Finite Group Databasebeta

← C2×#11722504 #13164748

Subgroups — C2×#11722504 #13164748

Order 1728.

3279 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88744C211yesmaximal, characteristic, complemented
2C2×#3830⋊C3C211yesmaximal, characteristic, complemented
3C2×D4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
4C2×#88676C212yesmaximal, complemented
5C2×#88672C212yesmaximal, complemented
6C2×#88671C212yesmaximal, complemented
7C22×((C3⋊D3)⋊C3)⋊C4C212yesmaximal, complemented
8#11722504C2116yesmaximal, direct product factor
9C2×C4×((C3⋊D3)⋊C3)⋊C2C211yesmaximal, characteristic, complemented
10C2×#88649C211yesmaximal, characteristic, complemented
11C2×#88648C211yesmaximal, characteristic, complemented
12C2×((C3⋊D3)⋊C3)⋊Q8C211yesmaximal, characteristic, complemented
13C2×#64312—31nomaximal
14C2×D3×#237—31nomaximal
15C23×(C3⋊D3)⋊C3C2212yes—
16C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
17C2×D4×H(3,𝔽3)C2211yescharacteristic, complemented
18C2×#6235C2212yescomplemented
19C22×#1084C2212yescomplemented
20#88744C2218yescomplemented
21C2×C4×#272C2211yescharacteristic, complemented
22C2×#6229C2211yescharacteristic, complemented
23C2×#638⋊C3C2212yescomplemented
24C2×#638⋊C3C2212yescomplemented
25C22×(C3⋊Dic3)⋊C3C2212yescomplemented
26#3830⋊C3C2218yescomplemented
27D4×(C3⋊D3)⋊C3C2218yescomplemented
28C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
29C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
30C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
31C2×#634⋊C3C2211yescharacteristic, complemented
32#88676C22116yescomplemented
33C2×#6200C2212yescomplemented
34C2×#6199C2211yescharacteristic, complemented
35C2×#6198C2212yescomplemented
36#88672C22116yescomplemented
37#88671C22116yescomplemented
38C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
39C2×((C3⋊D3)⋊C3)⋊C4C2212yes—
40C2×((C3⋊D3)⋊C3)⋊C4C22116yescomplemented
41C2×((C3⋊D3)⋊C3)⋊C4C2212yescomplemented
42C2×((C3⋊D3)⋊C3)⋊C4C2212yescomplemented
43C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
44C2×#6196C2212yescomplemented
45C4×((C3⋊D3)⋊C3)⋊C2C2218yescomplemented
46#88649C2218yescomplemented
47#88648C2218yescomplemented
48((C3⋊D3)⋊C3)⋊Q8C2218yescomplemented
49C2×#3830D311yescharacteristic, complemented
50C2×D4×C3⋊D3D311yescharacteristic, complemented
51C2×C3×#237—31no—
52C2×C3×#237—31no—
53C2×C3×#237—31no—
54C2×C3×#237—61no—
55C2×C3×D3×D4—31no—
56C2×#3811—32no—
57C2×D3×#67—32no—
58C22×#624—32no—
59C2×#3805—32no—
60C2×#3804—32no—
61C2×#3804—32no—
62C2×#3804—32no—
63C22×D3×Dic3—32no—
64#64312—316no—
65D3×#237—316no—
