Finite Group Databasebeta

← #13171930

Subgroups — #13171930

Order 1728.

1266 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723720C211yesmaximal, characteristic, complemented
2#11723642C211yesmaximal, characteristic, complemented
3#11723637C211yesmaximal, characteristic
4C2×Dic3×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×Dic3×#67C211yesmaximal, characteristic, complemented
6C3×#63962C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8#11723025C211yesmaximal, characteristic, complemented
9#11723022C211yesmaximal, characteristic, complemented
10#11723016C211yesmaximal, characteristic, complemented
11#11723009C211yesmaximal, characteristic, complemented
12#11722942C211yesmaximal, characteristic, complemented
13#11722930C211yesmaximal, characteristic, complemented
14#11722915C211yesmaximal, characteristic, complemented
15#11722913C211yesmaximal, characteristic, complemented
16#10595116—31nomaximal
17#10595033—31nomaximal
18#10594131—31nomaximal
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C2×#6293C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×C3×#624C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C3×#3757C2211yescharacteristic
29C32×#217C2211yescharacteristic
30#88815C2211yescharacteristic
31#88815C2211yescharacteristic
32#88814C2211yescharacteristic
33#88814C2211yescharacteristic
34#88807C2211yescharacteristic
35#88806C2211yescharacteristic
36#88806C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38#88803C2211yescharacteristic
39(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3×C3⋊Dic3C2211yescharacteristic
41Dic3×C3⋊Dic3C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64148—31no—
55C2×C4×C3⋊Dic3—31no—
56#64087—31no—
57C3×#935—31no—
58C3×D4×Dic3—31no—
59C3×C4×#67—31no—
60C3×C4×#67—31no—
61C3×#886—31no—
62C3×#67⋊C4—31no—
63#63982—31no—
64#63982—31no—
65#63982—61no—
66#63980—31no—
67#63980—31no—
68#63980—61no—
69Dic3×#67D311yescharacteristic, complemented
70#63966—31no—
71#63962—31no—
72#63962D311yescharacteristic, complemented
73#63961—31no—
74#63956—31no—
75#63955—31no—
76C2×Dic32—31no—
77C2×Dic32—31no—
78C2×Dic32—61no—
79#63953—31no—
80#63952—31no—
81#63952D311yescharacteristic, complemented
82C4×#627—31no—
83#63915—31no—
84#63913—31no—
85C4×#625—31no—
86#63879—31no—
87#63877—31no—
88#63870—31no—
89#63862—31no—
90#63862—31no—
91#63861—31no—
92#63858—31no—
93#63855—31no—
94#63855—31no—
95#63848—31no—
96#63847—31no—
97#63847—31no—
98#63844—31no—
99#63841—31no—
100#63837—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)—22no—
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C3×#638—22no—
