Finite Group Databasebeta

← #13178249

Subgroups — #13178249

Order 1728.

1328 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
1C3×#64090C211yesmaximal, characteristic, complemented
2C3×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C3×#64086C211yesmaximal, characteristic, complemented
4#11723727C211yesmaximal, characteristic
5#11723721C211yesmaximal, characteristic, complemented
6#11723720C211yesmaximal, characteristic, complemented
7C2×#88814C211yesmaximal, characteristic, complemented
8#11723694C211yesmaximal, characteristic, complemented
9#11723694C211yesmaximal, characteristic, complemented
10C4×#6295C211yesmaximal, characteristic, complemented
11#11723676C211yesmaximal, characteristic, complemented
12#11723676C211yesmaximal, characteristic, complemented
13#11723673C211yesmaximal, characteristic, complemented
14#11723672C211yesmaximal, characteristic, complemented
15#11723671C211yesmaximal, characteristic, complemented
16#10594209—31nomaximal
17#10594040—31nomaximal
18#10594037—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2211yescharacteristic
24C2×C3×C4×C3⋊D3C2211yescharacteristic
25C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
26C2×#6296C2211yescharacteristic, complemented
27C2×#6295C2211yescharacteristic
28C2×#6295C2211yescharacteristic
29C33×C22⋊C4C2211yescharacteristic
30C3×#3757C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C3×#3752C2211yescharacteristic
34C3×#3752C2211yescharacteristic, complemented
35C3×#3750C2211yescharacteristic, complemented
36C3×#3750C2211yescharacteristic, complemented
37C3×#3750C2211yescharacteristic, complemented
38C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
39C3×C4×C3⋊Dic3C2211yescharacteristic, 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#88814C2211yescharacteristic, complemented
53#88814C2211yescharacteristic, complemented
54#64090D311yescharacteristic, complemented
55C22⋊C4×C3⋊D3D311yescharacteristic, complemented
56#64086D311yescharacteristic, complemented
57C3×#67⋊C4—31no—
58C3×#67⋊C4—31no—
59C3×#67⋊C4—61no—
60C3×D3×C22⋊C4—31no—
61C3×D3×C22⋊C4—31no—
62C3×D3×C22⋊C4—61no—
63C3×#877—31no—
64C3×#877—31no—
65C3×#877—61no—
66#63982—31no—
67#63981—31no—
68#63977—31no—
69#63976—31no—
70#63966—31no—
71#63964—31no—
72#63964—31no—
73C2×#3722—31no—
74#63962—31no—
75#63961—31no—
76C2×(C2×D3)⋊Dic3—31no—
77C2×(C2×D3)⋊Dic3—31no—
78#63915—31no—
79#63905—31no—
80#63905—31no—
81C4×#626—31no—
82C4×#626—31no—
83C4×#625—31no—
84#63874—31no—
85#63868—31no—
86#63868—31no—
87#63865—31no—
88#63862—31no—
89#63862—31no—
90#63859—31no—
91#63859—31no—
92#63855—31no—
93#63855—31no—
94#63853—31no—
95#63853—31no—
96#63852—31no—
97#63852—31no—
98#63851—31no—
99#63851—31no—
100#63850—31no—
101#63850—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×C3×C3⋊D3C2311yescharacteristic
109C2×C33×C4C2311yescharacteristic
110C2×C33×C4C2311yescharacteristic