66C2×C4×D32—31no—
67C2×C4×D32—31no—
68C2×#3799—31no—
69C2×#3799—31no—
70C2×#3797—31no—
71C2×#3796—31no—
72C2×#3795—31no—
73C2×D3×Dic6—31no—
74C23×H(3,𝔽3)C2312yes—
75C22×#272C2311yescharacteristic
76C22×(C3⋊D3)⋊C3—28no—
77C22×(C3⋊D3)⋊C3C2311yescharacteristic
78C22×(C3⋊D3)⋊C3C2312yes—
79C22×(C3⋊D3)⋊C3C2318yes—
80C22×(C3⋊D3)⋊C3C2311yescharacteristic
81C2×((C3⋊D3)⋊C3)⋊C2—24no—
82C2×((C3⋊D3)⋊C3)⋊C2C2314yes—
83D4×H(3,𝔽3)C2314yescomplemented
84C2×C4×H(3,𝔽3)C2311yescharacteristic
85#6235C2318yescomplemented
86C2×#1084C2312yes—
87C2×#1084C2311yescharacteristic
88C2×#1084C2318yescomplemented
89C4×#272C2314yescomplemented
90#6229C2314yescomplemented
91#638⋊C3C2318yescomplemented
92#638⋊C3C2318yescomplemented
93C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
94C2×(C3⋊Dic3)⋊C3C2312yes—
95C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
96C2×(C3⋊Dic3)⋊C3C2318yescomplemented
97C4⋊((C3⋊D3)⋊C3)C2314yescomplemented
98C4×(C3⋊D3)⋊C3C2314yes—
99C4×(C3⋊D3)⋊C3C2314yescomplemented
100#634⋊C3C2314yescomplemented
101#6200C2318yescomplemented
102#6199C2314yescomplemented
103#6198C2318yescomplemented
104((C3⋊D3)⋊C3)⋊C4C2318yes—
105((C3⋊D3)⋊C3)⋊C4C2314yes—
106((C3⋊D3)⋊C3)⋊C4C2318yescomplemented
107((C3⋊D3)⋊C3)⋊C4C2318yescomplemented
108((C3⋊D3)⋊C3)⋊C4C2314yescomplemented
109#6196C2318yescomplemented
110C2×D3×#41—91no—
111C2×D3×#41—91no—
112C22×#237—91no—
113C23×C3⋊D3C2×D312yes—
114C23×C3×D3—32no—
115C22×D32—31no—
116C22×D32—31no—
117C2×C32×D4—21no—
118C2×C32×D4C2×D311yescharacteristic, complemented
119C2×C32×D4C2×D311yescharacteristic, complemented
120C2×#638C2×D312yescomplemented
121C2×#638C2×D312yescomplemented
122C22×C3⋊Dic3C2×D312yescomplemented
123#3830C2×D318yescomplemented
124D4×C3⋊D3C2×D318yescomplemented
125C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
126C2×C4×C3⋊D3C2×D311yescharacteristic
127C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
128C2×#634C2×D311yescharacteristic, complemented
129C2×C3×#67—32no—
130C2×C3×#67—32no—
131C2×C3×#67—32no—
132C2×C3×#67—32no—
133C2×C3×#67—62no—
134C22×C3×Dic3—32no—
135C22×C3×Dic3—32no—
136C22×C3×Dic3—32no—
137C22×C3×Dic3—62no—
138C3×#237—38no—
139C3×#237—38no—
140C3×#237—38no—
141C3×#237—68no—
142C3×D3×D4—38no—
143C2×C3×D12—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—31no—
148C2×C3×C4×D3—61no—
149C2×C3×Dic6—31no—
150C2×C3×Dic6—31no—
151C2×C3×Dic6—31no—
152C2×C3×Dic6—61no—
153#3811—316no—
154D3×#67—316no—
155C2×#627—32no—
156C2×#627—32no—
157C2×#626—32no—
158C2×#626—32no—
159C2×#626—32no—
160C2×#625—32no—
161C2×#624—32no—
162C2×#624—32no—
