Finite Group Databasebeta

← #13178645

Subgroups — #13178645

Order 1728.

1288 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64148C211yesmaximal, characteristic, complemented
2C3×#64148C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#11723726C211yesmaximal, characteristic, complemented
5#11723726C211yesmaximal, characteristic, complemented
6#11723726C211yesmaximal, characteristic, complemented
7#11723725C211yesmaximal, characteristic, complemented
8C2×#88815C211yesmaximal, characteristic, complemented
9#11723720C211yesmaximal, characteristic, complemented
10#11723717C211yesmaximal, characteristic, complemented
11#11723716C211yesmaximal, characteristic, complemented
12#11723690C211yesmaximal, characteristic, complemented
13#11723683C211yesmaximal, characteristic, complemented
14#11723676C211yesmaximal, characteristic, complemented
15#11723669C211yesmaximal, characteristic, complemented
16#10595204—31nomaximal
17#10595193—31nomaximal
18#10595189—31nomaximal
19C2×C33×D4C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C22×C3×C3⋊Dic3C2211yescharacteristic
25C22×C3×C3⋊Dic3C2211yescharacteristic
26C22×C3×C3⋊Dic3C2211yescharacteristic
27C22×C3×C3⋊Dic3C2211yescharacteristic
28C2×#6295C2211yescharacteristic
29C2×#6294C2211yescharacteristic
30C2×#6294C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
38C3×#3750C2211yescharacteristic
39C3×#3750C2211yescharacteristic
40C3×C4×C3⋊Dic3C2211yescharacteristic
41#88815C2211yescharacteristic
42#88815C2211yescharacteristic
43#88815C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88815C2211yescharacteristic
47#88815C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88813C2211yescharacteristic
53#88813C2211yescharacteristic
54#64148D311yescharacteristic, complemented
55#64148D311yescharacteristic, complemented
56D4×C3⋊Dic3D311yescharacteristic, complemented
57C3×#939—31no—
58C3×#939—31no—
59C3×#939—31no—
60C3×#939—31no—
61C3×#939—61no—
62C3×#939—61no—
63C3×D4×Dic3—31no—
64C3×D4×Dic3—31no—
65C3×D4×Dic3—61no—
66#63980—31no—
67#63978—31no—
68#63978—31no—
69#67⋊Dic3—31no—
70#67⋊Dic3—31no—
71#67⋊Dic3—31no—
72Dic3×#67—31no—
73Dic3×#67—31no—
74Dic3×#67—31no—
75#63971—31no—
76#63970—31no—
77C2×#3724—31no—
78#63966—31no—
79C2×Dic3⋊Dic3—31no—
80C2×Dic3⋊Dic3—31no—
81#63962—31no—
82#63961—31no—
83#63958—31no—
84#63956—31no—
85#63956—31no—
86#63956—31no—
87#63952—31no—
88#63952—31no—
89#63952—31no—
90#63891—31no—
91#63890—31no—
92#63878—31no—
93#63877—31no—
94#63868—31no—
95#63862—31no—
96#63859—31no—
97#63854—31no—
98#63847—31no—
99#63846—31no—
100#63845—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C23×C33C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C33×D4—22no—
107C2×C33×C4C2311yescharacteristic
108C3×#638—22no—
109C3×#638—22no—
110C3×#638—22no—
111C3×#638—41no—
112C2×C3×C3⋊Dic3—22no—
113C2×C3×C3⋊Dic3—41no—
