Finite Group Databasebeta

← #13172110

Subgroups — #13172110

Order 1728.

1710 conjugacy classes of subgroups.

The subgroup lattice has 1308 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#11723637C211yesmaximal, characteristic, complemented
4#11723626C211yesmaximal, characteristic, complemented
5C2×#88803C211yesmaximal, characteristic, complemented
6C3×#63981C211yesmaximal, characteristic, complemented
7C3×#63966C211yesmaximal, characteristic, complemented
8#11723007C211yesmaximal, characteristic, complemented
9#11722995C211yesmaximal, characteristic, complemented
10#11722979C211yesmaximal, characteristic, complemented
11#11722962C211yesmaximal, characteristic, complemented
12#11722960C211yesmaximal, characteristic, complemented
13#11722951C211yesmaximal, characteristic, complemented
14#11722927C211yesmaximal, characteristic, complemented
15#11722905C211yesmaximal, characteristic, complemented
16#10595304—31nomaximal
17#10595068—31nomaximal
18#10594294—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×#1113C2211yescharacteristic
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic, complemented
25C22×C32×Dic3C2211yescharacteristic, complemented
26#89049—24no—
27C2×#6295C2211yescharacteristic
28C2×#6295C2211yescharacteristic
29C2×#6294C2211yescharacteristic
30C2×#6290C2211yescharacteristic, complemented
31C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
32C2×C3×#627C2211yescharacteristic, complemented
33C2×C3×#626C2211yescharacteristic
34C2×C3×#626C2211yescharacteristic, complemented
35C2×C3×#626C2211yescharacteristic, complemented
36C2×C3×#624C2211yescharacteristic, complemented
37C3×#3804—24no—
38C2×C3×D3×Dic3C2211yescharacteristic, complemented
39C32×#217C2211yescharacteristic, complemented
40#88807C2211yescharacteristic, complemented
41#88806C2211yescharacteristic, complemented
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44#88803C2211yescharacteristic, complemented
45#88803C2211yescharacteristic, complemented
46#88803C2211yescharacteristic, complemented
47#88803C2211yescharacteristic, complemented
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49Dic3×C3⋊Dic3C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic
53C3×#3722C2211yescharacteristic, complemented
54C3×#3722C2211yescharacteristic, complemented
55C3×#3722C2211yescharacteristic, complemented
56C2×C3×#237—31no—
57C2×C3×#235—31no—
58C2×#3811—31no—
59C2×D3×#67—31no—
60C2×D3×#67—31no—
61C2×#3804D311yescharacteristic, complemented
62#64148—31no—
63C2×#3752—31no—
64#64090—31no—
65C3×#937—31no—
66C3×#929—31no—
67C3×#886—31no—
68C3×#882—31no—
69#63983—31no—
70#63981D311yescharacteristic, complemented
71#63980—31no—
72#63980—31no—
73#63980—61no—
74#63978—31no—
75#67⋊Dic3—31no—
76#67⋊Dic3—31no—
77#67⋊Dic3—61no—
78Dic3×#67—31no—
79#63970—31no—
80#63966D311yescharacteristic, complemented
81C2×(C2×D3)⋊Dic3—31no—
82C2×(C2×D3)⋊Dic3—31no—
83C2×(C2×D3)⋊Dic3—61no—
84#63922—31no—
85#63922—31no—
86#63921—31no—
87D3×(C2×D3)⋊C4—31no—
88D3×(C2×D3)⋊C4—31no—
89#63916—31no—
90#63915—31no—