111C3×#638—22no—
112C2×C3×C3⋊Dic3—22no—
113C2×C3×C3⋊Dic3—41no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
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
123C3×C4×C3⋊D3—22no—
124C3×C4×C3⋊D3—41no—
125C3×C4×C3⋊D3—41no—
126#6296—41no—
127#6295—22no—
128#6295—41no—
129#5556—91no—
130#5527—91no—
131#5495—91no—
132C23×C3⋊D3C2×D311yescharacteristic
133C23×C3×D3—31no—
134C23×C3×D3—31no—
135C23×C3×D3—61no—
136C2×#638C2×D311yescharacteristic
137C22×C3⋊Dic3C2×D311yescharacteristic
138C22×C3⋊Dic3C2×D311yescharacteristic
139C2×C4×C3⋊D3C2×D311yescharacteristic
140C2×C4×C3⋊D3C2×D311yescharacteristic
141C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—61no—
145C22×C3×Dic3—31no—
146C22×C3×Dic3—31no—
147C22×C3×Dic3—31no—
148C22×C3×Dic3—31no—
149C22×C3×Dic3—61no—
150C22×C3×Dic3—61no—
151C2×C3×C4×D3—31no—
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×C3×C4×D3—61no—
158C2×C3×C4×D3—61no—
159C2×C3×C4×D3—61no—
160C2×#627—31no—
161C2×#627—31no—
162C2×#627—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626—31no—
166C2×#626—31no—
167C2×#625—31no—
168C2×#625—31no—
169C32×C22⋊C4—21no—
170C32×C22⋊C4—21no—
171C32×C22⋊C4—21no—
172C32×C22⋊C4—41no—
173C32×C22⋊C4C2×D311yescharacteristic
174C32×C22⋊C4C2×D311yescharacteristic
175C32×C22⋊C4C2×D311yescharacteristic
176#3757C2×D311yescharacteristic
177#3757C2×D311yescharacteristic
178#3752C2×D311yescharacteristic
179#3752C2×D311yescharacteristic
180#3752C2×D311yescharacteristic, complemented
181#3750C2×D311yescharacteristic, complemented
182#3750C2×D311yescharacteristic, complemented
183#3750C2×D311yescharacteristic, complemented
184C4×C3⋊Dic3C2×D311yescharacteristic, complemented
185C4×C3⋊Dic3C2×D311yescharacteristic, complemented
186C4×C3⋊Dic3C2×D311yescharacteristic, complemented
187C3×#217—31no—
188C3×#217—31no—
189C3×#217—31no—
190C3×#217—31no—
191C3×#217—61no—
192C3×#217—61no—
193C3×(C2×D3)⋊C4—31no—
194C3×(C2×D3)⋊C4—31no—
195C3×(C2×D3)⋊C4—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—61no—
200C3×(C2×D3)⋊C4—61no—
201C3×(C2×D3)⋊C4—61no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—61no—
209C3×Dic3⋊C4—61no—
210C3×Dic3⋊C4—61no—
211C3×C4×Dic3—31no—
212C3×C4×Dic3—31no—
213C3×C4×Dic3—31no—
214C3×C4×Dic3—31no—
215C3×C4×Dic3—31no—
216C3×C4×Dic3—31no—
217C3×C4×Dic3—61no—
218C3×C4×Dic3—61no—
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#3722—31no—
242#3722—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—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—31no—
257(C2×D3)⋊Dic3—31no—
258(C2×D3)⋊Dic3—31no—
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—21no—
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—44no—
272C2×C3×C3⋊D3#4112yes—
273C33×C4—21no—
274C33×C4—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×C4×D4—91no—
285C3×#117—91no—
286C2×C3×C22⋊C4—91no—
287#953—91no—
288C2×#217—91no—
289#937—91no—
