Finite Group Databasebeta

← #13177377

Subgroups — #13177377

Order 1728.

3500 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×#89039C211yesmaximal, characteristic, complemented
3C2×#89039C211yesmaximal, characteristic, complemented
4C22×#6289C211yesmaximal, characteristic, complemented
5C3×#64148C211yesmaximal, characteristic, complemented
6C32×#939C211yesmaximal, characteristic, complemented
7#11723635C211yesmaximal, characteristic, complemented
8#11723632C211yesmaximal, characteristic, complemented
9#11723627C211yesmaximal, characteristic, complemented
10#11723623C211yesmaximal, characteristic, complemented
11#11723599C211yesmaximal, characteristic, complemented
12#11723539C211yesmaximal, characteristic, complemented
13#11723525C211yesmaximal, characteristic, complemented
14#11723486C211yesmaximal, characteristic, complemented
15#11723470C211yesmaximal, characteristic, complemented
16C3⋊D3×#121—31nomaximal
17#10595298—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C23×C3⋊(C3⋊D3)C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×C33×D4C2211yescharacteristic, complemented
22C2×#6312C2211yescharacteristic, complemented
23C2×#6312C2211yescharacteristic, complemented
24D4×C3⋊(C3⋊D3)—24no—
25C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
26C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
27C2×C3×#638C2211yescharacteristic, complemented
28C2×C3×#638C2211yescharacteristic, complemented
29C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
30C2×C32×#67C2211yescharacteristic, complemented
31C2×C32×#67C2211yescharacteristic, complemented
32C22×C32×Dic3C2211yescharacteristic, complemented
33#89039—24no—
34#89039—24no—
35C2×#6292C2211yescharacteristic, complemented
36C2×#6292C2211yescharacteristic, complemented
37C2×#6291C2211yescharacteristic, complemented
38C2×#6291C2211yescharacteristic, complemented
39C2×#6289—24no—
40C2×#6289C2211yescharacteristic
41C2×#6289C2211yescharacteristic
42C2×#6289C2211yescharacteristic
43C2×#6289C2211yescharacteristic, complemented
44C2×#6289C2211yescharacteristic, complemented
45C3×#3757C2211yescharacteristic, complemented
46C3×#3752C2211yescharacteristic, complemented
47C3×#3750C2211yescharacteristic, complemented
48C32×#217C2211yescharacteristic, complemented
49C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C32×Dic3⋊C4C2211yescharacteristic, complemented
51#88807C2211yescharacteristic, complemented
52Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53#88804C2211yescharacteristic, complemented
54#88804C2211yescharacteristic, complemented
55#88803C2211yescharacteristic, complemented
56(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
57C2×D4×C3⋊D3—31no—
58C2×D4×C3⋊D3—31no—
59C2×D4×C3⋊D3—31no—
60C2×D4×C3⋊D3—34no—
61C2×D4×C3⋊D3—64no—
62C22×C4×C3⋊D3—31no—
63C2×#3811—34no—
64C2×#3811—34no—
65C22×#624—34no—
66C32×#121—31no—
