Finite Group Databasebeta

← #13175459

Subgroups — #13175459

Order 1728.

2380 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
2C2×#89017C211yesmaximal, characteristic, complemented
3#11723925C211yesmaximal, characteristic, complemented
4C3×#64091C211yesmaximal, characteristic, complemented
5C32×#885C211yesmaximal, characteristic, complemented
6#11723636C211yesmaximal, characteristic, complemented
7#11723633C211yesmaximal, characteristic, complemented
8#11723624C211yesmaximal, characteristic, complemented
9#11723542C211yesmaximal, characteristic, complemented
10#11723541C211yesmaximal, characteristic, complemented
11#11723527C211yesmaximal, characteristic, complemented
12#11723519C211yesmaximal, characteristic, complemented
13#11723517C211yesmaximal, characteristic, complemented
14#11723464C211yesmaximal, characteristic, complemented
15#11723392C211yesmaximal, characteristic, complemented
16#10596145—31nomaximal
17#10594270—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
23C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic, complemented
25C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
26C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
27C2×C32×#67C2211yescharacteristic
28C2×C32×Dic6C2211yescharacteristic, complemented
29C3⋊D3×#67—24no—
30C2×#6292C2211yescharacteristic
31C2×#6292C2211yescharacteristic
32C2×#6292C2211yescharacteristic, complemented
33C2×#6292C2211yescharacteristic, complemented
34C2×#6292C2211yescharacteristic, complemented
35C2×#6291C2211yescharacteristic, complemented
36C2×#6290C2211yescharacteristic
37C2×#6290C2211yescharacteristic, complemented
38C2×Dic3×C3⋊D3C2211yescharacteristic
39C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
40#89017—24no—
41C33×C22⋊C4C2211yescharacteristic, complemented
42#88859C2211yescharacteristic, complemented
43#88857C2211yescharacteristic, complemented
44C3×#3752C2211yescharacteristic
45C3×#3752C2211yescharacteristic, complemented
46C32×#217C2211yescharacteristic, complemented
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C32×C4×Dic3C2211yescharacteristic, complemented
50#88806C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52#88803C2211yescharacteristic
53#88803C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C2×#3832—31no—
56C2×D4×C3⋊D3—31no—
57C2×D3×#67—34no—
58C2×#3796—34no—
59C32×#124—31no—
60#64156—31no—
61#64149—31no—
62#64093—31no—
63#64093—31no—
64#64093—31no—
65#64093—31no—
66#64093—34no—
67#64093—64no—
68#64091—31no—
69#64091—31no—
70#64091—31no—
71#64091D311yescharacteristic, complemented
72#64083—31no—
73#64081—31no—
74C3×#885D314yescomplemented
75C3×#882—34no—
76#63979—34no—
77#63977—34no—
78#63971—34no—
79#63923—34no—
80#63922—34no—
81#63912—34no—
82#63911—34no—
83#63907—34no—
84#63885—34no—
85#63877—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3×C3⋊D3—22no—
90C22×C3×C3⋊D3—41no—
91C22×C3×C3⋊D3—41no—
