Finite Group Databasebeta

← #13172861

Subgroups — #13172861

Order 1728.

1968 conjugacy classes of subgroups.

The subgroup lattice has 1378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6291C211yesmaximal, characteristic, complemented
2C2×#88962C211yesmaximal, characteristic, complemented
3#11723726C211yesmaximal, characteristic, complemented
4#11723639C211yesmaximal, characteristic, complemented
5#11723627C211yesmaximal, characteristic, complemented
6C3×#63982C211yesmaximal, characteristic, complemented
7C3×#63977C211yesmaximal, characteristic, complemented
8C3×D3×#217C211yesmaximal, characteristic, complemented
9#11723005C211yesmaximal, characteristic, complemented
10#11722996C211yesmaximal, characteristic, complemented
11#11722987C211yesmaximal, characteristic, complemented
12#11722966C211yesmaximal, characteristic, complemented
13#11722963C211yesmaximal, characteristic, complemented
14#11722959C211yesmaximal, characteristic, complemented
15#11722935C211yesmaximal, characteristic, complemented
16#10595500—31nomaximal
17#10594187—31nomaximal
18#10594063—31nomaximal
19C23×C3⋊(C3⋊D3)C2211yescharacteristic
20C23×C32×D3C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×#6294C2211yescharacteristic, complemented
24C2×#6292C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic, complemented
26C2×#6291—24no—
27C2×#6291C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6291C2211yescharacteristic
30C2×#6291C2211yescharacteristic
31C2×#6289C2211yescharacteristic, complemented
32C2×#6289C2211yescharacteristic, complemented
33C2×C3×#627C2211yescharacteristic, complemented
34C2×C3×#626C2211yescharacteristic, complemented
35C2×C3×#626C2211yescharacteristic, complemented
36C2×C3×D3×Dic3C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38#88962—24no—
39C3×#3757C2211yescharacteristic
40C32×#217C2211yescharacteristic
41C32×#217C2211yescharacteristic
42#88815C2211yescharacteristic, complemented
43#88814C2211yescharacteristic, complemented
44#88813C2211yescharacteristic, complemented
45#88804C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48#88804C2211yescharacteristic, complemented
49C3×#3724C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C22×#638—31no—
57C22×#626—31no—
58C22×#626—31no—
59C22×#626—61no—
60C2×#3804—31no—
61C2×#3799—31no—
62C2×#3796—31no—
63#64091—31no—
64C22⋊C4×C3⋊D3—31no—
65C3×#953—31no—
66C2×C3×#217—31no—
67C3×#882—31no—
68C3×D3×C22⋊C4—31no—
69C3×#878—31no—
70C3×#878—31no—
71#63982D311yescharacteristic, complemented
72#63981—31no—
73#63981—31no—
74#63981—61no—
75#63978—31no—
76#63977D311yescharacteristic, complemented
77#63975—31no—
78#63974—31no—
79#63974—31no—
80#63974—61no—
81#67⋊Dic3—31no—
82Dic3×#67—31no—
83#63971—31no—
84D3×#217D311yescharacteristic, complemented
85#63966—31no—
86#63958—31no—
87#63953—31no—
88#63952—31no—
89#63952—31no—
90#63916—31no—
91#63910—31no—
92#63910—31no—
93#63909—31no—
94#63907—31no—
95#63907—31no—
96#63904—31no—
97#63890—31no—
98#63886—31no—
99#63886—31no—
100#63881—31no—
101#63854—31no—
102#63853—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)—22no—
106C22×C3⋊(C3⋊D3)—22no—
107C22×C3⋊(C3⋊D3)—41no—
108C22×C3⋊(C3⋊D3)C2311yescharacteristic
109C22×C3⋊(C3⋊D3)C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C32×D3—22no—
112C22×C32×D3—22no—
113C22×C32×D3—41no—
114C22×C32×D3C2311yescharacteristic
115C22×C32×D3C2311yescharacteristic
116C3×#638—22no—
117C2×C3×C3⋊Dic3—22no—
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127#6294—22no—
128#6292—22no—
129#6292—41no—
130#6291—22no—
131#6291—22no—
132#6291—22no—
