Finite Group Databasebeta

← #13141179

Subgroups — #13141179

Order 1728.

1363 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6235C211yesmaximal, characteristic, complemented
2C22×#638⋊C3C211yesmaximal, characteristic, complemented
3C22×#6200C211yesmaximal, characteristic, complemented
4C2×#3757⋊C3C211yesmaximal, characteristic, complemented
5C2×#88451C211yesmaximal, characteristic, complemented
6C2×#88450C211yesmaximal, characteristic, complemented
7#11720334C211yesmaximal, characteristic, complemented
8#10591724—31nomaximal
9#10591723—31nomaximal
10C24×H(3,𝔽3)C2211yescharacteristic
11C23×#272C2211yescharacteristic
12C23×(C3⋊D3)⋊C3C2211yescharacteristic
13C2×#6235—22no—
14C2×#6235—22no—
15C2×#6235—22no—
16C22×#1084C2211yescharacteristic
17C2×#638⋊C3—22no—
18C2×#638⋊C3—22no—
19C2×#638⋊C3—22no—
20C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
22C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
23C2×#6200—22no—
24C2×#6200—22no—
25C2×#6200—22no—
26#3757⋊C3—22no—
27#88451—22no—
28#88450—22no—
29C22×#638D311yescharacteristic, complemented
30C22×C3×#67—31no—
31C22×C3×#67—31no—
32C22×C3×#67—31no—
33C22×C3×#67—61no—
34C22×#626—31no—
35C22×#625—31no—
36C2×#3757D311yescharacteristic, complemented
37C2×C3×#217—31no—
38C2×#3722—31no—
39C2×(C2×D3)⋊Dic3—31no—
40C2×(C2×D3)⋊Dic3—31no—
41C2×(C2×D3)⋊Dic3—31no—
42#63579—31no—
43#63579—31no—
44C23×H(3,𝔽3)—21no—
45C23×H(3,𝔽3)—21no—
46C23×H(3,𝔽3)—21no—
47C23×H(3,𝔽3)—21no—
48C23×H(3,𝔽3)—21no—
49C23×H(3,𝔽3)—21no—
50C23×H(3,𝔽3)D412yescomplemented
51C23×H(3,𝔽3)C2311yescharacteristic
52C22×#272—21no—
53C22×#272—21no—
54C22×#272—21no—
55C22×#272—21no—
56C22×#272—21no—
57C22×#272—21no—
58C22×#272D412yescomplemented
59C22×(C3⋊D3)⋊C3—21no—
60C22×(C3⋊D3)⋊C3—21no—
61C22×(C3⋊D3)⋊C3—21no—
62C22×(C3⋊D3)⋊C3—21no—
63C22×(C3⋊D3)⋊C3—21no—
64C22×(C3⋊D3)⋊C3—21no—
65C22×(C3⋊D3)⋊C3D412yescomplemented
66#6235—28no—
67C2×#1084—21no—
68C2×#1084—21no—
69C2×#1084D412yescomplemented
70#638⋊C3—28no—
71C2×(C3⋊Dic3)⋊C3—21no—
72C2×(C3⋊Dic3)⋊C3—21no—
73C2×(C3⋊Dic3)⋊C3—21no—
74C2×(C3⋊Dic3)⋊C3—21no—
75C2×(C3⋊Dic3)⋊C3—21no—
76C2×(C3⋊Dic3)⋊C3—21no—
77C2×(C3⋊Dic3)⋊C3—21no—
78C2×(C3⋊Dic3)⋊C3D412yescomplemented
79C2×(C3⋊Dic3)⋊C3D412yescomplemented
80#6200—28no—
81#5223—91no—
82#5223—91no—
83#4960—91no—
84C24×C32—21no—
85C24×C32C2×D311yescharacteristic
86C24×C32C2×D311yescharacteristic
87C23×C3⋊D3C2×D311yescharacteristic
88C23×C3×D3—31no—
89C23×C3×D3—31no—
90C23×C3×D3—31no—
91C23×C3×D3—61no—
92C2×#638—22no—
93C2×#638—22no—