92C22×C3×C3⋊D3C2311yescharacteristic
93C22×C3×C3⋊D3C2311yescharacteristic
94C22×C3×C3⋊D3C2311yescharacteristic
95C22×C32×D3C2311yescharacteristic
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×D3×C3⋊D3—41no—
99C2×C33×C4C2311yescharacteristic
100C2×C33×C4C2311yescharacteristic
101#6312—22no—
102#6312—41no—
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C4⋊(C3⋊(C3⋊D3))—41no—
106C4×C3⋊(C3⋊D3)—22no—
107C3×#638—41no—
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C3×C4⋊(C3⋊D3)—22no—
110C3×C4⋊(C3⋊D3)—41no—
111C32×#67—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C32×Dic6—22no—
116#6292—22no—
117#6292—22no—
118#6292—22no—
119#6292—41no—
120#6292—41no—
121#6291—41no—
122#6290—22no—
123#6290—41no—
124Dic3×C3⋊D3—22no—
125Dic3×C3⋊D3D414yescomplemented
126#5674—94no—
127#5592—91no—
128C23×C3⋊D3—31no—
129C23×C3⋊D3C2×D311yescharacteristic
130C23×C3×D3—34no—
131C22×D32—34no—
132C2×C32×Q8—31no—
133C2×C32×D4—31no—
134C2×#638—31no—
135C2×#638—34no—
136C2×#638—31no—
137C2×#638—31no—
138C2×#638—34no—
139C2×#638—31no—
140C2×#638—31no—
141C2×#638—64no—
142C2×#638—64no—
143C2×#638C2×D311yescharacteristic, complemented
144#3832—64no—
145D4×C3⋊D3—64no—
146C2×C4⋊(C3⋊D3)—31no—
147C2×C4⋊(C3⋊D3)—31no—
148C2×C4⋊(C3⋊D3)—31no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4⋊(C3⋊D3)—31no—
152C2×C4⋊(C3⋊D3)—34no—
153C2×C4⋊(C3⋊D3)—64no—
154C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
155C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
156C2×C4×C3⋊D3—31no—
157C2×C4×C3⋊D3—31no—
158C2×C4×C3⋊D3—31no—
159C2×C4×C3⋊D3—34no—
160C2×C4×C3⋊D3—64no—
161C2×C3×#67—34no—
162C2×C3×#67C2×D314yes—
163C2×C3×D12—34no—
164C2×C3×D12—34no—
165C2×C3×Dic6C2×D314yescomplemented
166D3×#67—616no—
167C2×#626—34no—
168C2×#626—34no—
169C2×#626—34no—
170C2×#626—34no—
171C2×#626—34no—
172C2×#626—34no—
173C2×#625—34no—
174C2×#625—34no—
175C2×D3×Dic3—34no—
176C2×D3×Dic3—34no—
177#3796—616no—
178C32×C22⋊C4—24no—
179C32×C22⋊C4—31no—
180C32×C22⋊C4—31no—
181C32×C22⋊C4—31no—
182C32×C22⋊C4C2×D314yescomplemented
183C32×C22⋊C4C2×D311yescharacteristic, complemented
184C32×C42—31no—
185#3752—31no—
186#3752—31no—
187#3752—31no—
188#3752—34no—
189#3752—31no—
190#3752—64no—
191#3752C2×D311yescharacteristic
192#3752C2×D311yescharacteristic, complemented
193#3750—31no—
194#3750—34no—
195#3750—31no—
196#3750—64no—
197C4×C3⋊Dic3—31no—
198C3×#217C2×D314yescomplemented
199C3×(C2×D3)⋊C4—34no—
200C3×(C2×D3)⋊C4—34no—
201C3×(C2×D3)⋊C4C2×D314yescomplemented
202C3×(C2×D3)⋊C4C2×D314yescomplemented
203C3×C4×Dic3C2×D314yescomplemented
204#3724—34no—
205#3722—34no—
206(C2×D3)⋊Dic3—34no—
207(C2×D3)⋊Dic3—34no—
208Dic32—34no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33C2411yescharacteristic
213C2×C3⋊(C3⋊D3)—21no—
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)—21no—
216C2×C3⋊(C3⋊D3)—21no—
217C2×C3⋊(C3⋊D3)—21no—
218C2×C3⋊(C3⋊D3)—21no—
219C2×C3×C3⋊D3—21no—
