Finite Group Databasebeta

← #13171755

Subgroups — #13171755

Order 1728.

1254 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723725C211yesmaximal, characteristic
2#11723626C211yesmaximal, characteristic, complemented
3#11723626C211yesmaximal, characteristic, complemented
4#11723598C211yesmaximal, characteristic, complemented
5C3×#63975C211yesmaximal, characteristic, complemented
6C3×#63956C211yesmaximal, characteristic, complemented
7C3×#63953C211yesmaximal, characteristic, complemented
8#11723024C211yesmaximal, characteristic, complemented
9#11723014C211yesmaximal, characteristic, complemented
10#11722995C211yesmaximal, characteristic, complemented
11#11722979C211yesmaximal, characteristic, complemented
12#11722941C211yesmaximal, characteristic, complemented
13#11722938C211yesmaximal, characteristic, complemented
14#11722921C211yesmaximal, characteristic, complemented
15Dic3×#624C211yesmaximal, characteristic, complemented
16#10594137—31nomaximal
17#10594130—31nomaximal
18#10594111—31nomaximal
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×#6295C2211yescharacteristic
23C2×#6294C2211yescharacteristic
24C2×Dic3×C3⋊D3C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28C3×#3757C2211yescharacteristic
29C32×#217C2211yescharacteristic
30C32×#217C2211yescharacteristic
31C32×#217C2211yescharacteristic
32#88815C2211yescharacteristic
33#88814C2211yescharacteristic
34#88807C2211yescharacteristic
35#88807C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38#88803C2211yescharacteristic
39#88803C2211yescharacteristic
40Dic3×C3⋊Dic3C2211yescharacteristic
41Dic3×C3⋊Dic3C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64090—31no—
55#64090—31no—
56#64086—31no—
57C3×#885—31no—
58C3×#885—31no—
59C3×#883—31no—
60C3×#883—31no—
61C3×#879—31no—
62C3×#879—31no—
63#63975D311yescharacteristic, complemented
64#67⋊Dic3—31no—
65#67⋊Dic3—31no—
66#67⋊Dic3—31no—
67#67⋊Dic3—31no—
68#67⋊Dic3—61no—
69#67⋊Dic3—61no—
70#63971—31no—
71#63970—31no—
72#63958—31no—
73#63957—31no—
74#63957—31no—
75#63957—61no—
76#63956D311yescharacteristic, complemented
77#63953D311yescharacteristic, complemented
78#63905—31no—
79#63902—31no—
80#63899—31no—
81#63888—31no—
82#63887—31no—
83C4×#624—31no—
84#63881—31no—
85#63881—31no—
86#63878—31no—
87#63878—31no—
88C4×D3×Dic3—31no—
89C4×D3×Dic3—31no—
90#63868—31no—
91#63867—31no—
92#63867—31no—
93#63859—31no—
94#63858—31no—
95#63854—31no—
96#63850—31no—
97#63849—31no—
98#63847—31no—
99#63843—31no—
100#63843—31no—
101#63838—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)—22no—
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C3×#638—22no—
109C3×#638—22no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120#6295—22no—
121#6294—22no—
122Dic3×C3⋊D3—22no—
123Dic3×C3⋊D3—22no—
124C3×#627—22no—
125C3×#624—22no—
126#5706—91no—
127#5680—91no—