133#6291D414yescomplemented
134#6289—22no—
135#6289—41no—
136C3×#627—22no—
137C3×#626—22no—
138C3×#626—41no—
139C3×D3×Dic3—22no—
140C3×D3×Dic3—41no—
141#5630—91no—
142#5591—91no—
143#5490—91no—
144C24×C32—31no—
145C23×C3⋊D3—31no—
146C23×C3⋊D3—31no—
147C23×C3⋊D3—31no—
148C23×C3⋊D3—61no—
149C23×C3⋊D3—61no—
150C23×C3⋊D3—61no—
151C23×C3⋊D3—121no—
152C23×C3×D3—21no—
153C23×C3×D3C2×D311yescharacteristic
154C23×C3×D3C2×D311yescharacteristic
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—64no—
160C2×#638C2×D311yescharacteristic
161C22×C3⋊Dic3C2×D311yescharacteristic
162C2×C4⋊(C3⋊D3)—31no—
163C2×C4⋊(C3⋊D3)—31no—
164C2×C4×C3⋊D3—31no—
165C2×C4×C3⋊D3—31no—
166C2×C3×#67—31no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—61no—
171C22×C3×Dic3—31no—
172C22×C3×Dic3—31no—
173C22×C3×Dic3—31no—
174C22×C3×Dic3—31no—
175C22×C3×Dic3—61no—
176C2×C3×D12—31no—
177C2×C3×D12—31no—
178C2×C3×C4×D3—31no—
179C2×C3×C4×D3—31no—
180C2×C3×Dic6—31no—
181C2×C3×Dic6—31no—
182C2×#627C2×D311yescharacteristic, complemented
183C2×#626—31no—
184C2×#626—31no—
185C2×#626—31no—
186C2×#626—31no—
187C2×#626—31no—
188C2×#626—31no—
189C2×#626—31no—
190C2×#626—31no—
191C2×#626—31no—
192C2×#626—31no—
193C2×#626—31no—
194C2×#626—31no—
195C2×#626—64no—
196C2×#626—64no—
197C2×#626—61no—
198C2×#626—61no—
199C2×#626—61no—
200C2×#626—61no—
201C2×#626—68no—
202C2×#626—61no—
203C2×#626—61no—
204C2×#626C2×D311yescharacteristic, complemented
205C2×#626C2×D311yescharacteristic, complemented
206C2×#624—31no—
207C2×#624—31no—
208C2×#624—31no—
209C2×#624—31no—
210C2×#624—31no—
211C2×#624—61no—
212C2×#624—61no—
213#3804—64no—
214C2×D3×Dic3—31no—
215C2×D3×Dic3—31no—
216C2×D3×Dic3C2×D311yescharacteristic, complemented
217C2×D3×Dic3C2×D311yescharacteristic, complemented
218#3799—64no—
219#3796—64no—
220C32×C22⋊C4—31no—
221C32×C22⋊C4—31no—
222#3757C2×D311yescharacteristic
223#3752—31no—
224#3752—31no—
225#3752—31no—
226#3752—31no—
227C3×#217—21no—
228C3×#217—21no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—31no—
234C3×#217—31no—
235C3×#217—61no—
236C3×#217C2×D311yescharacteristic
237C3×#217C2×D311yescharacteristic
238C3×#217C2×D311yescharacteristic
239C3×#217C2×D311yescharacteristic
240C3×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—31no—
242C3×(C2×D3)⋊C4—31no—
243C3×(C2×D3)⋊C4—31no—
244C3×C4⋊Dic3—31no—
245C3×C4⋊Dic3—31no—
246C3×Dic3⋊C4—31no—
247C3×Dic3⋊C4—31no—
248C3×Dic3⋊C4—31no—
249C3×Dic3⋊C4—31no—
250#3724—31no—
251#3724C2×D311yescharacteristic, complemented
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3C2×D311yescharacteristic, complemented
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—31no—
264#3722—31no—
265#3722—61no—
266#3722—61no—
267#3722—61no—
268#3722—61no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
272(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
273(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
274(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
275Dic32—31no—
276Dic32—31no—
277Dic32—31no—
278C22×C33—21no—
279C22×C33—21no—
280C22×C33#4112yescomplemented
281C22×C33C2411yescharacteristic
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)—44no—
288C2×C3⋊(C3⋊D3)C2×D412yes—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3—21no—
292C2×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3—21no—
296C2×C32×D3—21no—
297C2×C32×D3—44no—
298C2×C32×D3C2×D412yes—
299C3×C3⋊Dic3—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3C2×D412yes—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C22×#67—91no—
309C22×#67—91no—
310C22×#67—181no—
311C2×#239—91no—