67#64148—31no—
68#64148D311yescharacteristic, complemented
69#64147—31no—
70#64139—31no—
71#64104—31no—
72C4⋊C4×C3⋊D3—31no—
73#64093—31no—
74#64093—31no—
75C22⋊C4×C3⋊D3—31no—
76C22⋊C4×C3⋊D3—31no—
77C3×#939—34no—
78C3×#939D314yescomplemented
79#63978—34no—
80#63978—34no—
81#63974—34no—
82#63958—34no—
83#63958—34no—
84#63921—34no—
85#63910—34no—
86#63910—34no—
87#63883—34no—
88C23×C33C2311yescharacteristic
89C23×C33C2311yescharacteristic
90C22×C3⋊(C3⋊D3)—22no—
91C22×C3⋊(C3⋊D3)—22no—
92C22×C3⋊(C3⋊D3)—22no—
93C22×C3⋊(C3⋊D3)—22no—
94C22×C3⋊(C3⋊D3)—22no—
95C22×C3⋊(C3⋊D3)D414yescomplemented
96C22×C3⋊(C3⋊D3)C2311yescharacteristic
97C22×C3⋊(C3⋊D3)C2311yescharacteristic
98C22×C3⋊(C3⋊D3)C2311yescharacteristic
99C22×C3×C3⋊D3C2311yescharacteristic
100C22×C32×D3C2311yescharacteristic
101C2×D3×C3⋊D3—22no—
102C2×D3×C3⋊D3—22no—
103C2×D3×C3⋊D3—22no—
104C33×D4—22no—
105C2×C33×C4C2311yescharacteristic
106#6312—22no—
107#6312—22no—
108C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
109C4⋊(C3⋊(C3⋊D3))—22no—
110C4×C3⋊(C3⋊D3)—22no—
111C3×#638—22no—
112C3×#638—22no—
113C2×C3×C3⋊Dic3—22no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C32×#67—22no—
118C32×#67—22no—
119C2×C32×Dic3—22no—
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6292—22no—
124#6292—22no—
125#6291—22no—
126#6291—22no—
127#6289—22no—
128#6289—22no—
129#6289—22no—
130#6289—22no—
131#6289D414yescomplemented
132D3×#121—94no—
133D3×#121—91no—
134C23×C3⋊D3—31no—
135C23×C3⋊D3—34no—
136C23×C3⋊D3—31no—
137C23×C3⋊D3—34no—
138C23×C3⋊D3—31no—
139C23×C3⋊D3—64no—
140C23×C3⋊D3—64no—
141C22×D32—34no—
142C2×C32×D4—24no—
143C2×C32×D4—31no—
144C2×C32×D4—31no—
145C2×C32×D4C2×D314yescomplemented
146C2×C32×D4C2×D311yescharacteristic, complemented
147C22×C32×C4—31no—
148C2×#638—31no—
149C2×#638—31no—
150C2×#638—34no—
151C2×#638—34no—
152C2×#638—31no—
153C2×#638—31no—
154C2×#638—64no—
155C2×#638—64no—
156C2×#638C2×D311yescharacteristic, complemented
157C2×#638C2×D311yescharacteristic, complemented
158C22×C3⋊Dic3C2×D311yescharacteristic, complemented
159D4×C3⋊D3—64no—
160D4×C3⋊D3—64no—
161D4×C3⋊D3—64no—
162D4×C3⋊D3—616no—
163D4×C3⋊D3—632no—
164C2×C4⋊(C3⋊D3)—31no—
165C2×C4⋊(C3⋊D3)—31no—
166C2×C4⋊(C3⋊D3)—31no—
167C2×C4⋊(C3⋊D3)—34no—
168C2×C4⋊(C3⋊D3)—64no—
169C2×C4×C3⋊D3—31no—
170C2×C4×C3⋊D3—31no—
171C2×C4×C3⋊D3—34no—
172C2×C4×C3⋊D3—31no—
173C2×C4×C3⋊D3—31no—
174C2×C4×C3⋊D3—31no—
175C2×C4×C3⋊D3—31no—
176C2×C4×C3⋊D3—64no—
177C2×C4×C3⋊D3—64no—
178C2×C3×#67—34no—
179C2×C3×#67—34no—
180C2×C3×#67C2×D314yescomplemented
181C2×C3×#67C2×D314yescomplemented
182C22×C3×Dic3—34no—
183C22×C3×Dic3C2×D314yescomplemented
184#3811—616no—
185#3811—616no—
186C2×#626—34no—
187C2×#626—34no—
188C2×#626—34no—
189C2×#626—34no—
190C2×#624—34no—
191C2×#624—34no—
192C2×#624—34no—
193C2×#624—34no—
194C2×#624—34no—
195C2×#624—616no—
196C32×C4⋊C4—31no—
197C32×C22⋊C4—31no—
198C32×C22⋊C4—31no—