163C2×#624—32no—
164C2×#624—31no—
165C2×#624—31no—
166C2×#624—316no—
167#3805—316no—
168#3804—316no—
169#3804—316no—
170#3804—316no—
171C2×D3×Dic3—32no—
172C2×D3×Dic3—32no—
173C2×D3×Dic3—32no—
174C2×D3×Dic3—31no—
175C2×D3×Dic3—31no—
176C2×D3×Dic3—31no—
177C2×D3×Dic3—31no—
178C2×D3×Dic3—316no—
179C4×D32—38no—
180C4×D32—38no—
181#3799—38no—
182#3799—38no—
183#3797—38no—
184#3796—38no—
185#3795—38no—
186D3×Dic6—38no—
187C22×H(3,𝔽3)—24no—
188C22×H(3,𝔽3)C2414yes—
189C22×H(3,𝔽3)C2411yescharacteristic
190C2×#272—22no—
191C2×#272C2412yes—
192C2×(C3⋊D3)⋊C3—22no—
193C2×(C3⋊D3)⋊C3—24no—
194C2×(C3⋊D3)⋊C3—216no—
195C2×(C3⋊D3)⋊C3#4114yescomplemented
196C2×(C3⋊D3)⋊C3C2414yes—
197C2×(C3⋊D3)⋊C3C2412yes—
198C2×(C3⋊D3)⋊C3C2412yes—
199((C3⋊D3)⋊C3)⋊C2—28no—
200C4×H(3,𝔽3)C2412yes—
201#1084C2414yes—
202#1084C2412yes—
203(C3⋊Dic3)⋊C3C2412yes—
204(C3⋊Dic3)⋊C3C2414yes—
205(C3⋊Dic3)⋊C3C2412yes—
206C2×C3×#41—91no—
207C2×C3×#41—91no—
208C22×C3×D4—91no—
209C22×#67—92no—
210C23×Dic3—92no—
211D3×#41—916no—
212D3×#41—916no—
213C2×#239—91no—
214C2×#239—91no—
215C2×D3×Q8—91no—
216C2×D3×Q8—91no—
217C2×#237—31no—
218C2×#237—31no—
219C2×#237—31no—
220C2×#237—61no—
221C2×#237—91no—
222C2×#237—91no—
223C2×#237—91no—
224C2×#237—916no—
225C2×#237—92no—
226C2×#237—92no—
227C2×#237—92no—
228C2×#237—92no—
229C2×D3×D4—31no—
230C2×D3×D4—91no—
231C2×D3×D4—92no—
232C2×D3×D4—92no—
233C2×#235—91no—
234C2×#235—91no—
235C2×#235—92no—
236C2×#235—92no—
237C22×C4×D3—91no—
238C22×C4×D3—91no—
239C22×C4×D3—91no—
240C22×C4×D3—92no—
241C22×C4×D3—92no—
242C22×Dic6—91no—
243C23×C32—22no—
244C23×C32C22×D312yes—
245C23×C32C22×D312yes—
246C22×C3⋊D3—28no—
247C22×C3⋊D3C22×D311yescharacteristic
248C22×C3⋊D3C22×D312yes—
249C22×C3⋊D3C22×D318yes—
250C22×C3⋊D3C22×D311yescharacteristic
251C22×C3×D3—31no—
252C22×C3×D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C22×C3×D3—32no—
256C22×C3×D3—38no—
257C22×C3×D3—61no—
258C22×C3×D3—68no—
259C2×D32—34no—
260C2×D32—34no—
261C2×D32—64no—
262C2×D32—64no—
263C32×D4—24no—
264C32×D4C22×D314yescomplemented
265C32×D4C22×D314yescomplemented
266C2×C32×C4—21no—
267C2×C32×C4C22×D311yescharacteristic
268C2×C32×C4C22×D311yescharacteristic
269#638C22×D318yescomplemented
270#638C22×D318yescomplemented
271C2×C3⋊Dic3C22×D311yescharacteristic
272C2×C3⋊Dic3C22×D312yes—
273C2×C3⋊Dic3C22×D311yescharacteristic
274C2×C3⋊Dic3C22×D318yescomplemented
275C4⋊(C3⋊D3)C22×D314yescomplemented
276C4×C3⋊D3C22×D314yes—
277C4×C3⋊D3C22×D314yescomplemented
278#634C22×D314yescomplemented
279C3×#67—38no—
280C3×#67—38no—
281C3×#67—38no—
282C3×#67—38no—
