Finite Group Databasebeta

← #13172371

Subgroups — #13172371

Order 1728.

1672 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic, complemented
2C2×C3×#3804C211yesmaximal, characteristic, complemented
3#11723634C211yesmaximal, characteristic, complemented
4Dic3×#638C211yesmaximal, characteristic, complemented
5#11723605C211yesmaximal, characteristic, complemented
6C3×#63978C211yesmaximal, characteristic, complemented
7C2×C3×#3722C211yesmaximal, characteristic, complemented
8#11723007C211yesmaximal, characteristic, complemented
9#11722995C211yesmaximal, characteristic, complemented
10#11722979C211yesmaximal, characteristic, complemented
11#11722967C211yesmaximal, characteristic, complemented
12#11722960C211yesmaximal, characteristic, complemented
13#11722951C211yesmaximal, characteristic, complemented
14#11722936C211yesmaximal, characteristic, complemented
15#11722905C211yesmaximal, characteristic, complemented
16#10595305—31nomaximal
17#10595083—31nomaximal
18#10595065—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×#1113C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic, complemented
24C22×C32×Dic3C2211yescharacteristic, complemented
25C22×C32×Dic3C2211yescharacteristic, complemented
26#89049—24no—
27C2×#6295C2211yescharacteristic
28C2×#6295C2211yescharacteristic
29C2×#6294C2211yescharacteristic
30C2×#6290C2211yescharacteristic
31C2×#6290C2211yescharacteristic, complemented
32C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
33C2×C3×#627C2211yescharacteristic, complemented
34C2×C3×#626C2211yescharacteristic, complemented
35C2×C3×#626C2211yescharacteristic, complemented
36C2×C3×#624C2211yescharacteristic, complemented
37C3×#3804—24no—
38C2×C3×D3×Dic3C2211yescharacteristic, complemented
39#88864C2211yescharacteristic, complemented
40#88807C2211yescharacteristic, complemented
41#88806C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43#88803C2211yescharacteristic
44#88803C2211yescharacteristic, complemented
45#88803C2211yescharacteristic, complemented
46#88803C2211yescharacteristic, complemented
47#88803C2211yescharacteristic, complemented
48Dic3×C3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic, complemented
54C3×#3722C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×C3×#237—31no—
57C2×C3×#235—31no—
58C2×#3811—31no—
59C2×D3×#67—31no—
60C2×D3×#67—31no—
61C2×#3804D311yescharacteristic, complemented
62#64146—31no—
63#64138—31no—
64C4×#638—31no—
65C3×#939—31no—
66C3×#930—31no—
67C2×C3×(C2×D3)⋊C4—31no—
68C2×C3×(C2×D3)⋊C4—31no—
69#63983—31no—
70#63978—31no—
71#63978D311yescharacteristic, complemented
72#63976—31no—
73#63976—31no—
74#63976—61no—
75Dic3×#67—31no—
76Dic3×#67—31no—
77Dic3×#67—61no—
78#63971—31no—
79C2×#3722D311yescharacteristic, complemented
80#63961—31no—
81#63961—31no—
82#63961—61no—
83#63952—31no—
84#63922—31no—
85#63922—31no—
86#63921—31no—
87D3×(C2×D3)⋊C4—31no—
88D3×(C2×D3)⋊C4—31no—
89#63915—31no—
90#63912—31no—
91#63907—31no—
92#63907—31no—
93#63906—31no—
94#63905—31no—
95#63902—31no—
96#63899—31no—
97#63888—31no—
98#63887—31no—
99#63885—31no—
100#63885—31no—
101#63879—31no—
102#63854—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3—22no—
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—41no—
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C3×C3⋊D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C2×#1113—22no—
114C2×#1113—22no—
115C2×#1113—41no—
116C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#638—22no—
119C3×#638D414yescomplemented
