Finite Group Databasebeta

← #13175928

Subgroups — #13175928

Order 1728.

3084 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89039C211yesmaximal, characteristic, complemented
2C2×#89039C211yesmaximal, characteristic, complemented
3C2×#89026C211yesmaximal, characteristic, complemented
4C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
5C22⋊C4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
6C3×#64093C211yesmaximal, characteristic, complemented
7C32×#884C211yesmaximal, characteristic, complemented
8#11723631C211yesmaximal, characteristic, complemented
9#11723615C211yesmaximal, characteristic, complemented
10#11723539C211yesmaximal, characteristic, complemented
11#11723520C211yesmaximal, characteristic, complemented
12#11723514C211yesmaximal, characteristic, complemented
13#11723482C211yesmaximal, characteristic, complemented
14#11723475C211yesmaximal, characteristic, complemented
15#11723470C211yesmaximal, characteristic, complemented
16C3⋊D3×#121—31nomaximal
17#10594265—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic, complemented
25C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27C2×C32×#67C2211yescharacteristic, complemented
28C2×C32×#67C2211yescharacteristic, complemented
29C2×C32×D12C2211yescharacteristic, complemented
30C2×C32×C4×D3C2211yescharacteristic, complemented
31#89039—24no—
32#89039—24no—
33C2×#6292C2211yescharacteristic, complemented
34C2×#6292C2211yescharacteristic, complemented
35C2×#6291C2211yescharacteristic, complemented
36C2×#6291C2211yescharacteristic, complemented
37C2×#6290C2211yescharacteristic, complemented
38C2×#6290C2211yescharacteristic, complemented
39C2×#6289C2211yescharacteristic
40C2×#6289C2211yescharacteristic
41C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
42C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
43#89026—24no—
44C4×D3×C3⋊D3—24no—
45C33×C22⋊C4C2211yescharacteristic, complemented
46#88864C2211yescharacteristic, complemented
47#88859C2211yescharacteristic, complemented
48#88859C2211yescharacteristic, complemented
49C3×#3752C2211yescharacteristic, complemented
50C3×#3750C2211yescharacteristic, complemented
51C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
52C32×Dic3⋊C4C2211yescharacteristic, complemented
53#88807C2211yescharacteristic, complemented
54Dic3⋊(C3⋊Dic3)C2211yescharacteristic, 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—
60C22×C4×C3⋊D3—31no—
61C2×#3811—34no—
62C2×#3811—34no—
63C2×#3802—34no—
64C2×C4×D32—34no—
65C32×#121—31no—
66#64148—31no—
67#64148—31no—
68#64147—31no—
69#64139—31no—
70#64104—31no—
71C4⋊C4×C3⋊D3—31no—
72#64093—31no—
73#64093D311yescharacteristic, complemented
74C22⋊C4×C3⋊D3—31no—
75C22⋊C4×C3⋊D3—31no—
76C22⋊C4×C3⋊D3—34no—
77C22⋊C4×C3⋊D3—64no—
78C3×#884—34no—