290#935—91no—
291#929—91no—
292#929—91no—
293#929—91no—
294C4×#67—91no—
295C4×#67—91no—
296C2×(C2×D3)⋊C4—91no—
297C2×(C2×D3)⋊C4—91no—
298#926—91no—
299#924—91no—
300#924—91no—
301#898—91no—
302#898—91no—
303#896—91no—
304#896—91no—
305#894—91no—
306#894—91no—
307#886—91no—
308#885—91no—
309#885—91no—
310#883—91no—
311#883—91no—
312#882—91no—
313#67⋊C4—31no—
314#67⋊C4—31no—
315#67⋊C4—61no—
316D3×C22⋊C4—31no—
317D3×C22⋊C4—31no—
318D3×C22⋊C4—61no—
319#879—91no—
320#879—91no—
321#878—91no—
322#878—91no—
323#877—31no—
324#877—31no—
325#877—61no—
326#876—91no—
327#876—91no—
328#875—91no—
329C4×D12—91no—
330#872—91no—
331#872—91no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—41no—
336C23×C32C22×D311yescharacteristic
337C23×C32C22×D311yescharacteristic
338C23×C32C22×D311yescharacteristic
339C22×C3⋊D3—22no—
340C22×C3⋊D3—22no—
341C22×C3⋊D3—41no—
342C22×C3⋊D3C22×D311yescharacteristic
343C22×C3⋊D3C22×D311yescharacteristic
344C22×C3⋊D3C22×D311yescharacteristic
345C22×C3×D3—31no—
346C22×C3×D3—31no—
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—31no—
351C22×C3×D3—61no—
352C22×C3×D3—61no—
353C22×C3×D3—61no—
354C22×C3×D3—62no—
355C22×C3×D3—62no—
356C22×C3×D3—64no—
357C22×C3×D3—62no—
358C22×C3×D3—62no—
359C22×C3×D3—122no—
360C22×C3×D3—121no—
361C22×C3×D3—121no—
362C22×C3×D3—122no—
363C2×C32×C4—21no—
364C2×C32×C4—21no—
365C2×C32×C4—21no—
366C2×C32×C4—21no—
367C2×C32×C4—21no—
368C2×C32×C4—21no—
369C2×C32×C4—41no—
370C2×C32×C4—41no—
371C2×C32×C4C22×D311yescharacteristic
372C2×C32×C4C22×D311yescharacteristic
373C2×C32×C4C22×D311yescharacteristic
374C2×C32×C4C22×D311yescharacteristic
375C2×C32×C4C22×D311yescharacteristic
376C2×C32×C4C22×D311yescharacteristic
377#638—22no—
378C2×C3⋊Dic3—22no—
379C2×C3⋊Dic3—41no—
380C2×C3⋊Dic3C22×D311yescharacteristic
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C2×C3⋊Dic3C22×D311yescharacteristic
388C2×C3⋊Dic3C22×D311yescharacteristic
389C4×C3⋊D3—22no—
390C4×C3⋊D3—41no—
391C4×C3⋊D3—41no—
392C3×#67—64no—
393C3×#67—62no—
394C3×#67—62no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—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—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—61no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3—64no—
423C2×C3×Dic3—62no—
424C2×C3×Dic3—62no—
425C2×C3×Dic3—121no—
426C2×C3×Dic3—121no—
427C2×C3×Dic3—122no—
428C3×C4×D3—62no—
429C3×C4×D3—62no—
430C3×C4×D3—122no—
431C3×C4×D3—121no—
432C3×C4×D3—121no—
433C3×C4×D3—121no—
434C3×C4×D3—121no—
435C3×C4×D3—122no—
436C3×C4×D3—122no—
437#627—121no—
438#627—121no—
439#627—121no—
440#626—62no—
441#626—62no—
442#626—121no—
443#626—121no—
444#625—62no—
445#625—121no—
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—
453C3×C3⋊D3—41no—
454C24×C3—91no—
455C23×D3—31no—
456C23×D3—31no—
457C23×D3—61no—
458C2×C3×D4—91no—
459C22×C3×C4—91no—
460C22×C3×C4—91no—
461C22×C3×C4—91no—
