Finite Group Databasebeta

← #13178640

Subgroups — #13178640

Order 1728.

1348 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64146C211yesmaximal, characteristic
2C3×#64144C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#11723726C211yesmaximal, characteristic, complemented
5#11723724C211yesmaximal, characteristic, complemented
6#11723723C211yesmaximal, characteristic, complemented
7#11723721C211yesmaximal, characteristic, complemented
8#11723720C211yesmaximal, characteristic, complemented
9C2×#88814C211yesmaximal, characteristic, complemented
10#11723718C211yesmaximal, characteristic, complemented
11#11723715C211yesmaximal, characteristic, complemented
12#11723692C211yesmaximal, characteristic, complemented
13#11723683C211yesmaximal, characteristic, complemented
14#11723676C211yesmaximal, characteristic, complemented
15#11723675C211yesmaximal, characteristic, complemented
16#10595177—31nomaximal
17#10595175—31nomaximal
18#10595118—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic
24C22×C3×C3⋊Dic3C2211yescharacteristic
25C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
26C2×#6296C2211yescharacteristic, complemented
27C2×#6294C2211yescharacteristic
28C2×#6294C2211yescharacteristic
29C3×#3757C2211yescharacteristic
30C3×#3757C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3757C2211yescharacteristic, complemented
33C3×#3757C2211yescharacteristic, complemented
34C3×#3757C2211yescharacteristic, complemented
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38C3×#3750C2211yescharacteristic, complemented
39C3×#3750C2211yescharacteristic, complemented
40C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
41#88815C2211yescharacteristic, complemented
42#88815C2211yescharacteristic, complemented
43#88815C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88815C2211yescharacteristic, complemented
46#88814C2211yescharacteristic
47#88814C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88813C2211yescharacteristic, complemented
53#88813C2211yescharacteristic, complemented
54#64146D311yescharacteristic
55#64144D311yescharacteristic, complemented
56D4×C3⋊Dic3D311yescharacteristic, complemented
57C3×#937—31no—
58C3×#937—31no—
59C3×#937—61no—
60C3×#935—31no—
61C3×#935—31no—
62C3×#935—61no—
63C3×D4×Dic3—31no—
64C3×D4×Dic3—31no—
65C3×D4×Dic3—61no—
66#63982—31no—
67#63975—31no—
68#63974—31no—
69#67⋊Dic3—31no—
70Dic3×#67—31no—
71#63969—31no—
72#63969—31no—
73D3×#217—31no—
74D3×#217—31no—
75#63966—31no—
76#63964—31no—
77#63964—31no—
78C2×#3722—31no—
79#63962—31no—
80#63961—31no—
81C2×(C2×D3)⋊Dic3—31no—
82C2×(C2×D3)⋊Dic3—31no—
83#63959—31no—
84#63959—31no—
85#63957—31no—
86#63955—31no—
87#63955—31no—
88#63953—31no—
89#63952—31no—
90#63899—31no—
91#63895—31no—
92#63893—31no—
93#63878—31no—
94#63877—31no—
95#63868—31no—
96#63862—31no—
97#63861—31no—
98#63859—31no—
99#63858—31no—
100#63848—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C23×C33C2311yescharacteristic