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#6295—41no—
127#6294—22no—
128#6294—41no—
129#5618—91no—
130#5601—91no—
131#5540—91no—
132C2×C32×D4—21no—
133C2×C32×D4—21no—
134C2×C32×D4—21no—
135C2×C32×D4—41no—
136C2×C32×D4C2×D311yescharacteristic
137C2×C32×D4C2×D311yescharacteristic
138C2×C32×D4C2×D311yescharacteristic
139C2×#638C2×D311yescharacteristic
140C2×#638C2×D311yescharacteristic
141C2×#638C2×D311yescharacteristic
142C2×#638C2×D311yescharacteristic
143C22×C3⋊Dic3C2×D311yescharacteristic
144C22×C3⋊Dic3C2×D311yescharacteristic
145C22×C3⋊Dic3C2×D311yescharacteristic
146C22×C3⋊Dic3C2×D311yescharacteristic
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—61no—
156C2×C3×#67—61no—
157C2×C3×#67—61no—
158C2×C3×#67—61no—
159C22×C3×Dic3—31no—
160C22×C3×Dic3—31no—
161C22×C3×Dic3—31no—
162C22×C3×Dic3—31no—
163C22×C3×Dic3—31no—
164C22×C3×Dic3—31no—
165C22×C3×Dic3—31no—
166C22×C3×Dic3—31no—
167C22×C3×Dic3—61no—
168C22×C3×Dic3—61no—
169C22×C3×Dic3—61no—
170C22×C3×Dic3—61no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#625—31no—
174C2×#624—31no—
175C2×#624—31no—
176C2×D3×Dic3—31no—
177C2×D3×Dic3—31no—
178C2×D3×Dic3—31no—
179C2×D3×Dic3—31no—
180#3757C2×D311yescharacteristic
181#3757C2×D311yescharacteristic
182#3757C2×D311yescharacteristic
183#3757C2×D311yescharacteristic
184#3752C2×D311yescharacteristic
185#3752C2×D311yescharacteristic
186C4⋊(C3⋊Dic3)C2×D311yescharacteristic
187#3750C2×D311yescharacteristic
188#3750C2×D311yescharacteristic
189C4×C3⋊Dic3C2×D311yescharacteristic
190C3×#217—31no—
191C3×#217—31no—
192C3×#217—31no—
193C3×#217—31no—
194C3×#217—31no—
195C3×#217—31no—
196C3×#217—31no—
197C3×#217—31no—
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—
225#3724—31no—
226#3724—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—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238Dic3⋊Dic3—31no—
239Dic3⋊Dic3—31no—
240Dic3⋊Dic3—31no—
241#3722—31no—
242#3722—31no—
243#3722—31no—
244#3722—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—21no—
272C33×C4—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—
279C3×C3⋊Dic3—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3#4112yes—
283C3×#121—91no—
284C3×#121—91no—
285C3×C4×D4—91no—
286#939—31no—
287#939—31no—
288#939—31no—
289#939—31no—
290#939—61no—
291#939—61no—
292#939—91no—
293#939—91no—
294#939—91no—
295#938—91no—
296#935—91no—
297D4×Dic3—31no—
298D4×Dic3—31no—
299D4×Dic3—61no—
300D4×Dic3—91no—
301D4×Dic3—91no—
302D4×Dic3—91no—
303#930—91no—
304#929—91no—
305C4×#67—91no—
306C4×#67—91no—
307C4×#67—91no—
308C2×C4⋊Dic3—91no—
309C2×Dic3⋊C4—91no—
310C2×Dic3⋊C4—91no—
311#898—91no—
312#894—91no—
313#892—91no—
314#890—91no—
315#889—91no—
316#889—91no—
317#886—91no—
318#886—91no—
319#884—91no—
320#883—91no—
321#67⋊C4—91no—
322#67⋊C4—91no—
323#67⋊C4—91no—
324#879—91no—
325#879—91no—
326#879—91no—
327#879—91no—
328#877—91no—
