Finite Group Databasebeta

← #13141167

Subgroups — #13141167

Order 1728.

965 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#638⋊C3C211yesmaximal, characteristic
2C2×#88552C211yesmaximal, characteristic, complemented
3C2×#3757⋊C3C211yesmaximal, characteristic, complemented
4C2×#88450C211yesmaximal, characteristic, complemented
5C2×#88450C211yesmaximal, characteristic, complemented
6C2×#88449C211yesmaximal, characteristic, complemented
7#11720334C211yesmaximal, characteristic, complemented
8#10591712—31nomaximal
9#10591709—31nomaximal
10C24×H(3,𝔽3)C2211yescharacteristic
11C23×(C3⋊D3)⋊C3C2211yescharacteristic
12C22×#1084C2211yescharacteristic
13C22×#1084C2211yescharacteristic
14C2×#638⋊C3—22no—
15C2×#638⋊C3—22no—
16C2×#638⋊C3—22no—
17C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
18C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
19C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
20#88552—22no—
21#3757⋊C3—22no—
22#88450—22no—
23#88450—22no—
24#88449—22no—
25C22×#638D311yescharacteristic
26C22×C3×#67—31no—
27C2×#3757D311yescharacteristic, complemented
28C2×C3×#217—31no—
29C2×C3×#217—31no—
30C2×C3×#217—31no—
31C2×C3×#217—61no—
32C2×Dic3⋊Dic3—31no—
33C2×Dic3⋊Dic3—31no—
34C2×#3722—31no—
35C2×#3722—31no—
36C2×(C2×D3)⋊Dic3—31no—
37C2×(C2×D3)⋊Dic3—31no—
38#63579—31no—
39#63579—31no—
40C23×H(3,𝔽3)—21no—
41C23×H(3,𝔽3)—21no—
42C23×H(3,𝔽3)—21no—
43C23×H(3,𝔽3)—21no—
44C23×H(3,𝔽3)—21no—
45C23×H(3,𝔽3)—21no—
46C23×H(3,𝔽3)D412yes—
47C23×H(3,𝔽3)C2311yescharacteristic
48C22×(C3⋊D3)⋊C3—21no—
49C22×(C3⋊D3)⋊C3—21no—
50C22×(C3⋊D3)⋊C3—21no—
51C22×(C3⋊D3)⋊C3—21no—
52C22×(C3⋊D3)⋊C3—21no—
53C22×(C3⋊D3)⋊C3—21no—
54C22×(C3⋊D3)⋊C3D412yes—
55C2×#1084—21no—
56C2×#1084—21no—
57C2×#1084—21no—
58C2×#1084—21no—
59C2×#1084—21no—
60C2×#1084D412yescomplemented
61#638⋊C3—28no—
62C2×(C3⋊Dic3)⋊C3—21no—
63C2×(C3⋊Dic3)⋊C3—21no—
64C2×(C3⋊Dic3)⋊C3—21no—
65C2×(C3⋊Dic3)⋊C3—21no—
66C2×(C3⋊Dic3)⋊C3—21no—
67C2×(C3⋊Dic3)⋊C3—21no—
68C2×(C3⋊Dic3)⋊C3—21no—
69C2×(C3⋊Dic3)⋊C3—21no—
70C2×(C3⋊Dic3)⋊C3D412yes—
71#5222—91no—
72#4961—91no—
73#4959—91no—
74C24×C32—21no—
75C24×C32C2×D311yescharacteristic
76C24×C32C2×D311yescharacteristic
77C23×C3⋊D3C2×D311yescharacteristic
78C23×C3×D3—31no—
79C2×#638—22no—
80C2×#638—22no—
81C2×#638—22no—
82C22×C3⋊Dic3C2×D311yescharacteristic
83C22×C3⋊Dic3C2×D311yescharacteristic
84C22×C3⋊Dic3C2×D311yescharacteristic
85C2×C3×#67—62no—
86C2×C3×#67—62no—
87C2×C3×#67—62no—
88C22×C3×Dic3—31no—
89C22×C3×Dic3—31no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—31no—
92C22×C3×Dic3—31no—