109C2×C3×C3⋊Dic3—22no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C32×#67—22no—
116C2×C32×Dic3—22no—
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6293—22no—
123#6290—22no—
124C3×#624—22no—
125C3×D3×Dic3—22no—
126#5649—91no—
127#5538—91no—
128#5538—91no—
129C2×C32×D4—31no—
130C22×C32×C4—31no—
131C2×#638—31no—
132C2×#638C2×D311yescharacteristic
133C22×C3⋊Dic3—31no—
134C22×C3⋊Dic3—31no—
135C22×C3⋊Dic3—31no—
136C22×C3⋊Dic3—61no—
137C22×C3⋊Dic3—61no—
138C22×C3⋊Dic3—61no—
139C22×C3⋊Dic3—121no—
140C22×C3⋊Dic3C2×D311yescharacteristic
141C2×#634—31no—
142C2×C3×#67—21no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—61no—
146C2×C3×#67C2×D311yescharacteristic
147C2×C3×#67C2×D311yescharacteristic
148C22×C3×Dic3—21no—
149C22×C3×Dic3—31no—
150C22×C3×Dic3—31no—
151C22×C3×Dic3—31no—
152C22×C3×Dic3—61no—
153C22×C3×Dic3C2×D311yescharacteristic
154C22×C3×Dic3C2×D311yescharacteristic
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—31no—
157C2×C3×C4×D3—31no—
158C2×#627—31no—
159C2×#627—31no—
160C2×#627—61no—
161C2×#625—31no—
162C2×#625—31no—
163C2×#625—61no—
164C2×#624C2×D311yescharacteristic
165C2×D3×Dic3C2×D311yescharacteristic
166C32×C22⋊C4—31no—
167#3757—31no—
168#3757C2×D311yescharacteristic
169#3752—31no—
170C4⋊(C3⋊Dic3)—31no—
171#3750—31no—
172#3750—31no—
173#3750—31no—
174C4×C3⋊Dic3—31no—
175C4×C3⋊Dic3—31no—
176C4×C3⋊Dic3—31no—
177C4×C3⋊Dic3—31no—
178C3×#217—21no—
179C3×#217—31no—
180C3×#217—31no—
181C3×#217—31no—
182C3×#217—31no—
183C3×#217—31no—
184C3×#217—61no—
185C3×#217C2×D311yescharacteristic
186C3×#217C2×D311yescharacteristic
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—31no—
192C3×C4⋊Dic3—31no—
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×C4×Dic3—31no—
201C3×C4×Dic3—31no—
202C3×C4×Dic3—31no—
203C3×C4×Dic3—31no—
204#3724—31no—
205#3724—31no—
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—61no—
211#3724—61no—
212#3724C2×D311yescharacteristic
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—61no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3C2×D311yescharacteristic
224Dic3⋊Dic3C2×D311yescharacteristic
225Dic3⋊Dic3C2×D311yescharacteristic
226#3722—31no—
227#3722—31no—
228#3722C2×D311yescharacteristic
229(C2×D3)⋊Dic3—31no—
230(C2×D3)⋊Dic3—31no—
231(C2×D3)⋊Dic3—31no—
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—61no—
238(C2×D3)⋊Dic3—61no—
239(C2×D3)⋊Dic3C2×D311yescharacteristic
240(C2×D3)⋊Dic3C2×D311yescharacteristic
241(C2×D3)⋊Dic3C2×D311yescharacteristic
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—61no—
251Dic32—61no—
252Dic32—61no—
253Dic32—61no—
