Finite Group Databasebeta

← #13171976

Subgroups — #13171976

Order 1728.

1306 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88814C211yesmaximal, characteristic, complemented
2#11723641C211yesmaximal, characteristic, complemented
3#11723634C211yesmaximal, characteristic
4#11723595C211yesmaximal, characteristic, complemented
5C3×#63974C211yesmaximal, characteristic, complemented
6C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63962C211yesmaximal, characteristic, complemented
8#11723025C211yesmaximal, characteristic, complemented
9#11723024C211yesmaximal, characteristic, complemented
10#11723009C211yesmaximal, characteristic, complemented
11#11722992C211yesmaximal, characteristic, complemented
12#11722988C211yesmaximal, characteristic, complemented
13#11722972C211yesmaximal, characteristic, complemented
14#11722930C211yesmaximal, characteristic, complemented
15#11722915C211yesmaximal, characteristic, complemented
16#10595118—31nomaximal
17#10594211—31nomaximal
18#10594209—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×#6293C2211yescharacteristic, complemented
24C2×#6290C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×C3×#624C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic, complemented
29#88864C2211yescharacteristic
30C32×#217C2211yescharacteristic
31C32×#217C2211yescharacteristic
32#88814C2211yescharacteristic
33#88814C2211yescharacteristic
34#88814C2211yescharacteristic
35#88814C2211yescharacteristic
36#88807C2211yescharacteristic, complemented
37#88807C2211yescharacteristic, complemented
38#88807C2211yescharacteristic, complemented
39#88806C2211yescharacteristic, complemented
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic, complemented
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45C3×Dic3⋊Dic3C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64146—31no—
55#64087—31no—
56#64086—31no—
57C3×#935—31no—
58C3×D4×Dic3—31no—
59C3×#886—31no—
60C3×#67⋊C4—31no—
61C3×D3×C22⋊C4—31no—
62C3×D3×C22⋊C4—31no—
63#63976—31no—
64#63976—31no—
65#63976—61no—
66#63975—31no—
67#63974D311yescharacteristic, complemented
68#67⋊Dic3D311yescharacteristic, complemented
69#63966—31no—
70#63964—31no—
71#63964—31no—
72#63964—61no—
73C2×#3722—31no—
74#63962D311yescharacteristic, complemented
75C2×(C2×D3)⋊Dic3—31no—
76C2×(C2×D3)⋊Dic3—31no—
77#63955—31no—
78#63955—31no—
79#63955—61no—
80#63953—31no—
81#63952—31no—
82#63915—31no—
83#63913—31no—
84#63905—31no—
85#63905—31no—
86#63905—31no—
87C4×#625—31no—
88#63895—31no—
89#63891—31no—
90#63879—31no—
91#63868—31no—
92#63862—31no—
93#63859—31no—
94#63858—31no—
95#63858—31no—
96#63857—31no—
97#63855—31no—
98#63851—31no—
99#63848—31no—
100#63841—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3—22no—
104C22×C3×C3⋊D3—22no—
105C22×C3×C3⋊D3—41no—
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3×C3⋊Dic3—22no—