79C3×#884D314yescomplemented
80#63970—34no—
81#63970—34no—
82#63921—34no—
83#63906—34no—
84#63906—34no—
85#63886—34no—
86#63886—34no—
87#63883—34no—
88C23×C33C2311yescharacteristic
89C22×C3⋊(C3⋊D3)—22no—
90C22×C3⋊(C3⋊D3)—22no—
91C22×C3⋊(C3⋊D3)—22no—
92C22×C3⋊(C3⋊D3)C2311yescharacteristic
93C22×C3⋊(C3⋊D3)C2311yescharacteristic
94C22×C3×C3⋊D3C2311yescharacteristic
95C22×C3×C3⋊D3C2311yescharacteristic
96C22×C32×D3C2311yescharacteristic
97C22×C32×D3C2311yescharacteristic
98C2×D3×C3⋊D3—22no—
99C2×D3×C3⋊D3—22no—
100C2×D3×C3⋊D3—22no—
101C2×D3×C3⋊D3—22no—
102C2×D3×C3⋊D3—22no—
103C2×D3×C3⋊D3D414yescomplemented
104C2×C33×C4C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C4×C3⋊(C3⋊D3)—22no—
109C4×C3⋊(C3⋊D3)—22no—
110C3×#638—22no—
111C3×#638—22no—
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C3×C4⋊(C3⋊D3)—22no—
115C3×C4×C3⋊D3—22no—
116C32×#67—22no—
117C32×#67—22no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C32×D12—22no—
121C32×C4×D3—22no—
122#6292—22no—
123#6292—22no—
124#6291—22no—
125#6291—22no—
126#6290—22no—
127#6290—22no—
128#6289—22no—
129#6289D414yescomplemented
130Dic3×C3⋊D3—22no—
131D3×C3⋊Dic3—22no—
132D3×#121—94no—
133D3×#121—91no—
134C23×C3⋊D3—31no—
135C23×C3⋊D3—31no—
136C23×C3⋊D3—34no—
137C23×C3⋊D3—31no—
138C23×C3⋊D3—64no—
139C22×D32—34no—
140C22×D32—34no—
141C2×C32×D4—31no—
142C2×C32×D4—31no—
143C2×C32×D4—31no—
144C22×C32×C4—31no—
145C2×#638—31no—
146C2×#638—31no—
147C2×#638—31no—
148C2×#638—31no—
149C2×#638C2×D311yescharacteristic, complemented
150C2×#638C2×D311yescharacteristic, complemented
151C22×C3⋊Dic3—31no—
152D4×C3⋊D3—64no—
153D4×C3⋊D3—64no—
154D4×C3⋊D3—64no—
155C2×C4⋊(C3⋊D3)—31no—
156C2×C4⋊(C3⋊D3)—31no—
157C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
158C2×C4×C3⋊D3—31no—
159C2×C4×C3⋊D3—31no—
160C2×C4×C3⋊D3—31no—
161C2×C4×C3⋊D3—31no—
162C2×C4×C3⋊D3—34no—
163C2×C4×C3⋊D3—34no—
164C2×C4×C3⋊D3—31no—
165C2×C4×C3⋊D3—64no—
166C2×C4×C3⋊D3—64no—
167C2×C4×C3⋊D3—64no—
168C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
169C2×C3×#67—34no—
170C2×C3×#67—34no—
171C2×C3×#67C2×D314yescomplemented
172C2×C3×#67C2×D314yescomplemented
173C2×C3×D12—34no—
174C2×C3×D12C2×D314yescomplemented
175C2×C3×C4×D3—34no—
176C2×C3×C4×D3C2×D314yescomplemented
177#3811—616no—
178#3811—616no—
179C2×#626—34no—
180C2×#626—34no—
181C2×#626—34no—
182C2×#626—34no—
183C2×#625—34no—
184C2×#625—34no—
185C2×#624—34no—
186C2×#624—34no—
187C2×D3×Dic3—34no—
188C2×D3×Dic3—34no—
189#3802—616no—
190C4×D32—616no—
191C32×C4⋊C4—31no—
192C32×C22⋊C4—24no—
193C32×C22⋊C4—31no—
194C32×C22⋊C4C2×D314yescomplemented
195C32×C22⋊C4C2×D311yescharacteristic, complemented
196#3757—31no—
197#3757—34no—
198#3757—31no—
199#3757—64no—
200#3752—31no—
201#3752—31no—
202#3752—31no—
203#3752—34no—
204#3752—34no—
205#3752—64no—
206#3752—64no—