254Dic32C2×D311yescharacteristic
255Dic32C2×D311yescharacteristic
256C22×C33—21no—
257C22×C33—21no—
258C22×C33#4112yes—
259C22×C33C2411yescharacteristic
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3—21no—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3—21no—
266C3⋊(C3⋊Dic3)—21no—
267C3⋊(C3⋊Dic3)#4112yes—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3#4112yes—
278C3×#123—91no—
279C3×C4×D4—91no—
280C3×C4×D4—91no—
281#939—91no—
282#939—91no—
283#939—91no—
284#939—181no—
285#935—31no—
286#935—91no—
287D4×Dic3—31no—
288#929—91no—
289C4×#67—31no—
290C4×#67—31no—
291C4×#67—91no—
292C4×#67—91no—
293#926—91no—
294#926—91no—
295C2×C4×Dic3—91no—
296C2×C4×Dic3—91no—
297C2×C4×Dic3—91no—
298C2×C4×Dic3—181no—
299#898—91no—
300#898—91no—
301#898—91no—
302#892—91no—
303#889—91no—
304#889—91no—
305#889—91no—
306#887—91no—
307#886—31no—
308#886—91no—
309#885—91no—
310#885—91no—
311#885—91no—
312#67⋊C4—31no—
313#67⋊C4—91no—
314#879—91no—
315#879—91no—
316#879—91no—
317#878—91no—
318#878—91no—
319#878—91no—
320#878—181no—
321#877—91no—
322#872—91no—
323#872—91no—
324C4×Dic6—91no—
325C4×Dic6—91no—
326C23×C32—21no—
327C23×C32—21no—
328C23×C32—21no—
329C23×C32—31no—
330C23×C32—41no—
331C23×C32C22×D311yescharacteristic
332C23×C32C22×D311yescharacteristic
333C23×C32C22×D311yescharacteristic
334C22×C3⋊D3C22×D311yescharacteristic
335C22×C3×D3—21no—
336C22×C3×D3—31no—
337C22×C3×D3—31no—
338C22×C3×D3—61no—
339C22×C3×D3C22×D311yescharacteristic
340C22×C3×D3C22×D311yescharacteristic
341C32×D4—62no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—31no—
347C2×C32×C4—62no—
348#638—22no—
349#638—62no—
350C2×C3⋊Dic3—22no—
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—31no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—31no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—61no—
362C2×C3⋊Dic3—61no—
363C2×C3⋊Dic3—62no—
364C2×C3⋊Dic3—62no—
365C2×C3⋊Dic3—62no—
366C2×C3⋊Dic3—64no—
367C2×C3⋊Dic3—121no—
368C2×C3⋊Dic3—121no—
369C2×C3⋊Dic3—122no—
370C2×C3⋊Dic3—122no—
371C2×C3⋊Dic3—124no—
372C2×C3⋊Dic3C22×D311yescharacteristic
373C2×C3⋊Dic3C22×D311yescharacteristic
374C2×C3⋊Dic3C22×D311yescharacteristic
375C2×C3⋊Dic3C22×D311yescharacteristic
376C2×C3⋊Dic3C22×D311yescharacteristic
377#634—62no—
378C3×#67—22no—
379C3×#67—22no—
380C3×#67—42no—
381C3×#67—62no—
382C3×#67—62no—
383C3×#67—122no—
384C2×C3×Dic3—24no—
385C2×C3×Dic3—22no—
386C2×C3×Dic3—22no—
387C2×C3×Dic3—21no—
388C2×C3×Dic3—21no—
389C2×C3×Dic3—21no—
390C2×C3×Dic3—21no—
391C2×C3×Dic3—21no—
392C2×C3×Dic3—31no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—61no—
403C2×C3×Dic3—61no—
404C2×C3×Dic3—61no—
