Finite Group Databasebeta

← #13178248

Subgroups — #13178248

Order 1728.

1226 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64094C211yesmaximal, characteristic, complemented
2C3×#64092C211yesmaximal, characteristic, complemented
3C3×#64090C211yesmaximal, characteristic, complemented
4#11723728C211yesmaximal, characteristic
5#11723726C211yesmaximal, characteristic, complemented
6#11723720C211yesmaximal, characteristic, complemented
7#11723718C211yesmaximal, characteristic, complemented
8#11723694C211yesmaximal, characteristic, complemented
9C4×#6295C211yesmaximal, characteristic, complemented
10#11723690C211yesmaximal, characteristic, complemented
11#11723684C211yesmaximal, characteristic, complemented
12#11723672C211yesmaximal, characteristic, complemented
13#11723670C211yesmaximal, characteristic, complemented
14#11723668C211yesmaximal, characteristic, complemented
15#11723665C211yesmaximal, characteristic, complemented
16#10594219—31nomaximal
17#10594208—31nomaximal
18#10594200—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2211yescharacteristic
24C2×C3×C4×C3⋊D3C2211yescharacteristic
25C2×C3×#634C2211yescharacteristic
26C2×#6296C2211yescharacteristic
27C2×#6295C2211yescharacteristic
28C2×#6295C2211yescharacteristic
29C2×#6295C2211yescharacteristic
30C2×#6294C2211yescharacteristic
31C33×C22⋊C4C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
39C3×#3750C2211yescharacteristic
40C3×#3750C2211yescharacteristic
41C3×C4×C3⋊Dic3C2211yescharacteristic
42C3×C4×C3⋊Dic3C2211yescharacteristic
43#88815C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88814C2211yescharacteristic
47#88814C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88813C2211yescharacteristic
52#88813C2211yescharacteristic
53#88813C2211yescharacteristic
54#64094D311yescharacteristic, complemented
55#64092D311yescharacteristic, complemented
56#64090D311yescharacteristic, complemented
57C3×#885—31no—
58C3×#885—31no—
59C3×#885—61no—
60C3×#883—31no—
61C3×#883—31no—
62C3×#883—61no—
63C3×#67⋊C4—31no—
64C3×#67⋊C4—31no—
65C3×#67⋊C4—61no—
66#63979—31no—
67#63979—31no—
68#63979—31no—
69#67⋊Dic3—31no—
70Dic3×#67—31no—
71#63966—31no—
72#63962—31no—
73#63961—31no—
74#63959—31no—
75#63959—31no—
76#63953—31no—
77#63952—31no—
78#63915—31no—
79#63913—31no—
80#63907—31no—
81#63907—31no—
82#63905—31no—
83#63904—31no—
84C4×#626—31no—
85C4×#626—31no—
86C4×#625—31no—
87#63891—31no—
88#63890—31no—
89#63881—31no—
90#63879—31no—
91#63854—31no—
92#63853—31no—
93#63852—31no—
94#63852—31no—
95#63850—31no—
96#63844—31no—
97#63843—31no—
98Dic3×Dic6—31no—
99#63838—31no—
100#63837—31no—
101#63837—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C3×#638—22no—
109C3×#638—22no—
110C3×#638—41no—
111C2×C3×C3⋊Dic3—41no—
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
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
121C3×C4×C3⋊D3—41no—
122C3×C4×C3⋊D3—41no—
123C3×#634—22no—
124#6296—22no—
125#6295—22no—