128#5649—91no—
129C2×#638C2×D311yescharacteristic
130C2×#638C2×D311yescharacteristic
131C22×C3⋊Dic3—31no—
132C22×C3⋊Dic3—31no—
133C22×C3⋊Dic3—31no—
134C22×C3⋊Dic3—61no—
135C22×C3⋊Dic3—61no—
136C22×C3⋊Dic3—61no—
137C22×C3⋊Dic3—121no—
138C2×C4×C3⋊D3—31no—
139C2×C4×C3⋊D3—31no—
140C2×C3×#67—31no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—61no—
145C2×C3×#67—61no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—31no—
148C2×C3×Dic6—31no—
149C2×C3×Dic6—31no—
150C2×#627C2×D311yescharacteristic
151C2×#626—31no—
152C2×#626—31no—
153C2×#625—31no—
154C2×#624—31no—
155C2×#624C2×D311yescharacteristic
156C2×D3×Dic3—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—61no—
163C2×D3×Dic3—61no—
164C32×C22⋊C4—31no—
165C32×C22⋊C4—31no—
166C32×C22⋊C4—31no—
167#3757C2×D311yescharacteristic
168#3752—31no—
169#3752—31no—
170#3750—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—21no—
180C3×#217—21no—
181C3×#217—31no—
182C3×#217—31no—
183C3×#217—61no—
184C3×#217C2×D311yescharacteristic
185C3×#217C2×D311yescharacteristic
186C3×#217C2×D311yescharacteristic
187C3×#217C2×D311yescharacteristic
188C3×#217C2×D311yescharacteristic
189C3×#217C2×D311yescharacteristic
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—31no—
192C3×(C2×D3)⋊C4—31no—
193C3×(C2×D3)⋊C4—31no—
194C3×(C2×D3)⋊C4—31no—
195C3×(C2×D3)⋊C4—31no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—31no—
198C3×C4⋊Dic3—31no—
199C3×C4⋊Dic3—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×C4×Dic3—31no—
207C3×C4×Dic3—31no—
208C3×C4×Dic3—31no—
209C3×C4×Dic3—31no—
210#3724—31no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214#3724—31no—
215#3724—61no—
216#3724—61no—
217#3724C2×D311yescharacteristic
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3C2×D311yescharacteristic
227Dic3⋊Dic3C2×D311yescharacteristic
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230#3722—31no—
231#3722C2×D311yescharacteristic
232#3722C2×D311yescharacteristic
233#3722C2×D311yescharacteristic
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—61no—
241(C2×D3)⋊Dic3—61no—
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—21no—
259C22×C33C2411yescharacteristic
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3—21no—
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3#4112yes—
266C3⋊(C3⋊Dic3)—21no—
267C3⋊(C3⋊Dic3)#4112yes—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3#4112yes—
272C32×Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3—21no—
278C3×#126—91no—
279C3×#124—91no—
280C3×#123—91no—
281#946—91no—
282Q8×Dic3—91no—
283#939—91no—
284#938—91no—
285D4×Dic3—91no—
286D4×Dic3—91no—
287#929—91no—
288C2×C4×Dic3—91no—
289#898—91no—
290#896—91no—
291#894—91no—
292#893—91no—
293#892—91no—
294#892—91no—
295#889—91no—
296#889—91no—
297#887—91no—
298#887—91no—
299#885—31no—
300#885—31no—
301#884—91no—
