Finite Group Databasebeta

← #13172923

Subgroups — #13172923

Order 1728.

1538 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89046C211yesmaximal, characteristic, complemented
2C2×#88961C211yesmaximal, characteristic, complemented
3#11723631C211yesmaximal, characteristic, complemented
4#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
5#11723591C211yesmaximal, characteristic, complemented
6C3×#63979C211yesmaximal, characteristic, complemented
7C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#63958C211yesmaximal, characteristic, complemented
9#11723036C211yesmaximal, characteristic, complemented
10#11723006C211yesmaximal, characteristic, complemented
11#11722962C211yesmaximal, characteristic, complemented
12#11722957C211yesmaximal, characteristic, complemented
13#11722928C211yesmaximal, characteristic, complemented
14#11722927C211yesmaximal, characteristic, complemented
15Dic3×#624C211yesmaximal, characteristic, complemented
16#10595139—31nomaximal
17#10595133—31nomaximal
18#10594058—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×#6296C2211yescharacteristic
25C2×#6295C2211yescharacteristic
26#89046—24no—
27C2×#6294C2211yescharacteristic
28C2×#6294C2211yescharacteristic
29C2×#6293C2211yescharacteristic
30C2×#6290C2211yescharacteristic
31C2×Dic3×C3⋊D3C2211yescharacteristic
32C2×D3×C3⋊Dic3C2211yescharacteristic
33C2×C3×#626C2211yescharacteristic
34C2×C3×#626C2211yescharacteristic
35C2×C3×#626C2211yescharacteristic
36C2×C3×#625C2211yescharacteristic
37C2×C3×#624C2211yescharacteristic
38C2×C3×D3×Dic3C2211yescharacteristic
39#88961—24no—
40#88864C2211yescharacteristic
41C32×#217C2211yescharacteristic
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic
44#88803C2211yescharacteristic
45#88803C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
48Dic3×C3⋊Dic3C2211yescharacteristic
49Dic3×C3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×Dic3⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×Dic32C2211yescharacteristic
55C3×Dic32C2211yescharacteristic
56C2×#3805—31no—
57C2×#3805—31no—
58C2×#3804—31no—
59C2×#3804—31no—
60C2×#3804—31no—
61C2×#3795—31no—
62#64147—31no—
63D4×C3⋊Dic3—31no—
64#64094—31no—
65C3×#940—31no—
66C3×#940—31no—
67C3×#938—31no—
68C3×D4×Dic3—31no—
69C3×#884—31no—
70C3×#67⋊C4—31no—
71#63979D311yescharacteristic, complemented
72#67⋊Dic3—31no—
73#67⋊Dic3D311yescharacteristic, complemented
74Dic3×#67—31no—
75Dic3×#67—31no—
76Dic3×#67—31no—
77Dic3×#67—61no—
78#63970—31no—
79#63970—31no—
80#63970—31no—
81#63970—61no—
82#63959—31no—
83#63959—31no—
84#63959—31no—
85#63959—31no—
86#63959—61no—
87#63958—31no—
88#63958D311yescharacteristic, complemented
89#63918—31no—
90#63918—31no—
91#63916—31no—
92#63915—31no—
93#63908—31no—
94#63906—31no—
95#63904—31no—
96#63898—31no—
97Dic3×D12—31no—
98#63886—31no—
99C4×#624—31no—
100#63880—31no—
101C4×D3×Dic3—31no—
102C4×D3×Dic3—31no—
103#63840—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C3×#638—22no—
112C3×#638—22no—
113C2×C3×C3⋊Dic3—22no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C32×#67—22no—