329#876—91no—
330#872—91no—
331C23×C32—21no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—21no—
336C23×C32—21no—
337C23×C32—41no—
338C23×C32—41no—
339C23×C32C22×D311yescharacteristic
340C23×C32C22×D311yescharacteristic
341C23×C32C22×D311yescharacteristic
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C23×C32C22×D311yescharacteristic
345C22×C3⋊D3C22×D311yescharacteristic
346C22×C3⋊D3C22×D311yescharacteristic
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—31no—
351C22×C3×D3—61no—
352C22×C3×D3—61no—
353C32×D4—22no—
354C32×D4—24no—
355C32×D4—22no—
356C32×D4—22no—
357C32×D4—42no—
358C32×D4—42no—
359C32×D4—44no—
360C2×C32×C4—21no—
361C2×C32×C4—21no—
362C2×C32×C4—21no—
363C2×C32×C4—41no—
364C2×C32×C4C22×D311yescharacteristic
365C2×C32×C4C22×D311yescharacteristic
366C2×C32×C4C22×D311yescharacteristic
367#638—22no—
368#638—22no—
369#638—22no—
370#638—41no—
371C2×C3⋊Dic3—22no—
372C2×C3⋊Dic3—41no—
373C2×C3⋊Dic3—41no—
374C2×C3⋊Dic3—41no—
375C2×C3⋊Dic3C22×D311yescharacteristic
376C2×C3⋊Dic3C22×D311yescharacteristic
377C2×C3⋊Dic3C22×D311yescharacteristic
378C2×C3⋊Dic3C22×D311yescharacteristic
379C2×C3⋊Dic3C22×D311yescharacteristic
380C2×C3⋊Dic3C22×D311yescharacteristic
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C2×C3⋊Dic3C22×D311yescharacteristic
385C3×#67—62no—
386C3×#67—62no—
387C3×#67—62no—
388C3×#67—62no—
389C3×#67—62no—
390C3×#67—62no—
391C3×#67—122no—
392C3×#67—122no—
393C3×#67—122no—
394C3×#67—121no—
395C3×#67—121no—
396C3×#67—122no—
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—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—61no—
420C2×C3×Dic3—61no—
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—62no—
428C2×C3×Dic3—62no—
429C2×C3×Dic3—122no—
430C2×C3×Dic3—121no—
431C2×C3×Dic3—121no—
432C2×C3×Dic3—121no—
433C2×C3×Dic3—121no—
434C2×C3×Dic3—121no—
435C2×C3×Dic3—121no—
436C2×C3×Dic3—122no—
437C2×C3×Dic3—122no—
438C2×C3×Dic3—122no—
439#626—121no—
440#626—121no—
441#625—121no—
442#624—62no—
443#624—121no—
444D3×Dic3—62no—
445D3×Dic3—62no—
446D3×Dic3—121no—
447D3×Dic3—121no—
448#553—271noSylow
449C2×C33—22no—
450C2×C33—41no—
451C2×C33C2×#4111yescharacteristic
452C2×C33C2×#4111yescharacteristic
453C2×C33H(5,𝔽2)11yescharacteristic
454C3×C3⋊D3—41no—
455C3×C3⋊D3—41no—
456C2×C3×D4—21no—
457C2×C3×D4—21no—
458C2×C3×D4—21no—
459C2×C3×D4—41no—
460C2×C3×D4—91no—
461C2×C3×D4—91no—
462C2×C3×D4—91no—
463C2×C3×D4—91no—
464C2×C3×D4D3211yescharacteristic
465C2×C3×D4D3211yescharacteristic
466C2×C3×D4D3211yescharacteristic
467C22×C3×C4—91no—
468C22×C3×C4—91no—
469C22×C3×C4—91no—
470C22×C3×C4—91no—
471C2×#67—31no—
472C2×#67—31no—
473C2×#67—31no—
474C2×#67—31no—
475C2×#67—31no—
476C2×#67—31no—
477C2×#67—31no—
478C2×#67—31no—
479C2×#67—61no—
480C2×#67—61no—
481C2×#67—61no—
482C2×#67—61no—
483C2×#67—91no—
484C2×#67—91no—
485C22×Dic3—31no—
486C22×Dic3—31no—
487C22×Dic3—31no—