302#883—31no—
303#883—31no—
304#883—91no—
305#67⋊C4—91no—
306#67⋊C4—91no—
307#67⋊C4—91no—
308#67⋊C4—91no—
309#67⋊C4—91no—
310#67⋊C4—91no—
311#67⋊C4—181no—
312#67⋊C4—181no—
313#879—31no—
314#879—31no—
315#879—91no—
316#878—91no—
317#877—91no—
318#877—91no—
319#877—91no—
320#877—91no—
321#877—181no—
322#876—91no—
323C42×D3—91no—
324C42×D3—91no—
325#870—91no—
326C23×C32—21no—
327C23×C32—21no—
328C23×C32—21no—
329C23×C32—41no—
330C23×C32C22×D311yescharacteristic
331C23×C32C22×D311yescharacteristic
332C23×C32C22×D311yescharacteristic
333C22×C3⋊D3C22×D311yescharacteristic
334C22×C3⋊D3C22×D311yescharacteristic
335C22×C3×D3—31no—
336C22×C3×D3—31no—
337C22×C3×D3—31no—
338C22×C3×D3—31no—
339C22×C3×D3—61no—
340C22×C3×D3—61no—
341C2×C32×C4—31no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—31no—
347#638—22no—
348#638—22no—
349C2×C3⋊Dic3—31no—
350C2×C3⋊Dic3—31no—
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—31no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—61no—
356C2×C3⋊Dic3—61no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—62no—
362C2×C3⋊Dic3—62no—
363C2×C3⋊Dic3—62no—
364C2×C3⋊Dic3—64no—
365C2×C3⋊Dic3—121no—
366C2×C3⋊Dic3—121no—
367C2×C3⋊Dic3—122no—
368C2×C3⋊Dic3—122no—
369C2×C3⋊Dic3—124no—
370C2×C3⋊Dic3C22×D311yescharacteristic
371C2×C3⋊Dic3C22×D311yescharacteristic
372C2×C3⋊Dic3C22×D311yescharacteristic
373C2×C3⋊Dic3C22×D311yescharacteristic
374C4×C3⋊D3—62no—
375C4×C3⋊D3—62no—
376C3×#67—62no—
377C3×#67—62no—
378C3×#67—62no—
379C3×#67—62no—
380C3×#67—64no—
381C3×#67—64no—
382C2×C3×Dic3—21no—
383C2×C3×Dic3—21no—
384C2×C3×Dic3—21no—
385C2×C3×Dic3—21no—
386C2×C3×Dic3—21no—
387C2×C3×Dic3—21no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—31no—
391C2×C3×Dic3—31no—
392C2×C3×Dic3—31no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—61no—
397C2×C3×Dic3—61no—
398C2×C3×Dic3—61no—
399C2×C3×Dic3—61no—
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402C2×C3×Dic3C22×D311yescharacteristic
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C2×C3×Dic3C22×D311yescharacteristic
411C2×C3×Dic3C22×D311yescharacteristic
412C3×C4×D3—62no—
413C3×C4×D3—62no—
414C3×Dic6—62no—
415C3×Dic6—62no—
416#627—22no—
417#626—62no—
418#626—62no—
419#625—62no—
420#624—22no—
421#624—62no—
422D3×Dic3—62no—
423D3×Dic3—62no—
424D3×Dic3—62no—
425D3×Dic3—62no—
426D3×Dic3—62no—
427D3×Dic3—62no—
428D3×Dic3—122no—
429D3×Dic3—122no—
430#529—271noSylow
431C2×C33—41no—
432C2×C33C2×#4111yescharacteristic
433C2×C33C2×#4111yescharacteristic
434C2×C33C2×#4111yescharacteristic
435C3×C3⋊D3—22no—
436C3×C3⋊D3—41no—
437C2×C3×Q8—91no—
438C2×C3×D4—91no—
439C2×C3×D4—91no—
440C22×C3×C4—91no—
441C2×#67—31no—
442C2×#67—31no—
443C2×#67—31no—
444C2×#67—31no—
445C2×#67—61no—
446C2×#67—61no—
447C2×#67—91no—
448C2×#67—91no—
449C22×Dic3—91no—
450C22×Dic3—91no—
451C22×Dic3—91no—