119C32×#67—22no—
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124#6296—22no—
125#6295—22no—
126#6294—22no—
127#6294D414yescomplemented
128#6293—22no—
129#6290—22no—
130Dic3×C3⋊D3—22no—
131D3×C3⋊Dic3—22no—
132C3×#626—22no—
133C3×#626—22no—
134C3×#626—22no—
135C3×#625—22no—
136C3×#624—22no—
137C3×D3×Dic3—22no—
138#5716—91no—
139#5596—91no—
140#5548—91no—
141C2×C32×D4—31no—
142C2×C32×D4—31no—
143C2×#638—31no—
144C2×#638C2×D311yescharacteristic
145C2×#638C2×D311yescharacteristic
146C22×C3⋊Dic3—31no—
147C22×C3⋊Dic3C2×D311yescharacteristic
148C2×C4×C3⋊D3—31no—
149C2×#634—31no—
150C2×C3×#67—21no—
151C2×C3×#67—21no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—61no—
162C2×C3×#67—61no—
163C2×C3×#67C2×D311yescharacteristic
164C2×C3×#67C2×D311yescharacteristic
165C2×C3×#67C2×D311yescharacteristic
166C2×C3×#67C2×D311yescharacteristic
167C22×C3×Dic3—31no—
168C22×C3×Dic3—31no—
169C22×C3×Dic3—31no—
170C22×C3×Dic3—61no—
171C2×C3×D12—31no—
172C2×C3×D12—31no—
173C2×C3×D12—31no—
174C2×C3×C4×D3—31no—
175C2×C3×C4×D3—31no—
176C2×C3×C4×D3—31no—
177C2×#627—31no—
178C2×#627—31no—
179C2×#627—31no—
180C2×#627—31no—
181C2×#627—31no—
182C2×#627—61no—
183C2×#626—31no—
184C2×#626—31no—
185C2×#626C2×D311yescharacteristic
186C2×#626C2×D311yescharacteristic
187C2×#626C2×D311yescharacteristic
188C2×#625—31no—
189C2×#625—31no—
190C2×#625—31no—
191C2×#625—61no—
192C2×#625C2×D311yescharacteristic
193C2×#624—31no—
194C2×#624—31no—
195C2×#624C2×D311yescharacteristic
196#3805—64no—
197#3805—64no—
198#3804—64no—
199#3804—64no—
200#3804—64no—
201C2×D3×Dic3—31no—
202C2×D3×Dic3—31no—
203C2×D3×Dic3—31no—
204C2×D3×Dic3—31no—
205C2×D3×Dic3—31no—
206C2×D3×Dic3—31no—
207C2×D3×Dic3—31no—
208C2×D3×Dic3—31no—
209C2×D3×Dic3—61no—
210C2×D3×Dic3—61no—
211C2×D3×Dic3C2×D311yescharacteristic
212#3795—64no—
213C32×C22⋊C4—31no—
214#3757—31no—
215#3757—31no—
216#3757—31no—
217#3757—31no—
218#3757—31no—
219#3757—61no—
220#3757—61no—
221#3757—61no—
222#3757—121no—
223#3752—31no—
224#3752—31no—
225C4⋊(C3⋊Dic3)—31no—
226C4⋊(C3⋊Dic3)—31no—
227C4×C3⋊Dic3—31no—
228C4×C3⋊Dic3—31no—
229C3×#217—21no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217C2×D311yescharacteristic
233C3×#217C2×D311yescharacteristic
234C3×(C2×D3)⋊C4—31no—
235C3×(C2×D3)⋊C4—31no—
236C3×C4⋊Dic3—31no—
237C3×C4⋊Dic3—31no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—31no—
240C3×C4×Dic3—31no—
241C3×C4×Dic3—31no—
242C3×C4×Dic3—31no—
243C3×C4×Dic3—31no—
244Dic3⋊Dic3—31no—
245Dic3⋊Dic3—31no—
246Dic3⋊Dic3—31no—
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—61no—
249Dic3⋊Dic3—61no—
250Dic3⋊Dic3C2×D311yescharacteristic
251Dic3⋊Dic3C2×D311yescharacteristic
252(C2×D3)⋊Dic3—31no—
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—61no—
261(C2×D3)⋊Dic3—61no—
262(C2×D3)⋊Dic3—61no—
263(C2×D3)⋊Dic3—61no—
264(C2×D3)⋊Dic3C2×D311yescharacteristic
265(C2×D3)⋊Dic3C2×D311yescharacteristic
266Dic32—31no—
267Dic32—31no—
268Dic32—31no—
269Dic32—31no—
270Dic32—61no—
271Dic32—61no—
272Dic32C2×D311yescharacteristic
273Dic32C2×D311yescharacteristic
274C22×C33—21no—