93C22×C3×Dic3—31no—
94C22×C3×Dic3—31no—
95C22×C3×Dic3—61no—
96C22×C3×Dic3—61no—
97#3757—22no—
98C3×#217—62no—
99C3×#217—62no—
100C3×#217—64no—
101C3×#217—62no—
102Dic3⋊Dic3—62no—
103Dic3⋊Dic3—62no—
104#3722—62no—
105#3722—62no—
106(C2×D3)⋊Dic3—62no—
107(C2×D3)⋊Dic3—62no—
108C22×H(3,𝔽3)—22no—
109C22×H(3,𝔽3)—22no—
110C22×H(3,𝔽3)—22no—
111C22×H(3,𝔽3)—41no—
112C22×H(3,𝔽3)—41no—
113C22×H(3,𝔽3)—41no—
114C22×H(3,𝔽3)—41no—
115C22×H(3,𝔽3)C2×D411yescharacteristic
116C22×H(3,𝔽3)C2×D411yescharacteristic
117C22×H(3,𝔽3)C2×D411yescharacteristic
118C22×H(3,𝔽3)C2×D411yescharacteristic
119C22×H(3,𝔽3)#4111yescharacteristic
120C22×H(3,𝔽3)#4111yescharacteristic
121C22×H(3,𝔽3)#4111yescharacteristic
122C2×(C3⋊D3)⋊C3—22no—
123C2×(C3⋊D3)⋊C3—22no—
124C2×(C3⋊D3)⋊C3—22no—
125C2×(C3⋊D3)⋊C3—41no—
126C2×(C3⋊D3)⋊C3—41no—
127C2×(C3⋊D3)⋊C3—41no—
128C2×(C3⋊D3)⋊C3—41no—
129#1084—22no—
130#1084—41no—
131(C3⋊Dic3)⋊C3—22no—
132(C3⋊Dic3)⋊C3—41no—
133(C3⋊Dic3)⋊C3—41no—
134C22×C3×D4—91no—
135C22×#67—31no—
136C22×#67—91no—
137C2×C3×C22⋊C4—91no—
138C2×C3×C22⋊C4—91no—
139C2×#217—31no—
140C2×#217—31no—
141C2×#217—31no—
142C2×#217—61no—
143C2×#217—91no—
144C2×#217—91no—
145C2×#217—91no—
146C2×(C2×D3)⋊C4—91no—
147C2×(C2×D3)⋊C4—91no—
148C2×(C2×D3)⋊C4—91no—
149C2×(C2×D3)⋊C4—91no—
150C2×C4⋊Dic3—91no—
151C2×Dic3⋊C4—91no—
152C2×Dic3⋊C4—91no—
153C3⋊#95—91no—
154C3⋊#95—91no—
155C3⋊#95—91no—
156C23×C32—22no—
157C23×C32—22no—
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—21no—
164C23×C32—21no—
165C23×C32—21no—
166C23×C32—21no—
167C23×C32—21no—
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—22no—
171C23×C32—21no—
172C23×C32—41no—
173C23×C32—41no—
174C23×C32—41no—
175C23×C32—41no—
176C23×C32#6712yes—
177C23×C32#6712yes—
178C23×C32C22×D311yescharacteristic
179C23×C32C22×D311yescharacteristic
180C22×C3⋊D3—21no—
181C22×C3⋊D3—21no—
182C22×C3⋊D3—21no—
183C22×C3⋊D3—21no—
184C22×C3⋊D3—21no—
185C22×C3⋊D3—21no—
186C22×C3⋊D3#6712yes—
187C22×C3×D3—32no—
188C22×C3×D3—61no—
189C22×C3×D3—61no—
190C22×C3×D3—61no—
191C22×C3×D3—61no—
192C22×C3×D3—61no—
193C22×C3×D3—61no—
194#638—28no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3#6712yes—
204C3×#67—68no—
205C2×C3×Dic3—32no—
206C2×C3×Dic3—32no—
207C2×C3×Dic3—32no—
208C2×C3×Dic3—62no—
209C2×C3×Dic3—61no—
210C2×C3×Dic3—61no—
211C2×C3×Dic3—61no—
212C2×C3×Dic3—61no—
213C2×C3×Dic3—61no—
214C2×C3×Dic3—61no—
215C2×C3×Dic3—62no—
216C2×C3×Dic3—61no—
217C2×C3×Dic3—61no—
218C2×C3×Dic3—61no—
219C2×C3×Dic3—61no—
220C2×C3×Dic3—61no—
221C2×C3×Dic3—61no—
222C2×C3×Dic3—61no—
223C2×C3×Dic3—61no—
