Finite Group Databasebeta

← C2×#11721162 #13150872

Subgroups — C2×#11721162 #13150872

Order 1728.

2449 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×((C3⋊D3)⋊C3)⋊C2C211yesmaximal, characteristic, complemented
2C22×C4⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
3C22×#6200C211yesmaximal, characteristic, complemented
4C22×#6198C211yesmaximal, characteristic, complemented
5C2×#88542C211yesmaximal, characteristic, complemented
6C2×#3752⋊C3C211yesmaximal, characteristic, complemented
7C2×#88450C211yesmaximal, characteristic, complemented
8#11721162C218yesmaximal, direct product factor
9C2×#63923—31nomaximal
10C2×#63922—31nomaximal
11C23×#272C2211yescharacteristic
12C23×(C3⋊D3)⋊C3C2211yescharacteristic
13C23×(C3⋊D3)⋊C3C2211yescharacteristic
14C23×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
15C22×((C3⋊D3)⋊C3)⋊C2—24no—
16C22×((C3⋊D3)⋊C3)⋊C2—24no—
17C22×((C3⋊D3)⋊C3)⋊C2—24no—
18C22×((C3⋊D3)⋊C3)⋊C2C2214yescomplemented
19C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
20C22×#1084C2211yescharacteristic, complemented
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
22C2×C4⋊((C3⋊D3)⋊C3)—24no—
23C2×C4⋊((C3⋊D3)⋊C3)C2214yescomplemented
24C2×#6200—24no—
25C2×#6200C2214yescomplemented
26C2×#6198—24no—
27C2×#6198C2214yescomplemented
28#88542C2214yescomplemented
29#3752⋊C3C2214yescomplemented
30#88450C2214yescomplemented
31C23×D32—31no—
32C23×D32—31no—
33C22×C4⋊(C3⋊D3)D311yescharacteristic, complemented
34C22×C3×D12—31no—
35C22×#626—31no—
36C22×#626—31no—
37C22×#626—31no—
38C22×#625—31no—
39C2×#3752D311yescharacteristic, complemented
40C2×C3×(C2×D3)⋊C4—31no—
41C2×C3×(C2×D3)⋊C4—31no—
42C2×C3×(C2×D3)⋊C4—31no—
43C2×C3×(C2×D3)⋊C4—61no—
44C2×#3722—31no—
45C2×(C2×D3)⋊Dic3—31no—
46#63923—38no—
47#63922—38no—
48C23×H(3,𝔽3)C2311yescharacteristic
49C22×#272—22no—
50C22×#272—22no—
51C22×#272D414yescomplemented
52C22×#272C2312yes—
53C22×(C3⋊D3)⋊C3—22no—
54C22×(C3⋊D3)⋊C3—22no—
55C22×(C3⋊D3)⋊C3—22no—
56C22×(C3⋊D3)⋊C3—22no—
57C22×(C3⋊D3)⋊C3—22no—
58C22×(C3⋊D3)⋊C3—22no—
59C22×(C3⋊D3)⋊C3—22no—
60C22×(C3⋊D3)⋊C3D414yescomplemented
61C22×(C3⋊D3)⋊C3D414yescomplemented
62C22×(C3⋊D3)⋊C3C2312yes—
63C22×(C3⋊D3)⋊C3C2312yes—
64C22×(C3⋊D3)⋊C3C2312yescomplemented
65C2×((C3⋊D3)⋊C3)⋊C2—232no—
66C2×((C3⋊D3)⋊C3)⋊C2—28no—
67C2×((C3⋊D3)⋊C3)⋊C2—28no—
68C2×((C3⋊D3)⋊C3)⋊C2—28no—
69C2×C4×H(3,𝔽3)—22no—
