Finite Group Databasebeta

← #13171970

Subgroups — #13171970

Order 1728.

1216 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88813C211yesmaximal, characteristic, complemented
2#11723641C211yesmaximal, characteristic, complemented
3#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#11723602C211yesmaximal, characteristic, complemented
5C3×#63980C211yesmaximal, characteristic
6C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63962C211yesmaximal, characteristic, complemented
8#11723026C211yesmaximal, characteristic, complemented
9#11723026C211yesmaximal, characteristic, complemented
10#11723017C211yesmaximal, characteristic, complemented
11#11723004C211yesmaximal, characteristic, complemented
12#11722943C211yesmaximal, characteristic, complemented
13#11722924C211yesmaximal, characteristic, complemented
14#11722916C211yesmaximal, characteristic, complemented
15#11722914C211yesmaximal, characteristic, complemented
16#10595202—31nomaximal
17#10595187—31nomaximal
18#10594131—31nomaximal
19C22×C3×C3⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×#6293C2211yescharacteristic
25C2×D3×C3⋊Dic3C2211yescharacteristic
26C2×C3×#625C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28#88864C2211yescharacteristic
29C32×#217C2211yescharacteristic
30#88813C2211yescharacteristic
31#88813C2211yescharacteristic
32#88813C2211yescharacteristic
33#88813C2211yescharacteristic
34#88807C2211yescharacteristic
35#88806C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
41(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64144—31no—
55D4×C3⋊Dic3—31no—
56#64087—31no—
57C3×#939—31no—
58C3×#939—31no—
59C3×#935—31no—
60C3×D4×Dic3—31no—
61C3×#886—31no—
62C3×#67⋊C4—31no—
63#63980D311yescharacteristic
64#67⋊Dic3—31no—
65#67⋊Dic3D311yescharacteristic, complemented
66Dic3×#67—31no—
67Dic3×#67—31no—
68Dic3×#67—31no—
69Dic3×#67—61no—
70#63964—31no—
71#63964—31no—
72#63964—61no—
73#63962D311yescharacteristic, complemented
74#63961—31no—
75#63961—31no—
76#63961—61no—
77#63959—31no—
78#63959—31no—
79#63957—31no—
80#63956—31no—
81#63956—31no—
82#63955—31no—
83C2×Dic32—31no—
84C2×Dic32—31no—
85C2×Dic32—31no—
86#63913—31no—
87#63879—31no—
88#63878—31no—
89#63877—31no—
90#63877—31no—
91#63861—31no—
92#63861—31no—
93#63858—31no—
94#63858—31no—
95#63847—31no—
96#63846—31no—
97#63845—31no—
98#63844—31no—
99#63841—31no—
100#63838—31no—
101#63837—31no—
102C23×C33C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3×C3⋊Dic3—22no—
108C2×C3×C3⋊Dic3—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
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C32×#67—22no—
117C32×#67—22no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6293—22no—
123D3×C3⋊Dic3—22no—
124C3×#625—22no—
125C3×D3×Dic3—22no—
