Finite Group Databasebeta

← #13178673

Subgroups — #13178673

Order 1728.

1356 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64147C211yesmaximal, characteristic, complemented
2C3×#64146C211yesmaximal, characteristic, complemented
3C3×#64144C211yesmaximal, characteristic, complemented
4#11723727C211yesmaximal, characteristic, complemented
5#11723726C211yesmaximal, characteristic, complemented
6#11723725C211yesmaximal, characteristic, complemented
7#11723723C211yesmaximal, characteristic, complemented
8#11723718C211yesmaximal, characteristic, complemented
9#11723718C211yesmaximal, characteristic, complemented
10#11723717C211yesmaximal, characteristic, complemented
11#11723716C211yesmaximal, characteristic, complemented
12#11723694C211yesmaximal, characteristic, complemented
13#11723692C211yesmaximal, characteristic, complemented
14#11723684C211yesmaximal, characteristic, complemented
15#11723675C211yesmaximal, characteristic, complemented
16#10595255—31nomaximal
17#10595185—31nomaximal
18#10595180—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C3×#638C2211yescharacteristic, complemented
25C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27C2×#6296C2211yescharacteristic, complemented
28C2×#6295C2211yescharacteristic
29C2×#6295C2211yescharacteristic
30C2×#6294C2211yescharacteristic
31C2×#6294C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C3×#3757C2211yescharacteristic
36C3×#3757C2211yescharacteristic, complemented
37C3×#3757C2211yescharacteristic, complemented
38C3×#3752C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41C3×#3750C2211yescharacteristic, complemented
42C3×#3750C2211yescharacteristic, complemented
43#88815C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88815C2211yescharacteristic, complemented
46#88814C2211yescharacteristic
47#88814C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic, complemented
51#88814C2211yescharacteristic, complemented
52#88813C2211yescharacteristic, complemented
53#88813C2211yescharacteristic, complemented
54#64147D311yescharacteristic, complemented
55#64146D311yescharacteristic, complemented
56#64144D311yescharacteristic, complemented
57C3×#938—31no—
58C3×#938—31no—
59C3×#938—61no—
60C3×#937—31no—
61C3×#937—31no—
62C3×#937—61no—
63C3×#935—31no—
64C3×#935—31no—
65C3×#935—61no—
66#63981—31no—
67#63980—31no—
68#63978—31no—
69#63978—31no—
70#63977—31no—
71#63976—31no—
72#63974—31no—
73#67⋊Dic3—31no—
74Dic3×#67—31no—
75#63971—31no—
76#63970—31no—
77D3×#217—31no—
78D3×#217—31no—
79#63959—31no—
80#63959—31no—
81#63959—31no—
82#63959—31no—
83#63958—31no—
84#63956—31no—
85#63956—31no—
86#63956—31no—
87#63953—31no—
88#63953—31no—
89#63952—31no—
90#63905—31no—
91#63904—31no—
92#63899—31no—
93#63895—31no—
94#63893—31no—
95#63881—31no—
96#63879—31no—
97#63861—31no—
98#63858—31no—
99#63853—31no—
100#63850—31no—
101#63848—31no—
102C23×C33C2311yescharacteristic
103C23×C33C2311yescharacteristic
104C22×C3×C3⋊D3—22no—
105C22×C3×C3⋊D3—41no—
106C22×C3×C3⋊D3—41no—
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C3×C3⋊D3C2311yescharacteristic
