Finite Group Databasebeta

← #13150876

Subgroups — #13150876

Order 1728.

1585 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
2C2×#88676C212yesmaximal, complemented
3C2×#88654C211yesmaximal, characteristic, complemented
4#11721830C211yesmaximal, characteristic, complemented
5#64139⋊C3C211yesmaximal, characteristic, complemented
6#11721322C212yesmaximal, complemented
7#11721160C212yesmaximal, complemented
8#11721156C211yesmaximal, characteristic, complemented
9#11721141C211yesmaximal, characteristic, complemented
10#11721140C212yesmaximal, complemented
11#11721129C211yesmaximal, characteristic, complemented
12#10595081—31nomaximal
13D3×#930—31nomaximal
14C23×(C3⋊D3)⋊C3C2211yescharacteristic
15C22×((C3⋊D3)⋊C3)⋊C2C2212yes—
16C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
17C2×#6235C2212yescomplemented
18C2×C4⋊#272C2211yescharacteristic, complemented
19C2×#638⋊C3C2212yescomplemented
20C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
21C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
22C2×C4×(C3⋊D3)⋊C3—24no—
23C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
24C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
26C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
27#88676—28no—
28C2×#6200C2212yescomplemented
29C2×#6200C2212yescomplemented
30C2×#6198C2212yescomplemented
31C2×((C3⋊D3)⋊C3)⋊C4C2212yes—
32#88654—24no—
33#88542C2212yescomplemented
34C4⋊#1084C2211yescharacteristic, complemented
35#3752⋊C3C2212yescomplemented
36C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
37#88451C2212yescomplemented
38#88450C2212yescomplemented
39#88448C2212yescomplemented
40C22×C4×C3⋊D3D311yescharacteristic, complemented
41C22×C3×C4×D3—31no—
42C2×#3811—32no—
43C2×D3×#67—32no—
44C2×#3802—31no—
45C2×D3×D12—31no—
46#64139D311yescharacteristic, complemented
47C3×#930—31no—
48C3×#930—31no—
49C3×#930—31no—
50C3×#930—61no—
51#63980—32no—
52#63978—32no—
53#63921—32no—
54D3×(C2×D3)⋊C4—32no—
55#63916—31no—
56#63916—31no—
57#63912—32no—
58#63909—31no—
59#63908—31no—
60#63906—32no—
61#63900—31no—
62D3×C4⋊Dic3—31no—
63C23×H(3,𝔽3)C2311yescharacteristic
64C22×#272C2312yes—
65C22×(C3⋊D3)⋊C3—22no—
66C22×(C3⋊D3)⋊C3—22no—
67C22×(C3⋊D3)⋊C3D414yescomplemented
68C22×(C3⋊D3)⋊C3C2312yes—
69C22×(C3⋊D3)⋊C3C2311yescharacteristic
70C22×(C3⋊D3)⋊C3C2311yescharacteristic
71C2×((C3⋊D3)⋊C3)⋊C2—24no—
72C2×((C3⋊D3)⋊C3)⋊C2—24no—
73C2×((C3⋊D3)⋊C3)⋊C2—24no—
74C2×C4×H(3,𝔽3)—22no—
75C2×C4×H(3,𝔽3)C2311yescharacteristic
76C2×C4×H(3,𝔽3)C2311yescharacteristic
77#6235—24no—
78C2×#1084C2312yes—
79C4⋊#272—22no—
80#638⋊C3—24no—
81C2×(C3⋊Dic3)⋊C3—22no—