112C2×C3×C3⋊Dic3—41no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C32×#67—22no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6293—41no—
124#6290—22no—
125#6290—41no—
126C3×#624—22no—
127C3×#624—41no—
128C3×D3×Dic3—41no—
129#5658—91no—
130#5556—91no—
131#5495—91no—
132C23×C3⋊D3C2×D311yescharacteristic
133C23×C3×D3—31no—
134C23×C3×D3—31no—
135C23×C3×D3—61no—
136C2×C32×D4—31no—
137C2×#638—31no—
138C2×#638—31no—
139C22×C3⋊Dic3C2×D311yescharacteristic
140C22×C3⋊Dic3C2×D311yescharacteristic
141C2×#634—31no—
142C2×C3×#67—21no—
143C2×C3×#67C2×D311yescharacteristic
144C2×C3×#67C2×D311yescharacteristic
145C22×C3×Dic3—31no—
146C22×C3×Dic3—31no—
147C22×C3×Dic3—31no—
148C22×C3×Dic3—31no—
149C22×C3×Dic3—31no—
150C22×C3×Dic3—61no—
151C22×C3×Dic3—61no—
152C2×C3×C4×D3—31no—
153C2×C3×C4×D3—31no—
154C2×C3×C4×D3—31no—
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—31no—
157C2×#627—31no—
158C2×#627—31no—
159C2×#627—61no—
160C2×#625—31no—
161C2×#625—31no—
162C2×#625—31no—
163C2×#625—31no—
164C2×#625—61no—
165C2×#625—61no—
166C2×#624C2×D311yescharacteristic
167C2×#624C2×D311yescharacteristic
168C2×D3×Dic3C2×D311yescharacteristic, complemented
169C32×C22⋊C4—31no—
170C32×C22⋊C4—31no—
171#3757—31no—
172#3757—31no—
173#3757—31no—
174#3757—61no—
175#3757—61no—
176#3757—61no—
177#3757—121no—
178#3752—31no—
179#3752—31no—
180C4⋊(C3⋊Dic3)—31no—
181#3750—31no—
182#3750—31no—
183#3750—31no—
184#3750—31no—
185C4×C3⋊Dic3—31no—
186C4×C3⋊Dic3—31no—
187C3×#217—21no—
188C3×#217—21no—
189C3×#217—31no—
190C3×#217—31no—
191C3×#217—31no—
192C3×#217C2×D311yescharacteristic
193C3×#217C2×D311yescharacteristic
194C3×#217C2×D311yescharacteristic
195C3×#217C2×D311yescharacteristic
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—31no—
203C3×C4⋊Dic3—31no—
204C3×C4⋊Dic3—31no—
205C3×C4⋊Dic3—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×C4×Dic3—31no—
210C3×C4×Dic3—31no—
211#3724—31no—
212#3724—31no—
213#3724—61no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3C2×D311yescharacteristic, complemented
227Dic3⋊Dic3C2×D311yescharacteristic, complemented
228Dic3⋊Dic3C2×D311yescharacteristic, complemented
229#3722—31no—
230#3722—31no—
231#3722—31no—
232#3722—31no—
233#3722C2×D311yescharacteristic
234#3722C2×D311yescharacteristic
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—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—61no—
248(C2×D3)⋊Dic3—61no—
249(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
250(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
251(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—61no—
257Dic32—61no—
258Dic32C2×D311yescharacteristic, complemented
259C22×C33—21no—
260C22×C33—21no—
261C22×C33#4112yes—
262C22×C33C2411yescharacteristic
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3—21no—
