Finite Group Databasebeta

← C2×#11721160 #13150866

Subgroups — C2×#11721160 #13150866

Order 1728.

2491 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×((C3⋊D3)⋊C3)⋊C2C211yesmaximal, characteristic
2C22×C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
3C22×((C3⋊D3)⋊C3)⋊C4C211yesmaximal, characteristic, complemented
4C2×#88542C211yesmaximal, characteristic, complemented
5C2×#3752⋊C3C211yesmaximal, characteristic, complemented
6C2×#88451C211yesmaximal, characteristic, complemented
7C2×#88450C211yesmaximal, characteristic, complemented
8#11721160C218yesmaximal, direct product factor
9C2×#63921—31nomaximal
10C2×D3×(C2×D3)⋊C4—31nomaximal
11C23×#272C2211yescharacteristic
12C23×(C3⋊D3)⋊C3C2211yescharacteristic
13C23×(C3⋊D3)⋊C3C2211yescharacteristic
14C22×((C3⋊D3)⋊C3)⋊C2—24no—
15C22×((C3⋊D3)⋊C3)⋊C2—24no—
16C22×((C3⋊D3)⋊C3)⋊C2C418yescomplemented
17C22×((C3⋊D3)⋊C3)⋊C2C2214yes—
18C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
19C22×#1084C2211yescharacteristic, complemented
20C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
22C2×C4×(C3⋊D3)⋊C3—24no—
23C2×C4×(C3⋊D3)⋊C3C2214yescomplemented
24C2×((C3⋊D3)⋊C3)⋊C4—24no—
25C2×((C3⋊D3)⋊C3)⋊C4C2214yescomplemented
26#88542C2214yescomplemented
27#3752⋊C3C2214yescomplemented
28#88451C2214yescomplemented
29#88450C2214yescomplemented
30C23×D32—31no—
31C23×D32—31no—
32C22×C4×C3⋊D3D311yescharacteristic, complemented
33C22×C3×C4×D3—31no—
34C22×#624—31no—
35C22×D3×Dic3—31no—
36C2×#3752D311yescharacteristic, complemented
37C2×C3×(C2×D3)⋊C4—31no—
38C2×C3×(C2×D3)⋊C4—31no—
39C2×C3×(C2×D3)⋊C4—31no—
40C2×C3×(C2×D3)⋊C4—61no—
41C2×#3722—31no—
42C2×(C2×D3)⋊Dic3—31no—
43C2×(C2×D3)⋊Dic3—31no—
44C2×(C2×D3)⋊Dic3—31no—
45#63921—38no—
46D3×(C2×D3)⋊C4—38no—
47C23×H(3,𝔽3)C2311yescharacteristic
48C22×#272—22no—
49C22×#272—22no—
50C22×#272C2×C414yescomplemented
51C22×#272C2312yes—
52C22×(C3⋊D3)⋊C3—22no—
53C22×(C3⋊D3)⋊C3—22no—
54C22×(C3⋊D3)⋊C3C2×C414yes—
55C22×(C3⋊D3)⋊C3C2×C414yescomplemented
56C22×(C3⋊D3)⋊C3D414yes—
57C22×(C3⋊D3)⋊C3D414yes—
58C22×(C3⋊D3)⋊C3C2312yes—
59C22×(C3⋊D3)⋊C3C2312yes—
60C2×((C3⋊D3)⋊C3)⋊C2—232no—
61C2×((C3⋊D3)⋊C3)⋊C2—28no—
62C2×((C3⋊D3)⋊C3)⋊C2—28no—
63C2×((C3⋊D3)⋊C3)⋊C2C2×C4116yescomplemented
64C2×C4×H(3,𝔽3)—22no—
65C2×C4×H(3,𝔽3)C2312yescomplemented
66C2×#1084—22no—