283C3×#67—68no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—31no—
286C2×C3×Dic3—32no—
287C2×C3×Dic3—38no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—32no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—32no—
292C2×C3×Dic3—38no—
293C2×C3×Dic3—38no—
294C2×C3×Dic3—62no—
295C2×C3×Dic3—61no—
296C2×C3×Dic3—68no—
297C3×D12—34no—
298C3×C4×D3—34no—
299C3×C4×D3—34no—
300C3×C4×D3—34no—
301C3×C4×D3—34no—
302C3×C4×D3—64no—
303C3×Dic6—34no—
304C3×Dic6—34no—
305C3×Dic6—34no—
306C3×Dic6—64no—
307#627—38no—
308#627—38no—
309#626—38no—
310#626—38no—
311#626—38no—
312#625—38no—
313#624—38no—
314#624—34no—
315#624—38no—
316#624—38no—
317#624—34no—
318D3×Dic3—38no—
319D3×Dic3—34no—
320D3×Dic3—38no—
321D3×Dic3—38no—
322D3×Dic3—34no—
323D3×Dic3—34no—
324D3×Dic3—34no—
325C22×#41—271noSylow
326C2×H(3,𝔽3)—24no—
327C2×H(3,𝔽3)C2×#4112yescomplemented
328C2×H(3,𝔽3)C2511yescharacteristic
329#272—22no—
330(C3⋊D3)⋊C3—22no—
331(C3⋊D3)⋊C3—24no—
332(C3⋊D3)⋊C3C2×#4114yescomplemented
333C24×C3—92no—
334C23×D3—32no—
335C23×D3—92no—
336C23×D3—91no—
337C23×D3—91no—
338C23×D3—91no—
339C3×#41—98no—
340C3×#41—98no—
341C2×C3×Q8—91no—
342C2×C3×Q8—91no—
343C2×C3×D4—31no—
344C2×C3×D4—31no—
345C2×C3×D4—61no—
346C2×C3×D4—91no—
347C2×C3×D4—98no—
348C2×C3×D4—92no—
349C2×C3×D4—92no—
350C2×C3×D4—92no—
351C2×C3×D4D3211yescharacteristic
352C22×C3×C4—91no—
353C22×C3×C4—91no—
354C22×C3×C4—92no—
355C22×C3×C4—92no—
356C22×C3×C4—91no—
357C2×#67—32no—
358C2×#67—32no—
359C2×#67—32no—
360C2×#67—32no—
361C2×#67—62no—
362C2×#67—92no—
363C2×#67—92no—
364C2×#67—92no—
365C2×#67—92no—
366C2×#67—92no—
367C2×#67—916no—
368C2×#67—92no—
369C22×Dic3—32no—
370C22×Dic3—32no—
371C22×Dic3—32no—
372C22×Dic3—62no—
373C22×Dic3—92no—
374C22×Dic3—91no—
375C22×Dic3—92no—
376C22×Dic3—91no—
377C22×Dic3—91no—
378C22×Dic3—92no—
379C22×Dic3—92no—
380C22×Dic3—916no—
381#239—98no—
382#239—98no—
383D3×Q8—98no—
384D3×Q8—98no—
385#237—38no—
386#237—38no—
387#237—38no—
388#237—68no—
389#237—98no—
390#237—98no—
391#237—98no—
392#237—916no—
393#237—916no—
394#237—916no—
395#237—916no—
396D3×D4—38no—
397D3×D4—98no—
398D3×D4—916no—
399D3×D4—916no—
400#235—98no—
401#235—98no—
402#235—916no—
403#235—916no—
404C2×D12—31no—
405C2×D12—91no—
406C2×D12—92no—
407C2×D12—92no—
408C2×C4×D3—31no—
409C2×C4×D3—31no—
410C2×C4×D3—31no—
411C2×C4×D3—31no—
412C2×C4×D3—61no—
413C2×C4×D3—91no—
414C2×C4×D3—91no—
415C2×C4×D3—98no—
416C2×C4×D3—98no—
417C2×C4×D3—98no—
418C2×C4×D3—91no—
419C2×C4×D3—92no—
420C2×C4×D3—91no—
421C2×C4×D3—92no—
422C2×C4×D3—92no—
423C2×C4×D3—916no—
424C2×C4×D3—91no—
425C2×C4×D3—92no—