488C22×Dic3—31no—
489C22×Dic3—31no—
490C22×Dic3—31no—
491C22×Dic3—31no—
492C22×Dic3—31no—
493C22×Dic3—61no—
494C22×Dic3—61no—
495C22×Dic3—61no—
496C22×Dic3—61no—
497C22×Dic3—91no—
498C22×Dic3—91no—
499C2×D12—91no—
500C2×C4×D3—91no—
501C2×C4×D3—91no—
502C2×C4×D3—91no—
503C2×C4×D3—91no—
504C3×C4⋊C4—91no—
505C3×C4⋊C4—91no—
506C3×C4⋊C4—91no—
507C3×C22⋊C4—91no—
508C3×C22⋊C4—91no—
509C3×C22⋊C4—91no—
510C3×C22⋊C4—91no—
511C3×C22⋊C4—91no—
512C3×C22⋊C4—91no—
513C3×C42—91no—
514#217—31no—
515#217—31no—
516#217—31no—
517#217—31no—
518#217—31no—
519#217—31no—
520#217—31no—
521#217—31no—
522#217—61no—
523#217—61no—
524#217—61no—
525#217—61no—
526#217—91no—
527#217—91no—
528#217—91no—
529#217—91no—
530(C2×D3)⋊C4—31no—
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—31no—
533(C2×D3)⋊C4—31no—
534(C2×D3)⋊C4—61no—
535(C2×D3)⋊C4—61no—
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—
544C4⋊Dic3—31no—
545C4⋊Dic3—31no—
546C4⋊Dic3—61no—
547C4⋊Dic3—91no—
548C4⋊Dic3—91no—
549C4⋊Dic3—91no—
550C4⋊Dic3—91no—
551C4⋊Dic3—91no—
552C4⋊Dic3—91no—
553C4⋊Dic3—91no—
554Dic3⋊C4—31no—
555Dic3⋊C4—31no—
556Dic3⋊C4—31no—
557Dic3⋊C4—31no—
558Dic3⋊C4—61no—
559Dic3⋊C4—61no—
560Dic3⋊C4—91no—
561Dic3⋊C4—91no—
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—
572Dic3⋊C4—91no—
573Dic3⋊C4—91no—
574C4×Dic3—31no—
575C4×Dic3—31no—
576C4×Dic3—61no—
577C4×Dic3—91no—
578C4×Dic3—91no—
579C4×Dic3—91no—
580C4×Dic3—91no—
581C4×Dic3—91no—
582C4×Dic3—91no—
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—21no—
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—22no—
603C22×C32—22no—
604C22×C32—22no—
605C22×C32—41no—
606C22×C32—42no—
607C22×C32—41no—
608C22×C32—41no—
609C22×C32—42no—
610C22×C32—41no—
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—81no—
623C22×C32—81no—
624C22×C32—81no—
625C22×C32—81no—
626C22×C32#23512yes—
627C22×C32#23712yes—
628C22×C32#23712yes—
629C22×C32C23×D311yescharacteristic
630C22×C32C23×D311yescharacteristic
631C22×C32C23×D311yescharacteristic
632C2×C3⋊D3—21no—
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—21no—
637C2×C3⋊D3—21no—
638C2×C3×D3—61no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—61no—
642C2×C3×D3—61no—
643C2×C3×D3—61no—
644C2×C3×D3—61no—
645C2×C3×D3—61no—
646C2×C3×D3—61no—
647C2×C3×D3—61no—
648C2×C3×D3—61no—
649C2×C3×D3—61no—
650C2×C3×D3—121no—
651C2×C3×D3—121no—
652C2×C3×D3—121no—
653C2×C3×D3—121no—
654C2×C3×D3—121no—
655C2×C3×D3—121no—
656C32×C4—21no—
657C32×C4—22no—
658C32×C4—21no—
659C32×C4—21no—
660C32×C4—41no—
661C32×C4—41no—
662C32×C4—42no—
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#23712yes—
673C3×Dic3—32no—
674C3×Dic3—32no—
675C3×Dic3—62no—
676C3×Dic3—62no—
677C3×Dic3—62no—
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—61no—
695C3×Dic3—61no—
696C3×Dic3—121no—
697C3×Dic3—121no—
698C3×Dic3—121no—
699C3×Dic3—121no—
700C3×Dic3—121no—