104C22×C3×C3⋊D3—22no—
105C22×C3×C3⋊D3—22no—
106C22×C3×C3⋊D3—41no—
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C33×D4—22no—
110C2×C33×C4C2311yescharacteristic
111C3×#638—22no—
112C3×#638—41no—
113C2×C3×C3⋊Dic3—22no—
114C2×C3×C3⋊Dic3—41no—
115C2×C3×C3⋊Dic3—41no—
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C2×C3×C3⋊Dic3C2311yescharacteristic
126#6296—41no—
127#6294—22no—
128#6294—41no—
129#5658—91no—
130#5587—91no—
131#5556—91no—
132C23×C3⋊D3C2×D311yescharacteristic
133C23×C3×D3—31no—
134C23×C3×D3—31no—
135C23×C3×D3—61no—
136C2×C32×D4—21no—
137C2×C32×D4—21no—
138C2×C32×D4—21no—
139C2×C32×D4—41no—
140C2×C32×D4C2×D311yescharacteristic
141C2×C32×D4C2×D311yescharacteristic
142C2×C32×D4C2×D311yescharacteristic
143C2×#638C2×D311yescharacteristic
144C2×#638C2×D311yescharacteristic
145C22×C3⋊Dic3C2×D311yescharacteristic
146C22×C3⋊Dic3C2×D311yescharacteristic
147C22×C3⋊Dic3C2×D311yescharacteristic, complemented
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—61no—
153C2×C3×#67—61no—
154C22×C3×Dic3—31no—
155C22×C3×Dic3—31no—
156C22×C3×Dic3—31no—
157C22×C3×Dic3—31no—
158C22×C3×Dic3—31no—
159C22×C3×Dic3—31no—
160C22×C3×Dic3—61no—
161C22×C3×Dic3—61no—
162C22×C3×Dic3—61no—
163C2×#627—31no—
164C2×#627—31no—
165C2×#627—31no—
166C2×#624—31no—
167C2×#624—31no—
168C2×D3×Dic3—31no—
169C2×D3×Dic3—31no—
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172#3757C2×D311yescharacteristic
173#3757C2×D311yescharacteristic
174#3757C2×D311yescharacteristic
175#3757C2×D311yescharacteristic, complemented
176#3757C2×D311yescharacteristic, complemented
177#3757C2×D311yescharacteristic, complemented
178#3752C2×D311yescharacteristic
179#3752C2×D311yescharacteristic
180C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
181#3750C2×D311yescharacteristic, complemented
182#3750C2×D311yescharacteristic, complemented
183C4×C3⋊Dic3C2×D311yescharacteristic, complemented
184C3×#217—31no—
185C3×#217—31no—
186C3×#217—31no—
187C3×#217—31no—
188C3×#217—31no—
189C3×#217—31no—
190C3×#217—31no—
191C3×#217—31no—
192C3×#217—31no—
193C3×#217—31no—
194C3×#217—31no—
195C3×#217—31no—
196C3×#217—61no—
197C3×#217—61no—
198C3×#217—61no—
199C3×#217—61no—
200C3×#217—61no—
201C3×#217—61no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—61no—
207C3×(C2×D3)⋊C4—61no—
208C3×C4⋊Dic3—31no—
209C3×C4⋊Dic3—31no—
210C3×C4⋊Dic3—61no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—61no—
216C3×Dic3⋊C4—61no—
217C3×C4×Dic3—31no—
218C3×C4×Dic3—31no—
219C3×C4×Dic3—61no—
220#3724—31no—
221#3724—31no—
222#3724—31no—
223#3724—31no—
224#3724—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—31no—
240#3722—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—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—31no—
257Dic32—31no—
258Dic32—31no—
259C22×C33—21no—
260C22×C33—21no—
261C22×C33—21no—
262C22×C33—21no—
263C22×C33—21no—
264C22×C33#4112yes—
265C22×C33C2411yescharacteristic