110C33×D4—41no—
111C2×C33×C4C2311yescharacteristic
112C3×#638—22no—
113C3×#638—41no—
114C3×#638—41no—
115C3×#638—41no—
116C2×C3×C3⋊Dic3—41no—
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
126C3×C4×C3⋊D3—41no—
127#6296—41no—
128#6295—22no—
129#6295—41no—
130#6294—41no—
131#6294—41no—
132#5657—91no—
133#5613—91no—
134#5593—91no—
135C23×C3⋊D3C2×D311yescharacteristic
136C23×C3×D3—31no—
137C23×C3×D3—31no—
138C23×C3×D3—61no—
139C2×C32×D4—21no—
140C2×C32×D4—21no—
141C2×C32×D4—21no—
142C2×C32×D4—41no—
143C2×C32×D4C2×D311yescharacteristic
144C2×C32×D4C2×D311yescharacteristic
145C2×C32×D4C2×D311yescharacteristic
146C2×#638C2×D311yescharacteristic
147C2×#638C2×D311yescharacteristic
148C2×#638C2×D311yescharacteristic
149C2×#638C2×D311yescharacteristic, complemented
150C22×C3⋊Dic3C2×D311yescharacteristic, complemented
151C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—61no—
161C2×C3×#67—61no—
162C2×C3×#67—61no—
163C2×C3×#67—61no—
164C22×C3×Dic3—31no—
165C22×C3×Dic3—31no—
166C22×C3×Dic3—61no—
167C2×C3×C4×D3—31no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—61no—
170C2×#627—31no—
171C2×#627—31no—
172C2×#627—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#625—31no—
178C2×#625—31no—
179C2×#624—31no—
180C2×#624—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—31no—
183C2×D3×Dic3—31no—
184C2×D3×Dic3—31no—
185#3757C2×D311yescharacteristic
186#3757C2×D311yescharacteristic
187#3757C2×D311yescharacteristic
188#3757C2×D311yescharacteristic
189#3757C2×D311yescharacteristic, complemented
190#3757C2×D311yescharacteristic, complemented
191#3752C2×D311yescharacteristic
192#3752C2×D311yescharacteristic
193C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
194#3750C2×D311yescharacteristic, complemented
195#3750C2×D311yescharacteristic, complemented
196C3×#217—31no—
197C3×#217—31no—
198C3×#217—31no—
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—31no—
203C3×#217—31no—
204C3×#217—31no—
205C3×#217—31no—
206C3×#217—31no—
207C3×#217—31no—
208C3×#217—61no—
209C3×#217—61no—
210C3×#217—61no—
211C3×#217—61no—
212C3×#217—61no—
213C3×#217—61no—
214C3×(C2×D3)⋊C4—31no—
215C3×(C2×D3)⋊C4—31no—
216C3×(C2×D3)⋊C4—31no—
217C3×(C2×D3)⋊C4—31no—
218C3×(C2×D3)⋊C4—61no—
219C3×(C2×D3)⋊C4—61no—
220C3×C4⋊Dic3—31no—
221C3×C4⋊Dic3—31no—
222C3×C4⋊Dic3—61no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—31no—
225C3×Dic3⋊C4—31no—
226C3×Dic3⋊C4—31no—
227C3×Dic3⋊C4—61no—
228C3×Dic3⋊C4—61no—
229#3724—31no—
230#3724—31no—
231#3724—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—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—
256Dic32—31no—
257Dic32—31no—
258Dic32—31no—
259Dic32—31no—
260Dic32—31no—
261Dic32—31no—
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
265C22×C33—21no—
266C22×C33—21no—
267C22×C33—21no—
268C22×C33C2411yescharacteristic
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—21no—
272C2×C3×C3⋊D3—21no—
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3—21no—
275C2×C3×C3⋊D3—21no—
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3—44no—
278C2×C3×C3⋊D3#4112yes—