94C2×#638—22no—
95C22×C3⋊Dic3C2×D311yescharacteristic
96C22×C3⋊Dic3C2×D311yescharacteristic
97C22×C3⋊Dic3C2×D311yescharacteristic
98C2×C3×#67—62no—
99C2×C3×#67—62no—
100C2×C3×#67—62no—
101C2×C3×#67—62no—
102C2×C3×#67—62no—
103C2×C3×#67—62no—
104C2×C3×#67—64no—
105C2×C3×#67—64no—
106C2×C3×#67—64no—
107C2×C3×#67—62no—
108C2×C3×#67—62no—
109C2×C3×#67—62no—
110C22×C3×Dic3—31no—
111C22×C3×Dic3—31no—
112C22×C3×Dic3—31no—
113C22×C3×Dic3—31no—
114C22×C3×Dic3—31no—
115C22×C3×Dic3—61no—
116C2×#626—62no—
117C2×#626—62no—
118C2×#626—62no—
119C2×#625—62no—
120C2×#625—62no—
121C2×#625—62no—
122#3757—22no—
123C3×#217—62no—
124#3722—62no—
125(C2×D3)⋊Dic3—62no—
126(C2×D3)⋊Dic3—62no—
127(C2×D3)⋊Dic3—62no—
128C22×H(3,𝔽3)—22no—
129C22×H(3,𝔽3)—22no—
130C22×H(3,𝔽3)—22no—
131C22×H(3,𝔽3)—41no—
132C22×H(3,𝔽3)—41no—
133C22×H(3,𝔽3)—41no—
134C22×H(3,𝔽3)—41no—
135C22×H(3,𝔽3)C2×D411yescharacteristic
136C22×H(3,𝔽3)C2×D411yescharacteristic
137C22×H(3,𝔽3)C2×D411yescharacteristic
138C22×H(3,𝔽3)C2×D411yescharacteristic
139C22×H(3,𝔽3)C2×D411yescharacteristic
140C22×H(3,𝔽3)C2×D411yescharacteristic
141C22×H(3,𝔽3)#4111yescharacteristic
142C2×#272—22no—
143C2×#272—22no—
144C2×#272—22no—
145C2×#272—41no—
146C2×#272—41no—
147C2×#272—41no—
148C2×#272—41no—
149C2×(C3⋊D3)⋊C3—22no—
150C2×(C3⋊D3)⋊C3—22no—
151C2×(C3⋊D3)⋊C3—22no—
152C2×(C3⋊D3)⋊C3—41no—
153C2×(C3⋊D3)⋊C3—41no—
154C2×(C3⋊D3)⋊C3—41no—
155C2×(C3⋊D3)⋊C3—41no—
156#1084—22no—
157(C3⋊Dic3)⋊C3—22no—
158(C3⋊Dic3)⋊C3—22no—
159(C3⋊Dic3)⋊C3—41no—
160C22×C3×D4—91no—
161C22×C3×D4—91no—
162C22×#67—31no—
163C22×#67—31no—
164C22×#67—31no—
165C22×#67—61no—
166C22×#67—91no—
167C22×#67—91no—
168C22×#67—91no—
169C22×D12—91no—
170C2×C3×C22⋊C4—91no—
171C2×#217—31no—
172C2×#217—91no—
173C2×#217—91no—
174C2×#217—91no—
175C2×(C2×D3)⋊C4—91no—
176C2×(C2×D3)⋊C4—91no—
177C2×(C2×D3)⋊C4—91no—
178C2×(C2×D3)⋊C4—91no—
179C3⋊#95—91no—
180C3⋊#95—91no—
181C3⋊#95—91no—
182C23×C32—22no—
183C23×C32—22no—
184C23×C32—21no—
185C23×C32—21no—
186C23×C32—21no—
187C23×C32—21no—
188C23×C32—21no—
189C23×C32—21no—
190C23×C32—21no—
191C23×C32—21no—
192C23×C32—21no—
193C23×C32—21no—
194C23×C32—21no—
195C23×C32—21no—
196C23×C32—22no—
197C23×C32—21no—
198C23×C32—41no—
199C23×C32—41no—
200C23×C32—41no—
201C23×C32—41no—
202C23×C32D1212yescomplemented
203C23×C32#6712yescomplemented
204C23×C32C22×D311yescharacteristic
205C23×C32C22×D311yescharacteristic
206C22×C3⋊D3—21no—
207C22×C3⋊D3—21no—
208C22×C3⋊D3—21no—
209C22×C3⋊D3—21no—
210C22×C3⋊D3—21no—
211C22×C3⋊D3—21no—
212C22×C3⋊D3#6712yescomplemented