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—44no—
272C2×C3×C3⋊D3#4112yes—
273C33×C4—21no—
274C3×C3⋊Dic3—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3—21no—
279C3×C3⋊Dic3—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C3×#123—91no—
285C3×#120—91no—
286C3×C4×D4—91no—
287C2×#217—91no—
288C2×#217—91no—
289#937—31no—
290#937—31no—
291#937—61no—
292#936—91no—
293#935—31no—
294#935—31no—
295#935—61no—
296#935—91no—
297#935—91no—
298D4×Dic3—31no—
299D4×Dic3—31no—
300D4×Dic3—61no—
301D4×Dic3—91no—
302#929—91no—
303C4×#67—91no—
304C2×(C2×D3)⋊C4—91no—
305C2×(C2×D3)⋊C4—91no—
306#926—91no—
307#924—91no—
308#898—91no—
309#898—91no—
310#898—91no—
311#897—91no—
312#896—91no—
313#892—91no—
314#886—91no—
315#885—91no—
316#885—91no—
317#883—91no—
318#883—91no—
319#67⋊C4—91no—
320D3×C22⋊C4—91no—
321D3×C22⋊C4—91no—
322#879—91no—
323#879—91no—
324#878—91no—
325#878—91no—
326#878—91no—
327#877—91no—
328#877—91no—
329#877—91no—
330#876—91no—
331#872—91no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—21no—
336C23×C32—21no—
337C23×C32—21no—
338C23×C32—41no—
339C23×C32—41no—
340C23×C32C22×D311yescharacteristic
341C23×C32C22×D311yescharacteristic
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C23×C32C22×D311yescharacteristic
345C23×C32C22×D311yescharacteristic
346C22×C3⋊D3—22no—
347C22×C3⋊D3—22no—
348C22×C3⋊D3—41no—
349C22×C3⋊D3C22×D311yescharacteristic
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3×D3—31no—
352C22×C3×D3—31no—
353C22×C3×D3—31no—
354C22×C3×D3—31no—
355C22×C3×D3—61no—
356C22×C3×D3—61no—
357C22×C3×D3—62no—
358C22×C3×D3—62no—
359C22×C3×D3—62no—
360C22×C3×D3—62no—
361C22×C3×D3—122no—
362C22×C3×D3—122no—
363C22×C3×D3—121no—
364C22×C3×D3—121no—
365C22×C3×D3—122no—
366C32×D4—22no—
367C32×D4—24no—
368C32×D4—22no—
369C32×D4—22no—
370C32×D4—42no—
371C32×D4—42no—
372C32×D4—44no—
373C2×C32×C4—21no—
374C2×C32×C4—21no—
375C2×C32×C4—21no—
376C2×C32×C4—41no—
377C2×C32×C4C22×D311yescharacteristic
378C2×C32×C4C22×D311yescharacteristic
379C2×C32×C4C22×D311yescharacteristic
380#638—22no—
381#638—41no—
382C2×C3⋊Dic3—22no—
383C2×C3⋊Dic3—41no—
384C2×C3⋊Dic3—41no—
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C2×C3⋊Dic3C22×D311yescharacteristic
388C2×C3⋊Dic3C22×D311yescharacteristic
389C2×C3⋊Dic3C22×D311yescharacteristic
390C2×C3⋊Dic3C22×D311yescharacteristic
391C2×C3⋊Dic3C22×D311yescharacteristic
392C2×C3⋊Dic3C22×D311yescharacteristic
393C2×C3⋊Dic3C22×D311yescharacteristic
394C2×C3⋊Dic3C22×D311yescharacteristic
395C3×#67—62no—
396C3×#67—62no—
397C3×#67—122no—
398C3×#67—121no—
399C3×#67—121no—
400C3×#67—122no—
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—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—31no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3—61no—
423C2×C3×Dic3—61no—
424C2×C3×Dic3—61no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—61no—
427C2×C3×Dic3—61no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3—61no—