220C2×C3×C3⋊D3—21no—
221C2×C3×C3⋊D3—21no—
222C2×C3×C3⋊D3—21no—
223C2×C3×C3⋊D3—21no—
224C2×C3×C3⋊D3—21no—
225C2×C3×C3⋊D3—21no—
226C2×C3×C3⋊D3—21no—
227C2×C3×C3⋊D3—44no—
228C2×C3×C3⋊D3C2×D412yes—
229C2×C32×D3—21no—
230C2×C32×D3—21no—
231C2×C32×D3—21no—
232D3×C3⋊D3—44no—
233C33×C4—21no—
234C33×C4—21no—
235C3⋊(C3⋊Dic3)—21no—
236C3⋊(C3⋊Dic3)C2×D412yes—
237C3×C3⋊Dic3—21no—
238C32×Dic3—21no—
239C32×Dic3—21no—
240C32×Dic3C2×D412yes—
241C22×#67—91no—
242C2×#239—94no—
243C2×#237—91no—
244C2×D3×D4—94no—
245C3×#124—34no—
246C3×#120—91no—
247#953—91no—
248#947—94no—
249#940—94no—
250#940—91no—
251#940—91no—
252#939—91no—
253#939—91no—
254#937—91no—
255#885—91no—
256#885C3⋊D311yescharacteristic, complemented
257#884—94no—
258#884—94no—
259#884—94no—
260#884—94no—
261#884—91no—
262#884—91no—
263#884—184no—
264#882—34no—
265#882—94no—
266#882—94no—
267#882—94no—
268#882—91no—
269#877—91no—
270#874—94no—
271#872—94no—
272C23×C32—24no—
273C23×C32—31no—
274C23×C32C22×D314yes—
275C23×C32C22×D311yescharacteristic
276C22×C3⋊D3—22no—
277C22×C3⋊D3—31no—
278C22×C3⋊D3—31no—
279C22×C3⋊D3—34no—
280C22×C3⋊D3—34no—
281C22×C3⋊D3—41no—
282C22×C3⋊D3—41no—
283C22×C3⋊D3—64no—
284C22×C3⋊D3—64no—
285C22×C3⋊D3—62no—
286C22×C3⋊D3—121no—
287C22×C3⋊D3—121no—
288C22×C3⋊D3C22×D311yescharacteristic
289C22×C3⋊D3C22×D311yescharacteristic
290C22×C3⋊D3C22×D311yescharacteristic
291C22×C3×D3—34no—
292C22×C3×D3—34no—
293C22×C3×D3—34no—
294C22×C3×D3—68no—
295C22×C3×D3—124no—
296C22×C3×D3—124no—
297C22×C3×D3C22×D314yes—
298C2×D32—68no—
299C2×D32—124no—
300C2×D32—124no—
301C32×Q8—62no—
302C32×D4—62no—
303C2×C32×C4—24no—
304C2×C32×C4—24no—
305C2×C32×C4—31no—
306C2×C32×C4—31no—
307C2×C32×C4—31no—
308C2×C32×C4C22×D314yes—
309C2×C32×C4C22×D314yes—
310C2×C32×C4C22×D311yescharacteristic
311C2×C32×C4C22×D311yescharacteristic
312#638—41no—
313#638—62no—
314#638—62no—
315#638—68no—
316#638—128no—
317#638—121no—
318#638—121no—
319#638—121no—
320#638—124no—
321#638—128no—
322C2×C3⋊Dic3—31no—
323C2×C3⋊Dic3—31no—
324C2×C3⋊Dic3—34no—
325C2×C3⋊Dic3—34no—
326C2×C3⋊Dic3—64no—
327C2×C3⋊Dic3—64no—
328C2×C3⋊Dic3C22×D311yescharacteristic
329C4⋊(C3⋊D3)—22no—
330C4⋊(C3⋊D3)—41no—
331C4⋊(C3⋊D3)—62no—
332C4⋊(C3⋊D3)—62no—
333C4⋊(C3⋊D3)—62no—
334C4⋊(C3⋊D3)—121no—
335C4⋊(C3⋊D3)—124no—
336C4⋊(C3⋊D3)—128no—
337C4⋊(C3⋊D3)—121no—
338C4⋊(C3⋊D3)—121no—
339C4×C3⋊D3—34no—
340C4×C3⋊D3—62no—
341C4×C3⋊D3—62no—
342C4×C3⋊D3—68no—
343C4×C3⋊D3—128no—
344C3×#67—28no—
345C3×#67—124no—
346C2×C3×Dic3—34no—
347C2×C3×Dic3C22×D314yes—
348C2×C3×Dic3C22×D314yes—
349C2×C3×Dic3C22×D314yes—
350C3×D12—68no—
351C3×D12—124no—
352C3×Dic6—28no—
353#626—68no—
354#626—68no—
355#626—68no—
356#626—124no—
357#626—124no—
358#626—124no—
359#625—68no—
360#625—124no—
361D3×Dic3—316no—
362D3×Dic3—68no—
363#535—271noSylow
364C2×C33—41no—
365C2×C33C22×D411yescharacteristic
366C2×C33H(5,𝔽2)11yescharacteristic
367C2×C33H(5,𝔽2)11yescharacteristic