426C2×C4×D3—92no—
427C2×C4×D3—91no—
428C2×C4×D3—92no—
429C2×C4×D3—916no—
430C2×C4×D3—91no—
431C2×C4×D3—91no—
432C2×Dic6—31no—
433C2×Dic6—31no—
434C2×Dic6—31no—
435C2×Dic6—61no—
436C2×Dic6—91no—
437C2×Dic6—98no—
438C2×Dic6—92no—
439C2×Dic6—92no—
440C2×Dic6—92no—
441C22×C32—24no—
442C22×C32—24no—
443C22×C32—21no—
444C22×C32—24no—
445C22×C32—44no—
446C22×C32C23×D314yes—
447C22×C32C23×D314yes—
448C22×C32C23×D311yescharacteristic
449C22×C32C23×D311yescharacteristic
450C2×C3⋊D3—24no—
451C2×C3⋊D3—22no—
452C2×C3⋊D3—216no—
453C2×C3⋊D3#23714yescomplemented
454C2×C3⋊D3C23×D314yes—
455C2×C3⋊D3C23×D312yes—
456C2×C3⋊D3C23×D312yes—
457C2×C3×D3—34no—
458C2×C3×D3—32no—
459C2×C3×D3—34no—
460C2×C3×D3—32no—
461C2×C3×D3—32no—
462C2×C3×D3—32no—
463C2×C3×D3—62no—
464C2×C3×D3—616no—
465C2×C3×D3—62no—
466C2×C3×D3—62no—
467C2×C3×D3—64no—
468C2×C3×D3—62no—
469C2×C3×D3—122no—
470D32—68no—
471D32—68no—
472C32×C4—22no—
473C32×C4C23×D312yes—
474C32×C4C23×D312yes—
475C3⋊Dic3C23×D312yes—
476C3⋊Dic3C23×D314yes—
477C3⋊Dic3C23×D312yes—
478C3×Dic3—32no—
479C3×Dic3—32no—
480C3×Dic3—34no—
481C3×Dic3—32no—
482C3×Dic3—34no—
483C3×Dic3—32no—
484C3×Dic3—34no—
485C3×Dic3—64no—
486C3×Dic3—62no—
487C2×#41—91no—
488C2×#41—91no—
489C2×#41—272no—
490C2×#41—272no—
491C2×#41—271no—
492C2×#41—271no—
493C2×#41—2716no—
494C22×Q8—271no—
495C22×D4—91no—
496C22×D4—272no—
497C23×C4—271no—
498C23×C4—272no—
499H(3,𝔽3)C22×#4111yescharacteristic, complemented, Sylow
500C23×C3—32no—
501C23×C3—32no—
502C23×C3—62no—
503C23×C3—91no—
504C23×C3—98no—
505C23×C3—92no—
506C23×C3—91no—
507C23×C3—91no—
508C23×C3—188no—
509C23×C3C2×D3212yes—
510C22×D3—31no—
511C22×D3—31no—
512C22×D3—31no—
513C22×D3—31no—
514C22×D3—32no—
515C22×D3—38no—
516C22×D3—61no—
517C22×D3—68no—
518C22×D3—91no—
519C22×D3—92no—
520C22×D3—98no—
521C22×D3—91no—
522C22×D3—94no—
523C22×D3—94no—
524C22×D3—94no—
525C22×D3—188no—
526C22×D3—184no—
527C22×D3—184no—
528C22×D3—184no—
529C3×Q8—94no—
530C3×Q8—94no—
531C3×D4—34no—
532C3×D4—34no—
533C3×D4—64no—
534C3×D4—94no—
535C3×D4—98no—
536C3×D4—98no—
537C3×D4—98no—
538C3×D4C2×D3214yes—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—61no—
542C2×C3×C4—94no—
543C2×C3×C4—94no—
544C2×C3×C4—91no—
545C2×C3×C4—92no—
546C2×C3×C4—91no—
547C2×C3×C4—98no—
548C2×C3×C4—92no—
549C2×C3×C4—91no—
550C2×C3×C4—98no—
551C2×C3×C4—94no—
552C2×C3×C4C2×D3211yescharacteristic
553#67—38no—
554#67—38no—
555#67—38no—
556#67—38no—
557#67—68no—
558#67—98no—
559#67—98no—
560#67—98no—
561#67—98no—
562#67—98no—
563#67—98no—
564C2×Dic3—32no—
565C2×Dic3—32no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—38no—