199#3757—31no—
200#3757C2×D311yescharacteristic, complemented
201#3752—31no—
202#3752—31no—
203#3752—31no—
204#3752C2×D311yescharacteristic, complemented
205C4⋊(C3⋊Dic3)—31no—
206#3750—31no—
207#3750C2×D311yescharacteristic, complemented
208C3×#217—34no—
209C3×#217C2×D314yescomplemented
210C3×(C2×D3)⋊C4—34no—
211C3×(C2×D3)⋊C4C2×D314yescomplemented
212C3×Dic3⋊C4—34no—
213C3×Dic3⋊C4C2×D314yescomplemented
214Dic3⋊Dic3—34no—
215Dic3⋊Dic3—34no—
216#3722—34no—
217#3722—34no—
218(C2×D3)⋊Dic3—34no—
219(C2×D3)⋊Dic3—34no—
220C22×C33—21no—
221C22×C33—21no—
222C22×C33—21no—
223C22×C33—21no—
224C22×C33—21no—
225C22×C33C2×D412yescomplemented
226C22×C33C2411yescharacteristic
227C2×C3⋊(C3⋊D3)—21no—
228C2×C3⋊(C3⋊D3)—21no—
229C2×C3⋊(C3⋊D3)—28no—
230C2×C3⋊(C3⋊D3)—21no—
231C2×C3⋊(C3⋊D3)—21no—
232C2×C3⋊(C3⋊D3)—21no—
233C2×C3⋊(C3⋊D3)—44no—
234C2×C3⋊(C3⋊D3)C2×D412yes—
235C2×C3⋊(C3⋊D3)C2×D412yes—
236C2×C3⋊(C3⋊D3)C2×D412yescomplemented
237C2×C3⋊(C3⋊D3)#4112yes—
238C2×C3×C3⋊D3—21no—
239C2×C3×C3⋊D3—21no—
240C2×C3×C3⋊D3—21no—
241C2×C32×D3—21no—
242C2×C32×D3—21no—
243C2×C32×D3—21no—
244D3×C3⋊D3—44no—
245C33×C4—21no—
246C3⋊(C3⋊Dic3)—21no—
247C3×C3⋊Dic3—21no—
248C3×C3⋊Dic3—21no—
249C3×C3⋊Dic3C2×D412yescomplemented
250C32×Dic3—21no—
251C32×Dic3—21no—
252C32×Dic3C2×D412yescomplemented
253C2×D3×D4—94no—
254C2×D3×D4—94no—
255C2×D3×D4—94no—
256C2×D3×D4—91no—
257C2×D3×D4—91no—
258C2×D3×D4—91no—
259C2×D3×D4—184no—
260C22×C4×D3—94no—
261C22×C4×D3—91no—
262C3×#121—34no—
263C3×#121—91no—
264#939—34no—
265#939—94no—
266#939—91no—
267#939C3⋊D311yescharacteristic, complemented
268#938—94no—
269#938—91no—
270#930—94no—
271#930—91no—
272#895—94no—
273#895—91no—
274D3×C4⋊C4—94no—
275D3×C4⋊C4—91no—
276#884—94no—
277#884—94no—
278#884—91no—
279#884—91no—
280D3×C22⋊C4—94no—
281D3×C22⋊C4—94no—
282D3×C22⋊C4—91no—
283D3×C22⋊C4—91no—
284C23×C32—24no—
285C23×C32—24no—
286C23×C32—31no—
287C23×C32C22×D314yes—
288C23×C32C22×D314yes—
289C23×C32C22×D311yescharacteristic
290C23×C32C22×D311yescharacteristic
291C22×C3⋊D3—31no—
292C22×C3⋊D3—34no—
293C22×C3⋊D3—31no—
294C22×C3⋊D3—31no—
295C22×C3⋊D3—34no—
296C22×C3⋊D3—316no—
297C22×C3⋊D3—34no—
298C22×C3⋊D3—34no—
299C22×C3⋊D3—64no—
300C22×C3⋊D3—616no—
301C22×C3⋊D3—64no—
302C22×C3⋊D3—64no—
303C22×C3⋊D3—62no—
304C22×C3⋊D3—62no—
305C22×C3⋊D3—62no—
306C22×C3⋊D3—62no—
307C22×C3⋊D3—62no—
308C22×C3⋊D3—62no—
309C22×C3⋊D3—62no—
310C22×C3⋊D3—68no—
311C22×C3⋊D3—62no—
312C22×C3⋊D3—616no—
313C22×C3⋊D3—68no—
314C22×C3⋊D3—68no—
315C22×C3⋊D3—68no—
316C22×C3⋊D3—68no—
317C22×C3⋊D3—128no—
318C22×C3⋊D3—128no—
319C22×C3⋊D3—128no—
320C22×C3⋊D3—128no—
321C22×C3⋊D3C22×D311yescharacteristic
322C22×C3×D3—34no—
323C22×C3×D3C22×D314yes—
324C2×D32—68no—
325C2×D32—68no—
326C2×D32—68no—
327C32×D4—216no—
328C32×D4—28no—
329C32×D4—22no—
330C32×D4—62no—
331C32×D4—62no—
332C2×C32×C4—24no—
333C2×C32×C4—31no—
334C2×C32×C4—31no—
335C2×C32×C4—31no—