275C22×C33—21no—
276C22×C33—21no—
277C22×C33C2411yescharacteristic
278C2×C3×C3⋊D3—21no—
279C2×C3×C3⋊D3—21no—
280C2×C3×C3⋊D3—21no—
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3C2×D412yes—
284C2×C32×D3—21no—
285C2×C32×D3—21no—
286C2×C32×D3—21no—
287C2×C32×D3—21no—
288C2×C32×D3—21no—
289C2×C32×D3—21no—
290C3⋊(C3⋊Dic3)—21no—
291C3⋊(C3⋊Dic3)—21no—
292C3×C3⋊Dic3—21no—
293C3×C3⋊Dic3—21no—
294C3×C3⋊Dic3C2×D412yes—
295C3×C3⋊Dic3C2×D412yes—
296C32×Dic3—21no—
297C32×Dic3—21no—
298C32×Dic3#4112yescomplemented
299C32×Dic3#4112yescomplemented
300C2×#237—91no—
301C2×#237—91no—
302C2×#237—91no—
303C2×#237—91no—
304C2×#235—91no—
305C2×#235—91no—
306C3×#127—91no—
307C3×#121—91no—
308C3×C4×D4—91no—
309#940—31no—
310#940—31no—
311#939—91no—
312#939—91no—
313#938—31no—
314#938—91no—
315#938—91no—
316#938—91no—
317#938—91no—
318#938—181no—
319#936—91no—
320#936—91no—
321D4×Dic3—31no—
322D4×Dic3—91no—
323D4×Dic3—91no—
324D4×Dic3—91no—
325D4×Dic3—91no—
326D4×Dic3—181no—
327#930—91no—
328C4×#67—91no—
329C4×#67—91no—
330C2×C4×Dic3—91no—
331#895—91no—
332#893—91no—
333#888—91no—
334#888—91no—
335#885—91no—
336#885—91no—
337#885—91no—
338#885—91no—
339#885—181no—
340#884—31no—
341#884—91no—
342#67⋊C4—31no—
343#67⋊C4—91no—
344C4×D12—91no—
345C42×D3—91no—
346C42×D3—91no—
347#869—91no—
348C23×C32—21no—
349C23×C32—21no—
350C23×C32—21no—
351C23×C32—31no—
352C23×C32—31no—
353C23×C32—41no—
354C23×C32C22×D311yescharacteristic
355C23×C32C22×D311yescharacteristic
356C23×C32C22×D311yescharacteristic
357C22×C3⋊D3C22×D311yescharacteristic
358C22×C3⋊D3C22×D311yescharacteristic
359C22×C3×D3—21no—
360C22×C3×D3—21no—
361C22×C3×D3—31no—
362C22×C3×D3—31no—
363C22×C3×D3—31no—
364C22×C3×D3—31no—
365C22×C3×D3—61no—
366C22×C3×D3—61no—
367C22×C3×D3C22×D311yescharacteristic
368C22×C3×D3C22×D311yescharacteristic
369C22×C3×D3C22×D311yescharacteristic
370C22×C3×D3C22×D311yescharacteristic
371C32×D4—62no—
372C32×D4—62no—
373C2×C32×C4—31no—
374C2×C32×C4—31no—
375C2×C32×C4—31no—
376C2×C32×C4—31no—
377#638—22no—
378#638—22no—
379#638—62no—
380C2×C3⋊Dic3—22no—
381C2×C3⋊Dic3—31no—
382C2×C3⋊Dic3—31no—
383C2×C3⋊Dic3—31no—
384C2×C3⋊Dic3—31no—
385C2×C3⋊Dic3—31no—
386C2×C3⋊Dic3—31no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—61no—
390C2×C3⋊Dic3—61no—
391C2×C3⋊Dic3—61no—
392C2×C3⋊Dic3—61no—
393C2×C3⋊Dic3—62no—
394C2×C3⋊Dic3—121no—
395C2×C3⋊Dic3—121no—
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C2×C3⋊Dic3C22×D311yescharacteristic
399C2×C3⋊Dic3C22×D311yescharacteristic
400C4×C3⋊D3—62no—
401#634—62no—
402C3×#67—24no—
403C3×#67—22no—
404C3×#67—22no—
405C3×#67—22no—
406C3×#67—22no—
407C3×#67—42no—
408C3×#67—62no—
409C3×#67—62no—
410C3×#67—62no—
411C3×#67—62no—
412C3×#67—62no—
413C3×#67—62no—
414C3×#67—62no—
415C3×#67—62no—
416C3×#67—62no—
417C3×#67—122no—
418C3×#67—122no—
419C2×C3×Dic3—21no—
420C2×C3×Dic3—21no—
421C2×C3×Dic3—21no—
422C2×C3×Dic3—21no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—31no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—62no—
436C2×C3×Dic3—62no—
437C2×C3×Dic3—62no—
438C2×C3×Dic3—122no—