431C2×C3×Dic3—62no—
432C2×C3×Dic3—62no—
433C2×C3×Dic3—122no—
434C2×C3×Dic3—121no—
435C2×C3×Dic3—121no—
436C2×C3×Dic3—121no—
437C2×C3×Dic3—121no—
438C2×C3×Dic3—122no—
439C2×C3×Dic3—122no—
440#627—121no—
441#627—121no—
442#627—121no—
443#624—62no—
444#624—121no—
445D3×Dic3—62no—
446D3×Dic3—62no—
447D3×Dic3—121no—
448D3×Dic3—121no—
449#551—271noSylow
450C2×C33—22no—
451C2×C33—41no—
452C2×C33C2×#4111yescharacteristic
453C2×C33C2×#4111yescharacteristic
454C2×C33H(5,𝔽2)11yescharacteristic
455C3×C3⋊D3—22no—
456C3×C3⋊D3—41no—
457C24×C3—91no—
458C23×D3—31no—
459C23×D3—31no—
460C23×D3—61no—
461C2×C3×D4—21no—
462C2×C3×D4—21no—
463C2×C3×D4—21no—
464C2×C3×D4—41no—
465C2×C3×D4—91no—
466C2×C3×D4—91no—
467C2×C3×D4D3211yescharacteristic
468C2×C3×D4D3211yescharacteristic
469C2×C3×D4D3211yescharacteristic
470C22×C3×C4—91no—
471C22×C3×C4—91no—
472C22×C3×C4—91no—
473C2×#67—31no—
474C2×#67—31no—
475C2×#67—31no—
476C2×#67—31no—
477C2×#67—61no—
478C2×#67—61no—
479C22×Dic3—31no—
480C22×Dic3—31no—
481C22×Dic3—31no—
482C22×Dic3—31no—
483C22×Dic3—31no—
484C22×Dic3—31no—
485C22×Dic3—61no—
486C22×Dic3—61no—
487C22×Dic3—61no—
488C22×Dic3—91no—
489C22×Dic3—91no—
490C2×C4×D3—91no—
491C2×C4×D3—91no—
492C2×C4×D3—91no—
493C2×C4×D3—91no—
494C2×Dic6—91no—
495C2×Dic6—91no—
496C2×Dic6—91no—
497C3×C4⋊C4—91no—
498C3×C4⋊C4—91no—
499C3×C4⋊C4—91no—
500C3×C22⋊C4—91no—
501C3×C22⋊C4—91no—
502C3×C22⋊C4—91no—
503C3×C22⋊C4—91no—
504C3×C22⋊C4—91no—
505C3×C22⋊C4—91no—
506C3×C22⋊C4—91no—
507C3×C22⋊C4—91no—
508C3×C42—91no—
509#217—31no—
510#217—31no—
511#217—31no—
512#217—31no—
513#217—31no—
514#217—31no—
515#217—31no—
516#217—31no—
517#217—31no—
518#217—31no—
519#217—31no—
520#217—31no—
521#217—61no—
522#217—61no—
523#217—61no—
524#217—61no—
525#217—61no—
526#217—61no—
527#217—91no—
528#217—91no—
529#217—91no—
530#217—91no—
531#217—91no—
532#217—91no—
533(C2×D3)⋊C4—31no—
534(C2×D3)⋊C4—31no—
535(C2×D3)⋊C4—31no—
536(C2×D3)⋊C4—31no—
537(C2×D3)⋊C4—61no—
538(C2×D3)⋊C4—61no—
539(C2×D3)⋊C4—91no—
540(C2×D3)⋊C4—91no—
541(C2×D3)⋊C4—91no—
542(C2×D3)⋊C4—91no—
543(C2×D3)⋊C4—91no—
544(C2×D3)⋊C4—91no—
545(C2×D3)⋊C4—91no—
546(C2×D3)⋊C4—91no—
547(C2×D3)⋊C4—91no—
548(C2×D3)⋊C4—91no—
549(C2×D3)⋊C4—91no—
550(C2×D3)⋊C4—91no—
551C4⋊Dic3—31no—
552C4⋊Dic3—31no—
553C4⋊Dic3—61no—
554C4⋊Dic3—91no—
555C4⋊Dic3—91no—
556C4⋊Dic3—91no—
557C4⋊Dic3—91no—
558C4⋊Dic3—91no—
559Dic3⋊C4—31no—
560Dic3⋊C4—31no—
561Dic3⋊C4—31no—
562Dic3⋊C4—31no—
563Dic3⋊C4—61no—
564Dic3⋊C4—61no—
565Dic3⋊C4—91no—
566Dic3⋊C4—91no—
567Dic3⋊C4—91no—
568Dic3⋊C4—91no—
569Dic3⋊C4—91no—
570Dic3⋊C4—91no—
571Dic3⋊C4—91no—
572Dic3⋊C4—91no—
573Dic3⋊C4—91no—
574Dic3⋊C4—91no—
575C4×Dic3—31no—
576C4×Dic3—31no—
577C4×Dic3—61no—
578C4×Dic3—91no—
579C4×Dic3—91no—
580C4×Dic3—91no—
581C4×Dic3—91no—
582C4×Dic3—91no—
583C4×Dic3—91no—
584C22×C32—21no—
585C22×C32—21no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—21no—
591C22×C32—22no—
592C22×C32—21no—
593C22×C32—21no—
594C22×C32—21no—