336C2×C32×C4—62no—
337C2×C32×C4C22×D314yes—
338C2×C32×C4C22×D311yescharacteristic
339#638—22no—
340#638—22no—
341#638—62no—
342#638—62no—
343#638—68no—
344#638—616no—
345#638—616no—
346#638—68no—
347#638—62no—
348#638—62no—
349C2×C3⋊Dic3—22no—
350C2×C3⋊Dic3—31no—
351C2×C3⋊Dic3—34no—
352C2×C3⋊Dic3—64no—
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C4⋊(C3⋊D3)—62no—
357C4⋊(C3⋊D3)—68no—
358C4⋊(C3⋊D3)—616no—
359C4⋊(C3⋊D3)—62no—
360C4⋊(C3⋊D3)—62no—
361C4×C3⋊D3—34no—
362C4×C3⋊D3—62no—
363C4×C3⋊D3—62no—
364C4×C3⋊D3—62no—
365C4×C3⋊D3—62no—
366C4×C3⋊D3—68no—
367C4×C3⋊D3—616no—
368C4×C3⋊D3—62no—
369C3×#67—28no—
370C3×#67—28no—
371C3×#67—68no—
372C3×#67—68no—
373C2×C3×Dic3—28no—
374C2×C3×Dic3—34no—
375C2×C3×Dic3—34no—
376C2×C3×Dic3—34no—
377C2×C3×Dic3—68no—
378C2×C3×Dic3C22×D314yes—
379C2×C3×Dic3C22×D314yes—
380C2×C3×Dic3C22×D314yes—
381#626—68no—
382#626—68no—
383#626—68no—
384#626—68no—
385#624—316no—
386#624—68no—
387#624—68no—
388#624—68no—
389#624—68no—
390C2×#121—271noSylow
391C2×C33—22no—
392C2×C33—41no—
393C2×C33C22×D411yescharacteristic
394C2×C33C22×D411yescharacteristic
395C2×C33C2×#4111yescharacteristic
396C3⋊(C3⋊D3)—22no—
397C3⋊(C3⋊D3)—41no—
398C3⋊(C3⋊D3)#12114yescomplemented
399C3×C3⋊D3—41no—
400C32×D3—41no—
401C23×D3—94no—
402C23×D3—94no—
403C23×D3—91no—
404C23×D3—94no—
405C23×D3—91no—
406C23×D3—91no—
407C23×D3—184no—
408C23×D3—184no—
409C2×C3×D4—24no—
410C2×C3×D4—34no—
411C2×C3×D4—34no—
412C2×C3×D4—91no—
413C2×C3×D4—91no—
414C2×C3×D4D3214yescomplemented
415C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
416C22×C3×C4—34no—
417C22×C3×C4—91no—
418C2×#67—34no—
419C2×#67—34no—
420C2×#67—94no—
421C2×#67—94no—
422C2×#67—94no—
423C2×#67—94no—
424C2×#67—91no—
425C2×#67—91no—
426C2×#67—91no—
427C2×#67—91no—
428C2×#67—184no—
429C2×#67—184no—
430C2×#67C2×C3⋊D311yescharacteristic, complemented
431C2×#67C2×C3⋊D311yescharacteristic, complemented
432C22×Dic3—34no—
433C22×Dic3C2×C3⋊D311yescharacteristic, complemented
434D3×D4—184no—
435D3×D4—1816no—
436D3×D4—184no—
437D3×D4—1816no—
438D3×D4—1816no—
439D3×D4—184no—
440D3×D4—1832no—
441C2×D12—94no—
442C2×D12—94no—
443C2×D12—91no—
444C2×D12—91no—
445C2×D12—94no—
446C2×D12—91no—
447C2×D12—184no—
448C2×C4×D3—94no—
449C2×C4×D3—91no—
450C2×C4×D3—94no—
451C2×C4×D3—94no—
452C2×C4×D3—94no—
453C2×C4×D3—94no—
454C2×C4×D3—94no—
455C2×C4×D3—91no—
456C2×C4×D3—91no—
457C2×C4×D3—91no—
458C2×C4×D3—91no—
459C2×C4×D3—91no—
460C2×C4×D3—184no—
461C2×C4×D3—184no—
462C2×C4×D3—1816no—
463C3×C4⋊C4—34no—
464C3×C4⋊C4—91no—
465C3×C22⋊C4—34no—
466C3×C22⋊C4—34no—
467C3×C22⋊C4—91no—
468C3×C22⋊C4—91no—
469#217—34no—
470#217—94no—
471#217—91no—
472#217C2×C3⋊D311yescharacteristic, complemented
473(C2×D3)⋊C4—34no—
474(C2×D3)⋊C4—94no—
475(C2×D3)⋊C4—94no—
476(C2×D3)⋊C4—94no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—91no—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