70C2×C4×H(3,𝔽3)C2312yescomplemented
71C2×#1084—22no—
72C2×#1084C2312yescomplemented
73C2×(C3⋊Dic3)⋊C3—22no—
74C2×(C3⋊Dic3)⋊C3C2312yescomplemented
75C4⋊((C3⋊D3)⋊C3)—28no—
76#6200—28no—
77#6198—28no—
78C2×#937—91no—
79C2×#882—91no—
80C2×#882—91no—
81C23×C3⋊D3C2×D311yescharacteristic
82C23×C3⋊D3C2×D311yescharacteristic
83C23×C3⋊D3C2×D311yescharacteristic, complemented
84C23×C3×D3—31no—
85C23×C3×D3—31no—
86C23×C3×D3—31no—
87C23×C3×D3—31no—
88C23×C3×D3—31no—
89C23×C3×D3—61no—
90C22×D32—34no—
91C22×D32—34no—
92C22×D32—64no—
93C22×D32—64no—
94C22×D32—64no—
95C22×D32—64no—
96C22×D32—64no—
97C22×D32—64no—
98C22×C32×C4—21no—
99C22×C32×C4C2×D311yescharacteristic, complemented
100C22×C32×C4C2×D311yescharacteristic, complemented
101C22×C3⋊Dic3C2×D311yescharacteristic, complemented
102C2×C4⋊(C3⋊D3)—24no—
103C2×C4⋊(C3⋊D3)C2×D314yescomplemented
104C22×C3×Dic3—31no—
105C22×C3×Dic3—31no—
106C22×C3×Dic3—31no—
107C22×C3×Dic3—61no—
108C2×C3×D12—34no—
109C2×C3×D12—64no—
110C2×#626—34no—
111C2×#626—34no—
112C2×#626—34no—
113C2×#626—64no—
114C2×#626—64no—
115C2×#626—64no—
116C2×#625—34no—
117C2×#625—64no—
118#3752C2×D314yescomplemented
119C3×(C2×D3)⋊C4—34no—
120C3×(C2×D3)⋊C4—34no—
121C3×(C2×D3)⋊C4—34no—
122C3×(C2×D3)⋊C4—64no—
123#3722—34no—
124(C2×D3)⋊Dic3—34no—
125C22×H(3,𝔽3)C2×D412yes—
126C22×H(3,𝔽3)C2×D412yes—
127C22×H(3,𝔽3)C2×D412yes—
128C22×H(3,𝔽3)C2411yescharacteristic
129C2×#272—28no—
130C2×#272—22no—
131C2×#272—22no—
132C2×#272C2×D414yescomplemented
133C2×(C3⋊D3)⋊C3—28no—
134C2×(C3⋊D3)⋊C3—28no—
135C2×(C3⋊D3)⋊C3—22no—
136C2×(C3⋊D3)⋊C3—22no—
137C2×(C3⋊D3)⋊C3—22no—
138C2×(C3⋊D3)⋊C3—22no—
139C2×(C3⋊D3)⋊C3—22no—
140C2×(C3⋊D3)⋊C3—22no—
141C2×(C3⋊D3)⋊C3—22no—
142C2×(C3⋊D3)⋊C3—44no—
143C2×(C3⋊D3)⋊C3C2×D414yescomplemented
144C2×(C3⋊D3)⋊C3C2×D414yescomplemented
145((C3⋊D3)⋊C3)⋊C2—232no—
146C4×H(3,𝔽3)—22no—
147#1084—22no—
148(C3⋊Dic3)⋊C3—22no—
149C24×D3—91no—
150C24×D3—91no—
151C24×D3—91no—
152C22×C3×D4—91no—
153C22×#67—91no—
154C22×#67—91no—
155C22×#67—91no—
156C22×#67—91no—
157C22×D12—31no—
158C22×D12—91no—
159C22×D12—91no—
160C22×D12—91no—
161C2×C3×C22⋊C4—91no—
162C2×C3×C22⋊C4—91no—
163C2×#217—91no—
164#937—98no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—61no—
169C2×(C2×D3)⋊C4—91no—
170C2×(C2×D3)⋊C4—91no—
171C2×(C2×D3)⋊C4—91no—
172#882—98no—
173#882—98no—
174C23×C32—21no—
175C23×C32C22×D311yescharacteristic
176C23×C32C22×D311yescharacteristic