368C3⋊(C3⋊D3)—41no—
369C3⋊(C3⋊D3)—41no—
370C3×C3⋊D3—22no—
371C3×C3⋊D3—41no—
372C3×C3⋊D3—41no—
373C32×D3—41no—
374C24×C3—91no—
375C23×D3—34no—
376C23×D3—94no—
377C23×D3—91no—
378C2×C3×Q8—34no—
379C2×C3×D4—34no—
380C2×C3×D4—91no—
381C2×C3×D4—91no—
382C2×C3×D4—91no—
383C2×#67—34no—
384C2×#67—94no—
385C2×#67—94no—
386C2×#67—94no—
387C2×#67—91no—
388C2×#67—91no—
389C2×#67—94no—
390C2×#67—94no—
391C2×#67—91no—
392C2×#67—91no—
393C2×#67—91no—
394C2×#67—91no—
395C2×#67—91no—
396C2×#67—91no—
397C2×#67—91no—
398C2×#67—184no—
399C2×#67—184no—
400C2×#67—184no—
401C2×#67C2×C3⋊D311yescharacteristic
402C22×Dic3—91no—
403C22×Dic3—91no—
404#239—1816no—
405#237—184no—
406D3×D4—1816no—
407C2×D12—34no—
408C2×D12—34no—
409C2×D12—94no—
410C2×D12—94no—
411C2×D12—94no—
412C2×D12—94no—
413C2×D12—94no—
414C2×D12—91no—
415C2×D12—94no—
416C2×D12—91no—
417C2×D12—184no—
418C2×C4×D3—94no—
419C2×C4×D3—94no—
420C2×C4×D3—94no—
421C2×C4×D3—91no—
422C2×C4×D3—184no—
423C2×Dic6C2×C3⋊D311yescharacteristic, complemented
424C3×C22⋊C4—24no—
425C3×C22⋊C4—34no—
426C3×C22⋊C4—34no—
427C3×C22⋊C4—34no—
428C3×C22⋊C4—91no—
429C3×C22⋊C4—91no—
430C3×C22⋊C4D3214yescomplemented
431C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
432C3×C42—34no—
433#217—91no—
434#217—91no—
435#217C2×C3⋊D311yescharacteristic, complemented
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—94no—
439(C2×D3)⋊C4—94no—
440(C2×D3)⋊C4—94no—
441(C2×D3)⋊C4—94no—
442(C2×D3)⋊C4—91no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4—184no—
445(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
446(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
447Dic3⋊C4—94no—
448Dic3⋊C4—94no—
449Dic3⋊C4—91no—
450Dic3⋊C4—91no—
451Dic3⋊C4—184no—
452C4×Dic3—94no—
453C4×Dic3—91no—
454C4×Dic3C2×C3⋊D311yescharacteristic, complemented
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—24no—
459C22×C32—24no—
460C22×C32—24no—
461C22×C32—24no—
462C22×C32—44no—
463C22×C32—44no—
464C22×C32—44no—
465C22×C32—61no—
466C22×C32—61no—
467C22×C32—61no—
468C22×C32C23×D314yes—
469C22×C32C23×D311yescharacteristic
470C2×C3⋊D3—21no—
471C2×C3⋊D3—21no—
472C2×C3⋊D3—21no—
473C2×C3⋊D3—21no—
474C2×C3⋊D3—21no—
475C2×C3⋊D3—21no—
476C2×C3⋊D3—21no—
477C2×C3⋊D3—21no—
478C2×C3⋊D3—44no—
479C2×C3⋊D3—68no—
480C2×C3⋊D3—61no—
481C2×C3⋊D3—61no—
482C2×C3⋊D3—61no—
483C2×C3⋊D3—61no—
484C2×C3⋊D3—61no—
485C2×C3⋊D3—61no—
486C2×C3⋊D3—64no—
487C2×C3⋊D3—64no—
488C2×C3⋊D3—64no—
489C2×C3⋊D3—64no—
490C2×C3⋊D3—64no—
491C2×C3⋊D3—64no—
492C2×C3⋊D3—124no—
493C2×C3⋊D3—124no—
494C2×C3⋊D3—124no—
495C2×C3⋊D3—124no—
496C2×C3⋊D3—124no—
497C2×C3⋊D3—124no—
498C2×C3⋊D3D3×D412yes—
499C2×C3×D3—24no—
500C2×C3×D3—24no—
501C2×C3×D3—24no—
502C2×C3×D3—38no—
503C2×C3×D3—64no—
504C2×C3×D3—64no—
505C2×C3×D3—64no—
506C2×C3×D3—64no—
507C2×C3×D3—64no—
508C2×C3×D3—64no—
509C2×C3×D3—64no—
510C2×C3×D3—64no—
511C2×C3×D3—1216no—
512D32—1216no—
513C32×C4—21no—
514C32×C4—21no—