207#3752C2×D311yescharacteristic, complemented
208C4⋊(C3⋊Dic3)—31no—
209#3750—31no—
210#3750C2×D311yescharacteristic, complemented
211C3×(C2×D3)⋊C4—34no—
212C3×(C2×D3)⋊C4C2×D314yescomplemented
213C3×Dic3⋊C4—34no—
214C3×Dic3⋊C4C2×D314yescomplemented
215Dic3⋊Dic3—34no—
216Dic3⋊Dic3—34no—
217(C2×D3)⋊Dic3—34no—
218(C2×D3)⋊Dic3—34no—
219C22×C33—21no—
220C22×C33—21no—
221C22×C33—21no—
222C22×C33C2411yescharacteristic
223C2×C3⋊(C3⋊D3)—21no—
224C2×C3⋊(C3⋊D3)—21no—
225C2×C3⋊(C3⋊D3)—21no—
226C2×C3⋊(C3⋊D3)—44no—
227C2×C3⋊(C3⋊D3)C2×D412yes—
228C2×C3⋊(C3⋊D3)C2×D412yes—
229C2×C3⋊(C3⋊D3)#4112yes—
230C2×C3×C3⋊D3—21no—
231C2×C3×C3⋊D3—21no—
232C2×C3×C3⋊D3—21no—
233C2×C3×C3⋊D3—21no—
234C2×C3×C3⋊D3—21no—
235C2×C3×C3⋊D3C2×D412yescomplemented
236C2×C32×D3—21no—
237C2×C32×D3—21no—
238C2×C32×D3—21no—
239C2×C32×D3—21no—
240C2×C32×D3—21no—
241C2×C32×D3C2×D412yescomplemented
242D3×C3⋊D3—28no—
243D3×C3⋊D3—44no—
244C33×C4—21no—
245C33×C4—21no—
246C3⋊(C3⋊Dic3)—21no—
247C3⋊(C3⋊Dic3)—21no—
248C3×C3⋊Dic3—21no—
249C3×C3⋊Dic3C2×D412yescomplemented
250C32×Dic3—21no—
251C32×Dic3C2×D412yescomplemented
252C2×D3×D4—94no—
253C2×D3×D4—94no—
254C2×D3×D4—94no—
255C2×D3×D4—91no—
256C2×D3×D4—91no—
257C2×D3×D4—91no—
258C22×C4×D3—94no—
259C22×C4×D3—91no—
260C3×#121—34no—
261C3×#121—91no—
262#939—94no—
263#939—94no—
264#939—91no—
265#939—91no—
266#938—94no—
267#938—91no—
268#930—94no—
269#930—91no—
270#895—94no—
271#895—91no—
272D3×C4⋊C4—94no—
273D3×C4⋊C4—91no—
274#884—34no—
275#884—94no—
276#884—91no—
277#884C3⋊D311yescharacteristic, complemented
278D3×C22⋊C4—94no—
279D3×C22⋊C4—94no—
280D3×C22⋊C4—91no—
281D3×C22⋊C4—91no—
282D3×C22⋊C4—184no—
283C23×C32—24no—
284C23×C32—31no—
285C23×C32—31no—
286C23×C32C22×D314yes—
287C23×C32C22×D311yescharacteristic
288C22×C3⋊D3—31no—
289C22×C3⋊D3—34no—
290C22×C3⋊D3—31no—
291C22×C3⋊D3—34no—
292C22×C3⋊D3—34no—
293C22×C3⋊D3—64no—
294C22×C3⋊D3—64no—
295C22×C3⋊D3—62no—
296C22×C3⋊D3—62no—
297C22×C3⋊D3—62no—
298C22×C3⋊D3—62no—
299C22×C3⋊D3—62no—
300C22×C3⋊D3—62no—
301C22×C3⋊D3—68no—
302C22×C3⋊D3—62no—
303C22×C3⋊D3—62no—
304C22×C3⋊D3—616no—
305C22×C3⋊D3—68no—
306C22×C3⋊D3—68no—
307C22×C3⋊D3—128no—
308C22×C3⋊D3—128no—
309C22×C3⋊D3C22×D311yescharacteristic
310C22×C3⋊D3C22×D311yescharacteristic
311C22×C3×D3—34no—
312C22×C3×D3—34no—
313C22×C3×D3C22×D314yes—
314C22×C3×D3C22×D314yes—
315C2×D32—316no—
316C2×D32—68no—
317C2×D32—68no—
318C2×D32—68no—
319C2×D32—68no—
320C2×D32—68no—
321C32×D4—62no—
322C32×D4—62no—
323C32×D4—62no—
324C2×C32×C4—24no—
325C2×C32×C4—24no—
326C2×C32×C4—31no—
327C2×C32×C4—31no—
328C2×C32×C4—62no—
329C2×C32×C4C22×D314yes—
330C2×C32×C4C22×D314yes—
331C2×C32×C4C22×D311yescharacteristic
332C2×C32×C4C22×D311yescharacteristic
333#638—22no—
334#638—22no—
335#638—62no—
336#638—62no—
337#638—62no—
338#638—62no—
339C2×C3⋊Dic3—31no—