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C2×C3×Dic3C22×D311yescharacteristic
447C3×D12—62no—
448C3×D12—62no—
449C3×D12—62no—
450C3×C4×D3—62no—
451C3×C4×D3—62no—
452C3×C4×D3—62no—
453#627—62no—
454#627—62no—
455#627—62no—
456#627—62no—
457#627—62no—
458#627—122no—
459#626—22no—
460#626—22no—
461#626—22no—
462#626—62no—
463#626—62no—
464#625—22no—
465#625—62no—
466#625—62no—
467#625—62no—
468#625—122no—
469#624—22no—
470#624—34no—
471#624—62no—
472D3×Dic3—22no—
473D3×Dic3—34no—
474D3×Dic3—34no—
475D3×Dic3—62no—
476D3×Dic3—62no—
477D3×Dic3—62no—
478D3×Dic3—62no—
479D3×Dic3—62no—
480D3×Dic3—62no—
481D3×Dic3—122no—
482D3×Dic3—122no—
483#532—271noSylow
484C2×C33—41no—
485C2×C33C22×D411yescharacteristic
486C2×C33C2×#4111yescharacteristic
487C2×C33C2×#4111yescharacteristic
488C3×C3⋊D3—22no—
489C3×C3⋊D3—41no—
490C32×D3—41no—
491C32×D3—41no—
492C2×C3×D4—31no—
493C2×C3×D4—31no—
494C2×C3×D4—31no—
495C2×C3×D4—31no—
496C2×C3×D4—61no—
497C2×C3×D4—61no—
498C2×C3×D4—91no—
499C2×C3×D4—91no—
500C2×C3×D4—91no—
501C2×C3×D4—91no—
502C2×C3×D4—91no—
503C2×C3×D4—91no—
504C22×C3×C4—91no—
505C22×C3×C4—91no—
506C22×C3×C4—91no—
507C2×#67—31no—
508C2×#67—31no—
509C2×#67—31no—
510C2×#67—31no—
511C2×#67—31no—
512C2×#67—31no—
513C2×#67—31no—
514C2×#67—31no—
515C2×#67—31no—
516C2×#67—61no—
517C2×#67—61no—
518C2×#67—91no—
519C2×#67—91no—
520C2×#67—91no—
521C2×#67—91no—
522C2×#67—91no—
523C2×#67—181no—
524C2×#67D3211yescharacteristic
525C2×#67D3211yescharacteristic
526C22×Dic3—31no—
527C22×Dic3—31no—
528C22×Dic3—31no—
529C22×Dic3—61no—
530C22×Dic3—91no—
531C22×Dic3—91no—
532C22×Dic3—91no—
533C22×Dic3—91no—
534C22×Dic3—91no—
535C22×Dic3—181no—
536#237—184no—
537#237—184no—
538#237—184no—
539#237—184no—
540#235—184no—
541#235—184no—
542C2×D12—31no—
543C2×D12—31no—
544C2×D12—31no—
545C2×D12—91no—
546C2×C4×D3—31no—
547C2×C4×D3—31no—
548C2×C4×D3—31no—
549C2×C4×D3—91no—
550C2×C4×D3—91no—
551C2×C4×D3—91no—
552C2×C4×D3—91no—
553C2×C4×D3—91no—
554C2×C4×D3—91no—
555C2×C4×D3—91no—
556C2×C4×D3—181no—
557C2×Dic6—91no—
558C2×Dic6—91no—
559C2×Dic6—91no—
560C2×Dic6—91no—
561C2×Dic6—91no—
562C2×Dic6—91no—
563C2×Dic6—181no—
564C3×C4⋊C4—91no—
565C3×C4⋊C4—91no—
566C3×C22⋊C4—31no—
567C3×C22⋊C4—31no—
568C3×C22⋊C4—61no—
569C3×C22⋊C4—91no—
570C3×C22⋊C4—91no—
571C3×C42—91no—
572C3×C42—91no—
573#217—31no—
574#217—31no—
575#217—91no—
576#217—91no—
577#217—91no—
578#217—91no—
579#217—91no—
580#217—91no—
581#217—91no—
582#217—91no—
583#217—91no—
584#217—181no—
585#217—181no—
586#217—181no—
587#217—181no—
588#217—181no—
589#217—361no—
590#217D3211yescharacteristic
591(C2×D3)⋊C4—31no—
592(C2×D3)⋊C4—31no—
593(C2×D3)⋊C4—91no—
594(C2×D3)⋊C4—91no—
595(C2×D3)⋊C4—91no—
596(C2×D3)⋊C4—91no—
597(C2×D3)⋊C4—91no—
598(C2×D3)⋊C4—91no—
599(C2×D3)⋊C4—181no—
600(C2×D3)⋊C4—181no—
601C4⋊Dic3—31no—
602C4⋊Dic3—31no—
603C4⋊Dic3—91no—
604C4⋊Dic3—91no—
605C4⋊Dic3—91no—
606C4⋊Dic3—91no—
607C4⋊Dic3—181no—
608C4⋊Dic3—181no—
609Dic3⋊C4—31no—
610Dic3⋊C4—31no—
611Dic3⋊C4—91no—
612Dic3⋊C4—91no—
613C4×Dic3—31no—
614C4×Dic3—31no—
615C4×Dic3—31no—
616C4×Dic3—31no—
617C4×Dic3—91no—