126#6295—22no—
127#6295—41no—
128#6294—41no—
129#5681—91no—
130#5664—91no—
131#5559—91no—
132C2×#638C2×D311yescharacteristic
133C2×#638C2×D311yescharacteristic
134C2×#638C2×D311yescharacteristic
135C22×C3⋊Dic3C2×D311yescharacteristic
136C2×C4×C3⋊D3C2×D311yescharacteristic
137C2×C4×C3⋊D3C2×D311yescharacteristic
138C2×#634C2×D311yescharacteristic
139C2×C3×#67—31no—
140C2×C3×#67—31no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—61no—
146C2×C3×#67—61no—
147C2×C3×#67—61no—
148C22×C3×Dic3—31no—
149C22×C3×Dic3—31no—
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—61no—
156C2×C3×C4×D3—61no—
157C2×C3×Dic6—31no—
158C2×C3×Dic6—31no—
159C2×C3×Dic6—61no—
160C2×#627—31no—
161C2×#627—31no—
162C2×#627—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626—31no—
166C2×#626—31no—
167C2×#626—31no—
168C2×#626—31no—
169C2×#625—31no—
170C2×#625—31no—
171C2×#625—31no—
172C2×#624—31no—
173C2×D3×Dic3—31no—
174C2×D3×Dic3—31no—
175C32×C22⋊C4—21no—
176C32×C22⋊C4—21no—
177C32×C22⋊C4—21no—
178C32×C22⋊C4—41no—
179C32×C22⋊C4C2×D311yescharacteristic
180C32×C22⋊C4C2×D311yescharacteristic
181C32×C22⋊C4C2×D311yescharacteristic
182#3757C2×D311yescharacteristic
183#3757C2×D311yescharacteristic
184#3752C2×D311yescharacteristic
185#3752C2×D311yescharacteristic
186#3752C2×D311yescharacteristic
187#3752C2×D311yescharacteristic
188C4⋊(C3⋊Dic3)C2×D311yescharacteristic
189#3750C2×D311yescharacteristic
190#3750C2×D311yescharacteristic
191C4×C3⋊Dic3C2×D311yescharacteristic
192C4×C3⋊Dic3C2×D311yescharacteristic
193C3×#217—31no—
194C3×#217—31no—
195C3×#217—31no—
196C3×#217—31no—
197C3×#217—61no—
198C3×#217—61no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—61no—
208C3×(C2×D3)⋊C4—61no—
209C3×(C2×D3)⋊C4—61no—
210C3×(C2×D3)⋊C4—61no—
211C3×C4⋊Dic3—31no—
212C3×C4⋊Dic3—31no—
213C3×C4⋊Dic3—61no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—31no—
218C3×Dic3⋊C4—61no—
219C3×Dic3⋊C4—61no—
220C3×C4×Dic3—31no—
221C3×C4×Dic3—31no—
222C3×C4×Dic3—31no—
223C3×C4×Dic3—31no—
224C3×C4×Dic3—61no—
225C3×C4×Dic3—61no—
226#3724—31no—
227#3724—31no—
228#3724—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(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—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—31no—
257Dic32—31no—
258Dic32—31no—
259C22×C33—21no—
260C22×C33—21no—
261C22×C33—21no—
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—21no—
272C33×C4—21no—
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#4112yes—
282C3×C3⋊Dic3#4112yes—
283C3×#124—91no—
284C3×#123—91no—
285C3×C4×D4—91no—
286#947—91no—
287Q8×Dic3—91no—
288#940—91no—
289#940—91no—
290#940—91no—
291#936—91no—
292#935—91no—
293D4×Dic3—91no—
294#929—91no—
295#929—91no—
296C4×#67—91no—
297C4×#67—91no—
298C4×#67—91no—
299C4×#67—91no—
300#894—91no—
301#894—91no—
302#893—91no—
303#887—91no—
304#887—91no—
305#887—91no—
306#886—91no—
307#886—91no—
308#885—31no—
309#885—31no—
310#885—61no—
311#885—91no—
312#885—91no—