462C22×C3×C4—91no—
463C22×C3×C4—91no—
464C2×#67—31no—
465C2×#67—31no—
466C2×#67—61no—
467C2×#67—91no—
468C2×#67—91no—
469C2×#67—91no—
470C2×#67—91no—
471C22×Dic3—31no—
472C22×Dic3—31no—
473C22×Dic3—31no—
474C22×Dic3—31no—
475C22×Dic3—61no—
476C22×Dic3—61no—
477C2×D12—91no—
478C2×D12—91no—
479C2×C4×D3—31no—
480C2×C4×D3—31no—
481C2×C4×D3—31no—
482C2×C4×D3—31no—
483C2×C4×D3—31no—
484C2×C4×D3—31no—
485C2×C4×D3—61no—
486C2×C4×D3—61no—
487C2×C4×D3—61no—
488C2×Dic6—91no—
489C2×Dic6—91no—
490C2×Dic6—91no—
491C3×C4⋊C4—91no—
492C3×C4⋊C4—91no—
493C3×C4⋊C4—91no—
494C3×C22⋊C4—21no—
495C3×C22⋊C4—21no—
496C3×C22⋊C4—21no—
497C3×C22⋊C4—41no—
498C3×C22⋊C4—91no—
499C3×C22⋊C4—91no—
500C3×C22⋊C4—91no—
501C3×C22⋊C4—91no—
502C3×C22⋊C4—91no—
503C3×C22⋊C4D3211yescharacteristic
504C3×C22⋊C4D3211yescharacteristic
505C3×C22⋊C4D3211yescharacteristic
506C3×C42—91no—
507C3×C42—91no—
508C3×C42—91no—
509#217—31no—
510#217—31no—
511#217—31no—
512#217—31no—
513#217—61no—
514#217—61no—
515#217—91no—
516#217—91no—
517#217—91no—
518#217—91no—
519#217—91no—
520#217—91no—
521#217—91no—
522#217—91no—
523(C2×D3)⋊C4—31no—
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—61no—
530(C2×D3)⋊C4—61no—
531(C2×D3)⋊C4—61no—
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—91no—
544(C2×D3)⋊C4—91no—
545(C2×D3)⋊C4—91no—
546(C2×D3)⋊C4—91no—
547(C2×D3)⋊C4—91no—
548C4⋊Dic3—91no—
549C4⋊Dic3—91no—
550C4⋊Dic3—91no—
551C4⋊Dic3—91no—
552C4⋊Dic3—91no—
553Dic3⋊C4—31no—
554Dic3⋊C4—31no—
555Dic3⋊C4—31no—
556Dic3⋊C4—31no—
557Dic3⋊C4—31no—
558Dic3⋊C4—31no—
559Dic3⋊C4—61no—
560Dic3⋊C4—61no—
561Dic3⋊C4—61no—
562Dic3⋊C4—91no—
563Dic3⋊C4—91no—
564Dic3⋊C4—91no—
565Dic3⋊C4—91no—
566Dic3⋊C4—91no—
567Dic3⋊C4—91no—
568Dic3⋊C4—91no—
569Dic3⋊C4—91no—
570Dic3⋊C4—91no—
571Dic3⋊C4—91no—
572C4×Dic3—31no—
573C4×Dic3—31no—
574C4×Dic3—31no—
575C4×Dic3—31no—
576C4×Dic3—31no—
577C4×Dic3—31no—
578C4×Dic3—61no—
579C4×Dic3—61no—
580C4×Dic3—61no—
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—81no—
602C22×C32—81no—
603C22×C32#23512yes—
604C22×C32#23512yes—
605C22×C32#23512yes—
606C22×C32C23×D311yescharacteristic
607C22×C32C23×D311yescharacteristic
608C22×C32C23×D311yescharacteristic
609C2×C3⋊D3—21no—
610C2×C3⋊D3—21no—
611C2×C3⋊D3—21no—
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—32no—
620C2×C3×D3—32no—
621C2×C3×D3—62no—
622C2×C3×D3—62no—
623C2×C3×D3—62no—
624C2×C3×D3—61no—
625C2×C3×D3—61no—
626C2×C3×D3—61no—
627C2×C3×D3—61no—
628C2×C3×D3—62no—
629C2×C3×D3—62no—
630C2×C3×D3—61no—
631C2×C3×D3—61no—
632C2×C3×D3—61no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
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—21no—
650C32×C4—21no—
651C32×C4—21no—
652C32×C4—21no—
653C32×C4—21no—
654C32×C4—21no—
655C32×C4—41no—
656C32×C4—41no—
657C32×C4—41no—
658C32×C4—41no—
659C32×C4—41no—
660C32×C4—41no—
661C32×C4—81no—
662C32×C4—81no—
663C3⋊Dic3—21no—
664C3⋊Dic3—21no—