405C2×C3×Dic3—61no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3—64no—
408C2×C3×Dic3—62no—
409C2×C3×Dic3—62no—
410C2×C3×Dic3—62no—
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C3×C4×D3—62no—
422C3×C4×D3—62no—
423C3×C4×D3—62no—
424#627—62no—
425#627—62no—
426#627—122no—
427#625—62no—
428#625—62no—
429#625—122no—
430#624—22no—
431D3×Dic3—22no—
432#529—271noSylow
433C2×C33—22no—
434C2×C33C2×#4111yescharacteristic
435C2×C33C2×#4111yescharacteristic
436C2×C33C2×#4111yescharacteristic
437C3×C3⋊D3—41no—
438C32×D3—41no—
439C2×C3×D4—31no—
440C2×C3×D4—31no—
441C2×C3×D4—61no—
442C2×C3×D4—91no—
443C22×C3×C4—31no—
444C22×C3×C4—31no—
445C22×C3×C4—61no—
446C22×C3×C4—91no—
447C22×C3×C4—91no—
448C22×C3×C4—91no—
449C2×#67—31no—
450C2×#67—31no—
451C2×#67—61no—
452C2×#67—91no—
453C2×#67—91no—
454C2×#67—91no—
455C2×#67—181no—
456C2×#67D3211yescharacteristic
457C22×Dic3—31no—
458C22×Dic3—31no—
459C22×Dic3—31no—
460C22×Dic3—61no—
461C22×Dic3—91no—
462C22×Dic3—91no—
463C22×Dic3—91no—
464C22×Dic3—181no—
465C22×Dic3—181no—
466C22×Dic3—181no—
467C22×Dic3—361no—
468C22×Dic3D3211yescharacteristic
469C2×C4×D3—31no—
470C2×C4×D3—31no—
471C2×C4×D3—31no—
472C2×Dic6—91no—
473C2×Dic6—91no—
474C2×Dic6—91no—
475C2×Dic6—181no—
476C3×C4⋊C4—91no—
477C3×C4⋊C4—91no—
478C3×C4⋊C4—91no—
479C3×C4⋊C4—91no—
480C3×C22⋊C4—31no—
481C3×C22⋊C4—31no—
482C3×C22⋊C4—61no—
483C3×C22⋊C4—91no—
484C3×C22⋊C4—91no—
485C3×C22⋊C4—91no—
486C3×C22⋊C4—91no—
487C3×C22⋊C4—91no—
488C3×C42—91no—
489C3×C42—91no—
490#217—31no—
491#217—31no—
492#217—31no—
493#217—31no—
494#217—31no—
495#217—61no—
496#217—91no—
497#217—91no—
498#217—91no—
499#217—91no—
500#217—91no—
501#217—181no—
502#217D3211yescharacteristic
503(C2×D3)⋊C4—31no—
504(C2×D3)⋊C4—31no—
505(C2×D3)⋊C4—31no—
506(C2×D3)⋊C4—31no—
507(C2×D3)⋊C4—31no—
508(C2×D3)⋊C4—91no—
509(C2×D3)⋊C4—91no—
510(C2×D3)⋊C4—91no—
511(C2×D3)⋊C4—91no—
512(C2×D3)⋊C4—91no—
513(C2×D3)⋊C4—91no—
514(C2×D3)⋊C4—91no—
515(C2×D3)⋊C4—181no—
516C4⋊Dic3—31no—
517C4⋊Dic3—31no—
518C4⋊Dic3—31no—
519C4⋊Dic3—91no—
520C4⋊Dic3—91no—
521C4⋊Dic3—91no—
522C4⋊Dic3—91no—
523C4⋊Dic3—91no—
524C4⋊Dic3—181no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—31no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—91no—
531Dic3⋊C4—91no—
532Dic3⋊C4—91no—
533Dic3⋊C4—91no—
534Dic3⋊C4—91no—
535Dic3⋊C4—91no—
536Dic3⋊C4—91no—
537Dic3⋊C4—91no—
538Dic3⋊C4—91no—
539Dic3⋊C4—91no—
540Dic3⋊C4—91no—
541Dic3⋊C4—91no—
542Dic3⋊C4—91no—
543Dic3⋊C4—181no—
544Dic3⋊C4—181no—
545Dic3⋊C4—181no—
546C4×Dic3—31no—
547C4×Dic3—31no—
548C4×Dic3—31no—
549C4×Dic3—31no—
550C4×Dic3—91no—
551C4×Dic3—91no—
552C4×Dic3—91no—
