Finite Group Databasebeta

← #13177525

Subgroups — #13177525

Order 1728.

2524 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6291C211yesmaximal, characteristic, complemented
2C2×#89028C211yesmaximal, characteristic, complemented
3#11723978C211yesmaximal, characteristic, complemented
4C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C32×#937C211yesmaximal, characteristic, complemented
6#11723641C211yesmaximal, characteristic, complemented
7#11723635C211yesmaximal, characteristic, complemented
8#11723627C211yesmaximal, characteristic, complemented
9#11723616C211yesmaximal, characteristic, complemented
10D3×#3757C211yesmaximal, characteristic, complemented
11#11723599C211yesmaximal, characteristic, complemented
12#11723479C211yesmaximal, characteristic, complemented
13#11723461C211yesmaximal, characteristic, complemented
14#11723422C211yesmaximal, characteristic, complemented
15#11723419C211yesmaximal, characteristic, complemented
16#10596062—31nomaximal
17#10595135—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C23×C32×D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×#6312C2211yescharacteristic, complemented
23C22×C3×C3⋊Dic3C2211yescharacteristic
24C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic, complemented
26C2×C32×#67C2211yescharacteristic, complemented
27C2×#6293C2211yescharacteristic, complemented
28C2×#6291—24no—
29C2×#6291C2211yescharacteristic
30C2×#6291C2211yescharacteristic
31C2×#6291C2211yescharacteristic
32C2×#6291C2211yescharacteristic
33C2×#6289C2211yescharacteristic, complemented
34C2×#6289C2211yescharacteristic, complemented
35#89028—24no—
36C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38#88864C2211yescharacteristic
39#88859C2211yescharacteristic, complemented
40#88859C2211yescharacteristic, complemented
41C3×#3757C2211yescharacteristic
42C3×#3757C2211yescharacteristic, complemented
43C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
45C32×#217C2211yescharacteristic
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48#88807C2211yescharacteristic, complemented
49#88806C2211yescharacteristic, complemented
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52#88804C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C22×#638—31no—
56C2×#3830—31no—
57C22×#626—34no—
58C2×#3804—34no—
59C32×#120—31no—
60C2×#3757—31no—
61#64148—31no—
62#64148—31no—
63#64147—31no—
64#64146—31no—
65#64146—34no—
66#64146—64no—
67D4×C3⋊Dic3D311yescharacteristic, complemented
68#64095—31no—
69#64094—31no—
70#64092—31no—
71#64090—31no—
72C22⋊C4×C3⋊D3—31no—
73#64087—31no—
74C3×#937D314yescomplemented
75C3×D4×Dic3—34no—
76#63978—34no—
77#63974—34no—
78#63971—34no—
79D3×#217—34no—
80#63964—34no—
81#63958—34no—
82#63890—34no—
83#63880—34no—
84#63854—34no—
85#63852—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)—22no—