224C2×C3×Dic3—61no—
225C2×C3×Dic3—61no—
226C2×C3×Dic3—61no—
227C2×C3×Dic3—61no—
228C2×C3×Dic3—121no—
229C2×C3×Dic3—121no—
230C2×C3×Dic3—121no—
231C2×C3×Dic3—121no—
232#394—271noSylow
233C2×H(3,𝔽3)—42no—
234C2×H(3,𝔽3)#12011yescharacteristic
235C2×H(3,𝔽3)#12111yescharacteristic
236C2×H(3,𝔽3)#12111yescharacteristic
237C2×H(3,𝔽3)#12111yescharacteristic
238C2×H(3,𝔽3)#12311yescharacteristic
239C2×H(3,𝔽3)#12311yescharacteristic
240C2×H(3,𝔽3)#12411yescharacteristic
241(C3⋊D3)⋊C3—42no—
242C24×C3—31no—
243C24×C3—31no—
244C24×C3—61no—
245C24×C3—91no—
246C24×C3D3211yescharacteristic
247C23×D3—31no—
248C23×D3—91no—
249C2×C3×D4—182no—
250C2×C3×D4—182no—
251C2×C3×D4—182no—
252C22×C3×C4—91no—
253C22×C3×C4—91no—
254C22×C3×C4—91no—
255C22×C3×C4—91no—
256C22×C3×C4—91no—
257C2×#67—62no—
258C2×#67—62no—
259C2×#67—62no—
260C2×#67—182no—
261C2×#67—182no—
262C2×#67—182no—
263C22×Dic3—31no—
264C22×Dic3—31no—
265C22×Dic3—31no—
266C22×Dic3—31no—
267C22×Dic3—31no—
268C22×Dic3—31no—
269C22×Dic3—31no—
270C22×Dic3—61no—
271C22×Dic3—61no—
272C22×Dic3—91no—
273C22×Dic3—91no—
274C22×Dic3—91no—
275C3×C22⋊C4—182no—
276C3×C22⋊C4—182no—
277#217—62no—
278#217—62no—
279#217—64no—
280#217—62no—
281#217—182no—
282#217—182no—
283#217—182no—
284(C2×D3)⋊C4—182no—
285(C2×D3)⋊C4—182no—
286(C2×D3)⋊C4—182no—
287(C2×D3)⋊C4—182no—
288C4⋊Dic3—182no—
289Dic3⋊C4—182no—
290Dic3⋊C4—182no—
291C22×C32—24no—
292C22×C32—22no—
293C22×C32—22no—
294C22×C32—22no—
295C22×C32—22no—
296C22×C32—22no—
297C22×C32—22no—
298C22×C32—21no—
299C22×C32—21no—
300C22×C32—21no—
301C22×C32—21no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32—21no—
305C22×C32—42no—
306C22×C32—42no—
307C22×C32—42no—
308C22×C32—42no—
309C22×C32—42no—
310C22×C32—42no—
311C22×C32—41no—
312C22×C32—41no—
313C22×C32—41no—
314C22×C32—41no—
315C22×C32—41no—
316C22×C32—41no—
317C22×C32—41no—
318C22×C32—41no—
319C22×C32#23511yescharacteristic
320C22×C32#23511yescharacteristic
321C22×C32D3×D411yescharacteristic
322C22×C32D3×D411yescharacteristic
323C22×C32D3×D411yescharacteristic
324C22×C32D3×D411yescharacteristic
325C22×C32#23711yescharacteristic
326C22×C32#23711yescharacteristic
327C22×C32#23711yescharacteristic
328C22×C32#23711yescharacteristic
329C22×C32C2×#6711yescharacteristic
330C22×C32C2×#6711yescharacteristic
331C22×C32C2×#6711yescharacteristic
332C22×C32C2×#6711yescharacteristic
333C2×C3⋊D3—22no—
334C2×C3⋊D3—22no—
335C2×C3⋊D3—22no—
336C2×C3⋊D3—41no—
337C2×C3⋊D3—41no—
338C2×C3⋊D3—41no—
339C2×C3⋊D3—41no—
340C2×C3×D3—62no—
341C2×C3×D3—62no—
342C2×C3×D3—62no—
343C2×C3×D3—121no—