279C33×C4—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C3×C3⋊Dic3—21no—
285C3×C3⋊Dic3—21no—
286C3×C3⋊Dic3—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×#123—91no—
290C3×#121—91no—
291C3×#120—91no—
292#953—91no—
293C2×#217—91no—
294#939—91no—
295#939—91no—
296#939—91no—
297#938—31no—
298#938—31no—
299#938—61no—
300#938—91no—
301#937—31no—
302#937—31no—
303#937—61no—
304#937—91no—
305#936—91no—
306#936—91no—
307#935—31no—
308#935—31no—
309#935—61no—
310D4×Dic3—91no—
311#930—91no—
312#929—91no—
313C4×#67—91no—
314C4×#67—91no—
315#898—91no—
316#898—91no—
317#897—91no—
318#896—91no—
319#894—91no—
320#893—91no—
321#885—91no—
322#885—91no—
323#885—91no—
324#885—91no—
325#884—91no—
326#883—91no—
327#882—91no—
328#67⋊C4—91no—
329#67⋊C4—91no—
330D3×C22⋊C4—91no—
331D3×C22⋊C4—91no—
332#879—91no—
333#879—91no—
334#879—91no—
335#879—91no—
336#878—91no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—21no—
341C23×C32—21no—
342C23×C32—21no—
343C23×C32—41no—
344C23×C32—41no—
345C23×C32C22×D311yescharacteristic
346C23×C32C22×D311yescharacteristic
347C23×C32C22×D311yescharacteristic
348C23×C32C22×D311yescharacteristic
349C23×C32C22×D311yescharacteristic
350C23×C32C22×D311yescharacteristic
351C22×C3⋊D3—22no—
352C22×C3⋊D3—41no—
353C22×C3⋊D3—41no—
354C22×C3⋊D3C22×D311yescharacteristic
355C22×C3⋊D3C22×D311yescharacteristic
356C22×C3⋊D3C22×D311yescharacteristic
357C22×C3×D3—31no—
358C22×C3×D3—31no—
359C22×C3×D3—31no—
360C22×C3×D3—31no—
361C22×C3×D3—31no—
362C22×C3×D3—31no—
363C22×C3×D3—61no—
364C22×C3×D3—61no—
365C22×C3×D3—61no—
366C22×C3×D3—62no—
367C22×C3×D3—62no—
368C22×C3×D3—122no—
369C22×C3×D3—121no—
370C22×C3×D3—121no—
371C22×C3×D3—121no—
372C22×C3×D3—121no—
373C22×C3×D3—122no—
374C22×C3×D3—122no—
375C32×D4—41no—
376C32×D4—41no—
377C32×D4—41no—
378C32×D4—42no—
379C32×D4—42no—
380C32×D4—42no—
381C32×D4—44no—
382C2×C32×C4—21no—
383C2×C32×C4—21no—
384C2×C32×C4—21no—
385C2×C32×C4—41no—
386C2×C32×C4C22×D311yescharacteristic
387C2×C32×C4C22×D311yescharacteristic
388C2×C32×C4C22×D311yescharacteristic
389#638—22no—
390#638—41no—
391#638—41no—
392#638—41no—
393C2×C3⋊Dic3—41no—
394C2×C3⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C2×C3⋊Dic3C22×D311yescharacteristic
399C2×C3⋊Dic3C22×D311yescharacteristic
400C2×C3⋊Dic3C22×D311yescharacteristic
401C2×C3⋊Dic3C22×D311yescharacteristic
402C2×C3⋊Dic3C22×D311yescharacteristic
403C4×C3⋊D3—41no—
404C3×#67—62no—
405C3×#67—62no—
406C3×#67—122no—
407C3×#67—121no—
408C3×#67—121no—
409C3×#67—121no—
410C3×#67—121no—
411C3×#67—121no—
412C3×#67—121no—
413C3×#67—122no—
414C3×#67—122no—
415C3×#67—122no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—31no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—31no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—31no—
432C2×C3×Dic3—31no—
433C2×C3×Dic3—31no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—61no—
436C2×C3×Dic3—61no—
437C2×C3×Dic3—61no—
438C2×C3×Dic3—61no—
439C2×C3×Dic3—61no—
440C2×C3×Dic3—61no—
441C2×C3×Dic3—61no—
442C2×C3×Dic3—61no—
443C2×C3×Dic3—121no—
444C2×C3×Dic3—121no—