82C2×(C3⋊Dic3)⋊C3C2312yes—
83C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
84C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
85C4⋊((C3⋊D3)⋊C3)—22no—
86C4×(C3⋊D3)⋊C3—22no—
87C4×(C3⋊D3)⋊C3—22no—
88C4×(C3⋊D3)⋊C3—22no—
89C4×(C3⋊D3)⋊C3D414yescomplemented
90#6200—24no—
91#6200—24no—
92#6198—24no—
93((C3⋊D3)⋊C3)⋊C4—24no—
94C2×#930—91no—
95D3×#121—91no—
96D3×#121—91no—
97C23×C3⋊D3C2×D311yescharacteristic
98C23×C3×D3—31no—
99C22×D32—32no—
100C22×D32—32no—
101C22×C32×C4—21no—
102C22×C32×C4C2×D311yescharacteristic, complemented
103C22×C32×C4C2×D311yescharacteristic, complemented
104C2×#638C2×D312yescomplemented
105C22×C3⋊Dic3C2×D311yescharacteristic, complemented
106C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
107C2×C4×C3⋊D3—24no—
108C2×C4×C3⋊D3C2×D311yescharacteristic
109C2×C4×C3⋊D3C2×D311yescharacteristic
110C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
111C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
112C2×C3×#67—32no—
113C2×C3×#67—32no—
114C2×C3×#67—32no—
115C2×C3×#67—62no—
116C22×C3×Dic3—31no—
117C2×C3×D12—31no—
118C2×C3×D12—31no—
119C2×C3×D12—31no—
120C2×C3×D12—61no—
121C2×C3×C4×D3—31no—
122C2×C3×C4×D3—31no—
123C2×C3×C4×D3—31no—
124C2×C3×C4×D3—31no—
125C2×C3×C4×D3—64no—
126#3811—68no—
127D3×#67—68no—
128C2×#626—32no—
129C2×#626—32no—
130C2×#626—32no—
131C2×#626—32no—
132C2×#625—32no—
133C2×#625—32no—
134C2×#624—32no—
135C2×D3×Dic3—32no—
136#3802—64no—
137D3×D12—64no—
138#3752C2×D312yescomplemented
139C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×(C2×D3)⋊C4—32no—
143C3×(C2×D3)⋊C4—62no—
144C3×C4⋊Dic3—31no—
145C3×C4⋊Dic3—31no—
146C3×C4⋊Dic3—31no—
147C3×C4⋊Dic3—61no—
148#3724—32no—
149Dic3⋊Dic3—32no—
150#3722—32no—
151(C2×D3)⋊Dic3—32no—
152(C2×D3)⋊Dic3—32no—
153(C2×D3)⋊Dic3—32no—
154C22×H(3,𝔽3)—21no—
155C22×H(3,𝔽3)—21no—
156C22×H(3,𝔽3)C2×D412yescomplemented
157C22×H(3,𝔽3)C2411yescharacteristic
158C2×#272—22no—
159C2×#272—22no—
160C2×#272—22no—
161C2×(C3⋊D3)⋊C3—21no—
162C2×(C3⋊D3)⋊C3—21no—
163C2×(C3⋊D3)⋊C3—28no—
164C2×(C3⋊D3)⋊C3—22no—
165C2×(C3⋊D3)⋊C3—22no—
166C2×(C3⋊D3)⋊C3—22no—
167C2×(C3⋊D3)⋊C3C2×D412yes—
168C2×(C3⋊D3)⋊C3C2×D412yes—
169C2×(C3⋊D3)⋊C3C2×D412yescomplemented
170C2×(C3⋊D3)⋊C3#4112yes—
171((C3⋊D3)⋊C3)⋊C2—48no—
172C4×H(3,𝔽3)—21no—
173C4×H(3,𝔽3)C2×D412yescomplemented
174#1084—22no—
175(C3⋊Dic3)⋊C3—22no—
176(C3⋊Dic3)⋊C3—21no—
177(C3⋊Dic3)⋊C3C2×D412yescomplemented
178C23×C3×C4—91no—
179C22×#67—92no—
180C2×D3×D4—91no—
181C2×D3×D4—91no—
182C2×D3×D4—92no—
183C2×D3×D4—92no—
184C22×D12—91no—
185C22×C4×D3—31no—
186C22×C4×D3—91no—
187C3×#121—91no—
188C3×#121—91no—