344C2×C3×D3—121no—
345C2×C3×D3—121no—
346C2×C3×D3—121no—
347C3⋊Dic3—22no—
348C3⋊Dic3—41no—
349C3⋊Dic3—41no—
350C3×Dic3—62no—
351C3×Dic3—62no—
352C3×Dic3—62no—
353C3×Dic3—122no—
354C3×Dic3—122no—
355C3×Dic3—121no—
356C3×Dic3—121no—
357C3×Dic3—121no—
358C3×Dic3—121no—
359C22×D4—91no—
360C2×C4⋊C4—271no—
361C2×C22⋊C4—91no—
362C2×C22⋊C4—91no—
363C2×C22⋊C4—271no—
364C2×C22⋊C4—271no—
365#95—271no—
366H(3,𝔽3)#39411yescharacteristic, complemented, Sylow
367C23×C3—21no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—32no—
374C23×C3—32no—
375C23×C3—31no—
376C23×C3—31no—
377C23×C3—61no—
378C23×C3—61no—
379C23×C3—61no—
380C23×C3—61no—
381C23×C3—61no—
382C23×C3—61no—
383C23×C3—61no—
384C23×C3—61no—
385C23×C3—61no—
386C23×C3—61no—
387C23×C3—61no—
388C23×C3—61no—
389C23×C3—62no—
390C23×C3—62no—
391C23×C3—62no—
392C23×C3—61no—
393C23×C3—92no—
394C23×C3—121no—
395C23×C3—121no—
396C23×C3—121no—
397C23×C3—121no—
398C23×C3—181no—
399C23×C3—181no—
400C23×C3—181no—
401C23×C3—181no—
402C23×C3—181no—
403C23×C3—181no—
404C23×C3#62512yes—
405C23×C3C2×D3211yescharacteristic
406C22×D3—32no—
407C22×D3—61no—
408C22×D3—61no—
409C22×D3—61no—
410C22×D3—61no—
411C22×D3—61no—
412C22×D3—61no—
413C22×D3—92no—
414C22×D3—181no—
415C22×D3—181no—
416C22×D3—181no—
417C22×D3—181no—
418C22×D3—181no—
419C22×D3—181no—
420C3×D4—188no—
421C2×C3×C4—92no—
422C2×C3×C4—92no—
423C2×C3×C4—181no—
424C2×C3×C4—181no—
425C2×C3×C4—181no—
426C2×C3×C4—181no—
427C2×C3×C4—181no—
428C2×C3×C4—181no—
429C2×C3×C4—181no—
430C2×C3×C4—181no—
431C2×C3×C4—181no—
432C2×C3×C4—181no—
433C2×C3×C4—181no—
434C2×C3×C4—181no—
435C2×C3×C4—181no—
436#67—68no—
437#67—188no—
438C2×Dic3—32no—
439C2×Dic3—32no—
440C2×Dic3—32no—
441C2×Dic3—62no—
442C2×Dic3—61no—
443C2×Dic3—61no—
444C2×Dic3—61no—
445C2×Dic3—61no—
446C2×Dic3—61no—
447C2×Dic3—61no—
448C2×Dic3—61no—
449C2×Dic3—61no—
450C2×Dic3—61no—
451C2×Dic3—61no—
452C2×Dic3—61no—
453C2×Dic3—61no—
454C2×Dic3—62no—
455C2×Dic3—61no—
456C2×Dic3—61no—
457C2×Dic3—61no—
458C2×Dic3—61no—
459C2×Dic3—61no—
460C2×Dic3—61no—
461C2×Dic3—92no—
462C2×Dic3—121no—
463C2×Dic3—121no—
464C2×Dic3—121no—
465C2×Dic3—121no—
466C2×Dic3—181no—
467C2×Dic3—181no—
468C2×Dic3—181no—
469C2×Dic3—181no—
470C2×Dic3—181no—
471C2×Dic3—181no—
472C2×Dic3—181no—
473C2×Dic3—181no—
474C2×C32—21no—
475C2×C32—21no—
476C2×C32—21no—
477C2×C32—21no—
478C2×C32—21no—
479C2×C32—21no—
480C2×C32—21no—
481C2×C32—44no—
482C2×C32—42no—
483C2×C32—42no—
484C2×C32#88311yescharacteristic
485C2×C32#88411yescharacteristic
486C2×C32#88411yescharacteristic