445C2×C3×Dic3—122no—
446C3×C4×D3—121no—
447C3×C4×D3—121no—
448C3×C4×D3—122no—
449#627—121no—
450#627—121no—
451#627—121no—
452#626—62no—
453#626—62no—
454#626—121no—
455#626—121no—
456#625—62no—
457#625—121no—
458#624—121no—
459#624—121no—
460D3×Dic3—121no—
461D3×Dic3—121no—
462D3×Dic3—121no—
463D3×Dic3—121no—
464#538—271noSylow
465C2×C33—41no—
466C2×C33—41no—
467C2×C33C2×#4111yescharacteristic
468C2×C33H(5,𝔽2)11yescharacteristic
469C2×C33H(5,𝔽2)11yescharacteristic
470C3×C3⋊D3—22no—
471C3×C3⋊D3—41no—
472C3×C3⋊D3—41no—
473C24×C3—91no—
474C23×D3—31no—
475C23×D3—31no—
476C23×D3—61no—
477C2×C3×D4—21no—
478C2×C3×D4—21no—
479C2×C3×D4—21no—
480C2×C3×D4—41no—
481C2×C3×D4—91no—
482C2×C3×D4—91no—
483C2×C3×D4—91no—
484C2×C3×D4—91no—
485C2×C3×D4D3211yescharacteristic
486C2×C3×D4D3211yescharacteristic
487C2×C3×D4D3211yescharacteristic
488C22×C3×C4—91no—
489C22×C3×C4—91no—
490C2×#67—31no—
491C2×#67—31no—
492C2×#67—31no—
493C2×#67—31no—
494C2×#67—31no—
495C2×#67—31no—
496C2×#67—31no—
497C2×#67—31no—
498C2×#67—61no—
499C2×#67—61no—
500C2×#67—61no—
501C2×#67—61no—
502C2×#67—91no—
503C2×#67—91no—
504C2×#67—91no—
505C2×#67—91no—
506C22×Dic3—31no—
507C22×Dic3—31no—
508C22×Dic3—61no—
509C22×Dic3—91no—
510C22×Dic3—91no—
511C2×D12—91no—
512C2×D12—91no—
513C2×C4×D3—31no—
514C2×C4×D3—31no—
515C2×C4×D3—61no—
516C2×C4×D3—91no—
517C2×C4×D3—91no—
518C2×C4×D3—91no—
519C2×C4×D3—91no—
520C2×Dic6—91no—
521C2×Dic6—91no—
522C2×Dic6—91no—
523C3×C4⋊C4—91no—
524C3×C4⋊C4—91no—
525C3×C4⋊C4—91no—
526C3×C22⋊C4—91no—
527C3×C22⋊C4—91no—
528C3×C22⋊C4—91no—
529C3×C22⋊C4—91no—
530C3×C22⋊C4—91no—
531C3×C22⋊C4—91no—
532C3×C22⋊C4—91no—
533C3×C22⋊C4—91no—
534#217—31no—
535#217—31no—
536#217—31no—
537#217—31no—
538#217—31no—
539#217—31no—
540#217—31no—
541#217—31no—
542#217—31no—
543#217—31no—
544#217—31no—
545#217—31no—
546#217—61no—
547#217—61no—
548#217—61no—
549#217—61no—
550#217—61no—
551#217—61no—
552#217—91no—
553#217—91no—
554#217—91no—
555#217—91no—
556#217—91no—
557#217—91no—
558(C2×D3)⋊C4—31no—
559(C2×D3)⋊C4—31no—
560(C2×D3)⋊C4—31no—
561(C2×D3)⋊C4—31no—
562(C2×D3)⋊C4—61no—
563(C2×D3)⋊C4—61no—
564(C2×D3)⋊C4—91no—
565(C2×D3)⋊C4—91no—
566(C2×D3)⋊C4—91no—
567(C2×D3)⋊C4—91no—
568(C2×D3)⋊C4—91no—
569(C2×D3)⋊C4—91no—
570(C2×D3)⋊C4—91no—
571(C2×D3)⋊C4—91no—
572(C2×D3)⋊C4—91no—
573(C2×D3)⋊C4—91no—
574(C2×D3)⋊C4—91no—
575(C2×D3)⋊C4—91no—
576C4⋊Dic3—31no—
577C4⋊Dic3—31no—
578C4⋊Dic3—61no—
579C4⋊Dic3—91no—
580C4⋊Dic3—91no—
581C4⋊Dic3—91no—
582Dic3⋊C4—31no—
583Dic3⋊C4—31no—
584Dic3⋊C4—31no—
585Dic3⋊C4—31no—
586Dic3⋊C4—61no—
587Dic3⋊C4—61no—
588Dic3⋊C4—91no—
589Dic3⋊C4—91no—
590Dic3⋊C4—91no—
591Dic3⋊C4—91no—
592Dic3⋊C4—91no—
593Dic3⋊C4—91no—
594C4×Dic3—91no—
595C4×Dic3—91no—
596C4×Dic3—91no—
597C4×Dic3—91no—
598C4×Dic3—91no—
599C4×Dic3—91no—
600C22×C32—21no—
601C22×C32—21no—
602C22×C32—22no—
603C22×C32—22no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—21no—
607C22×C32—21no—
608C22×C32—21no—
609C22×C32—21no—
610C22×C32—21no—
611C22×C32—21no—
612C22×C32—21no—
613C22×C32—21no—
614C22×C32—21no—
615C22×C32—21no—
616C22×C32—21no—
617C22×C32—21no—