91#63907—31no—
92#63907—31no—
93#63906—31no—
94#63905—31no—
95#63904—31no—
96#63899—31no—
97#63898—31no—
98#63888—31no—
99#63887—31no—
100#63886—31no—
101#63885—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)—41no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
119C3×#638—22no—
120C3×#638D414yescomplemented
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C32×#67—22no—
124C2×C32×Dic3—22no—
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—41no—
134Dic3×C3⋊D3—41no—
135C3×#627—22no—
136C3×#626—22no—
137C3×#626—22no—
138C3×#626—41no—
139C3×#624—22no—
140C3×D3×Dic3—22no—
141#5829—91no—
142#5654—91no—
143#5591—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—
153C2×#638—31no—
154C2×#638C2×D311yescharacteristic
155C2×#638C2×D311yescharacteristic
156C22×C3⋊Dic3—31no—
157C22×C3⋊Dic3—31no—
158C22×C3⋊Dic3—31no—
159C22×C3⋊Dic3—61no—
160C22×C3⋊Dic3—61no—
161C22×C3⋊Dic3—61no—
162C22×C3⋊Dic3—121no—
163C2×C4×C3⋊D3—31no—
164C2×C3×#67—21no—
165C2×C3×#67—31no—
166C2×C3×#67—31no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—61no—
173C2×C3×#67—61no—
174C2×C3×#67C2×D311yescharacteristic, complemented
175C2×C3×#67C2×D311yescharacteristic, complemented
176C22×C3×Dic3—21no—
177C22×C3×Dic3—31no—
178C22×C3×Dic3C2×D311yescharacteristic, complemented
179C22×C3×Dic3C2×D311yescharacteristic, complemented
180C3×#237—64no—
181C3×#235—64no—
182C2×C3×D12—31no—
183C2×C3×D12—31no—
184C2×C3×D12—31no—
185C2×C3×C4×D3—31no—
186C2×C3×C4×D3—31no—
187C2×C3×C4×D3—31no—
188C2×C3×Dic6—31no—
189C2×C3×Dic6—31no—
190#3811—64no—
191D3×#67—64no—
192D3×#67—64no—
193C2×#627C2×D311yescharacteristic, complemented
194C2×#626—31no—
195C2×#626—31no—
196C2×#626—31no—
197C2×#626—31no—
198C2×#626C2×D311yescharacteristic
199C2×#626C2×D311yescharacteristic, complemented
200C2×#626C2×D311yescharacteristic, complemented
201C2×#625—31no—
202C2×#625—31no—
203C2×#625—31no—
204C2×#625—31no—
205C2×#625—61no—
206C2×#624—31no—
207C2×#624C2×D311yescharacteristic, complemented
208#3804—24no—
209C2×D3×Dic3—31no—
210C2×D3×Dic3—31no—
211C2×D3×Dic3—31no—
212C2×D3×Dic3—31no—
213C2×D3×Dic3—61no—
214C2×D3×Dic3C2×D311yescharacteristic, complemented
215C32×C22⋊C4—31no—
216#3757—31no—
217#3752—31no—
218#3752—31no—
219#3752—31no—
220#3752—31no—
221#3752—31no—
222#3752—31no—
223#3750—31no—
224#3750—31no—
225C4×C3⋊Dic3—31no—
226C3×#217—21no—
227C3×#217C2×D311yescharacteristic, complemented
228C3×#217C2×D311yescharacteristic, complemented
229C3×(C2×D3)⋊C4—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×C4⋊Dic3—31no—
238C3×C4⋊Dic3—31no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—31no—
241#3724—31no—
242#3724—31no—
243#3724—61no—
244Dic3⋊Dic3—31no—
245Dic3⋊Dic3—31no—
246Dic3⋊Dic3—61no—
247Dic3⋊Dic3C2×D311yescharacteristic, complemented
248Dic3⋊Dic3C2×D311yescharacteristic, complemented
249#3722C2×D311yescharacteristic
250#3722C2×D311yescharacteristic, complemented
251#3722C2×D311yescharacteristic, complemented
252#3722C2×D311yescharacteristic, complemented
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—31no—