312C2×#237—91no—
313C2×#235—91no—
314C22×D12—91no—
315C3×C22⋊Q8—91no—
316C3×#120—91no—
317C2×C3×C22⋊C4—91no—
318#953—31no—
319C2×#217—31no—
320#947—91no—
321#939—91no—
322#939—91no—
323#938—91no—
324#937—91no—
325D4×Dic3—91no—
326#930—91no—
327#929—91no—
328C4×#67—91no—
329C4×#67—91no—
330#895—91no—
331#895—91no—
332#895—91no—
333#894—91no—
334#894—91no—
335#893—91no—
336#886—91no—
337#885—91no—
338#885—91no—
339#884—91no—
340#884—91no—
341#883—91no—
342#883—91no—
343#882—31no—
344#882—91no—
345#882—91no—
346#882—181no—
347#67⋊C4—91no—
348#67⋊C4—91no—
349D3×C22⋊C4—31no—
350D3×C22⋊C4—91no—
351D3×C22⋊C4—91no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—181no—
354#878—31no—
355#878—31no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—31no—
360C23×C32—31no—
361C23×C32—41no—
362C23×C32—62no—
363C23×C32—62no—
364C23×C32—121no—
365C23×C32C22×D311yescharacteristic
366C23×C32C22×D311yescharacteristic
367C23×C32C22×D311yescharacteristic
368C22×C3⋊D3—31no—
369C22×C3⋊D3—31no—
370C22×C3⋊D3—31no—
371C22×C3⋊D3—31no—
372C22×C3⋊D3—31no—
373C22×C3⋊D3—31no—
374C22×C3⋊D3—61no—
375C22×C3⋊D3—61no—
376C22×C3⋊D3—61no—
377C22×C3⋊D3—61no—
378C22×C3⋊D3—61no—
379C22×C3⋊D3—61no—
380C22×C3⋊D3—62no—
381C22×C3⋊D3—62no—
382C22×C3⋊D3—62no—
383C22×C3⋊D3—62no—
384C22×C3⋊D3—64no—
385C22×C3⋊D3—64no—
386C22×C3⋊D3—62no—
387C22×C3⋊D3—62no—
388C22×C3⋊D3—121no—
389C22×C3⋊D3—121no—
390C22×C3⋊D3—122no—
391C22×C3⋊D3—122no—
392C22×C3⋊D3—122no—
393C22×C3⋊D3—122no—
394C22×C3⋊D3—124no—
395C22×C3⋊D3—124no—
396C22×C3⋊D3—121no—
397C22×C3⋊D3—121no—
398C22×C3⋊D3—121no—
399C22×C3⋊D3—122no—
400C22×C3⋊D3—122no—
401C22×C3⋊D3—122no—
402C22×C3⋊D3—124no—
403C22×C3⋊D3C22×D311yescharacteristic
404C22×C3×D3—24no—
405C22×C3×D3—22no—
406C22×C3×D3—22no—
407C22×C3×D3—22no—
408C22×C3×D3—22no—
409C22×C3×D3—21no—
410C22×C3×D3—21no—
411C22×C3×D3—31no—
412C22×C3×D3—31no—
413C22×C3×D3—42no—
414C22×C3×D3—41no—
415C22×C3×D3—41no—
416C22×C3×D3—42no—
417C22×C3×D3—61no—
418C22×C3×D3C22×D311yescharacteristic
419C22×C3×D3C22×D311yescharacteristic
420C22×C3×D3C22×D311yescharacteristic
421C22×C3×D3C22×D311yescharacteristic
422C2×C32×C4—31no—
423C2×C32×C4—31no—
424C2×C32×C4—31no—
425C2×C32×C4—31no—
426#638—22no—
427#638—34no—
428#638—62no—
429#638—62no—
430#638—62no—
431C2×C3⋊Dic3—22no—
432C2×C3⋊Dic3C22×D311yescharacteristic
433C2×C3⋊Dic3C22×D311yescharacteristic
434C2×C3⋊Dic3C22×D311yescharacteristic
435C2×C3⋊Dic3C22×D311yescharacteristic
436C2×C3⋊Dic3C22×D311yescharacteristic
437C4⋊(C3⋊D3)—62no—
438C4⋊(C3⋊D3)—121no—
439C4×C3⋊D3—62no—
440C4×C3⋊D3—121no—
441C3×#67—62no—
442C3×#67—62no—
443C3×#67—62no—
444C3×#67—122no—
445C3×#67—121no—
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—31no—
455C2×C3×Dic3—31no—
456C2×C3×Dic3—31no—
457C2×C3×Dic3—31no—
458C2×C3×Dic3—31no—
459C2×C3×Dic3—31no—
460C2×C3×Dic3—61no—
461C2×C3×Dic3—61no—
462C2×C3×Dic3—61no—
463C2×C3×Dic3—61no—
464C2×C3×Dic3—61no—
465C2×C3×Dic3—62no—
466C2×C3×Dic3—62no—
467C2×C3×Dic3—62no—
468C2×C3×Dic3—64no—
469C2×C3×Dic3—121no—
470C2×C3×Dic3C22×D311yescharacteristic
471C2×C3×Dic3C22×D311yescharacteristic
472C2×C3×Dic3C22×D311yescharacteristic
473C2×C3×Dic3C22×D311yescharacteristic
474C2×C3×Dic3C22×D311yescharacteristic
475C2×C3×Dic3C22×D311yescharacteristic
476C2×C3×Dic3C22×D311yescharacteristic
477C2×C3×Dic3C22×D311yescharacteristic
478C3×D12—62no—
479C3×D12—121no—
480C3×C4×D3—62no—
481C3×C4×D3—121no—
482C3×Dic6—62no—
483C3×Dic6—62no—
484#627—22no—
485#626—22no—
486#626—34no—
487#626—34no—
488#626—41no—
489#626—64no—
490#626—62no—
491#626—62no—
492#626—62no—
493#626—62no—