452C22×Dic3—91no—
453C22×Dic3—91no—
454C22×Dic3—91no—
455C22×Dic3—181no—
456C22×Dic3—181no—
457C22×Dic3—181no—
458C22×Dic3—361no—
459C2×D12—91no—
460C2×C4×D3—31no—
461C2×C4×D3—31no—
462C2×C4×D3—91no—
463C2×C4×D3—91no—
464C2×C4×D3—91no—
465C2×C4×D3—91no—
466C2×C4×D3—91no—
467C2×C4×D3—91no—
468C2×C4×D3—181no—
469C2×C4×D3—181no—
470C2×Dic6—31no—
471C2×Dic6—31no—
472C3×C4⋊C4—91no—
473C3×C4⋊C4—91no—
474C3×C4⋊C4—91no—
475C3×C4⋊C4—91no—
476C3×C4⋊C4—91no—
477C3×C22⋊C4—31no—
478C3×C22⋊C4—31no—
479C3×C22⋊C4—31no—
480C3×C22⋊C4—31no—
481C3×C22⋊C4—31no—
482C3×C22⋊C4—31no—
483C3×C22⋊C4—61no—
484C3×C22⋊C4—61no—
485C3×C22⋊C4—61no—
486C3×C22⋊C4—91no—
487C3×C22⋊C4—91no—
488C3×C22⋊C4—91no—
489C3×C22⋊C4—91no—
490C3×C42—91no—
491C3×C42—91no—
492#217—31no—
493#217—31no—
494#217—61no—
495#217—91no—
496#217—91no—
497#217—91no—
498#217D3211yescharacteristic
499#217D3211yescharacteristic
500#217D3211yescharacteristic
501(C2×D3)⋊C4—31no—
502(C2×D3)⋊C4—31no—
503(C2×D3)⋊C4—31no—
504(C2×D3)⋊C4—31no—
505(C2×D3)⋊C4—31no—
506(C2×D3)⋊C4—31no—
507(C2×D3)⋊C4—91no—
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—181no—
514(C2×D3)⋊C4—181no—
515C4⋊Dic3—31no—
516C4⋊Dic3—31no—
517C4⋊Dic3—31no—
518C4⋊Dic3—31no—
519C4⋊Dic3—91no—
520C4⋊Dic3—91no—
521C4⋊Dic3—91no—
522Dic3⋊C4—31no—
523Dic3⋊C4—31no—
524Dic3⋊C4—31no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—31no—
528Dic3⋊C4—91no—
529Dic3⋊C4—91no—
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—181no—
541Dic3⋊C4—181no—
542Dic3⋊C4—181no—
543Dic3⋊C4—181no—
544C4×Dic3—31no—
545C4×Dic3—31no—
546C4×Dic3—31no—
547C4×Dic3—31no—
548C4×Dic3—91no—
549C4×Dic3—91no—
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—181no—
561C4×Dic3—181no—
562C4×Dic3—181no—
563C4×Dic3—181no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—21no—
567C22×C32—22no—
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—21no—
578C22×C32—21no—
579C22×C32—41no—
580C22×C32—41no—
581C22×C32—41no—
582C22×C32—41no—
583C22×C32—41no—
584C22×C32—41no—
585C22×C32—41no—
586C22×C32—42no—
587C22×C32—42no—
588C22×C32—42no—
589C22×C32C23×D311yescharacteristic
590C22×C32C23×D311yescharacteristic
591C22×C32C23×D311yescharacteristic
592C2×C3⋊D3—21no—
593C2×C3⋊D3—21no—
594C2×C3⋊D3—21no—
595C2×C3⋊D3—21no—
596C2×C3⋊D3—21no—
597C2×C3⋊D3#23712yes—
598C2×C3×D3—32no—
599C2×C3×D3—32no—
600C2×C3×D3—62no—
601C2×C3×D3—61no—
602C2×C3×D3—61no—
603C2×C3×D3—61no—
604C2×C3×D3—61no—
605C2×C3×D3—62no—
606C2×C3×D3—61no—
607C2×C3×D3—61no—
608C2×C3×D3—61no—
609C2×C3×D3—61no—
610C2×C3×D3—61no—
611C2×C3×D3—61no—
612C2×C3×D3—121no—
613C2×C3×D3—121no—
614C2×C3×D3—121no—
615C2×C3×D3—121no—
616C32×C4—61no—
617C32×C4—61no—
618C32×C4—61no—
619C32×C4—61no—
620C32×C4—61no—
621C32×C4—61no—
622C3⋊Dic3—21no—
623C3⋊Dic3—21no—
624C3⋊Dic3—21no—
625C3⋊Dic3—32no—
626C3⋊Dic3—32no—
627C3⋊Dic3—32no—
628C3⋊Dic3—62no—
