Finite Group Databasebeta

← #13172857

Subgroups — #13172857

Order 1728.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6290C211yesmaximal, characteristic, complemented
2C2×#88961C211yesmaximal, characteristic, complemented
3#11723723C211yesmaximal, characteristic, complemented
4#11723642C211yesmaximal, characteristic, complemented
5#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
6C3×#63981C211yesmaximal, characteristic, complemented
7C3×#63976C211yesmaximal, characteristic, complemented
8C3×D3×#217C211yesmaximal, characteristic, complemented
9#11723009C211yesmaximal, characteristic, complemented
10#11722998C211yesmaximal, characteristic, complemented
11#11722988C211yesmaximal, characteristic, complemented
12#11722965C211yesmaximal, characteristic, complemented
13#11722956C211yesmaximal, characteristic, complemented
14#11722954C211yesmaximal, characteristic, complemented
15#11722936C211yesmaximal, characteristic, complemented
16#10595500—31nomaximal
17#10595225—31nomaximal
18#10594184—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C23×C32×D3C2211yescharacteristic
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×#6294C2211yescharacteristic, complemented
24C2×#6294C2211yescharacteristic, complemented
25C2×#6293C2211yescharacteristic, complemented
26C2×#6290—24no—
27C2×#6290C2211yescharacteristic
28C2×#6290C2211yescharacteristic
29C2×#6290C2211yescharacteristic
30C2×#6290C2211yescharacteristic
31C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
32C2×C3×#626C2211yescharacteristic, complemented
33C2×C3×#626C2211yescharacteristic, complemented
34C2×C3×#625C2211yescharacteristic, complemented
35C2×C3×#625C2211yescharacteristic, complemented
36C2×C3×D3×Dic3C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38#88961—24no—
39C3×#3757C2211yescharacteristic
40C3×#3757C2211yescharacteristic
41C32×#217C2211yescharacteristic
42#88814C2211yescharacteristic, complemented
43#88814C2211yescharacteristic, complemented
44#88807C2211yescharacteristic, complemented
45#88806C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49Dic3×C3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic, 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×#625—31no—
58C22×#625—31no—
59C22×#625—61no—
60C2×#3805—31no—
61C2×#3804—31no—
62C2×#3795—31no—
63D4×C3⋊Dic3—31no—
64#64087—31no—
65C3×#953—31no—
66C2×C3×#217—31no—
67C3×#937—31no—
68C3×#937—31no—
69C3×#882—31no—
70C3×D3×C22⋊C4—31no—
71#63982—31no—
72#63982—31no—
73#63982—61no—
74#63981D311yescharacteristic, complemented
75#63980—31no—
76#63978—31no—
77#63976D311yescharacteristic, complemented
78#63975—31no—
79#63974—31no—
80#67⋊Dic3—31no—
81#67⋊Dic3—31no—
82#67⋊Dic3—61no—
83#63971—31no—
84#63970—31no—
85#63970—31no—
86D3×#217—31no—
87D3×#217—31no—
88D3×#217D311yescharacteristic, complemented
89#63966—31no—
90#63958—31no—
91#63953—31no—
92#63952—31no—
93#63915—31no—
94#63913—31no—
95#63908—31no—
96#63905—31no—
97#63902—31no—
98#63891—31no—
99#63891—31no—
100#63891—31no—
101#63885—31no—
102#63885—31no—
103#63879—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×C32×D3—22no—
111C22×C32×D3—22no—
112C22×C32×D3—41no—
113C22×C32×D3C2311yescharacteristic
114C22×C32×D3C2311yescharacteristic
115C22×C32×D3C2311yescharacteristic