494#626—62no—
495#626—62no—
496#626—64no—
497#626—64no—
498#626—64no—
499#626—62no—
500#626—62no—
501#626—122no—
502#626—121no—
503#626—121no—
504#626—122no—
505#624—62no—
506#624—62no—
507#624—62no—
508#624—122no—
509#624—121no—
510#624—121no—
511#624—122no—
512D3×Dic3—22no—
513D3×Dic3—41no—
514D3×Dic3—62no—
515D3×Dic3—62no—
516#546—271noSylow
517C2×C33—22no—
518C2×C33C22×D411yescharacteristic
519C2×C33C2×#4111yescharacteristic
520C2×C33H(5,𝔽2)11yescharacteristic
521C3⋊(C3⋊D3)—22no—
522C3⋊(C3⋊D3)—41no—
523C3×C3⋊D3—41no—
524C32×D3—22no—
525C32×D3—41no—
526C24×C3—31no—
527C24×C3—31no—
528C24×C3—61no—
529C23×D3—91no—
530C23×D3—91no—
531C23×D3—91no—
532C23×D3—181no—
533C23×D3—181no—
534C23×D3—181no—
535C23×D3—361no—
536C23×D3D3211yescharacteristic
537C2×C3×Q8—91no—
538C2×C3×D4—91no—
539C2×C3×D4—91no—
540C2×C3×D4—91no—
541C22×C3×C4—91no—
542C22×C3×C4—91no—
543C22×C3×C4—91no—
544C2×#67—31no—
545C2×#67—31no—
546C2×#67—31no—
547C2×#67—31no—
548C2×#67—61no—
549C2×#67—91no—
550C2×#67—91no—
551C2×#67—91no—
552C2×#67—91no—
553C2×#67—91no—
554C2×#67—91no—
555C2×#67—91no—
556C2×#67—91no—
557C2×#67—91no—
558C2×#67—91no—
559C2×#67—181no—
560C2×#67—181no—
561C2×#67—181no—
562C2×#67—181no—
563C2×#67—184no—
564C2×#67—184no—
565C2×#67—188no—
566C22×Dic3—31no—
567C22×Dic3—31no—
568C22×Dic3—31no—
569C22×Dic3—31no—
570C22×Dic3—61no—
571C22×Dic3—91no—
572#239—184no—
573#237—184no—
574#235—184no—
575C2×D12—31no—
576C2×D12—31no—
577C2×D12—91no—
578C2×D12—91no—
579C2×D12—91no—
580C2×D12—91no—
581C2×D12—91no—
582C2×D12—91no—
583C2×D12—91no—
584C2×D12—91no—
585C2×D12—181no—
586C2×D12—181no—
587C2×D12—184no—
588C2×C4×D3—31no—
589C2×C4×D3—31no—
590C2×C4×D3—91no—
591C2×C4×D3—91no—
592C2×C4×D3—91no—
593C2×C4×D3—91no—
594C2×C4×D3—91no—
595C2×C4×D3—91no—
596C2×C4×D3—91no—
597C2×C4×D3—91no—
598C2×C4×D3—181no—
599C2×C4×D3—181no—
600C2×Dic6—31no—
601C2×Dic6—31no—
602C3×C4⋊C4—91no—
603C3×C4⋊C4—91no—
604C3×C4⋊C4—91no—
605C3×C22⋊C4—31no—
606C3×C22⋊C4—31no—
607C3×C22⋊C4—31no—
608C3×C22⋊C4—31no—
609C3×C22⋊C4—61no—
610C3×C22⋊C4—61no—
611C3×C22⋊C4—91no—
612C3×C22⋊C4—91no—
613C3×C22⋊C4—91no—
614C3×C22⋊C4—91no—
615C3×C22⋊C4—91no—
616#217—31no—
617#217—31no—
618#217—31no—
619#217—31no—
620#217—31no—
621#217—31no—
622#217—61no—
623#217—91no—
624#217D3211yescharacteristic
625#217D3211yescharacteristic
626(C2×D3)⋊C4—31no—
627(C2×D3)⋊C4—31no—
628(C2×D3)⋊C4—31no—
629(C2×D3)⋊C4—31no—
630(C2×D3)⋊C4—91no—
631(C2×D3)⋊C4—91no—
632(C2×D3)⋊C4—91no—
633(C2×D3)⋊C4—91no—
634(C2×D3)⋊C4—91no—
635(C2×D3)⋊C4—91no—
636(C2×D3)⋊C4—91no—
637(C2×D3)⋊C4—91no—
638(C2×D3)⋊C4—91no—
639(C2×D3)⋊C4—91no—
640(C2×D3)⋊C4—91no—
641(C2×D3)⋊C4—91no—
642(C2×D3)⋊C4—91no—
643(C2×D3)⋊C4—91no—
644(C2×D3)⋊C4—181no—
645(C2×D3)⋊C4—181no—
646(C2×D3)⋊C4—181no—
647(C2×D3)⋊C4—181no—
648C4⋊Dic3—31no—
649C4⋊Dic3—31no—
650C4⋊Dic3—91no—
651Dic3⋊C4—31no—
652Dic3⋊C4—31no—
653Dic3⋊C4—31no—
654Dic3⋊C4—31no—
655Dic3⋊C4—91no—
656Dic3⋊C4—91no—
657C4×Dic3—91no—
658C4×Dic3—91no—
659C4×Dic3—91no—
660C22×C32—21no—
661C22×C32—21no—
662C22×C32—22no—
663C22×C32—22no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—21no—
667C22×C32—21no—
668C22×C32—21no—
669C22×C32—21no—
670C22×C32—21no—
671C22×C32—22no—
672C22×C32—22no—
673C22×C32—22no—
674C22×C32—32no—
675C22×C32—42no—
676C22×C32—41no—
677C22×C32—41no—
678C22×C32—41no—
679C22×C32—41no—
680C22×C32—41no—
681C22×C32—42no—
682C22×C32—42no—
683C22×C32—61no—
684C22×C32—61no—
685C22×C32—61no—
686C22×C32—61no—
687C22×C32—61no—
688C22×C32—124no—
689C22×C32#23512yescomplemented
690C22×C32#23712yescomplemented
691C22×C32#23912yescomplemented