189#939—92no—
190#939—92no—
191#938—91no—
192#938—91no—
193#930—31no—
194#930—31no—
195#930—31no—
196#930—61no—
197#930—91no—
198#930—91no—
199#930—92no—
200#930—91no—
201#930—92no—
202C2×(C2×D3)⋊C4—92no—
203C2×C4⋊Dic3—91no—
204#895—91no—
205#895—91no—
206D3×C4⋊C4—91no—
207D3×C4⋊C4—91no—
208#884—92no—
209#884—92no—
210D3×C22⋊C4—92no—
211D3×C22⋊C4—92no—
212C23×C32—21no—
213C23×C32C22×D311yescharacteristic
214C23×C32C22×D311yescharacteristic
215C22×C3⋊D3—22no—
216C22×C3⋊D3—22no—
217C22×C3⋊D3D1214yescomplemented
218C22×C3⋊D3C22×D312yes—
219C22×C3⋊D3C22×D311yescharacteristic
220C22×C3⋊D3C22×D311yescharacteristic
221C22×C3×D3—31no—
222C22×C3×D3—34no—
223C22×C3×D3—31no—
224C22×C3×D3—32no—
225C22×C3×D3—32no—
226C22×C3×D3—32no—
227C22×C3×D3—62no—
228C22×C3×D3—62no—
229C22×C3×D3—62no—
230C2×D32—64no—
231C2×D32—64no—
232C2×D32—64no—
233C2×D32—64no—
234C2×D32—64no—
235C2×D32—64no—
236C2×C32×C4—22no—
237C2×C32×C4—22no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—42no—
241C2×C32×C4C22×D311yescharacteristic
242C2×C32×C4C22×D311yescharacteristic
243C2×C32×C4C22×D311yescharacteristic
244C2×C32×C4C22×D311yescharacteristic
245#638—24no—
246C2×C3⋊Dic3—22no—
247C2×C3⋊Dic3C22×D311yescharacteristic
248C2×C3⋊Dic3C22×D312yes—
249C2×C3⋊Dic3C22×D311yescharacteristic
250C4⋊(C3⋊D3)—22no—
251C4×C3⋊D3—22no—
252C4×C3⋊D3—22no—
253C4×C3⋊D3—22no—
254C4×C3⋊D3#6714yescomplemented
255C3×#67—64no—
256C3×#67—64no—
257C3×#67—64no—
258C3×#67—124no—
259C2×C3×Dic3—31no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—32no—
262C2×C3×Dic3—32no—
263C2×C3×Dic3—32no—
264C2×C3×Dic3—62no—
265C2×C3×Dic3—62no—
266C3×D12—62no—
267C3×D12—62no—
268C3×D12—62no—
269C3×D12—122no—
270C3×C4×D3—34no—
271C3×C4×D3—62no—
272C3×C4×D3—62no—
273C3×C4×D3—62no—
274#626—64no—
275#626—64no—
276#626—64no—
277#626—64no—
278#625—64no—
279#625—64no—
280#624—64no—
281D3×Dic3—64no—
282C2×#121—271noSylow
283C2×H(3,𝔽3)—22no—
284C2×H(3,𝔽3)C22×D411yescharacteristic
285C2×H(3,𝔽3)C22×D411yescharacteristic
286C2×H(3,𝔽3)C2×#4111yescharacteristic
287#272—42no—
288(C3⋊D3)⋊C3—22no—
289(C3⋊D3)⋊C3—42no—
290(C3⋊D3)⋊C3#12114yescomplemented
291C24×C3—91no—
292C23×D3—31no—
293C23×D3—91no—
294C23×D3—92no—
295C23×D3—92no—
296C23×D3—92no—
297C2×C3×D4—91no—
298C2×C3×D4—92no—
299C2×C3×D4—92no—
300C2×C3×D4—91no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C22×C3×C4—91no—
305C22×C3×C4—91no—
306C22×C3×C4—91no—
307C22×C3×C4—91no—
308C22×C3×C4—91no—
309C22×C3×C4—184no—
310C22×C3×C4D3211yescharacteristic
311C2×#67—32no—
312C2×#67—32no—
313C2×#67—32no—
314C2×#67—62no—
315C2×#67—92no—
316C2×#67—92no—