629C3⋊Dic3—62no—
630C3⋊Dic3—62no—
631C3⋊Dic3—61no—
632C3⋊Dic3—62no—
633C3⋊Dic3—61no—
634C3⋊Dic3—61no—
635C3⋊Dic3—122no—
636C3⋊Dic3—121no—
637C3⋊Dic3—121no—
638C3⋊Dic3—122no—
639C3⋊Dic3#23712yes—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
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—21no—
652C3×Dic3—32no—
653C3×Dic3—32no—
654C3×Dic3—41no—
655C3×Dic3—41no—
656C3×Dic3—41no—
657C3×Dic3—41no—
658C3×Dic3—41no—
659C3×Dic3—41no—
660C3×Dic3—62no—
661C3×Dic3—62no—
662C3×Dic3—61no—
663C3×Dic3—61no—
664C3×Dic3—61no—
665C3×Dic3—61no—
666C3×Dic3—61no—
667C3×Dic3—61no—
668C3×Dic3—121no—
669C3×Dic3—121no—
670#126—91no—
671#126—271no—
672#125—271no—
673#124—91no—
674#123—91no—
675#123—271no—
676C22⋊Q8—271no—
677#121—271no—
678C4×Q8—271no—
679C4×D4—271no—
680C4×D4—271no—
681C4×D4—271no—
682#117—271no—
683#117—271no—
684C2×C42—271no—
685C33#52911yescharacteristic, complemented, Sylow
686C23×C3—21no—
687C23×C3—21no—
688C23×C3—21no—
689C23×C3—41no—
690C23×C3—91no—
691C23×C3—91no—
692C23×C3C2×D3211yescharacteristic
693C23×C3C2×D3211yescharacteristic
694C23×C3C2×D3211yescharacteristic
695C22×D3—31no—
696C22×D3—31no—
697C22×D3—31no—
698C22×D3—31no—
699C22×D3—61no—
700C22×D3—61no—
701C3×Q8—182no—
702C3×D4—182no—
703C3×D4—182no—
704C2×C3×C4—31no—
705C2×C3×C4—31no—
706C2×C3×C4—31no—
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—61no—
717C2×C3×C4—61no—
718C2×C3×C4—61no—
719C2×C3×C4—61no—
720C2×C3×C4—61no—
721C2×C3×C4—61no—
722C2×C3×C4—91no—
723C2×C3×C4—91no—
724C2×C3×C4—91no—
725C2×C3×C4—91no—
726C2×C3×C4—182no—
727#67—62no—
728#67—62no—
729#67—62no—
730#67—62no—
731#67—64no—
732#67—64no—
733#67—182no—
734#67—182no—
735C2×Dic3—31no—
736C2×Dic3—31no—
737C2×Dic3—31no—
738C2×Dic3—31no—
739C2×Dic3—31no—
740C2×Dic3—31no—
741C2×Dic3—31no—
742C2×Dic3—31no—
743C2×Dic3—61no—
744C2×Dic3—61no—
745C2×Dic3—61no—
746C2×Dic3—61no—
747C2×Dic3—91no—
748C2×Dic3—91no—
749C2×Dic3—91no—
750C2×Dic3—91no—
751C2×Dic3—91no—
752C2×Dic3—91no—
753C2×Dic3—181no—
754C2×Dic3—181no—
755C2×Dic3—181no—
756C2×Dic3—181no—
757C2×Dic3—181no—
758C2×Dic3—181no—
759C2×Dic3—182no—
760C2×Dic3—182no—
761C2×Dic3—182no—
762C2×Dic3—182no—
763C2×Dic3—182no—
764C2×Dic3—182no—
765C2×Dic3—184no—
766C2×Dic3—361no—
767C2×Dic3—361no—
768C2×Dic3—362no—
769C2×Dic3—362no—
770C2×Dic3—364no—
771C2×Dic3C2×D3211yescharacteristic
772C2×Dic3C2×D3211yescharacteristic
773C2×Dic3C2×D3211yescharacteristic
774C2×Dic3C2×D3211yescharacteristic
775C2×Dic3C2×D3211yescharacteristic
776C2×Dic3C2×D3211yescharacteristic
777D12—182no—
778C4×D3—62no—
779C4×D3—62no—
780C4×D3—182no—
781C4×D3—182no—
782C4×D3—182no—
783C4×D3—182no—
784C4×D3—182no—
785C4×D3—182no—
786C4×D3—362no—
787C4×D3—362no—
788Dic6—62no—
789Dic6—62no—
790C2×C32—21no—
791C2×C32—21no—
792C2×C32—21no—
793C2×C32—21no—
794C2×C32—21no—
795C2×C32—21no—
796C2×C32—21no—
797C2×C32—21no—