481C4⋊Dic3—94no—
482C4⋊Dic3—91no—
483Dic3⋊C4—34no—
484Dic3⋊C4—94no—
485Dic3⋊C4—91no—
486Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
487C22×C32—21no—
488C22×C32—21no—
489C22×C32—28no—
490C22×C32—21no—
491C22×C32—24no—
492C22×C32—21no—
493C22×C32—21no—
494C22×C32—24no—
495C22×C32—28no—
496C22×C32—24no—
497C22×C32—24no—
498C22×C32—24no—
499C22×C32—24no—
500C22×C32—44no—
501C22×C32—44no—
502C22×C32—44no—
503C22×C32—44no—
504C22×C32—61no—
505C22×C32—61no—
506C22×C32—61no—
507C22×C32D3×D418yescomplemented
508C22×C32D3×D412yescomplemented
509C22×C32C23×D314yes—
510C22×C32C23×D311yescharacteristic
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—21no—
514C2×C3⋊D3—32no—
515C2×C3⋊D3—32no—
516C2×C3⋊D3—32no—
517C2×C3⋊D3—32no—
518C2×C3⋊D3—38no—
519C2×C3⋊D3—38no—
520C2×C3⋊D3—38no—
521C2×C3⋊D3—38no—
522C2×C3⋊D3—68no—
523C2×C3⋊D3—68no—
524C2×C3⋊D3—68no—
525C2×C3⋊D3—68no—
526C2×C3⋊D3—68no—
527C2×C3⋊D3—61no—
528C2×C3⋊D3—61no—
529C2×C3⋊D3—68no—
530C2×C3⋊D3—64no—
531C2×C3⋊D3—61no—
532C2×C3⋊D3—61no—
533C2×C3⋊D3—61no—
534C2×C3⋊D3—632no—
535C2×C3⋊D3—64no—
536C2×C3⋊D3—64no—
537C2×C3⋊D3—64no—
538C2×C3⋊D3—64no—
539C2×C3⋊D3—1232no—
540C2×C3⋊D3—124no—
541C2×C3⋊D3—124no—
542C2×C3⋊D3—124no—
543C2×C3⋊D3—124no—
544C2×C3⋊D3—124no—
545C2×C3⋊D3—124no—
546C2×C3⋊D3—1216no—
547C2×C3⋊D3—1232no—
548C2×C3×D3—24no—
549C2×C3×D3—24no—
550C2×C3×D3—24no—
551C2×C3×D3—64no—
552C2×C3×D3—64no—
553C2×C3×D3—64no—
554D32—1216no—
555C32×C4—28no—
556C32×C4—24no—
557C32×C4—21no—
558C32×C4—32no—
559C32×C4—61no—
560C32×C4—61no—
561C3⋊Dic3—21no—
562C3⋊Dic3—21no—
563C3⋊Dic3—68no—
564C3⋊Dic3—64no—
565C3⋊Dic3—61no—
566C3⋊Dic3D3×D412yescomplemented
567C3×Dic3—24no—
568C3×Dic3—24no—
569C3×Dic3—38no—
570C3×Dic3—64no—
571C3×Dic3—64no—
572C3×Dic3D3×D418yescomplemented
573C22×D4—271no—
574C22×D4—271no—
575C22×D4—271no—
576C23×C4—271no—
577#121—31no—
578#121—91no—
579#121—271no—
580#121—271no—
581#121—271no—
582#121—271no—
583#121—271no—
584#121—271no—
585C2×C4⋊C4—271no—
586C2×C22⋊C4—271no—
587C2×C22⋊C4—271no—
588C33C2×#12111yescharacteristic, complemented, Sylow
589C23×C3—24no—
590C23×C3—24no—
591C23×C3—34no—
592C23×C3—91no—
593C23×C3C2×D3214yes—
594C23×C3C2×D3214yes—
595C23×C3C22×C3⋊D311yescharacteristic
596C23×C3C22×C3⋊D311yescharacteristic
597C22×D3—34no—
598C22×D3—94no—
599C22×D3—91no—
600C22×D3—94no—
601C22×D3—91no—
602C22×D3—916no—
603C22×D3—94no—
604C22×D3—94no—
605C22×D3—91no—
606C22×D3—184no—
607C22×D3—184no—
608C22×D3—184no—
609C22×D3—1816no—
610C22×D3—182no—
611C22×D3—182no—
612C22×D3—182no—
613C22×D3—188no—
614C22×D3—188no—
615C22×D3—188no—
616C22×D3—182no—
617C22×D3—182no—
618C22×D3—188no—
619C22×D3—188no—
620C22×D3—188no—
621C22×D3—182no—
622C22×D3—182no—
623C22×D3—182no—
624C22×D3—188no—
625C22×D3—188no—
626C22×D3—1816no—
627C22×D3—368no—
628C22×D3—368no—
629C22×D3—368no—
630C22×D3—368no—
631C22×D3C22×C3⋊D311yescharacteristic
