Finite Group Databasebeta

← #13172309

Subgroups — #13172309

Order 1728.

1372 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723725C211yesmaximal, characteristic, complemented
2#11723643C211yesmaximal, characteristic, complemented
3#11723623C211yesmaximal, characteristic, complemented
4#11723618C211yesmaximal, characteristic, complemented
5C3×#63978C211yesmaximal, characteristic, complemented
6C3×#63966C211yesmaximal, characteristic, complemented
7C3×#63959C211yesmaximal, characteristic, complemented
8#11723024C211yesmaximal, characteristic, complemented
9#11723019C211yesmaximal, characteristic, complemented
10#11723007C211yesmaximal, characteristic, complemented
11#11722994C211yesmaximal, characteristic, complemented
12#11722973C211yesmaximal, characteristic, complemented
13#11722950C211yesmaximal, characteristic, complemented
14#11722937C211yesmaximal, characteristic, complemented
15#11722906C211yesmaximal, characteristic, complemented
16#10595207—31nomaximal
17#10595089—31nomaximal
18#10594307—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C32×#67C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic, complemented
25C2×#6295C2211yescharacteristic
26C2×#6294C2211yescharacteristic, complemented
27C2×#6292C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29C2×#6289C2211yescharacteristic
30C2×C3×#627C2211yescharacteristic, complemented
31C2×C3×#626C2211yescharacteristic
32C3×#3757C2211yescharacteristic, complemented
33C32×#217C2211yescharacteristic, complemented
34#88815C2211yescharacteristic, complemented
35#88814C2211yescharacteristic
36#88807C2211yescharacteristic, complemented
37#88806C2211yescharacteristic, complemented
38#88804C2211yescharacteristic
39#88804C2211yescharacteristic
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic, complemented
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic, complemented
44C3×Dic3⋊Dic3C2211yescharacteristic, complemented
45C3×Dic3⋊Dic3C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×#3722C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic, complemented
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54#64146—31no—
55C4×#638—31no—
56#64093—31no—
57C3×#939—31no—
58C3×#936—31no—
59C3×#930—31no—
60C3×#929—31no—
61C3×#886—31no—
62C3×#885—31no—
63#63983—31no—
64#63983—31no—
65#63983—61no—
66#63981—31no—
67#63978D311yescharacteristic, complemented
68#63974—31no—
69#63971—31no—
70#63970—31no—
71#63969—31no—
72#63966D311yescharacteristic, complemented
73#63959D311yescharacteristic, complemented
74#63958—31no—
75#63958—31no—
76#63958—31no—
77#63958—61no—
78#63956—31no—
79#63952—31no—
80#63952—31no—
81#63952—61no—
82#63923—31no—
83#63922—31no—
84#63921—31no—
85#63921—31no—
86#63915—31no—
87#63907—31no—
88#63907—31no—
89#63895—31no—
90#63894—31no—
91#63888—31no—
92#63884—31no—
93#63881—31no—
94#63880—31no—
95#63871—31no—
96#63868—31no—
97#63862—31no—
98#63859—31no—
99#63858—31no—