553C4×Dic3—91no—
554C4×Dic3—91no—
555C4×Dic3—91no—
556C4×Dic3—91no—
557C4×Dic3—91no—
558C4×Dic3—91no—
559C4×Dic3—91no—
560C4×Dic3—91no—
561C4×Dic3—91no—
562C4×Dic3—181no—
563C4×Dic3—181no—
564C4×Dic3—181no—
565C4×Dic3—181no—
566C22×C32—21no—
567C22×C32—21no—
568C22×C32—22no—
569C22×C32—22no—
570C22×C32—21no—
571C22×C32—21no—
572C22×C32—21no—
573C22×C32—21no—
574C22×C32—21no—
575C22×C32—21no—
576C22×C32—21no—
577C22×C32—22no—
578C22×C32—22no—
579C22×C32—22no—
580C22×C32—42no—
581C22×C32—41no—
582C22×C32—41no—
583C22×C32—41no—
584C22×C32—41no—
585C22×C32—41no—
586C22×C32—42no—
587C22×C32—42no—
588C22×C32—61no—
589C22×C32—61no—
590C22×C32—61no—
591C22×C32#23512yes—
592C22×C32#23512yes—
593C22×C32#23712yes—
594C22×C32C23×D311yescharacteristic
595C22×C32C23×D311yescharacteristic
596C22×C32C23×D311yescharacteristic
597C2×C3⋊D3—21no—
598C2×C3⋊D3—21no—
599C2×C3⋊D3—21no—
600C2×C3×D3—21no—
601C2×C3×D3—21no—
602C2×C3×D3—21no—
603C2×C3×D3—21no—
604C2×C3×D3—21no—
605C2×C3×D3—21no—
606C2×C3×D3—41no—
607C2×C3×D3—41no—
608C2×C3×D3—41no—
609C2×C3×D3—61no—
610C2×C3×D3—61no—
611C2×C3×D3—61no—
612C2×C3×D3—61no—
613C2×C3×D3—61no—
614C2×C3×D3—61no—
615C2×C3×D3—121no—
616C2×C3×D3—121no—
617C2×C3×D3—121no—
618C32×C4—32no—
619C32×C4—61no—
620C32×C4—61no—
621C32×C4—61no—
622C32×C4—61no—
623C3⋊Dic3—21no—
624C3⋊Dic3—21no—
625C3⋊Dic3—21no—
626C3⋊Dic3—21no—
627C3⋊Dic3—21no—
628C3⋊Dic3—32no—
629C3⋊Dic3—32no—
630C3⋊Dic3—32no—
631C3⋊Dic3—62no—
632C3⋊Dic3—62no—
633C3⋊Dic3—62no—
634C3⋊Dic3—61no—
635C3⋊Dic3—62no—
636C3⋊Dic3—61no—
637C3⋊Dic3—61no—
638C3⋊Dic3—122no—
639C3⋊Dic3—121no—
640C3⋊Dic3—121no—
641C3⋊Dic3—122no—
642C3×Dic3—22no—
643C3×Dic3—21no—
644C3×Dic3—21no—
645C3×Dic3—21no—
646C3×Dic3—21no—
647C3×Dic3—21no—
648C3×Dic3—21no—
649C3×Dic3—21no—
650C3×Dic3—21no—
651C3×Dic3—22no—
652C3×Dic3—41no—
653C3×Dic3—41no—
654C3×Dic3—41no—
655C3×Dic3—62no—
656C3×Dic3—62no—
657C3×Dic3—61no—
658C3×Dic3—61no—
659C3×Dic3—61no—
660C3×Dic3—61no—
661C3×Dic3—61no—
662C3×Dic3—61no—
663C3×Dic3—61no—
664C3×Dic3—61no—
665C3×Dic3—61no—
666C3×Dic3—61no—
667C3×Dic3—121no—
668C3×Dic3—121no—
669C3×Dic3—121no—
670C3×Dic3#23712yes—
671C3×Dic3#23712yes—
672#126—271no—
673#126—271no—
674#125—271no—
675#124—271no—
676#123—91no—
677#123—271no—
678C22⋊Q8—271no—
679#121—271no—
680C4×Q8—271no—
681C4×D4—91no—
682C4×D4—91no—
683C4×D4—271no—
684#117—271no—
685#117—271no—
686C2×C42—271no—
687C33#52911yescharacteristic, complemented, Sylow
688C23×C3—21no—
689C23×C3—21no—
690C23×C3—21no—
691C23×C3—31no—
692C23×C3—31no—
693C23×C3—41no—
694C23×C3—61no—
695C23×C3—91no—
696C23×C3C2×D3211yescharacteristic
697C23×C3C2×D3211yescharacteristic