317C2×#67—92no—
318C2×#67—92no—
319C2×#67—92no—
320C2×#67—92no—
321C2×#67—92no—
322C2×#67—188no—
323C22×Dic3—31no—
324C22×Dic3—91no—
325C22×Dic3—92no—
326D3×D4—184no—
327D3×D4—184no—
328D3×D4—188no—
329D3×D4—188no—
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—61no—
334C2×D12—91no—
335C2×D12—92no—
336C2×D12—92no—
337C2×D12—92no—
338C2×D12—184no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—64no—
344C2×C4×D3—91no—
345C2×C4×D3—91no—
346C2×C4×D3—91no—
347C2×C4×D3—91no—
348C2×C4×D3—92no—
349C2×C4×D3—92no—
350C2×C4×D3—184no—
351C3×C4⋊C4—91no—
352C3×C4⋊C4—91no—
353C3×C22⋊C4—92no—
354C3×C22⋊C4—92no—
355#217—92no—
356#217—92no—
357(C2×D3)⋊C4—32no—
358(C2×D3)⋊C4—32no—
359(C2×D3)⋊C4—32no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—92no—
362(C2×D3)⋊C4—92no—
363(C2×D3)⋊C4—92no—
364(C2×D3)⋊C4—92no—
365(C2×D3)⋊C4—92no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—91no—
371C4⋊Dic3—92no—
372Dic3⋊C4—92no—
373Dic3⋊C4—92no—
374C22×C32—21no—
375C22×C32—21no—
376C22×C32—21no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32—22no—
380C22×C32—41no—
381C22×C32—41no—
382C22×C32C2×D1212yescomplemented
383C22×C32D3×D412yescomplemented
384C22×C32C23×D311yescharacteristic
385C22×C32C23×D311yescharacteristic
386C2×C3⋊D3—21no—
387C2×C3⋊D3—21no—
388C2×C3⋊D3—28no—
389C2×C3⋊D3—22no—
390C2×C3⋊D3—22no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3C2×D1212yes—
393C2×C3⋊D3C2×D1212yescomplemented
394C2×C3⋊D3#23512yes—
395C2×C3⋊D3C2×#6712yes—
396C2×C3×D3—32no—
397C2×C3×D3—32no—
398C2×C3×D3—32no—
399C2×C3×D3—32no—
400C2×C3×D3—68no—
401C2×C3×D3—61no—
402C2×C3×D3—61no—
403C2×C3×D3—62no—
404C2×C3×D3—62no—
405C2×C3×D3—62no—
406C2×C3×D3—62no—
407C2×C3×D3—62no—
408C2×C3×D3—62no—
409C2×C3×D3—62no—
410C2×C3×D3—62no—
411C2×C3×D3—62no—
412C2×C3×D3—122no—
413C2×C3×D3—122no—
414C2×C3×D3—122no—
415D32—128no—
416D32—128no—
417C32×C4—21no—
418C32×C4—21no—
419C32×C4—22no—
420C32×C4—41no—
421C32×C4D3×D412yescomplemented
422C32×C4C2×#6712yescomplemented
423C3⋊Dic3—22no—
424C3⋊Dic3—21no—
425C3⋊Dic3C2×#6712yescomplemented
426C3×Dic3—32no—
427C3×Dic3—62no—
428C3×Dic3—62no—
429C3×Dic3—61no—
430C3×Dic3—62no—
431C3×Dic3—122no—
432C22×D4—271no—
433C22×D4—272no—
434C23×C4—91no—
435#121—91no—
436#121—91no—
437#121—272no—
438#121—271no—
439#121—271no—
440#121—272no—
441C2×C4⋊C4—271no—
442C2×C22⋊C4—272no—
443H(3,𝔽3)C2×#12111yescharacteristic, complemented, Sylow
444C23×C3—31no—
445C23×C3—31no—
446C23×C3—61no—
447C23×C3—91no—
448C23×C3—91no—
449C23×C3—94no—
450C23×C3—92no—
451C23×C3—92no—
452C23×C3—182no—
453C23×C3—182no—
454C23×C3C2×D3211yescharacteristic