89C22×C3⋊(C3⋊D3)—22no—
90C22×C3⋊(C3⋊D3)—41no—
91C22×C3⋊(C3⋊D3)C2311yescharacteristic
92C22×C3⋊(C3⋊D3)C2311yescharacteristic
93C22×C32×D3—22no—
94C22×C32×D3—22no—
95C22×C32×D3—41no—
96C22×C32×D3C2311yescharacteristic
97C22×C32×D3C2311yescharacteristic
98C33×D4—22no—
99C2×C33×C4C2311yescharacteristic
100#6312—22no—
101#6312—41no—
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3×C3⋊Dic3—22no—
105C2×C3×C3⋊Dic3—22no—
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C32×#67—22no—
111C32×#67—41no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114#6293—22no—
115#6291—22no—
116#6291—22no—
117#6291—22no—
118#6291D414yescomplemented
119#6289—22no—
120#6289—41no—
121D3×C3⋊Dic3—22no—
122D3×C3⋊Dic3—41no—
123#5591—94no—
124#5550—91no—
125C24×C32—31no—
126C23×C3⋊D3—31no—
127C23×C3⋊D3—34no—
128C23×C3⋊D3—64no—
129C23×C3×D3C2×D314yes—
130C2×C32×D4—24no—
131C2×C32×D4—31no—
132C2×C32×D4—31no—
133C2×C32×D4C2×D314yes—
134C2×C32×D4C2×D311yescharacteristic
135C2×#638—31no—
136C2×#638—34no—
137C2×#638—31no—
138C2×#638—34no—
139C2×#638—31no—
140C2×#638—31no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#638—64no—
144C2×#638—64no—
145C2×#638—64no—
146C22×C3⋊Dic3—31no—
147C22×C3⋊Dic3—31no—
148C22×C3⋊Dic3C2×D311yescharacteristic
149C22×C3⋊Dic3C2×D311yescharacteristic, complemented
150#3830—64no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—31no—
153C2×#634—31no—
154C2×C3×#67C2×D314yescomplemented
155C2×C3×#67C2×D314yescomplemented
156C22×C3×Dic3—34no—
157C22×C3×Dic3—34no—
158C2×#627—34no—
159C2×#626—34no—
160C2×#626—34no—
161C2×#626—34no—
162C2×#626—34no—
163C2×#626—616no—
164C2×#624—34no—
165C2×#624—34no—
166#3804—616no—
167C2×D3×Dic3—34no—
168C2×D3×Dic3—34no—
169C32×C22⋊C4—31no—
170C32×C22⋊C4—31no—
171C32×C22⋊C4—31no—
172#3757—31no—
173#3757—34no—
174#3757—31no—
175#3757—31no—
176#3757—64no—
177#3757C2×D311yescharacteristic
178#3757C2×D311yescharacteristic, complemented
179#3752—31no—
180#3752—31no—
181#3752—34no—
182#3752—34no—
183#3752—31no—
184#3752—31no—
185#3752—64no—
186#3752—64no—
187C4⋊(C3⋊Dic3)—31no—
188C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
189#3750—31no—
190#3750—31no—
191C4×C3⋊Dic3C2×D311yescharacteristic, complemented
192C3×#217—34no—
193C3×#217—34no—
194C3×#217C2×D314yes—
195C3×(C2×D3)⋊C4C2×D314yescomplemented
196C3×(C2×D3)⋊C4C2×D314yescomplemented
197C3×C4⋊Dic3—34no—
198C3×C4×Dic3—34no—
199#3724—34no—
200Dic3⋊Dic3—34no—
201Dic3⋊Dic3—34no—
202#3722—34no—
203#3722—34no—
204(C2×D3)⋊Dic3—34no—
205(C2×D3)⋊Dic3—34no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33—21no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33#4112yescomplemented
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)—44no—
219C2×C3⋊(C3⋊D3)C2×D412yes—
220C2×C32×D3—21no—
221C2×C32×D3—21no—