126#5649—91no—
127#5600—91no—
128#5538—91no—
129C2×C32×D4—31no—
130C2×C32×D4—31no—
131C22×C3⋊Dic3—31no—
132C22×C3⋊Dic3C2×D311yescharacteristic
133C22×C3⋊Dic3C2×D311yescharacteristic
134C22×C3⋊Dic3C2×D311yescharacteristic
135C2×#634—31no—
136C2×C3×#67—21no—
137C2×C3×#67—21no—
138C2×C3×#67—31no—
139C2×C3×#67—31no—
140C2×C3×#67C2×D311yescharacteristic
141C2×C3×#67C2×D311yescharacteristic
142C2×C3×#67C2×D311yescharacteristic
143C2×C3×#67C2×D311yescharacteristic
144C22×C3×Dic3—31no—
145C22×C3×Dic3—31no—
146C22×C3×Dic3—31no—
147C22×C3×Dic3—31no—
148C22×C3×Dic3—31no—
149C22×C3×Dic3—31no—
150C22×C3×Dic3—31no—
151C22×C3×Dic3—61no—
152C22×C3×Dic3—61no—
153C22×C3×Dic3—61no—
154C2×C3×C4×D3—31no—
155C2×#627—31no—
156C2×#627—31no—
157C2×#627—61no—
158C2×#625C2×D311yescharacteristic
159C2×D3×Dic3—31no—
160C2×D3×Dic3—31no—
161C2×D3×Dic3—61no—
162C2×D3×Dic3C2×D311yescharacteristic
163C32×C22⋊C4—31no—
164#3757—31no—
165#3757—31no—
166#3757—31no—
167#3757—31no—
168#3757—31no—
169#3757—31no—
170#3757—61no—
171#3757—61no—
172#3757—61no—
173#3757—121no—
174C4⋊(C3⋊Dic3)—31no—
175C4⋊(C3⋊Dic3)—31no—
176#3750—31no—
177#3750—31no—
178#3750—31no—
179#3750—31no—
180C4×C3⋊Dic3—31no—
181C3×#217—21no—
182C3×#217—31no—
183C3×#217—31no—
184C3×#217—31no—
185C3×#217—31no—
186C3×#217—31no—
187C3×#217C2×D311yescharacteristic
188C3×#217C2×D311yescharacteristic
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—31no—
192C3×(C2×D3)⋊C4—31no—
193C3×(C2×D3)⋊C4—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—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#3724—61no—
213#3724C2×D311yescharacteristic
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—61no—
221Dic3⋊Dic3—61no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3C2×D311yescharacteristic
224Dic3⋊Dic3C2×D311yescharacteristic
225Dic3⋊Dic3C2×D311yescharacteristic
226(C2×D3)⋊Dic3—31no—
227(C2×D3)⋊Dic3—31no—
228(C2×D3)⋊Dic3—31no—
229(C2×D3)⋊Dic3—31no—
230(C2×D3)⋊Dic3—31no—
231(C2×D3)⋊Dic3—31no—
232(C2×D3)⋊Dic3—61no—
233(C2×D3)⋊Dic3—61no—
234(C2×D3)⋊Dic3—61no—
235(C2×D3)⋊Dic3C2×D311yescharacteristic
236(C2×D3)⋊Dic3C2×D311yescharacteristic
237(C2×D3)⋊Dic3C2×D311yescharacteristic
238(C2×D3)⋊Dic3C2×D311yescharacteristic
239(C2×D3)⋊Dic3C2×D311yescharacteristic
240Dic32—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—61no—
255Dic32C2×D311yescharacteristic
256C22×C33—21no—
257C22×C33—21no—
258C22×C33#4112yes—
259C22×C33C2411yescharacteristic
260C2×C32×D3—21no—
261C2×C32×D3—21no—
262C2×C32×D3—21no—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3—21no—
266C3⋊(C3⋊Dic3)—21no—
267C3⋊(C3⋊Dic3)—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3#4112yes—
273C3×C3⋊Dic3#4112yes—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3—21no—