257(C2×D3)⋊Dic3—31no—
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—61no—
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)⋊Dic3—61no—
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×#123—91no—
314C3×#120—91no—
315C2×#217—91no—
316#947—91no—
317#946—91no—
318#939—91no—
319#939—91no—
320#939—91no—
321#939—91no—
322#939—91no—
323#939—181no—
324#938—91no—
325#937—31no—
326#937—91no—
327#937—91no—
328D4×Dic3—91no—
329D4×Dic3—91no—
330#930—91no—
331#929—31no—
332#929—91no—
333C4×#67—91no—
334C2×(C2×D3)⋊C4—91no—
335C2×(C2×D3)⋊C4—91no—
336C2×(C2×D3)⋊C4—91no—
337C2×(C2×D3)⋊C4—181no—
338#896—91no—
339#895—91no—
340#894—91no—
341#893—91no—
342#886—31no—
343#885—91no—
344#885—91no—
345#884—91no—
346#883—91no—
347#882—31no—
348#882—91no—
349#67⋊C4—91no—
350#67⋊C4—91no—
351#67⋊C4—181no—
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—64no—
386C22×C3×D3—62no—
387C22×C3×D3—62no—
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—
410#638—22no—
411#638—121no—
412#638#6714yescomplemented
413C2×C3⋊Dic3—31no—
414C2×C3⋊Dic3—31no—
415C2×C3⋊Dic3—31no—
416C2×C3⋊Dic3—31no—
417C2×C3⋊Dic3—31no—
418C2×C3⋊Dic3—31no—
419C2×C3⋊Dic3—61no—
420C2×C3⋊Dic3—61no—
421C2×C3⋊Dic3—61no—
422C2×C3⋊Dic3—61no—
423C2×C3⋊Dic3—61no—
424C2×C3⋊Dic3—61no—
425C2×C3⋊Dic3—121no—
426C2×C3⋊Dic3—121no—
427C2×C3⋊Dic3—121no—
428C2×C3⋊Dic3—121no—
429C2×C3⋊Dic3—121no—
430C2×C3⋊Dic3—122no—
431C2×C3⋊Dic3—122no—
432C2×C3⋊Dic3—122no—
433C2×C3⋊Dic3—124no—
434C2×C3⋊Dic3C22×D311yescharacteristic
435C2×C3⋊Dic3C22×D311yescharacteristic
436C4×C3⋊D3—121no—
437C3×#67—22no—
438C3×#67—22no—
439C3×#67—34no—
440C3×#67—34no—
441C3×#67—42no—
442C3×#67—64no—
443C3×#67—62no—
444C3×#67—62no—
445C3×#67—62no—
446C3×#67—62no—
447C3×#67—122no—
448C3×#67—121no—
449C2×C3×Dic3—22no—
450C2×C3×Dic3—22no—
451C2×C3×Dic3—21no—
452C2×C3×Dic3—21no—
453C2×C3×Dic3—21no—
454C2×C3×Dic3—21no—
455C2×C3×Dic3—21no—
456C2×C3×Dic3—31no—
457C2×C3×Dic3—31no—
458C2×C3×Dic3—31no—
459C2×C3×Dic3—31no—
460C2×C3×Dic3—42no—
461C2×C3×Dic3—61no—
462C2×C3×Dic3—61no—
463C2×C3×Dic3—62no—
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
471C2×C3×Dic3C22×D311yescharacteristic
472C2×C3×Dic3C22×D311yescharacteristic
473C2×C3×Dic3C22×D311yescharacteristic
474C3×D12—62no—
475C3×D12—62no—
476C3×D12—121no—
477C3×C4×D3—62no—
478C3×C4×D3—62no—
479C3×C4×D3—62no—
480C3×Dic6—62no—
481C3×Dic6—62no—
482#627—22no—
483#626—22no—
484#626—22no—
485#626—41no—
486#626—62no—
487#626—62no—
488#626—62no—
489#626—62no—
490#625—62no—
491#625—62no—
492#625—121no—
493#625—121no—
494#625—122no—
495#624—22no—
496#624—62no—
497D3×Dic3—22no—
498D3×Dic3—62no—
499D3×Dic3—62no—
500D3×Dic3—121no—
501D3×Dic3—121no—
502D3×Dic3—122no—
503#546—271noSylow
504C2×C33—22no—
505C2×C33C22×D411yescharacteristic
506C2×C33C2×#4111yescharacteristic
507C2×C33H(5,𝔽2)11yescharacteristic
508C3×C3⋊D3—22no—
509C3×C3⋊D3—22no—
510C3×C3⋊D3—41no—
511C3×C3⋊D3—41no—
512C32×D3—41no—
513C24×C3—91no—
514C23×D3—31no—
515C23×D3—31no—
516C23×D3—61no—
517C23×D3—91no—
518C23×D3—91no—
519C23×D3—91no—