67C2×#1084C2312yescomplemented
68C2×(C3⋊Dic3)⋊C3—22no—
69C2×(C3⋊Dic3)⋊C3—22no—
70C2×(C3⋊Dic3)⋊C3C2312yescomplemented
71C2×(C3⋊Dic3)⋊C3C2312yescomplemented
72C4×(C3⋊D3)⋊C3—28no—
73((C3⋊D3)⋊C3)⋊C4—28no—
74C22×(C2×D3)⋊C4—91no—
75C2×D3×C22⋊C4—91no—
76C2×D3×C22⋊C4—91no—
77C23×C3⋊D3C2×D311yescharacteristic
78C23×C3⋊D3C2×D311yescharacteristic
79C23×C3×D3—31no—
80C23×C3×D3—31no—
81C23×C3×D3—31no—
82C23×C3×D3—31no—
83C23×C3×D3—61no—
84C22×D32—38no—
85C22×D32—38no—
86C22×D32—34no—
87C22×D32—34no—
88C22×D32—64no—
89C22×D32—64no—
90C22×D32—64no—
91C22×D32—64no—
92C22×C32×C4—21no—
93C22×C32×C4C2×D311yescharacteristic, complemented
94C22×C32×C4C2×D311yescharacteristic, complemented
95C22×C3⋊Dic3C2×D311yescharacteristic, complemented
96C22×C3⋊Dic3C2×D311yescharacteristic, complemented
97C2×C4×C3⋊D3—24no—
98C2×C4×C3⋊D3C2×D314yescomplemented
99C22×C3×Dic3—31no—
100C22×C3×Dic3—31no—
101C22×C3×Dic3—31no—
102C22×C3×Dic3—31no—
103C22×C3×Dic3—61no—
104C2×C3×C4×D3—34no—
105C2×C3×C4×D3—64no—
106C2×#624—34no—
107C2×#624—64no—
108C2×D3×Dic3—34no—
109C2×D3×Dic3—64no—
110#3752C2×D314yescomplemented
111C3×(C2×D3)⋊C4—34no—
112C3×(C2×D3)⋊C4—34no—
113C3×(C2×D3)⋊C4—34no—
114C3×(C2×D3)⋊C4—64no—
115#3722—34no—
116(C2×D3)⋊Dic3—34no—
117(C2×D3)⋊Dic3—34no—
118(C2×D3)⋊Dic3—34no—
119C22×H(3,𝔽3)C22×C412yes—
120C22×H(3,𝔽3)C2×D412yes—
121C22×H(3,𝔽3)C2×D412yes—
122C22×H(3,𝔽3)C2411yescharacteristic
123C2×#272—28no—
124C2×#272—22no—
125C2×#272—22no—
126C2×#272C22×C414yescomplemented
127C2×(C3⋊D3)⋊C3—28no—
128C2×(C3⋊D3)⋊C3—22no—
129C2×(C3⋊D3)⋊C3—22no—
130C2×(C3⋊D3)⋊C3C22⋊C4116yescomplemented
131C2×(C3⋊D3)⋊C3C22×C414yes—
132C2×(C3⋊D3)⋊C3C22×C414yescomplemented
133C2×(C3⋊D3)⋊C3C2×D414yes—
134C2×(C3⋊D3)⋊C3C2×D414yes—
135((C3⋊D3)⋊C3)⋊C2—232no—
136C4×H(3,𝔽3)—22no—
137#1084—22no—
138(C3⋊Dic3)⋊C3—22no—
139(C3⋊Dic3)⋊C3—22no—
140C24×D3—91no—
141C24×D3—91no—
142C24×D3—91no—
143C23×C3×C4—91no—
144C23×Dic3—91no—
145C22×C4×D3—31no—
146C22×C4×D3—91no—
147C22×C4×D3—91no—
148C22×C4×D3—91no—
149C2×C3×C22⋊C4—91no—
150C2×C3×C22⋊C4—91no—
151C2×#217—91no—
152C2×#217—91no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—61no—
157C2×(C2×D3)⋊C4—91no—
158C2×(C2×D3)⋊C4—98no—
159C2×(C2×D3)⋊C4—91no—
160C2×(C2×D3)⋊C4—91no—
161C2×(C2×D3)⋊C4—91no—
162C2×(C2×D3)⋊C4—91no—
163D3×C22⋊C4—98no—
164D3×C22⋊C4—98no—