618C4×Dic3—91no—
619C4×Dic3—91no—
620C4×Dic3—91no—
621C4×Dic3—91no—
622C4×Dic3—91no—
623C4×Dic3—181no—
624C4×Dic3—181no—
625C22×C32—21no—
626C22×C32—22no—
627C22×C32—21no—
628C22×C32—21no—
629C22×C32—21no—
630C22×C32—21no—
631C22×C32—21no—
632C22×C32—21no—
633C22×C32—21no—
634C22×C32—21no—
635C22×C32—21no—
636C22×C32—21no—
637C22×C32—21no—
638C22×C32—41no—
639C22×C32—41no—
640C22×C32—41no—
641C22×C32—42no—
642C22×C32—41no—
643C22×C32—41no—
644C22×C32—41no—
645C22×C32—41no—
646C22×C32—41no—
647C22×C32—41no—
648C22×C32—61no—
649C22×C32—61no—
650C22×C32—61no—
651C22×C32—61no—
652C22×C32—61no—
653C22×C32—61no—
654C22×C32—81no—
655C22×C32—81no—
656C22×C32C23×D311yescharacteristic
657C22×C32C23×D311yescharacteristic
658C22×C32C23×D311yescharacteristic
659C2×C3⋊D3—21no—
660C2×C3⋊D3—21no—
661C2×C3⋊D3—21no—
662C2×C3⋊D3—21no—
663C2×C3⋊D3—21no—
664C2×C3⋊D3D3×D412yes—
665C2×C3×D3—22no—
666C2×C3×D3—21no—
667C2×C3×D3—21no—
668C2×C3×D3—21no—
669C2×C3×D3—21no—
670C2×C3×D3—21no—
671C2×C3×D3—21no—
672C2×C3×D3—21no—
673C2×C3×D3—21no—
674C2×C3×D3—21no—
675C2×C3×D3—21no—
676C2×C3×D3—21no—
677C2×C3×D3—21no—
678C2×C3×D3—32no—
679C2×C3×D3—32no—
680C2×C3×D3—41no—
681C2×C3×D3—41no—
682C2×C3×D3—41no—
683C2×C3×D3—41no—
684C2×C3×D3—41no—
685C2×C3×D3—62no—
686C2×C3×D3—61no—
687C2×C3×D3—61no—
688C2×C3×D3—61no—
689C2×C3×D3—61no—
690C2×C3×D3—61no—
691C2×C3×D3—61no—
692C2×C3×D3—61no—
693C2×C3×D3—61no—
694C2×C3×D3—61no—
695C2×C3×D3—61no—
696C2×C3×D3—121no—
697C2×C3×D3—121no—
698C2×C3×D3—121no—
699C2×C3×D3—121no—
700C2×C3×D3—121no—
701C32×C4—32no—
702C32×C4—32no—
703C32×C4—61no—
704C32×C4—61no—
705C3⋊Dic3—21no—
706C3⋊Dic3—21no—
707C3⋊Dic3—61no—
708C3⋊Dic3—61no—
709C3⋊Dic3—61no—
710C3⋊Dic3—61no—
711C3⋊Dic3—61no—
712C3⋊Dic3—61no—
713C3⋊Dic3—121no—
714C3⋊Dic3—121no—
715C3⋊Dic3—121no—
716C3⋊Dic3—121no—
717C3⋊Dic3—121no—
718C3⋊Dic3—121no—
719C3⋊Dic3—241no—
720C3⋊Dic3—241no—
721C3⋊Dic3D3×D412yes—
722C3⋊Dic3D3×D412yes—
723C3×Dic3—21no—
724C3×Dic3—21no—
725C3×Dic3—21no—
726C3×Dic3—21no—
727C3×Dic3—22no—
728C3×Dic3—22no—
729C3×Dic3—32no—
730C3×Dic3—32no—
731C3×Dic3—32no—
732C3×Dic3—32no—
733C3×Dic3—41no—
734C3×Dic3—41no—
735C3×Dic3—62no—
736C3×Dic3—62no—
737C3×Dic3—61no—
738C3×Dic3—61no—
739C3×Dic3—61no—
740C3×Dic3—61no—
741C3×Dic3—121no—
742C3×Dic3—121no—
743C3×Dic3#23512yescomplemented
744C3×Dic3#23712yescomplemented
745C3×Dic3#23712yescomplemented
746C3×Dic3#23712yescomplemented
747C2×#41—271no—
748C2×#41—271no—
749C4⋊Q8—271no—
750#127—91no—
751#124—271no—
752#124—271no—
753#121—91no—
754#121—271no—
755#121—271no—
756#121—271no—
757C4×D4—91no—
758C4×D4—271no—
759C4×D4—271no—
760C4×D4—271no—
761C2×C42—271no—
762C33#53211yescharacteristic, complemented, Sylow
763C23×C3—21no—
764C23×C3—21no—
765C23×C3—21no—
766C23×C3—31no—
767C23×C3—31no—
768C23×C3—31no—
769C23×C3—31no—
770C23×C3—41no—
771C23×C3—61no—
772C23×C3—61no—
773C23×C3—91no—
774C23×C3—91no—
775C23×C3C2×D3211yescharacteristic
776C23×C3C2×D3211yescharacteristic
777C23×C3C2×D3211yescharacteristic
778C22×D3—31no—
779C22×D3—31no—
780C22×D3—31no—
781C22×D3—31no—
782C22×D3—61no—