618C22×C32—21no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—21no—
622C22×C32—21no—
623C22×C32—41no—
624C22×C32—41no—
625C22×C32—41no—
626C22×C32—41no—
627C22×C32—41no—
628C22×C32—42no—
629C22×C32—42no—
630C22×C32—41no—
631C22×C32—41no—
632C22×C32—41no—
633C22×C32—41no—
634C22×C32—41no—
635C22×C32—41no—
636C22×C32—41no—
637C22×C32—41no—
638C22×C32—41no—
639C22×C32—41no—
640C22×C32—41no—
641C22×C32—41no—
642C22×C32—81no—
643C22×C32—81no—
644C22×C32—81no—
645C22×C32—81no—
646C22×C32C23×D311yescharacteristic
647C22×C32C23×D311yescharacteristic
648C22×C32C23×D311yescharacteristic
649C2×C3⋊D3—21no—
650C2×C3⋊D3—21no—
651C2×C3⋊D3—21no—
652C2×C3⋊D3—21no—
653C2×C3⋊D3—21no—
654C2×C3⋊D3—21no—
655C2×C3⋊D3—21no—
656C2×C3⋊D3—21no—
657C2×C3⋊D3—44no—
658C2×C3⋊D3#23712yes—
659C2×C3×D3—32no—
660C2×C3×D3—32no—
661C2×C3×D3—62no—
662C2×C3×D3—61no—
663C2×C3×D3—61no—
664C2×C3×D3—61no—
665C2×C3×D3—61no—
666C2×C3×D3—62no—
667C2×C3×D3—62no—
668C2×C3×D3—61no—
669C2×C3×D3—61no—
670C2×C3×D3—61no—
671C2×C3×D3—61no—
672C2×C3×D3—61no—
673C2×C3×D3—61no—
674C2×C3×D3—61no—
675C2×C3×D3—61no—
676C2×C3×D3—61no—
677C2×C3×D3—61no—
678C2×C3×D3—61no—
679C2×C3×D3—61no—
680C2×C3×D3—121no—
681C2×C3×D3—121no—
682C2×C3×D3—121no—
683C2×C3×D3—121no—
684C2×C3×D3—121no—
685C2×C3×D3—121no—
686C2×C3×D3—124no—
687C2×C3×D3—124no—
688C2×C3×D3—128no—
689C32×C4—21no—
690C32×C4—22no—
691C32×C4—21no—
692C32×C4—21no—
693C32×C4—41no—
694C32×C4—41no—
695C32×C4—42no—
696C3⋊Dic3—21no—
697C3⋊Dic3—21no—
698C3⋊Dic3—21no—
699C3⋊Dic3—21no—
700C3⋊Dic3—21no—
701C3⋊Dic3—21no—
702C3⋊Dic3—21no—
703C3⋊Dic3—21no—
704C3⋊Dic3—21no—
705C3×Dic3—61no—
706C3×Dic3—61no—
707C3×Dic3—61no—
708C3×Dic3—61no—
709C3×Dic3—61no—
710C3×Dic3—61no—
711C3×Dic3—61no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—61no—
719C3×Dic3—61no—
720C3×Dic3—61no—
721C3×Dic3—61no—
722C3×Dic3—61no—
723C3×Dic3—121no—
724C3×Dic3—121no—
725C3×Dic3—121no—
726C3×Dic3—121no—
727C3×Dic3—121no—
728C3×Dic3—121no—
729C3×Dic3—121no—
730C3×Dic3—121no—
731C3×Dic3—121no—
732#126—271no—
733#126—271no—
734#124—271no—
735#124—271no—
736#123—91no—
737#123—271no—
738C22⋊Q8—271no—
739#121—91no—
740#121—271no—
741#121—271no—
742#120—91no—
743#120—271no—
744C4×D4—271no—
745C4×D4—271no—
746C2×C22⋊C4—271no—
747C33#53811yescharacteristic, complemented, Sylow
748C23×C3—21no—
749C23×C3—21no—
750C23×C3—21no—
751C23×C3—21no—
752C23×C3—21no—
753C23×C3—21no—
754C23×C3—41no—
755C23×C3—41no—
756C23×C3—91no—
757C23×C3—91no—
758C23×C3—91no—
759C23×C3—182no—
760C23×C3—361no—
761C23×C3—361no—
762C23×C3C2×D3211yescharacteristic
763C23×C3C2×D3211yescharacteristic
764C23×C3C2×D3211yescharacteristic
765C23×C3C2×D3211yescharacteristic
766C23×C3C2×D3211yescharacteristic
767C23×C3C2×D3211yescharacteristic
768C22×D3—31no—
769C22×D3—31no—
770C22×D3—31no—
771C22×D3—31no—
772C22×D3—31no—
773C22×D3—31no—
774C22×D3—61no—
775C22×D3—61no—
776C22×D3—61no—
777C22×D3—62no—
778C22×D3—62no—
779C22×D3—122no—
780C22×D3—121no—
781C22×D3—121no—
782C22×D3—121no—
783C22×D3—121no—
784C22×D3—122no—
785C22×D3—122no—
786C3×D4—41no—
787C3×D4—41no—
788C3×D4—41no—