165C23×C32—21no—
166C23×C32C22×D311yescharacteristic
167C23×C32C22×D311yescharacteristic
168C22×C3⋊D3—22no—
169C22×C3⋊D3—22no—
170C22×C3⋊D3C4×D314yes—
171C22×C3⋊D3C4×D314yescomplemented
172C22×C3⋊D3D1214yes—
173C22×C3⋊D3#6714yes—
174C22×C3⋊D3C22×D312yes—
175C22×C3⋊D3C22×D312yes—
176C22×C3×D3—34no—
177C22×C3×D3—34no—
178C22×C3×D3—34no—
179C22×C3×D3—32no—
180C22×C3×D3—34no—
181C22×C3×D3—34no—
182C22×C3×D3—34no—
183C22×C3×D3—32no—
184C22×C3×D3—32no—
185C22×C3×D3—32no—
186C22×C3×D3—64no—
187C22×C3×D3—62no—
188C22×C3×D3—62no—
189C22×C3×D3—62no—
190C22×C3×D3—62no—
191C22×C3×D3—62no—
192C22×C3×D3—62no—
193C22×C3×D3—62no—
194C22×C3×D3—122no—
195C22×C3×D3—122no—
196C2×D32—316no—
197C2×D32—316no—
198C2×D32—632no—
199C2×D32—68no—
200C2×D32—68no—
201C2×D32—632no—
202C2×D32—68no—
203C2×D32—68no—
204C2×C32×C4—22no—
205C2×C32×C4—22no—
206C2×C32×C4—22no—
207C2×C32×C4—42no—
208C2×C32×C4C22×D312yescomplemented
209C2×C32×C4C22×D312yescomplemented
210C2×C3⋊Dic3—22no—
211C2×C3⋊Dic3—22no—
212C2×C3⋊Dic3C22×D312yescomplemented
213C2×C3⋊Dic3C22×D312yescomplemented
214C4×C3⋊D3—28no—
215C2×C3×Dic3—32no—
216C2×C3×Dic3—32no—
217C2×C3×Dic3—32no—
218C2×C3×Dic3—32no—
219C2×C3×Dic3—62no—
220C2×C3×Dic3—62no—
221C2×C3×Dic3—62no—
222C2×C3×Dic3—62no—
223C2×C3×Dic3—62no—
224C2×C3×Dic3—122no—
225C3×C4×D3—68no—
226#624—68no—
227D3×Dic3—68no—
228C22×C22⋊C4—271noSylow
229C2×H(3,𝔽3)C2×C22⋊C414yescomplemented
230C2×H(3,𝔽3)C23×C411yescharacteristic
231C2×H(3,𝔽3)C22×D411yescharacteristic
232C2×H(3,𝔽3)C22×D411yescharacteristic
233#272—24no—
234(C3⋊D3)⋊C3—24no—
235(C3⋊D3)⋊C3C2×C22⋊C418yescomplemented
236C24×C3—91no—
237C24×C3—91no—
238C24×C3—91no—
239C23×D3—31no—
240C23×D3—31no—
241C23×D3—31no—
242C23×D3—31no—
243C23×D3—61no—
244C23×D3—91no—
245C23×D3—91no—
246C23×D3—94no—
247C23×D3—98no—
248C23×D3—94no—
249C23×D3—94no—
250C23×D3—98no—
251C23×D3—98no—
252C23×D3—184no—
253C23×D3—184no—
254C23×D3—184no—
255C23×D3—184no—
256C23×D3—184no—
257C23×D3—184no—
258C22×C3×C4—31no—
259C22×C3×C4—31no—
260C22×C3×C4—61no—
261C22×C3×C4—94no—
262C22×C3×C4—91no—
263C22×C3×C4—91no—
264C22×C3×C4—91no—
265C22×C3×C4—184no—
266C22×C3×C4D3211yescharacteristic
267C22×Dic3—31no—
268C22×Dic3—31no—
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—61no—
272C22×Dic3—91no—
273C22×Dic3—91no—