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—21no—
601C22×C32—21no—
602C22×C32—21no—
603C22×C32—22no—
604C22×C32—22no—
605C22×C32—22no—
606C22×C32—41no—
607C22×C32—42no—
608C22×C32—41no—
609C22×C32—41no—
610C22×C32—42no—
611C22×C32—41no—
612C22×C32—41no—
613C22×C32—41no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—41no—
617C22×C32—41no—
618C22×C32—41no—
619C22×C32—41no—
620C22×C32—41no—
621C22×C32—41no—
622C22×C32—41no—
623C22×C32—81no—
624C22×C32—81no—
625C22×C32—81no—
626C22×C32—81no—
627C22×C32#23512yes—
628C22×C32#23712yes—
629C22×C32#23712yes—
630C22×C32C23×D311yescharacteristic
631C22×C32C23×D311yescharacteristic
632C22×C32C23×D311yescharacteristic
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—21no—
637C2×C3⋊D3—21no—
638C2×C3⋊D3—44no—
639C2×C3⋊D3#23712yes—
640C2×C3×D3—32no—
641C2×C3×D3—32no—
642C2×C3×D3—62no—
643C2×C3×D3—61no—
644C2×C3×D3—61no—
645C2×C3×D3—61no—
646C2×C3×D3—61no—
647C2×C3×D3—62no—
648C2×C3×D3—61no—
649C2×C3×D3—61no—
650C2×C3×D3—61no—
651C2×C3×D3—61no—
652C2×C3×D3—61no—
653C2×C3×D3—61no—
654C2×C3×D3—121no—
655C2×C3×D3—121no—
656C2×C3×D3—121no—
657C2×C3×D3—121no—
658C2×C3×D3—124no—
659C2×C3×D3—124no—
660C2×C3×D3—128no—
661C32×C4—21no—
662C32×C4—22no—
663C32×C4—21no—
664C32×C4—21no—
665C32×C4—41no—
666C32×C4—41no—
667C32×C4—42no—
668C3⋊Dic3—21no—
669C3⋊Dic3—21no—
670C3⋊Dic3—21no—
671C3⋊Dic3—21no—
672C3⋊Dic3—21no—
673C3⋊Dic3—21no—
674C3⋊Dic3—21no—
675C3⋊Dic3—21no—
676C3⋊Dic3—21no—
677C3⋊Dic3—21no—
678C3×Dic3—62no—
679C3×Dic3—61no—
680C3×Dic3—61no—
681C3×Dic3—61no—
682C3×Dic3—61no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—61no—
686C3×Dic3—61no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—61no—
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—61no—
699C3×Dic3—121no—
700C3×Dic3—121no—
701C3×Dic3—121no—
702C3×Dic3—121no—
703C3×Dic3—121no—
704C3×Dic3—121no—
705C3×Dic3—121no—
706C3×Dic3—121no—
707C3×Dic3—121no—
708#126—271no—
709#126—271no—
710#124—271no—
711#123—91no—
712#123—271no—
713#123—271no—
714C22⋊Q8—271no—
715C22⋊Q8—271no—
716#120—91no—
717C4×D4—91no—
718C4×D4—271no—
719#117—271no—
720#117—271no—
721C2×C22⋊C4—271no—
722C2×C22⋊C4—271no—
723C33#55111yescharacteristic, complemented, Sylow
724C23×C3—21no—
725C23×C3—21no—
726C23×C3—21no—
727C23×C3—21no—
728C23×C3—21no—
729C23×C3—21no—
730C23×C3—41no—
731C23×C3—41no—
732C23×C3—91no—
733C23×C3—91no—
734C23×C3—182no—
735C23×C3—182no—
736C23×C3—361no—
737C23×C3C2×D3211yescharacteristic
738C23×C3C2×D3211yescharacteristic
739C23×C3C2×D3211yescharacteristic
740C23×C3C2×D3211yescharacteristic
741C23×C3C2×D3211yescharacteristic
742C23×C3C2×D3211yescharacteristic
743C22×D3—31no—
744C22×D3—31no—
745C22×D3—31no—
746C22×D3—31no—
747C22×D3—61no—
748C22×D3—61no—
749C22×D3—62no—
750C22×D3—62no—
751C22×D3—62no—
752C22×D3—62no—
753C22×D3—122no—
754C22×D3—122no—
755C22×D3—121no—
756C22×D3—121no—
757C22×D3—122no—
758C3×D4—24no—
759C3×D4—22no—
760C3×D4—22no—
761C3×D4—22no—
762C3×D4—42no—