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C32×#67—22no—
123C2×C32×Dic3—22no—
124C2×C32×Dic3—41no—
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130#6295—22no—
131#6295—22no—
132#6294—22no—
133#6290—22no—
134#6290—41no—
135Dic3×C3⋊D3—41no—
136C3×#627—22no—
137C3×#626—22no—
138C3×#626—41no—
139C3×#624—22no—
140C3×D3×Dic3—22no—
141#5829—91no—
142#5610—91no—
143#5490—91no—
144C23×C3⋊D3C2×D311yescharacteristic
145C23×C3×D3—31no—
146C23×C3×D3—31no—
147C23×C3×D3—61no—
148C22×D32—31no—
149C22×D32—31no—
150C22×D32—31no—
151C2×C32×D4—31no—
152C22×C32×C4—31no—
153C22×C32×C4—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638C2×D311yescharacteristic
157C2×#638C2×D311yescharacteristic
158C2×C4×C3⋊D3—31no—
159C2×C3×#67—21no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—31no—
165C2×C3×#67—31no—
166C2×C3×#67—61no—
167C2×C3×#67—61no—
168C2×C3×#67C2×D311yescharacteristic, complemented
169C2×C3×#67C2×D311yescharacteristic, complemented
170C22×C3×Dic3—21no—
171C22×C3×Dic3—21no—
172C22×C3×Dic3—31no—
173C22×C3×Dic3C2×D311yescharacteristic, complemented
174C22×C3×Dic3C2×D311yescharacteristic, complemented
175C22×C3×Dic3C2×D311yescharacteristic, complemented
176C22×C3×Dic3C2×D311yescharacteristic, complemented
177C3×#237—64no—
178C3×#235—64no—
179C2×C3×D12—31no—
180C2×C3×D12—31no—
181C2×C3×C4×D3—31no—
182C2×C3×C4×D3—31no—
183C2×C3×C4×D3—31no—
184C2×C3×Dic6—31no—
185C2×C3×Dic6—31no—
186#3811—64no—
187D3×#67—64no—
188D3×#67—64no—
189C2×#627C2×D311yescharacteristic, complemented
190C2×#626—31no—
191C2×#626—31no—
192C2×#626—31no—
193C2×#626—31no—
194C2×#626C2×D311yescharacteristic, complemented
195C2×#626C2×D311yescharacteristic, complemented
196C2×#625—31no—
197C2×#625—31no—
198C2×#625—31no—
199C2×#625—31no—
200C2×#625—31no—
201C2×#625—31no—
202C2×#625—61no—
203C2×#625—61no—
204C2×#624—31no—
205C2×#624C2×D311yescharacteristic, complemented
206#3804—24no—
207C2×D3×Dic3—31no—
208C2×D3×Dic3—31no—
209C2×D3×Dic3—31no—
210C2×D3×Dic3—31no—
211C2×D3×Dic3—61no—
212C2×D3×Dic3C2×D311yescharacteristic, complemented
213#3757—31no—
214#3757—31no—
215#3757—31no—
216#3757—61no—
217#3757—61no—
218#3757—61no—
219#3757—121no—
220#3752—31no—
221#3752—31no—
222#3752—31no—
223#3752—31no—
224#3752—31no—
225#3750—31no—
226#3750—31no—
227#3750—31no—
228C4×C3⋊Dic3—31no—
229C3×#217—31no—
230C3×(C2×D3)⋊C4—31no—
231C3×(C2×D3)⋊C4—31no—
232C3×(C2×D3)⋊C4—31no—
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4—31no—
235C3×(C2×D3)⋊C4—31no—
236C3×(C2×D3)⋊C4—31no—
237C3×(C2×D3)⋊C4—31no—
238C3×(C2×D3)⋊C4—31no—
239C3×(C2×D3)⋊C4—31no—
240C3×(C2×D3)⋊C4—31no—
241C3×C4⋊Dic3—31no—
242C3×Dic3⋊C4—31no—
243#3724—31no—
244#3724—31no—
245#3724—31no—
246#3724—31no—
247#3724—61no—
248#3724—61no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—61no—
252Dic3⋊Dic3C2×D311yescharacteristic, complemented
253#3722C2×D311yescharacteristic
254#3722C2×D311yescharacteristic
255#3722C2×D311yescharacteristic, complemented
256#3722C2×D311yescharacteristic, complemented
257#3722C2×D311yescharacteristic, complemented
258(C2×D3)⋊Dic3—31no—
259(C2×D3)⋊Dic3—31no—
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—61no—
269(C2×D3)⋊Dic3—61no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3—61no—
272(C2×D3)⋊Dic3—61no—
273(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
274Dic32—31no—
275Dic32—31no—
276Dic32—61no—
277C22×C33—21no—
278C22×C33—21no—
279C22×C33C2×D412yes—
280C22×C33C2411yescharacteristic
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3—21no—