274C22×Dic3—94no—
275C22×Dic3—184no—
276C2×C4×D3—34no—
277C2×C4×D3—64no—
278C2×C4×D3—94no—
279C2×C4×D3—94no—
280C2×C4×D3—94no—
281C2×C4×D3—184no—
282C2×C4×D3—184no—
283C2×C4×D3—184no—
284C3×C22⋊C4—94no—
285C3×C22⋊C4—94no—
286#217—94no—
287#217—94no—
288(C2×D3)⋊C4—34no—
289(C2×D3)⋊C4—34no—
290(C2×D3)⋊C4—34no—
291(C2×D3)⋊C4—64no—
292(C2×D3)⋊C4—94no—
293(C2×D3)⋊C4—94no—
294(C2×D3)⋊C4—94no—
295(C2×D3)⋊C4—94no—
296(C2×D3)⋊C4—94no—
297C22×C32—21no—
298C22×C32—22no—
299C22×C32—22no—
300C22×C32—22no—
301C22×C32C2×C4×D312yes—
302C22×C32C2×C4×D312yes—
303C22×C32C2×D1212yes—
304C22×C32D3×D412yes—
305C22×C32D3×D412yes—
306C22×C32C2×#6712yes—
307C22×C32C23×D311yescharacteristic
308C22×C32C23×D311yescharacteristic
309C2×C3⋊D3—28no—
310C2×C3⋊D3—22no—
311C2×C3⋊D3—22no—
312C2×C3⋊D3(C2×D3)⋊C4116yescomplemented
313C2×C3⋊D3C2×C4×D314yes—
314C2×C3⋊D3C2×C4×D314yescomplemented
315C2×C3⋊D3C2×D1214yes—
316C2×C3⋊D3C2×#6714yes—
317C2×C3×D3—316no—
318C2×C3×D3—34no—
319C2×C3×D3—34no—
320C2×C3×D3—34no—
321C2×C3×D3—34no—
322C2×C3×D3—34no—
323C2×C3×D3—34no—
324C2×C3×D3—64no—
325C2×C3×D3—68no—
326C2×C3×D3—68no—
327C2×C3×D3—68no—
328C2×C3×D3—62no—
329C2×C3×D3—62no—
330C2×C3×D3—62no—
331C2×C3×D3—62no—
332C2×C3×D3—62no—
333C2×C3×D3—62no—
334C2×C3×D3—122no—
335C2×C3×D3—122no—
336C2×C3×D3—128no—
337D32—632no—
338D32—632no—
339C32×C4—22no—
340C32×C4—22no—
341C32×C4—42no—
342C3⋊Dic3—22no—
343C3⋊Dic3—22no—
344C3×Dic3—62no—
345C3×Dic3—62no—
346C3×Dic3—62no—
347C3×Dic3—62no—
348C3×Dic3—122no—
349C25—271no—
350C23×C4—91no—
351C23×C4—271no—
352C2×C22⋊C4—91no—
353C2×C22⋊C4—91no—
354C2×C22⋊C4—278no—
355C2×C22⋊C4—271no—
356C2×C22⋊C4—271no—
357H(3,𝔽3)C22×C22⋊C411yescharacteristic, complemented, Sylow
358C23×C3—31no—
359C23×C3—31no—
360C23×C3—61no—
361C23×C3—92no—
362C23×C3—94no—
363C23×C3—94no—
364C23×C3—94no—
365C23×C3—92no—
366C23×C3—94no—
367C23×C3—92no—
368C23×C3—94no—
369C23×C3—182no—
370C23×C3—182no—
371C23×C3—182no—
372C23×C3—182no—
373C23×C3C2×D3211yescharacteristic
374C22×D3—32no—
375C22×D3—34no—
376C22×D3—34no—
377C22×D3—34no—
378C22×D3—32no—
379C22×D3—32no—
380C22×D3—34no—
381C22×D3—34no—
382C22×D3—32no—
383C22×D3—34no—
384C22×D3—62no—
385C22×D3—64no—
386C22×D3—62no—
387C22×D3—62no—
388C22×D3—62no—
389C22×D3—62no—
390C22×D3—62no—
391C22×D3—62no—
392C22×D3—94no—