763C3×D4—42no—
764C3×D4—44no—
765C3×D4—182no—
766C3×D4—361no—
767C2×C3×C4—21no—
768C2×C3×C4—21no—
769C2×C3×C4—21no—
770C2×C3×C4—41no—
771C2×C3×C4—91no—
772C2×C3×C4—91no—
773C2×C3×C4—91no—
774C2×C3×C4—91no—
775C2×C3×C4—91no—
776C2×C3×C4—91no—
777C2×C3×C4—91no—
778C2×C3×C4—91no—
779C2×C3×C4—91no—
780C2×C3×C4—91no—
781C2×C3×C4—182no—
782C2×C3×C4—361no—
783C2×C3×C4—361no—
784C2×C3×C4C2×D3211yescharacteristic
785C2×C3×C4C2×D3211yescharacteristic
786C2×C3×C4C2×D3211yescharacteristic
787#67—62no—
788#67—62no—
789#67—122no—
790#67—121no—
791#67—121no—
792#67—122no—
793C2×Dic3—31no—
794C2×Dic3—31no—
795C2×Dic3—31no—
796C2×Dic3—31no—
797C2×Dic3—31no—
798C2×Dic3—31no—
799C2×Dic3—31no—
800C2×Dic3—31no—
801C2×Dic3—31no—
802C2×Dic3—31no—
803C2×Dic3—31no—
804C2×Dic3—31no—
805C2×Dic3—31no—
806C2×Dic3—31no—
807C2×Dic3—31no—
808C2×Dic3—31no—
809C2×Dic3—31no—
810C2×Dic3—31no—
811C2×Dic3—31no—
812C2×Dic3—31no—
813C2×Dic3—61no—
814C2×Dic3—61no—
815C2×Dic3—61no—
816C2×Dic3—61no—
817C2×Dic3—61no—
818C2×Dic3—61no—
819C2×Dic3—61no—
820C2×Dic3—61no—
821C2×Dic3—61no—
822C2×Dic3—61no—
823C2×Dic3—62no—
824C2×Dic3—62no—
825C2×Dic3—122no—
826C2×Dic3—121no—
827C2×Dic3—121no—
828C2×Dic3—121no—
829C2×Dic3—121no—
830C2×Dic3—122no—
831C2×Dic3—122no—
832C2×Dic3—182no—
833C2×Dic3—361no—
834C4×D3—182no—
835C4×D3—182no—
836C4×D3—361no—
837C4×D3—361no—
838Dic6—361no—
839Dic6—361no—
840Dic6—361no—
841C2×C32—22no—
842C2×C32—22no—
843C2×C32—22no—
844C2×C32—21no—
845C2×C32—21no—
846C2×C32—21no—
847C2×C32—21no—
848C2×C32—21no—
849C2×C32—21no—
850C2×C32—21no—
851C2×C32—21no—
852C2×C32—21no—
853C2×C32—41no—
854C2×C32—41no—
855C2×C32—41no—
856C2×C32—42no—
857C2×C32—42no—
858C2×C32—42no—
859C2×C32—41no—
860C2×C32—42no—
861C2×C32—41no—
862C2×C32—41no—
863C2×C32—82no—
864C2×C32—81no—
865C2×C32—81no—
866C2×C32—82no—
867C2×C32C2×#23511yescharacteristic
868C2×C32C2×#23711yescharacteristic
869C2×C32C2×#23711yescharacteristic
870C2×C32C2×#23711yescharacteristic
871C2×C32#100411yescharacteristic
872C2×C32#100411yescharacteristic
873C2×C32D3×#4111yescharacteristic
874C2×C32D3×#4111yescharacteristic
875C2×C32#100911yescharacteristic
876C3⋊D3—22no—
877C3⋊D3—41no—
878C3×D3—62no—
879C3×D3—62no—
880C3×D3—122no—
881C3×D3—122no—
882C3×D3—121no—
883C3×D3—121no—
884C24—91no—
885C2×Q8—271no—
886C2×D4—91no—
887C2×D4—91no—
888C2×D4#111311yescharacteristic
889C22×C4—91no—
890C22×C4—91no—
891C22×C4—91no—
892C22×C4—271no—
893C22×C4—271no—
894C4⋊C4—91no—
895C4⋊C4—91no—
896C4⋊C4—91no—
897C4⋊C4—271no—
898C4⋊C4—271no—
899C4⋊C4—271no—
900C4⋊C4—271no—
901C4⋊C4—271no—
902C22⋊C4—91no—
903C22⋊C4—91no—
904C22⋊C4—91no—
905C22⋊C4—91no—
906C22⋊C4—91no—
907C22⋊C4—91no—
908C22⋊C4—91no—
909C22⋊C4—91no—
910C22⋊C4—271no—
911C22⋊C4—271no—
912C22⋊C4—271no—
913C22⋊C4—271no—
914C22⋊C4—271no—
915C22⋊C4—271no—
916C42—91no—
917C42—271no—
918C42—271no—
919C22×C3—21no—
920C22×C3—21no—
921C22×C3—21no—
922C22×C3—21no—
923C22×C3—21no—
924C22×C3—21no—
925C22×C3—22no—