701C3×Dic3—121no—
702C3×Dic3—121no—
703#126—271no—
704#126—271no—
705#125—271no—
706#123—271no—
707#123—271no—
708#121—91no—
709#121—91no—
710#121—271no—
711#121—271no—
712C4×D4—91no—
713C4×D4—271no—
714C4×D4—271no—
715C4×D4—271no—
716#117—271no—
717C2×C4⋊C4—271no—
718C33#55311yescharacteristic, complemented, Sylow
719C23×C3—21no—
720C23×C3—21no—
721C23×C3—21no—
722C23×C3—21no—
723C23×C3—21no—
724C23×C3—21no—
725C23×C3—41no—
726C23×C3—41no—
727C23×C3—91no—
728C23×C3—91no—
729C23×C3C2×D3211yescharacteristic
730C23×C3C2×D3211yescharacteristic
731C23×C3C2×D3211yescharacteristic
732C23×C3C2×D3211yescharacteristic
733C23×C3C2×D3211yescharacteristic
734C23×C3C2×D3211yescharacteristic
735C22×D3—31no—
736C22×D3—31no—
737C22×D3—31no—
738C22×D3—31no—
739C22×D3—61no—
740C22×D3—61no—
741C3×D4—24no—
742C3×D4—22no—
743C3×D4—22no—
744C3×D4—22no—
745C3×D4—42no—
746C3×D4—42no—
747C3×D4—44no—
748C3×D4—182no—
749C3×D4—182no—
750C3×D4—182no—
751C3×D4—361no—
752C2×C3×C4—21no—
753C2×C3×C4—21no—
754C2×C3×C4—21no—
755C2×C3×C4—41no—
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—91no—
765C2×C3×C4—91no—
766C2×C3×C4—182no—
767C2×C3×C4—361no—
768C2×C3×C4—361no—
769C2×C3×C4—361no—
770C2×C3×C4C2×D3211yescharacteristic
771C2×C3×C4C2×D3211yescharacteristic
772C2×C3×C4C2×D3211yescharacteristic
773#67—62no—
774#67—62no—
775#67—62no—
776#67—62no—
777#67—62no—
778#67—62no—
779#67—122no—
780#67—122no—
781#67—122no—
782#67—121no—
783#67—121no—
784#67—122no—
785#67—361no—
786#67—361no—
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—31no—
801C2×Dic3—31no—
802C2×Dic3—31no—
803C2×Dic3—31no—
804C2×Dic3—31no—
805C2×Dic3—31no—
806C2×Dic3—31no—
807C2×Dic3—61no—
808C2×Dic3—61no—
809C2×Dic3—61no—
810C2×Dic3—61no—
811C2×Dic3—61no—
812C2×Dic3—61no—
813C2×Dic3—61no—
814C2×Dic3—61no—
815C2×Dic3—61no—
816C2×Dic3—61no—
817C2×Dic3—62no—
818C2×Dic3—62no—
819C2×Dic3—122no—
820C2×Dic3—121no—
821C2×Dic3—121no—
822C2×Dic3—121no—
823C2×Dic3—121no—
824C2×Dic3—121no—
825C2×Dic3—121no—
826C2×Dic3—122no—
827C2×Dic3—122no—
828C2×Dic3—122no—
829C2×Dic3—182no—
830C2×Dic3—361no—
831D12—361no—
832C4×D3—182no—
833C4×D3—182no—
834C4×D3—361no—
835C4×D3—361no—
836C2×C32—22no—
837C2×C32—22no—
838C2×C32—22no—
839C2×C32—21no—
840C2×C32—21no—
841C2×C32—21no—
842C2×C32—21no—
843C2×C32—21no—
844C2×C32—21no—
845C2×C32—21no—
846C2×C32—21no—
847C2×C32—21no—
848C2×C32—41no—
849C2×C32—41no—
850C2×C32—41no—
851C2×C32—42no—
852C2×C32—42no—
853C2×C32—42no—
854C2×C32—41no—
855C2×C32—42no—
856C2×C32—41no—
857C2×C32—41no—
858C2×C32—82no—
859C2×C32—81no—
860C2×C32—81no—
861C2×C32—82no—
862C2×C32C2×#23511yescharacteristic
863C2×C32C2×#23711yescharacteristic
864C2×C32C2×#23711yescharacteristic
865C2×C32C2×#23711yescharacteristic
866C2×C32#100411yescharacteristic
867C2×C32#100411yescharacteristic
868C2×C32D3×#4111yescharacteristic
869C2×C32D3×#4111yescharacteristic