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—44no—
269C2×C3×C3⋊D3#4112yes—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
272C2×C32×D3—21no—
273C3⋊(C3⋊Dic3)—21no—
274C3⋊(C3⋊Dic3)—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#123—91no—
285C3×C4×D4—91no—
286C2×C3×C22⋊C4—91no—
287#953—91no—
288C2×#217—91no—
289#937—91no—
290#937—91no—
291#937—181no—
292#935—31no—
293D4×Dic3—31no—
294#929—91no—
295#929—91no—
296C4×#67—91no—
297C4×#67—91no—
298C2×(C2×D3)⋊C4—91no—
299C2×(C2×D3)⋊C4—91no—
300#926—91no—
301#926—91no—
302#924—91no—
303#924—91no—
304#898—91no—
305#898—91no—
306#898—91no—
307#897—91no—
308#896—91no—
309#892—91no—
310#886—31no—
311#886—91no—
312#885—91no—
313#885—91no—
314#885—91no—
315#883—91no—
316#883—91no—
317#883—91no—
318#67⋊C4—31no—
319#67⋊C4—91no—
320D3×C22⋊C4—31no—
321D3×C22⋊C4—31no—
322#879—91no—
323#879—91no—
324#878—91no—
325#878—91no—
326#878—181no—
327#877—91no—
328#877—91no—
329#877—181no—
330#876—91no—
331#872—91no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—31no—
336C23×C32—41no—
337C23×C32C22×D311yescharacteristic
338C23×C32C22×D311yescharacteristic
339C23×C32C22×D311yescharacteristic
340C22×C3⋊D3—22no—
341C22×C3⋊D3—22no—
342C22×C3⋊D3—41no—
343C22×C3⋊D3C22×D311yescharacteristic
344C22×C3⋊D3C22×D311yescharacteristic
345C22×C3×D3—21no—
346C22×C3×D3—31no—
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—61no—
351C22×C3×D3—61no—
352C22×C3×D3—62no—
353C22×C3×D3—62no—
354C22×C3×D3—62no—
355C22×C3×D3—62no—
356C22×C3×D3—122no—
357C22×C3×D3—122no—
358C22×C3×D3—121no—
359C22×C3×D3—121no—
360C22×C3×D3—122no—
361C22×C3×D3C22×D311yescharacteristic
362C22×C3×D3C22×D311yescharacteristic
363C32×D4—62no—
364C2×C32×C4—31no—
365C2×C32×C4—31no—
366C2×C32×C4—31no—
367C2×C32×C4—31no—
368C2×C32×C4—31no—
369#638—62no—
370#638—121no—
371C2×C3⋊Dic3—22no—
372C2×C3⋊Dic3—31no—
373C2×C3⋊Dic3—31no—
374C2×C3⋊Dic3—31no—
375C2×C3⋊Dic3—31no—
376C2×C3⋊Dic3—31no—
377C2×C3⋊Dic3—31no—
378C2×C3⋊Dic3—41no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—61no—
381C2×C3⋊Dic3—61no—
382C2×C3⋊Dic3—61no—
383C2×C3⋊Dic3—61no—
384C2×C3⋊Dic3—61no—
385C2×C3⋊Dic3—121no—
386C2×C3⋊Dic3—121no—
387C2×C3⋊Dic3C22×D311yescharacteristic
388C2×C3⋊Dic3C22×D311yescharacteristic
389C2×C3⋊Dic3C22×D311yescharacteristic
390C2×C3⋊Dic3C22×D311yescharacteristic
391#634—121no—
392C3×#67—22no—
393C3×#67—22no—
394C3×#67—42no—
395C2×C3×Dic3—21no—
396C2×C3×Dic3—21no—
397C2×C3×Dic3—21no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—61no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—64no—
413C2×C3×Dic3—62no—
414C2×C3×Dic3—62no—
415C2×C3×Dic3—121no—
416C2×C3×Dic3—121no—
417C2×C3×Dic3—121no—
418C2×C3×Dic3—122no—
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C3×C4×D3—62no—
430C3×C4×D3—62no—
431C3×C4×D3—121no—
432C3×C4×D3—121no—
433C3×C4×D3—121no—
434#627—121no—
435#627—121no—