665C3⋊Dic3—21no—
666C3⋊Dic3—21no—
667C3⋊Dic3—21no—
668C3⋊Dic3—21no—
669C3⋊Dic3—21no—
670C3⋊Dic3—21no—
671C3⋊Dic3—21no—
672C3×Dic3—62no—
673C3×Dic3—62no—
674C3×Dic3—62no—
675C3×Dic3—62no—
676C3×Dic3—61no—
677C3×Dic3—61no—
678C3×Dic3—61no—
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—121no—
695C3×Dic3—121no—
696C3×Dic3—121no—
697C3×Dic3—121no—
698C3×Dic3—121no—
699#126—271no—
700#126—271no—
701#124—271no—
702#123—271no—
703#123—271no—
704#123—271no—
705C22⋊Q8—271no—
706C22⋊Q8—271no—
707#120—271no—
708C4×D4—91no—
709C4×D4—271no—
710#117—91no—
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—41no—
719C23×C3—91no—
720C23×C3—91no—
721C23×C3—91no—
722C23×C3—182no—
723C23×C3—182no—
724C23×C3—361no—
725C23×C3C2×D3211yescharacteristic
726C23×C3C2×D3211yescharacteristic
727C23×C3C2×D3211yescharacteristic
728C22×D3—31no—
729C22×D3—31no—
730C22×D3—31no—
731C22×D3—31no—
732C22×D3—31no—
733C22×D3—31no—
734C22×D3—61no—
735C22×D3—61no—
736C22×D3—61no—
737C22×D3—62no—
738C22×D3—62no—
739C22×D3—64no—
740C22×D3—62no—
741C22×D3—62no—
742C22×D3—122no—
743C22×D3—121no—
744C22×D3—121no—
745C22×D3—122no—
746C3×D4—182no—
747C2×C3×C4—21no—
748C2×C3×C4—21no—
749C2×C3×C4—21no—
750C2×C3×C4—21no—
751C2×C3×C4—21no—
752C2×C3×C4—21no—
753C2×C3×C4—41no—
754C2×C3×C4—41no—
755C2×C3×C4—91no—
756C2×C3×C4—91no—
757C2×C3×C4—91no—
758C2×C3×C4—91no—
759C2×C3×C4—91no—
760C2×C3×C4—91no—
761C2×C3×C4—91no—
762C2×C3×C4—91no—
763C2×C3×C4—91no—
764C2×C3×C4—182no—
765C2×C3×C4—182no—
766C2×C3×C4—361no—
767C2×C3×C4—361no—
768C2×C3×C4—361no—
769C2×C3×C4C2×D3211yescharacteristic
770C2×C3×C4C2×D3211yescharacteristic
771C2×C3×C4C2×D3211yescharacteristic
772C2×C3×C4C2×D3211yescharacteristic
773C2×C3×C4C2×D3211yescharacteristic
774C2×C3×C4C2×D3211yescharacteristic
775#67—64no—
776#67—62no—
777#67—62no—
778#67—182no—
779#67—182no—
780#67—361no—
781#67—361no—
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—31no—
791C2×Dic3—31no—
792C2×Dic3—31no—
793C2×Dic3—31no—
794C2×Dic3—31no—
795C2×Dic3—31no—
796C2×Dic3—31no—
797C2×Dic3—31no—
798C2×Dic3—31no—
799C2×Dic3—31no—
800C2×Dic3—61no—
801C2×Dic3—61no—
802C2×Dic3—61no—
803C2×Dic3—61no—
804C2×Dic3—61no—
805C2×Dic3—61no—
806C2×Dic3—61no—
807C2×Dic3—61no—
808C2×Dic3—61no—
809C2×Dic3—64no—
810C2×Dic3—62no—
811C2×Dic3—62no—
812C2×Dic3—121no—
813C2×Dic3—121no—
814C2×Dic3—122no—
815D12—182no—
816D12—361no—
817C4×D3—62no—
818C4×D3—62no—
819C4×D3—122no—
820C4×D3—121no—
821C4×D3—121no—
822C4×D3—121no—
823C4×D3—121no—
824C4×D3—122no—
825C4×D3—122no—
826Dic6—361no—
827Dic6—361no—
828Dic6—361no—
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×C32C2×#23511yescharacteristic
849C2×C32C2×#23511yescharacteristic
850C2×C32C2×#23511yescharacteristic
851C2×C32C2×#23711yescharacteristic
852C2×C32#100411yescharacteristic
853C2×C32#100411yescharacteristic
854C2×C32D3×#4111yescharacteristic
855C2×C32D3×#4111yescharacteristic