313#885—91no—
314#885—91no—
315#885—91no—
316#885—91no—
317#883—31no—
318#883—31no—
319#883—61no—
320#883—91no—
321#883—91no—
322#67⋊C4—31no—
323#67⋊C4—31no—
324#67⋊C4—61no—
325#67⋊C4—91no—
326#67⋊C4—91no—
327#875—91no—
328C4×D12—91no—
329C4×Dic6—91no—
330C4×Dic6—91no—
331C23×C32—21no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—41no—
335C23×C32C22×D311yescharacteristic
336C23×C32C22×D311yescharacteristic
337C23×C32C22×D311yescharacteristic
338C22×C3⋊D3C22×D311yescharacteristic
339C22×C3⋊D3C22×D311yescharacteristic
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3×D3—31no—
342C22×C3×D3—31no—
343C22×C3×D3—31no—
344C22×C3×D3—31no—
345C22×C3×D3—31no—
346C22×C3×D3—31no—
347C22×C3×D3—61no—
348C22×C3×D3—61no—
349C22×C3×D3—61no—
350C2×C32×C4—21no—
351C2×C32×C4—21no—
352C2×C32×C4—21no—
353C2×C32×C4—21no—
354C2×C32×C4—21no—
355C2×C32×C4—21no—
356C2×C32×C4—41no—
357C2×C32×C4—41no—
358C2×C32×C4C22×D311yescharacteristic
359C2×C32×C4C22×D311yescharacteristic
360C2×C32×C4C22×D311yescharacteristic
361C2×C32×C4C22×D311yescharacteristic
362C2×C32×C4C22×D311yescharacteristic
363C2×C32×C4C22×D311yescharacteristic
364#638—22no—
365#638—22no—
366#638—41no—
367C2×C3⋊Dic3—41no—
368C2×C3⋊Dic3C22×D311yescharacteristic
369C2×C3⋊Dic3C22×D311yescharacteristic
370C2×C3⋊Dic3C22×D311yescharacteristic
371C2×C3⋊Dic3C22×D311yescharacteristic
372C2×C3⋊Dic3C22×D311yescharacteristic
373C2×C3⋊Dic3C22×D311yescharacteristic
374C2×C3⋊Dic3C22×D311yescharacteristic
375C2×C3⋊Dic3C22×D311yescharacteristic
376C2×C3⋊Dic3C22×D311yescharacteristic
377C4×C3⋊D3—41no—
378C4×C3⋊D3—41no—
379#634—22no—
380C3×#67—62no—
381C3×#67—62no—
382C3×#67—62no—
383C3×#67—62no—
384C3×#67—64no—
385C3×#67—122no—
386C3×#67—121no—
387C3×#67—121no—
388C3×#67—122no—
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—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—61no—
408C2×C3×Dic3—61no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—121no—
417C2×C3×Dic3—121no—
418C2×C3×Dic3—122no—
419C3×C4×D3—121no—
420C3×C4×D3—121no—
421C3×C4×D3—121no—
422C3×C4×D3—121no—
423C3×C4×D3—122no—
424C3×C4×D3—122no—
425C3×Dic6—62no—
426C3×Dic6—62no—
427C3×Dic6—122no—
428#627—62no—
429#627—62no—
430#627—62no—
431#626—62no—
432#626—62no—
433#626—62no—
434#626—62no—
435#626—121no—
436#626—121no—
437#625—62no—
438#625—62no—
439#625—121no—
440#624—121no—
441D3×Dic3—121no—
442D3×Dic3—121no—
443#559—271noSylow
444C2×C33—41no—
445C2×C33C2×#4111yescharacteristic
446C2×C33C2×#4111yescharacteristic
447C2×C33H(5,𝔽2)11yescharacteristic
448C3×C3⋊D3—41no—
449C3×C3⋊D3—41no—
450C3×C3⋊D3—41no—
451C2×C3×Q8—91no—
452C2×C3×D4—91no—
453C2×C3×D4—91no—
454C2×C3×D4—91no—
455C22×C3×C4—91no—
456C22×C3×C4—91no—
457C22×C3×C4—91no—
458C2×#67—31no—
459C2×#67—31no—
460C2×#67—31no—
461C2×#67—31no—
462C2×#67—31no—
463C2×#67—31no—
464C2×#67—61no—
465C2×#67—61no—
466C2×#67—61no—
467C2×#67—91no—
468C2×#67—91no—
469C2×#67—91no—
470C2×#67—91no—
471C2×#67—91no—