436#627—122no—
437#625—62no—
438#625—62no—
439#625—122no—
440#625—121no—
441#625—121no—
442#625—122no—
443#624—22no—
444#624—41no—
445D3×Dic3—41no—
446#551—271noSylow
447C2×C33—22no—
448C2×C33C2×#4111yescharacteristic
449C2×C33C2×#4111yescharacteristic
450C2×C33H(5,𝔽2)11yescharacteristic
451C3×C3⋊D3—22no—
452C3×C3⋊D3—41no—
453C32×D3—41no—
454C24×C3—91no—
455C23×D3—31no—
456C23×D3—31no—
457C23×D3—61no—
458C2×C3×D4—31no—
459C2×C3×D4—31no—
460C2×C3×D4—61no—
461C22×C3×C4—91no—
462C22×C3×C4—91no—
463C22×C3×C4—91no—
464C22×C3×C4—91no—
465C22×C3×C4—91no—
466C2×#67—91no—
467C2×#67—91no—
468C2×#67—91no—
469C2×#67—91no—
470C2×#67—91no—
471C2×#67—91no—
472C2×#67—181no—
473C2×#67—181no—
474C2×#67D3211yescharacteristic
475C22×Dic3—31no—
476C22×Dic3—31no—
477C22×Dic3—31no—
478C22×Dic3—31no—
479C22×Dic3—31no—
480C22×Dic3—61no—
481C22×Dic3—61no—
482C2×C4×D3—31no—
483C2×C4×D3—31no—
484C2×C4×D3—31no—
485C2×C4×D3—31no—
486C2×C4×D3—31no—
487C2×Dic6—91no—
488C2×Dic6—91no—
489C2×Dic6—91no—
490C2×Dic6—181no—
491C3×C4⋊C4—91no—
492C3×C4⋊C4—91no—
493C3×C4⋊C4—91no—
494C3×C22⋊C4—31no—
495C3×C22⋊C4—31no—
496C3×C22⋊C4—31no—
497C3×C22⋊C4—31no—
498C3×C22⋊C4—61no—
499C3×C22⋊C4—61no—
500C3×C22⋊C4—91no—
501C3×C22⋊C4—91no—
502C3×C22⋊C4—91no—
503C3×C22⋊C4—91no—
504C3×C22⋊C4—91no—
505C3×C42—91no—
506#217—31no—
507#217—31no—
508#217—31no—
509#217—91no—
510#217—91no—
511#217—91no—
512#217—91no—
513#217—91no—
514#217—91no—
515#217—91no—
516#217—91no—
517#217—91no—
518#217—181no—
519#217—181no—
520#217—181no—
521#217—361no—
522#217D3211yescharacteristic
523#217D3211yescharacteristic
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—31no—
527(C2×D3)⋊C4—31no—
528(C2×D3)⋊C4—31no—
529(C2×D3)⋊C4—31no—
530(C2×D3)⋊C4—31no—
531(C2×D3)⋊C4—91no—
532(C2×D3)⋊C4—91no—
533(C2×D3)⋊C4—91no—
534(C2×D3)⋊C4—91no—
535(C2×D3)⋊C4—91no—
536(C2×D3)⋊C4—91no—
537(C2×D3)⋊C4—91no—
538(C2×D3)⋊C4—91no—
539(C2×D3)⋊C4—91no—
540(C2×D3)⋊C4—91no—
541(C2×D3)⋊C4—91no—
542(C2×D3)⋊C4—91no—
543(C2×D3)⋊C4—181no—
544(C2×D3)⋊C4—181no—
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—181no—
554Dic3⋊C4—31no—
555Dic3⋊C4—31no—
556Dic3⋊C4—31no—
557Dic3⋊C4—91no—
558Dic3⋊C4—91no—
559Dic3⋊C4—91no—
560Dic3⋊C4—91no—
561Dic3⋊C4—91no—
562Dic3⋊C4—91no—
563Dic3⋊C4—91no—
564Dic3⋊C4—91no—
565Dic3⋊C4—91no—
566Dic3⋊C4—91no—
567Dic3⋊C4—181no—
568Dic3⋊C4—181no—
569Dic3⋊C4—181no—
570Dic3⋊C4—181no—
571C4×Dic3—31no—
572C4×Dic3—31no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—91no—
579C4×Dic3—181no—
580C4×Dic3—181no—
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—21no—
585C22×C32—21no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—22no—
591C22×C32—22no—
592C22×C32—22no—
593C22×C32—41no—
594C22×C32—42no—
595C22×C32—41no—
596C22×C32—41no—
597C22×C32—41no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—61no—
602C22×C32—61no—
603C22×C32—61no—