213C22×C3×D3—32no—
214C22×C3×D3—32no—
215C22×C3×D3—32no—
216C22×C3×D3—62no—
217C22×C3×D3—62no—
218C22×C3×D3—62no—
219C22×C3×D3—61no—
220C22×C3×D3—61no—
221C22×C3×D3—61no—
222C22×C3×D3—61no—
223C22×C3×D3—61no—
224C22×C3×D3—61no—
225C22×C3×D3—61no—
226C22×C3×D3—61no—
227C22×C3×D3—61no—
228C22×C3×D3—61no—
229C22×C3×D3—61no—
230C22×C3×D3—61no—
231C22×C3×D3—61no—
232C22×C3×D3—61no—
233C22×C3×D3—61no—
234C22×C3×D3—61no—
235C22×C3×D3—61no—
236C22×C3×D3—61no—
237C22×C3×D3—121no—
238C22×C3×D3—121no—
239C22×C3×D3—121no—
240C22×C3×D3—121no—
241#638—28no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3#6712yescomplemented
250C2×C3⋊Dic3#6712yescomplemented
251C3×#67—68no—
252C3×#67—616no—
253C3×#67—68no—
254C3×#67—68no—
255C2×C3×Dic3—32no—
256C2×C3×Dic3—32no—
257C2×C3×Dic3—32no—
258C2×C3×Dic3—32no—
259C2×C3×Dic3—62no—
260C2×C3×Dic3—62no—
261C2×C3×Dic3—62no—
262C2×C3×Dic3—61no—
263C2×C3×Dic3—61no—
264C2×C3×Dic3—61no—
265C2×C3×Dic3—61no—
266C2×C3×Dic3—61no—
267C2×C3×Dic3—61no—
268C2×C3×Dic3—61no—
269C2×C3×Dic3—61no—
270C2×C3×Dic3—61no—
271C2×C3×Dic3—61no—
272C2×C3×Dic3—61no—
273#626—68no—
274#625—68no—
275#392—271noSylow
276C2×H(3,𝔽3)—42no—
277C2×H(3,𝔽3)#12011yescharacteristic
278C2×H(3,𝔽3)#12011yescharacteristic
279C2×H(3,𝔽3)#12011yescharacteristic
280C2×H(3,𝔽3)#12111yescharacteristic
281C2×H(3,𝔽3)#12111yescharacteristic
282C2×H(3,𝔽3)#12111yescharacteristic
283C2×H(3,𝔽3)#12711yescharacteristic
284#272—42no—
285(C3⋊D3)⋊C3—42no—
286C24×C3—31no—
287C24×C3—31no—
288C24×C3—61no—
289C24×C3—91no—
290C24×C3—91no—
291C24×C3D3211yescharacteristic
292C23×D3—31no—
293C23×D3—31no—
294C23×D3—31no—
295C23×D3—61no—
296C23×D3—91no—
297C2×C3×D4—182no—
298C2×C3×D4—182no—
299C2×C3×D4—182no—
300C2×C3×D4—182no—
301C2×C3×D4—182no—
302C2×C3×D4—182no—
303C22×C3×C4—91no—
304C22×C3×C4—91no—
305C22×C3×C4—91no—
306C22×C3×C4—91no—
307C2×#67—62no—
308C2×#67—62no—
309C2×#67—62no—
310C2×#67—62no—
311C2×#67—62no—
312C2×#67—62no—
313C2×#67—62no—
314C2×#67—62no—
315C2×#67—64no—
316C2×#67—64no—
317C2×#67—64no—
318C2×#67—62no—
319C2×#67—182no—
320C2×#67—182no—
321C2×#67—182no—
322C2×#67—182no—
323C2×#67—182no—
324C2×#67—182no—
325C2×#67—182no—
326C2×#67—182no—
327C2×#67—182no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—61no—
334C22×Dic3—91no—
335C22×Dic3—91no—
336C22×Dic3—91no—
337C2×D12—182no—
338C2×D12—182no—
339C2×D12—182no—
340C3×C22⋊C4—182no—
341#217—62no—
342#217—182no—
343#217—182no—
344#217—182no—
345(C2×D3)⋊C4—182no—
346(C2×D3)⋊C4—182no—
347(C2×D3)⋊C4—182no—
