic, complemented
45#64133D311yescharacteristic, complemented
46C3×#930—31no—
47C3×#924—31no—
48#63977—32no—
49#63976—32no—
50Dic3×#67—32no—
51#63952—32no—
52#63909—31no—
53#63908—31no—
54#63905—32no—
55#63904—32no—
56#63879—32no—
57#63857—31no—
58#63856—31no—
59#63850—32no—
60#63841—31no—
61#63841—31no—
62C23×H(3,𝔽3)C2311yescharacteristic
63C22×#272—22no—
64C22×#272—22no—
65C22×#272—22no—
66C22×#272C2311yescharacteristic
67C22×#272C2311yescharacteristic
68C22×(C3⋊D3)⋊C3C2312yes—
69C2×C4×H(3,𝔽3)—22no—
70C2×C4×H(3,𝔽3)C2311yescharacteristic
71C2×C4×H(3,𝔽3)C2311yescharacteristic
72C2×#1084—22no—
73C2×#1084C2311yescharacteristic
74C2×#1084C2311yescharacteristic
75C4×#272—22no—
76C4×#272—22no—
77C4×#272—22no—
78C4×#272D414yescomplemented
79#638⋊C3—24no—
80C2×(C3⋊Dic3)⋊C3C2312yes—
81C2×(C3⋊Dic3)⋊C3C2312yes—
82C2×(C3⋊Dic3)⋊C3C2312yes—
83C4⋊((C3⋊D3)⋊C3)—22no—
84#634⋊C3—22no—
85#6200—24no—
86#6200—24no—
87((C3⋊D3)⋊C3)⋊C4—24no—
88#5791—91no—
89#5627—91no—
90#5606—91no—
91C23×C3×D3—31no—
92C23×C3×D3—31no—
93C23×C3×D3—61no—
94C22×C32×C4—21no—
95C22×C32×C4C2×D311yescharacteristic
96C22×C32×C4C2×D311yescharacteristic
97C2×#638C2×D312yes—
98C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
99C2×#634C2×D311yescharacteristic, complemented
100C2×C3×#67—32no—
101C22×C3×Dic3—31no—
102C22×C3×Dic3—31no—
103C22×C3×Dic3—61no—
104C2×C3×D12—31no—
105C2×C3×C4×D3—31no—
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—31no—
108C2×C3×C4×D3—31no—
109C2×C3×C4×D3—31no—
110C2×C3×C4×D3—31no—
111C2×C3×C4×D3—31no—
112C2×C3×C4×D3—31no—
113C2×C3×C4×D3—64no—
114C2×C3×C4×D3—64no—
115C2×C3×C4×D3—61no—
116C2×C3×C4×D3—61no—
117C2×C3×C4×D3—61no—
118C2×C3×C4×D3—61no—
119C2×C3×C4×D3—68no—
120C2×C3×Dic6—31no—
121C2×#626—32no—
122C2×#626—32no—
123C2×#625—32no—
124C2×#625—32no—
125C2×#624—32no—
126C2×D3×Dic3—32no—
127#3799—64no—
128#3795—64no—
129#3757C2×D312yes—
130#3752C2×D312yescomplemented
131C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
132C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
133#3750C2×D312yescomplemented
134C3×#217—32no—
135C3×(C2×D3)⋊C4—32no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—31no—
138C3×Dic3⋊C4—32no—
139#3724—32no—
140Dic3⋊Dic3—32no—
141#3722—32no—
142(C2×D3)⋊Dic3—32no—
143(C2×D3)⋊Dic3—32no—
144(C2×D3)⋊Dic3—32no—
145(C2×D3)⋊Dic3—32no—
146(C2×D3)⋊Dic3—32no—
147Dic32—32no—
148Dic32—32no—
149C22×H(3,𝔽3)—21no—
150C22×H(3,𝔽3)—21no—
151C22×H(3,𝔽3)#4112yescomplemented
152C22×H(3,𝔽3)C2411yescharacteristic
153C2×#272—28no—
154C2×#272—21no—
155C2×#272—21no—
156C2×#272—21no—
157C2×#272—21no—
158C2×#272C2×D412yes—
159C2×#272#4112yescomplemented
160C2×(C3⋊D3)⋊C3—22no—
161C2×(C3⋊D3)⋊C3—22no—
162C2×(C3⋊D3)⋊C3—22no—
163C4×H(3,𝔽3)—21no—
164C4×H(3,𝔽3)C2×D412yes—
165#1084—21no—
166#1084C2×D412yes—
167(C3⋊Dic3)⋊C3—22no—
168(C3⋊Dic3)⋊C3—22no—
169(C3⋊Dic3)⋊C3—22no—
170C23×C3×C4—91no—
171C2×#239—91no—
172C2×#237—91no—