604C22×C32—81no—
605C22×C32—81no—
606C22×C32#23512yes—
607C22×C32#23512yes—
608C22×C32#23712yes—
609C22×C32C23×D311yescharacteristic
610C22×C32C23×D311yescharacteristic
611C22×C32C23×D311yescharacteristic
612C2×C3⋊D3—21no—
613C2×C3⋊D3—21no—
614C2×C3⋊D3—21no—
615C2×C3⋊D3—21no—
616C2×C3⋊D3—21no—
617C2×C3⋊D3—44no—
618C2×C3⋊D3#23712yes—
619C2×C3×D3—21no—
620C2×C3×D3—21no—
621C2×C3×D3—21no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—32no—
626C2×C3×D3—32no—
627C2×C3×D3—41no—
628C2×C3×D3—41no—
629C2×C3×D3—41no—
630C2×C3×D3—62no—
631C2×C3×D3—61no—
632C2×C3×D3—61no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—62no—
636C2×C3×D3—61no—
637C2×C3×D3—61no—
638C2×C3×D3—61no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—61no—
642C2×C3×D3—121no—
643C2×C3×D3—121no—
644C2×C3×D3—121no—
645C2×C3×D3—121no—
646C2×C3×D3—124no—
647C2×C3×D3—124no—
648C2×C3×D3—128no—
649C32×C4—61no—
650C32×C4—61no—
651C32×C4—61no—
652C32×C4—61no—
653C32×C4—61no—
654C3⋊Dic3—21no—
655C3⋊Dic3—21no—
656C3⋊Dic3—21no—
657C3⋊Dic3—21no—
658C3⋊Dic3—61no—
659C3⋊Dic3—61no—
660C3⋊Dic3—61no—
661C3⋊Dic3—61no—
662C3⋊Dic3—61no—
663C3⋊Dic3—61no—
664C3⋊Dic3—121no—
665C3⋊Dic3—121no—
666C3⋊Dic3—121no—
667C3⋊Dic3—121no—
668C3⋊Dic3—121no—
669C3⋊Dic3—121no—
670C3⋊Dic3—241no—
671C3⋊Dic3—241no—
672C3×Dic3—21no—
673C3×Dic3—21no—
674C3×Dic3—21no—
675C3×Dic3—21no—
676C3×Dic3—21no—
677C3×Dic3—21no—
678C3×Dic3—21no—
679C3×Dic3—21no—
680C3×Dic3—21no—
681C3×Dic3—21no—
682C3×Dic3—41no—
683C3×Dic3—41no—
684C3×Dic3—41no—
685C3×Dic3—41no—
686C3×Dic3—41no—
687C3×Dic3—62no—
688C3×Dic3—62no—
689C3×Dic3—62no—
690C3×Dic3—61no—
691C3×Dic3—61no—
692C3×Dic3—61no—
693C3×Dic3—61no—
694C3×Dic3—61no—
695C3×Dic3—61no—
696C3×Dic3—61no—
697C3×Dic3—61no—
698C3×Dic3—121no—
699#126—271no—
700#126—271no—
701#124—271no—
702#123—91no—
703#123—271no—
704#123—271no—
705C22⋊Q8—271no—
706C22⋊Q8—271no—
707#120—271no—
708C4×D4—91no—
709C4×D4—271no—
710#117—271no—
711#117—271no—
712C2×C22⋊C4—91no—
713C2×C22⋊C4—271no—
714C33#55111yescharacteristic, complemented, Sylow
715C23×C3—21no—
716C23×C3—21no—
717C23×C3—21no—
718C23×C3—31no—
719C23×C3—31no—
720C23×C3—41no—
721C23×C3—61no—
722C23×C3—91no—
723C23×C3—91no—
724C23×C3—182no—
725C23×C3—182no—
726C23×C3—361no—
727C23×C3C2×D3211yescharacteristic
728C23×C3C2×D3211yescharacteristic
729C23×C3C2×D3211yescharacteristic
730C22×D3—31no—
731C22×D3—31no—
732C22×D3—31no—
733C22×D3—31no—
734C22×D3—61no—
735C22×D3—61no—
736C22×D3—62no—
737C22×D3—62no—
738C22×D3—62no—
739C22×D3—62no—
740C22×D3—122no—
741C22×D3—122no—
742C22×D3—121no—
743C22×D3—121no—
744C22×D3—122no—
745C22×D3C2×D3211yescharacteristic
746C3×D4—62no—
747C3×D4—62no—
748C3×D4—122no—
749C2×C3×C4—31no—
750C2×C3×C4—31no—
751C2×C3×C4—31no—
752C2×C3×C4—31no—
753C2×C3×C4—31no—
754C2×C3×C4—31no—
755C2×C3×C4—31no—
756C2×C3×C4—31no—
757C2×C3×C4—31no—