348(C2×D3)⋊C4—182no—
349C22×C32—24no—
350C22×C32—22no—
351C22×C32—22no—
352C22×C32—22no—
353C22×C32—22no—
354C22×C32—22no—
355C22×C32—22no—
356C22×C32—21no—
357C22×C32—21no—
358C22×C32—21no—
359C22×C32—21no—
360C22×C32—21no—
361C22×C32—21no—
362C22×C32—21no—
363C22×C32—42no—
364C22×C32—42no—
365C22×C32—42no—
366C22×C32—42no—
367C22×C32—42no—
368C22×C32—42no—
369C22×C32—41no—
370C22×C32—41no—
371C22×C32—41no—
372C22×C32—41no—
373C22×C32—41no—
374C22×C32—41no—
375C22×C32—41no—
376C22×C32—41no—
377C22×C32C2×D1211yescharacteristic
378C22×C32#23511yescharacteristic
379C22×C32D3×D411yescharacteristic
380C22×C32D3×D411yescharacteristic
381C22×C32D3×D411yescharacteristic
382C22×C32D3×D411yescharacteristic
383C22×C32D3×D411yescharacteristic
384C22×C32D3×D411yescharacteristic
385C22×C32D3×D411yescharacteristic
386C22×C32#23711yescharacteristic
387C22×C32C2×#6711yescharacteristic
388C22×C32C2×#6711yescharacteristic
389C22×C32C2×#6711yescharacteristic
390C22×C32C2×#6711yescharacteristic
391C2×C3⋊D3—22no—
392C2×C3⋊D3—22no—
393C2×C3⋊D3—22no—
394C2×C3⋊D3—41no—
395C2×C3⋊D3—41no—
396C2×C3⋊D3—41no—
397C2×C3⋊D3—41no—
398C2×C3×D3—64no—
399C2×C3×D3—62no—
400C2×C3×D3—62no—
401C2×C3×D3—62no—
402C2×C3×D3—62no—
403C2×C3×D3—62no—
404C2×C3×D3—62no—
405C2×C3×D3—62no—
406C2×C3×D3—62no—
407C2×C3×D3—62no—
408C2×C3×D3—122no—
409C2×C3×D3—122no—
410C2×C3×D3—122no—
411C2×C3×D3—122no—
412C2×C3×D3—122no—
413C2×C3×D3—122no—
414C2×C3×D3—121no—
415C2×C3×D3—121no—
416C2×C3×D3—121no—
417C2×C3×D3—121no—
418C2×C3×D3—121no—
419C2×C3×D3—121no—
420C2×C3×D3—121no—
421C2×C3×D3—121no—
422C2×C3×D3—121no—
423C2×C3×D3—121no—
424C2×C3×D3—121no—
425C2×C3×D3—121no—
426C3⋊Dic3—22no—
427C3⋊Dic3—22no—
428C3⋊Dic3—41no—
429C3×Dic3—64no—
430C3×Dic3—62no—
431C3×Dic3—62no—
432C3×Dic3—62no—
433C3×Dic3—62no—
434C3×Dic3—121no—
435C22×D4—91no—
436C22×D4—91no—
437C22×D4—271no—
438C2×C22⋊C4—91no—
439C2×C22⋊C4—271no—
440C2×C22⋊C4—271no—
441#95—271no—
442H(3,𝔽3)#39211yescharacteristic, complemented, Sylow
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—32no—
450C23×C3—32no—
451C23×C3—31no—
452C23×C3—31no—
453C23×C3—61no—
454C23×C3—61no—
455C23×C3—61no—
456C23×C3—61no—
457C23×C3—61no—
458C23×C3—61no—
459C23×C3—61no—
460C23×C3—61no—
461C23×C3—61no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—62no—
466C23×C3—62no—
467C23×C3—62no—
468C23×C3—61no—
469C23×C3—92no—
470C23×C3—92no—
471C23×C3—121no—
472C23×C3—121no—
473C23×C3—121no—
474C23×C3—121no—
475C23×C3—181no—
476C23×C3—181no—
477C23×C3—181no—