116C2×C3⋊(C3⋊Dic3)—22no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C32×#67—22no—
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127#6294—22no—
128#6294—41no—
129#6293—22no—
130#6290—22no—
131#6290—22no—
132#6290—22no—
133#6290D414yescomplemented
134D3×C3⋊Dic3—22no—
135C3×#626—22no—
136C3×#626—41no—
137C3×#625—22no—
138C3×#625—41no—
139C3×D3×Dic3—22no—
140C3×D3×Dic3—41no—
141#5591—91no—
142#5591—91no—
143#5490—91no—
144C24×C32—31no—
145C23×C3⋊D3C2×D311yescharacteristic
146C23×C3×D3—21no—
147C23×C3×D3—31no—
148C23×C3×D3—31no—
149C23×C3×D3—61no—
150C23×C3×D3C2×D311yescharacteristic
151C23×C3×D3C2×D311yescharacteristic
152C2×C32×D4—31no—
153C2×#638—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—64no—
158C22×C3⋊Dic3—31no—
159C22×C3⋊Dic3—31no—
160C22×C3⋊Dic3—31no—
161C22×C3⋊Dic3—31no—
162C22×C3⋊Dic3—61no—
163C22×C3⋊Dic3—61no—
164C22×C3⋊Dic3—61no—
165C22×C3⋊Dic3—121no—
166C2×#634—31no—
167C2×C3×#67—21no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67C2×D311yescharacteristic
175C2×C3×#67C2×D311yescharacteristic
176C22×C3×Dic3—31no—
177C22×C3×Dic3—31no—
178C2×C3×D12—31no—
179C2×C3×D12—31no—
180C2×C3×C4×D3—31no—
181C2×C3×C4×D3—31no—
182C2×#627—31no—
183C2×#627—31no—
184C2×#627—61no—
185C2×#626C2×D311yescharacteristic, complemented
186C2×#626C2×D311yescharacteristic, complemented
187C2×#625—31no—
188C2×#625—31no—
189C2×#625—31no—
190C2×#625—31no—
191C2×#625—31no—
192C2×#625—31no—
193C2×#625—31no—
194C2×#625—31no—
195C2×#625—64no—
196C2×#625—64no—
197C2×#625—61no—
198C2×#625—61no—
199C2×#625—61no—
200C2×#625—61no—
201C2×#625—68no—
202C2×#625C2×D311yescharacteristic, complemented
203C2×#625C2×D311yescharacteristic, complemented
204C2×#624—31no—
205C2×#624—31no—
206#3805—64no—
207#3804—64no—
208C2×D3×Dic3—31no—
209C2×D3×Dic3—31no—
210C2×D3×Dic3—31no—
211C2×D3×Dic3—31no—
212C2×D3×Dic3—31no—
213C2×D3×Dic3—31no—
214C2×D3×Dic3—61no—
215C2×D3×Dic3C2×D311yescharacteristic, complemented
216C2×D3×Dic3C2×D311yescharacteristic, complemented
217#3795—64no—
218C32×C22⋊C4—31no—
219#3757—31no—
220#3757C2×D311yescharacteristic
221#3757C2×D311yescharacteristic
222C4⋊(C3⋊Dic3)—31no—
223C4⋊(C3⋊Dic3)—31no—
224#3750—31no—
225#3750—31no—
226C4×C3⋊Dic3—31no—
227C3×#217—21no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—31no—
234C3×#217—31no—
235C3×#217—31no—
236C3×#217—61no—
237C3×#217—61no—
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×(C2×D3)⋊C4—31no—
245C3×(C2×D3)⋊C4—31no—
246C3×(C2×D3)⋊C4—31no—
247C3×(C2×D3)⋊C4—31no—
248#3724—31no—
249#3724—31no—
250#3724—61no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—31no—
257Dic3⋊Dic3—61no—
258Dic3⋊Dic3—61no—
259Dic3⋊Dic3—61no—
260#3722—31no—
261#3722—31no—
262#3722C2×D311yescharacteristic, complemented
263#3722C2×D311yescharacteristic, complemented
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—61no—
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—61no—
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⋊D3C2×D412yes—
289C2×C32×D3—21no—
290C2×C32×D3—21no—
291C2×C32×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)C2×D412yes—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C3×C3⋊Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3—21no—
308C22×#67—91no—
309C22×#67—91no—
310C22×#67—91no—
311C22×#67—181no—
312C2×#237—91no—
313C2×#237—91no—
314C2×#235—91no—
315C3×#120—91no—