926C22×C3—21no—
927C22×C3—21no—
928C22×C3—21no—
929C22×C3—21no—
930C22×C3—21no—
931C22×C3—21no—
932C22×C3—21no—
933C22×C3—21no—
934C22×C3—21no—
935C22×C3—21no—
936C22×C3—21no—
937C22×C3—21no—
938C22×C3—22no—
939C22×C3—22no—
940C22×C3—22no—
941C22×C3—41no—
942C22×C3—41no—
943C22×C3—41no—
944C22×C3—41no—
945C22×C3—41no—
946C22×C3—41no—
947C22×C3—41no—
948C22×C3—41no—
949C22×C3—41no—
950C22×C3—41no—
951C22×C3—41no—
952C22×C3—41no—
953C22×C3—41no—
954C22×C3—41no—
955C22×C3—42no—
956C22×C3—41no—
957C22×C3—42no—
958C22×C3—81no—
959C22×C3—81no—
960C22×C3—81no—
961C22×C3—81no—
962C22×C3—92no—
963C22×C3—181no—
964C22×C3—181no—
965C22×C3—181no—
966C22×C3—181no—
967C22×C3—181no—
968C22×C3—364no—
969C22×C3#380412yes—
970C22×C3#380412yes—
971C22×C3#380512yes—
972C22×C3C22×D3211yescharacteristic
973C22×C3C22×D3211yescharacteristic
974C22×C3C22×D3211yescharacteristic
975C2×D3—32no—
976C2×D3—32no—
977C2×D3—62no—
978C2×D3—61no—
979C2×D3—61no—
980C2×D3—61no—
981C2×D3—61no—
982C2×D3—62no—
983C2×D3—61no—
984C2×D3—61no—
985C2×D3—61no—
986C2×D3—61no—
987C2×D3—61no—
988C2×D3—61no—
989C2×D3—121no—
990C2×D3—121no—
991C2×D3—121no—
992C2×D3—121no—
993C2×D3—124no—
994C2×D3—124no—
995C2×D3—128no—
996C3×C4—22no—
997C3×C4—21no—
998C3×C4—21no—
999C3×C4—21no—
1000C3×C4—41no—
1001C3×C4—41no—
1002C3×C4—42no—
1003C3×C4—181no—
1004C3×C4—181no—
1005C3×C4—181no—
1006C3×C4—181no—
1007C3×C4—181no—
1008C3×C4—181no—
1009C3×C4—181no—
1010C3×C4—181no—
1011C3×C4—181no—
1012C3×C4—181no—
1013Dic3—62no—
1014Dic3—61no—
1015Dic3—61no—
1016Dic3—61no—
1017Dic3—61no—
1018Dic3—61no—
1019Dic3—61no—
1020Dic3—61no—
1021Dic3—61no—
1022Dic3—61no—
1023Dic3—61no—
1024Dic3—61no—
1025Dic3—61no—
1026Dic3—61no—
1027Dic3—61no—
1028Dic3—61no—
1029Dic3—61no—
1030Dic3—61no—
1031Dic3—61no—
1032Dic3—61no—
1033Dic3—61no—
1034Dic3—121no—
1035Dic3—121no—
1036Dic3—121no—
1037Dic3—121no—
1038Dic3—121no—
1039Dic3—121no—
1040Dic3—121no—
1041Dic3—121no—
1042Dic3—121no—
1043C32—21no—
1044C32—21no—
1045C32—21no—
1046C32—41no—
1047C32#555611yescharacteristic, complemented
1048C32#558711yescharacteristic, complemented
1049C32#565811yescharacteristic, complemented
1050C23—91no—
1051C23—91no—
1052C23—182no—
1053C23—182no—
1054C23—361no—
1055C23C2×#111311yescharacteristic
1056C23C2×#111311yescharacteristic
1057Q8—1081no—
1058D4—22no—
1059D4—182no—
1060D4—361no—
1061C2×C4—91no—
1062C2×C4—91no—
1063C2×C4—91no—
1064C2×C4—91no—
1065C2×C4—91no—
1066C2×C4—91no—
1067C2×C4—91no—
1068C2×C4—91no—
1069C2×C4—91no—
1070C2×C4—91no—
1071C2×C4—182no—
1072C2×C4—361no—
1073C2×C4—361no—
1074C2×C4—542no—
1075C2×C4—1081no—
1076C2×C4C2×#111311yescharacteristic
1077C2×C3—22no—
1078C2×C3—22no—
1079C2×C3—22no—
1080C2×C3—21no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—21no—
1084C2×C3—21no—
1085C2×C3—21no—
1086C2×C3—21no—
1087C2×C3—21no—
1088C2×C3—21no—
1089C2×C3—42no—
1090C2×C3—42no—
1091C2×C3—42no—
1092C2×C3—42no—
1093C2×C3—41no—
1094C2×C3—41no—
1095C2×C3—41no—