783C22×D3—61no—
784C22×D3C2×D3211yescharacteristic
785C22×D3C2×D3211yescharacteristic
786C3×D4—62no—
787C3×D4—62no—
788C3×D4—62no—
789C3×D4—62no—
790C3×D4—64no—
791C3×D4—122no—
792C3×D4—182no—
793C3×D4—182no—
794C3×D4—182no—
795C3×D4—182no—
796C3×D4—182no—
797C3×D4—182no—
798C2×C3×C4—31no—
799C2×C3×C4—31no—
800C2×C3×C4—31no—
801C2×C3×C4—31no—
802C2×C3×C4—31no—
803C2×C3×C4—31no—
804C2×C3×C4—31no—
805C2×C3×C4—31no—
806C2×C3×C4—61no—
807C2×C3×C4—61no—
808C2×C3×C4—61no—
809C2×C3×C4—61no—
810C2×C3×C4—91no—
811C2×C3×C4—91no—
812C2×C3×C4—91no—
813C2×C3×C4—91no—
814C2×C3×C4—182no—
815C2×C3×C4—182no—
816C2×C3×C4—182no—
817#67—22no—
818#67—22no—
819#67—62no—
820#67—62no—
821#67—62no—
822#67—62no—
823#67—62no—
824#67—62no—
825#67—62no—
826#67—62no—
827#67—62no—
828#67—122no—
829#67—122no—
830#67—182no—
831#67—182no—
832#67—182no—
833#67—182no—
834#67—182no—
835#67—362no—
836C2×Dic3—31no—
837C2×Dic3—31no—
838C2×Dic3—31no—
839C2×Dic3—31no—
840C2×Dic3—31no—
841C2×Dic3—31no—
842C2×Dic3—31no—
843C2×Dic3—31no—
844C2×Dic3—61no—
845C2×Dic3—61no—
846C2×Dic3—61no—
847C2×Dic3—61no—
848C2×Dic3—62no—
849C2×Dic3—62no—
850C2×Dic3—62no—
851C2×Dic3—94no—
852C2×Dic3—91no—
853C2×Dic3—91no—
854C2×Dic3—91no—
855C2×Dic3—91no—
856C2×Dic3—91no—
857C2×Dic3—91no—
858C2×Dic3—122no—
859C2×Dic3—181no—
860C2×Dic3—181no—
861C2×Dic3—181no—
862C2×Dic3—181no—
863C2×Dic3—181no—
864C2×Dic3—181no—
865C2×Dic3—182no—
866C2×Dic3—182no—
867C2×Dic3—182no—
868C2×Dic3—182no—
869C2×Dic3—361no—
870C2×Dic3—361no—
871C2×Dic3—362no—
872C2×Dic3C2×D3211yescharacteristic
873C2×Dic3C2×D3211yescharacteristic
874C2×Dic3C2×D3211yescharacteristic
875C2×Dic3C2×D3211yescharacteristic
876D12—62no—
877D12—62no—
878D12—62no—
879D12—182no—
880C4×D3—62no—
881C4×D3—62no—
882C4×D3—62no—
883C4×D3—94no—
884C4×D3—94no—
885C4×D3—182no—
886C4×D3—182no—
887C4×D3—182no—
888C4×D3—182no—
889C4×D3—182no—
890C4×D3—362no—
891Dic6—182no—
892Dic6—182no—
893Dic6—182no—
894Dic6—182no—
895Dic6—182no—
896Dic6—182no—
897Dic6—362no—
898C2×C32—21no—
899C2×C32—21no—
900C2×C32—21no—
901C2×C32—21no—
902C2×C32—21no—
903C2×C32—21no—
904C2×C32—21no—
905C2×C32—21no—
906C2×C32—21no—
907C2×C32—41no—
908C2×C32—41no—
909C2×C32—41no—
910C2×C32—41no—
911C2×C32—42no—
912C2×C32—41no—
913C2×C32—41no—
914C2×C32—81no—
915C2×C32—81no—
916C2×C32—82no—
917C2×C32—121no—
918C2×C32—121no—
919C2×C32C2×#23511yescharacteristic
920C2×C32C2×D3×D411yescharacteristic
921C2×C32C2×D3×D411yescharacteristic
922C2×C32C2×D3×D411yescharacteristic
923C2×C32C2×#23711yescharacteristic
924C2×C32C2×#23711yescharacteristic
925C2×C32C2×#23711yescharacteristic
926C2×C32D3×#4111yescharacteristic
927C2×C32D3×#4111yescharacteristic
928C3⋊D3—22no—
929C3⋊D3—41no—
930C3×D3—42no—
931C3×D3—41no—
932C3×D3—41no—
933C3×D3—41no—
934C3×D3—41no—
935C3×D3—62no—
936C3×D3—62no—
937C3×D3—81no—
938C3×D3—122no—
939C3×D3—121no—
940C3×D3—121no—
941C3×D3—241no—
942#41—544no—
943#41—544no—
944C2×Q8—271no—
945C2×Q8—271no—
946C2×D4—31no—
947C2×D4—31no—
948C2×D4—91no—
949C2×D4—91no—
950C2×D4—91no—
951C2×D4—91no—
952C2×D4—91no—
953C2×D4—91no—