692C22×C32C23×D311yescharacteristic
693C22×C32C23×D311yescharacteristic
694C22×C32C23×D311yescharacteristic
695C2×C3⋊D3—21no—
696C2×C3⋊D3—21no—
697C2×C3⋊D3—21no—
698C2×C3⋊D3—32no—
699C2×C3⋊D3—32no—
700C2×C3⋊D3—32no—
701C2×C3⋊D3—62no—
702C2×C3⋊D3—62no—
703C2×C3⋊D3—62no—
704C2×C3⋊D3—61no—
705C2×C3⋊D3—61no—
706C2×C3⋊D3—61no—
707C2×C3⋊D3—61no—
708C2×C3⋊D3—61no—
709C2×C3⋊D3—62no—
710C2×C3⋊D3—62no—
711C2×C3⋊D3—61no—
712C2×C3⋊D3—61no—
713C2×C3⋊D3—61no—
714C2×C3⋊D3—61no—
715C2×C3⋊D3—62no—
716C2×C3⋊D3—62no—
717C2×C3⋊D3—62no—
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—122no—
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—121no—
734C2×C3⋊D3—121no—
735C2×C3⋊D3—122no—
736C2×C3⋊D3—122no—
737C2×C3⋊D3—122no—
738C2×C3⋊D3—122no—
739C2×C3⋊D3—122no—
740C2×C3⋊D3—124no—
741C2×C3⋊D3—124no—
742C2×C3⋊D3—124no—
743C2×C3⋊D3—128no—
744C2×C3⋊D3—128no—
745C2×C3⋊D3—128no—
746C2×C3⋊D3—1216no—
747C2×C3×D3—21no—
748C2×C3×D3—21no—
749C2×C3×D3—21no—
750C2×C3×D3—21no—
751C2×C3×D3—22no—
752C2×C3×D3—21no—
753C2×C3×D3—21no—
754C2×C3×D3—21no—
755C2×C3×D3—21no—
756C2×C3×D3—21no—
757C2×C3×D3—21no—
758C2×C3×D3—22no—
759C2×C3×D3—41no—
760C2×C3×D3—41no—
761C2×C3×D3—41no—
762C2×C3×D3—41no—
763C2×C3×D3—44no—
764C2×C3×D3—44no—
765C2×C3×D3—48no—
766C2×C3×D3—61no—
767C2×C3×D3—61no—
768C2×C3×D3—61no—
769C2×C3×D3—61no—
770C2×C3×D3—61no—
771C2×C3×D3—61no—
772C2×C3×D3—121no—
773C2×C3×D3—121no—
774C2×C3×D3—121no—
775C2×C3×D3D3×D412yes—
776C2×C3×D3D3×D412yes—
777C32×C4—61no—
778C32×C4—61no—
779C32×C4—61no—
780C32×C4—61no—
781C3⋊Dic3—21no—
782C3⋊Dic3—21no—
783C3⋊Dic3—21no—
784C3⋊Dic3—21no—
785C3⋊Dic3D3×D412yes—
786C3×Dic3—21no—
787C3×Dic3—21no—
788C3×Dic3—21no—
789C3×Dic3—21no—
790C3×Dic3—21no—
791C3×Dic3—21no—
792C3×Dic3—21no—
793C3×Dic3—21no—
794C3×Dic3—32no—
795C3×Dic3—32no—
796C3×Dic3—41no—
797C3×Dic3—41no—
798C3×Dic3—41no—
799C3×Dic3—41no—
800C3×Dic3—62no—
801C3×Dic3—62no—
802C3×Dic3—61no—
803C3×Dic3—61no—
804C3×Dic3—61no—
805C3×Dic3—61no—
806C3×Dic3—61no—
807C3×Dic3—61no—
808C3×Dic3—61no—
809C3×Dic3—61no—
810C3×Dic3—121no—
811C3×Dic3—121no—
812C3×Dic3—121no—
813C2×#41—271no—
814C22×D4—271no—
815#124—271no—
816#123—271no—
817#123—271no—
818C22⋊Q8—91no—
819#121—271no—
820#121—271no—
821#121—271no—
822#120—91no—
823#120—271no—
824C4×D4—271no—
825C4×D4—271no—
826C2×C22⋊C4—91no—
827C2×C22⋊C4—271no—
828C33#54611yescharacteristic, complemented, Sylow
829C23×C3—21no—
830C23×C3—21no—
831C23×C3—21no—
832C23×C3—31no—
833C23×C3—31no—
834C23×C3—31no—
835C23×C3—31no—
836C23×C3—41no—
837C23×C3—61no—
838C23×C3—61no—
839C23×C3—62no—
840C23×C3—62no—
841C23×C3—64no—
842C23×C3—62no—
843C23×C3—62no—
844C23×C3—91no—
845C23×C3—122no—
846C23×C3—121no—
847C23×C3—121no—
848C23×C3—122no—
849C23×C3C2×D3211yescharacteristic
850C23×C3C2×D3211yescharacteristic
851C23×C3C2×D3211yescharacteristic
852C22×D3—22no—
853C22×D3—22no—
854C22×D3—31no—
855C22×D3—31no—
856C22×D3—41no—
857C22×D3—61no—
858C22×D3—91no—
859C22×D3—91no—
860C22×D3—91no—
861C22×D3—91no—
862C22×D3—91no—
863C22×D3—91no—
864C22×D3—181no—
865C22×D3—181no—
866C22×D3—181no—
867C22×D3—181no—
868C22×D3—181no—
869C22×D3—181no—
870C22×D3—182no—
871C22×D3—182no—
872C22×D3—182no—
873C22×D3—184no—
874C22×D3—184no—
875C22×D3—182no—
876C22×D3—182no—
877C22×D3—182no—
878C22×D3—361no—
879C22×D3—361no—
880C22×D3—362no—
881C22×D3—362no—
882C22×D3—362no—
883C22×D3—362no—
884C22×D3—364no—
885C22×D3—364no—
886C22×D3—361no—
887C22×D3—361no—
888C22×D3—361no—
889C22×D3—362no—
890C22×D3—362no—
891C22×D3—362no—
892C22×D3—364no—
893C22×D3C2×D3211yescharacteristic
894C22×D3C2×D3211yescharacteristic
895C3×Q8—182no—