870C2×C32#100911yescharacteristic
871C3⋊D3—41no—
872C3⋊D3—41no—
873C3×D3—121no—
874C3×D3—121no—
875C3×D3—121no—
876C3×D3—121no—
877C3×D3—241no—
878C3×D3—241no—
879C2×D4—91no—
880C2×D4—91no—
881C2×D4—91no—
882C2×D4—91no—
883C2×D4—271no—
884C2×D4#111311yescharacteristic
885C22×C4—91no—
886C22×C4—91no—
887C22×C4—91no—
888C22×C4—91no—
889C22×C4—271no—
890C22×C4—271no—
891C4⋊C4—91no—
892C4⋊C4—91no—
893C4⋊C4—91no—
894C4⋊C4—271no—
895C4⋊C4—271no—
896C4⋊C4—271no—
897C4⋊C4—271no—
898C4⋊C4—271no—
899C4⋊C4—271no—
900C4⋊C4—271no—
901C22⋊C4—91no—
902C22⋊C4—91no—
903C22⋊C4—91no—
904C22⋊C4—91no—
905C22⋊C4—91no—
906C22⋊C4—91no—
907C22⋊C4—271no—
908C22⋊C4—271no—
909C22⋊C4—271no—
910C22⋊C4—271no—
911C42—91no—
912C42—271no—
913C42—271no—
914C22×C3—21no—
915C22×C3—21no—
916C22×C3—21no—
917C22×C3—21no—
918C22×C3—21no—
919C22×C3—21no—
920C22×C3—22no—
921C22×C3—21no—
922C22×C3—21no—
923C22×C3—21no—
924C22×C3—21no—
925C22×C3—21no—
926C22×C3—21no—
927C22×C3—21no—
928C22×C3—21no—
929C22×C3—21no—
930C22×C3—21no—
931C22×C3—21no—
932C22×C3—21no—
933C22×C3—22no—
934C22×C3—22no—
935C22×C3—22no—
936C22×C3—41no—
937C22×C3—41no—
938C22×C3—41no—
939C22×C3—41no—
940C22×C3—41no—
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—42no—
951C22×C3—41no—
952C22×C3—42no—
953C22×C3—81no—
954C22×C3—81no—
955C22×C3—81no—
956C22×C3—81no—
957C22×C3—181no—
958C22×C3—181no—
959C22×C3—181no—
960C22×C3—181no—
961C22×C3—181no—
962C22×C3—181no—
963C22×C3#380412yes—
964C22×C3#380412yes—
965C22×C3#380512yes—
966C22×C3C22×D3211yescharacteristic
967C22×C3C22×D3211yescharacteristic
968C22×C3C22×D3211yescharacteristic
969C2×D3—61no—
970C2×D3—61no—
971C2×D3—61no—
972C2×D3—61no—
973C2×D3—61no—
974C2×D3—61no—
975C2×D3—61no—
976C2×D3—61no—
977C2×D3—61no—
978C2×D3—61no—
979C2×D3—61no—
980C2×D3—61no—
981C2×D3—121no—
982C2×D3—121no—
983C2×D3—121no—
984C2×D3—121no—
985C2×D3—121no—
986C2×D3—121no—
987C3×C4—22no—
988C3×C4—21no—
989C3×C4—21no—
990C3×C4—21no—
991C3×C4—41no—
992C3×C4—41no—
993C3×C4—42no—
994C3×C4—92no—
995C3×C4—181no—
996C3×C4—181no—
997C3×C4—181no—
998C3×C4—181no—
999C3×C4—181no—
1000C3×C4—181no—
1001C3×C4—181no—
1002C3×C4—181no—
1003C3×C4—181no—
1004Dic3—32no—
1005Dic3—32no—
1006Dic3—62no—
1007Dic3—62no—
1008Dic3—62no—
1009Dic3—61no—
1010Dic3—61no—
1011Dic3—61no—
1012Dic3—61no—
1013Dic3—61no—
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—121no—
1028Dic3—121no—
1029Dic3—121no—
1030Dic3—121no—
1031Dic3—121no—
1032Dic3—121no—
1033Dic3—121no—
1034C32—21no—
1035C32—21no—
1036C32—21no—
1037C32—41no—
1038C32#554011yescharacteristic, complemented
1039C32#560111yescharacteristic, complemented
1040C32#561811yescharacteristic, complemented
1041C23—91no—
1042C23—91no—
1043C23C2×#111311yescharacteristic
1044C23C2×#111311yescharacteristic
1045D4—22no—
1046D4—182no—
1047D4—182no—
1048D4—182no—
1049D4—361no—
1050D4—1081no—
1051C2×C4—91no—