177C22×C3⋊D3—22no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3—22no—
180C22×C3⋊D3—22no—
181C22×C3⋊D3—22no—
182C22×C3⋊D3—22no—
183C22×C3⋊D3—22no—
184C22×C3⋊D3D1214yescomplemented
185C22×C3⋊D3#6714yescomplemented
186C22×C3⋊D3C22×D312yes—
187C22×C3⋊D3C22×D312yes—
188C22×C3⋊D3C22×D312yescomplemented
189C22×C3×D3—34no—
190C22×C3×D3—34no—
191C22×C3×D3—34no—
192C22×C3×D3—34no—
193C22×C3×D3—32no—
194C22×C3×D3—32no—
195C22×C3×D3—32no—
196C22×C3×D3—32no—
197C22×C3×D3—32no—
198C22×C3×D3—64no—
199C22×C3×D3—62no—
200C22×C3×D3—62no—
201C22×C3×D3—62no—
202C22×C3×D3—62no—
203C22×C3×D3—62no—
204C22×C3×D3—62no—
205C22×C3×D3—62no—
206C22×C3×D3—62no—
207C22×C3×D3—62no—
208C22×C3×D3—62no—
209C22×C3×D3—62no—
210C22×C3×D3—62no—
211C22×C3×D3—122no—
212C22×C3×D3—122no—
213C2×D32—68no—
214C2×D32—68no—
215C2×D32—68no—
216C2×D32—68no—
217C2×D32—632no—
218C2×D32—632no—
219C2×D32—68no—
220C2×D32—68no—
221C2×C32×C4—22no—
222C2×C32×C4—22no—
223C2×C32×C4—22no—
224C2×C32×C4—42no—
225C2×C32×C4C22×D312yescomplemented
226C2×C32×C4C22×D312yescomplemented
227C2×C3⋊Dic3—22no—
228C2×C3⋊Dic3C22×D312yescomplemented
229C4⋊(C3⋊D3)—28no—
230C2×C3×Dic3—32no—
231C2×C3×Dic3—32no—
232C2×C3×Dic3—32no—
233C2×C3×Dic3—62no—
234C2×C3×Dic3—62no—
235C2×C3×Dic3—62no—
236C2×C3×Dic3—62no—
237C2×C3×Dic3—122no—
238C3×D12—68no—
239#626—68no—
240#626—68no—
241#626—68no—
242#625—68no—
243C2×#120—271noSylow
244C2×H(3,𝔽3)#12014yescomplemented
245C2×H(3,𝔽3)C22×D411yescharacteristic
246C2×H(3,𝔽3)C22×D411yescharacteristic
247C2×H(3,𝔽3)C22×D411yescharacteristic
248#272—24no—
249(C3⋊D3)⋊C3—24no—
250(C3⋊D3)⋊C3—24no—
251(C3⋊D3)⋊C3—42no—
252C24×C3—91no—
253C24×C3—91no—
254C24×C3—91no—
255C24×C3—91no—
256C23×D3—31no—
257C23×D3—31no—
258C23×D3—31no—
259C23×D3—31no—
260C23×D3—31no—
261C23×D3—61no—
262C23×D3—91no—
263C23×D3—91no—
264C23×D3—91no—
265C23×D3—94no—
266C23×D3—94no—
267C23×D3—94no—
268C23×D3—184no—
269C23×D3—184no—
270C23×D3—184no—
271C23×D3—184no—
272C23×D3—184no—
273C23×D3—184no—
274C23×D3—184no—
275C23×D3—184no—
276C23×D3—184no—
277C2×C3×D4—94no—
278C2×C3×D4—184no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—61no—
282C22×C3×C4—91no—
283C22×C3×C4—91no—
284C22×C3×C4D3211yescharacteristic
285C2×#67—94no—
286C2×#67—94no—
287C2×#67—94no—
288C2×#67—94no—
289C2×#67—184no—
290C2×#67—184no—
291C2×#67—184no—
292C2×#67—184no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—61no—