515C32×C4—24no—
516C32×C4—24no—
517C32×C4—32no—
518C32×C4—44no—
519C32×C4—44no—
520C32×C4—61no—
521C32×C4—61no—
522C3⋊Dic3—21no—
523C3⋊Dic3—32no—
524C3⋊Dic3—38no—
525C3⋊Dic3—68no—
526C3⋊Dic3—61no—
527C3⋊Dic3—64no—
528C3⋊Dic3—124no—
529C3×Dic3—24no—
530C3×Dic3—24no—
531C3×Dic3—64no—
532C3×Dic3D3×D418yes—
533C2×#41—271no—
534C22×D4—271no—
535#127—271no—
536#127—271no—
537#124—31no—
538#124—271no—
539#121—271no—
540#121—271no—
541#121—271no—
542#121—271no—
543#120—91no—
544#120—271no—
545#120—271no—
546#120—271no—
547#117—271no—
548C33#53511yescharacteristic, complemented, Sylow
549C23×C3—24no—
550C23×C3—34no—
551C23×C3—91no—
552C23×C3—91no—
553C23×C3—91no—
554C23×C3—182no—
555C23×C3—361no—
556C23×C3—361no—
557C23×C3C2×D3214yes—
558C23×C3C22×C3⋊D311yescharacteristic
559C22×D3—34no—
560C22×D3—34no—
561C22×D3—34no—
562C22×D3—68no—
563C22×D3—94no—
564C22×D3—94no—
565C22×D3—91no—
566C22×D3—91no—
567C22×D3—124no—
568C22×D3—124no—
569C22×D3—184no—
570C22×D3—184no—
571C22×D3—182no—
572C22×D3—188no—
573C22×D3—361no—
574C22×D3—361no—
575C22×D3—364no—
576C22×D3—364no—
577C22×D3C22×C3⋊D311yescharacteristic
578C3×Q8—68no—
579C3×D4—68no—
580C3×D4—182no—
581C3×D4—361no—
582C3×D4—361no—
583C2×C3×C4—24no—
584C2×C3×C4—24no—
585C2×C3×C4—34no—
586C2×C3×C4—34no—
587C2×C3×C4—34no—
588C2×C3×C4—91no—
589C2×C3×C4C2×D3214yes—
590C2×C3×C4C2×D3214yes—
591C2×C3×C4C22×C3⋊D311yescharacteristic
592C2×C3×C4C22×C3⋊D311yescharacteristic
593#67—22no—
594#67—124no—
595#67—182no—
596#67—182no—
597#67—188no—
598#67—182no—
599#67—188no—
600#67—182no—
601#67—182no—
602#67—368no—
603#67—361no—
604#67—361no—
605#67—364no—
606#67—361no—
607#67—364no—
608#67—364no—
609#67—361no—
610#67—368no—
611C2×Dic3—34no—
612C2×Dic3—94no—
613C2×Dic3—91no—
614C2×Dic3—94no—
615C2×Dic3—94no—
616C2×Dic3—91no—
617C2×Dic3—184no—
618C2×Dic3—184no—
619C2×Dic3—182no—
620C2×Dic3C22×C3⋊D311yescharacteristic
621C2×Dic3C22×C3⋊D311yescharacteristic
622C2×Dic3C22×C3⋊D311yescharacteristic
623D12—68no—
624D12—124no—
625D12—188no—
626D12—188no—
627D12—188no—
628D12—364no—
629D12—361no—
630D12—368no—
631D12—364no—
632D12—364no—
633D12—361no—
634C4×D3—916no—
635C4×D3—182no—
636C4×D3—188no—
637C4×D3—188no—
638C4×D3—368no—
639Dic6—22no—
640C2×C32—24no—
641C2×C32—24no—
642C2×C32—24no—
643C2×C32—41no—
644C2×C32—44no—
645C2×C32—84no—
646C2×C32—121no—
647C2×C32C2×D3×D414yes—
648C2×C32C2×D3×D411yescharacteristic
649C2×C32#100411yescharacteristic
650C2×C32#100411yescharacteristic
651C2×C32#100914yes—
652C2×C32#100914yes—
653C3⋊D3—22no—
654C3⋊D3—41no—
655C3⋊D3—41no—
656C3⋊D3—128no—
657C3⋊D3—124no—
658C3⋊D3—121no—
659C3⋊D3—121no—
660C3⋊D3—124no—
661C3⋊D3—244no—
662C3×D3—44no—
663C3×D3—68no—
664C3×D3—124no—
665C3×D3—124no—
666C24—91no—
667C24—271no—
668#41—544no—
669C2×Q8—31no—
670C2×D4—31no—
671C2×D4—91no—
672C2×D4—91no—
673C2×D4—91no—
674C2×D4—271no—
675C2×D4—271no—
676C2×D4—271no—
677C2×D4—271no—
678C2×D4—271no—