954C2×D4—271no—
955C2×D4—271no—
956C22×C4—91no—
957C22×C4—91no—
958C22×C4—91no—
959C22×C4—271no—
960C22×C4—271no—
961C22×C4—271no—
962C22×C4—271no—
963C4⋊C4—91no—
964C4⋊C4—91no—
965C4⋊C4—271no—
966C4⋊C4—271no—
967C22⋊C4—31no—
968C22⋊C4—91no—
969C22⋊C4—91no—
970C22⋊C4—271no—
971C22⋊C4—271no—
972C22⋊C4—271no—
973C22⋊C4—271no—
974C22⋊C4—271no—
975C42—91no—
976C42—91no—
977C42—271no—
978C42—271no—
979C22×C3—22no—
980C22×C3—21no—
981C22×C3—21no—
982C22×C3—21no—
983C22×C3—21no—
984C22×C3—21no—
985C22×C3—21no—
986C22×C3—21no—
987C22×C3—21no—
988C22×C3—21no—
989C22×C3—21no—
990C22×C3—21no—
991C22×C3—21no—
992C22×C3—41no—
993C22×C3—41no—
994C22×C3—41no—
995C22×C3—41no—
996C22×C3—41no—
997C22×C3—41no—
998C22×C3—41no—
999C22×C3—41no—
1000C22×C3—42no—
1001C22×C3—41no—
1002C22×C3—62no—
1003C22×C3—61no—
1004C22×C3—61no—
1005C22×C3—61no—
1006C22×C3—61no—
1007C22×C3—61no—
1008C22×C3—61no—
1009C22×C3—61no—
1010C22×C3—61no—
1011C22×C3—61no—
1012C22×C3—61no—
1013C22×C3—61no—
1014C22×C3—61no—
1015C22×C3—81no—
1016C22×C3—81no—
1017C22×C3—92no—
1018C22×C3—121no—
1019C22×C3—121no—
1020C22×C3—121no—
1021C22×C3—121no—
1022C22×C3—121no—
1023C22×C3—181no—
1024C22×C3—181no—
1025C22×C3—181no—
1026C22×C3—181no—
1027C22×C3—181no—
1028C22×C3C22×D3211yescharacteristic
1029C22×C3C22×D3211yescharacteristic
1030C22×C3C22×D3211yescharacteristic
1031C2×D3—21no—
1032C2×D3—21no—
1033C2×D3—21no—
1034C2×D3—21no—
1035C2×D3—21no—
1036C2×D3—21no—
1037C2×D3—32no—
1038C2×D3—32no—
1039C2×D3—62no—
1040C2×D3—61no—
1041C2×D3—61no—
1042C2×D3—61no—
1043C2×D3—61no—
1044C2×D3—61no—
1045C2×D3—61no—
1046C2×D3—61no—
1047C2×D3—61no—
1048C2×D3—61no—
1049C2×D3—61no—
1050C2×D3—121no—
1051C2×D3—121no—
1052C2×D3—121no—
1053C2×D3—121no—
1054C2×D3—121no—
1055C3×C4—32no—
1056C3×C4—32no—
1057C3×C4—32no—
1058C3×C4—32no—
1059C3×C4—62no—
1060C3×C4—62no—
1061C3×C4—61no—
1062C3×C4—61no—
1063C3×C4—61no—
1064C3×C4—61no—
1065C3×C4—92no—
1066C3×C4—92no—
1067C3×C4—121no—
1068C3×C4—121no—
1069C3×C4—181no—
1070C3×C4—181no—
1071Dic3—21no—
1072Dic3—21no—
1073Dic3—32no—
1074Dic3—32no—
1075Dic3—32no—
1076Dic3—32no—
1077Dic3—62no—
1078Dic3—62no—
1079Dic3—61no—
1080Dic3—61no—
1081Dic3—61no—
1082Dic3—61no—
1083Dic3—121no—
1084Dic3—121no—
1085Dic3—181no—
1086Dic3—181no—
1087Dic3—181no—
1088Dic3—181no—
1089Dic3—181no—
1090Dic3—181no—
1091Dic3—361no—
1092Dic3—361no—
1093Dic3—361no—
1094Dic3—361no—
1095Dic3—361no—
1096Dic3—361no—
1097Dic3—721no—
1098Dic3—721no—
1099Dic3#380412yescomplemented
1100Dic3#380512yescomplemented
1101C32—21no—
1102C32—21no—
1103C32—21no—
1104C32—41no—
1105C32#554811yescharacteristic, complemented
1106C32#559611yescharacteristic, complemented
1107C32#571611yescharacteristic, complemented
1108C23—31no—
1109C23—31no—
1110C23—91no—
1111C23—91no—
1112C23D3311yescharacteristic
1113Q8—542no—
1114Q8—542no—
1115D4—62no—
1116D4—62no—
1117D4—182no—
1118D4—182no—
1119D4—182no—
1120D4—182no—
1121D4—182no—
1122D4—182no—
1123D4—542no—
1124D4—542no—
1125C2×C4—31no—
1126C2×C4—31no—
1127C2×C4—31no—
1128C2×C4—31no—
1129C2×C4—91no—
1130C2×C4—91no—
1131C2×C4—91no—