340C2×C3⋊Dic3—31no—
341C2×C3⋊Dic3—34no—
342C2×C3⋊Dic3—34no—
343C2×C3⋊Dic3—64no—
344C2×C3⋊Dic3—64no—
345C2×C3⋊Dic3—62no—
346C2×C3⋊Dic3C22×D311yescharacteristic
347C2×C3⋊Dic3C22×D311yescharacteristic
348C4⋊(C3⋊D3)—22no—
349C4⋊(C3⋊D3)—62no—
350C4⋊(C3⋊D3)—62no—
351C4×C3⋊D3—22no—
352C4×C3⋊D3—34no—
353C4×C3⋊D3—62no—
354C4×C3⋊D3—62no—
355C4×C3⋊D3—62no—
356C4×C3⋊D3—62no—
357C4×C3⋊D3—68no—
358C4×C3⋊D3—68no—
359C4×C3⋊D3—128no—
360C4×C3⋊D3—128no—
361C3×#67—28no—
362C3×#67—28no—
363C3×#67—68no—
364C3×#67—68no—
365C2×C3×Dic3—34no—
366C2×C3×Dic3—34no—
367C2×C3×Dic3C22×D314yes—
368C2×C3×Dic3C22×D314yes—
369C3×D12—28no—
370C3×D12—68no—
371C3×C4×D3—28no—
372C3×C4×D3—68no—
373#626—68no—
374#626—68no—
375#626—68no—
376#626—68no—
377#625—68no—
378#625—68no—
379#624—316no—
380#624—68no—
381D3×Dic3—68no—
382D3×Dic3—68no—
383C2×#121—271noSylow
384C2×C33—41no—
385C2×C33C22×D411yescharacteristic
386C2×C33C22×D411yescharacteristic
387C2×C33C2×#4111yescharacteristic
388C3⋊(C3⋊D3)—41no—
389C3⋊(C3⋊D3)#12114yescomplemented
390C3×C3⋊D3—22no—
391C3×C3⋊D3—41no—
392C32×D3—22no—
393C32×D3—41no—
394C23×D3—94no—
395C23×D3—94no—
396C23×D3—91no—
397C23×D3—94no—
398C23×D3—91no—
399C23×D3—91no—
400C23×D3—184no—
401C2×C3×D4—34no—
402C2×C3×D4—34no—
403C2×C3×D4—34no—
404C2×C3×D4—91no—
405C2×C3×D4—91no—
406C2×C3×D4—91no—
407C22×C3×C4—34no—
408C22×C3×C4—91no—
409C2×#67—34no—
410C2×#67—34no—
411C2×#67—94no—
412C2×#67—94no—
413C2×#67—94no—
414C2×#67—94no—
415C2×#67—91no—
416C2×#67—91no—
417C2×#67—91no—
418C2×#67—91no—
419C2×#67C2×C3⋊D311yescharacteristic, complemented
420C2×#67C2×C3⋊D311yescharacteristic, complemented
421C22×Dic3—94no—
422C22×Dic3—91no—
423D3×D4—184no—
424D3×D4—1816no—
425D3×D4—184no—
426D3×D4—1816no—
427D3×D4—184no—
428D3×D4—1816no—
429C2×D12—34no—
430C2×D12—94no—
431C2×D12—94no—
432C2×D12—91no—
433C2×D12—91no—
434C2×D12C2×C3⋊D311yescharacteristic, complemented
435C2×C4×D3—34no—
436C2×C4×D3—94no—
437C2×C4×D3—91no—
438C2×C4×D3—94no—
439C2×C4×D3—94no—
440C2×C4×D3—91no—
441C2×C4×D3—94no—
442C2×C4×D3—94no—
443C2×C4×D3—91no—
444C2×C4×D3—91no—
445C2×C4×D3—91no—
446C2×C4×D3—184no—
447C2×C4×D3—184no—
448C2×C4×D3—184no—
449C2×C4×D3—1816no—
450C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
451C3×C4⋊C4—34no—
452C3×C4⋊C4—91no—
453C3×C22⋊C4—24no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—91no—
456C3×C22⋊C4D3214yescomplemented
457C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
458#217—94no—
459#217—94no—
460#217—91no—
461#217—91no—
462#217—184no—
463(C2×D3)⋊C4—34no—
464(C2×D3)⋊C4—94no—
465(C2×D3)⋊C4—91no—
466(C2×D3)⋊C4—94no—
467(C2×D3)⋊C4—94no—
468(C2×D3)⋊C4—91no—
469(C2×D3)⋊C4—91no—
470(C2×D3)⋊C4—184no—
471(C2×D3)⋊C4—184no—
472(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
473C4⋊Dic3—94no—
474C4⋊Dic3—91no—