798C2×C32—21no—
799C2×C32—41no—
800C2×C32—41no—
801C2×C32—41no—
802C2×C32—42no—
803C2×C32—42no—
804C2×C32—42no—
805C2×C32—44no—
806C2×C32—41no—
807C2×C32—41no—
808C2×C32—41no—
809C2×C32C2×#23711yescharacteristic
810C2×C32C2×#23711yescharacteristic
811C2×C32D3×#4111yescharacteristic
812C2×C32D3×#4111yescharacteristic
813C2×C32D3×#4111yescharacteristic
814C2×C32D3×#4111yescharacteristic
815C2×C32D3×#4111yescharacteristic
816C2×C32D3×#4111yescharacteristic
817C2×C32D3×#4111yescharacteristic
818C3⋊D3—22no—
819C3⋊D3—41no—
820C3×D3—62no—
821C3×D3—62no—
822C3×D3—122no—
823C3×D3—122no—
824C3×D3—121no—
825C3×D3—121no—
826C2×Q8—91no—
827C2×D4—91no—
828C2×D4—91no—
829C2×D4—271no—
830C22×C4—91no—
831C22×C4—271no—
832C22×C4—271no—
833C22×C4—271no—
834C22×C4—271no—
835C4⋊C4—91no—
836C4⋊C4—91no—
837C4⋊C4—91no—
838C4⋊C4—91no—
839C4⋊C4—91no—
840C4⋊C4—271no—
841C4⋊C4—271no—
842C4⋊C4—271no—
843C4⋊C4—271no—
844C4⋊C4—271no—
845C22⋊C4—31no—
846C22⋊C4—31no—
847C22⋊C4—31no—
848C22⋊C4—91no—
849C22⋊C4—91no—
850C22⋊C4—91no—
851C22⋊C4—91no—
852C22⋊C4—271no—
853C22⋊C4—271no—
854C22⋊C4—271no—
855C42—91no—
856C42—91no—
857C42—271no—
858C42—271no—
859C42—271no—
860C42—271no—
861C22×C3—22no—
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—21no—
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—41no—
877C22×C3—41no—
878C22×C3—41no—
879C22×C3—41no—
880C22×C3—41no—
881C22×C3—41no—
882C22×C3—42no—
883C22×C3—42no—
884C22×C3—42no—
885C22×C3—41no—
886C22×C3—92no—
887C22×C3—181no—
888C22×C3—181no—
889C22×C3—181no—
890C22×C3—181no—
891C22×C3—181no—
892C22×C3C22×D3211yescharacteristic
893C22×C3C22×D3211yescharacteristic
894C22×C3C22×D3211yescharacteristic
895C2×D3—32no—
896C2×D3—32no—
897C2×D3—62no—
898C2×D3—61no—
899C2×D3—61no—
900C2×D3—61no—
901C2×D3—61no—
902C2×D3—62no—
903C2×D3—61no—
904C2×D3—61no—
905C2×D3—61no—
906C2×D3—61no—
907C2×D3—61no—
908C2×D3—61no—
909C2×D3—121no—
910C2×D3—121no—
911C2×D3—121no—
912C2×D3—121no—
913C3×C4—61no—
914C3×C4—61no—
915C3×C4—61no—
916C3×C4—61no—
917C3×C4—61no—
918C3×C4—61no—
919C3×C4—61no—
920C3×C4—61no—
921C3×C4—61no—
922C3×C4—61no—
923C3×C4—61no—
924C3×C4—61no—
925C3×C4—92no—
926C3×C4—121no—
927C3×C4—121no—
928C3×C4—121no—
929C3×C4—121no—
930C3×C4—121no—
931C3×C4—121no—
932C3×C4—181no—
933C3×C4—181no—
934C3×C4—181no—
935Dic3—21no—
936Dic3—21no—
937Dic3—21no—
938Dic3—21no—
939Dic3—21no—
940Dic3—21no—
941Dic3—32no—
942Dic3—32no—
943Dic3—62no—
944Dic3—62no—
945Dic3—61no—
946Dic3—61no—
947Dic3—61no—
948Dic3—61no—
949Dic3—61no—
950Dic3—61no—
951Dic3—92no—
952Dic3—92no—
953Dic3—92no—
954Dic3—121no—
955Dic3—121no—
956Dic3—182no—
957Dic3—182no—
958Dic3—182no—
959Dic3—182no—
960Dic3—181no—
961Dic3—181no—
962Dic3—181no—
963Dic3—362no—
964Dic3—361no—
965Dic3—361no—
966Dic3—362no—
967C32—21no—
968C32—21no—
969C32—21no—
970C32—41no—
971C32#564911yescharacteristic, complemented