100#63858—31no—
101#63854—31no—
102C23×C33C2311yescharacteristic
103C22×C3⋊(C3⋊D3)C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×D3×C3⋊D3—22no—
108C2×D3×C3⋊D3—41no—
109C2×D3×C3⋊D3—41no—
110#6312—22no—
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C3×#638—41no—
113C3×#638—41no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C32×#67—41no—
119C2×C32×Dic3—41no—
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125#6295—41no—
126#6294—41no—
127#6292—22no—
128#6289—41no—
129#6289—41no—
130C3×#627—41no—
131C3×#626—41no—
132#5678—91no—
133#5657—91no—
134#5613—91no—
135C23×C3⋊D3—31no—
136C22×D32—31no—
137C22×D32—31no—
138C22×D32—61no—
139C2×C32×D4—31no—
140C22×C32×C4—31no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#638—31no—
144C2×#638—61no—
145C2×#638—61no—
146C2×#638—61no—
147C2×#638—121no—
148C2×#638C2×D311yescharacteristic
149C2×#638C2×D311yescharacteristic, complemented
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—31no—
153C2×C3×#67—21no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—61no—
160C2×C3×#67—61no—
161C2×C3×#67C2×D311yescharacteristic
162C2×C3×#67C2×D311yescharacteristic
163C22×C3×Dic3—21no—
164C22×C3×Dic3C2×D311yescharacteristic, complemented
165C22×C3×Dic3C2×D311yescharacteristic, complemented
166C2×C3×D12—31no—
167C2×C3×Dic6—31no—
168C2×C3×Dic6—31no—
169C2×#627C2×D311yescharacteristic, complemented
170C2×#626—31no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626—61no—
175C2×#626C2×D311yescharacteristic
176C2×#625—31no—
177C2×#624—31no—
178C2×#624—31no—
179C2×#624—31no—
180C2×#624—31no—
181C2×#624—31no—
182C2×#624—61no—
183C2×#624—61no—
184C2×D3×Dic3—31no—
185C2×D3×Dic3—31no—
186C32×C22⋊C4—31no—
187#3757—31no—
188#3757C2×D311yescharacteristic, complemented
189#3752—31no—
190#3752—31no—
191#3752—31no—
192#3752—31no—
193#3750—31no—
194#3750—31no—
195C4×C3⋊Dic3—31no—
196C3×#217—21no—
197C3×#217—31no—
198C3×#217—31no—
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—61no—
203C3×#217C2×D311yescharacteristic, complemented
204C3×#217C2×D311yescharacteristic, complemented
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4—31no—
211C3×(C2×D3)⋊C4—31no—
212C3×(C2×D3)⋊C4—31no—
213C3×(C2×D3)⋊C4—31no—
214C3×C4⋊Dic3—31no—
215C3×C4⋊Dic3—31no—
216C3×C4⋊Dic3—31no—
217C3×Dic3⋊C4—31no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×C4×Dic3—31no—
221C3×C4×Dic3—31no—
222#3724—31no—
223#3724—31no—
224#3724—31no—
225#3724—61no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3C2×D311yescharacteristic, complemented
232Dic3⋊Dic3C2×D311yescharacteristic, complemented
233Dic3⋊Dic3C2×D311yescharacteristic, complemented
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—61no—
240#3722—61no—
241#3722C2×D311yescharacteristic
242#3722C2×D311yescharacteristic
243#3722C2×D311yescharacteristic, complemented
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—61no—
253(C2×D3)⋊Dic3—61no—
254(C2×D3)⋊Dic3—61no—