222C2×C32×D3—21no—
223C2×C32×D3—21no—
224C2×C32×D3—21no—
225C2×C32×D3—44no—
226C2×C32×D3C2×D412yes—
227C33×C4—21no—
228C3⋊(C3⋊Dic3)—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3×C3⋊Dic3—21no—
231C3×C3⋊Dic3—21no—
232C3×C3⋊Dic3—21no—
233C3×C3⋊Dic3C2×D412yes—
234C32×Dic3—21no—
235C32×Dic3—21no—
236C22×#67—94no—
237C2×#237—94no—
238C2×#235—91no—
239C22×D12—91no—
240C3×#120—34no—
241C3×C4×D4—91no—
242C2×#217—94no—
243#939—94no—
244#939—94no—
245#938—94no—
246#937—94no—
247#937—91no—
248#937—184no—
249#937C3⋊D311yescharacteristic, complemented
250D4×Dic3—34no—
251#930—91no—
252#924—91no—
253#894—91no—
254#894—91no—
255#886—94no—
256#885—94no—
257#884—91no—
258#884—91no—
259#883—94no—
260#67⋊C4—94no—
261D3×C22⋊C4—94no—
262D3×C22⋊C4—91no—
263D3×C22⋊C4—91no—
264#878—94no—
265#875—91no—
266C4×D12—91no—
267C23×C32—24no—
268C23×C32—24no—
269C23×C32—31no—
270C23×C32—31no—
271C23×C32—62no—
272C23×C32—62no—
273C23×C32—121no—
274C23×C32C22×D314yes—
275C23×C32C22×D314yes—
276C23×C32C22×D311yescharacteristic
277C23×C32C22×D311yescharacteristic
278C22×C3⋊D3—31no—
279C22×C3⋊D3—31no—
280C22×C3⋊D3—34no—
281C22×C3⋊D3—34no—
282C22×C3⋊D3—64no—
283C22×C3⋊D3—64no—
284C22×C3⋊D3—62no—
285C22×C3⋊D3—62no—
286C22×C3⋊D3—68no—
287C22×C3⋊D3—68no—
288C22×C3⋊D3—128no—
289C22×C3⋊D3—128no—
290C22×C3⋊D3—121no—
291C22×C3⋊D3—124no—
292C22×C3⋊D3—128no—
293C22×C3×D3—28no—
294C22×C3×D3—28no—
295C22×C3×D3—44no—
296C22×C3×D3C22×D314yes—
297C22×C3×D3C22×D314yes—
298C32×D4—22no—
299C32×D4—28no—
300C32×D4—48no—
301C32×D4—62no—
302C32×D4—121no—
303C2×C32×C4—24no—
304C2×C32×C4—31no—
305C2×C32×C4—31no—
306C2×C32×C4C22×D314yes—
307C2×C32×C4C22×D311yescharacteristic
308#638—34no—
309#638—62no—
310#638—62no—
311#638—62no—
312#638—62no—
313#638—68no—
314#638—128no—
315#638—121no—
316#638—124no—
317#638—128no—
318C2×C3⋊Dic3—22no—
319C2×C3⋊Dic3—22no—
320C2×C3⋊Dic3—31no—
321C2×C3⋊Dic3—31no—
322C2×C3⋊Dic3—34no—
323C2×C3⋊Dic3—34no—
324C2×C3⋊Dic3—64no—
325C2×C3⋊Dic3—64no—
326C2×C3⋊Dic3—62no—
327C2×C3⋊Dic3—121no—
328C2×C3⋊Dic3C22×D311yescharacteristic
329C2×C3⋊Dic3C22×D311yescharacteristic
330C2×C3⋊Dic3C22×D311yescharacteristic
331C2×C3⋊Dic3C22×D311yescharacteristic
332C4×C3⋊D3—62no—
333C4×C3⋊D3—121no—
334#634—62no—
335C3×#67—28no—
336C3×#67—44no—
337C2×C3×Dic3—34no—
338C2×C3×Dic3—34no—
339C2×C3×Dic3—34no—
340C2×C3×Dic3—34no—
341C2×C3×Dic3—68no—
342C2×C3×Dic3—68no—
343C2×C3×Dic3C22×D314yes—
344C2×C3×Dic3C22×D314yes—
345#627—68no—
346#626—316no—
347#626—68no—
348#626—68no—
349#626—68no—
350#624—68no—
351#624—124no—
352D3×Dic3—68no—
353D3×Dic3—124no—
354#546—271noSylow
355C2×C33—22no—
356C2×C33—41no—
357C2×C33C22×D411yescharacteristic
358C2×C33C2×#4111yescharacteristic
359C2×C33H(5,𝔽2)11yescharacteristic
360C3⋊(C3⋊D3)—22no—
361C3⋊(C3⋊D3)—41no—
362C32×D3—22no—
363C32×D3—41no—
364C24×C3—34no—