455C22×D3—31no—
456C22×D3—31no—
457C22×D3—34no—
458C22×D3—32no—
459C22×D3—32no—
460C22×D3—32no—
461C22×D3—62no—
462C22×D3—62no—
463C22×D3—62no—
464C22×D3—91no—
465C22×D3—94no—
466C22×D3—91no—
467C22×D3—92no—
468C22×D3—182no—
469C22×D3—182no—
470C22×D3—184no—
471C22×D3—184no—
472C22×D3—184no—
473C22×D3—184no—
474C22×D3—184no—
475C22×D3—184no—
476C22×D3—184no—
477C22×D3—184no—
478C22×D3—184no—
479C3×D4—182no—
480C3×D4—184no—
481C3×D4—184no—
482C3×D4—182no—
483C2×C3×C4—22no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—31no—
488C2×C3×C4—62no—
489C2×C3×C4—62no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—94no—
493C2×C3×C4—91no—
494C2×C3×C4—92no—
495C2×C3×C4—91no—
496C2×C3×C4—92no—
497C2×C3×C4—122no—
498C2×C3×C4—182no—
499C2×C3×C4—182no—
500C2×C3×C4—182no—
501C2×C3×C4—182no—
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504#67—64no—
505#67—64no—
506#67—64no—
507#67—124no—
508#67—184no—
509#67—184no—
510#67—184no—
511#67—184no—
512#67—184no—
513#67—184no—
514#67—184no—
515C2×Dic3—31no—
516C2×Dic3—32no—
517C2×Dic3—32no—
518C2×Dic3—32no—
519C2×Dic3—31no—
520C2×Dic3—62no—
521C2×Dic3—62no—
522C2×Dic3—91no—
523C2×Dic3—92no—
524C2×Dic3—91no—
525C2×Dic3—182no—
526C2×Dic3—184no—
527D12—62no—
528D12—62no—
529D12—62no—
530D12—122no—
531D12—182no—
532D12—184no—
533D12—184no—
534D12—184no—
535C4×D3—34no—
536C4×D3—62no—
537C4×D3—62no—
538C4×D3—62no—
539C4×D3—94no—
540C4×D3—182no—
541C4×D3—182no—
542C4×D3—182no—
543C4×D3—184no—
544C4×D3—184no—
545C2×C32—22no—
546C2×C32—22no—
547C2×C32—21no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—42no—
551C2×C32C22×D1211yescharacteristic
552C2×C32C2×#23511yescharacteristic
553C2×C32C2×D3×D411yescharacteristic
554C2×C32C2×D3×D411yescharacteristic
555C2×C32D3×#4111yescharacteristic
556C2×C32C22×#6711yescharacteristic
557C3⋊D3—22no—
558C3⋊D3—42no—
559C3⋊D3#93014yescomplemented
560C3×D3—34no—
561C3×D3—62no—
562C3×D3—122no—
563C3×D3—122no—
564C3×D3—122no—
565C3×D3—242no—
566C24—91no—
567C24—272no—
568C2×D4—92no—
569C2×D4—92no—
570C2×D4—91no—
571C2×D4—91no—
572C2×D4—272no—
573C2×D4—272no—
574C2×D4—272no—
575C2×D4—544no—
576C2×D4—548no—
577C22×C4—91no—
578C22×C4—91no—
579C22×C4—91no—
580C22×C4—91no—
581C22×C4—91no—
582C22×C4—184no—
583C22×C4—272no—
584C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
585C4⋊C4—91no—
586C4⋊C4—91no—
587C4⋊C4—272no—
588C22⋊C4—92no—
589C22⋊C4—92no—
590C22⋊C4—272no—
591C22⋊C4—272no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—31no—
595C22×C3—31no—
596C22×C3—32no—
597C22×C3—32no—
598C22×C3—61no—
599C22×C3—61no—
600C22×C3—61no—
601C22×C3—61no—