255(C2×D3)⋊Dic3C2×D311yescharacteristic
256(C2×D3)⋊Dic3C2×D311yescharacteristic
257(C2×D3)⋊Dic3C2×D311yescharacteristic
258Dic32—31no—
259Dic32—31no—
260Dic32—61no—
261Dic32C2×D311yescharacteristic, complemented
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
265C22×C33C2411yescharacteristic
266C2×C3⋊(C3⋊D3)—21no—
267C2×C3⋊(C3⋊D3)—21no—
268C2×C3⋊(C3⋊D3)#4112yes—
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×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278D3×C3⋊D3—44no—
279C3⋊(C3⋊Dic3)—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#124—91no—
290C3×#123—91no—
291C3×#121—91no—
292#947—91no—
293#946—91no—
294#939—31no—
295#939—91no—
296#938—91no—
297#938—91no—
298#937—91no—
299#937—91no—
300#937—91no—
301#937—91no—
302#937—181no—
303#936—31no—
304#935—91no—
305#930—31no—
306#929—31no—
307C4×#67—91no—
308C4×#67—91no—
309C4×#67—181no—
310#898—91no—
311#898—91no—
312#897—91no—
313#896—91no—
314#894—91no—
315#893—91no—
316#886—31no—
317#885—31no—
318#885—91no—
319#885—91no—
320#884—91no—
321#884—91no—
322#884—91no—
323#884—181no—
324#883—91no—
325#882—91no—
326#882—91no—
327#67⋊C4—91no—
328#67⋊C4—91no—
329D3×C22⋊C4—91no—
330D3×C22⋊C4—91no—
331D3×C22⋊C4—91no—
332#879—91no—
333#879—91no—
334#879—91no—
335#876—91no—
336C4×D12—91no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—31no—
341C23×C32—41no—
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C23×C32C22×D311yescharacteristic
345C22×C3⋊D3—31no—
346C22×C3⋊D3—31no—
347C22×C3⋊D3—31no—
348C22×C3⋊D3—61no—
349C22×C3⋊D3—61no—
350C22×C3⋊D3—61no—
351C22×C3⋊D3—62no—
352C22×C3⋊D3—121no—
353C22×C3⋊D3—121no—
354C22×C3⋊D3—121no—
355C22×C3⋊D3C22×D311yescharacteristic
356C22×C3⋊D3C22×D311yescharacteristic
357C22×C3×D3—21no—
358C22×C3×D3—31no—
359C22×C3×D3—31no—
360C22×C3×D3—31no—
361C22×C3×D3—31no—
362C22×C3×D3—61no—
363C22×C3×D3—61no—
364C22×C3×D3C22×D311yescharacteristic
365C22×C3×D3C22×D311yescharacteristic
366C2×D32—62no—
367C2×D32—62no—
368C2×D32—122no—
369C2×D32—121no—
370C2×D32—121no—
371C2×D32—121no—
372C2×D32—121no—
373C2×D32—122no—
374C2×D32—122no—
375C32×D4—121no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—31no—
379C2×C32×C4—31no—
380C2×C32×C4—31no—
381C2×C32×C4—121no—
382#638—41no—
383#638—41no—
384#638—62no—
385#638—62no—
386#638—62no—
387#638—64no—
388#638—122no—
389#638—122no—
390#638—124no—
391C2×C3⋊Dic3—31no—
392C2×C3⋊Dic3—31no—
393C2×C3⋊Dic3—31no—
394C2×C3⋊Dic3—61no—
395C2×C3⋊Dic3—61no—
396C2×C3⋊Dic3—61no—
397C2×C3⋊Dic3—121no—
398C2×C3⋊Dic3C22×D311yescharacteristic
399C2×C3⋊Dic3C22×D311yescharacteristic
400C2×C3⋊Dic3C22×D311yescharacteristic
401C2×C3⋊Dic3C22×D311yescharacteristic
402C4⋊(C3⋊D3)—62no—
403C4×C3⋊D3—121no—
404C4×C3⋊D3—121no—
405C3×#67—41no—
406C3×#67—41no—
407C3×#67—42no—
408C3×#67—121no—
409C3×#67—121no—
410C3×#67—121no—
411C3×#67—121no—
412C3×#67—121no—
413C3×#67—122no—
414C3×#67—122no—
415C2×C3×Dic3—21no—
416C2×C3×Dic3—21no—
417C2×C3×Dic3—21no—
418C2×C3×Dic3—21no—