632C3×D4—216no—
633C3×D4—28no—
634C3×D4—22no—
635C3×D4—68no—
636C3×D4—68no—
637C3×D4—182no—
638C3×D4—182no—
639C2×C3×C4—24no—
640C2×C3×C4—34no—
641C2×C3×C4—34no—
642C2×C3×C4—34no—
643C2×C3×C4—68no—
644C2×C3×C4—91no—
645C2×C3×C4—91no—
646C2×C3×C4—91no—
647C2×C3×C4—182no—
648C2×C3×C4C2×D3214yes—
649C2×C3×C4C22×C3⋊D311yescharacteristic
650#67—22no—
651#67—22no—
652#67—68no—
653#67—68no—
654#67—182no—
655#67—188no—
656#67—188no—
657#67—188no—
658#67—182no—
659#67—1816no—
660#67—1816no—
661#67—188no—
662#67—182no—
663#67—182no—
664C2×Dic3—22no—
665C2×Dic3—34no—
666C2×Dic3—34no—
667C2×Dic3—34no—
668C2×Dic3—68no—
669C2×Dic3—94no—
670C2×Dic3—91no—
671C2×Dic3—184no—
672C2×Dic3C22×C3⋊D311yescharacteristic
673C2×Dic3C22×C3⋊D311yescharacteristic
674C2×Dic3C22×C3⋊D311yescharacteristic
675D12—188no—
676D12—182no—
677D12—1816no—
678D12—188no—
679D12—188no—
680D12—182no—
681D12—182no—
682C4×D3—916no—
683C4×D3—94no—
684C4×D3—182no—
685C4×D3—182no—
686C4×D3—182no—
687C4×D3—188no—
688C4×D3—188no—
689C4×D3—188no—
690C4×D3—188no—
691C4×D3—188no—
692C4×D3—182no—
693C4×D3—1816no—
694C4×D3—182no—
695C2×C32—22no—
696C2×C32—24no—
697C2×C32—24no—
698C2×C32—24no—
699C2×C32—28no—
700C2×C32—48no—
701C2×C32—48no—
702C2×C32—44no—
703C2×C32—41no—
704C2×C32—121no—
705C2×C32C2×D3×D414yes—
706C2×C32C2×D3×D414yes—
707C2×C32C2×D3×D411yescharacteristic
708C2×C32C2×D3×D411yescharacteristic
709C2×C32D3×#4114yes—
710C2×C32D3×#4111yescharacteristic
711C3⋊D3—34no—
712C3⋊D3—316no—
713C3⋊D3—41no—
714C3⋊D3—616no—
715C3⋊D3—62no—
716C3⋊D3—68no—
717C3⋊D3—128no—
718C3⋊D3—128no—
719C3⋊D3—124no—
720C3⋊D3—121no—
721C3×D3—44no—
722C3×D3—124no—
723C24—271no—
724C24—271no—
725C24—271no—
726C2×D4—31no—
727C2×D4—31no—
728C2×D4—91no—
729C2×D4—91no—
730C2×D4—271no—
731C2×D4—271no—
732C2×D4—271no—
733C2×D4—271no—
734C2×D4—271no—
735C2×D4—271no—
736C2×D4—271no—
737C2×D4—544no—
738C2×D4—544no—
739C2×D4—544no—
740C2×D4D3×C3⋊D311yescharacteristic, complemented
741C22×C4—31no—
742C22×C4—91no—
743C22×C4—271no—
744C22×C4—271no—
745C22×C4—271no—
746C22×C4—271no—
747C22×C4—271no—
748C22×C4—271no—
749C22×C4—544no—
750C4⋊C4—31no—
751C4⋊C4—91no—
752C4⋊C4—271no—
753C4⋊C4—271no—
754C22⋊C4—31no—
755C22⋊C4—31no—
756C22⋊C4—91no—
757C22⋊C4—91no—
758C22⋊C4—271no—
759C22⋊C4—271no—
760C22⋊C4—271no—
761C22⋊C4—271no—
762C22×C3—24no—
763C22×C3—24no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—28no—
767C22×C3—24no—
768C22×C3—24no—
769C22×C3—24no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—24no—
774C22×C3—28no—
775C22×C3—44no—
776C22×C3—44no—
777C22×C3—44no—
778C22×C3—44no—
779C22×C3—64no—
780C22×C3—64no—
781C22×C3—64no—
782C22×C3—181no—
783C22×C3—181no—
784C22×C3—181no—
785C22×C3#381118yescomplemented
786C22×C3D4×C3⋊D312yescomplemented
787C22×C3C22×D3214yes—
788C22×C3C23×C3⋊D311yescharacteristic
789C2×D3—21no—
790C2×D3—21no—
791C2×D3—21no—
792C2×D3—64no—
793C2×D3—64no—