856C2×C32#100911yescharacteristic
857C3⋊D3—22no—
858C3⋊D3—41no—
859C3⋊D3—41no—
860C3×D3—64no—
861C3×D3—62no—
862C3×D3—62no—
863C3×D3—122no—
864C3×D3—122no—
865C3×D3—121no—
866C3×D3—121no—
867C3×D3—121no—
868C3×D3—121no—
869C24—91no—
870C2×Q8—271no—
871C2×D4—91no—
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—91no—
888C22⋊C4—91no—
889C22⋊C4—91no—
890C22⋊C4—91no—
891C22⋊C4—91no—
892C22⋊C4—271no—
893C22⋊C4—271no—
894C22⋊C4—271no—
895C22⋊C4—271no—
896C22⋊C4—271no—
897C22⋊C4—271no—
898C22⋊C4—271no—
899C22⋊C4—271no—
900C22⋊C4#111311yescharacteristic
901C42—91no—
902C42—91no—
903C42—91no—
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—81no—
925C22×C3—81no—
926C22×C3—92no—
927C22×C3—181no—
928C22×C3—181no—
929C22×C3—181no—
930C22×C3—181no—
931C22×C3—181no—
932C22×C3—181no—
933C22×C3—181no—
934C22×C3—181no—
935C22×C3—364no—
936C22×C3#379812yes—
937C22×C3#379812yes—
938C22×C3#379812yes—
939C22×C3C22×D3211yescharacteristic
940C22×C3C22×D3211yescharacteristic
941C22×C3C22×D3211yescharacteristic
942C2×D3—32no—
943C2×D3—32no—
944C2×D3—62no—
945C2×D3—62no—
946C2×D3—62no—
947C2×D3—61no—
948C2×D3—61no—
949C2×D3—61no—
950C2×D3—61no—
951C2×D3—62no—
952C2×D3—62no—
953C2×D3—61no—
954C2×D3—61no—
955C2×D3—61no—
956C2×D3—61no—
957C2×D3—61no—
958C2×D3—61no—
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—21no—
973C3×C4—21no—
974C3×C4—21no—
975C3×C4—21no—
976C3×C4—21no—
977C3×C4—21no—
978C3×C4—41no—
979C3×C4—41no—
980C3×C4—41no—
981C3×C4—41no—
982C3×C4—41no—
983C3×C4—41no—
984C3×C4—81no—
985C3×C4—81no—
986C3×C4—181no—
987C3×C4—181no—
988C3×C4—181no—
989C3×C4—181no—
990C3×C4—181no—
991C3×C4—181no—
992C3×C4—181no—
993C3×C4—181no—
994C3×C4—181no—
995Dic3—62no—
996Dic3—62no—
997Dic3—62no—
998Dic3—62no—
999Dic3—61no—
1000Dic3—61no—
1001Dic3—61no—
1002Dic3—61no—
1003Dic3—61no—
1004Dic3—61no—
1005Dic3—61no—
1006Dic3—61no—
1007Dic3—61no—
1008Dic3—61no—
1009Dic3—61no—
1010Dic3—61no—
1011Dic3—61no—
1012Dic3—61no—
1013Dic3—61no—
1014Dic3—61no—
1015Dic3—61no—
1016Dic3—61no—
1017Dic3—121no—
1018Dic3—121no—
1019Dic3—121no—
1020Dic3—121no—
1021Dic3—121no—
1022C32—21no—
1023C32—21no—
1024C32—21no—
1025C32—41no—
1026C32#549511yescharacteristic, complemented
1027C32#552711yescharacteristic, complemented
1028C32#555611yescharacteristic, complemented
1029C23—91no—
1030C23—91no—
1031C23—91no—
1032C23—182no—
1033C23—182no—
1034C23—361no—
1035C23C2×#111311yescharacteristic
1036Q8—1081no—
1037D4—182no—
1038D4—542no—
1039D4—1081no—
1040C2×C4—91no—
1041C2×C4—91no—
1042C2×C4—91no—
1043C2×C4—91no—
1044C2×C4—91no—
1045C2×C4—91no—
1046C2×C4—91no—
1047C2×C4—91no—
1048C2×C4—91no—
1049C2×C4—182no—
1050C2×C4—182no—
1051C2×C4—361no—
1052C2×C4—361no—
1053C2×C4—361no—
1054C2×C4C2×#111311yescharacteristic
1055C2×C4C2×#111311yescharacteristic
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—182no—
1076C2×C3—361no—
1077C2×C3—361no—