284C2×C3×C3⋊D3—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3—44no—
292C2×C3×C3⋊D3C2×D412yes—
293C2×C3×C3⋊D3#4112yescomplemented
294C2×C32×D3—21no—
295C2×C32×D3—21no—
296C2×C32×D3—21no—
297#1113—44no—
298C3⋊(C3⋊Dic3)—21no—
299C3⋊(C3⋊Dic3)—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3C2×D412yes—
302C32×Dic3—21no—
303C32×Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C2×C3×#41—91no—
308C22×#67—91no—
309C2×#237—31no—
310C2×D3×D4—91no—
311C2×D3×D4—91no—
312C2×#235—31no—
313C3×#121—91no—
314C2×C3×C22⋊C4—91no—
315#953—91no—
316#947—91no—
317#946—91no—
318#939—31no—
319#939—91no—
320#939—91no—
321#937—91no—
322#937—91no—
323#937—91no—
324#937—91no—
325#937—181no—
326#935—91no—
327D4×Dic3—91no—
328#930—31no—
329#930—91no—
330#929—91no—
331#929—91no—
332#929—91no—
333#929—181no—
334C4×#67—91no—
335C4×#67—91no—
336C4×#67—91no—
337C4×#67—181no—
338C2×(C2×D3)⋊C4—31no—
339C2×(C2×D3)⋊C4—31no—
340C2×(C2×D3)⋊C4—91no—
341#896—91no—
342#894—91no—
343#885—91no—
344#885—91no—
345#884—91no—
346#884—91no—
347#884—91no—
348#883—91no—
349#882—91no—
350#67⋊C4—91no—
351#67⋊C4—91no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
354#878—91no—
355C23×C32—21no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—31no—
359C23×C32—41no—
360C23×C32C22×D311yescharacteristic
361C23×C32C22×D311yescharacteristic
362C23×C32C22×D311yescharacteristic
363C22×C3⋊D3—22no—
364C22×C3⋊D3—22no—
365C22×C3⋊D3—41no—
366C22×C3⋊D3C22×D311yescharacteristic
367C22×C3⋊D3C22×D311yescharacteristic
368C22×C3⋊D3C22×D311yescharacteristic
369C22×C3⋊D3C22×D311yescharacteristic
370C22×C3×D3—21no—
371C22×C3×D3—31no—
372C22×C3×D3—31no—
373C22×C3×D3—31no—
374C22×C3×D3—31no—
375C22×C3×D3—31no—
376C22×C3×D3—31no—
377C22×C3×D3—31no—
378C22×C3×D3—31no—
379C22×C3×D3—61no—
380C22×C3×D3—61no—
381C22×C3×D3—61no—
382C22×C3×D3—61no—
383C22×C3×D3—62no—
384C22×C3×D3—62no—
385C22×C3×D3—62no—
386C22×C3×D3—62no—
387C22×C3×D3—122no—
388C22×C3×D3—122no—
389C22×C3×D3—121no—
390C22×C3×D3—121no—
391C22×C3×D3—122no—
392C22×C3×D3C22×D311yescharacteristic
393C22×C3×D3C22×D311yescharacteristic
394C2×D32—62no—
395C2×D32—62no—
396C2×D32—62no—
397C2×D32—62no—
398C2×D32—62no—
399C2×D32—62no—
400C2×D32—121no—
401C2×D32—121no—
402C2×D32—121no—
403C32×D4—62no—
404C2×C32×C4—31no—
405C2×C32×C4—31no—
406C2×C32×C4—31no—
407C2×C32×C4—31no—
408C2×C32×C4—31no—
409C2×C32×C4—62no—
410C2×C32×C4—121no—
411#638—22no—
412#638—62no—
413#638—121no—
414#638#6714yescomplemented
415C2×C3⋊Dic3—31no—
416C2×C3⋊Dic3—31no—
417C2×C3⋊Dic3—31no—
418C2×C3⋊Dic3—31no—
419C2×C3⋊Dic3—31no—
420C2×C3⋊Dic3—31no—
421C2×C3⋊Dic3—61no—
422C2×C3⋊Dic3—61no—
423C2×C3⋊Dic3—61no—
424C2×C3⋊Dic3—61no—
425C2×C3⋊Dic3—61no—
426C2×C3⋊Dic3—61no—
427C2×C3⋊Dic3—121no—
428C2×C3⋊Dic3—121no—
429C2×C3⋊Dic3C22×D311yescharacteristic
430C2×C3⋊Dic3C22×D311yescharacteristic
431C4×C3⋊D3—121no—
432C3×#67—22no—
433C3×#67—22no—
434C3×#67—34no—
435C3×#67—34no—
436C3×#67—42no—
437C3×#67—64no—
438C3×#67—62no—
439C3×#67—62no—
440C3×#67—62no—
441C3×#67—122no—
442C3×#67—121no—
443C2×C3×Dic3—22no—
444C2×C3×Dic3—22no—
445C2×C3×Dic3—21no—
446C2×C3×Dic3—21no—
447C2×C3×Dic3—21no—
448C2×C3×Dic3—21no—
449C2×C3×Dic3—21no—
450C2×C3×Dic3—31no—
451C2×C3×Dic3—31no—
452C2×C3×Dic3—31no—
453C2×C3×Dic3—31no—
454C2×C3×Dic3—42no—
455C2×C3×Dic3—41no—
456C2×C3×Dic3—41no—
457C2×C3×Dic3—42no—
458C2×C3×Dic3—61no—
459C2×C3×Dic3—61no—
460C2×C3×Dic3—62no—
461C2×C3×Dic3C22×D311yescharacteristic
462C2×C3×Dic3C22×D311yescharacteristic
463C2×C3×Dic3C22×D311yescharacteristic