569C2×Dic3—38no—
570C2×Dic3—32no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—38no—
574C2×Dic3—62no—
575C2×Dic3—61no—
576C2×Dic3—68no—
577C2×Dic3—91no—
578C2×Dic3—92no—
579C2×Dic3—91no—
580C2×Dic3—98no—
581C2×Dic3—94no—
582C2×Dic3—98no—
583C2×Dic3—94no—
584C2×Dic3—94no—
585C2×Dic3—98no—
586C2×Dic3—98no—
587D12—34no—
588D12—94no—
589D12—98no—
590D12—98no—
591C4×D3—34no—
592C4×D3—34no—
593C4×D3—34no—
594C4×D3—34no—
595C4×D3—64no—
596C4×D3—94no—
597C4×D3—94no—
598C4×D3—94no—
599C4×D3—98no—
600C4×D3—94no—
601C4×D3—98no—
602C4×D3—98no—
603C4×D3—94no—
604C4×D3—98no—
605C4×D3—98no—
606C4×D3—94no—
607C4×D3—98no—
608C4×D3—94no—
609C4×D3—94no—
610Dic6—34no—
611Dic6—34no—
612Dic6—34no—
613Dic6—64no—
614Dic6—94no—
615Dic6—98no—
616Dic6—98no—
617Dic6—98no—
618C2×C32—24no—
619C2×C32—24no—
620C2×C32—22no—
621C2×C32—21no—
622C2×C32—44no—
623C2×C32C2×#23712yescomplemented
624C2×C32D3×#4112yescomplemented
625C2×C32C24×D311yescharacteristic
626C2×C32C24×D311yescharacteristic
627C3⋊D3—24no—
628C3⋊D3—22no—
629C3⋊D3C2×#23714yescomplemented
630C3×D3—34no—
631C3×D3—62no—
632C3×D3—62no—
633C3×D3—64no—
634C3×D3—62no—
635C3×D3—122no—
636C24—92no—
637C24—271no—
638#41—98no—
639#41—98no—
640#41—2716no—
641#41—2716no—
642#41—278no—
643#41—278no—
644C2×Q8—91no—
645C2×Q8—91no—
646C2×Q8—272no—
647C2×Q8—278no—
648C2×D4—92no—
649C2×D4—92no—
650C2×D4—92no—
651C2×D4—98no—
652C2×D4—91no—
653C2×D4—272no—
654C2×D4—272no—
655C2×D4—2716no—
656C2×D4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
657C22×C4—92no—
658C22×C4—92no—
659C22×C4—91no—
660C22×C4—91no—
661C22×C4—91no—
662C22×C4—278no—
663C22×C4—271no—
664C22×C4—272no—
665C22×C4—2716no—
666C22×C4—271no—
667C22×C4—272no—
668C22×C4—271no—
669C22×C4—272no—
670C22×C3—24no—
671C22×C3—34no—
672C22×C3—34no—
673C22×C3—31no—
674C22×C3—31no—
675C22×C3—64no—
676C22×C3—64no—
677C22×C3—64no—
678C22×C3—61no—
679C22×C3—92no—
680C22×C3—94no—
681C22×C3—94no—
682C22×C3—92no—
683C22×C3—92no—
684C22×C3—124no—
685C22×C3—182no—
686C22×C3—184no—
687C22×C3—1816no—
688C22×C3—182no—
689C22×C3C22×D3214yes—
690C22×C3C22×D3211yescharacteristic
691C2×D3—34no—
692C2×D3—32no—
693C2×D3—32no—
694C2×D3—32no—
695C2×D3—32no—
696C2×D3—34no—
697C2×D3—62no—
698C2×D3—616no—
699C2×D3—62no—
700C2×D3—62no—
701C2×D3—64no—
702C2×D3—62no—
703C2×D3—92no—
704C2×D3—94no—
705C2×D3—94no—
706C2×D3—92no—
707C2×D3—122no—
708C2×D3—1816no—
709C2×D3—184no—
710C2×D3—182no—
711C2×D3—188no—
712C2×D3—188no—
713C2×D3—188no—
714C3×C4—32no—
715C3×C4—32no—
716C3×C4—62no—
717C3×C4—92no—
718C3×C4—94no—
719C3×C4—92no—