316C3×#120—91no—
317C2×C3×C22⋊C4—91no—
318#953—31no—
319C2×#217—31no—
320C2×#217—91no—
321#939—91no—
322#939—91no—
323#939—91no—
324#939—91no—
325#938—91no—
326#938—91no—
327#937—31no—
328#937—31no—
329D4×Dic3—91no—
330D4×Dic3—91no—
331D4×Dic3—181no—
332#930—91no—
333#929—91no—
334C4×#67—91no—
335#886—91no—
336#886—91no—
337#885—91no—
338#885—91no—
339#885—91no—
340#884—91no—
341#884—91no—
342#883—91no—
343#883—91no—
344#883—91no—
345#882—31no—
346#67⋊C4—91no—
347#67⋊C4—91no—
348#67⋊C4—91no—
349D3×C22⋊C4—31no—
350D3×C22⋊C4—91no—
351D3×C22⋊C4—91no—
352#878—91no—
353#878—91no—
354#878—91no—
355#878—181no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—31no—
360C23×C32—31no—
361C23×C32—31no—
362C23×C32—41no—
363C23×C32—62no—
364C23×C32—62no—
365C23×C32—121no—
366C23×C32C22×D311yescharacteristic
367C23×C32C22×D311yescharacteristic
368C23×C32C22×D311yescharacteristic
369C22×C3⋊D3—22no—
370C22×C3⋊D3—22no—
371C22×C3⋊D3—41no—
372C22×C3⋊D3C22×D311yescharacteristic
373C22×C3⋊D3C22×D311yescharacteristic
374C22×C3×D3—24no—
375C22×C3×D3—22no—
376C22×C3×D3—22no—
377C22×C3×D3—22no—
378C22×C3×D3—22no—
379C22×C3×D3—21no—
380C22×C3×D3—21no—
381C22×C3×D3—21no—
382C22×C3×D3—31no—
383C22×C3×D3—31no—
384C22×C3×D3—31no—
385C22×C3×D3—31no—
386C22×C3×D3—42no—
387C22×C3×D3—41no—
388C22×C3×D3—41no—
389C22×C3×D3—42no—
390C22×C3×D3—61no—
391C22×C3×D3—61no—
392C22×C3×D3—62no—
393C22×C3×D3—62no—
394C22×C3×D3—64no—
395C22×C3×D3—62no—
396C22×C3×D3—62no—
397C22×C3×D3—122no—
398C22×C3×D3—121no—
399C22×C3×D3—121no—
400C22×C3×D3—122no—
401C22×C3×D3C22×D311yescharacteristic
402C22×C3×D3C22×D311yescharacteristic
403C22×C3×D3C22×D311yescharacteristic
404C22×C3×D3C22×D311yescharacteristic
405C22×C3×D3C22×D311yescharacteristic
406C22×C3×D3C22×D311yescharacteristic
407C32×D4—62no—
408C2×C32×C4—31no—
409C2×C32×C4—31no—
410C2×C32×C4—31no—
411#638—34no—
412#638—62no—
413#638—62no—
414#638—62no—
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—62no—
428C2×C3⋊Dic3—62no—
429C2×C3⋊Dic3—62no—
430C2×C3⋊Dic3—62no—
431C2×C3⋊Dic3—64no—
432C2×C3⋊Dic3—121no—
433C2×C3⋊Dic3—121no—
434C2×C3⋊Dic3—122no—
435C2×C3⋊Dic3—122no—
436C2×C3⋊Dic3—124no—
437C2×C3⋊Dic3C22×D311yescharacteristic
438C2×C3⋊Dic3C22×D311yescharacteristic
439C2×C3⋊Dic3C22×D311yescharacteristic
440C2×C3⋊Dic3C22×D311yescharacteristic
441#634—62no—
442C3×#67—24no—
443C3×#67—22no—
444C3×#67—22no—
445C3×#67—62no—
446C3×#67—62no—
447C3×#67—62no—
448C3×#67—121no—
449C3×#67—121no—
450C3×#67—121no—
451C2×C3×Dic3—21no—
452C2×C3×Dic3—21no—
453C2×C3×Dic3—21no—
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—31no—
461C2×C3×Dic3—31no—
462C2×C3×Dic3—61no—
463C2×C3×Dic3—61no—
464C2×C3×Dic3—61no—
465C2×C3×Dic3—61no—
466C2×C3×Dic3—62no—
467C2×C3×Dic3—121no—
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—121no—
476C3×C4×D3—62no—
477C3×C4×D3—121no—
478#627—62no—
479#627—62no—
480#627—122no—
481#626—22no—
482#626—41no—
483#625—22no—
484#625—34no—
485#625—34no—
486#625—41no—
487#625—64no—
488#625—62no—
489#625—62no—
490#625—62no—
491#625—62no—
492#625—64no—
493#625—64no—
494#625—64no—
495#625—62no—
496#625—62no—
497#624—62no—
498#624—121no—
499D3×Dic3—22no—
500D3×Dic3—41no—
501D3×Dic3—62no—
502D3×Dic3—62no—
503D3×Dic3—62no—
504D3×Dic3—62no—
505D3×Dic3—122no—
506D3×Dic3—121no—
507D3×Dic3—121no—