365C23×D3—94no—
366C23×D3—91no—
367C23×D3—184no—
368C23×D3C2×C3⋊D311yescharacteristic
369C2×C3×D4—24no—
370C2×C3×D4—34no—
371C2×C3×D4—34no—
372C2×C3×D4D3214yes—
373C2×C3×D4C2×C3⋊D311yescharacteristic
374C22×C3×C4—91no—
375C22×C3×C4—91no—
376C2×#67—94no—
377C2×#67—94no—
378C2×#67—94no—
379C2×#67—94no—
380C2×#67—94no—
381C2×#67—91no—
382C2×#67—94no—
383C2×#67—91no—
384C2×#67—184no—
385C2×#67—184no—
386C2×#67—1816no—
387C2×#67C2×C3⋊D311yescharacteristic, complemented
388C2×#67C2×C3⋊D311yescharacteristic, complemented
389C22×Dic3—34no—
390C22×Dic3—34no—
391C22×Dic3—94no—
392C22×Dic3—94no—
393#237—1816no—
394#235—184no—
395C2×D12—91no—
396C2×D12—91no—
397C2×D12—91no—
398C2×D12—91no—
399C2×D12—184no—
400C2×C4×D3—94no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—94no—
404C2×C4×D3—91no—
405C2×C4×D3—91no—
406C2×Dic6—94no—
407C2×Dic6—91no—
408C3×C4⋊C4—91no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4—34no—
411C3×C22⋊C4—34no—
412C3×C22⋊C4—91no—
413C3×C22⋊C4—91no—
414C3×C42—91no—
415#217—34no—
416#217—34no—
417#217—94no—
418#217—94no—
419#217—94no—
420#217—91no—
421#217—184no—
422#217C2×C3⋊D311yescharacteristic
423(C2×D3)⋊C4—94no—
424(C2×D3)⋊C4—94no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—94no—
428(C2×D3)⋊C4—94no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—184no—
434(C2×D3)⋊C4—184no—
435(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
436(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
437C4⋊Dic3—34no—
438C4⋊Dic3—94no—
439C4⋊Dic3—91no—
440Dic3⋊C4—94no—
441Dic3⋊C4—94no—
442Dic3⋊C4—91no—
443Dic3⋊C4—91no—
444C4×Dic3—34no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—24no—
451C22×C32—28no—
452C22×C32—24no—
453C22×C32—24no—
454C22×C32—24no—
455C22×C32—24no—
456C22×C32—24no—
457C22×C32—32no—
458C22×C32—44no—
459C22×C32—44no—
460C22×C32—44no—
461C22×C32—44no—
462C22×C32—44no—
463C22×C32—61no—
464C22×C32—61no—
465C22×C32—61no—
466C22×C32—61no—
467C22×C32—61no—
468C22×C32—124no—
469C22×C32#23512yescomplemented
470C22×C32#23718yescomplemented
471C22×C32C23×D314yes—
472C22×C32C23×D311yescharacteristic
473C2×C3⋊D3—32no—
474C2×C3⋊D3—38no—
475C2×C3⋊D3—68no—
476C2×C3⋊D3—61no—
477C2×C3⋊D3—61no—
478C2×C3⋊D3—68no—
479C2×C3⋊D3—61no—
480C2×C3⋊D3—61no—
481C2×C3⋊D3—64no—
482C2×C3⋊D3—61no—
483C2×C3⋊D3—64no—
484C2×C3⋊D3—64no—
485C2×C3⋊D3—64no—
486C2×C3⋊D3—64no—
487C2×C3⋊D3—124no—
488C2×C3⋊D3—124no—
489C2×C3⋊D3—124no—
490C2×C3⋊D3—124no—
491C2×C3⋊D3—124no—
492C2×C3⋊D3—1216no—
493C2×C3⋊D3—1232no—
494C2×C3×D3—24no—
495C2×C3×D3—24no—
496C2×C3×D3—24no—
497C2×C3×D3—24no—
498C2×C3×D3—24no—
499C2×C3×D3—416no—
500C2×C3×D3D3×D418yes—
501C32×C4—21no—
502C32×C4—24no—
503C32×C4—44no—
504C32×C4—61no—
505C32×C4—61no—
506C3⋊Dic3—21no—
507C3⋊Dic3—21no—
508C3⋊Dic3—21no—
509C3⋊Dic3—61no—
510C3⋊Dic3—61no—
511C3⋊Dic3—64no—
512C3⋊Dic3—64no—