297C22×Dic3—91no—
298C2×D12—34no—
299C2×D12—64no—
300C2×D12—94no—
301C2×D12—94no—
302C2×D12—94no—
303C2×D12—184no—
304C2×D12—184no—
305C2×D12—184no—
306C3×C22⋊C4—94no—
307C3×C22⋊C4—94no—
308#217—94no—
309(C2×D3)⋊C4—34no—
310(C2×D3)⋊C4—34no—
311(C2×D3)⋊C4—34no—
312(C2×D3)⋊C4—64no—
313(C2×D3)⋊C4—94no—
314(C2×D3)⋊C4—94no—
315(C2×D3)⋊C4—94no—
316C22×C32—21no—
317C22×C32—22no—
318C22×C32—22no—
319C22×C32—22no—
320C22×C32C2×D1212yes—
321C22×C32D3×D412yes—
322C22×C32D3×D412yes—
323C22×C32D3×D412yes—
324C22×C32D3×D412yes—
325C22×C32C2×#6712yes—
326C22×C32C23×D311yescharacteristic
327C22×C32C23×D311yescharacteristic
328C2×C3⋊D3—28no—
329C2×C3⋊D3—28no—
330C2×C3⋊D3—22no—
331C2×C3⋊D3—22no—
332C2×C3⋊D3—22no—
333C2×C3⋊D3—22no—
334C2×C3⋊D3—22no—
335C2×C3⋊D3—22no—
336C2×C3⋊D3—22no—
337C2×C3⋊D3—44no—
338C2×C3⋊D3C2×D1214yescomplemented
339C2×C3⋊D3C2×#6714yescomplemented
340C2×C3×D3—34no—
341C2×C3×D3—34no—
342C2×C3×D3—34no—
343C2×C3×D3—34no—
344C2×C3×D3—64no—
345C2×C3×D3—68no—
346C2×C3×D3—68no—
347C2×C3×D3—68no—
348C2×C3×D3—68no—
349C2×C3×D3—62no—
350C2×C3×D3—62no—
351C2×C3×D3—62no—
352C2×C3×D3—62no—
353C2×C3×D3—62no—
354C2×C3×D3—62no—
355C2×C3×D3—62no—
356C2×C3×D3—62no—
357C2×C3×D3—62no—
358C2×C3×D3—62no—
359C2×C3×D3—62no—
360C2×C3×D3—122no—
361C2×C3×D3—122no—
362C2×C3×D3—128no—
363C2×C3×D3—124no—
364D32—632no—
365D32—632no—
366C32×C4—22no—
367C32×C4—22no—
368C32×C4—42no—
369C3⋊Dic3—22no—
370C3×Dic3—62no—
371C3×Dic3—62no—
372C3×Dic3—62no—
373C3×Dic3—122no—
374C25—271no—
375C22×D4—91no—
376C22×D4—271no—
377C22×D4—271no—
378#120—278no—
379C2×C22⋊C4—91no—
380C2×C22⋊C4—91no—
381C2×C22⋊C4—271no—
382H(3,𝔽3)C2×#12011yescharacteristic, complemented, Sylow
383C23×C3—31no—
384C23×C3—31no—
385C23×C3—61no—
386C23×C3—92no—
387C23×C3—92no—
388C23×C3—94no—
389C23×C3—94no—
390C23×C3—92no—
391C23×C3—92no—
392C23×C3—94no—
393C23×C3—182no—
394C23×C3—182no—
395C23×C3—182no—
396C23×C3—182no—
397C23×C3—182no—
398C23×C3—182no—
399C23×C3—182no—
400C23×C3—182no—
401C23×C3—182no—
402C23×C3C2×D3211yescharacteristic
403C22×D3—32no—
404C22×D3—32no—
405C22×D3—34no—
406C22×D3—34no—
407C22×D3—32no—
408C22×D3—32no—
409C22×D3—34no—
410C22×D3—34no—
411C22×D3—32no—
412C22×D3—62no—
413C22×D3—64no—
414C22×D3—62no—
415C22×D3—62no—
416C22×D3—62no—
417C22×D3—62no—
418C22×D3—62no—
419C22×D3—62no—
420C22×D3—62no—
421C22×D3—62no—