508#546—271noSylow
509C2×C33—22no—
510C2×C33C22×D411yescharacteristic
511C2×C33C2×#4111yescharacteristic
512C2×C33H(5,𝔽2)11yescharacteristic
513C3×C3⋊D3—22no—
514C3×C3⋊D3—41no—
515C32×D3—22no—
516C32×D3—41no—
517C32×D3—41no—
518C24×C3—31no—
519C24×C3—31no—
520C24×C3—61no—
521C24×C3—91no—
522C23×D3—31no—
523C23×D3—31no—
524C23×D3—61no—
525C23×D3D3211yescharacteristic
526C2×C3×D4—31no—
527C2×C3×D4—31no—
528C2×C3×D4—61no—
529C2×C3×D4—91no—
530C2×C3×D4—91no—
531C2×C3×D4—91no—
532C2×C3×D4—91no—
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—91no—
542C2×#67—91no—
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—181no—
556C2×#67—181no—
557C2×#67—184no—
558C2×#67—184no—
559C2×#67—184no—
560C2×#67—188no—
561C2×#67D3211yescharacteristic
562C22×Dic3—31no—
563C22×Dic3—31no—
564C22×Dic3—91no—
565C22×Dic3—91no—
566C22×Dic3—91no—
567C22×Dic3—91no—
568C22×Dic3—91no—
569C22×Dic3—91no—
570C22×Dic3—91no—
571C22×Dic3—181no—
572C22×Dic3—181no—
573C22×Dic3—181no—
574C22×Dic3—181no—
575C22×Dic3—361no—
576#237—184no—
577#237—184no—
578#235—184no—
579C2×D12—31no—
580C2×D12—31no—
581C2×C4×D3—31no—
582C2×C4×D3—31no—
583C2×C4×D3—91no—
584C2×C4×D3—91no—
585C2×C4×D3—91no—
586C2×C4×D3—91no—
587C2×C4×D3—91no—
588C2×Dic6—91no—
589C2×Dic6—91no—
590C2×Dic6—91no—
591C2×Dic6—181no—
592C3×C22⋊C4—31no—
593C3×C22⋊C4—31no—
594C3×C22⋊C4—61no—
595C3×C22⋊C4—91no—
596C3×C22⋊C4—91no—
597C3×C22⋊C4—91no—
598C3×C22⋊C4—91no—
599C3×C22⋊C4—91no—
600C3×C22⋊C4—91no—
601C3×C22⋊C4—91no—
602C3×C22⋊C4—91no—
603#217—31no—
604#217—31no—
605#217—31no—
606#217—31no—
607#217—31no—
608#217—31no—
609#217—31no—
610#217—31no—
611#217—61no—
612#217—61no—
613#217—91no—
614#217—91no—
615#217—91no—
616#217—91no—
617#217—181no—
618#217D3211yescharacteristic
619(C2×D3)⋊C4—31no—
620(C2×D3)⋊C4—31no—
621(C2×D3)⋊C4—31no—
622(C2×D3)⋊C4—31no—
623(C2×D3)⋊C4—31no—
624(C2×D3)⋊C4—31no—
625(C2×D3)⋊C4—31no—
626(C2×D3)⋊C4—31no—
627(C2×D3)⋊C4—91no—
628(C2×D3)⋊C4—91no—
629(C2×D3)⋊C4—91no—
630(C2×D3)⋊C4—91no—
631(C2×D3)⋊C4—91no—
632C4⋊Dic3—91no—
633C4⋊Dic3—91no—
634C4⋊Dic3—91no—
635C4⋊Dic3—91no—
636C4⋊Dic3—91no—
637C4⋊Dic3—181no—
638C4⋊Dic3—181no—
639Dic3⋊C4—91no—
640Dic3⋊C4—91no—
641Dic3⋊C4—91no—
642Dic3⋊C4—91no—
643Dic3⋊C4—91no—
644Dic3⋊C4—91no—
645Dic3⋊C4—91no—
646Dic3⋊C4—181no—
647Dic3⋊C4—181no—
648C4×Dic3—91no—
649C4×Dic3—91no—
650C4×Dic3—91no—
651C4×Dic3—181no—
652C22×C32—21no—
653C22×C32—21no—
654C22×C32—22no—
655C22×C32—22no—
656C22×C32—21no—
657C22×C32—21no—
658C22×C32—21no—
659C22×C32—21no—
660C22×C32—21no—
661C22×C32—21no—
662C22×C32—21no—
663C22×C32—22no—
664C22×C32—22no—
665C22×C32—22no—
666C22×C32—32no—
667C22×C32—42no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—41no—
671C22×C32—41no—
672C22×C32—41no—
673C22×C32—42no—
674C22×C32—42no—
675C22×C32—61no—
676C22×C32—61no—
677C22×C32—61no—
678C22×C32—61no—
679C22×C32—61no—
680C22×C32—61no—
681C22×C32—61no—
682C22×C32—61no—
683C22×C32—124no—
684C22×C32#23512yescomplemented
685C22×C32#23712yescomplemented
686C22×C32#23712yescomplemented
687C22×C32C23×D311yescharacteristic
688C22×C32C23×D311yescharacteristic
689C22×C32C23×D311yescharacteristic
690C2×C3⋊D3—21no—
691C2×C3⋊D3—21no—
692C2×C3⋊D3—21no—
693C2×C3⋊D3—21no—
694C2×C3⋊D3—21no—
695C2×C3⋊D3—44no—
696C2×C3⋊D3D3×D412yes—
697C2×C3×D3—21no—
698C2×C3×D3—21no—
699C2×C3×D3—21no—