472C2×#67—91no—
473C22×Dic3—31no—
474C22×Dic3—31no—
475C22×Dic3—61no—
476C22×Dic3—91no—
477C2×D12—91no—
478C2×D12—91no—
479C2×D12—91no—
480C2×C4×D3—31no—
481C2×C4×D3—31no—
482C2×C4×D3—31no—
483C2×C4×D3—31no—
484C2×C4×D3—61no—
485C2×C4×D3—61no—
486C2×C4×D3—91no—
487C2×C4×D3—91no—
488C2×Dic6—31no—
489C2×Dic6—31no—
490C2×Dic6—61no—
491C2×Dic6—91no—
492C2×Dic6—91no—
493C2×Dic6—91no—
494C3×C4⋊C4—91no—
495C3×C4⋊C4—91no—
496C3×C4⋊C4—91no—
497C3×C22⋊C4—21no—
498C3×C22⋊C4—21no—
499C3×C22⋊C4—21no—
500C3×C22⋊C4—41no—
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⋊C4D3211yescharacteristic
508C3×C22⋊C4D3211yescharacteristic
509C3×C22⋊C4D3211yescharacteristic
510C3×C42—91no—
511C3×C42—91no—
512#217—31no—
513#217—31no—
514#217—31no—
515#217—31no—
516#217—61no—
517#217—61no—
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—31no—
530(C2×D3)⋊C4—31no—
531(C2×D3)⋊C4—61no—
532(C2×D3)⋊C4—61no—
533(C2×D3)⋊C4—61no—
534(C2×D3)⋊C4—61no—
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—
545C4⋊Dic3—31no—
546C4⋊Dic3—31no—
547C4⋊Dic3—61no—
548C4⋊Dic3—91no—
549C4⋊Dic3—91no—
550C4⋊Dic3—91no—
551Dic3⋊C4—31no—
552Dic3⋊C4—31no—
553Dic3⋊C4—31no—
554Dic3⋊C4—31no—
555Dic3⋊C4—61no—
556Dic3⋊C4—61no—
557Dic3⋊C4—91no—
558Dic3⋊C4—91no—
559Dic3⋊C4—91no—
560Dic3⋊C4—91no—
561Dic3⋊C4—91no—
562Dic3⋊C4—91no—
563C4×Dic3—31no—
564C4×Dic3—31no—
565C4×Dic3—31no—
566C4×Dic3—31no—
567C4×Dic3—61no—
568C4×Dic3—61no—
569C4×Dic3—91no—
570C4×Dic3—91no—
571C4×Dic3—91no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C22×C32—21no—
579C22×C32—22no—
580C22×C32—21no—
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—21no—
591C22×C32—41no—
592C22×C32—41no—
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×C32C23×D311yescharacteristic
604C22×C32C23×D311yescharacteristic
605C22×C32C23×D311yescharacteristic
606C2×C3⋊D3—21no—
607C2×C3⋊D3—21no—
608C2×C3⋊D3—21no—
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—62no—
616C2×C3×D3—62no—
617C2×C3×D3—61no—
618C2×C3×D3—61no—
619C2×C3×D3—61no—
620C2×C3×D3—61no—
621C2×C3×D3—61no—
622C2×C3×D3—61no—
623C2×C3×D3—61no—
624C2×C3×D3—61no—
625C2×C3×D3—61no—
626C2×C3×D3—61no—
627C2×C3×D3—61no—
628C2×C3×D3—61no—
629C2×C3×D3—61no—
630C2×C3×D3—61no—
631C2×C3×D3—61no—
632C2×C3×D3—61no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—121no—
636C2×C3×D3—121no—
637C2×C3×D3—121no—
638C2×C3×D3—121no—
639C2×C3×D3—121no—
640C2×C3×D3—121no—
641C2×C3×D3—121no—
642C32×C4—21no—
643C32×C4—21no—
644C32×C4—21no—
645C32×C4—21no—
646C32×C4—21no—
647C32×C4—21no—
648C32×C4—41no—
649C32×C4—41no—
650C32×C4—41no—
651C32×C4—41no—
652C32×C4—41no—
653C32×C4—41no—
654C32×C4—81no—
655C32×C4—81no—
656C3⋊Dic3—21no—
657C3⋊Dic3—21no—
658C3⋊Dic3—21no—
659C3⋊Dic3—21no—
660C3⋊Dic3—21no—
661C3⋊Dic3—21no—
662C3⋊Dic3—21no—
663C3⋊Dic3#23512yes—
664C3⋊Dic3#23712yes—
665C3×Dic3—32no—
666C3×Dic3—32no—
667C3×Dic3—32no—
668C3×Dic3—32no—
669C3×Dic3—62no—
670C3×Dic3—62no—
671C3×Dic3—62no—
672C3×Dic3—61no—