896C3×D4—182no—
897C3×D4—182no—
898C3×D4—361no—
899C2×C3×C4—31no—
900C2×C3×C4—31no—
901C2×C3×C4—31no—
902C2×C3×C4—31no—
903C2×C3×C4—31no—
904C2×C3×C4—31no—
905C2×C3×C4—31no—
906C2×C3×C4—31no—
907C2×C3×C4—61no—
908C2×C3×C4—61no—
909C2×C3×C4—61no—
910C2×C3×C4—61no—
911C2×C3×C4—91no—
912C2×C3×C4—91no—
913C2×C3×C4—91no—
914C2×C3×C4—91no—
915C2×C3×C4—91no—
916C2×C3×C4—182no—
917C2×C3×C4—182no—
918C2×C3×C4—361no—
919#67—62no—
920#67—62no—
921#67—62no—
922#67—94no—
923#67—94no—
924#67—122no—
925#67—121no—
926#67—184no—
927#67—182no—
928#67—182no—
929#67—182no—
930#67—182no—
931#67—182no—
932#67—182no—
933#67—182no—
934#67—184no—
935#67—184no—
936#67—184no—
937#67—361no—
938C2×Dic3—31no—
939C2×Dic3—31no—
940C2×Dic3—31no—
941C2×Dic3—31no—
942C2×Dic3—31no—
943C2×Dic3—31no—
944C2×Dic3—31no—
945C2×Dic3—31no—
946C2×Dic3—31no—
947C2×Dic3—31no—
948C2×Dic3—61no—
949C2×Dic3—61no—
950C2×Dic3—61no—
951C2×Dic3—61no—
952C2×Dic3—61no—
953C2×Dic3—62no—
954C2×Dic3—62no—
955C2×Dic3—62no—
956C2×Dic3—64no—
957C2×Dic3—121no—
958C2×Dic3—182no—
959C2×Dic3C2×D3211yescharacteristic
960C2×Dic3C2×D3211yescharacteristic
961C2×Dic3C2×D3211yescharacteristic
962C2×Dic3C2×D3211yescharacteristic
963D12—62no—
964D12—94no—
965D12—121no—
966D12—182no—
967D12—182no—
968D12—182no—
969D12—182no—
970D12—182no—
971D12—362no—
972D12—361no—
973D12—361no—
974D12—362no—
975C4×D3—62no—
976C4×D3—121no—
977C4×D3—182no—
978C4×D3—182no—
979C4×D3—182no—
980C4×D3—182no—
981C4×D3—182no—
982C4×D3—362no—
983C4×D3—361no—
984C4×D3—361no—
985C4×D3—361no—
986C4×D3—362no—
987Dic6—62no—
988Dic6—62no—
989C2×C32—22no—
990C2×C32—24no—
991C2×C32—22no—
992C2×C32—22no—
993C2×C32—21no—
994C2×C32—21no—
995C2×C32—21no—
996C2×C32—21no—
997C2×C32—21no—
998C2×C32—21no—
999C2×C32—21no—
1000C2×C32—21no—
1001C2×C32—21no—
1002C2×C32—41no—
1003C2×C32—41no—
1004C2×C32—41no—
1005C2×C32—42no—
1006C2×C32—42no—
1007C2×C32—44no—
1008C2×C32—62no—
1009C2×C32—121no—
1010C2×C32C2×#23511yescharacteristic
1011C2×C32C2×D3×D411yescharacteristic
1012C2×C32C2×D3×D411yescharacteristic
1013C2×C32C2×D3×D411yescharacteristic
1014C2×C32C2×#23711yescharacteristic
1015C2×C32#100411yescharacteristic
1016C2×C32#100411yescharacteristic
1017C2×C32C2×#23911yescharacteristic
1018C2×C32#100911yescharacteristic
1019C3⋊D3—41no—
1020C3⋊D3—62no—
1021C3⋊D3—64no—
1022C3⋊D3—62no—
1023C3⋊D3—62no—
1024C3⋊D3—122no—
1025C3⋊D3—122no—
1026C3⋊D3—124no—
1027C3⋊D3—122no—
1028C3⋊D3—122no—
1029C3⋊D3—122no—
1030C3⋊D3—124no—
1031C3⋊D3—121no—
1032C3⋊D3—121no—
1033C3⋊D3—121no—
1034C3×D3—22no—
1035C3×D3—22no—
1036C3×D3—42no—
1037C3×D3—42no—
1038C3×D3—41no—
1039C3×D3—41no—
1040C3×D3—121no—
1041C3×D3—121no—
1042C3×D3—241no—
1043C24—31no—
1044C24—271no—
1045#41—544no—
1046C2×Q8—91no—
1047C2×D4—91no—
1048C2×D4—91no—
1049C2×D4—91no—
1050C2×D4—271no—
1051C2×D4—271no—
1052C2×D4—271no—
1053C2×D4—271no—
1054C2×D4—271no—
1055C2×D4—271no—
1056C2×D4—544no—
1057C22×C4—91no—
1058C22×C4—91no—
1059C22×C4—91no—
1060C22×C4—271no—
1061C22×C4—271no—
1062C22×C4—271no—
1063C4⋊C4—91no—
1064C4⋊C4—91no—
1065C4⋊C4—91no—
1066C4⋊C4—271no—
1067C22⋊C4—31no—
1068C22⋊C4—31no—
1069C22⋊C4—91no—
1070C22⋊C4—91no—
1071C22⋊C4—91no—
1072C22⋊C4—91no—
1073C22⋊C4—91no—
1074C22⋊C4—271no—
1075C22⋊C4—271no—
1076C22⋊C4—271no—
1077C22⋊C4—271no—
1078C22⋊C4—271no—
1079C42—271no—
1080C22×C3—22no—
1081C22×C3—22no—
1082C22×C3—21no—
1083C22×C3—21no—
1084C22×C3—21no—
1085C22×C3—21no—
1086C22×C3—21no—
1087C22×C3—21no—
1088C22×C3—21no—
1089C22×C3—21no—
1090C22×C3—21no—
1091C22×C3—22no—
1092C22×C3—22no—
1093C22×C3—22no—
1094C22×C3—32no—
1095C22×C3—32no—
1096C22×C3—41no—