700C2×C3×D3—21no—
701C2×C3×D3—22no—
702C2×C3×D3—22no—
703C2×C3×D3—21no—
704C2×C3×D3—21no—
705C2×C3×D3—21no—
706C2×C3×D3—21no—
707C2×C3×D3—21no—
708C2×C3×D3—21no—
709C2×C3×D3—21no—
710C2×C3×D3—21no—
711C2×C3×D3—21no—
712C2×C3×D3—21no—
713C2×C3×D3—21no—
714C2×C3×D3—21no—
715C2×C3×D3—22no—
716C2×C3×D3—32no—
717C2×C3×D3—32no—
718C2×C3×D3—41no—
719C2×C3×D3—41no—
720C2×C3×D3—41no—
721C2×C3×D3—41no—
722C2×C3×D3—41no—
723C2×C3×D3—41no—
724C2×C3×D3—44no—
725C2×C3×D3—44no—
726C2×C3×D3—48no—
727C2×C3×D3—62no—
728C2×C3×D3—61no—
729C2×C3×D3—61no—
730C2×C3×D3—61no—
731C2×C3×D3—61no—
732C2×C3×D3—62no—
733C2×C3×D3—61no—
734C2×C3×D3—61no—
735C2×C3×D3—61no—
736C2×C3×D3—61no—
737C2×C3×D3—61no—
738C2×C3×D3—61no—
739C2×C3×D3—121no—
740C2×C3×D3—121no—
741C2×C3×D3—121no—
742C2×C3×D3—121no—
743C2×C3×D3—124no—
744C2×C3×D3—124no—
745C2×C3×D3—128no—
746C2×C3×D3D3×D412yes—
747C2×C3×D3D3×D412yes—
748C32×C4—61no—
749C32×C4—61no—
750C32×C4—61no—
751C3⋊Dic3—21no—
752C3⋊Dic3—21no—
753C3⋊Dic3—21no—
754C3⋊Dic3—21no—
755C3⋊Dic3—32no—
756C3⋊Dic3—32no—
757C3⋊Dic3—32no—
758C3⋊Dic3—62no—
759C3⋊Dic3—62no—
760C3⋊Dic3—62no—
761C3⋊Dic3—61no—
762C3⋊Dic3—62no—
763C3⋊Dic3—61no—
764C3⋊Dic3—61no—
765C3⋊Dic3—122no—
766C3⋊Dic3—121no—
767C3⋊Dic3—121no—
768C3⋊Dic3—122no—
769C3×Dic3—22no—
770C3×Dic3—21no—
771C3×Dic3—21no—
772C3×Dic3—21no—
773C3×Dic3—21no—
774C3×Dic3—21no—
775C3×Dic3—21no—
776C3×Dic3—41no—
777C3×Dic3—41no—
778C3×Dic3—61no—
779C3×Dic3—61no—
780C3×Dic3—61no—
781C3×Dic3—61no—
782C3×Dic3—61no—
783C3×Dic3—61no—
784C3×Dic3—61no—
785C3×Dic3—61no—
786C3×Dic3—121no—
787C3×Dic3—121no—
788C3×Dic3—121no—
789C3×Dic3—121no—
790C2×#41—271no—
791C22×D4—271no—
792#124—271no—
793#123—271no—
794#123—271no—
795C22⋊Q8—271no—
796#121—271no—
797#121—271no—
798#121—271no—
799#120—91no—
800#120—91no—
801C4×D4—271no—
802C4×D4—271no—
803C2×C22⋊C4—91no—
804C2×C22⋊C4—271no—
805C33#54611yescharacteristic, complemented, Sylow
806C23×C3—21no—
807C23×C3—21no—
808C23×C3—21no—
809C23×C3—31no—
810C23×C3—31no—
811C23×C3—31no—
812C23×C3—31no—
813C23×C3—31no—
814C23×C3—31no—
815C23×C3—41no—
816C23×C3—61no—
817C23×C3—61no—
818C23×C3—61no—
819C23×C3—62no—
820C23×C3—62no—
821C23×C3—64no—
822C23×C3—62no—
823C23×C3—62no—
824C23×C3—91no—
825C23×C3—91no—
826C23×C3—122no—
827C23×C3—121no—
828C23×C3—121no—
829C23×C3—122no—
830C23×C3—182no—
831C23×C3—182no—
832C23×C3—361no—
833C23×C3C2×D3211yescharacteristic
834C23×C3C2×D3211yescharacteristic
835C23×C3C2×D3211yescharacteristic
836C22×D3—22no—
837C22×D3—22no—
838C22×D3—31no—
839C22×D3—31no—
840C22×D3—31no—
841C22×D3—31no—
842C22×D3—41no—
843C22×D3—61no—
844C22×D3—61no—
845C22×D3—62no—
846C22×D3—62no—
847C22×D3—64no—
848C22×D3—62no—
849C22×D3—62no—
850C22×D3—122no—
851C22×D3—121no—
852C22×D3—121no—
853C22×D3—122no—
854C22×D3C2×D3211yescharacteristic
855C22×D3C2×D3211yescharacteristic
856C22×D3C2×D3211yescharacteristic
857C3×D4—64no—
858C3×D4—62no—
859C3×D4—62no—
860C3×D4—182no—
861C3×D4—182no—
862C3×D4—361no—
863C3×D4—361no—
864C2×C3×C4—31no—
865C2×C3×C4—31no—
866C2×C3×C4—31no—
867C2×C3×C4—31no—
868C2×C3×C4—31no—
869C2×C3×C4—31no—
870C2×C3×C4—61no—
871C2×C3×C4—61no—
872C2×C3×C4—61no—
873C2×C3×C4—91no—
874C2×C3×C4—91no—
875C2×C3×C4—91no—
876C2×C3×C4—91no—
877C2×C3×C4—182no—
878C2×C3×C4—361no—
879#67—22no—
880#67—62no—
881#67—62no—
882#67—62no—
883#67—94no—