673C3×Dic3—61no—
674C3×Dic3—61no—
675C3×Dic3—61no—
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—121no—
687C3×Dic3—121no—
688C3×Dic3—121no—
689C3×Dic3—121no—
690C3×Dic3—121no—
691C3×Dic3—121no—
692#127—271no—
693#124—91no—
694#124—271no—
695#124—271no—
696#124—271no—
697#123—91no—
698#123—271no—
699#123—271no—
700#123—271no—
701C4×Q8—271no—
702C4×Q8—271no—
703C4×D4—91no—
704C4×D4—271no—
705C4×D4—271no—
706C4×D4—271no—
707C33#55911yescharacteristic, complemented, Sylow
708C23×C3—21no—
709C23×C3—21no—
710C23×C3—21no—
711C23×C3—41no—
712C23×C3—91no—
713C23×C3—91no—
714C23×C3—91no—
715C23×C3C2×D3211yescharacteristic
716C23×C3C2×D3211yescharacteristic
717C23×C3C2×D3211yescharacteristic
718C22×D3—31no—
719C22×D3—31no—
720C22×D3—31no—
721C22×D3—31no—
722C22×D3—31no—
723C22×D3—31no—
724C22×D3—61no—
725C22×D3—61no—
726C22×D3—61no—
727C3×Q8—182no—
728C3×D4—182no—
729C3×D4—182no—
730C3×D4—361no—
731C2×C3×C4—21no—
732C2×C3×C4—21no—
733C2×C3×C4—21no—
734C2×C3×C4—21no—
735C2×C3×C4—21no—
736C2×C3×C4—21no—
737C2×C3×C4—41no—
738C2×C3×C4—41no—
739C2×C3×C4—91no—
740C2×C3×C4—91no—
741C2×C3×C4—91no—
742C2×C3×C4—91no—
743C2×C3×C4—91no—
744C2×C3×C4—91no—
745C2×C3×C4—91no—
746C2×C3×C4—91no—
747C2×C3×C4—91no—
748C2×C3×C4—361no—
749C2×C3×C4—361no—
750C2×C3×C4—361no—
751C2×C3×C4C2×D3211yescharacteristic
752C2×C3×C4C2×D3211yescharacteristic
753C2×C3×C4C2×D3211yescharacteristic
754C2×C3×C4C2×D3211yescharacteristic
755C2×C3×C4C2×D3211yescharacteristic
756C2×C3×C4C2×D3211yescharacteristic
757#67—62no—
758#67—62no—
759#67—62no—
760#67—62no—
761#67—64no—
762#67—122no—
763#67—121no—
764#67—121no—
765#67—122no—
766#67—182no—
767#67—182no—
768#67—182no—
769#67—182no—
770#67—361no—
771#67—361no—
772C2×Dic3—31no—
773C2×Dic3—31no—
774C2×Dic3—31no—
775C2×Dic3—31no—
776C2×Dic3—31no—
777C2×Dic3—31no—
778C2×Dic3—31no—
779C2×Dic3—31no—
780C2×Dic3—31no—
781C2×Dic3—31no—
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—61no—
795C2×Dic3—61no—
796C2×Dic3—61no—
797C2×Dic3—61no—
798C2×Dic3—61no—
799C2×Dic3—121no—
800C2×Dic3—121no—
801C2×Dic3—122no—
802C2×Dic3—361no—
803D12—182no—
804D12—182no—
805D12—361no—
806C4×D3—121no—
807C4×D3—121no—
808C4×D3—121no—
809C4×D3—121no—
810C4×D3—122no—
811C4×D3—122no—
812C4×D3—361no—
813C4×D3—361no—
814Dic6—62no—
815Dic6—62no—
816Dic6—122no—
817Dic6—182no—
818Dic6—182no—
819Dic6—182no—
820C2×C32—21no—
821C2×C32—21no—
822C2×C32—21no—
823C2×C32—21no—
824C2×C32—21no—
825C2×C32—21no—
826C2×C32—21no—
827C2×C32—21no—
828C2×C32—21no—
829C2×C32—41no—
830C2×C32—41no—
831C2×C32—41no—
832C2×C32—41no—
833C2×C32—42no—
834C2×C32—41no—
835C2×C32—41no—
836C2×C32—81no—
837C2×C32—81no—
838C2×C32—82no—
839C2×C32C2×#23511yescharacteristic
840C2×C32C2×#23711yescharacteristic
841C2×C32#100411yescharacteristic
842C2×C32#100411yescharacteristic
843C2×C32D3×#4111yescharacteristic
844C2×C32D3×#4111yescharacteristic
845C2×C32D3×#4111yescharacteristic
846C2×C32D3×#4111yescharacteristic