513C3⋊Dic3—124no—
514C3⋊Dic3—124no—
515C3⋊Dic3D3×D412yes—
516C3×Dic3—24no—
517C3×Dic3—24no—
518C3×Dic3—38no—
519C3×Dic3—64no—
520C3×Dic3—64no—
521C3×Dic3—64no—
522C2×#41—271no—
523C22×D4—271no—
524#124—271no—
525#123—271no—
526#123—271no—
527C22⋊Q8—271no—
528#121—271no—
529#121—271no—
530#121—271no—
531#120—31no—
532#120—271no—
533C4×D4—91no—
534C4×D4—271no—
535C2×C22⋊C4—271no—
536C2×C22⋊C4—271no—
537C33#54611yescharacteristic, complemented, Sylow
538C23×C3—24no—
539C23×C3—24no—
540C23×C3—34no—
541C23×C3—34no—
542C23×C3—68no—
543C23×C3—68no—
544C23×C3—124no—
545C23×C3C2×D3214yes—
546C23×C3C2×D3214yes—
547C23×C3C22×C3⋊D311yescharacteristic
548C23×C3C22×C3⋊D311yescharacteristic
549C22×D3—22no—
550C22×D3—22no—
551C22×D3—41no—
552C22×D3—94no—
553C22×D3—91no—
554C22×D3—94no—
555C22×D3—91no—
556C22×D3—184no—
557C22×D3—184no—
558C22×D3—182no—
559C22×D3—188no—
560C22×D3—188no—
561C22×D3—182no—
562C22×D3—368no—
563C22×D3—368no—
564C22×D3—364no—
565C22×D3—361no—
566C22×D3—368no—
567C22×D3C22×C3⋊D311yescharacteristic
568C22×D3C22×C3⋊D311yescharacteristic
569C3×D4—28no—
570C3×D4—22no—
571C3×D4—48no—
572C3×D4—68no—
573C3×D4—124no—
574C2×C3×C4—24no—
575C2×C3×C4—34no—
576C2×C3×C4—34no—
577C2×C3×C4—91no—
578C2×C3×C4—91no—
579C2×C3×C4—91no—
580C2×C3×C4—91no—
581C2×C3×C4—182no—
582C2×C3×C4—182no—
583C2×C3×C4C2×D3214yes—
584C2×C3×C4C22×C3⋊D311yescharacteristic
585#67—22no—
586#67—41no—
587#67—916no—
588#67—188no—
589#67—188no—
590#67—188no—
591#67—182no—
592#67—188no—
593#67—368no—
594#67—364no—
595#67—361no—
596#67—368no—
597C2×Dic3—34no—
598C2×Dic3—34no—
599C2×Dic3—34no—
600C2×Dic3—34no—
601C2×Dic3—68no—
602C2×Dic3—68no—
603C2×Dic3—94no—
604C2×Dic3—94no—
605C2×Dic3—91no—
606C2×Dic3—91no—
607C2×Dic3—184no—
608C2×Dic3—184no—
609C2×Dic3—188no—
610C2×Dic3—364no—
611C2×Dic3C22×C3⋊D311yescharacteristic
612C2×Dic3C22×C3⋊D311yescharacteristic
613D12—94no—
614D12—182no—
615D12—182no—
616D12—182no—
617C4×D3—182no—
618C4×D3—188no—
619C4×D3—182no—
620C4×D3—361no—
621C4×D3—364no—
622C4×D3—361no—
623Dic6—182no—
624Dic6—188no—
625C2×C32—22no—
626C2×C32—24no—
627C2×C32—24no—
628C2×C32—24no—
629C2×C32—28no—
630C2×C32—48no—
631C2×C32—41no—
632C2×C32—44no—
633C2×C32—62no—
634C2×C32—84no—
635C2×C32—121no—
636C2×C32C2×#23511yescharacteristic
637C2×C32C2×D3×D414yes—
638C2×C32C2×D3×D411yescharacteristic
639C2×C32C2×#23714yes—
640C2×C32#100414yes—
641C2×C32#100911yescharacteristic
642C3⋊D3—62no—
643C3⋊D3—68no—
644C3⋊D3—128no—
645C3⋊D3—128no—
646C3⋊D3—121no—
647C3⋊D3—124no—
648C3×D3—28no—
649C3×D3—44no—
650C24—31no—
651C24—271no—
652#41—544no—
653C2×Q8—271no—
654C2×D4—31no—
655C2×D4—31no—
656C2×D4—271no—
657C2×D4—271no—
658C2×D4—271no—
659C2×D4—271no—
660C2×D4—271no—
661C2×D4—271no—
662C2×D4—544no—
663C2×D4D3×C3⋊D311yescharacteristic
664C22×C4—91no—
665C22×C4—91no—