884#67—94no—
885#67—94no—
886#67—121no—
887#67—121no—
888#67—121no—
889#67—184no—
890#67—182no—
891#67—182no—
892#67—182no—
893#67—182no—
894#67—182no—
895#67—182no—
896#67—182no—
897#67—182no—
898#67—184no—
899#67—184no—
900#67—184no—
901#67—182no—
902C2×Dic3—31no—
903C2×Dic3—31no—
904C2×Dic3—31no—
905C2×Dic3—31no—
906C2×Dic3—31no—
907C2×Dic3—31no—
908C2×Dic3—31no—
909C2×Dic3—31no—
910C2×Dic3—61no—
911C2×Dic3—61no—
912C2×Dic3—61no—
913C2×Dic3—61no—
914C2×Dic3—62no—
915C2×Dic3—91no—
916C2×Dic3—91no—
917C2×Dic3—91no—
918C2×Dic3—91no—
919C2×Dic3—91no—
920C2×Dic3—91no—
921C2×Dic3—121no—
922C2×Dic3—181no—
923C2×Dic3—181no—
924C2×Dic3—181no—
925C2×Dic3—181no—
926C2×Dic3—181no—
927C2×Dic3—181no—
928C2×Dic3—182no—
929C2×Dic3—182no—
930C2×Dic3—182no—
931C2×Dic3—182no—
932C2×Dic3—182no—
933C2×Dic3—182no—
934C2×Dic3—184no—
935C2×Dic3—361no—
936C2×Dic3—361no—
937C2×Dic3—362no—
938C2×Dic3—362no—
939C2×Dic3—362no—
940C2×Dic3—364no—
941C2×Dic3—361no—
942C2×Dic3C2×D3211yescharacteristic
943C2×Dic3C2×D3211yescharacteristic
944C2×Dic3C2×D3211yescharacteristic
945D12—62no—
946D12—121no—
947C4×D3—62no—
948C4×D3—121no—
949C4×D3—182no—
950C4×D3—182no—
951C4×D3—182no—
952C4×D3—361no—
953C4×D3—361no—
954Dic6—182no—
955Dic6—182no—
956Dic6—182no—
957Dic6—362no—
958C2×C32—22no—
959C2×C32—24no—
960C2×C32—22no—
961C2×C32—22no—
962C2×C32—21no—
963C2×C32—21no—
964C2×C32—21no—
965C2×C32—21no—
966C2×C32—21no—
967C2×C32—21no—
968C2×C32—21no—
969C2×C32—21no—
970C2×C32—21no—
971C2×C32—41no—
972C2×C32—41no—
973C2×C32—41no—
974C2×C32—42no—
975C2×C32—42no—
976C2×C32—44no—
977C2×C32—62no—
978C2×C32—121no—
979C2×C32—121no—
980C2×C32C2×#23511yescharacteristic
981C2×C32C2×D3×D411yescharacteristic
982C2×C32C2×D3×D411yescharacteristic
983C2×C32C2×D3×D411yescharacteristic
984C2×C32C2×#23711yescharacteristic
985C2×C32C2×#23711yescharacteristic
986C2×C32#100411yescharacteristic
987C2×C32#100411yescharacteristic
988C2×C32#100411yescharacteristic
989C3⋊D3—22no—
990C3⋊D3—41no—
991C3×D3—22no—
992C3×D3—22no—
993C3×D3—42no—
994C3×D3—42no—
995C3×D3—42no—
996C3×D3—41no—
997C3×D3—41no—
998C3×D3—41no—
999C3×D3—41no—
1000C3×D3—62no—
1001C3×D3—62no—
1002C3×D3—122no—
1003C3×D3—122no—
1004C3×D3—121no—
1005C3×D3—121no—
1006C24—31no—
1007C24—91no—
1008#41—544no—
1009C2×Q8—271no—
1010C2×D4—31no—
1011C2×D4—91no—
1012C2×D4—91no—
1013C2×D4—91no—
1014C2×D4—91no—
1015C2×D4—271no—
1016C2×D4—271no—
1017C2×D4—271no—
1018C2×D4—271no—
1019C2×D4—544no—
1020C22×C4—91no—
1021C22×C4—91no—
1022C22×C4—271no—
1023C22×C4—271no—
1024C22×C4—271no—
1025C22×C4—271no—
1026C4⋊C4—271no—
1027C4⋊C4—271no—
1028C4⋊C4—271no—
1029C4⋊C4—271no—
1030C22⋊C4—31no—
1031C22⋊C4—91no—
1032C22⋊C4—91no—
1033C22⋊C4—91no—
1034C22⋊C4—91no—
1035C22⋊C4—91no—
1036C22⋊C4—91no—
1037C22⋊C4—91no—
1038C22⋊C4—91no—
1039C22⋊C4—271no—
1040C22⋊C4—271no—
1041C22⋊C4—271no—
1042C42—271no—
1043C22×C3—22no—
1044C22×C3—22no—
1045C22×C3—21no—
1046C22×C3—21no—
1047C22×C3—21no—
1048C22×C3—21no—
1049C22×C3—21no—
1050C22×C3—21no—
1051C22×C3—21no—
1052C22×C3—21no—
1053C22×C3—21no—
1054C22×C3—22no—
1055C22×C3—22no—
1056C22×C3—22no—
1057C22×C3—32no—
1058C22×C3—32no—
1059C22×C3—41no—
1060C22×C3—41no—
1061C22×C3—41no—
1062C22×C3—41no—
1063C22×C3—42no—
1064C22×C3—42no—
1065C22×C3—41no—
1066C22×C3—42no—
1067C22×C3—62no—
1068C22×C3—62no—