278C3×#123—91no—
279C3×#121—91no—
280C3×C4×D4—91no—
281#939—31no—
282#939—31no—
283#936—91no—
284#935—31no—
285#935—91no—
286#935—91no—
287#935—181no—
288D4×Dic3—31no—
289D4×Dic3—91no—
290D4×Dic3—91no—
291D4×Dic3—91no—
292D4×Dic3—181no—
293#929—91no—
294C4×#67—91no—
295C4×#67—91no—
296#926—91no—
297#924—91no—
298C2×C4×Dic3—91no—
299C2×C4×Dic3—91no—
300C2×C4×Dic3—91no—
301#898—91no—
302#898—91no—
303#892—91no—
304#890—91no—
305#889—91no—
306#889—91no—
307#887—91no—
308#887—91no—
309#886—31no—
310#885—91no—
311#885—91no—
312#67⋊C4—31no—
313#67⋊C4—91no—
314#879—91no—
315#879—91no—
316#879—91no—
317#879—91no—
318#878—91no—
319#878—91no—
320#878—181no—
321#877—91no—
322#877—91no—
323#877—91no—
324#872—91no—
325C4×Dic6—91no—
326C23×C32—21no—
327C23×C32—21no—
328C23×C32—21no—
329C23×C32—31no—
330C23×C32—31no—
331C23×C32—41no—
332C23×C32C22×D311yescharacteristic
333C23×C32C22×D311yescharacteristic
334C23×C32C22×D311yescharacteristic
335C22×C3×D3—21no—
336C22×C3×D3—21no—
337C22×C3×D3C22×D311yescharacteristic
338C22×C3×D3C22×D311yescharacteristic
339C22×C3×D3C22×D311yescharacteristic
340C22×C3×D3C22×D311yescharacteristic
341C32×D4—62no—
342C32×D4—62no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—31no—
347C2×C3⋊Dic3—22no—
348C2×C3⋊Dic3—22no—
349C2×C3⋊Dic3—22no—
350C2×C3⋊Dic3—31no—
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—31no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—61no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—61no—
362C2×C3⋊Dic3—62no—
363C2×C3⋊Dic3—121no—
364C2×C3⋊Dic3—121no—
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C2×C3⋊Dic3C22×D311yescharacteristic
369C2×C3⋊Dic3C22×D311yescharacteristic
370C2×C3⋊Dic3C22×D311yescharacteristic
371#634—62no—
372C3×#67—24no—
373C3×#67—22no—
374C3×#67—22no—
375C3×#67—22no—
376C3×#67—22no—
377C3×#67—42no—
378C3×#67—62no—
379C3×#67—62no—
380C2×C3×Dic3—21no—
381C2×C3×Dic3—21no—
382C2×C3×Dic3—21no—
383C2×C3×Dic3—21no—
384C2×C3×Dic3—31no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—31no—
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×Dic3—61no—
401C2×C3×Dic3—61no—
402C2×C3×Dic3—62no—
403C2×C3×Dic3—62no—
404C2×C3×Dic3—62no—
405C2×C3×Dic3—62no—
406C2×C3×Dic3—62no—
407C2×C3×Dic3—62no—
408C2×C3×Dic3—62no—
409C2×C3×Dic3—122no—
410C2×C3×Dic3—122no—
411C2×C3×Dic3—122no—
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
420C3×C4×D3—62no—
421#627—62no—
422#627—62no—
423#627—122no—
424#625—22no—
425D3×Dic3—22no—
426D3×Dic3—62no—
427D3×Dic3—62no—
428D3×Dic3—122no—
429#529—271noSylow
430C2×C33—22no—
431C2×C33C2×#4111yescharacteristic
432C2×C33C2×#4111yescharacteristic
433C2×C33C2×#4111yescharacteristic
434C32×D3—41no—
435C32×D3—41no—
436C2×C3×D4—31no—
437C2×C3×D4—31no—
438C2×C3×D4—31no—