475Dic3⋊C4—34no—
476Dic3⋊C4—94no—
477Dic3⋊C4—91no—
478Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
479C22×C32—28no—
480C22×C32—21no—
481C22×C32—21no—
482C22×C32—24no—
483C22×C32—21no—
484C22×C32—24no—
485C22×C32—24no—
486C22×C32—24no—
487C22×C32—32no—
488C22×C32—44no—
489C22×C32—44no—
490C22×C32—61no—
491C22×C32—61no—
492C22×C32—61no—
493C22×C32—61no—
494C22×C32—61no—
495C22×C32C23×D314yes—
496C22×C32C23×D311yescharacteristic
497C2×C3⋊D3—21no—
498C2×C3⋊D3—21no—
499C2×C3⋊D3—21no—
500C2×C3⋊D3—21no—
501C2×C3⋊D3—21no—
502C2×C3⋊D3—32no—
503C2×C3⋊D3—32no—
504C2×C3⋊D3—32no—
505C2×C3⋊D3—38no—
506C2×C3⋊D3—38no—
507C2×C3⋊D3—38no—
508C2×C3⋊D3—68no—
509C2×C3⋊D3—68no—
510C2×C3⋊D3—68no—
511C2×C3⋊D3—68no—
512C2×C3⋊D3—68no—
513C2×C3⋊D3—61no—
514C2×C3⋊D3—61no—
515C2×C3⋊D3—64no—
516C2×C3⋊D3—61no—
517C2×C3⋊D3—64no—
518C2×C3⋊D3—64no—
519C2×C3⋊D3—124no—
520C2×C3⋊D3—124no—
521C2×C3⋊D3—124no—
522C2×C3⋊D3—124no—
523C2×C3⋊D3—1216no—
524C2×C3⋊D3—1232no—
525C2×C3⋊D3D3×D412yescomplemented
526C2×C3×D3—24no—
527C2×C3×D3—24no—
528C2×C3×D3—24no—
529C2×C3×D3—24no—
530C2×C3×D3—24no—
531C2×C3×D3—38no—
532C2×C3×D3—64no—
533C2×C3×D3—64no—
534C2×C3×D3—64no—
535C2×C3×D3—64no—
536C2×C3×D3—64no—
537C2×C3×D3D3×D418yescomplemented
538D32—632no—
539D32—1216no—
540C32×C4—21no—
541C32×C4—21no—
542C32×C4—24no—
543C32×C4—24no—
544C32×C4—32no—
545C32×C4—44no—
546C32×C4—44no—
547C32×C4—61no—
548C3⋊Dic3—21no—
549C3⋊Dic3—61no—
550C3⋊Dic3—61no—
551C3⋊Dic3—64no—
552C3⋊Dic3—64no—
553C3⋊Dic3—124no—
554C3⋊Dic3—124no—
555C3⋊Dic3D3×D412yescomplemented
556C3×Dic3—24no—
557C3×Dic3—38no—
558C3×Dic3—64no—
559C3×Dic3D3×D418yescomplemented
560C22×D4—271no—
561C22×D4—271no—
562C22×D4—271no—
563C23×C4—271no—
564#121—31no—
565#121—91no—
566#121—271no—
567#121—271no—
568#121—271no—
569#121—271no—
570#121—271no—
571#121—271no—
572C2×C4⋊C4—271no—
573C2×C22⋊C4—271no—
574C2×C22⋊C4—271no—
575C33C2×#12111yescharacteristic, complemented, Sylow
576C23×C3—24no—
577C23×C3—34no—
578C23×C3—34no—
579C23×C3—91no—
580C23×C3—91no—
581C23×C3C2×D3214yes—
582C23×C3C22×C3⋊D311yescharacteristic
583C22×D3—34no—
584C22×D3—34no—
585C22×D3—916no—
586C22×D3—94no—
587C22×D3—91no—
588C22×D3—94no—
589C22×D3—94no—
590C22×D3—91no—
591C22×D3—184no—
592C22×D3—184no—
593C22×D3—182no—
594C22×D3—182no—
595C22×D3—182no—
596C22×D3—182no—
597C22×D3—182no—
598C22×D3—188no—
599C22×D3—188no—
600C22×D3—188no—
601C22×D3—188no—
602C22×D3—188no—
603C22×D3—182no—
604C22×D3—182no—
605C22×D3—188no—
606C22×D3—182no—
607C22×D3—188no—
608C22×D3—188no—
609C22×D3—1816no—
610C22×D3—368no—
611C22×D3—368no—
612C22×D3C22×C3⋊D311yescharacteristic
613C22×D3C22×C3⋊D311yescharacteristic
614C3×D4—68no—
615C3×D4—68no—
616C3×D4—68no—
617C3×D4—182no—
618C3×D4—182no—
619C3×D4—182no—
620C2×C3×C4—24no—
621C2×C3×C4—24no—