464C2×C3×Dic3C22×D311yescharacteristic
465C2×C3×Dic3C22×D311yescharacteristic
466C2×C3×Dic3C22×D311yescharacteristic
467C2×C3×Dic3C22×D311yescharacteristic
468C2×C3×Dic3C22×D311yescharacteristic
469C2×C3×Dic3C22×D311yescharacteristic
470C2×C3×Dic3C22×D311yescharacteristic
471C3×D12—62no—
472C3×D12—121no—
473C3×C4×D3—62no—
474C3×C4×D3—62no—
475C3×C4×D3—62no—
476C3×Dic6—62no—
477C3×Dic6—62no—
478#627—22no—
479#626—22no—
480#626—41no—
481#626—62no—
482#626—62no—
483#626—62no—
484#626—62no—
485#625—62no—
486#625—62no—
487#625—62no—
488#625—62no—
489#625—122no—
490#625—121no—
491#625—121no—
492#625—122no—
493#624—22no—
494#624—62no—
495D3×Dic3—22no—
496D3×Dic3—62no—
497D3×Dic3—62no—
498D3×Dic3—121no—
499D3×Dic3—121no—
500D3×Dic3—122no—
501#546—271noSylow
502C2×C33—22no—
503C2×C33C22×D411yescharacteristic
504C2×C33C2×#4111yescharacteristic
505C2×C33H(5,𝔽2)11yescharacteristic
506C3×C3⋊D3—22no—
507C3×C3⋊D3—22no—
508C3×C3⋊D3—41no—
509C3×C3⋊D3—41no—
510C32×D3—41no—
511C24×C3—91no—
512C23×D3—31no—
513C23×D3—31no—
514C23×D3—61no—
515C23×D3—91no—
516C23×D3—91no—
517C23×D3—91no—
518C3×#41—184no—
519C2×C3×Q8—91no—
520C2×C3×D4—31no—
521C2×C3×D4—31no—
522C2×C3×D4—61no—
523C2×C3×D4—91no—
524C2×C3×D4—91no—
525C2×C3×D4—91no—
526C2×C3×D4—91no—
527C22×C3×C4—31no—
528C22×C3×C4—31no—
529C22×C3×C4—31no—
530C22×C3×C4—31no—
531C22×C3×C4—61no—
532C22×C3×C4—61no—
533C22×C3×C4—91no—
534C22×C3×C4—91no—
535C2×#67—31no—
536C2×#67—31no—
537C2×#67—31no—
538C2×#67—31no—
539C2×#67—31no—
540C2×#67—31no—
541C2×#67—61no—
542C2×#67—61no—
543C2×#67—91no—
544C2×#67—91no—
545C2×#67—91no—
546C2×#67—91no—
547C2×#67—91no—
548C2×#67—91no—
549C2×#67—91no—
550C2×#67—91no—
551C2×#67—91no—
552C2×#67—91no—
553C2×#67—181no—
554C2×#67—181no—
555C2×#67—184no—
556C2×#67D3211yescharacteristic, complemented
557C22×Dic3—31no—
558C22×Dic3—91no—
559C22×Dic3—91no—
560C22×Dic3D3211yescharacteristic, complemented
561C22×Dic3D3211yescharacteristic, complemented
562#237—64no—
563D3×D4—184no—
564D3×D4—184no—
565#235—64no—
566C2×D12—31no—
567C2×D12—31no—
568C2×D12—91no—
569C2×D12—91no—
570C2×C4×D3—31no—
571C2×C4×D3—31no—
572C2×C4×D3—31no—
573C2×C4×D3—91no—
574C2×C4×D3—91no—
575C2×C4×D3—91no—
576C2×C4×D3—91no—
577C2×C4×D3—181no—
578C2×Dic6—31no—
579C2×Dic6—31no—
580C3×C4⋊C4—91no—
581C3×C22⋊C4—91no—
582C3×C22⋊C4—91no—
583C3×C22⋊C4—91no—
584C3×C22⋊C4—91no—
585C3×C22⋊C4—91no—
586C3×C22⋊C4—91no—
587#217—31no—
588#217—91no—
589#217—91no—
590#217—91no—
591#217—91no—
592#217—91no—
593#217—91no—
594#217—91no—
595#217—91no—
596#217—181no—
597#217—181no—
598#217—181no—
599#217—361no—
600(C2×D3)⋊C4—31no—
601(C2×D3)⋊C4—31no—
602(C2×D3)⋊C4—31no—
603(C2×D3)⋊C4—31no—
604(C2×D3)⋊C4—31no—
605(C2×D3)⋊C4—31no—
606(C2×D3)⋊C4—31no—
607(C2×D3)⋊C4—31no—
608(C2×D3)⋊C4—31no—
609(C2×D3)⋊C4—31no—
610(C2×D3)⋊C4—31no—
611(C2×D3)⋊C4—91no—
612(C2×D3)⋊C4—91no—
613(C2×D3)⋊C4—91no—
614(C2×D3)⋊C4—91no—
615(C2×D3)⋊C4—91no—
616(C2×D3)⋊C4—91no—
617(C2×D3)⋊C4—91no—
618(C2×D3)⋊C4—91no—
619(C2×D3)⋊C4—91no—
620(C2×D3)⋊C4—91no—
621(C2×D3)⋊C4—181no—
622(C2×D3)⋊C4—181no—
623(C2×D3)⋊C4—181no—
624(C2×D3)⋊C4—181no—
625(C2×D3)⋊C4—181no—
626C4⋊Dic3—31no—
627C4⋊Dic3—91no—
628Dic3⋊C4—31no—
629Dic3⋊C4—91no—
630Dic3⋊C4—91no—
631Dic3⋊C4—91no—
632Dic3⋊C4—91no—
633Dic3⋊C4—91no—
634Dic3⋊C4—91no—
635Dic3⋊C4—91no—
636Dic3⋊C4—91no—
637Dic3⋊C4—181no—
638Dic3⋊C4—181no—
639Dic3⋊C4—181no—
640C4×Dic3—91no—
641C4×Dic3—91no—
642C4×Dic3—91no—
643C4×Dic3—181no—
644C22×C32—21no—
645C22×C32—21no—
646C22×C32—21no—
647C22×C32—21no—
648C22×C32—21no—