1069C22×C3—62no—
1070C22×C3—61no—
1071C22×C3—61no—
1072C22×C3—61no—
1073C22×C3—61no—
1074C22×C3—61no—
1075C22×C3—61no—
1076C22×C3—61no—
1077C22×C3—61no—
1078C22×C3—61no—
1079C22×C3—61no—
1080C22×C3—61no—
1081C22×C3—61no—
1082C22×C3—61no—
1083C22×C3—61no—
1084C22×C3—61no—
1085C22×C3—61no—
1086C22×C3—92no—
1087C22×C3—121no—
1088C22×C3—121no—
1089C22×C3—121no—
1090C22×C3—121no—
1091C22×C3—121no—
1092C22×C3—121no—
1093C22×C3—124no—
1094C22×C3—124no—
1095C22×C3—128no—
1096C22×C3—181no—
1097C22×C3—181no—
1098C22×C3—181no—
1099C22×C3—181no—
1100C22×C3—181no—
1101C22×C3—364no—
1102C22×C3#379512yescomplemented
1103C22×C3#380412yescomplemented
1104C22×C3#380512yescomplemented
1105C22×C3C22×D3211yescharacteristic
1106C22×C3C22×D3211yescharacteristic
1107C22×C3C22×D3211yescharacteristic
1108C2×D3—21no—
1109C2×D3—21no—
1110C2×D3—21no—
1111C2×D3—21no—
1112C2×D3—21no—
1113C2×D3—21no—
1114C2×D3—21no—
1115C2×D3—21no—
1116C2×D3—32no—
1117C2×D3—32no—
1118C2×D3—44no—
1119C2×D3—62no—
1120C2×D3—61no—
1121C2×D3—61no—
1122C2×D3—61no—
1123C2×D3—61no—
1124C2×D3—62no—
1125C2×D3—61no—
1126C2×D3—61no—
1127C2×D3—61no—
1128C2×D3—61no—
1129C2×D3—61no—
1130C2×D3—61no—
1131C2×D3—121no—
1132C2×D3—121no—
1133C2×D3—121no—
1134C2×D3—121no—
1135C2×D3—124no—
1136C2×D3—124no—
1137C2×D3—128no—
1138C2×D3#381112yes—
1139C3×C4—62no—
1140C3×C4—61no—
1141C3×C4—61no—
1142C3×C4—61no—
1143C3×C4—61no—
1144C3×C4—61no—
1145C3×C4—61no—
1146C3×C4—121no—
1147C3×C4—121no—
1148C3×C4—181no—
1149C3×C4—181no—
1150C3×C4—181no—
1151C3×C4—181no—
1152Dic3—21no—
1153Dic3—21no—
1154Dic3—21no—
1155Dic3—61no—
1156Dic3—61no—
1157Dic3—61no—
1158Dic3—61no—
1159Dic3—61no—
1160Dic3—61no—
1161Dic3—61no—
1162Dic3—61no—
1163Dic3—92no—
1164Dic3—92no—
1165Dic3—92no—
1166Dic3—121no—
1167Dic3—121no—
1168Dic3—121no—
1169Dic3—121no—
1170Dic3—182no—
1171Dic3—182no—
1172Dic3—182no—
1173Dic3—182no—
1174Dic3—181no—
1175Dic3—181no—
1176Dic3—181no—
1177Dic3—362no—
1178Dic3—361no—
1179Dic3—361no—
1180Dic3—362no—
1181C32—21no—
1182C32—21no—
1183C32—21no—
1184C32—41no—
1185C32#549011yescharacteristic, complemented
1186C32#559111yescharacteristic, complemented
1187C32#559111yescharacteristic, complemented
1188C23—31no—
1189C23—31no—
1190C23—31no—
1191C23—62no—
1192C23—62no—
1193C23—91no—
1194C23—91no—
1195C23—121no—
1196C23—182no—
1197C23—182no—
1198C23—361no—
1199C23D3311yescharacteristic
1200Q8—542no—
1201D4—62no—
1202D4—182no—
1203D4—182no—
1204D4—274no—
1205D4—361no—
1206D4—361no—
1207D4—542no—
1208D4—542no—
1209D4—542no—
1210C2×C4—31no—
1211C2×C4—31no—
1212C2×C4—31no—
1213C2×C4—91no—
1214C2×C4—91no—
1215C2×C4—91no—
1216C2×C4—91no—
1217C2×C4—182no—
1218C2×C4—271no—
1219C2×C4—271no—
1220C2×C4—361no—
1221C2×C4—542no—
1222C2×C4—542no—
1223C2×C4—542no—
1224C2×C4—1081no—
1225C2×C3—24no—
1226C2×C3—22no—
1227C2×C3—22no—
1228C2×C3—22no—
1229C2×C3—21no—
1230C2×C3—21no—
1231C2×C3—21no—
1232C2×C3—21no—
1233C2×C3—21no—
1234C2×C3—21no—
1235C2×C3—21no—
1236C2×C3—21no—
1237C2×C3—21no—
1238C2×C3—42no—
1239C2×C3—42no—
1240C2×C3—44no—
1241C2×C3—41no—
1242C2×C3—41no—
1243C2×C3—41no—
1244C2×C3—62no—
1245C2×C3—62no—
1246C2×C3—122no—
1247C2×C3—122no—
1248C2×C3—122no—
1249C2×C3—121no—
1250C2×C3—121no—
1251C2×C3—121no—
1252C2×C3—121no—
1253C2×C3—182no—
1254C2×C3—361no—
1255C2×C3C2×#379511yescharacteristic
1256C2×C3D32×D411yescharacteristic