478C23×C3—181no—
479C23×C3—181no—
480C23×C3—181no—
481C23×C3—181no—
482C23×C3—181no—
483C23×C3—181no—
484C23×C3—181no—
485C23×C3—181no—
486C23×C3—181no—
487C23×C3#62612yes—
488C23×C3C2×D3211yescharacteristic
489C22×D3—32no—
490C22×D3—32no—
491C22×D3—32no—
492C22×D3—62no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—62no—
506C22×D3—62no—
507C22×D3—61no—
508C22×D3—61no—
509C22×D3—61no—
510C22×D3—61no—
511C22×D3—61no—
512C22×D3—61no—
513C22×D3—92no—
514C22×D3—121no—
515C22×D3—121no—
516C22×D3—121no—
517C22×D3—121no—
518C22×D3—181no—
519C22×D3—181no—
520C22×D3—181no—
521C22×D3—181no—
522C22×D3—181no—
523C22×D3—181no—
524C3×D4—188no—
525C3×D4—188no—
526C2×C3×C4—92no—
527C2×C3×C4—92no—
528C2×C3×C4—92no—
529C2×C3×C4—181no—
530C2×C3×C4—181no—
531C2×C3×C4—181no—
532C2×C3×C4—181no—
533C2×C3×C4—181no—
534C2×C3×C4—181no—
535C2×C3×C4—181no—
536C2×C3×C4—181no—
537C2×C3×C4—181no—
538#67—68no—
539#67—68no—
540#67—68no—
541#67—616no—
542#67—188no—
543#67—188no—
544#67—188no—
545C2×Dic3—32no—
546C2×Dic3—32no—
547C2×Dic3—32no—
548C2×Dic3—32no—
549C2×Dic3—62no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—62no—
555C2×Dic3—62no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—92no—
564C2×Dic3—92no—
565C2×Dic3—181no—
566C2×Dic3—181no—
567C2×Dic3—181no—
568C2×Dic3—181no—
569C2×Dic3—181no—
570C2×Dic3—181no—
571C2×Dic3—181no—
572D12—188no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—44no—
581C2×C32—42no—
582C2×C32—42no—
583C2×C32#88211yescharacteristic
584C2×C32#88211yescharacteristic
585C2×C32#88411yescharacteristic
586C2×C32#88411yescharacteristic
587C2×C32#93011yescharacteristic
588C2×C32#93711yescharacteristic
589C2×C32#93711yescharacteristic
590C2×C32#93711yescharacteristic
591C2×C32#93811yescharacteristic
592C2×C32#93911yescharacteristic
593C2×C32#93911yescharacteristic
594C2×C32#94011yescharacteristic
595C2×C32#94011yescharacteristic
596C2×C32#95311yescharacteristic
597C3⋊D3—42no—
598C3×D3—124no—
599C3×D3—122no—
600C3×D3—122no—
601C3×D3—122no—
602C24—91no—
603C24—91no—
604C24((C3⋊D3)⋊C3)⋊C211yescharacteristic
605C2×D4—182no—
606C2×D4—182no—
607C2×D4—182no—
608C2×D4—182no—
609C2×D4—182no—
610C2×D4—182no—
611C2×D4—542no—
612C2×D4—542no—
613C2×D4—542no—
614C22×C4—91no—
615C22×C4—91no—
616C22×C4—91no—
617C22×C4—91no—
618C22⋊C4—182no—
619C22⋊C4—542no—
620C22⋊C4—542no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—31no—
625C22×C3—31no—
626C22×C3—31no—
627C22×C3—31no—
628C22×C3—31no—
629C22×C3—31no—
630C22×C3—31no—
631C22×C3—31no—