698C23×C3C2×D3211yescharacteristic
699C22×D3—31no—
700C22×D3—31no—
701C22×D3—61no—
702C22×D3C2×D3211yescharacteristic
703C3×D4—62no—
704C3×D4—62no—
705C3×D4—122no—
706C3×D4—182no—
707C2×C3×C4—31no—
708C2×C3×C4—31no—
709C2×C3×C4—31no—
710C2×C3×C4—31no—
711C2×C3×C4—31no—
712C2×C3×C4—31no—
713C2×C3×C4—31no—
714C2×C3×C4—31no—
715C2×C3×C4—31no—
716C2×C3×C4—31no—
717C2×C3×C4—61no—
718C2×C3×C4—61no—
719C2×C3×C4—61no—
720C2×C3×C4—61no—
721C2×C3×C4—61no—
722C2×C3×C4—62no—
723C2×C3×C4—62no—
724C2×C3×C4—64no—
725C2×C3×C4—91no—
726C2×C3×C4—91no—
727C2×C3×C4—91no—
728C2×C3×C4—91no—
729C2×C3×C4—91no—
730C2×C3×C4—182no—
731C2×C3×C4—182no—
732C2×C3×C4—182no—
733#67—22no—
734#67—62no—
735#67—62no—
736#67—122no—
737#67—182no—
738#67—182no—
739#67—182no—
740#67—362no—
741C2×Dic3—22no—
742C2×Dic3—31no—
743C2×Dic3—31no—
744C2×Dic3—31no—
745C2×Dic3—31no—
746C2×Dic3—31no—
747C2×Dic3—31no—
748C2×Dic3—31no—
749C2×Dic3—31no—
750C2×Dic3—31no—
751C2×Dic3—31no—
752C2×Dic3—61no—
753C2×Dic3—61no—
754C2×Dic3—61no—
755C2×Dic3—61no—
756C2×Dic3—61no—
757C2×Dic3—64no—
758C2×Dic3—62no—
759C2×Dic3—62no—
760C2×Dic3—62no—
761C2×Dic3—91no—
762C2×Dic3—91no—
763C2×Dic3—91no—
764C2×Dic3—91no—
765C2×Dic3—91no—
766C2×Dic3—91no—
767C2×Dic3—181no—
768C2×Dic3—181no—
769C2×Dic3—181no—
770C2×Dic3—181no—
771C2×Dic3—181no—
772C2×Dic3—181no—
773C2×Dic3—182no—
774C2×Dic3—182no—
775C2×Dic3—182no—
776C2×Dic3—184no—
777C2×Dic3—361no—
778C2×Dic3—361no—
779C2×Dic3—362no—
780C2×Dic3—362no—
781C2×Dic3—364no—
782C2×Dic3C2×D3211yescharacteristic
783C2×Dic3C2×D3211yescharacteristic
784C2×Dic3C2×D3211yescharacteristic
785C2×Dic3C2×D3211yescharacteristic
786C2×Dic3C2×D3211yescharacteristic
787C4×D3—62no—
788C4×D3—62no—
789C4×D3—62no—
790Dic6—182no—
791Dic6—182no—
792Dic6—182no—
793Dic6—362no—
794C2×C32—22no—
795C2×C32—24no—
796C2×C32—22no—
797C2×C32—22no—
798C2×C32—21no—
799C2×C32—21no—
800C2×C32—21no—
801C2×C32—21no—
802C2×C32—21no—
803C2×C32—21no—
804C2×C32—21no—
805C2×C32—21no—
806C2×C32—21no—
807C2×C32—41no—
808C2×C32—41no—
809C2×C32—41no—
810C2×C32—42no—
811C2×C32—42no—
812C2×C32—44no—
813C2×C32—121no—
814C2×C32C2×#23511yescharacteristic
815C2×C32C2×#23511yescharacteristic
816C2×C32C2×#23711yescharacteristic
817C2×C32C2×#23711yescharacteristic
818C2×C32C2×#23711yescharacteristic
819C2×C32D3×#4111yescharacteristic
820C2×C32D3×#4111yescharacteristic
821C2×C32D3×#4111yescharacteristic
822C2×C32D3×#4111yescharacteristic
823C3⋊D3—41no—
824C3×D3—41no—
825C3×D3—41no—
826C3×D3—81no—
827C3×D3—121no—
828C3×D3—121no—
829C3×D3—241no—
830C2×Q8—271no—
831C2×D4—31no—
832C2×D4—91no—
833C2×D4—271no—