789C3×D4—42no—
790C3×D4—42no—
791C3×D4—42no—
792C3×D4—44no—
793C3×D4—182no—
794C3×D4—361no—
795C3×D4—361no—
796C3×D4—361no—
797C2×C3×C4—21no—
798C2×C3×C4—21no—
799C2×C3×C4—21no—
800C2×C3×C4—41no—
801C2×C3×C4—91no—
802C2×C3×C4—91no—
803C2×C3×C4—91no—
804C2×C3×C4—91no—
805C2×C3×C4—91no—
806C2×C3×C4—91no—
807C2×C3×C4—91no—
808C2×C3×C4—91no—
809C2×C3×C4—91no—
810C2×C3×C4—361no—
811C2×C3×C4—361no—
812C2×C3×C4C2×D3211yescharacteristic
813C2×C3×C4C2×D3211yescharacteristic
814C2×C3×C4C2×D3211yescharacteristic
815#67—62no—
816#67—62no—
817#67—122no—
818#67—121no—
819#67—121no—
820#67—121no—
821#67—121no—
822#67—121no—
823#67—121no—
824#67—122no—
825#67—122no—
826#67—122no—
827#67—182no—
828#67—182no—
829#67—361no—
830#67—361no—
831C2×Dic3—31no—
832C2×Dic3—31no—
833C2×Dic3—31no—
834C2×Dic3—31no—
835C2×Dic3—31no—
836C2×Dic3—31no—
837C2×Dic3—31no—
838C2×Dic3—31no—
839C2×Dic3—31no—
840C2×Dic3—31no—
841C2×Dic3—31no—
842C2×Dic3—31no—
843C2×Dic3—31no—
844C2×Dic3—31no—
845C2×Dic3—31no—
846C2×Dic3—31no—
847C2×Dic3—31no—
848C2×Dic3—31no—
849C2×Dic3—61no—
850C2×Dic3—61no—
851C2×Dic3—61no—
852C2×Dic3—61no—
853C2×Dic3—61no—
854C2×Dic3—61no—
855C2×Dic3—61no—
856C2×Dic3—61no—
857C2×Dic3—61no—
858C2×Dic3—121no—
859C2×Dic3—121no—
860C2×Dic3—122no—
861C2×Dic3—361no—
862C2×Dic3—361no—
863D12—182no—
864D12—361no—
865C4×D3—121no—
866C4×D3—121no—
867C4×D3—122no—
868C4×D3—361no—
869C4×D3—361no—
870C4×D3—361no—
871C4×D3—361no—
872Dic6—361no—
873Dic6—361no—
874Dic6—361no—
875C2×C32—21no—
876C2×C32—21no—
877C2×C32—21no—
878C2×C32—21no—
879C2×C32—21no—
880C2×C32—21no—
881C2×C32—21no—
882C2×C32—21no—
883C2×C32—21no—
884C2×C32—41no—
885C2×C32—41no—
886C2×C32—41no—
887C2×C32—41no—
888C2×C32—41no—
889C2×C32—42no—
890C2×C32—42no—
891C2×C32—41no—
892C2×C32—41no—
893C2×C32—41no—
894C2×C32—41no—
895C2×C32—81no—
896C2×C32—81no—
897C2×C32—81no—
898C2×C32—81no—
899C2×C32—82no—
900C2×C32—82no—
901C2×C32C2×#23711yescharacteristic
902C2×C32#100411yescharacteristic
903C2×C32#100411yescharacteristic
904C2×C32#100411yescharacteristic
905C2×C32#100411yescharacteristic
906C2×C32#100411yescharacteristic
907C2×C32D3×#4111yescharacteristic
908C2×C32D3×#4111yescharacteristic
909C2×C32#100911yescharacteristic
910C3⋊D3—22no—
911C3⋊D3—41no—
912C3⋊D3—41no—
913C3×D3—62no—
914C3×D3—62no—
915C3×D3—122no—
916C3×D3—122no—
917C3×D3—122no—
918C3×D3—121no—
919C3×D3—121no—
920C3×D3—121no—
921C3×D3—121no—
922C24—91no—
923C2×Q8—271no—
924C2×D4—91no—
925C2×D4—91no—
926C2×D4—91no—
927C2×D4—91no—
928C2×D4—271no—
929C2×D4—271no—
930C2×D4#111311yescharacteristic
931C22×C4—91no—
932C22×C4—91no—
933C22×C4—271no—
934C22×C4—271no—
935C4⋊C4—91no—
936C4⋊C4—91no—
937C4⋊C4—91no—
938C4⋊C4—271no—
939C4⋊C4—271no—
940C4⋊C4—271no—
941C22⋊C4—91no—
942C22⋊C4—91no—
943C22⋊C4—91no—
944C22⋊C4—91no—
945C22⋊C4—91no—
946C22⋊C4—91no—
947C22⋊C4—91no—
948C22⋊C4—91no—
949C22⋊C4—271no—
950C22⋊C4—271no—
951C22⋊C4—271no—
952C22⋊C4—271no—
953C22⋊C4—271no—
954C22⋊C4—271no—
955C42—271no—
956C42—271no—
957C22×C3—22no—
958C22×C3—22no—
959C22×C3—21no—
960C22×C3—21no—
961C22×C3—21no—
962C22×C3—21no—