173C2×#235—91no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—61no—
177C3×C22⋊Q8—91no—
178C3×#121—91no—
179#953—92no—
180#946—91no—
181#938—91no—
182#937—92no—
183D4×Dic3—92no—
184#930—31no—
185#930—91no—
186#930—91no—
187#929—92no—
188C4×#67—92no—
189C4×#67—92no—
190#926—91no—
191#924—31no—
192#924—91no—
193#924—91no—
194#897—91no—
195#895—91no—
196#894—92no—
197#893—92no—
198#892—91no—
199#892—91no—
200#883—92no—
201#882—92no—
202#67⋊C4—92no—
203#67⋊C4—92no—
204C23×C32—21no—
205C23×C32C22×D311yescharacteristic
206C23×C32C22×D311yescharacteristic
207C22×C3⋊D3C22×D312yes—
208C22×C3×D3—31no—
209C22×C3×D3—31no—
210C22×C3×D3—31no—
211C22×C3×D3—31no—
212C22×C3×D3—32no—
213C22×C3×D3—61no—
214C22×C3×D3—61no—
215C22×C3×D3—62no—
216C22×C3×D3—62no—
217C22×C3×D3—62no—
218C22×C3×D3—62no—
219C22×C3×D3—64no—
220C22×C3×D3—64no—
221C22×C3×D3—64no—
222C22×C3×D3—62no—
223C22×C3×D3—62no—
224C2×C32×C4—24no—
225C2×C32×C4—22no—
226C2×C32×C4—22no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4C22×D311yescharacteristic
230C2×C32×C4C22×D311yescharacteristic
231C2×C32×C4C22×D311yescharacteristic
232C2×C32×C4C22×D311yescharacteristic
233#638—24no—
234C2×C3⋊Dic3C22×D312yes—
235C2×C3⋊Dic3C22×D312yes—
236C2×C3⋊Dic3C22×D312yes—
237C4⋊(C3⋊D3)—22no—
238#634—22no—
239C3×#67—64no—
240C2×C3×Dic3—31no—
241C2×C3×Dic3—31no—
242C2×C3×Dic3—32no—
243C2×C3×Dic3—32no—
244C2×C3×Dic3—32no—
245C2×C3×Dic3—31no—
246C2×C3×Dic3—31no—
247C2×C3×Dic3—61no—
248C2×C3×Dic3—61no—
249C2×C3×Dic3—62no—
250C2×C3×Dic3—62no—
251C2×C3×Dic3—64no—
252C3×D12—62no—
253C3×C4×D3—34no—
254C3×C4×D3—34no—
255C3×C4×D3—64no—
256C3×C4×D3—62no—
257C3×C4×D3—62no—
258C3×C4×D3—62no—
259C3×C4×D3—62no—
260C3×C4×D3—64no—
261C3×C4×D3—64no—
262C3×C4×D3—64no—
263C3×C4×D3—62no—
264C3×C4×D3—62no—
265C3×Dic6—62no—
266#626—64no—
267#626—64no—
268#625—64no—
269#625—64no—
270#624—64no—
271D3×Dic3—64no—
272#525—271noSylow
273C2×H(3,𝔽3)—22no—
274C2×H(3,𝔽3)C22×D411yescharacteristic
275C2×H(3,𝔽3)C2×#4111yescharacteristic
276C2×H(3,𝔽3)C2×#4111yescharacteristic
277#272—22no—
278#272—22no—
279(C3⋊D3)⋊C3—42no—
280C24×C3—91no—
281C23×D3—31no—
282C23×D3—31no—
283C23×D3—61no—
284C2×C3×Q8—91no—
285C2×C3×D4—91no—
286C2×C3×D4—92no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—61no—
290C22×C3×C4—91no—
291C22×C3×C4—91no—
292C22×C3×C4—91no—
293C22×C3×C4—91no—
294C22×C3×C4—91no—
295C22×C3×C4—184no—
296C22×C3×C4D3211yescharacteristic
297C2×#67—32no—
298C2×#67—92no—
299C2×#67—92no—
300C2×#67—92no—
301C2×#67—92no—
302C2×#67—92no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—61no—
306C22×Dic3—92no—
307#239—184no—
308#237—184no—
309#235—184no—
310C2×D12—31no—
311C2×D12—91no—
312C2×D12—92no—
313C2×D12—92no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—64no—
327C2×C4×D3—64no—
328C2×C4×D3—68no—
329C2×C4×D3—92no—
330C2×C4×D3—92no—
331C2×Dic6—31no—
332C2×Dic6—91no—
333C3×C4⋊C4—91no—