439C2×C3×D4—31no—
440C2×C3×D4—61no—
441C2×C3×D4—61no—
442C2×C3×D4—91no—
443C22×C3×C4—91no—
444C22×C3×C4—91no—
445C22×C3×C4—91no—
446C22×C3×C4—91no—
447C2×#67—31no—
448C2×#67—31no—
449C2×#67D3211yescharacteristic
450C2×#67D3211yescharacteristic
451C22×Dic3—31no—
452C22×Dic3—31no—
453C22×Dic3—31no—
454C22×Dic3—31no—
455C22×Dic3—31no—
456C22×Dic3—31no—
457C22×Dic3—31no—
458C22×Dic3—61no—
459C22×Dic3—61no—
460C22×Dic3—61no—
461C22×Dic3—91no—
462C22×Dic3—91no—
463C22×Dic3—181no—
464C2×C4×D3—31no—
465C2×C4×D3—91no—
466C2×Dic6—91no—
467C2×Dic6—91no—
468C2×Dic6—91no—
469C2×Dic6—181no—
470C3×C4⋊C4—91no—
471C3×C4⋊C4—91no—
472C3×C4⋊C4—91no—
473C3×C4⋊C4—91no—
474C3×C22⋊C4—31no—
475C3×C22⋊C4—31no—
476C3×C22⋊C4—61no—
477C3×C22⋊C4—91no—
478C3×C22⋊C4—91no—
479C3×C22⋊C4—91no—
480C3×C22⋊C4—91no—
481C3×C22⋊C4—91no—
482C3×C42—91no—
483#217—31no—
484#217—31no—
485#217—31no—
486#217—31no—
487#217—31no—
488#217—91no—
489#217—91no—
490#217—91no—
491#217—91no—
492#217—91no—
493#217—91no—
494#217—91no—
495#217—91no—
496#217—91no—
497#217—181no—
498#217—181no—
499#217—181no—
500#217—181no—
501#217—181no—
502#217—181no—
503#217—361no—
504#217D3211yescharacteristic
505(C2×D3)⋊C4—31no—
506(C2×D3)⋊C4—31no—
507(C2×D3)⋊C4—31no—
508(C2×D3)⋊C4—31no—
509(C2×D3)⋊C4—31no—
510(C2×D3)⋊C4—91no—
511(C2×D3)⋊C4—91no—
512(C2×D3)⋊C4—91no—
513C4⋊Dic3—31no—
514C4⋊Dic3—31no—
515C4⋊Dic3—31no—
516C4⋊Dic3—91no—
517C4⋊Dic3—91no—
518C4⋊Dic3—91no—
519C4⋊Dic3—91no—
520C4⋊Dic3—91no—
521C4⋊Dic3—181no—
522C4⋊Dic3—181no—
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—91no—
541Dic3⋊C4—181no—
542Dic3⋊C4—181no—
543Dic3⋊C4—181no—
544Dic3⋊C4—181no—
545C4×Dic3—31no—
546C4×Dic3—31no—
547C4×Dic3—91no—
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—91no—
561C4×Dic3—91no—
562C4×Dic3—181no—
563C22×C32—21no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—21no—
567C22×C32—21no—
568C22×C32—21no—
569C22×C32—21no—
570C22×C32—21no—
571C22×C32—21no—
572C22×C32—22no—
573C22×C32—22no—
574C22×C32—22no—
575C22×C32—41no—
576C22×C32—42no—
577C22×C32—41no—
578C22×C32—41no—
579C22×C32—41no—
580C22×C32—41no—
581C22×C32—41no—
582C22×C32—41no—
583C22×C32—61no—
584C22×C32—61no—
585C22×C32—61no—
586C22×C32—61no—
587C22×C32—61no—
588C22×C32—61no—
589C22×C32—81no—
590C22×C32—81no—
591C22×C32#23512yes—
592C22×C32#23712yes—
593C22×C32#23712yes—
594C22×C32C23×D311yescharacteristic
595C22×C32C23×D311yescharacteristic
596C22×C32C23×D311yescharacteristic
597C2×C3×D3—22no—
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—21no—
607C2×C3×D3—21no—
608C2×C3×D3—21no—
609C2×C3×D3—21no—
610C2×C3×D3—41no—
611C2×C3×D3—41no—
612C2×C3×D3—41no—
613C2×C3×D3—41no—
614C2×C3×D3—41no—
615C32×C4—61no—
616C32×C4—61no—
617C32×C4—61no—
618C32×C4—61no—
619C3⋊Dic3—21no—
620C3⋊Dic3—21no—