1078C2×C3C2×#379811yescharacteristic
1079C2×C3C2×#379811yescharacteristic
1080C2×C3C2×#379811yescharacteristic
1081C2×C3D3×#23711yescharacteristic
1082C2×C3D3×#23711yescharacteristic
1083C2×C3#6431211yescharacteristic
1084C2×C3#6431311yescharacteristic
1085C2×C3#6431411yescharacteristic
1086C2×C3#6431411yescharacteristic
1087D3—64no—
1088D3—62no—
1089D3—62no—
1090D3—122no—
1091D3—122no—
1092D3—121no—
1093D3—121no—
1094D3—121no—
1095D3—121no—
1096C22—21no—
1097C22—21no—
1098C22—92no—
1099C22—181no—
1100C22—181no—
1101C22—181no—
1102C22—181no—
1103C22—181no—
1104C22—181no—
1105C22—181no—
1106C22—181no—
1107C22—364no—
1108C22#8904212yes—
1109C22C22×#111311yescharacteristic
1110C4—21no—
1111C4—21no—
1112C4—181no—
1113C4—181no—
1114C4—181no—
1115C4—181no—
1116C4—181no—
1117C4—181no—
1118C4—181no—
1119C4—181no—
1120C4—181no—
1121C3—21no—
1122C3—21no—
1123C3—21no—
1124C3—41no—
1125C3#1059403711yescharacteristic, complemented
1126C3#1059404011yescharacteristic, complemented
1127C3#1059420911yescharacteristic, complemented
1128C2—22no—
1129C2—182no—
1130C2—361no—
1131C2—361no—
1132C2C2×#8904211yescharacteristic
1133C2#1172462211yescharacteristic
1134C2#1172462311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radical#11723727C2
hypercenterC22⋊C4#1113
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64090C2semidirect
2. C3×C22⋊C4×C3⋊D3C2semidirect
3. C3×#64086C2semidirect
5. #11723721C2semidirect
6. #11723720C2semidirect
7. C2×#88814C2semidirect
8. #11723694C2semidirect
9. #11723694C2semidirect
10. C4×#6295C2semidirect
11. #11723676C2semidirect
12. #11723676C2semidirect
13. #11723673C2semidirect
14. #11723672C2semidirect
15. #11723671C2semidirect
25. C2×C3×C4×C3⋊D3C22semidirect
26. C2×#6296C22semidirect
34. C3×#3752C22semidirect
35. C3×#3750C22semidirect
36. C3×#3750C22semidirect
37. C3×#3750C22semidirect
38. C3×C4×C3⋊Dic3C22semidirect
39. C3×C4×C3⋊Dic3C22semidirect
40. C3×C4×C3⋊Dic3C22semidirect
41. #88815C22semidirect
42. #88815C22semidirect
43. #88815C22semidirect
44. #88815C22semidirect
45. #88815C22semidirect
52. #88814C22semidirect
53. #88814C22semidirect
54. #64090D3semidirect
55. C22⋊C4×C3⋊D3D3semidirect
56. #64086D3semidirect
141. C2×C4×C3⋊D3C2×D3semidirect
180. #3752C2×D3semidirect
181. #3750C2×D3semidirect
182. #3750C2×D3semidirect
183. #3750C2×D3semidirect
184. C4×C3⋊Dic3C2×D3semidirect
185. C4×C3⋊Dic3C2×D3semidirect
186. C4×C3⋊Dic3C2×D3semidirect
714. C33#551semidirect
1026. C32#5495semidirect
1027. C32#5527semidirect
1028. C32#5556semidirect
1125. C3#10594037semidirect
1126. C3#10594040semidirect
1127. C3#10594209semidirect

Maximal subgroups

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

subgroupindex
C3×#640902
C3×C22⋊C4×C3⋊D32
C3×#640862
#117237272
#117237212
#117237202
C2×#888142
#117236942
C4×#62952
#117236762
#117236732
#117236722
#117236712
#105942093
#105940403
#105940373