1052C2×C4—91no—
1053C2×C4—91no—
1054C2×C4—91no—
1055C2×C4—91no—
1056C2×C4—91no—
1057C2×C4—91no—
1058C2×C4—91no—
1059C2×C4—91no—
1060C2×C4—91no—
1061C2×C4—182no—
1062C2×C4—361no—
1063C2×C4—361no—
1064C2×C4—361no—
1065C2×C4—542no—
1066C2×C4—1081no—
1067C2×C4C2×#111311yescharacteristic
1068C2×C3—22no—
1069C2×C3—22no—
1070C2×C3—22no—
1071C2×C3—21no—
1072C2×C3—21no—
1073C2×C3—21no—
1074C2×C3—21no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—21no—
1080C2×C3—42no—
1081C2×C3—42no—
1082C2×C3—42no—
1083C2×C3—42no—
1084C2×C3—41no—
1085C2×C3—41no—
1086C2×C3—41no—
1087C2×C3—41no—
1088C2×C3—41no—
1089C2×C3—41no—
1090C2×C3—82no—
1091C2×C3—81no—
1092C2×C3—81no—
1093C2×C3—82no—
1094C2×C3—361no—
1095C2×C3—361no—
1096C2×C3D3×#23711yescharacteristic
1097C2×C3D3×#23711yescharacteristic
1098C2×C3#6431211yescharacteristic
1099C2×C3#6431311yescharacteristic
1100C2×C3#6431411yescharacteristic
1101C2×C3#6431411yescharacteristic
1102C2×C3C2×#380411yescharacteristic
1103C2×C3C2×#380411yescharacteristic
1104C2×C3C2×#380511yescharacteristic
1105D3—121no—
1106D3—121no—
1107D3—121no—
1108D3—121no—
1109D3—241no—
1110D3—241no—
1111C22—21no—
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—21no—
1116C22—181no—
1117C22—181no—
1118C22—181no—
1119C22—181no—
1120C22—181no—
1121C22—181no—
1122C22#8904612yes—
1123C22C22×#111311yescharacteristic
1124C4—21no—
1125C4—92no—
1126C4—181no—
1127C4—181no—
1128C4—181no—
1129C4—181no—
1130C4—181no—
1131C4—181no—
1132C4—181no—
1133C4—181no—
1134C4—181no—
1135C3—21no—
1136C3—21no—
1137C3—21no—
1138C3—41no—
1139C3#1059518911yescharacteristic, complemented
1140C3#1059519311yescharacteristic, complemented
1141C3#1059520411yescharacteristic, complemented
1142C2—22no—
1143C2—41no—
1144C2—361no—
1145C2—361no—
1146C2#1172462211yescharacteristic
1147C2#1172462311yescharacteristic
1148C2C2×#8904611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#553
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C3×#64148C2semidirect
2. C3×#64148C2semidirect
3. C3×D4×C3⋊Dic3C2semidirect
4. #11723726C2semidirect
5. #11723726C2semidirect
6. #11723726C2semidirect
7. #11723725C2semidirect
8. C2×#88815C2semidirect
9. #11723720C2semidirect
10. #11723717C2semidirect
11. #11723716C2semidirect
12. #11723690C2semidirect
13. #11723683C2semidirect
14. #11723676C2semidirect
15. #11723669C2semidirect
54. #64148D3semidirect
55. #64148D3semidirect
56. D4×C3⋊Dic3D3semidirect
718. C33#553semidirect
1038. C32#5540semidirect
1039. C32#5601semidirect
1040. C32#5618semidirect
1139. C3#10595189semidirect
1140. C3#10595193semidirect
1141. C3#10595204semidirect

Maximal subgroups

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

subgroupindex
C3×#641482
C3×D4×C3⋊Dic32
#117237262
#117237252
C2×#888152
#117237202
#117237172
#117237162
#117236902
#117236832
#117236762
#117236692
#105952043
#105951933
#105951893