834C22×C4—31no—
835C22×C4—91no—
836C22×C4—91no—
837C22×C4—91no—
838C22×C4—271no—
839C4⋊C4—91no—
840C4⋊C4—91no—
841C4⋊C4—91no—
842C4⋊C4—91no—
843C4⋊C4—271no—
844C4⋊C4—271no—
845C4⋊C4—271no—
846C4⋊C4—271no—
847C4⋊C4—271no—
848C4⋊C4—271no—
849C22⋊C4—31no—
850C22⋊C4—91no—
851C22⋊C4—91no—
852C22⋊C4—91no—
853C22⋊C4—91no—
854C22⋊C4—91no—
855C22⋊C4—271no—
856C22⋊C4—271no—
857C22⋊C4—271no—
858C22⋊C4—271no—
859C42—91no—
860C42—91no—
861C42—271no—
862C42—271no—
863C42—271no—
864C42—271no—
865C22×C3—22no—
866C22×C3—22no—
867C22×C3—21no—
868C22×C3—21no—
869C22×C3—21no—
870C22×C3—21no—
871C22×C3—21no—
872C22×C3—21no—
873C22×C3—21no—
874C22×C3—21no—
875C22×C3—21no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—41no—
880C22×C3—41no—
881C22×C3—41no—
882C22×C3—41no—
883C22×C3—42no—
884C22×C3—42no—
885C22×C3—41no—
886C22×C3—42no—
887C22×C3—61no—
888C22×C3—61no—
889C22×C3—61no—
890C22×C3—61no—
891C22×C3—61no—
892C22×C3—61no—
893C22×C3—121no—
894C22×C3—121no—
895C22×C3—121no—
896C22×C3—181no—
897C22×C3—181no—
898C22×C3—181no—
899C22×C3#379512yes—
900C22×C3#379812yes—
901C22×C3#380412yes—
902C22×C3C22×D3211yescharacteristic
903C22×C3C22×D3211yescharacteristic
904C22×C3C22×D3211yescharacteristic
905C2×D3—21no—
906C2×D3—21no—
907C2×D3—21no—
908C2×D3—61no—
909C2×D3—61no—
910C2×D3—61no—
911C2×D3—61no—
912C2×D3—61no—
913C2×D3—61no—
914C2×D3—121no—
915C2×D3—121no—
916C2×D3—121no—
917C3×C4—32no—
918C3×C4—32no—
919C3×C4—62no—
920C3×C4—62no—
921C3×C4—61no—
922C3×C4—61no—
923C3×C4—61no—
924C3×C4—61no—
925C3×C4—61no—
926C3×C4—61no—
927C3×C4—61no—
928C3×C4—61no—
929C3×C4—121no—
930C3×C4—121no—
931C3×C4—121no—
932C3×C4—181no—
933C3×C4—181no—
934C3×C4—181no—
935C3×C4—181no—
936C3×C4—181no—
937Dic3—21no—
938Dic3—21no—
939Dic3—21no—
940Dic3—21no—
941Dic3—62no—
942Dic3—62no—
943Dic3—61no—
944Dic3—61no—
945Dic3—61no—
946Dic3—61no—
947Dic3—61no—
948Dic3—61no—
949Dic3—61no—
950Dic3—61no—
951Dic3—61no—
952Dic3—61no—
953Dic3—92no—
954Dic3—92no—
955Dic3—92no—
956Dic3—121no—
957Dic3—121no—
958Dic3—121no—
959Dic3—182no—
960Dic3—182no—
961Dic3—182no—
962Dic3—182no—
963Dic3—181no—
964Dic3—181no—
965Dic3—181no—
966Dic3—362no—
967Dic3—361no—
968Dic3—361no—
969Dic3—362no—
970Dic3#380512yes—
971C32—21no—
972C32—21no—
973C32—21no—
974C32—41no—
975C32#553811yescharacteristic, complemented
976C32#553811yescharacteristic, complemented
977C32#564911yescharacteristic, complemented
978C23—31no—
979C23—91no—
980C23D3311yescharacteristic
981Q8—542no—
982D4—62no—
983D4—182no—
984D4—542no—
985C2×C4—31no—
986C2×C4—31no—
987C2×C4—31no—
988C2×C4—31no—
989C2×C4—31no—
990C2×C4—62no—
991C2×C4—91no—
992C2×C4—91no—