487C2×C32#88511yescharacteristic
488C2×C32#92911yescharacteristic
489C2×C32#93511yescharacteristic
490C2×C32#93511yescharacteristic
491C2×C32#93611yescharacteristic
492C2×C32#93711yescharacteristic
493C2×C32#93811yescharacteristic
494C2×C32#93911yescharacteristic
495C2×C32#93911yescharacteristic
496C2×C32#93911yescharacteristic
497C2×C32#95311yescharacteristic
498C3⋊D3—42no—
499C3×D3—122no—
500C24—91no—
501C24((C3⋊D3)⋊C3)⋊C211yescharacteristic
502C2×D4—182no—
503C2×D4—182no—
504C2×D4—182no—
505C22×C4—91no—
506C22×C4—91no—
507C22×C4—91no—
508C22×C4—91no—
509C22×C4—91no—
510C4⋊C4—542no—
511C22⋊C4—182no—
512C22⋊C4—182no—
513C22⋊C4—542no—
514C22⋊C4—542no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—31no—
519C22×C3—31no—
520C22×C3—31no—
521C22×C3—31no—
522C22×C3—31no—
523C22×C3—31no—
524C22×C3—31no—
525C22×C3—31no—
526C22×C3—31no—
527C22×C3—31no—
528C22×C3—31no—
529C22×C3—31no—
530C22×C3—31no—
531C22×C3—31no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—41no—
535C22×C3—41no—
536C22×C3—62no—
537C22×C3—62no—
538C22×C3—62no—
539C22×C3—62no—
540C22×C3—62no—
541C22×C3—62no—
542C22×C3—64no—
543C22×C3—61no—
544C22×C3—61no—
545C22×C3—61no—
546C22×C3—61no—
547C22×C3—61no—
548C22×C3—61no—
549C22×C3—61no—
550C22×C3—122no—
551C22×C3—122no—
552C22×C3—121no—
553C22×C3—121no—
554C22×C3—121no—
555C22×C3—121no—
556C22×C3—121no—
557C22×C3—121no—
558C22×C3—121no—
559C22×C3—121no—
560C22×C3—122no—
561C22×C3—122no—
562C22×C3—122no—
563C22×C3—122no—
564C22×C3—182no—
565C22×C3—182no—
566C22×C3—182no—
567C22×C3—361no—
568C22×C3—361no—
569C22×C3—361no—
570C22×C3—361no—
571C22×C3#380411yescharacteristic
572C22×C3#380411yescharacteristic
573C22×C3#380511yescharacteristic
574C22×C3C2×#62511yescharacteristic
575C22×C3D3×#6711yescharacteristic
576C22×C3D3×#6711yescharacteristic
577C22×C3#381111yescharacteristic
578C2×D3—62no—
579C2×D3—62no—
580C2×D3—62no—
581C2×D3—121no—
582C2×D3—121no—
583C2×D3—121no—
584C2×D3—121no—
585C2×D3—182no—
586C2×D3—182no—
587C2×D3—182no—
588C2×D3—361no—
589C2×D3—361no—
590C2×D3—361no—
591C2×D3—361no—
592C3×C4—182no—
593C3×C4—182no—
594C3×C4—361no—
595C3×C4—361no—
596C3×C4—361no—
597Dic3—62no—
598Dic3—62no—
599Dic3—62no—
600Dic3—122no—
601Dic3—121no—
602Dic3—121no—
603Dic3—122no—
604Dic3—121no—
605Dic3—121no—
606Dic3—182no—
607Dic3—361no—
608Dic3—361no—
609C32—21no—
610C32#495911yescharacteristic, complemented
611C32#522211yescharacteristic, complemented
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—92no—
619C23—181no—
620C23—181no—
621C23—181no—
622C23—181no—
623C23—181no—