520C3×#41—184no—
521C2×C3×Q8—91no—
522C2×C3×D4—31no—
523C2×C3×D4—31no—
524C2×C3×D4—61no—
525C2×C3×D4—91no—
526C2×C3×D4—91no—
527C2×C3×D4—91no—
528C2×C3×D4—91no—
529C2×C3×D4—91no—
530C22×C3×C4—31no—
531C22×C3×C4—31no—
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—31no—
542C2×#67—61no—
543C2×#67—61no—
544C2×#67—91no—
545C2×#67—91no—
546C2×#67—91no—
547C2×#67—91no—
548C2×#67—91no—
549C2×#67—91no—
550C2×#67—91no—
551C2×#67—181no—
552C2×#67—184no—
553C2×#67D3211yescharacteristic, complemented
554C22×Dic3—31no—
555C22×Dic3—91no—
556C22×Dic3—91no—
557C22×Dic3—91no—
558C22×Dic3—91no—
559C22×Dic3—91no—
560C22×Dic3—181no—
561C22×Dic3—181no—
562C22×Dic3—181no—
563C22×Dic3—361no—
564C22×Dic3D3211yescharacteristic, complemented
565#237—64no—
566D3×D4—184no—
567D3×D4—184no—
568#235—64no—
569C2×D12—31no—
570C2×D12—31no—
571C2×D12—31no—
572C2×D12—91no—
573C2×D12—91no—
574C2×C4×D3—31no—
575C2×C4×D3—31no—
576C2×C4×D3—31no—
577C2×C4×D3—91no—
578C2×C4×D3—91no—
579C2×C4×D3—91no—
580C2×C4×D3—91no—
581C2×C4×D3—181no—
582C2×Dic6—31no—
583C2×Dic6—31no—
584C3×C4⋊C4—91no—
585C3×C4⋊C4—91no—
586C3×C22⋊C4—31no—
587C3×C22⋊C4—31no—
588C3×C22⋊C4—61no—
589C3×C22⋊C4—91no—
590C3×C22⋊C4—91no—
591C3×C22⋊C4—91no—
592C3×C22⋊C4—91no—
593#217—91no—
594#217—91no—
595#217—91no—
596#217—91no—
597#217—91no—
598#217—91no—
599#217—91no—
600#217—91no—
601#217—181no—
602#217D3211yescharacteristic, complemented
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—91no—
622(C2×D3)⋊C4—91no—
623(C2×D3)⋊C4—91no—
624(C2×D3)⋊C4—181no—
625(C2×D3)⋊C4—181no—
626(C2×D3)⋊C4—181no—
627(C2×D3)⋊C4—181no—
628(C2×D3)⋊C4—181no—
629(C2×D3)⋊C4—181no—
630C4⋊Dic3—31no—
631C4⋊Dic3—31no—
632C4⋊Dic3—91no—
633Dic3⋊C4—31no—
634Dic3⋊C4—31no—
635Dic3⋊C4—91no—
636Dic3⋊C4—91no—
637Dic3⋊C4—91no—
638Dic3⋊C4—91no—
639Dic3⋊C4—91no—
640Dic3⋊C4—181no—
641Dic3⋊C4—181no—
642C4×Dic3—91no—
643C4×Dic3—91no—
644C4×Dic3—91no—
645C4×Dic3—181no—
646C22×C32—21no—
647C22×C32—21no—
648C22×C32—22no—
649C22×C32—22no—
650C22×C32—21no—
651C22×C32—21no—
652C22×C32—21no—
653C22×C32—21no—
654C22×C32—21no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—22no—
658C22×C32—22no—
659C22×C32—22no—
660C22×C32—42no—
661C22×C32—41no—
662C22×C32—41no—
663C22×C32—41no—
664C22×C32—41no—
665C22×C32—41no—
666C22×C32—42no—
667C22×C32—42no—
668C22×C32—61no—
669C22×C32—61no—
670C22×C32—61no—
671C22×C32D3×D412yes—
672C22×C32D3×D412yes—
673C22×C32C2×#6712yes—
674C22×C32C23×D311yescharacteristic
675C22×C32C23×D311yescharacteristic
676C22×C32C23×D311yescharacteristic
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—21no—
686C2×C3⋊D3—21no—
687C2×C3⋊D3—44no—
688C2×C3⋊D3#23712yescomplemented
689C2×C3⋊D3C2×#6712yes—
690C2×C3×D3—21no—
691C2×C3×D3—21no—
692C2×C3×D3—21no—
693C2×C3×D3—21no—
694C2×C3×D3—21no—
695C2×C3×D3—21no—
696C2×C3×D3—32no—
697C2×C3×D3—32no—
698C2×C3×D3—32no—
699C2×C3×D3—32no—
700C2×C3×D3—41no—
701C2×C3×D3—41no—
702C2×C3×D3—41no—
703C2×C3×D3—62no—
704C2×C3×D3—62no—
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—61no—
712C2×C3×D3—61no—
713C2×C3×D3—62no—