847C2×C32#100911yescharacteristic
848C3⋊D3—41no—
849C3⋊D3—41no—
850C3⋊D3—41no—
851C3×D3—122no—
852C3×D3—122no—
853C3×D3—121no—
854C3×D3—121no—
855C3×D3—121no—
856C3×D3—121no—
857C3×D3—121no—
858C3×D3—121no—
859C3×D3—241no—
860C2×Q8—91no—
861C2×Q8—271no—
862C2×D4—91no—
863C2×D4—91no—
864C2×D4—91no—
865C2×D4—271no—
866C2×D4—271no—
867C2×D4—271no—
868C22×C4—91no—
869C22×C4—91no—
870C22×C4—91no—
871C22×C4—271no—
872C4⋊C4—91no—
873C4⋊C4—91no—
874C4⋊C4—91no—
875C4⋊C4—271no—
876C4⋊C4—271no—
877C4⋊C4—271no—
878C22⋊C4—91no—
879C22⋊C4—91no—
880C22⋊C4—91no—
881C22⋊C4—91no—
882C22⋊C4—91no—
883C22⋊C4—91no—
884C22⋊C4—271no—
885C22⋊C4—271no—
886C22⋊C4—271no—
887C22⋊C4—271no—
888C22⋊C4—271no—
889C22⋊C4#111311yescharacteristic
890C42—91no—
891C42—91no—
892C42—271no—
893C42—271no—
894C42—271no—
895C22×C3—22no—
896C22×C3—21no—
897C22×C3—21no—
898C22×C3—21no—
899C22×C3—21no—
900C22×C3—21no—
901C22×C3—21no—
902C22×C3—21no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—21no—
907C22×C3—21no—
908C22×C3—41no—
909C22×C3—41no—
910C22×C3—41no—
911C22×C3—41no—
912C22×C3—41no—
913C22×C3—41no—
914C22×C3—41no—
915C22×C3—41no—
916C22×C3—42no—
917C22×C3—41no—
918C22×C3—81no—
919C22×C3—81no—
920C22×C3—181no—
921C22×C3—181no—
922C22×C3—181no—
923C22×C3—181no—
924C22×C3—181no—
925C22×C3—181no—
926C22×C3—181no—
927C22×C3—181no—
928C22×C3—181no—
929C22×C3C22×D3211yescharacteristic
930C22×C3C22×D3211yescharacteristic
931C22×C3C22×D3211yescharacteristic
932C2×D3—62no—
933C2×D3—62no—
934C2×D3—61no—
935C2×D3—61no—
936C2×D3—61no—
937C2×D3—61no—
938C2×D3—61no—
939C2×D3—61no—
940C2×D3—61no—
941C2×D3—61no—
942C2×D3—61no—
943C2×D3—61no—
944C2×D3—61no—
945C2×D3—61no—
946C2×D3—61no—
947C2×D3—61no—
948C2×D3—61no—
949C2×D3—61no—
950C2×D3—61no—
951C2×D3—61no—
952C2×D3—121no—
953C2×D3—121no—
954C2×D3—121no—
955C2×D3—121no—
956C2×D3—121no—
957C2×D3—121no—
958C2×D3—121no—
959C3×C4—21no—
960C3×C4—21no—
961C3×C4—21no—
962C3×C4—21no—
963C3×C4—21no—
964C3×C4—21no—
965C3×C4—41no—
966C3×C4—41no—
967C3×C4—41no—
968C3×C4—41no—
969C3×C4—41no—
970C3×C4—41no—
971C3×C4—81no—
972C3×C4—81no—
973C3×C4—92no—
974C3×C4—92no—
975C3×C4—181no—
976C3×C4—181no—
977C3×C4—181no—
978C3×C4—181no—
979C3×C4—181no—
980C3×C4—181no—
981C3×C4—181no—
982Dic3—32no—
983Dic3—32no—
984Dic3—32no—
985Dic3—32no—
986Dic3—62no—
987Dic3—62no—
988Dic3—62no—
989Dic3—61no—
990Dic3—61no—
991Dic3—61no—
992Dic3—61no—
993Dic3—61no—
994Dic3—61no—
995Dic3—61no—
996Dic3—61no—
997Dic3—61no—
998Dic3—61no—
999Dic3—61no—
1000Dic3—61no—
1001Dic3—61no—
1002Dic3—61no—
1003Dic3—121no—
1004Dic3—121no—
1005Dic3—121no—
1006Dic3—121no—
1007Dic3—121no—
1008Dic3—121no—
1009C32—21no—
1010C32—21no—
1011C32—21no—
1012C32—41no—
1013C32#555911yescharacteristic, complemented
1014C32#566411yescharacteristic, complemented
1015C32#568111yescharacteristic, complemented
1016C23—91no—
1017C23—91no—
1018C23—91no—
1019C23C2×#111311yescharacteristic
1020Q8—182no—
1021Q8—542no—
1022D4—182no—