758C2×C3×C4—31no—
759C2×C3×C4—61no—
760C2×C3×C4—61no—
761C2×C3×C4—61no—
762C2×C3×C4—61no—
763C2×C3×C4—61no—
764C2×C3×C4—91no—
765C2×C3×C4—91no—
766C2×C3×C4—91no—
767C2×C3×C4—91no—
768C2×C3×C4—182no—
769C2×C3×C4—182no—
770C2×C3×C4—361no—
771C2×C3×C4—361no—
772C2×C3×C4—361no—
773#67—22no—
774#67—182no—
775#67—182no—
776#67—182no—
777#67—362no—
778#67—361no—
779#67—361no—
780#67—361no—
781#67—362no—
782C2×Dic3—31no—
783C2×Dic3—31no—
784C2×Dic3—31no—
785C2×Dic3—31no—
786C2×Dic3—31no—
787C2×Dic3—31no—
788C2×Dic3—31no—
789C2×Dic3—31no—
790C2×Dic3—61no—
791C2×Dic3—61no—
792C2×Dic3—61no—
793C2×Dic3—61no—
794C2×Dic3—64no—
795C2×Dic3—62no—
796C2×Dic3—62no—
797C2×Dic3—91no—
798C2×Dic3—91no—
799C2×Dic3—91no—
800C2×Dic3—91no—
801C2×Dic3—91no—
802C2×Dic3—91no—
803C2×Dic3—121no—
804C2×Dic3—121no—
805C2×Dic3—121no—
806C2×Dic3—122no—
807C2×Dic3—181no—
808C2×Dic3—181no—
809C2×Dic3—181no—
810C2×Dic3—181no—
811C2×Dic3—181no—
812C2×Dic3—181no—
813C2×Dic3—361no—
814C2×Dic3—361no—
815C2×Dic3C2×D3211yescharacteristic
816C2×Dic3C2×D3211yescharacteristic
817C2×Dic3C2×D3211yescharacteristic
818C2×Dic3C2×D3211yescharacteristic
819C2×Dic3C2×D3211yescharacteristic
820C4×D3—62no—
821C4×D3—62no—
822C4×D3—121no—
823C4×D3—121no—
824C4×D3—121no—
825Dic6—361no—
826Dic6—361no—
827Dic6—361no—
828Dic6—362no—
829C2×C32—22no—
830C2×C32—22no—
831C2×C32—22no—
832C2×C32—21no—
833C2×C32—21no—
834C2×C32—21no—
835C2×C32—21no—
836C2×C32—21no—
837C2×C32—21no—
838C2×C32—21no—
839C2×C32—21no—
840C2×C32—21no—
841C2×C32—41no—
842C2×C32—41no—
843C2×C32—41no—
844C2×C32—42no—
845C2×C32—42no—
846C2×C32—42no—
847C2×C32—82no—
848C2×C32—121no—
849C2×C32C2×#23511yescharacteristic
850C2×C32C2×#23511yescharacteristic
851C2×C32C2×#23711yescharacteristic
852C2×C32C2×#23711yescharacteristic
853C2×C32#100411yescharacteristic
854C2×C32#100411yescharacteristic
855C2×C32D3×#4111yescharacteristic
856C2×C32D3×#4111yescharacteristic
857C2×C32#100911yescharacteristic
858C3⋊D3—22no—
859C3⋊D3—41no—
860C3×D3—41no—
861C3×D3—41no—
862C3×D3—62no—
863C3×D3—62no—
864C3×D3—81no—
865C3×D3—122no—
866C3×D3—122no—
867C3×D3—121no—
868C3×D3—121no—
869C24—91no—
870C2×Q8—271no—
871C2×D4—31no—
872C2×D4—271no—
873C2×D4—271no—
874C22×C4—91no—
875C22×C4—91no—
876C22×C4—91no—
877C22×C4—91no—
878C22×C4—91no—
879C4⋊C4—91no—
880C4⋊C4—91no—
881C4⋊C4—91no—
882C4⋊C4—271no—
883C4⋊C4—271no—
884C4⋊C4—271no—
885C4⋊C4—271no—
886C4⋊C4—271no—
887C22⋊C4—31no—
888C22⋊C4—31no—
889C22⋊C4—91no—
890C22⋊C4—91no—
891C22⋊C4—91no—
892C22⋊C4—91no—
893C22⋊C4—91no—
894C22⋊C4—271no—
895C22⋊C4—271no—
896C22⋊C4—271no—
897C22⋊C4—271no—
898C22⋊C4—271no—
899C22⋊C4—271no—
900C22⋊C4—271no—
901C42—91no—
902C42—271no—
903C42—271no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—21no—
907C22×C3—21no—
908C22×C3—21no—
909C22×C3—21no—
910C22×C3—21no—
911C22×C3—21no—
912C22×C3—21no—
913C22×C3—22no—