393C22×D3—94no—
394C22×D3—94no—
395C22×D3—92no—
396C22×D3—94no—
397C22×D3—92no—
398C22×D3—916no—
399C22×D3—916no—
400C22×D3—916no—
401C22×D3—122no—
402C22×D3—122no—
403C22×D3—182no—
404C22×D3—182no—
405C22×D3—188no—
406C22×D3—188no—
407C22×D3—1832no—
408C22×D3—188no—
409C22×D3—188no—
410C22×D3—1832no—
411C22×D3—188no—
412C22×D3—188no—
413C22×D3—1832no—
414C2×C3×C4—22no—
415C2×C3×C4—32no—
416C2×C3×C4—32no—
417C2×C3×C4—62no—
418C2×C3×C4—62no—
419C2×C3×C4—62no—
420C2×C3×C4—92no—
421C2×C3×C4—92no—
422C2×C3×C4—92no—
423C2×C3×C4—122no—
424C2×C3×C4—188no—
425C2×C3×C4—182no—
426C2×C3×C4—182no—
427C2×C3×C4—182no—
428C2×C3×C4C2×D3212yes—
429C2×Dic3—32no—
430C2×Dic3—32no—
431C2×Dic3—32no—
432C2×Dic3—32no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—62no—
438C2×Dic3—92no—
439C2×Dic3—92no—
440C2×Dic3—122no—
441C2×Dic3—182no—
442C2×Dic3—182no—
443C2×Dic3—188no—
444C4×D3—68no—
445C4×D3—188no—
446C4×D3—188no—
447C4×D3—188no—
448C2×C32—21no—
449C2×C32—21no—
450C2×C32—21no—
451C2×C32—24no—
452C2×C32D3×C22⋊C414yescomplemented
453C2×C32C2×(C2×D3)⋊C414yescomplemented
454C2×C32C22×C4×D311yescharacteristic
455C2×C32C22×C4×D311yescharacteristic
456C2×C32C22×D1211yescharacteristic
457C2×C32C2×D3×D411yescharacteristic
458C2×C32C2×D3×D411yescharacteristic
459C2×C32C22×#6711yescharacteristic
460C3⋊D3—24no—
461C3⋊D3C2×(C2×D3)⋊C418yescomplemented
462C3×D3—38no—
463C3×D3—64no—
464C3×D3—64no—
465C3×D3—64no—
466C3×D3—124no—
467C24—91no—
468C24—91no—
469C24—91no—
470C24—274no—
471C24—278no—
472C24—544no—
473C24—544no—
474C22×C4—91no—
475C22×C4—91no—
476C22×C4—91no—
477C22×C4—94no—
478C22×C4—184no—
479C22×C4—274no—
480C22×C4—544no—
481C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
482C22⋊C4—94no—
483C22⋊C4—94no—
484C22⋊C4—274no—
485C22⋊C4—274no—
486C22×C3—31no—
487C22×C3—31no—
488C22×C3—32no—
489C22×C3—32no—
490C22×C3—32no—
491C22×C3—32no—
492C22×C3—32no—
493C22×C3—32no—
494C22×C3—61no—
495C22×C3—62no—
496C22×C3—62no—
497C22×C3—62no—
498C22×C3—94no—
499C22×C3—94no—
500C22×C3—94no—
501C22×C3—916no—
502C22×C3—94no—
503C22×C3—94no—
504C22×C3—182no—
505C22×C3—188no—
506C22×C3—182no—
507C22×C3—182no—
508C22×C3—182no—
509C22×C3—188no—
510C22×C3C4×D3212yes—
511C22×C3D3×D1212yes—
512C22×C3D3×#6712yes—
513C22×C3C22×D3211yescharacteristic
514C2×D3—34no—