632C22×C3—31no—
633C22×C3—31no—
634C22×C3—31no—
635C22×C3—31no—
636C22×C3—31no—
637C22×C3—31no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—62no—
643C22×C3—62no—
644C22×C3—62no—
645C22×C3—62no—
646C22×C3—62no—
647C22×C3—62no—
648C22×C3—64no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—122no—
657C22×C3—122no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—122no—
667C22×C3—122no—
668C22×C3—122no—
669C22×C3—122no—
670C22×C3—182no—
671C22×C3—182no—
672C22×C3—182no—
673C22×C3—182no—
674C22×C3—182no—
675C22×C3—182no—
676C22×C3—361no—
677C22×C3—361no—
678C22×C3—361no—
679C22×C3—361no—
680C22×C3—361no—
681C22×C3—361no—
682C22×C3—361no—
683C22×C3—361no—
684C22×C3#380411yescharacteristic
685C22×C3C2×#62611yescharacteristic
686C22×C3D3×#6711yescharacteristic
687C22×C3D3×#6711yescharacteristic
688C22×C3D3×#6711yescharacteristic
689C22×C3#381111yescharacteristic
690C22×C3#381111yescharacteristic
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—62no—
694C2×D3—62no—
695C2×D3—62no—
696C2×D3—62no—
697C2×D3—64no—
698C2×D3—62no—
699C2×D3—62no—
700C2×D3—62no—
701C2×D3—122no—
702C2×D3—122no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—122no—
712C2×D3—122no—
713C2×D3—122no—
714C2×D3—122no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—121no—
718C2×D3—121no—
719C2×D3—182no—
720C2×D3—182no—
721C2×D3—182no—
722C2×D3—361no—
723C2×D3—361no—
724C2×D3—361no—
725C2×D3—361no—
726C3×C4—182no—
727C3×C4—182no—
728C3×C4—182no—
729C3×C4—361no—
730Dic3—62no—
731Dic3—62no—
732Dic3—64no—
733Dic3—62no—
734Dic3—62no—
735Dic3—121no—
736Dic3—182no—
737Dic3—182no—
738Dic3—361no—
739C32—21no—
740C32#496011yescharacteristic, complemented
741C32#522311yescharacteristic, complemented
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—92no—
749C23—92no—
750C23—181no—
751C23—181no—
752C23—181no—
753C23—181no—
754C23—181no—
755C23—181no—
756C23—181no—
757C23—181no—
758C23—181no—
759C23—181no—
760C23—181no—
761C23—181no—
762C23#620012yescomplemented
763C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
764D4—188no—
765D4—188no—
766D4—548no—
767C2×C4—92no—
768C2×C4—92no—
769C2×C4—92no—
770C2×C4—181no—
771C2×C4—181no—
772C2×C4—181no—
773C2×C4—181no—
774C2×C4—181no—
775C2×C4—181no—
776C2×C4—181no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C3—31no—
780C2×C3—31no—
781C2×C3—31no—
782C2×C3—31no—
783C2×C3—31no—
784C2×C3—31no—
785C2×C3—31no—
786C2×C3—31no—
787C2×C3—31no—
788C2×C3—31no—
789C2×C3—31no—
790C2×C3—31no—
791C2×C3—31no—