1097C22×C3—41no—
1098C22×C3—41no—
1099C22×C3—41no—
1100C22×C3—42no—
1101C22×C3—42no—
1102C22×C3—41no—
1103C22×C3—42no—
1104C22×C3—62no—
1105C22×C3—62no—
1106C22×C3—61no—
1107C22×C3—61no—
1108C22×C3—61no—
1109C22×C3—61no—
1110C22×C3—61no—
1111C22×C3—61no—
1112C22×C3—61no—
1113C22×C3—61no—
1114C22×C3—61no—
1115C22×C3—61no—
1116C22×C3—121no—
1117C22×C3—121no—
1118C22×C3—121no—
1119C22×C3—121no—
1120C22×C3—124no—
1121C22×C3—124no—
1122C22×C3—128no—
1123C22×C3—181no—
1124C22×C3—181no—
1125C22×C3—181no—
1126C22×C3#379612yescomplemented
1127C22×C3#379912yescomplemented
1128C22×C3#380412yescomplemented
1129C22×C3C22×D3211yescharacteristic
1130C22×C3C22×D3211yescharacteristic
1131C22×C3C22×D3211yescharacteristic
1132C2×D3—21no—
1133C2×D3—21no—
1134C2×D3—21no—
1135C2×D3—21no—
1136C2×D3—21no—
1137C2×D3—44no—
1138C2×D3—61no—
1139C2×D3—61no—
1140C2×D3—61no—
1141C2×D3—61no—
1142C2×D3—61no—
1143C2×D3—61no—
1144C2×D3—92no—
1145C2×D3—92no—
1146C2×D3—92no—
1147C2×D3—121no—
1148C2×D3—121no—
1149C2×D3—121no—
1150C2×D3—182no—
1151C2×D3—182no—
1152C2×D3—182no—
1153C2×D3—182no—
1154C2×D3—182no—
1155C2×D3—181no—
1156C2×D3—181no—
1157C2×D3—181no—
1158C2×D3—181no—
1159C2×D3—181no—
1160C2×D3—181no—
1161C2×D3—182no—
1162C2×D3—182no—
1163C2×D3—182no—
1164C2×D3—181no—
1165C2×D3—181no—
1166C2×D3—181no—
1167C2×D3—181no—
1168C2×D3—181no—
1169C2×D3—181no—
1170C2×D3—181no—
1171C2×D3—181no—
1172C2×D3—181no—
1173C2×D3—362no—
1174C2×D3—361no—
1175C2×D3—361no—
1176C2×D3—361no—
1177C2×D3—361no—
1178C2×D3—361no—
1179C2×D3—361no—
1180C2×D3—361no—
1181C2×D3—361no—
1182C2×D3—361no—
1183C2×D3—361no—
1184C2×D3—362no—
1185C2×D3—362no—
1186C2×D3—362no—
1187C2×D3—362no—
1188C2×D3—362no—
1189C2×D3—364no—
1190C2×D3—364no—
1191C2×D3—364no—
1192C2×D3—368no—
1193C2×D3—368no—
1194C2×D3—368no—
1195C2×D3—3616no—
1196C2×D3#381112yes—
1197C3×C4—61no—
1198C3×C4—61no—
1199C3×C4—61no—
1200C3×C4—61no—
1201C3×C4—61no—
1202C3×C4—61no—
1203C3×C4—61no—
1204C3×C4—61no—
1205C3×C4—92no—
1206C3×C4—121no—
1207C3×C4—121no—
1208C3×C4—121no—
1209C3×C4—121no—
1210C3×C4—181no—
1211C3×C4—181no—
1212C3×C4—181no—
1213C3×C4—181no—
1214Dic3—21no—
1215Dic3—21no—
1216Dic3—21no—
1217Dic3—21no—
1218Dic3—32no—
1219Dic3—32no—
1220Dic3—62no—
1221Dic3—62no—
1222Dic3—61no—
1223Dic3—61no—
1224Dic3—61no—
1225Dic3—61no—
1226Dic3—61no—
1227Dic3—61no—
1228Dic3—61no—
1229Dic3—61no—
1230Dic3—121no—
1231Dic3—121no—
1232Dic3—121no—
1233C32—21no—
1234C32—21no—
1235C32—21no—
1236C32—41no—
1237C32#549011yescharacteristic, complemented
1238C32#559111yescharacteristic, complemented
1239C32#563011yescharacteristic, complemented
1240C23—31no—
1241C23—31no—
1242C23—62no—
1243C23—62no—
1244C23—91no—
1245C23—121no—
1246C23—271no—
1247C23—271no—
1248C23—542no—
1249C23—542no—
1250C23—1081no—
1251C23D3311yescharacteristic
1252Q8—182no—
1253D4—182no—
1254D4—182no—
1255D4—274no—
1256D4—361no—
1257D4—542no—
1258D4—542no—
1259D4—542no—
1260D4—542no—
1261D4—1081no—
1262C2×C4—31no—
1263C2×C4—31no—
1264C2×C4—31no—
1265C2×C4—31no—
1266C2×C4—91no—
1267C2×C4—91no—
1268C2×C4—91no—
1269C2×C4—91no—
1270C2×C4—91no—
1271C2×C4—182no—
1272C2×C4—182no—
1273C2×C4—361no—
1274C2×C4—542no—
1275C2×C4—542no—
1276C2×C4—1081no—
1277C2×C3—24no—
1278C2×C3—22no—
1279C2×C3—22no—
1280C2×C3—22no—
1281C2×C3—21no—
1282C2×C3—21no—
1283C2×C3—21no—
1284C2×C3—21no—
1285C2×C3—21no—
1286C2×C3—21no—
1287C2×C3—21no—
1288C2×C3—21no—
1289C2×C3—21no—
1290C2×C3—42no—
1291C2×C3—42no—
1292C2×C3—44no—
1293C2×C3—41no—
1294C2×C3—41no—
1295C2×C3—41no—
1296C2×C3—62no—
1297C2×C3—62no—
1298C2×C3—122no—
1299C2×C3—122no—
1300C2×C3—121no—