649C22×C32—21no—
650C22×C32—21no—
651C22×C32—21no—
652C22×C32—21no—
653C22×C32—22no—
654C22×C32—22no—
655C22×C32—22no—
656C22×C32—41no—
657C22×C32—42no—
658C22×C32—41no—
659C22×C32—41no—
660C22×C32—41no—
661C22×C32—41no—
662C22×C32—41no—
663C22×C32—41no—
664C22×C32—61no—
665C22×C32—61no—
666C22×C32—61no—
667C22×C32—81no—
668C22×C32—81no—
669C22×C32D3×D412yes—
670C22×C32D3×D412yes—
671C22×C32C2×#6712yes—
672C22×C32C23×D311yescharacteristic
673C22×C32C23×D311yescharacteristic
674C22×C32C23×D311yescharacteristic
675C2×C3⋊D3—21no—
676C2×C3⋊D3—21no—
677C2×C3⋊D3—21no—
678C2×C3⋊D3—21no—
679C2×C3⋊D3—21no—
680C2×C3⋊D3—21no—
681C2×C3⋊D3—21no—
682C2×C3⋊D3—21no—
683C2×C3⋊D3—21no—
684C2×C3⋊D3—21no—
685C2×C3⋊D3—44no—
686C2×C3⋊D3#23512yescomplemented
687C2×C3⋊D3C2×#6712yes—
688C2×C3×D3—21no—
689C2×C3×D3—21no—
690C2×C3×D3—21no—
691C2×C3×D3—21no—
692C2×C3×D3—21no—
693C2×C3×D3—21no—
694C2×C3×D3—32no—
695C2×C3×D3—32no—
696C2×C3×D3—32no—
697C2×C3×D3—32no—
698C2×C3×D3—41no—
699C2×C3×D3—41no—
700C2×C3×D3—41no—
701C2×C3×D3—62no—
702C2×C3×D3—62no—
703C2×C3×D3—61no—
704C2×C3×D3—61no—
705C2×C3×D3—61no—
706C2×C3×D3—61no—
707C2×C3×D3—61no—
708C2×C3×D3—61no—
709C2×C3×D3—61no—
710C2×C3×D3—61no—
711C2×C3×D3—62no—
712C2×C3×D3—61no—
713C2×C3×D3—61no—
714C2×C3×D3—61no—
715C2×C3×D3—61no—
716C2×C3×D3—61no—
717C2×C3×D3—61no—
718C2×C3×D3—61no—
719C2×C3×D3—61no—
720C2×C3×D3—61no—
721C2×C3×D3—61no—
722C2×C3×D3—61no—
723C2×C3×D3—61no—
724C2×C3×D3—121no—
725C2×C3×D3—121no—
726C2×C3×D3—121no—
727C2×C3×D3—121no—
728C2×C3×D3—121no—
729C2×C3×D3—121no—
730C2×C3×D3—121no—
731C2×C3×D3—121no—
732C2×C3×D3—121no—
733C2×C3×D3—124no—
734C2×C3×D3—124no—
735C2×C3×D3—128no—
736D32—124no—
737D32—124no—
738D32—124no—
739C32×C4—61no—
740C32×C4—61no—
741C32×C4—61no—
742C32×C4—61no—
743C32×C4—61no—
744C3⋊Dic3—21no—
745C3⋊Dic3—61no—
746C3⋊Dic3—61no—
747C3⋊Dic3—61no—
748C3⋊Dic3—61no—
749C3⋊Dic3—61no—
750C3⋊Dic3—61no—
751C3⋊Dic3—121no—
752C3⋊Dic3—121no—
753C3⋊Dic3—121no—
754C3⋊Dic3—121no—
755C3⋊Dic3—121no—
756C3⋊Dic3—121no—
757C3⋊Dic3—241no—
758C3⋊Dic3—241no—
759C3⋊Dic3C2×#6712yes—
760C3×Dic3—22no—
761C3×Dic3—21no—
762C3×Dic3—21no—
763C3×Dic3—21no—
764C3×Dic3—21no—
765C3×Dic3—21no—
766C3×Dic3—21no—
767C3×Dic3—21no—
768C3×Dic3—21no—
769C3×Dic3—21no—
770C3×Dic3—21no—
771C3×Dic3—32no—
772C3×Dic3—32no—
773C3×Dic3—41no—
774C3×Dic3—41no—
775C3×Dic3—41no—
776C3×Dic3—41no—
777C3×Dic3—62no—
778C3×Dic3—61no—
779C3×Dic3—61no—
780C3×Dic3—121no—
781C2×#41—91no—
782C22×D4—271no—
783#124—271no—
784#123—271no—
785#123—271no—
786C22⋊Q8—271no—
787#121—91no—
788#121—271no—
789#121—271no—
790#120—271no—
791#120—271no—
792C4×D4—271no—
793C4×D4—271no—
794C2×C22⋊C4—91no—
795C2×C22⋊C4—271no—
796C33#54611yescharacteristic, complemented, Sylow
797C23×C3—21no—
798C23×C3—21no—
799C23×C3—21no—
800C23×C3—31no—
801C23×C3—31no—
802C23×C3—41no—
803C23×C3—61no—
804C23×C3—91no—
805C23×C3—91no—
806C23×C3—91no—
807C23×C3—91no—
808C23×C3—182no—
809C23×C3—182no—
810C23×C3—361no—
811C23×C3C2×D3211yescharacteristic
812C23×C3C2×D3211yescharacteristic
813C23×C3C2×D3211yescharacteristic
814C22×D3—31no—
815C22×D3—31no—
816C22×D3—31no—
817C22×D3—31no—
818C22×D3—31no—
819C22×D3—31no—
820C22×D3—31no—
821C22×D3—31no—
822C22×D3—61no—
823C22×D3—61no—
824C22×D3—61no—
825C22×D3—61no—
826C22×D3—62no—
827C22×D3—62no—
828C22×D3—62no—
829C22×D3—62no—
830C22×D3—122no—
831C22×D3—122no—
832C22×D3—121no—
833C22×D3—121no—
834C22×D3—122no—
835C22×D3—182no—
836C22×D3—182no—
837C22×D3—182no—
838C22×D3—182no—
839C22×D3—182no—
840C22×D3—182no—