914C22×C3—22no—
915C22×C3—22no—
916C22×C3—41no—
917C22×C3—41no—
918C22×C3—41no—
919C22×C3—41no—
920C22×C3—41no—
921C22×C3—41no—
922C22×C3—41no—
923C22×C3—42no—
924C22×C3—61no—
925C22×C3—61no—
926C22×C3—61no—
927C22×C3—61no—
928C22×C3—61no—
929C22×C3—61no—
930C22×C3—81no—
931C22×C3—81no—
932C22×C3—92no—
933C22×C3—121no—
934C22×C3—121no—
935C22×C3—121no—
936C22×C3—181no—
937C22×C3—181no—
938C22×C3—181no—
939C22×C3—181no—
940C22×C3—181no—
941C22×C3—364no—
942C22×C3#379512yes—
943C22×C3#379812yes—
944C22×C3#380412yes—
945C22×C3C22×D3211yescharacteristic
946C22×C3C22×D3211yescharacteristic
947C22×C3C22×D3211yescharacteristic
948C2×D3—21no—
949C2×D3—21no—
950C2×D3—21no—
951C2×D3—32no—
952C2×D3—32no—
953C2×D3—62no—
954C2×D3—61no—
955C2×D3—61no—
956C2×D3—61no—
957C2×D3—61no—
958C2×D3—62no—
959C2×D3—61no—
960C2×D3—61no—
961C2×D3—61no—
962C2×D3—61no—
963C2×D3—61no—
964C2×D3—61no—
965C2×D3—121no—
966C2×D3—121no—
967C2×D3—121no—
968C2×D3—121no—
969C2×D3—124no—
970C2×D3—124no—
971C2×D3—128no—
972C3×C4—61no—
973C3×C4—61no—
974C3×C4—61no—
975C3×C4—61no—
976C3×C4—61no—
977C3×C4—61no—
978C3×C4—61no—
979C3×C4—61no—
980C3×C4—61no—
981C3×C4—61no—
982C3×C4—121no—
983C3×C4—121no—
984C3×C4—121no—
985C3×C4—121no—
986C3×C4—121no—
987C3×C4—181no—
988C3×C4—181no—
989C3×C4—181no—
990C3×C4—181no—
991Dic3—21no—
992Dic3—21no—
993Dic3—21no—
994Dic3—21no—
995Dic3—21no—
996Dic3—62no—
997Dic3—62no—
998Dic3—62no—
999Dic3—61no—
1000Dic3—61no—
1001Dic3—61no—
1002Dic3—61no—
1003Dic3—61no—
1004Dic3—61no—
1005Dic3—61no—
1006Dic3—61no—
1007Dic3—121no—
1008Dic3—181no—
1009Dic3—181no—
1010Dic3—181no—
1011Dic3—181no—
1012Dic3—181no—
1013Dic3—181no—
1014Dic3—361no—
1015Dic3—361no—
1016Dic3—361no—
1017Dic3—361no—
1018Dic3—361no—
1019Dic3—361no—
1020Dic3—721no—
1021Dic3—721no—
1022C32—21no—
1023C32—21no—
1024C32—21no—
1025C32—41no—
1026C32#549511yescharacteristic, complemented
1027C32#555611yescharacteristic, complemented
1028C32#565811yescharacteristic, complemented
1029C23—31no—
1030C23—91no—
1031C23—91no—
1032C23—182no—
1033C23—182no—
1034C23—361no—
1035C23D3311yescharacteristic
1036Q8—1081no—
1037D4—62no—
1038D4—542no—
1039D4—1081no—
1040C2×C4—31no—
1041C2×C4—31no—
1042C2×C4—31no—
1043C2×C4—31no—
1044C2×C4—31no—
1045C2×C4—91no—
1046C2×C4—91no—
1047C2×C4—91no—
1048C2×C4—91no—
1049C2×C4—182no—
1050C2×C4—182no—
1051C2×C4—271no—
1052C2×C4—271no—
1053C2×C4—361no—
1054C2×C4—361no—
1055C2×C4—361no—
1056C2×C3—22no—
1057C2×C3—22no—
1058C2×C3—22no—
1059C2×C3—21no—
1060C2×C3—21no—
1061C2×C3—21no—
1062C2×C3—21no—
1063C2×C3—21no—
1064C2×C3—21no—
1065C2×C3—21no—
1066C2×C3—21no—
1067C2×C3—21no—
1068C2×C3—42no—
1069C2×C3—42no—
1070C2×C3—42no—
1071C2×C3—41no—
1072C2×C3—41no—
1073C2×C3—41no—
1074C2×C3—82no—
1075C2×C3—121no—
1076C2×C3—121no—
1077C2×C3—182no—
1078C2×C3—241no—
1079C2×C3—361no—
1080C2×C3C2×#379511yescharacteristic