993C2×C4—91no—
994C2×C4—91no—
995C2×C4—91no—
996C2×C4—182no—
997C2×C4—182no—
998C2×C4—182no—
999C2×C4—271no—
1000C2×C4—271no—
1001C2×C4—542no—
1002C2×C3—24no—
1003C2×C3—22no—
1004C2×C3—22no—
1005C2×C3—22no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—21no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—21no—
1015C2×C3—42no—
1016C2×C3—42no—
1017C2×C3—44no—
1018C2×C3—41no—
1019C2×C3—41no—
1020C2×C3—41no—
1021C2×C3—121no—
1022C2×C3—121no—
1023C2×C3—241no—
1024C2×C3—361no—
1025C2×C3C2×#379511yescharacteristic
1026C2×C3C2×#379811yescharacteristic
1027C2×C3#6430611yescharacteristic
1028C2×C3D3×#23711yescharacteristic
1029C2×C3D3×#23711yescharacteristic
1030C2×C3#6431211yescharacteristic
1031C2×C3#6431211yescharacteristic
1032C2×C3C2×#380411yescharacteristic
1033C2×C3C2×#380511yescharacteristic
1034D3—41no—
1035D3—121no—
1036D3—121no—
1037D3—241no—
1038C22—21no—
1039C22—21no—
1040C22—61no—
1041C22—61no—
1042C22—61no—
1043C22—181no—
1044C22—181no—
1045C22—181no—
1046C22#8896012yes—
1047C22C2×D3311yescharacteristic
1048C4—32no—
1049C4—61no—
1050C4—61no—
1051C4—61no—
1052C4—61no—
1053C4—181no—
1054C4—181no—
1055C4—181no—
1056C4—181no—
1057C4—181no—
1058C4—272no—
1059C4—541no—
1060C3—21no—
1061C3—21no—
1062C3—21no—
1063C3—41no—
1064C3#1059413111yescharacteristic, complemented
1065C3#1059503311yescharacteristic, complemented
1066C3#1059511611yescharacteristic, complemented
1067C2—22no—
1068C2—121no—
1069C2—361no—
1070C2D3×#380511yescharacteristic
1071C2#1172441111yescharacteristic
1072C2C2×#8896011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radical#11723637C2
hypercenterC23D33
hypocenterC33#529
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723720C2semidirect
2. #11723642C2semidirect
4. C2×Dic3×C3⋊Dic3C2semidirect
5. C3×Dic3×#67C2semidirect
6. C3×#63962C2semidirect
7. C3×#63952C2semidirect
8. #11723025C2semidirect
9. #11723022C2semidirect
10. #11723016C2semidirect
11. #11723009C2semidirect
12. #11722942C2semidirect
13. #11722930C2semidirect
14. #11722915C2semidirect
15. #11722913C2semidirect
69. Dic3×#67D3semidirect
72. #63962D3semidirect
81. #63952D3semidirect
687. C33#529semidirect
975. C32#5538semidirect
976. C32#5538semidirect
977. C32#5649semidirect
1064. C3#10594131semidirect
1065. C3#10595033semidirect
1066. C3#10595116semidirect

Maximal subgroups

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

subgroupindex
#117237202
#117236422
#117236372
C2×Dic3×C3⋊Dic32
C3×Dic3×#672
C3×#639622
C3×#639522
#117230252
#117230222
#117230162
#117230092
#117229422
#117229302
#117229152
#117229132
#105951163
#105950333
#105941313