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—61no—
725C2×C3×D3—61no—
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—121no—
734C2×C3×D3—121no—
735C2×C3×D3—124no—
736C2×C3×D3—124no—
737C2×C3×D3—128no—
738D32—124no—
739D32—124no—
740D32—124no—
741C32×C4—61no—
742C32×C4—61no—
743C32×C4—61no—
744C32×C4—61no—
745C32×C4—61no—
746C3⋊Dic3—21no—
747C3⋊Dic3—61no—
748C3⋊Dic3—61no—
749C3⋊Dic3—62no—
750C3⋊Dic3—62no—
751C3⋊Dic3—61no—
752C3⋊Dic3—61no—
753C3⋊Dic3—61no—
754C3⋊Dic3—61no—
755C3⋊Dic3—121no—
756C3⋊Dic3—121no—
757C3⋊Dic3—121no—
758C3⋊Dic3—121no—
759C3⋊Dic3—122no—
760C3⋊Dic3—122no—
761C3⋊Dic3C2×#6712yes—
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—21no—
772C3×Dic3—32no—
773C3×Dic3—32no—
774C3×Dic3—41no—
775C3×Dic3—41no—
776C3×Dic3—41no—
777C3×Dic3—41no—
778C3×Dic3—41no—
779C3×Dic3—62no—
780C3×Dic3—61no—
781C3×Dic3—61no—
782C3×Dic3—121no—
783C2×#41—91no—
784C22×D4—271no—
785#124—271no—
786#123—91no—
787#123—271no—
788C22⋊Q8—271no—
789#121—271no—
790#121—271no—
791#121—271no—
792#120—91no—
793#120—271no—
794C4×D4—271no—
795C4×D4—271no—
796C2×C22⋊C4—271no—
797C2×C22⋊C4—271no—
798C33#54611yescharacteristic, complemented, Sylow
799C23×C3—21no—
800C23×C3—21no—
801C23×C3—21no—
802C23×C3—31no—
803C23×C3—31no—
804C23×C3—41no—
805C23×C3—61no—
806C23×C3—91no—
807C23×C3—91no—
808C23×C3—91no—
809C23×C3—91no—
810C23×C3—182no—
811C23×C3—182no—
812C23×C3—361no—
813C23×C3C2×D3211yescharacteristic
814C23×C3C2×D3211yescharacteristic
815C23×C3C2×D3211yescharacteristic
816C22×D3—31no—
817C22×D3—31no—
818C22×D3—31no—
819C22×D3—31no—
820C22×D3—31no—
821C22×D3—31no—
822C22×D3—31no—
823C22×D3—31no—
824C22×D3—61no—
825C22×D3—61no—
826C22×D3—61no—
827C22×D3—61no—
828C22×D3—62no—
829C22×D3—62no—
830C22×D3—64no—
831C22×D3—62no—
832C22×D3—62no—
833C22×D3—122no—
834C22×D3—121no—
835C22×D3—121no—
836C22×D3—122no—
837C22×D3—182no—
838C22×D3—182no—
839C22×D3—182no—
840C22×D3—182no—
841C22×D3—182no—
842C22×D3—182no—
843C22×D3—361no—
844C22×D3—361no—
845C22×D3—361no—
846C22×D3C2×D3211yescharacteristic
847C3×Q8—182no—
848C3×D4—62no—
849C3×D4—62no—
850C3×D4—94no—
851C3×D4—122no—
852C3×D4—182no—
853C3×D4—182no—
854C3×D4—182no—
855C3×D4—361no—
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—31no—
864C2×C3×C4—31no—
865C2×C3×C4—31no—
866C2×C3×C4—61no—
867C2×C3×C4—61no—
868C2×C3×C4—61no—
869C2×C3×C4—61no—
870C2×C3×C4—61no—
871C2×C3×C4—62no—
872C2×C3×C4—62no—
873C2×C3×C4—91no—
874C2×C3×C4—91no—
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—62no—
886#67—122no—
887#67—121no—
888#67—182no—
889#67—182no—
890#67—182no—
891#67—182no—
892#67—361no—
893#67—361no—
894#67—361no—
895#67—362no—
896C2×Dic3—22no—
897C2×Dic3—31no—
898C2×Dic3—31no—
899C2×Dic3—31no—
900C2×Dic3—31no—
901C2×Dic3—61no—
902C2×Dic3—61no—
903C2×Dic3—62no—
904C2×Dic3—91no—
905C2×Dic3—91no—
906C2×Dic3—91no—
907C2×Dic3—91no—
908C2×Dic3—91no—
909C2×Dic3—91no—
910C2×Dic3—181no—
911C2×Dic3—181no—
912C2×Dic3—181no—
913C2×Dic3—181no—
914C2×Dic3—181no—
915C2×Dic3—181no—
916C2×Dic3—182no—
917C2×Dic3—361no—