1301C2×C3—121no—
1302C2×C3—361no—
1303C2×C3C2×#379611yescharacteristic
1304C2×C3C2×#379911yescharacteristic
1305C2×C3D32×D411yescharacteristic
1306C2×C3D32×D411yescharacteristic
1307C2×C3#6431411yescharacteristic
1308C2×C3#6431411yescharacteristic
1309C2×C3C2×#380411yescharacteristic
1310C2×C3C2×#381111yescharacteristic
1311C2×C3#6433011yescharacteristic
1312D3—22no—
1313D3—41no—
1314D3—121no—
1315D3—121no—
1316D3—184no—
1317D3—182no—
1318D3—182no—
1319D3—182no—
1320D3—241no—
1321D3—362no—
1322D3—362no—
1323D3—364no—
1324D3—362no—
1325D3—362no—
1326D3—362no—
1327D3—364no—
1328D3—361no—
1329D3—361no—
1330D3—361no—
1331C22—21no—
1332C22—21no—
1333C22—32no—
1334C22—61no—
1335C22—61no—
1336C22—61no—
1337C22—61no—
1338C22—61no—
1339C22—124no—
1340C22—181no—
1341C22—181no—
1342C22—181no—
1343C22—272no—
1344C22—541no—
1345C22—541no—
1346C22—541no—
1347C22—541no—
1348C22—541no—
1349C22—1084no—
1350C22#8896212yescomplemented
1351C22C2×D3311yescharacteristic
1352C4—61no—
1353C4—61no—
1354C4—61no—
1355C4—61no—
1356C4—92no—
1357C4—181no—
1358C4—181no—
1359C4—181no—
1360C4—181no—
1361C3—21no—
1362C3—21no—
1363C3—21no—
1364C3—41no—
1365C3#1059406311yescharacteristic, complemented
1366C3#1059418711yescharacteristic, complemented
1367C3#1059550011yescharacteristic, complemented
1368C2—22no—
1369C2—62no—
1370C2—121no—
1371C2—361no—
1372C2—542no—
1373C2—1081no—
1374C2#1172441911yescharacteristic
1375C2C2×#8896211yescharacteristic
1376C2D3×#381111yescharacteristic
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. C22×#6291C2semidirect
2. C2×#88962C2semidirect
3. #11723726C2semidirect
4. #11723639C2semidirect
5. #11723627C2semidirect
6. C3×#63982C2semidirect
7. C3×#63977C2semidirect
8. C3×D3×#217C2semidirect
9. #11723005C2semidirect
10. #11722996C2semidirect
11. #11722987C2semidirect
12. #11722966C2semidirect
13. #11722963C2semidirect
14. #11722959C2semidirect
15. #11722935C2semidirect
23. C2×#6294C22semidirect
24. C2×#6292C22semidirect
25. C2×#6292C22semidirect
31. C2×#6289C22semidirect
32. C2×#6289C22semidirect
33. C2×C3×#627C22semidirect
34. C2×C3×#626C22semidirect
35. C2×C3×#626C22semidirect
36. C2×C3×D3×Dic3C22semidirect
37. C2×C3×D3×Dic3C22semidirect
42. #88815C22semidirect
43. #88814C22semidirect
44. #88813C22semidirect
45. #88804C22semidirect
46. #88804C22semidirect
47. #88804C22semidirect
48. #88804C22semidirect
49. C3×#3724C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
71. #63982D3semidirect
76. #63977D3semidirect
84. D3×#217D3semidirect
133. #6291D4semidirect
182. C2×#627C2×D3semidirect
204. C2×#626C2×D3semidirect
205. C2×#626C2×D3semidirect
216. C2×D3×Dic3C2×D3semidirect
217. C2×D3×Dic3C2×D3semidirect
251. #3724C2×D3semidirect
254. Dic3⋊Dic3C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
271. (C2×D3)⋊Dic3C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
274. (C2×D3)⋊Dic3C2×D3semidirect
280. C22×C33#41semidirect
689. C22×C32#235semidirect
690. C22×C32#237semidirect
691. C22×C32#239semidirect
828. C33#546semidirect
1126. C22×C3#3796semidirect
1127. C22×C3#3799semidirect
1128. C22×C3#3804semidirect
1237. C32#5490semidirect
1238. C32#5591semidirect
1239. C32#5630semidirect
1350. C22#88962semidirect
1365. C3#10594063semidirect
1366. C3#10594187semidirect
1367. C3#10595500semidirect

Maximal subgroups

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

subgroupindex
C22×#62912
C2×#889622
#117237262
#117236392
#117236272
C3×#639822
C3×#639772
C3×D3×#2172
#117230052
#117229962
#117229872
#117229662
#117229632
#117229592
#117229352
#105955003
#105941873
#105940633