720C3×C4—94no—
721C3×C4—92no—
722C3×C4C22×D3212yes—
723Dic3—34no—
724Dic3—34no—
725Dic3—32no—
726Dic3—32no—
727Dic3—34no—
728Dic3—32no—
729Dic3—32no—
730Dic3—64no—
731Dic3—62no—
732Dic3—92no—
733Dic3—94no—
734Dic3—92no—
735C32—21no—
736C32C22×#23711yescharacteristic, complemented
737C32C2×D3×#4111yescharacteristic, complemented
738C23—91no—
739C23—98no—
740C23—91no—
741C23—91no—
742C23—92no—
743C23—188no—
744C23—274no—
745C23—544no—
746C23C2×((C3⋊D3)⋊C3)⋊C212yes—
747Q8—94no—
748Q8—94no—
749Q8—278no—
750D4—98no—
751D4—98no—
752D4—98no—
753D4—94no—
754D4—278no—
755D4—278no—
756D4C2×((C3⋊D3)⋊C3)⋊C214yescomplemented
757C2×C4—98no—
758C2×C4—98no—
759C2×C4—91no—
760C2×C4—91no—
761C2×C4—91no—
762C2×C4—92no—
763C2×C4—92no—
764C2×C4—94no—
765C2×C4—94no—
766C2×C4—94no—
767C2×C4—274no—
768C2×C4—278no—
769C2×C4—274no—
770C2×C4—278no—
771C2×C4—274no—
772C2×C4—278no—
773C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
774C2×C3—24no—
775C2×C3—32no—
776C2×C3—32no—
777C2×C3—31no—
778C2×C3—31no—
779C2×C3—64no—
780C2×C3—64no—
781C2×C3—62no—
782C2×C3—61no—
783C2×C3—94no—
784C2×C3—124no—
785C2×C3—182no—
786C2×C3—184no—
787C2×C3—182no—
788C2×C3D3×#23712yes—
789C2×C3C23×D3211yescharacteristic
790D3—34no—
791D3—62no—
792D3—62no—
793D3—64no—
794D3—62no—
795D3—94no—
796D3—122no—
797D3—184no—
798D3—182no—
799C22—24no—
800C22—94no—
801C22—92no—
802C22—92no—
803C22—92no—
804C22—94no—
805C22—1816no—
806C22—184no—
807C22—182no—
808C22—182no—
809C22—548no—
810C22C22×((C3⋊D3)⋊C3)⋊C214yes—
811C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
812C4—92no—
813C4—92no—
814C4—92no—
815C4—94no—
816C4—94no—
817C4C22×((C3⋊D3)⋊C3)⋊C212yes—
818C3—31no—
819C3—31no—
820C3—61no—
821C3C2×D3×#23711yescharacteristic
822C2—24no—
823C2—94no—
824C2—184no—
825C2—182no—
826C2—182no—
827C2#1172250412yesdirect product factor
828C2C23×((C3⋊D3)⋊C3)⋊C211yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC2×H(3,𝔽3)C25
FrattiniC2×C3C23×D32
FittingC2×D4×H(3,𝔽3)C22
socleC22×C3C22×D32
hypercenterC2×D4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C22×#41
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#88744C2semidirect
2. C2×#3830⋊C3C2semidirect
3. C2×D4×(C3⋊D3)⋊C3C2semidirect
4. C2×#88676C2semidirect
5. C2×#88672C2semidirect
6. C2×#88671C2semidirect
7. C22×((C3⋊D3)⋊C3)⋊C4C2semidirect
8. #11722504C2direct (N × H)
9. C2×C4×((C3⋊D3)⋊C3)⋊C2C2semidirect
10. C2×#88649C2semidirect
11. C2×#88648C2semidirect
12. C2×((C3⋊D3)⋊C3)⋊Q8C2semidirect
17. C2×D4×H(3,𝔽3)C22semidirect
18. C2×#6235C22semidirect
19. C22×#1084C22semidirect
20. #88744C22semidirect