918C2×Dic3—361no—
919C2×Dic3—361no—
920C2×Dic3—361no—
921C2×Dic3—361no—
922C2×Dic3—361no—
923C2×Dic3—362no—
924C2×Dic3—362no—
925C2×Dic3—362no—
926C2×Dic3—364no—
927C2×Dic3C2×D3211yescharacteristic
928C2×Dic3C2×D3211yescharacteristic
929C2×Dic3C2×D3211yescharacteristic
930C2×Dic3C2×D3211yescharacteristic
931C2×Dic3C2×D3211yescharacteristic
932D12—62no—
933D12—62no—
934D12—121no—
935D12—182no—
936D12—182no—
937C4×D3—62no—
938C4×D3—62no—
939C4×D3—62no—
940C4×D3—182no—
941C4×D3—182no—
942C4×D3—361no—
943C4×D3—361no—
944C4×D3—362no—
945Dic6—62no—
946Dic6—62no—
947C2×C32—22no—
948C2×C32—24no—
949C2×C32—22no—
950C2×C32—22no—
951C2×C32—21no—
952C2×C32—21no—
953C2×C32—21no—
954C2×C32—21no—
955C2×C32—21no—
956C2×C32—21no—
957C2×C32—21no—
958C2×C32—21no—
959C2×C32—21no—
960C2×C32—41no—
961C2×C32—41no—
962C2×C32—41no—
963C2×C32—42no—
964C2×C32—42no—
965C2×C32—44no—
966C2×C32—121no—
967C2×C32C2×D3×D411yescharacteristic
968C2×C32C2×D3×D411yescharacteristic
969C2×C32C2×#23711yescharacteristic
970C2×C32#100411yescharacteristic
971C2×C32D3×#4111yescharacteristic
972C2×C32D3×#4111yescharacteristic
973C2×C32#100911yescharacteristic
974C2×C32#100911yescharacteristic
975C2×C32C22×#6711yescharacteristic
976C3⋊D3—22no—
977C3⋊D3—22no—
978C3⋊D3—41no—
979C3⋊D3—41no—
980C3×D3—41no—
981C3×D3—41no—
982C3×D3—62no—
983C3×D3—62no—
984C3×D3—62no—
985C3×D3—62no—
986C3×D3—81no—
987C3×D3—122no—
988C3×D3—122no—
989C3×D3—122no—
990C3×D3—121no—
991C3×D3—121no—
992C3×D3—121no—
993C3×D3—121no—
994C3×D3—241no—
995C24—91no—
996C24—271no—
997#41—184no—
998C2×Q8—91no—
999C2×D4—31no—
1000C2×D4—91no—
1001C2×D4—91no—
1002C2×D4—91no—
1003C2×D4—91no—
1004C2×D4—91no—
1005C2×D4—271no—
1006C2×D4—271no—
1007C2×D4—271no—
1008C2×D4—544no—
1009C22×C4—31no—
1010C22×C4—91no—
1011C22×C4—91no—
1012C22×C4—271no—
1013C22×C4—271no—
1014C22×C4—271no—
1015C4⋊C4—91no—
1016C4⋊C4—91no—
1017C4⋊C4—271no—
1018C4⋊C4—271no—
1019C22⋊C4—31no—
1020C22⋊C4—91no—
1021C22⋊C4—91no—
1022C22⋊C4—91no—
1023C22⋊C4—91no—
1024C22⋊C4—271no—
1025C22⋊C4—271no—
1026C22⋊C4—271no—
1027C22⋊C4—271no—
1028C22⋊C4—271no—
1029C22⋊C4—271no—
1030C22⋊C4—271no—
1031C42—271no—
1032C22×C3—22no—
1033C22×C3—22no—
1034C22×C3—21no—
1035C22×C3—21no—
1036C22×C3—21no—
1037C22×C3—21no—
1038C22×C3—21no—
1039C22×C3—21no—
1040C22×C3—21no—
1041C22×C3—21no—
1042C22×C3—21no—
1043C22×C3—22no—
1044C22×C3—22no—
1045C22×C3—22no—
1046C22×C3—41no—
1047C22×C3—41no—
1048C22×C3—41no—
1049C22×C3—41no—
1050C22×C3—42no—
1051C22×C3—42no—
1052C22×C3—41no—
1053C22×C3—42no—
1054C22×C3—61no—
1055C22×C3—61no—
1056C22×C3—61no—
1057C22×C3—61no—
1058C22×C3—61no—
1059C22×C3—61no—
1060C22×C3—92no—
1061C22×C3—92no—
1062C22×C3—121no—
1063C22×C3—121no—
1064C22×C3—121no—
1065C22×C3—181no—
1066C22×C3—181no—
1067C22×C3—181no—
1068C22×C3—181no—
1069C22×C3—181no—
1070C22×C3—181no—
1071C22×C3—181no—
1072C22×C3—181no—
1073C22×C3—181no—
1074C22×C3—181no—
1075C22×C3—364no—
1076C22×C3#380212yes—
1077C22×C3D3×#6712yes—
1078C22×C3D3×#6712yes—
1079C22×C3C22×D3211yescharacteristic
1080C22×C3C22×D3211yescharacteristic