666C22×C4—271no—
667C22×C4—271no—
668C22×C4—271no—
669C22×C4—271no—
670C4⋊C4—91no—
671C4⋊C4—271no—
672C4⋊C4—271no—
673C4⋊C4—271no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—31no—
677C22⋊C4—91no—
678C22⋊C4—91no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C22⋊C4—271no—
682C22⋊C4—271no—
683C22⋊C4—271no—
684C22⋊C4—271no—
685C22⋊C4—271no—
686C42—91no—
687C22×C3—24no—
688C22×C3—24no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—24no—
692C22×C3—24no—
693C22×C3—24no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—24no—
698C22×C3—28no—
699C22×C3—38no—
700C22×C3—44no—
701C22×C3—44no—
702C22×C3—44no—
703C22×C3—44no—
704C22×C3—44no—
705C22×C3—64no—
706C22×C3—64no—
707C22×C3—64no—
708C22×C3—64no—
709C22×C3—64no—
710C22×C3—1216no—
711C22×C3#380418yescomplemented
712C22×C3#383012yescomplemented
713C22×C3C22×D3214yes—
714C22×C3C23×C3⋊D311yescharacteristic
715C2×D3—21no—
716C2×D3—21no—
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—44no—
721C2×D3—98no—
722C2×D3—92no—
723C2×D3—188no—
724C2×D3—184no—
725C2×D3—184no—
726C2×D3—181no—
727C2×D3—181no—
728C2×D3—188no—
729C2×D3—184no—
730C2×D3—184no—
731C2×D3—184no—
732C2×D3—181no—
733C2×D3—181no—
734C2×D3—181no—
735C2×D3—364no—
736C2×D3—364no—
737C2×D3—364no—
738C2×D3—364no—
739C2×D3—3616no—
740C2×D3—364no—
741C2×D3—3632no—
742C2×D3D4×C3⋊D312yes—
743C3×C4—24no—
744C3×C4—21no—
745C3×C4—44no—
746C3×C4—64no—
747C3×C4—64no—
748C3×C4—92no—
749C3×C4—181no—
750C3×C4—181no—
751C3×C4—181no—
752Dic3—21no—
753Dic3—21no—
754Dic3—38no—
755Dic3—64no—
756Dic3—64no—
757Dic3—64no—
758Dic3—184no—
759Dic3—184no—
760Dic3—181no—
761Dic3—181no—
762Dic3—364no—
763Dic3—364no—
764C32—24no—
765C32#555011yescharacteristic, complemented
766C32#559114yescomplemented
767C23—31no—
768C23—31no—
769C23—62no—
770C23—62no—
771C23—121no—
772C23—271no—
773C23—271no—
774C23—542no—
775C23—542no—
776C23—1081no—
777C23C2×D3×C3⋊D311yescharacteristic
778C23C2×D3×C3⋊D311yescharacteristic
779Q8—542no—
780D4—22no—
781D4—62no—
782D4—121no—
783D4—274no—
784D4—542no—
785D4—542no—
786D4—542no—
787D4—542no—
788D4—1081no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—91no—
792C2×C4—91no—
793C2×C4—91no—
794C2×C4—91no—
795C2×C4—182no—
796C2×C4—182no—
797C2×C4—271no—
798C2×C4—271no—
799C2×C4—542no—
800C2×C4—542no—
801C2×C4—1081no—
802C2×C4—1081no—
803C2×C4C2×D3×C3⋊D311yescharacteristic
804C2×C3—28no—
805C2×C3—22no—
806C2×C3—24no—
807C2×C3—24no—
808C2×C3—24no—
809C2×C3—48no—
810C2×C3—44no—
811C2×C3—41no—
812C2×C3—68no—
813C2×C3—84no—
814C2×C3—124no—
815C2×C3D32×D414yes—
816C2×C3#6431414yes—
817C2×C3C2×#380414yes—
818C2×C3C2×D4×C3⋊D311yescharacteristic
819C2×C3C2×#383011yescharacteristic
820C2×C3#6436111yescharacteristic
821D3—22no—
822D3—41no—
823D3—188no—
824D3—182no—
825D3—368no—
826D3—368no—
827D3—364no—