621C3⋊Dic3—21no—
622C3⋊Dic3—21no—
623C3⋊Dic3—61no—
624C3⋊Dic3—61no—
625C3⋊Dic3—61no—
626C3⋊Dic3—61no—
627C3⋊Dic3—61no—
628C3⋊Dic3—61no—
629C3⋊Dic3—121no—
630C3⋊Dic3—121no—
631C3⋊Dic3—121no—
632C3⋊Dic3—121no—
633C3⋊Dic3—121no—
634C3⋊Dic3—121no—
635C3⋊Dic3—241no—
636C3⋊Dic3—241no—
637C3⋊Dic3#23712yes—
638C3⋊Dic3#23712yes—
639C3×Dic3—22no—
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—32no—
649C3×Dic3—32no—
650C3×Dic3—32no—
651C3×Dic3—32no—
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—121no—
666C3×Dic3—121no—
667C3×Dic3—121no—
668C3×Dic3—121no—
669#126—271no—
670#126—271no—
671#125—271no—
672#124—271no—
673#123—91no—
674#123—271no—
675C22⋊Q8—271no—
676#121—91no—
677C4×Q8—271no—
678C4×D4—91no—
679C4×D4—271no—
680C4×D4—271no—
681#117—271no—
682#117—271no—
683C2×C42—271no—
684C33#52911yescharacteristic, complemented, Sylow
685C23×C3—21no—
686C23×C3—21no—
687C23×C3—21no—
688C23×C3—31no—
689C23×C3—31no—
690C23×C3—31no—
691C23×C3—31no—
692C23×C3—41no—
693C23×C3—61no—
694C23×C3—61no—
695C23×C3C2×D3211yescharacteristic
696C23×C3C2×D3211yescharacteristic
697C23×C3C2×D3211yescharacteristic
698C22×D3C2×D3211yescharacteristic
699C22×D3C2×D3211yescharacteristic
700C3×D4—64no—
701C3×D4—62no—
702C3×D4—62no—
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—61no—
716C2×C3×C4—61no—
717C2×C3×C4—61no—
718C2×C3×C4—61no—
719C2×C3×C4—91no—
720C2×C3×C4—91no—
721C2×C3×C4—91no—
722C2×C3×C4—91no—
723C2×C3×C4—91no—
724C2×C3×C4—91no—
725C2×C3×C4—182no—
726C2×C3×C4—182no—
727C2×C3×C4—182no—
728C2×C3×C4—182no—
729#67—22no—
730#67—22no—
731#67—62no—
732#67—62no—
733C2×Dic3—31no—
734C2×Dic3—31no—
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—31no—
744C2×Dic3—31no—
745C2×Dic3—61no—
746C2×Dic3—61no—
747C2×Dic3—61no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—61no—
751C2×Dic3—62no—
752C2×Dic3—62no—
753C2×Dic3—62no—
754C2×Dic3—62no—
755C2×Dic3—62no—
756C2×Dic3—62no—
757C2×Dic3—62no—
758C2×Dic3—91no—
759C2×Dic3—91no—
760C2×Dic3—91no—
761C2×Dic3—91no—
762C2×Dic3—91no—
763C2×Dic3—91no—
764C2×Dic3—122no—
765C2×Dic3—122no—
766C2×Dic3—122no—
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—361no—
776C2×Dic3—361no—
777C2×Dic3—362no—
778C2×Dic3C2×D3211yescharacteristic
779C2×Dic3C2×D3211yescharacteristic
780C2×Dic3C2×D3211yescharacteristic
781C2×Dic3C2×D3211yescharacteristic
782C4×D3—62no—
783C4×D3—182no—
784Dic6—182no—
785Dic6—182no—
786Dic6—182no—
787Dic6—362no—
788C2×C32—22no—
789C2×C32—22no—
790C2×C32—22no—
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—21no—
800C2×C32—41no—
801C2×C32—41no—
802C2×C32—41no—
803C2×C32—42no—
804C2×C32—42no—
805C2×C32—42no—
806C2×C32—82no—
807C2×C32—121no—
808C2×C32—121no—
809C2×C32C2×#23511yescharacteristic
810C2×C32C2×#23711yescharacteristic