334C3×C4⋊C4—91no—
335C3×C4⋊C4—92no—
336C3×C22⋊C4—92no—
337C3×C22⋊C4—92no—
338#217—32no—
339#217—92no—
340#217—92no—
341#217—92no—
342#217—92no—
343(C2×D3)⋊C4—32no—
344(C2×D3)⋊C4—92no—
345(C2×D3)⋊C4—92no—
346(C2×D3)⋊C4—92no—
347(C2×D3)⋊C4—92no—
348(C2×D3)⋊C4—92no—
349(C2×D3)⋊C4—92no—
350(C2×D3)⋊C4—92no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—91no—
354C4⋊Dic3—91no—
355C4⋊Dic3—92no—
356Dic3⋊C4—32no—
357Dic3⋊C4—92no—
358Dic3⋊C4—92no—
359Dic3⋊C4—92no—
360C4×Dic3—92no—
361C4×Dic3—92no—
362C4×Dic3—92no—
363C22×C32—22no—
364C22×C32—22no—
365C22×C32—21no—
366C22×C32—21no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—21no—
370C22×C32—22no—
371C22×C32#23712yescomplemented
372C22×C32#23912yescomplemented
373C22×C32C23×D311yescharacteristic
374C22×C32C23×D311yescharacteristic
375C2×C3⋊D3—22no—
376C2×C3⋊D3—22no—
377C2×C3⋊D3—22no—
378C2×C3×D3—32no—
379C2×C3×D3—32no—
380C2×C3×D3—32no—
381C2×C3×D3—32no—
382C2×C3×D3—62no—
383C2×C3×D3—62no—
384C2×C3×D3—62no—
385C2×C3×D3—616no—
386C2×C3×D3—68no—
387C2×C3×D3—68no—
388C2×C3×D3—62no—
389C2×C3×D3—62no—
390C2×C3×D3—62no—
391C2×C3×D3—61no—
392C2×C3×D3—61no—
393C2×C3×D3—61no—
394C2×C3×D3—61no—
395C2×C3×D3—61no—
396C2×C3×D3—61no—
397C2×C3×D3—61no—
398C2×C3×D3—61no—
399C2×C3×D3—62no—
400C2×C3×D3—62no—
401C2×C3×D3—62no—
402C32×C4—22no—
403C32×C4—21no—
404C32×C4—21no—
405C32×C4—22no—
406C32×C4D3×D412yes—
407C32×C4D3×D412yes—
408C3⋊Dic3—22no—
409C3⋊Dic3—22no—
410C3⋊Dic3—22no—
411C3×Dic3—32no—
412C3×Dic3—32no—
413C3×Dic3—62no—
414C3×Dic3—62no—
415C3×Dic3—62no—
416C3×Dic3—61no—
417C3×Dic3—61no—
418C3×Dic3—62no—
419C3×Dic3—62no—
420C2×#41—271no—
421C23×C4—91no—
422#123—272no—
423C22⋊Q8—91no—
424C22⋊Q8—271no—
425#121—91no—
426#121—271no—
427#120—272no—
428C4×D4—272no—
429C4×D4—272no—
430#117—271no—
431H(3,𝔽3)#52511yescharacteristic, complemented, Sylow
432C23×C3—31no—
433C23×C3—31no—
434C23×C3—61no—
435C23×C3—92no—
436C23×C3—91no—
437C23×C3—91no—
438C23×C3—182no—
439C23×C3—182no—
440C23×C3—182no—
441C23×C3C2×D3211yescharacteristic
442C22×D3—31no—
443C22×D3—31no—
444C22×D3—31no—
445C22×D3—31no—
446C22×D3—32no—
447C22×D3—61no—
448C22×D3—61no—
449C22×D3—62no—
450C22×D3—62no—
451C22×D3—62no—
452C22×D3—62no—
453C22×D3—62no—
454C22×D3—62no—
455C22×D3—64no—
456C22×D3—64no—
457C22×D3—64no—
458C22×D3—92no—
459C3×Q8—182no—
460C3×D4—182no—
461C3×D4—184no—
462C2×C3×C4—22no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—62no—
468C2×C3×C4—62no—
469C2×C3×C4—64no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—91no—
473C2×C3×C4—94no—
474C2×C3×C4—92no—
475C2×C3×C4—92no—
476C2×C3×C4—92no—
477C2×C3×C4—91no—
478C2×C3×C4—182no—
479C2×C3×C4—182no—
480C2×C3×C4—182no—
481C2×C3×C4—182no—
482C2×C3×C4C2×D3211yescharacteristic
483C2×C3×C4C2×D3211yescharacteristic
484#67—64no—
485#67—184no—
486#67—184no—
487#67—184no—
488#67—184no—
489#67—184no—
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—32no—