841C22×D3—361no—
842C22×D3—361no—
843C22×D3—361no—
844C22×D3C2×D3211yescharacteristic
845C3×Q8—182no—
846C3×D4—62no—
847C3×D4—62no—
848C3×D4—94no—
849C3×D4—122no—
850C3×D4—182no—
851C3×D4—182no—
852C3×D4—361no—
853C2×C3×C4—31no—
854C2×C3×C4—31no—
855C2×C3×C4—31no—
856C2×C3×C4—31no—
857C2×C3×C4—31no—
858C2×C3×C4—31no—
859C2×C3×C4—31no—
860C2×C3×C4—31no—
861C2×C3×C4—31no—
862C2×C3×C4—31no—
863C2×C3×C4—61no—
864C2×C3×C4—61no—
865C2×C3×C4—61no—
866C2×C3×C4—61no—
867C2×C3×C4—61no—
868C2×C3×C4—62no—
869C2×C3×C4—62no—
870C2×C3×C4—91no—
871C2×C3×C4—91no—
872C2×C3×C4—122no—
873C2×C3×C4—121no—
874C2×C3×C4—121no—
875C2×C3×C4—122no—
876C2×C3×C4—182no—
877C2×C3×C4—182no—
878#67—22no—
879#67—34no—
880#67—34no—
881#67—64no—
882#67—62no—
883#67—62no—
884#67—62no—
885#67—122no—
886#67—121no—
887#67—182no—
888#67—182no—
889#67—182no—
890#67—182no—
891#67—182no—
892#67—182no—
893#67—182no—
894#67—362no—
895#67—361no—
896#67—361no—
897#67—361no—
898#67—362no—
899C2×Dic3—22no—
900C2×Dic3—31no—
901C2×Dic3—31no—
902C2×Dic3—31no—
903C2×Dic3—31no—
904C2×Dic3—41no—
905C2×Dic3—61no—
906C2×Dic3—61no—
907C2×Dic3—62no—
908C2×Dic3—91no—
909C2×Dic3—91no—
910C2×Dic3—91no—
911C2×Dic3—91no—
912C2×Dic3—91no—
913C2×Dic3—91no—
914C2×Dic3—181no—
915C2×Dic3—181no—
916C2×Dic3—181no—
917C2×Dic3—181no—
918C2×Dic3—181no—
919C2×Dic3—181no—
920C2×Dic3—182no—
921C2×Dic3—361no—
922C2×Dic3—361no—
923C2×Dic3—361no—
924C2×Dic3C2×D3211yescharacteristic
925C2×Dic3C2×D3211yescharacteristic
926C2×Dic3C2×D3211yescharacteristic
927C2×Dic3C2×D3211yescharacteristic
928C2×Dic3C2×D3211yescharacteristic
929D12—62no—
930D12—121no—
931D12—182no—
932D12—182no—
933C4×D3—62no—
934C4×D3—62no—
935C4×D3—62no—
936C4×D3—182no—
937C4×D3—182no—
938C4×D3—361no—
939C4×D3—361no—
940C4×D3—362no—
941Dic6—62no—
942Dic6—62no—
943C2×C32—22no—
944C2×C32—22no—
945C2×C32—22no—
946C2×C32—21no—
947C2×C32—21no—
948C2×C32—21no—
949C2×C32—21no—
950C2×C32—21no—
951C2×C32—21no—
952C2×C32—21no—
953C2×C32—21no—
954C2×C32—21no—
955C2×C32—41no—
956C2×C32—41no—
957C2×C32—41no—
958C2×C32—42no—
959C2×C32—42no—
960C2×C32—42no—
961C2×C32—82no—
962C2×C32—121no—
963C2×C32C2×#23511yescharacteristic
964C2×C32C2×D3×D411yescharacteristic
965C2×C32C2×D3×D411yescharacteristic
966C2×C32#100411yescharacteristic
967C2×C32#100411yescharacteristic
968C2×C32D3×#4111yescharacteristic
969C2×C32D3×#4111yescharacteristic
970C2×C32#100911yescharacteristic
971C2×C32C22×#6711yescharacteristic
972C3⋊D3—22no—
973C3⋊D3—22no—
974C3⋊D3—41no—
975C3⋊D3—41no—
976C3×D3—41no—
977C3×D3—41no—
978C3×D3—62no—
979C3×D3—62no—
980C3×D3—62no—
981C3×D3—62no—
982C3×D3—81no—
983C3×D3—122no—
984C3×D3—122no—
985C3×D3—122no—
986C3×D3—121no—
987C3×D3—121no—
988C3×D3—121no—
989C3×D3—121no—
990C3×D3—241no—
991C24—91no—
992C24—271no—
993#41—184no—
994C2×Q8—91no—
995C2×D4—31no—
996C2×D4—91no—
997C2×D4—91no—
998C2×D4—91no—
999C2×D4—91no—
1000C2×D4—271no—
1001C2×D4—271no—
1002C2×D4—271no—
1003C2×D4—271no—
1004C2×D4—544no—
1005C22×C4—31no—
1006C22×C4—31no—
1007C22×C4—91no—
1008C22×C4—91no—
1009C22×C4—271no—
1010C22×C4—271no—
1011C4⋊C4—91no—
1012C4⋊C4—271no—
1013C4⋊C4—271no—
1014C4⋊C4—271no—
1015C22⋊C4—91no—
1016C22⋊C4—91no—
1017C22⋊C4—91no—
1018C22⋊C4—91no—
1019C22⋊C4—91no—
1020C22⋊C4—91no—
1021C22⋊C4—271no—
1022C22⋊C4—271no—
1023C22⋊C4—271no—
1024C22⋊C4—271no—
1025C22⋊C4—271no—
1026C22⋊C4—271no—
1027C42—271no—
1028C22×C3—21no—
1029C22×C3—21no—
1030C22×C3—21no—
1031C22×C3—21no—
1032C22×C3—21no—
1033C22×C3—21no—
1034C22×C3—21no—
1035C22×C3—21no—
1036C22×C3—21no—