1081C22×C3C22×D3211yescharacteristic
1082C2×D3—21no—
1083C2×D3—21no—
1084C2×D3—21no—
1085C2×D3—32no—
1086C2×D3—32no—
1087C2×D3—32no—
1088C2×D3—32no—
1089C2×D3—62no—
1090C2×D3—62no—
1091C2×D3—61no—
1092C2×D3—61no—
1093C2×D3—61no—
1094C2×D3—61no—
1095C2×D3—61no—
1096C2×D3—61no—
1097C2×D3—61no—
1098C2×D3—61no—
1099C2×D3—62no—
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—61no—
1109C2×D3—61no—
1110C2×D3—61no—
1111C2×D3—61no—
1112C2×D3—121no—
1113C2×D3—121no—
1114C2×D3—121no—
1115C2×D3—121no—
1116C2×D3—121no—
1117C2×D3—121no—
1118C2×D3—121no—
1119C2×D3—121no—
1120C2×D3—121no—
1121C2×D3—124no—
1122C2×D3—124no—
1123C2×D3—128no—
1124C2×D3—364no—
1125C2×D3—364no—
1126C2×D3—364no—
1127C3×C4—61no—
1128C3×C4—61no—
1129C3×C4—61no—
1130C3×C4—61no—
1131C3×C4—61no—
1132C3×C4—61no—
1133C3×C4—61no—
1134C3×C4—61no—
1135C3×C4—61no—
1136C3×C4—61no—
1137C3×C4—92no—
1138C3×C4—121no—
1139C3×C4—121no—
1140C3×C4—121no—
1141C3×C4—121no—
1142C3×C4—121no—
1143C3×C4—181no—
1144Dic3—21no—
1145Dic3—21no—
1146Dic3—21no—
1147Dic3—21no—
1148Dic3—21no—
1149Dic3—32no—
1150Dic3—32no—
1151Dic3—62no—
1152Dic3—61no—
1153Dic3—61no—
1154Dic3—121no—
1155Dic3—182no—
1156Dic3—182no—
1157Dic3—181no—
1158Dic3—181no—
1159Dic3—181no—
1160Dic3—181no—
1161Dic3—181no—
1162Dic3—181no—
1163Dic3—361no—
1164Dic3—361no—
1165Dic3—361no—
1166Dic3—361no—
1167Dic3—362no—
1168Dic3—362no—
1169C32—21no—
1170C32—21no—
1171C32—21no—
1172C32—41no—
1173C32#559111yescharacteristic, complemented
1174C32#565411yescharacteristic, complemented
1175C32#582911yescharacteristic, complemented
1176C23—31no—
1177C23—91no—
1178C23—91no—
1179C23—91no—
1180C23—91no—
1181C23—182no—
1182C23—182no—
1183C23—361no—
1184C23—542no—
1185C23—542no—
1186C23—1081no—
1187C23D3311yescharacteristic
1188Q8—182no—
1189D4—62no—
1190D4—94no—
1191D4—182no—
1192D4—182no—
1193D4—182no—
1194D4—361no—
1195D4—542no—
1196D4—542no—
1197D4—1081no—
1198C2×C4—31no—
1199C2×C4—31no—
1200C2×C4—31no—
1201C2×C4—31no—
1202C2×C4—31no—
1203C2×C4—62no—
1204C2×C4—91no—
1205C2×C4—91no—
1206C2×C4—182no—
1207C2×C4—182no—
1208C2×C4—271no—
1209C2×C4—271no—
1210C2×C4—542no—
1211C2×C4—1081no—
1212C2×C4—1081no—
1213C2×C3—24no—
1214C2×C3—22no—
1215C2×C3—22no—
1216C2×C3—22no—
1217C2×C3—21no—
1218C2×C3—21no—
1219C2×C3—21no—
1220C2×C3—21no—
1221C2×C3—21no—
1222C2×C3—21no—
1223C2×C3—21no—
1224C2×C3—21no—
1225C2×C3—21no—
1226C2×C3—42no—
1227C2×C3—42no—
1228C2×C3—44no—
1229C2×C3—41no—
1230C2×C3—41no—
1231C2×C3—41no—
1232C2×C3—121no—
1233C2×C3—121no—
1234C2×C3—182no—
1235C2×C3—182no—
1236C2×C3—241no—
1237C2×C3—361no—
1238C2×C3—361no—
1239C2×C3C2×#380211yescharacteristic
1240C2×C3#6430611yescharacteristic
1241C2×C3#6430811yescharacteristic
1242C2×C3D3×#23711yescharacteristic
1243C2×C3D3×#23711yescharacteristic
1244C2×C3#6431411yescharacteristic
1245C2×C3#6431411yescharacteristic
1246C2×C3C2×D3×#6711yescharacteristic
1247C2×C3C2×D3×#6711yescharacteristic
1248D3—41no—
1249D3—62no—
1250D3—62no—
1251D3—62no—
1252D3—62no—
1253D3—122no—
1254D3—122no—
1255D3—122no—
1256D3—121no—
1257D3—121no—
1258D3—121no—