515C2×D3—34no—
516C2×D3—34no—
517C2×D3—316no—
518C2×D3—34no—
519C2×D3—34no—
520C2×D3—34no—
521C2×D3—64no—
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—68no—
525C2×D3—68no—
526C2×D3—62no—
527C2×D3—62no—
528C2×D3—62no—
529C2×D3—62no—
530C2×D3—68no—
531C2×D3—94no—
532C2×D3—94no—
533C2×D3—94no—
534C2×D3—916no—
535C2×D3—94no—
536C2×D3—122no—
537C2×D3—128no—
538C2×D3—122no—
539C2×D3—182no—
540C2×D3—188no—
541C2×D3—182no—
542C2×D3—1832no—
543C2×D3—1832no—
544C2×D3—1832no—
545C3×C4—22no—
546C3×C4—62no—
547C3×C4—62no—
548C3×C4—122no—
549C3×C4—182no—
550C3×C4—182no—
551C3×C4—182no—
552Dic3—62no—
553Dic3—62no—
554Dic3—62no—
555Dic3—62no—
556Dic3—122no—
557Dic3—182no—
558Dic3—182no—
559C32—21no—
560C32C2×D3×C22⋊C411yescharacteristic, complemented
561C32C22×(C2×D3)⋊C411yescharacteristic, complemented
562C23—92no—
563C23—94no—
564C23—94no—
565C23—94no—
566C23—92no—
567C23—92no—
568C23—94no—
569C23—94no—
570C23—182no—
571C23—182no—
572C23—182no—
573C23—182no—
574C23—2716no—
575C23—548no—
576C23—5432no—
577C23—548no—
578C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
579C2×C4—22no—
580C2×C4—92no—
581C2×C4—92no—
582C2×C4—92no—
583C2×C4—188no—
584C2×C4—182no—
585C2×C4—182no—
586C2×C4—182no—
587C2×C4—548no—
588C2×C4C2×((C3⋊D3)⋊C3)⋊C212yescomplemented
589C2×C3—31no—
590C2×C3—31no—
591C2×C3—34no—
592C2×C3—34no—
593C2×C3—31no—
594C2×C3—31no—
595C2×C3—31no—
596C2×C3—31no—
597C2×C3—61no—
598C2×C3—64no—
599C2×C3—61no—
600C2×C3—61no—
601C2×C3—98no—
602C2×C3—184no—
603C2×C3—184no—
604C2×C3D3×(C2×D3)⋊C414yes—
605C2×C3C2×C4×D3211yescharacteristic
606C2×C3C2×D3×D1211yescharacteristic
607C2×C3C2×D3×#6711yescharacteristic
608D3—38no—
609D3—64no—
610D3—64no—
611D3—64no—
612D3—98no—
613D3—124no—
614D3—184no—
615C22—94no—
616C22—916no—
617C22—94no—
618C22—94no—
619C22—94no—
620C22—94no—
621C22—182no—
622C22—182no—
623C22—188no—
624C22—188no—
625C22—182no—
626C22—182no—
627C22—5432no—
628C22C4×((C3⋊D3)⋊C3)⋊C212yes—
629C22#8865412yes—
630C22#8867612yes—
631C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
632C4—22no—
633C4—182no—
634C4—182no—
635C4—182no—
636C3—31no—
637C3—31no—
638C3—61no—
639C3C2×D3×(C2×D3)⋊C411yescharacteristic
640C2—98no—
641C2—184no—
642C2—184no—
643C2#1172116014yesdirect product factor
644C2C2×C4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