624C23—181no—
625C23#619812yes—
626C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
627D4—188no—
628C2×C4—92no—
629C2×C4—92no—
630C2×C4—181no—
631C2×C4—181no—
632C2×C4—181no—
633C2×C4—181no—
634C2×C4—181no—
635C2×C4—181no—
636C2×C4—181no—
637C2×C4—181no—
638C2×C4—181no—
639C2×C4—181no—
640C2×C4—181no—
641C2×C4—181no—
642C2×C4—181no—
643C2×C3—31no—
644C2×C3—31no—
645C2×C3—31no—
646C2×C3—31no—
647C2×C3—31no—
648C2×C3—31no—
649C2×C3—31no—
650C2×C3—31no—
651C2×C3—31no—
652C2×C3—31no—
653C2×C3—31no—
654C2×C3—31no—
655C2×C3—31no—
656C2×C3—31no—
657C2×C3—42no—
658C2×C3—61no—
659C2×C3—61no—
660C2×C3—61no—
661C2×C3—61no—
662C2×C3—61no—
663C2×C3—61no—
664C2×C3—61no—
665C2×C3—122no—
666C2×C3—122no—
667C2×C3—124no—
668C2×C3—362no—
669C2×C3#6395811yescharacteristic
670C2×C3#6395911yescharacteristic
671C2×C3#6396111yescharacteristic
672C2×C3#6396911yescharacteristic
673C2×C3#6397111yescharacteristic
674C2×C3#6397611yescharacteristic
675C2×C3#6398011yescharacteristic
676D3—122no—
677D3—362no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—182no—
686C22—182no—
687C22—182no—
688C22—361no—
689C22—361no—
690C22—361no—
691C22—361no—
692C22#8867111yescharacteristic
693C22#8867111yescharacteristic
694C22#8867211yescharacteristic
695C22C2×#619811yescharacteristic
696C22#8867611yescharacteristic
697C22#8867611yescharacteristic
698C22#8867711yescharacteristic
699C4—182no—
700C4—182no—
701C4—361no—
702C4—361no—
703C4—361no—
704C3—31no—
705C3—31no—
706C3—61no—
707C3#1059170811yescharacteristic
708C2—42no—
709C2—362no—
710C2#1172130311yescharacteristic
711C2#1172130411yescharacteristic
712C2#1172130611yescharacteristic
713C2#1172131111yescharacteristic
714C2#1172131211yescharacteristic
715C2#1172131611yescharacteristic
716C2#1172131811yescharacteristic
subgroupG/H
centerC23C2×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC23×H(3,𝔽3)C23
Frattini, socleC23×C3C2×D32
FittingC24×H(3,𝔽3)C22
prime radicalC22×#638⋊C3C2
hypercenterC24((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#394
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
2. C2×#88552C2semidirect
3. C2×#3757⋊C3C2semidirect
4. C2×#88450C2semidirect
5. C2×#88450C2semidirect
6. C2×#88449C2semidirect
7. #11720334C2semidirect
27. C2×#3757D3semidirect
60. C2×#1084D4semidirect
366. H(3,𝔽3)#394semidirect
610. C32#4959semidirect
611. C32#5222semidirect

Maximal subgroups

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

subgroupindex
C22×#638⋊C32
C2×#885522
C2×#3757⋊C32
C2×#884502
C2×#884492
#117203342
#105917123
#105917093