422C22×D3—62no—
423C22×D3—62no—
424C22×D3—62no—
425C22×D3—94no—
426C22×D3—94no—
427C22×D3—92no—
428C22×D3—92no—
429C22×D3—92no—
430C22×D3—122no—
431C22×D3—122no—
432C22×D3—182no—
433C22×D3—182no—
434C22×D3—182no—
435C22×D3—182no—
436C22×D3—182no—
437C22×D3—182no—
438C22×D3—182no—
439C22×D3—188no—
440C22×D3—188no—
441C22×D3—188no—
442C22×D3—188no—
443C22×D3—188no—
444C22×D3—1832no—
445C22×D3—188no—
446C22×D3—188no—
447C22×D3—188no—
448C22×D3—188no—
449C22×D3—1832no—
450C22×D3—1832no—
451C3×D4—188no—
452C2×C3×C4—22no—
453C2×C3×C4—32no—
454C2×C3×C4—32no—
455C2×C3×C4—62no—
456C2×C3×C4—62no—
457C2×C3×C4—62no—
458C2×C3×C4—92no—
459C2×C3×C4—92no—
460C2×C3×C4—122no—
461C2×C3×C4—182no—
462C2×C3×C4—182no—
463C2×C3×C4C2×D3212yes—
464#67—188no—
465#67—188no—
466#67—188no—
467#67—188no—
468C2×Dic3—32no—
469C2×Dic3—32no—
470C2×Dic3—32no—
471C2×Dic3—62no—
472C2×Dic3—62no—
473C2×Dic3—62no—
474C2×Dic3—62no—
475C2×Dic3—92no—
476C2×Dic3—122no—
477C2×Dic3—182no—
478D12—68no—
479D12—188no—
480D12—188no—
481D12—188no—
482C2×C32—21no—
483C2×C32—21no—
484C2×C32—21no—
485C2×C32—24no—
486C2×C32#88214yescomplemented
487C2×C32#93714yescomplemented
488C2×C32C22×D1211yescharacteristic
489C2×C32C2×D3×D411yescharacteristic
490C2×C32C2×D3×D411yescharacteristic
491C2×C32C2×D3×D411yescharacteristic
492C2×C32C2×D3×D411yescharacteristic
493C2×C32C22×#6711yescharacteristic
494C3⋊D3—24no—
495C3⋊D3—24no—
496C3⋊D3—42no—
497C3×D3—64no—
498C3×D3—64no—
499C3×D3—64no—
500C3×D3—64no—
501C3×D3—124no—
502C3×D3—122no—
503C24—91no—
504C24—91no—
505C24—91no—
506C24—91no—
507C24—274no—
508C24—544no—
509C24—544no—
510C24—544no—
511C2×D4—94no—
512C2×D4—184no—
513C2×D4—274no—
514C2×D4—274no—
515C2×D4—544no—
516C2×D4—544no—
517C22×C4—91no—
518C22×C4—91no—
519C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
520C22⋊C4—94no—
521C22⋊C4—94no—
522C22⋊C4—274no—
523C22×C3—31no—
524C22×C3—31no—
525C22×C3—32no—
526C22×C3—32no—
527C22×C3—32no—
528C22×C3—32no—
529C22×C3—32no—
530C22×C3—32no—
531C22×C3—61no—
532C22×C3—62no—
533C22×C3—62no—
534C22×C3—62no—
535C22×C3—94no—
536C22×C3—94no—
537C22×C3—94no—
538C22×C3—182no—
539C22×C3—188no—
540C22×C3—188no—
541C22×C3—182no—
542C22×C3—182no—
543C22×C3—182no—
544C22×C3—182no—
545C22×C3—182no—
546C22×C3—182no—
547C22×C3—182no—
548C22×C3—182no—
549C22×C3—188no—
550C22×C3—364no—
551C22×C3D3×D1212yes—
552C22×C3#380212yes—