495C2×Dic3—32no—
496C2×Dic3—32no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—62no—
500C2×Dic3—62no—
501C2×Dic3—64no—
502C2×Dic3—92no—
503C2×Dic3—92no—
504C2×Dic3—92no—
505C2×Dic3—184no—
506D12—62no—
507D12—182no—
508D12—184no—
509D12—184no—
510C4×D3—34no—
511C4×D3—34no—
512C4×D3—64no—
513C4×D3—62no—
514C4×D3—62no—
515C4×D3—62no—
516C4×D3—62no—
517C4×D3—62no—
518C4×D3—62no—
519C4×D3—64no—
520C4×D3—64no—
521C4×D3—64no—
522C4×D3—184no—
523C4×D3—184no—
524Dic6—62no—
525Dic6—182no—
526C2×C32—24no—
527C2×C32—22no—
528C2×C32—22no—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32C2×D3×D411yescharacteristic
533C2×C32C2×D3×D411yescharacteristic
534C2×C32C2×#23711yescharacteristic
535C2×C32C2×#23911yescharacteristic
536C2×C32D3×#4111yescharacteristic
537C2×C32D3×#4111yescharacteristic
538C3⋊D3—42no—
539C3×D3—64no—
540C3×D3—64no—
541C3×D3—62no—
542C3×D3—62no—
543C3×D3—62no—
544C3×D3—62no—
545C3×D3—122no—
546C24—91no—
547#41—544no—
548C2×Q8—91no—
549C2×D4—92no—
550C2×D4—91no—
551C2×D4—272no—
552C2×D4—272no—
553C22×C4—91no—
554C22×C4—91no—
555C22×C4—91no—
556C22×C4—91no—
557C22×C4—91no—
558C22×C4—184no—
559C22×C4—272no—
560C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
561C4⋊C4—91no—
562C4⋊C4—91no—
563C4⋊C4—92no—
564C4⋊C4—272no—
565C22⋊C4—92no—
566C22⋊C4—92no—
567C22⋊C4—272no—
568C22⋊C4—272no—
569C22⋊C4—272no—
570C42—272no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—31no—
574C22×C3—31no—
575C22×C3—32no—
576C22×C3—32no—
577C22×C3—61no—
578C22×C3—61no—
579C22×C3—61no—
580C22×C3—61no—
581C22×C3—62no—
582C22×C3—62no—
583C22×C3—61no—
584C22×C3—62no—
585C22×C3—92no—
586C22×C3—92no—
587C22×C3—188no—
588C22×C3—182no—
589C22×C3—182no—
590C22×C3—182no—
591C22×C3—181no—
592C22×C3—181no—
593C22×C3—181no—
594C22×C3—181no—
595C22×C3#379612yes—
596C22×C3C22×D3211yescharacteristic
597C2×D3—32no—
598C2×D3—32no—
599C2×D3—32no—
600C2×D3—32no—
601C2×D3—62no—
602C2×D3—62no—
603C2×D3—61no—
604C2×D3—61no—
605C2×D3—61no—
606C2×D3—61no—
607C2×D3—61no—
608C2×D3—61no—
609C2×D3—61no—
610C2×D3—61no—
611C2×D3—62no—
612C2×D3—68no—
613C2×D3—68no—
614C2×D3—616no—
615C2×D3—62no—
616C2×D3—62no—
617C2×D3—62no—
618C2×D3—62no—
619C2×D3—62no—
620C2×D3—62no—
621C2×D3—182no—
622C2×D3—182no—
623C2×D3—182no—
624C3×C4—21no—
625C3×C4—32no—
626C3×C4—32no—
627C3×C4—61no—
628C3×C4—61no—
629C3×C4—62no—
630C3×C4—62no—
631C3×C4—92no—
632C3×C4—182no—
633C3×C4—182no—
634C3×C4—182no—
635C3×C4—181no—
636C3×C4#381112yes—
637Dic3—32no—
638Dic3—32no—
639Dic3—62no—
640Dic3—61no—
641Dic3—61no—
642Dic3—62no—
643Dic3—62no—
644Dic3—62no—
645Dic3—62no—
646Dic3—182no—
647Dic3—182no—
648Dic3—182no—
649C32—21no—
650C32#560611yescharacteristic, complemented
651C32#562711yescharacteristic, complemented
652C23—91no—
653C23—91no—
654C23—92no—
655C23—182no—
656C23—182no—
657C23—182no—
658C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