963C22×C3—21no—
964C22×C3—21no—
965C22×C3—21no—
966C22×C3—21no—
967C22×C3—21no—
968C22×C3—21no—
969C22×C3—21no—
970C22×C3—21no—
971C22×C3—21no—
972C22×C3—21no—
973C22×C3—21no—
974C22×C3—21no—
975C22×C3—21no—
976C22×C3—21no—
977C22×C3—21no—
978C22×C3—21no—
979C22×C3—21no—
980C22×C3—41no—
981C22×C3—41no—
982C22×C3—41no—
983C22×C3—41no—
984C22×C3—41no—
985C22×C3—41no—
986C22×C3—41no—
987C22×C3—41no—
988C22×C3—41no—
989C22×C3—41no—
990C22×C3—41no—
991C22×C3—41no—
992C22×C3—41no—
993C22×C3—41no—
994C22×C3—41no—
995C22×C3—41no—
996C22×C3—42no—
997C22×C3—42no—
998C22×C3—41no—
999C22×C3—81no—
1000C22×C3—81no—
1001C22×C3—81no—
1002C22×C3—81no—
1003C22×C3—92no—
1004C22×C3—181no—
1005C22×C3—181no—
1006C22×C3—181no—
1007C22×C3—181no—
1008C22×C3—181no—
1009C22×C3—181no—
1010C22×C3—181no—
1011C22×C3—181no—
1012C22×C3—364no—
1013C22×C3C22×D3211yescharacteristic
1014C22×C3C22×D3211yescharacteristic
1015C22×C3C22×D3211yescharacteristic
1016C2×D3—32no—
1017C2×D3—32no—
1018C2×D3—62no—
1019C2×D3—61no—
1020C2×D3—61no—
1021C2×D3—61no—
1022C2×D3—61no—
1023C2×D3—62no—
1024C2×D3—62no—
1025C2×D3—61no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—61no—
1030C2×D3—61no—
1031C2×D3—61no—
1032C2×D3—61no—
1033C2×D3—61no—
1034C2×D3—61no—
1035C2×D3—61no—
1036C2×D3—61no—
1037C2×D3—121no—
1038C2×D3—121no—
1039C2×D3—121no—
1040C2×D3—121no—
1041C2×D3—121no—
1042C2×D3—121no—
1043C2×D3—124no—
1044C2×D3—124no—
1045C2×D3—128no—
1046C3×C4—22no—
1047C3×C4—21no—
1048C3×C4—21no—
1049C3×C4—21no—
1050C3×C4—41no—
1051C3×C4—41no—
1052C3×C4—42no—
1053C3×C4—181no—
1054C3×C4—181no—
1055C3×C4—181no—
1056C3×C4—181no—
1057C3×C4—181no—
1058C3×C4—181no—
1059C3×C4—181no—
1060C3×C4—181no—
1061C3×C4—181no—
1062Dic3—61no—
1063Dic3—61no—
1064Dic3—61no—
1065Dic3—61no—
1066Dic3—61no—
1067Dic3—61no—
1068Dic3—61no—
1069Dic3—61no—
1070Dic3—61no—
1071Dic3—61no—
1072Dic3—61no—
1073Dic3—61no—
1074Dic3—61no—
1075Dic3—61no—
1076Dic3—61no—
1077Dic3—61no—
1078Dic3—61no—
1079Dic3—61no—
1080Dic3—121no—
1081Dic3—121no—
1082Dic3—121no—
1083Dic3—121no—
1084Dic3—121no—
1085Dic3—121no—
1086Dic3—121no—
1087Dic3—121no—
1088Dic3—121no—
1089C32—21no—
1090C32—21no—
1091C32—21no—
1092C32—41no—
1093C32#559311yescharacteristic, complemented
1094C32#561311yescharacteristic, complemented
1095C32#565711yescharacteristic, complemented
1096C23—91no—
1097C23—91no—
1098C23—91no—
1099C23—182no—
1100C23—361no—
1101C23—361no—
1102C23C2×#111311yescharacteristic
1103C23C2×#111311yescharacteristic
1104Q8—1081no—
1105D4—41no—
1106D4—182no—
1107D4—361no—
1108D4—361no—
1109D4—361no—
1110D4—542no—
1111D4—1081no—
1112C2×C4—91no—
1113C2×C4—91no—
1114C2×C4—91no—
1115C2×C4—91no—
1116C2×C4—91no—
1117C2×C4—91no—
1118C2×C4—91no—
1119C2×C4—91no—
1120C2×C4—91no—
1121C2×C4—361no—
1122C2×C4—361no—
1123C2×C4—1081no—
1124C2×C4—1081no—
1125C2×C4C2×#111311yescharacteristic
1126C2×C3—21no—
1127C2×C3—21no—
1128C2×C3—21no—
1129C2×C3—21no—
1130C2×C3—21no—
1131C2×C3—21no—
1132C2×C3—21no—
1133C2×C3—21no—
1134C2×C3—21no—
1135C2×C3—42no—
1136C2×C3—42no—
1137C2×C3—41no—
1138C2×C3—41no—
1139C2×C3—41no—
1140C2×C3—41no—