1081C2×C3C2×#379811yescharacteristic
1082C2×C3D3×#23711yescharacteristic
1083C2×C3D3×#23711yescharacteristic
1084C2×C3#6431211yescharacteristic
1085C2×C3#6431311yescharacteristic
1086C2×C3#6431411yescharacteristic
1087C2×C3#6431411yescharacteristic
1088C2×C3C2×#380411yescharacteristic
1089D3—41no—
1090D3—62no—
1091D3—62no—
1092D3—122no—
1093D3—122no—
1094D3—121no—
1095D3—121no—
1096C22—21no—
1097C22—21no—
1098C22—61no—
1099C22—61no—
1100C22—61no—
1101C22—92no—
1102C22—181no—
1103C22—181no—
1104C22—181no—
1105C22—181no—
1106C22—181no—
1107C22—364no—
1108C22#8896012yes—
1109C22C2×D3311yescharacteristic
1110C4—61no—
1111C4—61no—
1112C4—61no—
1113C4—61no—
1114C4—61no—
1115C4—181no—
1116C4—181no—
1117C4—181no—
1118C4—181no—
1119C4—541no—
1120C4—541no—
1121C3—21no—
1122C3—21no—
1123C3—21no—
1124C3—41no—
1125C3#1059420911yescharacteristic, complemented
1126C3#1059421111yescharacteristic, complemented
1127C3#1059511811yescharacteristic, complemented
1128C2—22no—
1129C2—121no—
1130C2—182no—
1131C2—361no—
1132C2#1172440811yescharacteristic
1133C2#1172441611yescharacteristic
1134C2C2×#8896011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radical#11723634C2
hypercenterC23D33
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#88814C2semidirect
2. #11723641C2semidirect
4. #11723595C2semidirect
5. C3×#63974C2semidirect
6. C3×#67⋊Dic3C2semidirect
7. C3×#63962C2semidirect
8. #11723025C2semidirect
9. #11723024C2semidirect
10. #11723009C2semidirect
11. #11722992C2semidirect
12. #11722988C2semidirect
13. #11722972C2semidirect
14. #11722930C2semidirect
15. #11722915C2semidirect
23. C2×#6293C22semidirect
28. C2×C3×D3×Dic3C22semidirect
36. #88807C22semidirect
37. #88807C22semidirect
38. #88807C22semidirect
39. #88806C22semidirect
40. Dic3⋊(C3⋊Dic3)C22semidirect
43. Dic3×C3⋊Dic3C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. C3×Dic3⋊Dic3C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
50. C3×(C2×D3)⋊Dic3C22semidirect
51. C3×(C2×D3)⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
67. #63974D3semidirect
68. #67⋊Dic3D3semidirect
74. #63962D3semidirect
168. C2×D3×Dic3C2×D3semidirect
226. Dic3⋊Dic3C2×D3semidirect
227. Dic3⋊Dic3C2×D3semidirect
228. Dic3⋊Dic3C2×D3semidirect
249. (C2×D3)⋊Dic3C2×D3semidirect
250. (C2×D3)⋊Dic3C2×D3semidirect
251. (C2×D3)⋊Dic3C2×D3semidirect
258. Dic32C2×D3semidirect
714. C33#551semidirect
1026. C32#5495semidirect
1027. C32#5556semidirect
1028. C32#5658semidirect
1125. C3#10594209semidirect
1126. C3#10594211semidirect
1127. C3#10595118semidirect

Maximal subgroups

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

subgroupindex
C2×#888142
#117236412
#117236342
#117235952
C3×#639742
C3×#67⋊Dic32
C3×#639622
#117230252
#117230242
#117230092
#117229922
#117229882
#117229722
#117229302
#117229152
#105951183
#105942113
#105942093