1037C22×C3—22no—
1038C22×C3—22no—
1039C22×C3—22no—
1040C22×C3—41no—
1041C22×C3—41no—
1042C22×C3—41no—
1043C22×C3—41no—
1044C22×C3—41no—
1045C22×C3—41no—
1046C22×C3—41no—
1047C22×C3—42no—
1048C22×C3—61no—
1049C22×C3—61no—
1050C22×C3—61no—
1051C22×C3—61no—
1052C22×C3—61no—
1053C22×C3—61no—
1054C22×C3—81no—
1055C22×C3—81no—
1056C22×C3—92no—
1057C22×C3—92no—
1058C22×C3—121no—
1059C22×C3—121no—
1060C22×C3—121no—
1061C22×C3—181no—
1062C22×C3—181no—
1063C22×C3—181no—
1064C22×C3—181no—
1065C22×C3—181no—
1066C22×C3—181no—
1067C22×C3—181no—
1068C22×C3—181no—
1069C22×C3—181no—
1070C22×C3—181no—
1071C22×C3—364no—
1072C22×C3#380212yes—
1073C22×C3D3×#6712yes—
1074C22×C3D3×#6712yes—
1075C22×C3C22×D3211yescharacteristic
1076C22×C3C22×D3211yescharacteristic
1077C22×C3C22×D3211yescharacteristic
1078C2×D3—21no—
1079C2×D3—21no—
1080C2×D3—21no—
1081C2×D3—32no—
1082C2×D3—32no—
1083C2×D3—32no—
1084C2×D3—32no—
1085C2×D3—62no—
1086C2×D3—62no—
1087C2×D3—61no—
1088C2×D3—61no—
1089C2×D3—61no—
1090C2×D3—61no—
1091C2×D3—61no—
1092C2×D3—61no—
1093C2×D3—61no—
1094C2×D3—61no—
1095C2×D3—62no—
1096C2×D3—61no—
1097C2×D3—61no—
1098C2×D3—61no—
1099C2×D3—61no—
1100C2×D3—61no—
1101C2×D3—61no—
1102C2×D3—61no—
1103C2×D3—61no—
1104C2×D3—61no—
1105C2×D3—61no—
1106C2×D3—61no—
1107C2×D3—61no—
1108C2×D3—121no—
1109C2×D3—121no—
1110C2×D3—121no—
1111C2×D3—121no—
1112C2×D3—121no—
1113C2×D3—121no—
1114C2×D3—121no—
1115C2×D3—121no—
1116C2×D3—121no—
1117C2×D3—124no—
1118C2×D3—124no—
1119C2×D3—128no—
1120C2×D3—364no—
1121C2×D3—364no—
1122C2×D3—364no—
1123C3×C4—62no—
1124C3×C4—61no—
1125C3×C4—61no—
1126C3×C4—61no—
1127C3×C4—61no—
1128C3×C4—61no—
1129C3×C4—61no—
1130C3×C4—61no—
1131C3×C4—61no—
1132C3×C4—61no—
1133C3×C4—61no—
1134C3×C4—92no—
1135C3×C4—121no—
1136C3×C4—121no—
1137C3×C4—121no—
1138C3×C4—121no—
1139C3×C4—181no—
1140Dic3—21no—
1141Dic3—21no—
1142Dic3—21no—
1143Dic3—21no—
1144Dic3—21no—
1145Dic3—32no—
1146Dic3—32no—
1147Dic3—62no—
1148Dic3—61no—
1149Dic3—61no—
1150Dic3—121no—
1151Dic3—181no—
1152Dic3—181no—
1153Dic3—181no—
1154Dic3—181no—
1155Dic3—181no—
1156Dic3—181no—
1157Dic3—361no—
1158Dic3—361no—
1159Dic3—361no—
1160Dic3—361no—
1161Dic3—361no—
1162Dic3—361no—
1163Dic3—721no—
1164Dic3—721no—
1165C32—21no—
1166C32—21no—
1167C32—21no—
1168C32—41no—
1169C32#549011yescharacteristic, complemented
1170C32#561011yescharacteristic, complemented
1171C32#582911yescharacteristic, complemented
1172C23—31no—
1173C23—91no—
1174C23—91no—
1175C23—91no—
1176C23—91no—
1177C23—182no—
1178C23—182no—
1179C23—361no—
1180C23—542no—
1181C23—542no—
1182C23—1081no—
1183C23D3311yescharacteristic
1184Q8—182no—
1185D4—62no—
1186D4—94no—
1187D4—182no—
1188D4—182no—
1189D4—361no—
1190D4—542no—
1191D4—542no—
1192D4—542no—
1193D4—1081no—
1194C2×C4—31no—
1195C2×C4—31no—
1196C2×C4—31no—
1197C2×C4—31no—
1198C2×C4—31no—
1199C2×C4—62no—
1200C2×C4—91no—
1201C2×C4—91no—
1202C2×C4—121no—
1203C2×C4—182no—
1204C2×C4—182no—
1205C2×C4—271no—
1206C2×C4—271no—
1207C2×C4—542no—
1208C2×C4—1081no—
1209C2×C3—22no—
1210C2×C3—22no—
1211C2×C3—22no—
1212C2×C3—21no—
1213C2×C3—21no—
1214C2×C3—21no—
1215C2×C3—21no—
1216C2×C3—21no—
1217C2×C3—21no—
1218C2×C3—21no—
1219C2×C3—21no—
1220C2×C3—21no—
1221C2×C3—42no—
1222C2×C3—42no—
1223C2×C3—42no—
1224C2×C3—41no—
1225C2×C3—41no—
1226C2×C3—41no—
1227C2×C3—82no—
1228C2×C3—121no—
1229C2×C3—121no—
1230C2×C3—182no—
1231C2×C3—182no—
1232C2×C3—241no—
1233C2×C3—361no—
1234C2×C3—361no—
1235C2×C3C2×#380211yescharacteristic
1236C2×C3D3×#23511yescharacteristic
1237C2×C3D3×#23511yescharacteristic