679C2×D4—271no—
680C2×D4—271no—
681C2×D4—271no—
682C2×D4—271no—
683C2×D4—271no—
684C2×D4—271no—
685C2×D4—544no—
686C22×C4—271no—
687C22×C4—271no—
688C22×C4—271no—
689C4⋊C4—271no—
690C4⋊C4—271no—
691C22⋊C4—31no—
692C22⋊C4—31no—
693C22⋊C4—31no—
694C22⋊C4—91no—
695C22⋊C4—91no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4D3×C3⋊D311yescharacteristic, complemented
701C42—31no—
702C42—271no—
703C22×C3—24no—
704C22×C3—24no—
705C22×C3—24no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—24no—
710C22×C3—44no—
711C22×C3—44no—
712C22×C3—44no—
713C22×C3—64no—
714C22×C3—64no—
715C22×C3—64no—
716C22×C3—92no—
717C22×C3—181no—
718C22×C3—181no—
719C22×C3—181no—
720C22×C3—181no—
721C22×C3—181no—
722C22×C3—181no—
723C22×C3—181no—
724C22×C3—181no—
725C22×C3—364no—
726C22×C3C22×D3214yes—
727C22×C3C23×C3⋊D311yescharacteristic
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—38no—
732C2×D3—64no—
733C2×D3—64no—
734C2×D3—64no—
735C2×D3—64no—
736C2×D3—64no—
737C2×D3—64no—
738C2×D3—64no—
739C2×D3—64no—
740C2×D3—1216no—
741C2×D3—188no—
742C2×D3—184no—
743C2×D3—184no—
744C2×D3—184no—
745C2×D3—184no—
746C2×D3—184no—
747C2×D3—184no—
748C2×D3—181no—
749C2×D3—181no—
750C2×D3—181no—
751C2×D3—181no—
752C2×D3—181no—
753C2×D3—181no—
754C2×D3—364no—
755C2×D3—364no—
756C2×D3—364no—
757C2×D3—364no—
758C2×D3—364no—
759C2×D3—364no—
760C2×D3—3616no—
761C3×C4—24no—
762C3×C4—24no—
763C3×C4—21no—
764C3×C4—21no—
765C3×C4—38no—
766C3×C4—44no—
767C3×C4—44no—
768C3×C4—64no—
769C3×C4—64no—
770C3×C4—181no—
771Dic3—21no—
772Dic3—21no—
773Dic3—64no—
774Dic3—98no—
775Dic3—92no—
776Dic3—188no—
777Dic3—184no—
778Dic3—181no—
779Dic3—364no—
780Dic3D4×C3⋊D312yes—
781C32—24no—
782C32#559211yescharacteristic, complemented
783C32#567414yescomplemented
784C23—31no—
785C23—91no—
786C23—91no—
787C23—91no—
788C23—182no—
789C23—271no—
790C23—271no—
791C23—361no—
792C23—361no—
793C23—542no—
794C23—1081no—
795C23—1081no—
796C23C2×D3×C3⋊D311yescharacteristic
797Q8—62no—
798D4—62no—
799D4—182no—
800D4—361no—
801D4—361no—
802D4—542no—
803D4—542no—
804D4—542no—
805D4—542no—
806D4—542no—
807D4—1081no—
808D4—1081no—
809D4—1081no—
810D4—1081no—
811D4—1081no—
812D4—1081no—
813C2×C4—31no—
814C2×C4—31no—
815C2×C4—31no—
816C2×C4—91no—
817C2×C4—274no—
818C2×C4—271no—
819C2×C4—271no—
820C2×C4—542no—
821C2×C4—542no—
822C2×C4C2×D3×C3⋊D311yescharacteristic
823C2×C4C2×D3×C3⋊D311yescharacteristic
824C2×C3—24no—
825C2×C3—24no—
826C2×C3—24no—
827C2×C3—41no—
828C2×C3—44no—
829C2×C3—84no—
830C2×C3—124no—
831C2×C3—182no—
832C2×C3—361no—
833C2×C3—361no—
834C2×C3#6430714yes—
835C2×C3D32×D414yes—
836C2×C3#6431414yes—
837C2×C3C2×D4×C3⋊D311yescharacteristic
838C2×C3#6436611yescharacteristic
839C2×C3#6436611yescharacteristic
840D3—41no—
841D3—68no—
842D3—124no—
843D3—124no—
844D3—368no—
845D3—361no—
846D3—361no—
847D3—364no—
848D3—364no—
849D3—724no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—61no—