419C2×C3×Dic3—21no—
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—41no—
429C2×C3×Dic3—41no—
430C2×C3×Dic3—42no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C3×D12—121no—
446C3×Dic6—121no—
447C3×Dic6—121no—
448#627—41no—
449#626—41no—
450#626—62no—
451#626—62no—
452#626—122no—
453#626—121no—
454#626—121no—
455#625—121no—
456#624—121no—
457#624—121no—
458#624—121no—
459#624—121no—
460#624—122no—
461#624—122no—
462#624—121no—
463D3×Dic3—121no—
464D3×Dic3—121no—
465#538—271noSylow
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—
473C32×D3—41no—
474C23×D3—91no—
475C23×D3—91no—
476C23×D3—91no—
477C23×D3—181no—
478C2×C3×Q8—91no—
479C2×C3×D4—31no—
480C2×C3×D4—31no—
481C2×C3×D4—61no—
482C2×C3×D4—91no—
483C2×C3×D4—91no—
484C2×C3×D4—91no—
485C22×C3×C4—31no—
486C22×C3×C4—31no—
487C22×C3×C4—61no—
488C2×#67—31no—
489C2×#67—31no—
490C2×#67—31no—
491C2×#67—31no—
492C2×#67—31no—
493C2×#67—61no—
494C2×#67—61no—
495C2×#67—91no—
496C2×#67—91no—
497C2×#67—91no—
498C2×#67—91no—
499C2×#67—91no—
500C2×#67—91no—
501C2×#67—181no—
502C2×#67—181no—
503C2×#67—181no—
504C2×#67—361no—
505C2×#67D3211yescharacteristic
506C22×Dic3—91no—
507C22×Dic3D3211yescharacteristic, complemented
508C2×D12—31no—
509C2×D12—91no—
510C2×D12—91no—
511C2×D12—91no—
512C2×D12—181no—
513C2×C4×D3—91no—
514C2×C4×D3—91no—
515C2×C4×D3—91no—
516C2×C4×D3—91no—
517C2×C4×D3—91no—
518C2×C4×D3—91no—
519C2×C4×D3—91no—
520C2×C4×D3—91no—
521C2×C4×D3—181no—
522C2×C4×D3—181no—
523C2×Dic6—31no—
524C2×Dic6—31no—
525C3×C4⋊C4—91no—
526C3×C4⋊C4—91no—
527C3×C4⋊C4—91no—
528C3×C22⋊C4—31no—
529C3×C22⋊C4—31no—
530C3×C22⋊C4—61no—
531C3×C22⋊C4—91no—
532C3×C22⋊C4—91no—
533C3×C22⋊C4—91no—
534C3×C22⋊C4—91no—
535C3×C22⋊C4—91no—
536C3×C22⋊C4—91no—
537C3×C22⋊C4—91no—
538C3×C42—91no—
539#217—31no—
540#217—31no—
541#217—31no—
542#217—31no—
543#217—31no—
544#217—61no—
545#217—91no—
546#217—91no—
547#217—91no—
548#217—91no—
549#217—91no—
550#217—181no—
551#217D3211yescharacteristic, complemented
552(C2×D3)⋊C4—31no—
553(C2×D3)⋊C4—31no—
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—31no—
556(C2×D3)⋊C4—31no—
557(C2×D3)⋊C4—31no—
558(C2×D3)⋊C4—31no—
559(C2×D3)⋊C4—31no—
560(C2×D3)⋊C4—31no—
561(C2×D3)⋊C4—91no—
562(C2×D3)⋊C4—91no—
563(C2×D3)⋊C4—91no—
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—181no—
575(C2×D3)⋊C4—181no—
576(C2×D3)⋊C4—181no—
577(C2×D3)⋊C4—181no—
578C4⋊Dic3—31no—
579C4⋊Dic3—31no—
580C4⋊Dic3—31no—
581C4⋊Dic3—91no—
582C4⋊Dic3—91no—
583Dic3⋊C4—31no—
584Dic3⋊C4—31no—
585Dic3⋊C4—31no—
586Dic3⋊C4—91no—
587Dic3⋊C4—91no—
588Dic3⋊C4—91no—
589Dic3⋊C4—91no—
590Dic3⋊C4—91no—
591Dic3⋊C4—91no—
592Dic3⋊C4—91no—
593Dic3⋊C4—181no—
594Dic3⋊C4—181no—
595C4×Dic3—31no—
596C4×Dic3—31no—
597C4×Dic3—91no—
598C4×Dic3—91no—
599C4×Dic3—91no—
600C4×Dic3—181no—
601C22×C32—21no—
602C22×C32—22no—
603C22×C32—21no—
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—41no—
615C22×C32—41no—
616C22×C32—41no—
617C22×C32—42no—
618C22×C32—41no—