622C2×C3×C4—34no—
623C2×C3×C4—34no—
624C2×C3×C4—68no—
625C2×C3×C4—91no—
626C2×C3×C4—91no—
627C2×C3×C4—182no—
628C2×C3×C4C2×D3214yes—
629C2×C3×C4C2×D3214yes—
630C2×C3×C4C22×C3⋊D311yescharacteristic
631C2×C3×C4C22×C3⋊D311yescharacteristic
632#67—22no—
633#67—22no—
634#67—68no—
635#67—68no—
636#67—182no—
637#67—188no—
638#67—188no—
639#67—182no—
640#67—188no—
641#67—188no—
642#67—182no—
643#67—182no—
644C2×Dic3—34no—
645C2×Dic3—34no—
646C2×Dic3—94no—
647C2×Dic3—94no—
648C2×Dic3—91no—
649C2×Dic3—91no—
650C2×Dic3—184no—
651C2×Dic3—184no—
652C2×Dic3—188no—
653C2×Dic3—182no—
654C2×Dic3C22×C3⋊D311yescharacteristic
655C2×Dic3C22×C3⋊D311yescharacteristic
656D12—22no—
657D12—68no—
658D12—188no—
659D12—188no—
660D12—182no—
661D12—182no—
662C4×D3—22no—
663C4×D3—68no—
664C4×D3—916no—
665C4×D3—94no—
666C4×D3—182no—
667C4×D3—188no—
668C4×D3—182no—
669C4×D3—182no—
670C4×D3—188no—
671C4×D3—188no—
672C4×D3—188no—
673C4×D3—182no—
674C4×D3—368no—
675C4×D3—368no—
676C2×C32—24no—
677C2×C32—24no—
678C2×C32—24no—
679C2×C32—48no—
680C2×C32—44no—
681C2×C32—41no—
682C2×C32—62no—
683C2×C32—121no—
684C2×C32C2×D3×D414yes—
685C2×C32C2×D3×D414yes—
686C2×C32C2×D3×D411yescharacteristic
687C2×C32C2×D3×D411yescharacteristic
688C2×C32D3×#4114yes—
689C2×C32D3×#4111yescharacteristic
690C3⋊D3—22no—
691C3⋊D3—34no—
692C3⋊D3—316no—
693C3⋊D3—41no—
694C3⋊D3—616no—
695C3⋊D3—128no—
696C3⋊D3—124no—
697C3⋊D3—121no—
698C3×D3—28no—
699C3×D3—44no—
700C3×D3—68no—
701C3×D3—124no—
702C24—271no—
703C24—271no—
704C24—271no—
705C2×D4—31no—
706C2×D4—31no—
707C2×D4—31no—
708C2×D4—91no—
709C2×D4—91no—
710C2×D4—91no—
711C2×D4—271no—
712C2×D4—271no—
713C2×D4—271no—
714C2×D4—271no—
715C2×D4—271no—
716C2×D4—271no—
717C2×D4—544no—
718C2×D4—544no—
719C2×D4—544no—
720C22×C4—31no—
721C22×C4—91no—
722C22×C4—271no—
723C22×C4—271no—
724C22×C4—271no—
725C22×C4—271no—
726C22×C4—271no—
727C22×C4—271no—
728C22×C4—544no—
729C4⋊C4—31no—
730C4⋊C4—91no—
731C4⋊C4—271no—
732C4⋊C4—271no—
733C22⋊C4—31no—
734C22⋊C4—91no—
735C22⋊C4—271no—
736C22⋊C4—271no—
737C22⋊C4—271no—
738C22⋊C4—271no—
739C22⋊C4—271no—
740C22⋊C4D3×C3⋊D311yescharacteristic, complemented
741C22×C3—28no—
742C22×C3—24no—
743C22×C3—24no—
744C22×C3—24no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—24no—
749C22×C3—38no—
750C22×C3—44no—
751C22×C3—44no—
752C22×C3—64no—
753C22×C3—64no—
754C22×C3—64no—
755C22×C3—64no—
756C22×C3—64no—
757C22×C3—92no—
758C22×C3—181no—
759C22×C3—181no—
760C22×C3—181no—
761C22×C3—181no—
762C22×C3—181no—
763C22×C3C22×D3214yes—
764C22×C3C23×C3⋊D311yescharacteristic
765C2×D3—21no—
766C2×D3—21no—
767C2×D3—21no—
768C2×D3—21no—
769C2×D3—21no—
770C2×D3—38no—
771C2×D3—64no—
772C2×D3—64no—
773C2×D3—64no—
774C2×D3—64no—
775C2×D3—64no—
776C2×D3—98no—
777C2×D3—98no—
778C2×D3—98no—
779C2×D3—92no—
780C2×D3—92no—