811C2×C32C2×#23711yescharacteristic
812C2×C32C2×#23711yescharacteristic
813C2×C32C2×#23711yescharacteristic
814C2×C32D3×#4111yescharacteristic
815C2×C32D3×#4111yescharacteristic
816C2×C32D3×#4111yescharacteristic
817C2×C32D3×#4111yescharacteristic
818C3×D3—42no—
819C3×D3—41no—
820C3×D3—41no—
821C3×D3—41no—
822C3×D3—41no—
823C3×D3—81no—
824C2×Q8—271no—
825C2×D4—31no—
826C2×D4—31no—
827C2×D4—91no—
828C22×C4—91no—
829C22×C4—91no—
830C22×C4—91no—
831C22×C4—91no—
832C22×C4—271no—
833C4⋊C4—91no—
834C4⋊C4—91no—
835C4⋊C4—91no—
836C4⋊C4—91no—
837C4⋊C4—271no—
838C4⋊C4—271no—
839C4⋊C4—271no—
840C4⋊C4—271no—
841C4⋊C4—271no—
842C4⋊C4—271no—
843C22⋊C4—31no—
844C22⋊C4—91no—
845C22⋊C4—91no—
846C22⋊C4—91no—
847C22⋊C4—91no—
848C22⋊C4—91no—
849C22⋊C4—271no—
850C22⋊C4—271no—
851C22⋊C4—271no—
852C22⋊C4—271no—
853C42—91no—
854C42—271no—
855C42—271no—
856C42—271no—
857C42—271no—
858C42—271no—
859C22×C3—21no—
860C22×C3—21no—
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—21no—
867C22×C3—21no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—22no—
871C22×C3—41no—
872C22×C3—41no—
873C22×C3—41no—
874C22×C3—41no—
875C22×C3—41no—
876C22×C3—41no—
877C22×C3—41no—
878C22×C3—42no—
879C22×C3—62no—
880C22×C3—61no—
881C22×C3—61no—
882C22×C3—61no—
883C22×C3—61no—
884C22×C3—61no—
885C22×C3—61no—
886C22×C3—61no—
887C22×C3—61no—
888C22×C3—61no—
889C22×C3—61no—
890C22×C3—61no—
891C22×C3—61no—
892C22×C3—81no—
893C22×C3—81no—
894C22×C3—121no—
895C22×C3—121no—
896C22×C3—121no—
897C22×C3—121no—
898C22×C3—121no—
899C22×C3#379512yes—
900C22×C3#380412yes—
901C22×C3#380512yes—
902C22×C3C22×D3211yescharacteristic
903C22×C3C22×D3211yescharacteristic
904C22×C3C22×D3211yescharacteristic
905C2×D3—21no—
906C2×D3—21no—
907C2×D3—21no—
908C2×D3—21no—
909C2×D3—21no—
910C2×D3—21no—
911C3×C4—62no—
912C3×C4—61no—
913C3×C4—61no—
914C3×C4—61no—
915C3×C4—61no—
916C3×C4—61no—
917C3×C4—61no—
918C3×C4—61no—
919C3×C4—61no—
920C3×C4—92no—
921C3×C4—92no—
922C3×C4—121no—
923C3×C4—121no—
924C3×C4—121no—
925C3×C4—181no—
926C3×C4—181no—
927C3×C4—181no—
928C3×C4—181no—
929Dic3—21no—
930Dic3—21no—
931Dic3—21no—
932Dic3—21no—
933Dic3—32no—
934Dic3—32no—
935Dic3—32no—
936Dic3—32no—
937Dic3—62no—
938Dic3—62no—
939Dic3—61no—
940Dic3—61no—
941Dic3—61no—
942Dic3—61no—
943Dic3—61no—
944Dic3—61no—
945Dic3—61no—
946Dic3—61no—
947Dic3—121no—
948Dic3—121no—
949Dic3—121no—
950Dic3—121no—
951Dic3—181no—
952Dic3—181no—
953Dic3—181no—
954Dic3—181no—
955Dic3—181no—
956Dic3—181no—
957Dic3—361no—
958Dic3—361no—
959Dic3—361no—
960Dic3—361no—
961Dic3—361no—
962Dic3—361no—
963Dic3—721no—
964Dic3—721no—
965C32—21no—
966C32—21no—
967C32—21no—
968C32—41no—
969C32#553811yescharacteristic, complemented
970C32#560011yescharacteristic, complemented