1023D4—182no—
1024D4—361no—
1025D4—542no—
1026D4—542no—
1027D4—1081no—
1028C2×C4—91no—
1029C2×C4—91no—
1030C2×C4—91no—
1031C2×C4—91no—
1032C2×C4—91no—
1033C2×C4—91no—
1034C2×C4—91no—
1035C2×C4—91no—
1036C2×C4—91no—
1037C2×C4—361no—
1038C2×C4—361no—
1039C2×C4—361no—
1040C2×C4—1081no—
1041C2×C4C2×#111311yescharacteristic
1042C2×C4C2×#111311yescharacteristic
1043C2×C3—21no—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—21no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—21no—
1051C2×C3—21no—
1052C2×C3—42no—
1053C2×C3—41no—
1054C2×C3—41no—
1055C2×C3—41no—
1056C2×C3—41no—
1057C2×C3—41no—
1058C2×C3—41no—
1059C2×C3—81no—
1060C2×C3—81no—
1061C2×C3—82no—
1062C2×C3—361no—
1063C2×C3—361no—
1064C2×C3—361no—
1065C2×C3D3×#23511yescharacteristic
1066C2×C3D3×#23511yescharacteristic
1067C2×C3#6430611yescharacteristic
1068C2×C3D3×#23711yescharacteristic
1069C2×C3D3×#23711yescharacteristic
1070C2×C3#6431211yescharacteristic
1071C2×C3#6431311yescharacteristic
1072C2×C3#6431411yescharacteristic
1073C2×C3#6431411yescharacteristic
1074D3—122no—
1075D3—122no—
1076D3—121no—
1077D3—121no—
1078D3—121no—
1079D3—121no—
1080D3—121no—
1081D3—121no—
1082D3—241no—
1083C22—21no—
1084C22—21no—
1085C22—21no—
1086C22—181no—
1087C22—181no—
1088C22—181no—
1089C22—181no—
1090C22—181no—
1091C22—181no—
1092C22—181no—
1093C22—181no—
1094C22—181no—
1095C22C22×#111311yescharacteristic
1096C4—21no—
1097C4—21no—
1098C4—92no—
1099C4—92no—
1100C4—181no—
1101C4—181no—
1102C4—181no—
1103C4—181no—
1104C4—181no—
1105C4—181no—
1106C4—181no—
1107C3—21no—
1108C3—21no—
1109C3—21no—
1110C3—41no—
1111C3#1059420011yescharacteristic, complemented
1112C3#1059420811yescharacteristic, complemented
1113C3#1059421911yescharacteristic, complemented
1114C2—41no—
1115C2—361no—
1116C2—361no—
1117C2—361no—
1118C2#1172461811yescharacteristic
1119C2#1172462211yescharacteristic
1120C2#1172462311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radical#11723728C2
hypercenterC22⋊C4#1113
hypocenterC33#559
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64094C2semidirect
2. C3×#64092C2semidirect
3. C3×#64090C2semidirect
5. #11723726C2semidirect
6. #11723720C2semidirect
7. #11723718C2semidirect
8. #11723694C2semidirect
9. C4×#6295C2semidirect
10. #11723690C2semidirect
11. #11723684C2semidirect
12. #11723672C2semidirect
13. #11723670C2semidirect
14. #11723668C2semidirect
15. #11723665C2semidirect
54. #64094D3semidirect
55. #64092D3semidirect
56. #64090D3semidirect
707. C33#559semidirect
1013. C32#5559semidirect
1014. C32#5664semidirect
1015. C32#5681semidirect
1111. C3#10594200semidirect
1112. C3#10594208semidirect
1113. C3#10594219semidirect

Maximal subgroups

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

subgroupindex
C3×#640942
C3×#640922
C3×#640902
#117237282
#117237262
#117237202
#117237182
#117236942
C4×#62952
#117236902
#117236842
#117236722
#117236702
#117236682
#117236652
#105942193
#105942083
#105942003