1257C2×C3D32×D411yescharacteristic
1258C2×C3#6431311yescharacteristic
1259C2×C3#6431311yescharacteristic
1260C2×C3C2×#380411yescharacteristic
1261C2×C3C2×#380511yescharacteristic
1262C2×C3C2×#381111yescharacteristic
1263C2×C3#6433011yescharacteristic
1264D3—22no—
1265D3—41no—
1266D3—41no—
1267D3—62no—
1268D3—62no—
1269D3—122no—
1270D3—122no—
1271D3—121no—
1272D3—121no—
1273C22—21no—
1274C22—21no—
1275C22—32no—
1276C22—61no—
1277C22—61no—
1278C22—61no—
1279C22—61no—
1280C22—61no—
1281C22—61no—
1282C22—61no—
1283C22—61no—
1284C22—92no—
1285C22—124no—
1286C22—181no—
1287C22—181no—
1288C22—181no—
1289C22—181no—
1290C22—181no—
1291C22—364no—
1292C22#8896112yescomplemented
1293C22C2×D3311yescharacteristic
1294C4—61no—
1295C4—61no—
1296C4—61no—
1297C4—181no—
1298C4—181no—
1299C4—181no—
1300C4—181no—
1301C4—272no—
1302C4—541no—
1303C3—21no—
1304C3—21no—
1305C3—21no—
1306C3—41no—
1307C3#1059418411yescharacteristic, complemented
1308C3#1059522511yescharacteristic, complemented
1309C3#1059550011yescharacteristic, complemented
1310C2—22no—
1311C2—62no—
1312C2—121no—
1313C2—121no—
1314C2—182no—
1315C2—361no—
1316C2#1172441511yescharacteristic
1317C2C2×#8896111yescharacteristic
1318C2D3×#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×#6290C2semidirect
2. C2×#88961C2semidirect
3. #11723723C2semidirect
4. #11723642C2semidirect
5. #67⋊(C3⋊Dic3)C2semidirect
6. C3×#63981C2semidirect
7. C3×#63976C2semidirect
8. C3×D3×#217C2semidirect
9. #11723009C2semidirect
10. #11722998C2semidirect
11. #11722988C2semidirect
12. #11722965C2semidirect
13. #11722956C2semidirect
14. #11722954C2semidirect
15. #11722936C2semidirect
23. C2×#6294C22semidirect
24. C2×#6294C22semidirect
25. C2×#6293C22semidirect
31. C2×D3×C3⋊Dic3C22semidirect
32. C2×C3×#626C22semidirect
33. C2×C3×#626C22semidirect
34. C2×C3×#625C22semidirect
35. C2×C3×#625C22semidirect
36. C2×C3×D3×Dic3C22semidirect
37. C2×C3×D3×Dic3C22semidirect
42. #88814C22semidirect
43. #88814C22semidirect
44. #88807C22semidirect
45. #88806C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
47. Dic3⋊(C3⋊Dic3)C22semidirect
48. (C2×D3)⋊(C3⋊Dic3)C22semidirect
49. Dic3×C3⋊Dic3C22semidirect
50. C3×#3722C22semidirect
51. C3×#3722C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
74. #63981D3semidirect
77. #63976D3semidirect
88. D3×#217D3semidirect
133. #6290D4semidirect
185. C2×#626C2×D3semidirect
186. C2×#626C2×D3semidirect
202. C2×#625C2×D3semidirect
203. C2×#625C2×D3semidirect
215. C2×D3×Dic3C2×D3semidirect
216. C2×D3×Dic3C2×D3semidirect
262. #3722C2×D3semidirect
263. #3722C2×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
684. C22×C32#235semidirect
685. C22×C32#237semidirect
686. C22×C32#237semidirect
805. C33#546semidirect
1102. C22×C3#3795semidirect
1103. C22×C3#3804semidirect
1104. C22×C3#3805semidirect
1185. C32#5490semidirect
1186. C32#5591semidirect
1187. C32#5591semidirect
1292. C22#88961semidirect
1307. C3#10594184semidirect
1308. C3#10595225semidirect
1309. C3#10595500semidirect

Maximal subgroups

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

subgroupindex
C22×#62902
C2×#889612
#117237232
#117236422
#67⋊(C3⋊Dic3)2
C3×#639812
C3×#639762
C3×D3×#2172
#117230092
#117229982
#117229882
#117229652
#117229562
#117229542
#117229362
#105955003
#105952253
#105941843