792C2×C3—31no—
793C2×C3—42no—
794C2×C3—61no—
795C2×C3—61no—
796C2×C3—61no—
797C2×C3—61no—
798C2×C3—61no—
799C2×C3—61no—
800C2×C3—61no—
801C2×C3—122no—
802C2×C3—122no—
803C2×C3—124no—
804C2×C3—362no—
805C2×C3—362no—
806C2×C3#6395811yescharacteristic
807C2×C3#6397111yescharacteristic
808C2×C3#6397711yescharacteristic
809C2×C3#6397811yescharacteristic
810C2×C3#6397911yescharacteristic
811C2×C3#6398111yescharacteristic
812C2×C3#6398311yescharacteristic
813D3—122no—
814D3—122no—
815D3—124no—
816D3—122no—
817D3—362no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—182no—
826C22—182no—
827C22—182no—
828C22—182no—
829C22—182no—
830C22—182no—
831C22—361no—
832C22—361no—
833C22—361no—
834C22—361no—
835C22—361no—
836C22—361no—
837C22—361no—
838C22—361no—
839C22#8867111yescharacteristic
840C22C2×#620011yescharacteristic
841C22#8867611yescharacteristic
842C22#8867611yescharacteristic
843C22#8867611yescharacteristic
844C22#8867711yescharacteristic
845C22#8867711yescharacteristic
846C4—182no—
847C4—182no—
848C4—182no—
849C4—361no—
850C3—31no—
851C3—31no—
852C3—61no—
853C3#1059172411yescharacteristic
854C2—42no—
855C2—362no—
856C2—362no—
857C2#1172130311yescharacteristic
858C2#1172131211yescharacteristic
859C2#1172131711yescharacteristic
860C2#1172132111yescharacteristic
861C2#1172132211yescharacteristic
862C2#1172132311yescharacteristic
863C2#1172132411yescharacteristic
subgroupG/H
centerC23C2×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC23×H(3,𝔽3)C23
Frattini, socleC23×C3C2×D32
FittingC24×H(3,𝔽3)C22
hypercenterC24((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#392
LCSG ▷ C23×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×#6235C2semidirect
2. C22×#638⋊C3C2semidirect
3. C22×#6200C2semidirect
4. C2×#3757⋊C3C2semidirect
5. C2×#88451C2semidirect
6. C2×#88450C2semidirect
7. #11720334C2semidirect
29. C22×#638D3semidirect
36. C2×#3757D3semidirect
50. C23×H(3,𝔽3)D4semidirect
58. C22×#272D4semidirect
65. C22×(C3⋊D3)⋊C3D4semidirect
69. C2×#1084D4semidirect
78. C2×(C3⋊Dic3)⋊C3D4semidirect
79. C2×(C3⋊Dic3)⋊C3D4semidirect
202. C23×C32D12semidirect
203. C23×C32#67semidirect
212. C22×C3⋊D3#67semidirect
249. C2×C3⋊Dic3#67semidirect
250. C2×C3⋊Dic3#67semidirect
442. H(3,𝔽3)#392semidirect
740. C32#4960semidirect
741. C32#5223semidirect
762. C23#6200semidirect

Maximal subgroups

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

subgroupindex
C22×#62352
C22×#638⋊C32
C22×#62002
C2×#3757⋊C32
C2×#884512
C2×#884502
#117203342
#105917243
#105917233