645C2C2×#8865411yescharacteristic
646C2C2×#8867611yescharacteristic
subgroupG/H
centerC23C2×((C3⋊D3)⋊C3)⋊C2
commutatorC2×H(3,𝔽3)C23×C4
FrattiniC22×C3C22×D32
FittingC22×C4×H(3,𝔽3)C22
socleC23×C3C2×D32
prime radicalC23×((C3⋊D3)⋊C3)⋊C2C2
cosocleC22×H(3,𝔽3)C24
hypercenterC22×C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C22×C22⋊C4
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×(C3⋊D3)⋊C3C2semidirect
3. C22×((C3⋊D3)⋊C3)⋊C4C2semidirect
4. C2×#88542C2semidirect
5. C2×#3752⋊C3C2semidirect
6. C2×#88451C2semidirect
7. C2×#88450C2semidirect
8. #11721160C2direct (N × H)
16. C22×((C3⋊D3)⋊C3)⋊C2C4semidirect
18. C22×C4×H(3,𝔽3)C22semidirect
19. C22×#1084C22semidirect
20. C22×(C3⋊Dic3)⋊C3C22semidirect
21. C22×(C3⋊Dic3)⋊C3C22semidirect
23. C2×C4×(C3⋊D3)⋊C3C22semidirect
25. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
26. #88542C22semidirect
27. #3752⋊C3C22semidirect
28. #88451C22semidirect
29. #88450C22semidirect
32. C22×C4×C3⋊D3D3semidirect
36. C2×#3752D3semidirect
50. C22×#272C2×C4semidirect
55. C22×(C3⋊D3)⋊C3C2×C4semidirect
63. C2×((C3⋊D3)⋊C3)⋊C2C2×C4semidirect
65. C2×C4×H(3,𝔽3)C23semidirect
67. C2×#1084C23semidirect
70. C2×(C3⋊Dic3)⋊C3C23semidirect
71. C2×(C3⋊Dic3)⋊C3C23semidirect
93. C22×C32×C4C2×D3semidirect
94. C22×C32×C4C2×D3semidirect
95. C22×C3⋊Dic3C2×D3semidirect
96. C22×C3⋊Dic3C2×D3semidirect
98. C2×C4×C3⋊D3C2×D3semidirect
110. #3752C2×D3semidirect
126. C2×#272C22×C4semidirect
130. C2×(C3⋊D3)⋊C3C22⋊C4semidirect
132. C2×(C3⋊D3)⋊C3C22×C4semidirect
171. C22×C3⋊D3C4×D3semidirect
208. C2×C32×C4C22×D3semidirect
209. C2×C32×C4C22×D3semidirect
212. C2×C3⋊Dic3C22×D3semidirect
213. C2×C3⋊Dic3C22×D3semidirect
229. C2×H(3,𝔽3)C2×C22⋊C4semidirect
235. (C3⋊D3)⋊C3C2×C22⋊C4semidirect
312. C2×C3⋊D3(C2×D3)⋊C4semidirect
314. C2×C3⋊D3C2×C4×D3semidirect
357. H(3,𝔽3)C22×C22⋊C4semidirect
452. C2×C32D3×C22⋊C4semidirect
453. C2×C32C2×(C2×D3)⋊C4semidirect
461. C3⋊D3C2×(C2×D3)⋊C4semidirect
481. C22×C4((C3⋊D3)⋊C3)⋊C2semidirect
560. C32C2×D3×C22⋊C4semidirect
561. C32C22×(C2×D3)⋊C4semidirect
588. C2×C4C2×((C3⋊D3)⋊C3)⋊C2semidirect
643. C2#11721160direct (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)⋊C32
C22×((C3⋊D3)⋊C3)⋊C42
C2×#885422
C2×#3752⋊C32
C2×#884512
C2×#884502
#117211602
C2×#639213
C2×D3×(C2×D3)⋊C43