828D3—361no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—32no—
835C22—61no—
836C22—61no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—124no—
841C22—272no—
842C22—541no—
843C22—541no—
844C22—541no—
845C22—541no—
846C22—541no—
847C22—1084no—
848C22#8902812yescomplemented
849C22C22×D3×C3⋊D311yescharacteristic
850C4—21no—
851C4—61no—
852C4—61no—
853C4—92no—
854C4—181no—
855C4—181no—
856C4—181no—
857C4—541no—
858C4—541no—
859C3—24no—
860C3#1059513514yescomplemented
861C3#1059606211yescharacteristic, complemented
862C2—22no—
863C2—41no—
864C2—62no—
865C2—121no—
866C2—542no—
867C2—1081no—
868C2D3×D4×C3⋊D311yescharacteristic
869C2#1172458811yescharacteristic
870C2C2×#8902811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C22×#6291C2semidirect
2. C2×#89028C2semidirect
3. #11723978C2semidirect
4. C3×D4×C3⋊Dic3C2semidirect
5. C32×#937C2semidirect
6. #11723641C2semidirect
7. #11723635C2semidirect
8. #11723627C2semidirect
9. #11723616C2semidirect
10. D3×#3757C2semidirect
11. #11723599C2semidirect
12. #11723479C2semidirect
13. #11723461C2semidirect
14. #11723422C2semidirect
15. #11723419C2semidirect
21. C2×#6312C22semidirect
22. C2×#6312C22semidirect
24. C22×C3×C3⋊Dic3C22semidirect
25. C2×C32×#67C22semidirect
26. C2×C32×#67C22semidirect
27. C2×#6293C22semidirect
33. C2×#6289C22semidirect
34. C2×#6289C22semidirect
36. C2×D3×C3⋊Dic3C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
39. #88859C22semidirect
40. #88859C22semidirect
42. C3×#3757C22semidirect
43. C3×C4⋊(C3⋊Dic3)C22semidirect
44. C3×C4×C3⋊Dic3C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. #88807C22semidirect
49. #88806C22semidirect
50. Dic3⋊(C3⋊Dic3)C22semidirect
51. #88804C22semidirect
52. #88804C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
67. D4×C3⋊Dic3D3semidirect
74. C3×#937D3semidirect
118. #6291D4semidirect
149. C22×C3⋊Dic3C2×D3semidirect
154. C2×C3×#67C2×D3semidirect
155. C2×C3×#67C2×D3semidirect
178. #3757C2×D3semidirect
188. C4⋊(C3⋊Dic3)C2×D3semidirect
191. C4×C3⋊Dic3C2×D3semidirect
195. C3×(C2×D3)⋊C4C2×D3semidirect
196. C3×(C2×D3)⋊C4C2×D3semidirect
211. C22×C33#41semidirect
249. #937C3⋊D3semidirect
387. C2×#67C2×C3⋊D3semidirect
388. C2×#67C2×C3⋊D3semidirect
435. (C2×D3)⋊C4C2×C3⋊D3semidirect
436. (C2×D3)⋊C4C2×C3⋊D3semidirect
469. C22×C32#235semidirect
470. C22×C32#237semidirect
537. C33#546semidirect
711. C22×C3#3804semidirect
712. C22×C3#3830semidirect
765. C32#5550semidirect
766. C32#5591semidirect
848. C22#89028semidirect
860. C3#10595135semidirect
861. C3#10596062semidirect

Maximal subgroups

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

subgroupindex
C22×#62912
C2×#890282
#117239782
C3×D4×C3⋊Dic32
C32×#9372
#117236412
#117236352
#117236272
#117236162
D3×#37572
#117235992
#117234792
#117234612
#117234222
#117234192
#105960623
#105951353