794C2×D3—64no—
795C2×D3—98no—
796C2×D3—98no—
797C2×D3—98no—
798C2×D3—92no—
799C2×D3—92no—
800C2×D3—92no—
801C2×D3—98no—
802C2×D3—92no—
803C2×D3—188no—
804C2×D3—188no—
805C2×D3—188no—
806C2×D3—188no—
807C2×D3—188no—
808C2×D3—1832no—
809C2×D3—184no—
810C2×D3—184no—
811C2×D3—181no—
812C2×D3—181no—
813C2×D3—188no—
814C2×D3—184no—
815C2×D3—184no—
816C2×D3—184no—
817C2×D3—181no—
818C2×D3—181no—
819C2×D3—181no—
820C2×D3—3632no—
821C2×D3—364no—
822C2×D3—364no—
823C2×D3—364no—
824C2×D3—364no—
825C2×D3—364no—
826C2×D3—3616no—
827C2×D3—3616no—
828C2×D3—364no—
829C2×D3—3632no—
830C3×C4—28no—
831C3×C4—24no—
832C3×C4—21no—
833C3×C4—38no—
834C3×C4—64no—
835C3×C4—64no—
836C3×C4—92no—
837C3×C4—181no—
838C3×C4—181no—
839Dic3—21no—
840Dic3—21no—
841Dic3—38no—
842Dic3—64no—
843Dic3—64no—
844Dic3—188no—
845Dic3—184no—
846Dic3—181no—
847Dic3D4×C3⋊D312yescomplemented
848C32—24no—
849C32D3×#12114yescomplemented
850C32D3×#12111yescharacteristic, complemented
851C23—31no—
852C23—91no—
853C23—271no—
854C23—271no—
855C23—274no—
856C23—271no—
857C23—542no—
858C23—542no—
859C23—542no—
860C23—542no—
861C23—542no—
862C23—542no—
863C23—542no—
864C23—542no—
865C23C2×D3×C3⋊D311yescharacteristic
866C23C2×D3×C3⋊D311yescharacteristic
867D4—22no—
868D4—62no—
869D4—62no—
870D4—182no—
871D4—182no—
872D4—542no—
873D4—542no—
874D4—542no—
875D4—542no—
876D4—542no—
877D4—542no—
878D4—542no—
879C2×C4—31no—
880C2×C4—31no—
881C2×C4—31no—
882C2×C4—62no—
883C2×C4—91no—
884C2×C4—91no—
885C2×C4—91no—
886C2×C4—182no—
887C2×C4—274no—
888C2×C4—271no—
889C2×C4—542no—
890C2×C4—542no—
891C2×C4—542no—
892C2×C4—542no—
893C2×C4—542no—
894C2×C4C2×D3×C3⋊D311yescharacteristic
895C2×C3—28no—
896C2×C3—22no—
897C2×C3—24no—
898C2×C3—24no—
899C2×C3—24no—
900C2×C3—48no—
901C2×C3—48no—
902C2×C3—44no—
903C2×C3—41no—
904C2×C3—124no—
905C2×C3—361no—
906C2×C3D32×D414yes—
907C2×C3#6431214yes—
908C2×C3C2×#381114yes—
909C2×C3C2×D4×C3⋊D311yescharacteristic
910C2×C3C2×D4×C3⋊D311yescharacteristic
911C2×C3#41×C3⋊D311yescharacteristic
912D3—41no—
913D3—916no—
914D3—94no—
915D3—124no—
916D3—1816no—
917D3—188no—
918D3—182no—
919D3—368no—
920D3—368no—
921D3—364no—
922D3—361no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—61no—
929C22—61no—
930C22—61no—
931C22—181no—
932C22—181no—
933C22—181no—
934C22—272no—
935C22—272no—
936C22—272no—
937C22—272no—
938C22—548no—
939C22—541no—
940C22—541no—
941C22—541no—
942C22—541no—
943C22—541no—
944C22—1084no—
945C22—1084no—
946C22#8903912yescomplemented
947C22C22×D3×C3⋊D311yescharacteristic
948C4—21no—
949C4—32no—
950C4—61no—
951C4—61no—
952C4—92no—
953C4—181no—
954C4—181no—
955C4—541no—
956C3—24no—
957C3#1059529814yescomplemented
958C3C3⋊D3×#12111yescharacteristic, complemented
959C2—22no—
960C2—41no—
961C2—121no—
962C2—274no—
963C2—361no—
964C2—542no—
965C2—1081no—
966C2D3×D4×C3⋊D311yescharacteristic
967C2#1172458611yescharacteristic