971C32#564911yescharacteristic, complemented
972C23—31no—
973C23—31no—
974C23D3311yescharacteristic
975Q8—542no—
976D4—62no—
977D4—62no—
978D4—182no—
979C2×C4—31no—
980C2×C4—31no—
981C2×C4—31no—
982C2×C4—31no—
983C2×C4—91no—
984C2×C4—91no—
985C2×C4—91no—
986C2×C4—91no—
987C2×C4—91no—
988C2×C4—91no—
989C2×C4—182no—
990C2×C4—182no—
991C2×C4—182no—
992C2×C4—182no—
993C2×C4—271no—
994C2×C4—271no—
995C2×C4—542no—
996C2×C3—22no—
997C2×C3—22no—
998C2×C3—22no—
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—21no—
1008C2×C3—42no—
1009C2×C3—42no—
1010C2×C3—42no—
1011C2×C3—41no—
1012C2×C3—41no—
1013C2×C3—41no—
1014C2×C3—82no—
1015C2×C3—122no—
1016C2×C3—121no—
1017C2×C3—121no—
1018C2×C3—121no—
1019C2×C3—121no—
1020C2×C3—241no—
1021C2×C3C2×#379511yescharacteristic
1022C2×C3D3×#23711yescharacteristic
1023C2×C3D3×#23711yescharacteristic
1024C2×C3D3×#23711yescharacteristic
1025C2×C3D3×#23711yescharacteristic
1026C2×C3#6431211yescharacteristic
1027C2×C3#6431211yescharacteristic
1028C2×C3C2×#380411yescharacteristic
1029C2×C3C2×#380511yescharacteristic
1030D3—41no—
1031D3—41no—
1032C22—21no—
1033C22—21no—
1034C22—61no—
1035C22—61no—
1036C22—61no—
1037C22—61no—
1038C22—61no—
1039C22—61no—
1040C22#8896112yes—
1041C22C2×D3311yescharacteristic
1042C4—61no—
1043C4—61no—
1044C4—61no—
1045C4—61no—
1046C4—92no—
1047C4—92no—
1048C4—181no—
1049C4—181no—
1050C4—181no—
1051C4—181no—
1052C4—541no—
1053C4—541no—
1054C3—21no—
1055C3—21no—
1056C3—21no—
1057C3—41no—
1058C3#1059413111yescharacteristic, complemented
1059C3#1059518711yescharacteristic, complemented
1060C3#1059520211yescharacteristic, complemented
1061C2—22no—
1062C2—121no—
1063C2—121no—
1064C2#1172440811yescharacteristic
1065C2#1172440811yescharacteristic
1066C2C2×#8896111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radicalC3×#63980C2
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. C2×#88813C2semidirect
2. #11723641C2semidirect
3. #67×C3⋊Dic3C2semidirect
4. #11723602C2semidirect
6. C3×#67⋊Dic3C2semidirect
7. C3×#63962C2semidirect
8. #11723026C2semidirect
9. #11723026C2semidirect
10. #11723017C2semidirect
11. #11723004C2semidirect
12. #11722943C2semidirect
13. #11722924C2semidirect
14. #11722916C2semidirect
15. #11722914C2semidirect
65. #67⋊Dic3D3semidirect
73. #63962D3semidirect
684. C33#529semidirect
969. C32#5538semidirect
970. C32#5600semidirect
971. C32#5649semidirect
1058. C3#10594131semidirect
1059. C3#10595187semidirect
1060. C3#10595202semidirect

Maximal subgroups

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

subgroupindex
C2×#888132
#117236412
#67×C3⋊Dic32
#117236022
C3×#639802
C3×#67⋊Dic32
C3×#639622
#117230262
#117230172
#117230042
#117229432
#117229242
#117229162
#117229142
#105952023
#105951873
#105941313