553C22×C3D3×#6712yes—
554C22×C3C22×D3211yescharacteristic
555C2×D3—34no—
556C2×D3—34no—
557C2×D3—34no—
558C2×D3—34no—
559C2×D3—64no—
560C2×D3—62no—
561C2×D3—62no—
562C2×D3—68no—
563C2×D3—68no—
564C2×D3—62no—
565C2×D3—62no—
566C2×D3—62no—
567C2×D3—62no—
568C2×D3—62no—
569C2×D3—62no—
570C2×D3—68no—
571C2×D3—68no—
572C2×D3—62no—
573C2×D3—62no—
574C2×D3—62no—
575C2×D3—94no—
576C2×D3—94no—
577C2×D3—122no—
578C2×D3—128no—
579C2×D3—122no—
580C2×D3—124no—
581C2×D3—182no—
582C2×D3—188no—
583C2×D3—188no—
584C2×D3—182no—
585C2×D3—182no—
586C2×D3—182no—
587C2×D3—182no—
588C2×D3—182no—
589C2×D3—182no—
590C2×D3—1832no—
591C2×D3—1832no—
592C2×D3—1832no—
593C2×D3—364no—
594C3×C4—22no—
595C3×C4—62no—
596C3×C4—62no—
597C3×C4—122no—
598C3×C4—182no—
599C3×C4—182no—
600Dic3—62no—
601Dic3—62no—
602Dic3—62no—
603Dic3—122no—
604Dic3—182no—
605C32—21no—
606C32C2×#88211yescharacteristic, complemented
607C32C2×#93711yescharacteristic, complemented
608C23—92no—
609C23—92no—
610C23—92no—
611C23—94no—
612C23—94no—
613C23—94no—
614C23—92no—
615C23—182no—
616C23—182no—
617C23—182no—
618C23—182no—
619C23—182no—
620C23—182no—
621C23—182no—
622C23—182no—
623C23—182no—
624C23—548no—
625C23—548no—
626C23—548no—
627C23—5432no—
628C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
629D4—188no—
630D4—548no—
631D4—548no—
632C2×C4—22no—
633C2×C4—92no—
634C2×C4—92no—
635C2×C4—182no—
636C2×C4—182no—
637C2×C4C2×((C3⋊D3)⋊C3)⋊C212yescomplemented
638C2×C3—31no—
639C2×C3—31no—
640C2×C3—34no—
641C2×C3—34no—
642C2×C3—31no—
643C2×C3—31no—
644C2×C3—31no—
645C2×C3—31no—
646C2×C3—61no—
647C2×C3—64no—
648C2×C3—61no—
649C2×C3—61no—
650C2×C3—184no—
651C2×C3—184no—
652C2×C3—184no—
653C2×C3—362no—
654C2×C3#6392214yes—
655C2×C3C2×D3×D1211yescharacteristic
656C2×C3C2×#380211yescharacteristic
657C2×C3C2×D3×#6711yescharacteristic
658D3—64no—
659D3—64no—
660D3—64no—
661D3—64no—
662D3—124no—
663D3—122no—
664D3—184no—
665D3—184no—
666D3—362no—
667C22—94no—
668C22—94no—
669C22—94no—
670C22—182no—
671C22—182no—
672C22—188no—
673C22—188no—
674C22—188no—
675C22—182no—
676C22—182no—
677C22—182no—
678C22—182no—
679C22—182no—
680C22—182no—
681C22—182no—
682C22—364no—
683C22—5432no—
684C22#8865412yes—
685C22#8865512yes—
686C22#8867612yes—
687C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
688C4—22no—
689C4—182no—
690C4—182no—
691C3—31no—
692C3—31no—
693C3—61no—