21. C2×C4×#272C22semidirect
22. C2×#6229C22semidirect
23. C2×#638⋊C3C22semidirect
24. C2×#638⋊C3C22semidirect
25. C22×(C3⋊Dic3)⋊C3C22semidirect
26. #3830⋊C3C22semidirect
27. D4×(C3⋊D3)⋊C3C22semidirect
28. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
30. C2×C4×(C3⋊D3)⋊C3C22semidirect
31. C2×#634⋊C3C22semidirect
32. #88676C22semidirect
33. C2×#6200C22semidirect
34. C2×#6199C22semidirect
35. C2×#6198C22semidirect
36. #88672C22semidirect
37. #88671C22semidirect
40. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
41. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
42. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
43. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
44. C2×#6196C22semidirect
45. C4×((C3⋊D3)⋊C3)⋊C2C22semidirect
46. #88649C22semidirect
47. #88648C22semidirect
48. ((C3⋊D3)⋊C3)⋊Q8C22semidirect
49. C2×#3830D3semidirect
50. C2×D4×C3⋊D3D3semidirect
83. D4×H(3,𝔽3)C23semidirect
85. #6235C23semidirect
88. C2×#1084C23semidirect
89. C4×#272C23semidirect
90. #6229C23semidirect
91. #638⋊C3C23semidirect
92. #638⋊C3C23semidirect
96. C2×(C3⋊Dic3)⋊C3C23semidirect
97. C4⋊((C3⋊D3)⋊C3)C23semidirect
99. C4×(C3⋊D3)⋊C3C23semidirect
100. #634⋊C3C23semidirect
101. #6200C23semidirect
102. #6199C23semidirect
103. #6198C23semidirect
106. ((C3⋊D3)⋊C3)⋊C4C23semidirect
107. ((C3⋊D3)⋊C3)⋊C4C23semidirect
108. ((C3⋊D3)⋊C3)⋊C4C23semidirect
109. #6196C23semidirect
118. C2×C32×D4C2×D3semidirect
119. C2×C32×D4C2×D3semidirect
120. C2×#638C2×D3semidirect
121. C2×#638C2×D3semidirect
122. C22×C3⋊Dic3C2×D3semidirect
123. #3830C2×D3semidirect
124. D4×C3⋊D3C2×D3semidirect
125. C2×C4⋊(C3⋊D3)C2×D3semidirect
127. C2×C4×C3⋊D3C2×D3semidirect
128. C2×#634C2×D3semidirect
195. C2×(C3⋊D3)⋊C3#41semidirect
264. C32×D4C22×D3semidirect
265. C32×D4C22×D3semidirect
269. #638C22×D3semidirect
270. #638C22×D3semidirect
274. C2×C3⋊Dic3C22×D3semidirect
275. C4⋊(C3⋊D3)C22×D3semidirect
277. C4×C3⋊D3C22×D3semidirect
278. #634C22×D3semidirect
327. C2×H(3,𝔽3)C2×#41semidirect
332. (C3⋊D3)⋊C3C2×#41semidirect
453. C2×C3⋊D3#237semidirect
499. H(3,𝔽3)C22×#41semidirect
623. C2×C32C2×#237semidirect
624. C2×C32D3×#41semidirect
629. C3⋊D3C2×#237semidirect
656. C2×D4((C3⋊D3)⋊C3)⋊C2semidirect
736. C32C22×#237semidirect
737. C32C2×D3×#41semidirect
756. D4C2×((C3⋊D3)⋊C3)⋊C2semidirect
827. C2#11722504direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#887442
C2×#3830⋊C32
C2×D4×(C3⋊D3)⋊C32
C2×#886762
C2×#886722
C2×#886712
C22×((C3⋊D3)⋊C3)⋊C42
#117225042
C2×C4×((C3⋊D3)⋊C3)⋊C22
C2×#886492
C2×#886482
C2×((C3⋊D3)⋊C3)⋊Q82
C2×#643123
C2×D3×#2373