781C2×D3—92no—
782C2×D3—188no—
783C2×D3—188no—
784C2×D3—188no—
785C2×D3—188no—
786C2×D3—1832no—
787C2×D3—188no—
788C2×D3—184no—
789C2×D3—184no—
790C2×D3—184no—
791C2×D3—181no—
792C2×D3—181no—
793C2×D3—181no—
794C2×D3—364no—
795C2×D3—364no—
796C2×D3—364no—
797C2×D3—3616no—
798C2×D3—3616no—
799C2×D3—364no—
800C2×D3—3632no—
801C2×D3D4×C3⋊D312yescomplemented
802C3×C4—24no—
803C3×C4—24no—
804C3×C4—21no—
805C3×C4—21no—
806C3×C4—38no—
807C3×C4—44no—
808C3×C4—44no—
809C3×C4—64no—
810C3×C4—92no—
811C3×C4—181no—
812Dic3—21no—
813Dic3—38no—
814Dic3—64no—
815Dic3—184no—
816Dic3—184no—
817Dic3—181no—
818Dic3—181no—
819Dic3—364no—
820Dic3—364no—
821Dic3D4×C3⋊D312yescomplemented
822C32—24no—
823C32D3×#12114yescomplemented
824C32D3×#12111yescharacteristic, complemented
825C23—31no—
826C23—31no—
827C23—91no—
828C23—91no—
829C23—274no—
830C23—271no—
831C23—271no—
832C23—542no—
833C23—542no—
834C23—542no—
835C23—542no—
836C23—542no—
837C23—542no—
838C23—542no—
839C23—542no—
840C23C2×D3×C3⋊D311yescharacteristic
841D4—62no—
842D4—62no—
843D4—62no—
844D4—182no—
845D4—182no—
846D4—182no—
847D4—542no—
848D4—542no—
849D4—542no—
850D4—542no—
851D4—542no—
852D4—542no—
853C2×C4—31no—
854C2×C4—31no—
855C2×C4—62no—
856C2×C4—91no—
857C2×C4—91no—
858C2×C4—182no—
859C2×C4—274no—
860C2×C4—271no—
861C2×C4—271no—
862C2×C4—542no—
863C2×C4—542no—
864C2×C4—542no—
865C2×C4—542no—
866C2×C4—542no—
867C2×C4C2×D3×C3⋊D311yescharacteristic
868C2×C4C2×D3×C3⋊D311yescharacteristic
869C2×C3—24no—
870C2×C3—24no—
871C2×C3—24no—
872C2×C3—48no—
873C2×C3—44no—
874C2×C3—41no—
875C2×C3—68no—
876C2×C3—124no—
877C2×C3—182no—
878C2×C3—361no—
879C2×C3#6430614yes—
880C2×C3D32×D414yes—
881C2×C3D32×D414yes—
882C2×C3C2×D4×C3⋊D311yescharacteristic
883C2×C3C2×D4×C3⋊D311yescharacteristic
884C2×C3#41×C3⋊D311yescharacteristic
885D3—22no—
886D3—41no—
887D3—68no—
888D3—916no—
889D3—94no—
890D3—124no—
891D3—1816no—
892D3—368no—
893D3—364no—
894D3—361no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—32no—
899C22—61no—
900C22—61no—
901C22—61no—
902C22—61no—
903C22—61no—
904C22—92no—
905C22—181no—
906C22—181no—
907C22—181no—
908C22—181no—
909C22—181no—
910C22—272no—
911C22—272no—
912C22—272no—
913C22—548no—
914C22—541no—
915C22—541no—
916C22—541no—
917C22—1084no—
918C22—1084no—
919C22C22×D3×C3⋊D311yescharacteristic
920C4—21no—
921C4—21no—
922C4—32no—
923C4—61no—
924C4—92no—
925C4—181no—
926C4—541no—
927C4—541no—
928C3—24no—
929C3#1059426514yescomplemented
930C3C3⋊D3×#12111yescharacteristic, complemented
931C2—41no—
932C2—62no—
933C2—121no—
934C2—182no—
935C2—274no—
936C2—361no—
937C2—1081no—
938C2#1172457811yescharacteristic
939C2D3×D4×C3⋊D311yescharacteristic
940C2D3×D4×C3⋊D311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33C2×#121