659Q8—182no—
660D4—184no—
661D4—182no—
662D4—544no—
663D4—544no—
664C2×C4—22no—
665C2×C4—91no—
666C2×C4—94no—
667C2×C4—92no—
668C2×C4—92no—
669C2×C4—92no—
670C2×C4—91no—
671C2×C4—182no—
672C2×C4—182no—
673C2×C4—182no—
674C2×C4—182no—
675C2×C4—544no—
676C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
677C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
678C2×C3—22no—
679C2×C3—31no—
680C2×C3—31no—
681C2×C3—31no—
682C2×C3—31no—
683C2×C3—31no—
684C2×C3—31no—
685C2×C3—62no—
686C2×C3—62no—
687C2×C3—64no—
688C2×C3—61no—
689C2×C3—61no—
690C2×C3—61no—
691C2×C3—182no—
692C2×C3—182no—
693C2×C3—362no—
694C2×C3C2×#379611yescharacteristic
695C2×C3#6430611yescharacteristic
696C2×C3C2×#381111yescharacteristic
697D3—62no—
698D3—62no—
699D3—62no—
700D3—62no—
701D3—64no—
702D3—64no—
703D3—122no—
704D3—362no—
705C22—21no—
706C22—21no—
707C22—92no—
708C22—92no—
709C22—188no—
710C22—181no—
711C22—181no—
712C22—181no—
713C22—181no—
714C22—182no—
715C22—182no—
716C22—182no—
717C22#8864912yescomplemented
718C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
719C4—21no—
720C4—92no—
721C4—181no—
722C4—182no—
723C4—182no—
724C4—182no—
725C4#8867712yes—
726C3—31no—
727C3—31no—
728C3—61no—
729C3#1059492211yescharacteristic
730C2—22no—
731C2—182no—
732C2—182no—
733C2—362no—
734C2C2×#8864911yescharacteristic
735C2#1172249111yescharacteristic
736C2C2×#8867711yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC22×C4×H(3,𝔽3)C22
hypercenterC22×C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#525
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×#272C2semidirect
2. C2×#88649C2semidirect
3. #64139⋊C3C2semidirect
4. #64133⋊C3C2semidirect
5. #11721323C2semidirect
6. #11721315C2semidirect
7. #11721159C2semidirect
8. #11721124C2semidirect
9. #11721104C2semidirect
10. #11721094C2semidirect
11. #11721089C2semidirect
23. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
24. C2×#634⋊C3C22semidirect
27. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
30. #3752⋊C3C22semidirect
31. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
32. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
33. #3750⋊C3C22semidirect
36. #88450C22semidirect
37. #88448C22semidirect
38. #88447C22semidirect
44. #64139D3semidirect
45. #64133D3semidirect
78. C4×#272D4semidirect
98. C2×C4⋊(C3⋊D3)C2×D3semidirect
99. C2×#634C2×D3semidirect
130. #3752C2×D3semidirect
131. C4⋊(C3⋊Dic3)C2×D3semidirect
132. C4⋊(C3⋊Dic3)C2×D3semidirect
133. #3750C2×D3semidirect
151. C22×H(3,𝔽3)#41semidirect
159. C2×#272#41semidirect
371. C22×C32#237semidirect
372. C22×C32#239semidirect
431. H(3,𝔽3)#525semidirect
650. C32#5606semidirect
651. C32#5627semidirect
717. C22#88649semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#2722
C2×#886492
#64139⋊C32
#64133⋊C32
#117213232
#117213152
#117211592
#117211242
#117211042
#117210942
#117210892
#105950053
#105948923