602C22×C3—61no—
603C22×C3—62no—
604C22×C3—92no—
605C22×C3—92no—
606C22×C3—92no—
607C22×C3—92no—
608C22×C3—121no—
609C22×C3—121no—
610C22×C3—181no—
611C22×C3—181no—
612C22×C3—182no—
613C22×C3—182no—
614C22×C3—182no—
615C22×C3—188no—
616C22×C3—182no—
617C22×C3—182no—
618C22×C3—182no—
619C22×C3D3×D1212yes—
620C22×C3C22×D3211yescharacteristic
621C2×D3—32no—
622C2×D3—32no—
623C2×D3—32no—
624C2×D3—32no—
625C2×D3—68no—
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—62no—
629C2×D3—62no—
630C2×D3—62no—
631C2×D3—62no—
632C2×D3—62no—
633C2×D3—62no—
634C2×D3—62no—
635C2×D3—62no—
636C2×D3—62no—
637C2×D3—92no—
638C2×D3—92no—
639C2×D3—92no—
640C2×D3—92no—
641C2×D3—122no—
642C2×D3—122no—
643C2×D3—122no—
644C2×D3—188no—
645C2×D3—181no—
646C2×D3—181no—
647C2×D3—182no—
648C2×D3—182no—
649C2×D3—182no—
650C2×D3—368no—
651C2×D3—368no—
652C2×D3—368no—
653C3×C4—21no—
654C3×C4—32no—
655C3×C4—32no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—62no—
659C3×C4—92no—
660C3×C4—121no—
661C3×C4—182no—
662C3×C4—181no—
663C3×C4—182no—
664C3×C4D3×#6712yes—
665Dic3—32no—
666Dic3—62no—
667Dic3—62no—
668Dic3—62no—
669Dic3—61no—
670Dic3—92no—
671Dic3—122no—
672Dic3—181no—
673Dic3—182no—
674C32—21no—
675C32D3×#12111yescharacteristic, complemented
676C32C2×#93011yescharacteristic, complemented
677C23—91no—
678C23—91no—
679C23—94no—
680C23—92no—
681C23—92no—
682C23—182no—
683C23—182no—
684C23—544no—
685C23—544no—
686C23—544no—
687C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
688D4—184no—
689D4—184no—
690D4—182no—
691D4—182no—
692D4—544no—
693D4—544no—
694D4—544no—
695C2×C4—22no—
696C2×C4—91no—
697C2×C4—94no—
698C2×C4—92no—
699C2×C4—92no—
700C2×C4—91no—
701C2×C4—182no—
702C2×C4—182no—
703C2×C4—182no—
704C2×C4—182no—
705C2×C4—544no—
706C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
707C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
708C2×C3—22no—
709C2×C3—31no—
710C2×C3—31no—
711C2×C3—31no—
712C2×C3—31no—
713C2×C3—31no—
714C2×C3—31no—
715C2×C3—62no—
716C2×C3—62no—
717C2×C3—61no—
718C2×C3—61no—
719C2×C3—61no—
720C2×C3—94no—
721C2×C3—122no—
722C2×C3—182no—
723C2×C3—362no—
724C2×C3—362no—
725C2×C3C2×D3×D1211yescharacteristic
726C2×C3D3×#23511yescharacteristic
727C2×C3C2×D3×#6711yescharacteristic
728D3—34no—
729D3—62no—
730D3—94no—
731D3—122no—
732D3—122no—
733D3—122no—
734D3—182no—
735D3—242no—
736D3—362no—
737C22—21no—
738C22—21no—
739C22—92no—
740C22—92no—
741C22—92no—
742C22—92no—
743C22—188no—
744C22—181no—
745C22—181no—
746C22—182no—
747C22—182no—
748C22—182no—
749C22—182no—
750C22—182no—
751C22—182no—
752C22—1088no—