619C22×C32—41no—
620C22×C32—41no—
621C22×C32—41no—
622C22×C32—41no—
623C22×C32—41no—
624C22×C32—61no—
625C22×C32—61no—
626C22×C32—61no—
627C22×C32—81no—
628C22×C32—81no—
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—32no—
639C2×C3⋊D3—32no—
640C2×C3⋊D3—32no—
641C2×C3⋊D3—62no—
642C2×C3⋊D3—62no—
643C2×C3⋊D3—62no—
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—122no—
651C2×C3⋊D3—121no—
652C2×C3⋊D3—121no—
653C2×C3⋊D3—121no—
654C2×C3⋊D3—121no—
655C2×C3⋊D3—121no—
656C2×C3⋊D3—121no—
657C2×C3⋊D3—124no—
658C2×C3⋊D3—241no—
659C2×C3⋊D3—241no—
660C2×C3×D3—22no—
661C2×C3×D3—21no—
662C2×C3×D3—21no—
663C2×C3×D3—21no—
664C2×C3×D3—21no—
665C2×C3×D3—21no—
666C2×C3×D3—21no—
667C2×C3×D3—41no—
668C2×C3×D3—41no—
669C2×C3×D3—62no—
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—61no—
681C2×C3×D3—61no—
682C2×C3×D3—121no—
683C2×C3×D3—121no—
684C2×C3×D3—121no—
685C2×C3×D3—121no—
686C2×C3×D3—121no—
687D32—124no—
688D32—124no—
689D32—128no—
690C32×C4—61no—
691C32×C4—61no—
692C32×C4—61no—
693C32×C4—61no—
694C32×C4—61no—
695C3⋊Dic3—21no—
696C3⋊Dic3—21no—
697C3⋊Dic3—21no—
698C3⋊Dic3—21no—
699C3⋊Dic3—61no—
700C3⋊Dic3—62no—
701C3⋊Dic3—61no—
702C3⋊Dic3—61no—
703C3⋊Dic3—121no—
704C3⋊Dic3—121no—
705C3⋊Dic3—122no—
706C3×Dic3—22no—
707C3×Dic3—21no—
708C3×Dic3—21no—
709C3×Dic3—21no—
710C3×Dic3—21no—
711C3×Dic3—21no—
712C3×Dic3—21no—
713C3×Dic3—21no—
714C3×Dic3—21no—
715C3×Dic3—21no—
716C3×Dic3—21no—
717C3×Dic3—41no—
718C3×Dic3—41no—
719C3×Dic3—41no—
720C3×Dic3—41no—
721C3×Dic3—62no—
722C3×Dic3—61no—
723C3×Dic3—61no—
724C3×Dic3—61no—
725C3×Dic3—61no—
726C3×Dic3—61no—
727C3×Dic3—61no—
728C3×Dic3—61no—
729C3×Dic3—61no—
730C3×Dic3—121no—
731C3×Dic3—121no—
732C3×Dic3—121no—
733#126—271no—
734#126—271no—
735#124—91no—
736#124—271no—
737#123—91no—
738#123—271no—
739C22⋊Q8—271no—
740#121—91no—
741#121—271no—
742#121—271no—
743#120—271no—
744#120—271no—
745C4×D4—271no—
746C4×D4—271no—
747C2×C22⋊C4—271no—
748C33#53811yescharacteristic, complemented, Sylow
749C23×C3—21no—
750C23×C3—21no—
751C23×C3—21no—
752C23×C3—31no—
753C23×C3—31no—
754C23×C3—41no—
755C23×C3—61no—
756C23×C3—91no—
757C23×C3—91no—
758C23×C3C2×D3211yescharacteristic
759C23×C3C2×D3211yescharacteristic
760C23×C3C2×D3211yescharacteristic
761C22×D3—31no—
762C22×D3—31no—
763C22×D3—31no—
764C22×D3—31no—
765C22×D3—61no—
766C22×D3—61no—
767C22×D3—91no—
768C22×D3—91no—
769C22×D3—91no—
770C22×D3—181no—
771C22×D3—181no—
772C22×D3—181no—
773C22×D3—182no—
774C22×D3—182no—
775C22×D3—182no—
776C22×D3—361no—
777C22×D3—362no—
778C22×D3—361no—
779C22×D3—361no—
780C22×D3—361no—
781C22×D3—361no—
782C22×D3—361no—
783C22×D3—361no—
784C22×D3—362no—
785C22×D3—362no—
786C22×D3C2×D3211yescharacteristic
787C3×Q8—361no—
788C3×D4—121no—
789C3×D4—121no—
790C3×D4—122no—
791C3×D4—361no—
792C3×D4—361no—
793C3×D4—361no—
794C2×C3×C4—31no—
795C2×C3×C4—31no—
796C2×C3×C4—31no—
797C2×C3×C4—31no—
798C2×C3×C4—31no—
799C2×C3×C4—31no—
800C2×C3×C4—31no—