854C22—61no—
855C22—61no—
856C22—92no—
857C22—181no—
858C22—181no—
859C22—181no—
860C22—181no—
861C22—181no—
862C22—181no—
863C22—181no—
864C22—181no—
865C22—364no—
866C22—541no—
867C22—541no—
868C22—541no—
869C22—541no—
870C22—541no—
871C22—541no—
872C22—1084no—
873C22C22×D3×C3⋊D311yescharacteristic
874C4—21no—
875C4—21no—
876C4—32no—
877C4—61no—
878C4—61no—
879C4—181no—
880C4—272no—
881C4—541no—
882C3—24no—
883C3#1059427014yescomplemented
884C3#1059614511yescharacteristic, complemented
885C2—41no—
886C2—121no—
887C2—182no—
888C2—361no—
889C2—361no—
890C2—1081no—
891C2—1081no—
892C2#1172458011yescharacteristic
893C2D3×D4×C3⋊D311yescharacteristic
894C2#1172458911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#535
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊D3×#67C2semidirect
2. C2×#89017C2semidirect
3. #11723925C2semidirect
4. C3×#64091C2semidirect
5. C32×#885C2semidirect
6. #11723636C2semidirect
7. #11723633C2semidirect
8. #11723624C2semidirect
9. #11723542C2semidirect
10. #11723541C2semidirect
11. #11723527C2semidirect
12. #11723519C2semidirect
13. #11723517C2semidirect
14. #11723464C2semidirect
15. #11723392C2semidirect
21. C2×#6312C22semidirect
22. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
23. C2×C4×C3⋊(C3⋊D3)C22semidirect
24. C2×C3×#638C22semidirect
26. C2×C3×C4⋊(C3⋊D3)C22semidirect
28. C2×C32×Dic6C22semidirect
32. C2×#6292C22semidirect
33. C2×#6292C22semidirect
34. C2×#6292C22semidirect
35. C2×#6291C22semidirect
37. C2×#6290C22semidirect
39. C2×Dic3×C3⋊D3C22semidirect
41. C33×C22⋊C4C22semidirect
42. #88859C22semidirect
43. #88857C22semidirect
45. C3×#3752C22semidirect
46. C32×#217C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. C32×(C2×D3)⋊C4C22semidirect
49. C32×C4×Dic3C22semidirect
50. #88806C22semidirect
51. #88804C22semidirect
53. #88803C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
71. #64091D3semidirect
74. C3×#885D3semidirect
125. Dic3×C3⋊D3D4semidirect
143. C2×#638C2×D3semidirect
155. C2×C4⋊(C3⋊D3)C2×D3semidirect
165. C2×C3×Dic6C2×D3semidirect
182. C32×C22⋊C4C2×D3semidirect
183. C32×C22⋊C4C2×D3semidirect
192. #3752C2×D3semidirect
198. C3×#217C2×D3semidirect
201. C3×(C2×D3)⋊C4C2×D3semidirect
202. C3×(C2×D3)⋊C4C2×D3semidirect
203. C3×C4×Dic3C2×D3semidirect
256. #885C3⋊D3semidirect
423. C2×Dic6C2×C3⋊D3semidirect
430. C3×C22⋊C4D32semidirect
431. C3×C22⋊C4C2×C3⋊D3semidirect
435. #217C2×C3⋊D3semidirect
445. (C2×D3)⋊C4C2×C3⋊D3semidirect
446. (C2×D3)⋊C4C2×C3⋊D3semidirect
454. C4×Dic3C2×C3⋊D3semidirect
548. C33#535semidirect
700. C22⋊C4D3×C3⋊D3semidirect
782. C32#5592semidirect
783. C32#5674semidirect
883. C3#10594270semidirect
884. C3#10596145semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×#672
C2×#890172
#117239252
C3×#640912
C32×#8852
#117236362
#117236332
#117236242
#117235422
#117235412
#117235272
#117235192
#117235172
#117234642
#117233922
#105961453
#105942703