968C2C2×#8903911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33C2×#121
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊(C3⋊D3)C2semidirect
2. C2×#89039C2semidirect
3. C2×#89039C2semidirect
4. C22×#6289C2semidirect
5. C3×#64148C2semidirect
6. C32×#939C2semidirect
7. #11723635C2semidirect
8. #11723632C2semidirect
9. #11723627C2semidirect
10. #11723623C2semidirect
11. #11723599C2semidirect
12. #11723539C2semidirect
13. #11723525C2semidirect
14. #11723486C2semidirect
15. #11723470C2semidirect
21. C2×C33×D4C22semidirect
22. C2×#6312C22semidirect
23. C2×#6312C22semidirect
25. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
27. C2×C3×#638C22semidirect
28. C2×C3×#638C22semidirect
29. C22×C3×C3⋊Dic3C22semidirect
30. C2×C32×#67C22semidirect
31. C2×C32×#67C22semidirect
32. C22×C32×Dic3C22semidirect
35. C2×#6292C22semidirect
36. C2×#6292C22semidirect
37. C2×#6291C22semidirect
38. C2×#6291C22semidirect
43. C2×#6289C22semidirect
44. C2×#6289C22semidirect
45. C3×#3757C22semidirect
46. C3×#3752C22semidirect
47. C3×#3750C22semidirect
48. C32×#217C22semidirect
49. C32×(C2×D3)⋊C4C22semidirect
50. C32×Dic3⋊C4C22semidirect
51. #88807C22semidirect
52. Dic3⋊(C3⋊Dic3)C22semidirect
53. #88804C22semidirect
54. #88804C22semidirect
55. #88803C22semidirect
56. (C2×D3)⋊(C3⋊Dic3)C22semidirect
68. #64148D3semidirect
78. C3×#939D3semidirect
95. C22×C3⋊(C3⋊D3)D4semidirect
131. #6289D4semidirect
145. C2×C32×D4C2×D3semidirect
146. C2×C32×D4C2×D3semidirect
156. C2×#638C2×D3semidirect
157. C2×#638C2×D3semidirect
158. C22×C3⋊Dic3C2×D3semidirect
180. C2×C3×#67C2×D3semidirect
181. C2×C3×#67C2×D3semidirect
183. C22×C3×Dic3C2×D3semidirect
200. #3757C2×D3semidirect
204. #3752C2×D3semidirect
207. #3750C2×D3semidirect
209. C3×#217C2×D3semidirect
211. C3×(C2×D3)⋊C4C2×D3semidirect
213. C3×Dic3⋊C4C2×D3semidirect
225. C22×C33C2×D4semidirect
236. C2×C3⋊(C3⋊D3)C2×D4semidirect
249. C3×C3⋊Dic3C2×D4semidirect
252. C32×Dic3C2×D4semidirect
267. #939C3⋊D3semidirect
398. C3⋊(C3⋊D3)#121semidirect
414. C2×C3×D4D32semidirect
415. C2×C3×D4C2×C3⋊D3semidirect
430. C2×#67C2×C3⋊D3semidirect
431. C2×#67C2×C3⋊D3semidirect
433. C22×Dic3C2×C3⋊D3semidirect
472. #217C2×C3⋊D3semidirect
480. (C2×D3)⋊C4C2×C3⋊D3semidirect
486. Dic3⋊C4C2×C3⋊D3semidirect
507. C22×C32D3×D4semidirect
508. C22×C32D3×D4semidirect
566. C3⋊Dic3D3×D4semidirect
572. C3×Dic3D3×D4semidirect
588. C33C2×#121semidirect
740. C2×D4D3×C3⋊D3semidirect
785. C22×C3#3811semidirect
786. C22×C3D4×C3⋊D3semidirect
847. Dic3D4×C3⋊D3semidirect
849. C32D3×#121semidirect
850. C32D3×#121semidirect
946. C22#89039semidirect
957. C3#10595298semidirect
958. C3C3⋊D3×#121semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊(C3⋊D3)2
C2×#890392
C22×#62892
C3×#641482
C32×#9392
#117236352
#117236322
#117236272
#117236232
#117235992
#117235392
#117235252
#117234862
#117234702
C3⋊D3×#1213
#105952983