694C3C2×#6392211yescharacteristic
695C2—184no—
696C2—184no—
697C2—184no—
698C2—362no—
699C2#1172116214yesdirect product factor
700C2C2×#8865411yescharacteristic
701C2C2×#8865511yescharacteristic
702C2C2×#8867611yescharacteristic
subgroupG/H
centerC23C2×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
FrattiniC22×C3C22×D32
FittingC22×C4×H(3,𝔽3)C22
socleC23×C3C2×D32
hypercenterC22×C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C2×#120
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C23×((C3⋊D3)⋊C3)⋊C2C2semidirect
2. C22×C4⋊((C3⋊D3)⋊C3)C2semidirect
3. C22×#6200C2semidirect
4. C22×#6198C2semidirect
5. C2×#88542C2semidirect
6. C2×#3752⋊C3C2semidirect
7. C2×#88450C2semidirect
8. #11721162C2direct (N × H)
14. C23×(C3⋊D3)⋊C3C22semidirect
18. C22×((C3⋊D3)⋊C3)⋊C2C22semidirect
19. C22×C4×H(3,𝔽3)C22semidirect
20. C22×#1084C22semidirect
21. C22×(C3⋊Dic3)⋊C3C22semidirect
23. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
25. C2×#6200C22semidirect
27. C2×#6198C22semidirect
28. #88542C22semidirect
29. #3752⋊C3C22semidirect
30. #88450C22semidirect
33. C22×C4⋊(C3⋊D3)D3semidirect
39. C2×#3752D3semidirect
51. C22×#272D4semidirect
60. C22×(C3⋊D3)⋊C3D4semidirect
61. C22×(C3⋊D3)⋊C3D4semidirect
64. C22×(C3⋊D3)⋊C3C23semidirect
70. C2×C4×H(3,𝔽3)C23semidirect
72. C2×#1084C23semidirect
74. C2×(C3⋊Dic3)⋊C3C23semidirect
83. C23×C3⋊D3C2×D3semidirect
99. C22×C32×C4C2×D3semidirect
100. C22×C32×C4C2×D3semidirect
101. C22×C3⋊Dic3C2×D3semidirect
103. C2×C4⋊(C3⋊D3)C2×D3semidirect
118. #3752C2×D3semidirect
132. C2×#272C2×D4semidirect
143. C2×(C3⋊D3)⋊C3C2×D4semidirect
144. C2×(C3⋊D3)⋊C3C2×D4semidirect
184. C22×C3⋊D3D12semidirect
185. C22×C3⋊D3#67semidirect
188. C22×C3⋊D3C22×D3semidirect
225. C2×C32×C4C22×D3semidirect
226. C2×C32×C4C22×D3semidirect
228. C2×C3⋊Dic3C22×D3semidirect
244. C2×H(3,𝔽3)#120semidirect
338. C2×C3⋊D3C2×D12semidirect
339. C2×C3⋊D3C2×#67semidirect
382. H(3,𝔽3)C2×#120semidirect
486. C2×C32#882semidirect
487. C2×C32#937semidirect
519. C22×C4((C3⋊D3)⋊C3)⋊C2semidirect
606. C32C2×#882semidirect
607. C32C2×#937semidirect
637. C2×C4C2×((C3⋊D3)⋊C3)⋊C2semidirect
699. C2#11721162direct (N × H)

Maximal subgroups

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

subgroupindex
C23×((C3⋊D3)⋊C3)⋊C22
C22×C4⋊((C3⋊D3)⋊C3)2
C22×#62002
C22×#61982
C2×#885422
C2×#3752⋊C32
C2×#884502
#117211622
C2×#639233
C2×#639223