1096C2×C3—41no—
1097C2×C3—41no—
1098C2×C3—41no—
1099C2×C3—82no—
1100C2×C3—81no—
1101C2×C3—81no—
1102C2×C3—82no—
1103C2×C3—182no—
1104C2×C3—361no—
1105C2×C3D3×#23711yescharacteristic
1106C2×C3D3×#23711yescharacteristic
1107C2×C3#6431211yescharacteristic
1108C2×C3#6431311yescharacteristic
1109C2×C3#6431411yescharacteristic
1110C2×C3#6431411yescharacteristic
1111C2×C3C2×#380411yescharacteristic
1112C2×C3C2×#380411yescharacteristic
1113C2×C3C2×#380511yescharacteristic
1114D3—62no—
1115D3—62no—
1116D3—122no—
1117D3—122no—
1118D3—121no—
1119D3—121no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—92no—
1126C22—181no—
1127C22—181no—
1128C22—181no—
1129C22—181no—
1130C22—181no—
1131C22—364no—
1132C22#8904612yes—
1133C22C22×#111311yescharacteristic
1134C4—21no—
1135C4—181no—
1136C4—181no—
1137C4—181no—
1138C4—181no—
1139C4—181no—
1140C4—181no—
1141C4—181no—
1142C4—181no—
1143C4—181no—
1144C4—181no—
1145C3—21no—
1146C3—21no—
1147C3—21no—
1148C3—41no—
1149C3#1059511811yescharacteristic, complemented
1150C3#1059517511yescharacteristic, complemented
1151C3#1059517711yescharacteristic, complemented
1152C2—22no—
1153C2—41no—
1154C2—182no—
1155C2—361no—
1156C2#1172462211yescharacteristic
1157C2#1172462311yescharacteristic
1158C2C2×#8904611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
prime radicalC3×#64146C2
hypercenterC2×D4#1113
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C3×#64144C2semidirect
3. C3×D4×C3⋊Dic3C2semidirect
4. #11723726C2semidirect
5. #11723724C2semidirect
6. #11723723C2semidirect
7. #11723721C2semidirect
8. #11723720C2semidirect
9. C2×#88814C2semidirect
10. #11723718C2semidirect
11. #11723715C2semidirect
12. #11723692C2semidirect
13. #11723683C2semidirect
14. #11723676C2semidirect
15. #11723675C2semidirect
25. C22×C3×C3⋊Dic3C22semidirect
26. C2×#6296C22semidirect
32. C3×#3757C22semidirect
33. C3×#3757C22semidirect
34. C3×#3757C22semidirect
37. C3×C4⋊(C3⋊Dic3)C22semidirect
38. C3×#3750C22semidirect
39. C3×#3750C22semidirect
40. C3×C4×C3⋊Dic3C22semidirect
41. #88815C22semidirect
42. #88815C22semidirect
43. #88815C22semidirect
44. #88815C22semidirect
45. #88815C22semidirect
52. #88813C22semidirect
53. #88813C22semidirect
55. #64144D3semidirect
56. D4×C3⋊Dic3D3semidirect
147. C22×C3⋊Dic3C2×D3semidirect
175. #3757C2×D3semidirect
176. #3757C2×D3semidirect
177. #3757C2×D3semidirect
180. C4⋊(C3⋊Dic3)C2×D3semidirect
181. #3750C2×D3semidirect
182. #3750C2×D3semidirect
183. C4×C3⋊Dic3C2×D3semidirect
723. C33#551semidirect
1047. C32#5556semidirect
1048. C32#5587semidirect
1049. C32#5658semidirect
1149. C3#10595118semidirect
1150. C3#10595175semidirect
1151. C3#10595177semidirect

Maximal subgroups

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

subgroupindex
C3×#641462
C3×#641442
C3×D4×C3⋊Dic32
#117237262
#117237242
#117237232
#117237212
#117237202
C2×#888142
#117237182
#117237152
#117236922
#117236832
#117236762
#117236752
#105951773
#105951753
#105951183