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#89039C2semidirect
2. C2×#89039C2semidirect
3. C2×#89026C2semidirect
4. C2×C4×D3×C3⋊D3C2semidirect
5. C22⋊C4×C3⋊(C3⋊D3)C2semidirect
6. C3×#64093C2semidirect
7. C32×#884C2semidirect
8. #11723631C2semidirect
9. #11723615C2semidirect
10. #11723539C2semidirect
11. #11723520C2semidirect
12. #11723514C2semidirect
13. #11723482C2semidirect
14. #11723475C2semidirect
15. #11723470C2semidirect
23. C2×C3×#638C22semidirect
24. C2×C3×#638C22semidirect
25. C2×C3×C4⋊(C3⋊D3)C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
27. C2×C32×#67C22semidirect
28. C2×C32×#67C22semidirect
29. C2×C32×D12C22semidirect
30. C2×C32×C4×D3C22semidirect
33. C2×#6292C22semidirect
34. C2×#6292C22semidirect
35. C2×#6291C22semidirect
36. C2×#6291C22semidirect
37. C2×#6290C22semidirect
38. C2×#6290C22semidirect
41. C2×Dic3×C3⋊D3C22semidirect
42. C2×D3×C3⋊Dic3C22semidirect
45. C33×C22⋊C4C22semidirect
46. #88864C22semidirect
47. #88859C22semidirect
48. #88859C22semidirect
49. C3×#3752C22semidirect
50. C3×#3750C22semidirect
51. C32×(C2×D3)⋊C4C22semidirect
52. C32×Dic3⋊C4C22semidirect
53. #88807C22semidirect
54. Dic3⋊(C3⋊Dic3)C22semidirect
55. #88803C22semidirect
56. (C2×D3)⋊(C3⋊Dic3)C22semidirect
73. #64093D3semidirect
79. C3×#884D3semidirect
103. C2×D3×C3⋊D3D4semidirect
129. #6289D4semidirect
149. C2×#638C2×D3semidirect
150. C2×#638C2×D3semidirect
157. C2×C4⋊(C3⋊D3)C2×D3semidirect
168. C2×C4×C3⋊D3C2×D3semidirect
171. C2×C3×#67C2×D3semidirect
172. C2×C3×#67C2×D3semidirect
174. C2×C3×D12C2×D3semidirect
176. C2×C3×C4×D3C2×D3semidirect
194. C32×C22⋊C4C2×D3semidirect
195. C32×C22⋊C4C2×D3semidirect
207. #3752C2×D3semidirect
210. #3750C2×D3semidirect
212. C3×(C2×D3)⋊C4C2×D3semidirect
214. C3×Dic3⋊C4C2×D3semidirect
235. C2×C3×C3⋊D3C2×D4semidirect
241. C2×C32×D3C2×D4semidirect
249. C3×C3⋊Dic3C2×D4semidirect
251. C32×Dic3C2×D4semidirect
277. #884C3⋊D3semidirect
389. C3⋊(C3⋊D3)#121semidirect
419. C2×#67C2×C3⋊D3semidirect
420. C2×#67C2×C3⋊D3semidirect
434. C2×D12C2×C3⋊D3semidirect
450. C2×C4×D3C2×C3⋊D3semidirect
456. C3×C22⋊C4D32semidirect
457. C3×C22⋊C4C2×C3⋊D3semidirect
472. (C2×D3)⋊C4C2×C3⋊D3semidirect
478. Dic3⋊C4C2×C3⋊D3semidirect
525. C2×C3⋊D3D3×D4semidirect
537. C2×C3×D3D3×D4semidirect
555. C3⋊Dic3D3×D4semidirect
559. C3×Dic3D3×D4semidirect
575. C33C2×#121semidirect
740. C22⋊C4D3×C3⋊D3semidirect
801. C2×D3D4×C3⋊D3semidirect
821. Dic3D4×C3⋊D3semidirect
823. C32D3×#121semidirect
824. C32D3×#121semidirect
929. C3#10594265semidirect
930. C3C3⋊D3×#121semidirect

Maximal subgroups

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

subgroupindex
C2×#890392
C2×#890262
C2×C4×D3×C3⋊D32
C22⋊C4×C3⋊(C3⋊D3)2
C3×#640932
C32×#8842
#117236312
#117236152
#117235392
#117235202
#117235142
#117234822
#117234752
#117234702
C3⋊D3×#1213
#105942653