1132C2×C4—91no—
1133C2×C4—182no—
1134C2×C4—182no—
1135C2×C4—182no—
1136C2×C4—274no—
1137C2×C4—271no—
1138C2×C4—271no—
1139C2×C4—542no—
1140C2×C4—542no—
1141C2×C4—542no—
1142C2×C3—21no—
1143C2×C3—21no—
1144C2×C3—21no—
1145C2×C3—21no—
1146C2×C3—21no—
1147C2×C3—21no—
1148C2×C3—21no—
1149C2×C3—21no—
1150C2×C3—21no—
1151C2×C3—42no—
1152C2×C3—41no—
1153C2×C3—41no—
1154C2×C3—41no—
1155C2×C3—41no—
1156C2×C3—41no—
1157C2×C3—41no—
1158C2×C3—81no—
1159C2×C3—81no—
1160C2×C3—82no—
1161C2×C3—122no—
1162C2×C3—121no—
1163C2×C3—121no—
1164C2×C3—121no—
1165C2×C3—121no—
1166C2×C3—182no—
1167C2×C3—241no—
1168C2×C3—361no—
1169C2×C3D3×#23511yescharacteristic
1170C2×C3D32×D411yescharacteristic
1171C2×C3D32×D411yescharacteristic
1172C2×C3D32×D411yescharacteristic
1173C2×C3D3×#23711yescharacteristic
1174C2×C3D3×#23711yescharacteristic
1175C2×C3D3×#23711yescharacteristic
1176C2×C3C2×#380411yescharacteristic
1177C2×C3C2×#380511yescharacteristic
1178D3—41no—
1179D3—41no—
1180D3—62no—
1181D3—62no—
1182D3—122no—
1183D3—121no—
1184D3—121no—
1185D3—241no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—61no—
1190C22—61no—
1191C22—61no—
1192C22—61no—
1193C22—61no—
1194C22—61no—
1195C22—92no—
1196C22—181no—
1197C22—181no—
1198C22—181no—
1199C22—181no—
1200C22—181no—
1201C22C2×D3311yescharacteristic
1202C4—32no—
1203C4—32no—
1204C4—61no—
1205C4—61no—
1206C4—92no—
1207C4—92no—
1208C4—181no—
1209C4—181no—
1210C4—541no—
1211C4—541no—
1212C3—21no—
1213C3—21no—
1214C3—21no—
1215C3—41no—
1216C3#1059405811yescharacteristic, complemented
1217C3#1059513311yescharacteristic, complemented
1218C3#1059513911yescharacteristic, complemented
1219C2—41no—
1220C2—121no—
1221C2—121no—
1222C2—182no—
1223C2—361no—
1224C2D3×#380411yescharacteristic
1225C2D3×#380511yescharacteristic
1226C2#1172444011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#532
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#89046C2semidirect
2. C2×#88961C2semidirect
3. #11723631C2semidirect
4. #67×C3⋊Dic3C2semidirect
5. #11723591C2semidirect
6. C3×#63979C2semidirect
7. C3×#67⋊Dic3C2semidirect
8. C3×#63958C2semidirect
9. #11723036C2semidirect
10. #11723006C2semidirect
11. #11722962C2semidirect
12. #11722957C2semidirect
13. #11722928C2semidirect
14. #11722927C2semidirect
15. Dic3×#624C2semidirect
71. #63979D3semidirect
73. #67⋊Dic3D3semidirect
88. #63958D3semidirect
127. #6294D4semidirect
298. C32×Dic3#41semidirect
299. C32×Dic3#41semidirect
743. C3×Dic3#235semidirect
744. C3×Dic3#237semidirect
745. C3×Dic3#237semidirect
746. C3×Dic3#237semidirect
762. C33#532semidirect
1099. Dic3#3804semidirect
1100. Dic3#3805semidirect
1105. C32#5548semidirect
1106. C32#5596semidirect
1107. C32#5716semidirect
1216. C3#10594058semidirect
1217. C3#10595133semidirect
1218. C3#10595139semidirect

Maximal subgroups

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

subgroupindex
C2×#890462
C2×#889612
#117236312
#67×C3⋊Dic32
#117235912
C3×#639792
C3×#67⋊Dic32
C3×#639582
#117230362
#117230062
#117229622
#117229572
#117229282
#117229272
Dic3×#6242
#105951393
#105951333
#105940583