1238C2×C3#6430711yescharacteristic
1239C2×C3#6431211yescharacteristic
1240C2×C3#6431411yescharacteristic
1241C2×C3C2×D3×#6711yescharacteristic
1242C2×C3C2×D3×#6711yescharacteristic
1243C2×C3#6433011yescharacteristic
1244D3—41no—
1245D3—62no—
1246D3—62no—
1247D3—62no—
1248D3—62no—
1249D3—122no—
1250D3—122no—
1251D3—122no—
1252D3—121no—
1253D3—121no—
1254D3—121no—
1255D3—121no—
1256D3—241no—
1257C22—21no—
1258C22—21no—
1259C22—61no—
1260C22—61no—
1261C22—61no—
1262C22—92no—
1263C22—92no—
1264C22—181no—
1265C22—181no—
1266C22—181no—
1267C22—181no—
1268C22—181no—
1269C22—181no—
1270C22—181no—
1271C22—181no—
1272C22—181no—
1273C22—181no—
1274C22—364no—
1275C22—1084no—
1276C22#8895312yes—
1277C22C2×D3311yescharacteristic
1278C4—61no—
1279C4—61no—
1280C4—61no—
1281C4—61no—
1282C4—61no—
1283C4—92no—
1284C4—181no—
1285C4—541no—
1286C4—541no—
1287C3—21no—
1288C3—21no—
1289C3—21no—
1290C3—41no—
1291C3#1059506511yescharacteristic, complemented
1292C3#1059508311yescharacteristic, complemented
1293C3#1059530511yescharacteristic, complemented
1294C2—22no—
1295C2—121no—
1296C2—182no—
1297C2—182no—
1298C2—361no—
1299C2—361no—
1300C2#1172441011yescharacteristic
1301C2#1172441811yescharacteristic
1302C2C2×#8895311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#89049C2semidirect
2. C2×C3×#3804C2semidirect
3. #11723634C2semidirect
4. Dic3×#638C2semidirect
5. #11723605C2semidirect
6. C3×#63978C2semidirect
7. C2×C3×#3722C2semidirect
8. #11723007C2semidirect
9. #11722995C2semidirect
10. #11722979C2semidirect
11. #11722967C2semidirect
12. #11722960C2semidirect
13. #11722951C2semidirect
14. #11722936C2semidirect
15. #11722905C2semidirect
23. C2×C32×#67C22semidirect
24. C22×C32×Dic3C22semidirect
25. C22×C32×Dic3C22semidirect
31. C2×#6290C22semidirect
32. C2×Dic3×C3⋊D3C22semidirect
33. C2×C3×#627C22semidirect
34. C2×C3×#626C22semidirect
35. C2×C3×#626C22semidirect
36. C2×C3×#624C22semidirect
38. C2×C3×D3×Dic3C22semidirect
39. #88864C22semidirect
40. #88807C22semidirect
41. #88806C22semidirect
42. #88806C22semidirect
44. #88803C22semidirect
45. #88803C22semidirect
46. #88803C22semidirect
47. #88803C22semidirect
48. Dic3×C3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
52. C3×#3722C22semidirect
53. C3×#3722C22semidirect
54. C3×#3722C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
61. C2×#3804D3semidirect
71. #63978D3semidirect
79. C2×#3722D3semidirect
119. C3×#638D4semidirect
168. C2×C3×#67C2×D3semidirect
169. C2×C3×#67C2×D3semidirect
173. C22×C3×Dic3C2×D3semidirect
174. C22×C3×Dic3C2×D3semidirect
175. C22×C3×Dic3C2×D3semidirect
176. C22×C3×Dic3C2×D3semidirect
189. C2×#627C2×D3semidirect
194. C2×#626C2×D3semidirect
195. C2×#626C2×D3semidirect
205. C2×#624C2×D3semidirect
212. C2×D3×Dic3C2×D3semidirect
252. Dic3⋊Dic3C2×D3semidirect
255. #3722C2×D3semidirect
256. #3722C2×D3semidirect
257. #3722C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
293. C2×C3×C3⋊D3#41semidirect
414. #638#67semidirect
556. C2×#67D32semidirect
560. C22×Dic3D32semidirect
561. C22×Dic3D32semidirect
686. C2×C3⋊D3#235semidirect
796. C33#546semidirect
1169. C32#5490semidirect
1170. C32#5610semidirect
1171. C32#5829semidirect
1291. C3#10595065semidirect
1292. C3#10595083semidirect
1293. C3#10595305semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
C2×C3×#38042
#117236342
Dic3×#6382
#117236052
C3×#639782
C2×C3×#37222
#117230072
#117229952
#117229792
#117229672
#117229602
#117229512
#117229362
#117229052
#105953053
#105950833
#105950653