1259D3—121no—
1260D3—241no—
1261C22—21no—
1262C22—21no—
1263C22—61no—
1264C22—61no—
1265C22—61no—
1266C22—92no—
1267C22—92no—
1268C22—181no—
1269C22—181no—
1270C22—181no—
1271C22—181no—
1272C22—181no—
1273C22—181no—
1274C22—181no—
1275C22—181no—
1276C22—181no—
1277C22—181no—
1278C22—364no—
1279C22—1084no—
1280C22#8895312yes—
1281C22C2×D3311yescharacteristic
1282C4—61no—
1283C4—61no—
1284C4—61no—
1285C4—61no—
1286C4—61no—
1287C4—92no—
1288C4—181no—
1289C4—541no—
1290C4—541no—
1291C3—21no—
1292C3—21no—
1293C3—21no—
1294C3—41no—
1295C3#1059429411yescharacteristic, complemented
1296C3#1059506811yescharacteristic, complemented
1297C3#1059530411yescharacteristic, complemented
1298C2—22no—
1299C2—121no—
1300C2—182no—
1301C2—182no—
1302C2—361no—
1303C2—361no—
1304C2#1172440711yescharacteristic
1305C2#1172442011yescharacteristic
1306C2C2×#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. #11723637C2semidirect
4. #11723626C2semidirect
5. C2×#88803C2semidirect
6. C3×#63981C2semidirect
7. C3×#63966C2semidirect
8. #11723007C2semidirect
9. #11722995C2semidirect
10. #11722979C2semidirect
11. #11722962C2semidirect
12. #11722960C2semidirect
13. #11722951C2semidirect
14. #11722927C2semidirect
15. #11722905C2semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
24. C2×C32×#67C22semidirect
25. C22×C32×Dic3C22semidirect
30. C2×#6290C22semidirect
31. C2×Dic3×C3⋊D3C22semidirect
32. C2×C3×#627C22semidirect
34. C2×C3×#626C22semidirect
35. C2×C3×#626C22semidirect
36. C2×C3×#624C22semidirect
38. C2×C3×D3×Dic3C22semidirect
39. C32×#217C22semidirect
40. #88807C22semidirect
41. #88806C22semidirect
44. #88803C22semidirect
45. #88803C22semidirect
46. #88803C22semidirect
47. #88803C22semidirect
48. (C2×D3)⋊(C3⋊Dic3)C22semidirect
49. Dic3×C3⋊Dic3C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
53. C3×#3722C22semidirect
54. C3×#3722C22semidirect
55. C3×#3722C22semidirect
61. C2×#3804D3semidirect
70. #63981D3semidirect
80. #63966D3semidirect
120. C3×#638D4semidirect
174. C2×C3×#67C2×D3semidirect
175. C2×C3×#67C2×D3semidirect
178. C22×C3×Dic3C2×D3semidirect
179. C22×C3×Dic3C2×D3semidirect
193. C2×#627C2×D3semidirect
199. C2×#626C2×D3semidirect
200. C2×#626C2×D3semidirect
207. C2×#624C2×D3semidirect
214. C2×D3×Dic3C2×D3semidirect
227. C3×#217C2×D3semidirect
228. C3×#217C2×D3semidirect
247. Dic3⋊Dic3C2×D3semidirect
248. Dic3⋊Dic3C2×D3semidirect
250. #3722C2×D3semidirect
251. #3722C2×D3semidirect
252. #3722C2×D3semidirect
293. C2×C3×C3⋊D3#41semidirect
412. #638#67semidirect
553. C2×#67D32semidirect
564. C22×Dic3D32semidirect
602. #217D32semidirect
688. C2×C3⋊D3#237semidirect
798. C33#546semidirect
1173. C32#5591semidirect
1174. C32#5654semidirect
1175. C32#5829semidirect
1295. C3#10594294semidirect
1296. C3#10595068semidirect
1297. C3#10595304semidirect

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
#117236372
#117236262
C2×#888032
C3×#639812
C3×#639662
#117230072
#117229952
#117229792
#117229622
#117229602
#117229512
#117229272
#117229052
#105953043
#105950683
#105942943