753C22#8865412yescomplemented
754C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
755C4—21no—
756C4—92no—
757C4—181no—
758C4—182no—
759C4—182no—
760C4#8867612yescomplemented
761C3—31no—
762C3—31no—
763C3—61no—
764C3D3×#93011yescharacteristic
765C2—22no—
766C2—94no—
767C2—182no—
768C2—362no—
769C2—362no—
770C2C2×#8865411yescharacteristic
771C2#1172249011yescharacteristic
772C2C2×#8867611yescharacteristic
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)C2×#121
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×(C3⋊D3)⋊C3C2semidirect
2. C2×#88676C2semidirect
3. C2×#88654C2semidirect
4. #11721830C2semidirect
5. #64139⋊C3C2semidirect
6. #11721322C2semidirect
7. #11721160C2semidirect
8. #11721156C2semidirect
9. #11721141C2semidirect
10. #11721140C2semidirect
11. #11721129C2semidirect
16. C22×C4×H(3,𝔽3)C22semidirect
17. C2×#6235C22semidirect
18. C2×C4⋊#272C22semidirect
19. C2×#638⋊C3C22semidirect
20. C22×(C3⋊Dic3)⋊C3C22semidirect
21. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
25. C2×C4×(C3⋊D3)⋊C3C22semidirect
26. C2×C4×(C3⋊D3)⋊C3C22semidirect
28. C2×#6200C22semidirect
29. C2×#6200C22semidirect
30. C2×#6198C22semidirect
33. #88542C22semidirect
34. C4⋊#1084C22semidirect
35. #3752⋊C3C22semidirect
36. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
37. #88451C22semidirect
38. #88450C22semidirect
39. #88448C22semidirect
40. C22×C4×C3⋊D3D3semidirect
46. #64139D3semidirect
67. C22×(C3⋊D3)⋊C3D4semidirect
89. C4×(C3⋊D3)⋊C3D4semidirect
102. C22×C32×C4C2×D3semidirect
103. C22×C32×C4C2×D3semidirect
104. C2×#638C2×D3semidirect
105. C22×C3⋊Dic3C2×D3semidirect
106. C2×C4⋊(C3⋊D3)C2×D3semidirect
110. C2×C4×C3⋊D3C2×D3semidirect
111. C2×C4×C3⋊D3C2×D3semidirect
138. #3752C2×D3semidirect
139. C4⋊(C3⋊Dic3)C2×D3semidirect
156. C22×H(3,𝔽3)C2×D4semidirect
169. C2×(C3⋊D3)⋊C3C2×D4semidirect
173. C4×H(3,𝔽3)C2×D4semidirect
177. (C3⋊Dic3)⋊C3C2×D4semidirect
217. C22×C3⋊D3D12semidirect
254. C4×C3⋊D3#67semidirect
290. (C3⋊D3)⋊C3#121semidirect
382. C22×C32C2×D12semidirect
383. C22×C32D3×D4semidirect
393. C2×C3⋊D3C2×D12semidirect
421. C32×C4D3×D4semidirect
422. C32×C4C2×#67semidirect
425. C3⋊Dic3C2×#67semidirect
443. H(3,𝔽3)C2×#121semidirect
559. C3⋊D3#930semidirect
584. C22×C4((C3⋊D3)⋊C3)⋊C2semidirect
675. C32D3×#121semidirect
676. C32C2×#930semidirect
753. C22#88654semidirect
760. C4#88676semidirect

Maximal subgroups

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

subgroupindex
C22×C4×(C3⋊D3)⋊C32
C2×#886762
C2×#886542
#117218302
#64139⋊C32
#117213222
#117211602
#117211562
#117211412
#117211402
#117211292
#105950813
D3×#9303