1141C2×C3—41no—
1142C2×C3—41no—
1143C2×C3—41no—
1144C2×C3—41no—
1145C2×C3—41no—
1146C2×C3—81no—
1147C2×C3—81no—
1148C2×C3—81no—
1149C2×C3—81no—
1150C2×C3—82no—
1151C2×C3—82no—
1152C2×C3—182no—
1153C2×C3—361no—
1154C2×C3—361no—
1155C2×C3D3×#23711yescharacteristic
1156C2×C3D3×#23711yescharacteristic
1157C2×C3#6431211yescharacteristic
1158C2×C3#6431311yescharacteristic
1159C2×C3#6431411yescharacteristic
1160C2×C3#6431411yescharacteristic
1161C2×C3#6433011yescharacteristic
1162C2×C3#6433011yescharacteristic
1163C2×C3#6433011yescharacteristic
1164D3—62no—
1165D3—62no—
1166D3—122no—
1167D3—122no—
1168D3—122no—
1169D3—121no—
1170D3—121no—
1171D3—121no—
1172D3—121no—
1173C22—21no—
1174C22—21no—
1175C22—21no—
1176C22—21no—
1177C22—21no—
1178C22—21no—
1179C22—92no—
1180C22—181no—
1181C22—181no—
1182C22—181no—
1183C22—181no—
1184C22—181no—
1185C22—181no—
1186C22—181no—
1187C22—181no—
1188C22—364no—
1189C22C22×#111311yescharacteristic
1190C4—21no—
1191C4—181no—
1192C4—181no—
1193C4—181no—
1194C4—181no—
1195C4—181no—
1196C4—181no—
1197C4—181no—
1198C4—181no—
1199C4—181no—
1200C3—21no—
1201C3—21no—
1202C3—21no—
1203C3—41no—
1204C3#1059518011yescharacteristic, complemented
1205C3#1059518511yescharacteristic, complemented
1206C3#1059525511yescharacteristic, complemented
1207C2—41no—
1208C2—41no—
1209C2—182no—
1210C2—361no—
1211C2—361no—
1212C2#1172462211yescharacteristic
1213C2#1172462311yescharacteristic
1214C2#1172463311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C3×#64147C2semidirect
2. C3×#64146C2semidirect
3. C3×#64144C2semidirect
4. #11723727C2semidirect
5. #11723726C2semidirect
6. #11723725C2semidirect
7. #11723723C2semidirect
8. #11723718C2semidirect
9. #11723718C2semidirect
10. #11723717C2semidirect
11. #11723716C2semidirect
12. #11723694C2semidirect
13. #11723692C2semidirect
14. #11723684C2semidirect
15. #11723675C2semidirect
24. C2×C3×#638C22semidirect
25. C22×C3×C3⋊Dic3C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
27. C2×#6296C22semidirect
36. C3×#3757C22semidirect
37. C3×#3757C22semidirect
40. C3×C4⋊(C3⋊Dic3)C22semidirect
41. C3×#3750C22semidirect
42. C3×#3750C22semidirect
43. #88815C22semidirect
44. #88815C22semidirect
45. #88815C22semidirect
50. #88814C22semidirect
51. #88814C22semidirect
52. #88813C22semidirect
53. #88813C22semidirect
54. #64147D3semidirect
55. #64146D3semidirect
56. #64144D3semidirect
149. C2×#638C2×D3semidirect
150. C22×C3⋊Dic3C2×D3semidirect
151. C2×C4×C3⋊D3C2×D3semidirect
189. #3757C2×D3semidirect
190. #3757C2×D3semidirect
193. C4⋊(C3⋊Dic3)C2×D3semidirect
194. #3750C2×D3semidirect
195. #3750C2×D3semidirect
747. C33#538semidirect
1093. C32#5593semidirect
1094. C32#5613semidirect
1095. C32#5657semidirect
1204. C3#10595180semidirect
1205. C3#10595185semidirect
1206. C3#10595255semidirect

Maximal subgroups

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

subgroupindex
C3×#641472
C3×#641462
C3×#641442
#117237272
#117237262
#117237252
#117237232
#117237182
#117237172
#117237162
#117236942
#117236922
#117236842
#117236752
#105952553
#105951853
#105951803