972C32#568011yescharacteristic, complemented
973C32#570611yescharacteristic, complemented
974C23—91no—
975C23—91no—
976C23D3311yescharacteristic
977Q8—182no—
978D4—182no—
979D4—182no—
980D4—542no—
981C2×C4—31no—
982C2×C4—31no—
983C2×C4—31no—
984C2×C4—31no—
985C2×C4—31no—
986C2×C4—31no—
987C2×C4—91no—
988C2×C4—91no—
989C2×C4—91no—
990C2×C4—91no—
991C2×C4—182no—
992C2×C4—271no—
993C2×C4—271no—
994C2×C4—542no—
995C2×C4—542no—
996C2×C4—542no—
997C2×C4—542no—
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—42no—
1008C2×C3—42no—
1009C2×C3—42no—
1010C2×C3—44no—
1011C2×C3—41no—
1012C2×C3—41no—
1013C2×C3—41no—
1014C2×C3—41no—
1015C2×C3—41no—
1016C2×C3—41no—
1017C2×C3—182no—
1018C2×C3—361no—
1019C2×C3#6430611yescharacteristic
1020C2×C3#6430611yescharacteristic
1021C2×C3#6430611yescharacteristic
1022C2×C3D3×#23711yescharacteristic
1023C2×C3D3×#23711yescharacteristic
1024C2×C3D3×#23711yescharacteristic
1025C2×C3D3×#23711yescharacteristic
1026C2×C3#6431211yescharacteristic
1027C2×C3#6431211yescharacteristic
1028D3—62no—
1029D3—62no—
1030D3—122no—
1031D3—122no—
1032D3—121no—
1033D3—121no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—92no—
1038C22—181no—
1039C22—181no—
1040C22—181no—
1041C22—181no—
1042C22—181no—
1043C22C2×D3311yescharacteristic
1044C4—61no—
1045C4—61no—
1046C4—61no—
1047C4—61no—
1048C4—61no—
1049C4—61no—
1050C4—92no—
1051C4—181no—
1052C4—181no—
1053C4—181no—
1054C4—272no—
1055C4—541no—
1056C3—21no—
1057C3—21no—
1058C3—21no—
1059C3—41no—
1060C3#1059411111yescharacteristic, complemented
1061C3#1059413011yescharacteristic, complemented
1062C3#1059413711yescharacteristic, complemented
1063C2—41no—
1064C2—182no—
1065C2—361no—
1066C2#1172440711yescharacteristic
1067C2#1172440711yescharacteristic
1068C2#1172441111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radical#11723725C2
hypercenterC23D33
hypocenterC33#529
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. #11723626C2semidirect
3. #11723626C2semidirect
4. #11723598C2semidirect
5. C3×#63975C2semidirect
6. C3×#63956C2semidirect
7. C3×#63953C2semidirect
8. #11723024C2semidirect
9. #11723014C2semidirect
10. #11722995C2semidirect
11. #11722979C2semidirect
12. #11722941C2semidirect
13. #11722938C2semidirect
14. #11722921C2semidirect
15. Dic3×#624C2semidirect
63. #63975D3semidirect
76. #63956D3semidirect
77. #63953D3semidirect
685. C33#529semidirect
971. C32#5649semidirect
972. C32#5680semidirect
973. C32#5706semidirect
1060. C3#10594111semidirect
1061. C3#10594130semidirect
1062. C3#10594137semidirect

Maximal subgroups

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

subgroupindex
#117237252
#117236262
#117235982
C3×#639752
C3×#639562
C3×#639532
#117230242
#117230142
#117229952
#117229792
#117229412
#117229382
#117229212
Dic3×#6242
#105941373
#105941303
#105941113