801C2×C3×C4—31no—
802C2×C3×C4—31no—
803C2×C3×C4—31no—
804C2×C3×C4—61no—
805C2×C3×C4—61no—
806C2×C3×C4—61no—
807C2×C3×C4—61no—
808C2×C3×C4—61no—
809C2×C3×C4—91no—
810C2×C3×C4—91no—
811C2×C3×C4—91no—
812C2×C3×C4—91no—
813C2×C3×C4—121no—
814C2×C3×C4—121no—
815C2×C3×C4—122no—
816#67—41no—
817#67—121no—
818#67—121no—
819#67—121no—
820#67—121no—
821#67—121no—
822#67—122no—
823#67—122no—
824#67—182no—
825#67—182no—
826#67—182no—
827#67—182no—
828#67—184no—
829#67—362no—
830#67—362no—
831#67—364no—
832#67—361no—
833#67—361no—
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—41no—
843C2×Dic3—61no—
844C2×Dic3—61no—
845C2×Dic3—61no—
846C2×Dic3—61no—
847C2×Dic3—91no—
848C2×Dic3—91no—
849C2×Dic3—91no—
850C2×Dic3—181no—
851C2×Dic3—181no—
852C2×Dic3—181no—
853C2×Dic3—361no—
854C2×Dic3—361no—
855C2×Dic3C2×D3211yescharacteristic
856C2×Dic3C2×D3211yescharacteristic
857C2×Dic3C2×D3211yescharacteristic
858C2×Dic3C2×D3211yescharacteristic
859C2×Dic3C2×D3211yescharacteristic
860D12—121no—
861D12—182no—
862D12—182no—
863D12—362no—
864D12—361no—
865C4×D3—361no—
866C4×D3—361no—
867C4×D3—361no—
868C4×D3—361no—
869C4×D3—361no—
870C4×D3—361no—
871C4×D3—362no—
872C4×D3—361no—
873C4×D3—361no—
874C4×D3—362no—
875Dic6—121no—
876Dic6—121no—
877C2×C32—21no—
878C2×C32—21no—
879C2×C32—21no—
880C2×C32—21no—
881C2×C32—21no—
882C2×C32—21no—
883C2×C32—21no—
884C2×C32—21no—
885C2×C32—21no—
886C2×C32—41no—
887C2×C32—41no—
888C2×C32—41no—
889C2×C32—41no—
890C2×C32—42no—
891C2×C32—41no—
892C2×C32—41no—
893C2×C32—81no—
894C2×C32—81no—
895C2×C32—82no—
896C2×C32—121no—
897C2×C32#100411yescharacteristic
898C2×C32#100411yescharacteristic
899C2×C32#100411yescharacteristic
900C2×C32#100411yescharacteristic
901C2×C32D3×#4111yescharacteristic
902C2×C32D3×#4111yescharacteristic
903C2×C32D3×#4111yescharacteristic
904C2×C32#100911yescharacteristic
905C2×C32#100911yescharacteristic
906C3⋊D3—41no—
907C3⋊D3—41no—
908C3⋊D3—62no—
909C3⋊D3—62no—
910C3⋊D3—62no—
911C3⋊D3—122no—
912C3⋊D3—122no—
913C3⋊D3—122no—
914C3⋊D3—242no—
915C3×D3—42no—
916C3×D3—41no—
917C3×D3—41no—
918C3×D3—122no—
919C3×D3—121no—
920C3×D3—121no—
921C3×D3—121no—
922C3×D3—121no—
923C3×D3—241no—
924C24—271no—
925C2×Q8—91no—
926C2×D4—31no—
927C2×D4—91no—
928C2×D4—91no—
929C2×D4—91no—
930C2×D4—271no—
931C2×D4—271no—
932C2×D4—271no—
933C22×C4—31no—
934C22×C4—271no—
935C22×C4—271no—
936C22×C4—271no—
937C4⋊C4—91no—
938C4⋊C4—91no—
939C4⋊C4—91no—
940C4⋊C4—271no—
941C4⋊C4—271no—
942C4⋊C4—271no—
943C22⋊C4—31no—
944C22⋊C4—91no—
945C22⋊C4—91no—
946C22⋊C4—91no—
947C22⋊C4—91no—
948C22⋊C4—91no—
949C22⋊C4—91no—
950C22⋊C4—91no—
951C22⋊C4—271no—
952C22⋊C4—271no—
953C22⋊C4—271no—
954C22⋊C4—271no—
955C22⋊C4—271no—
956C22⋊C4—271no—
957C42—91no—
958C42—271no—
959C22×C3—22no—
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—41no—
973C22×C3—41no—
974C22×C3—41no—
975C22×C3—41no—
976C22×C3—41no—
977C22×C3—41no—
978C22×C3—41no—
979C22×C3—41no—
980C22×C3—42no—
981C22×C3—41no—
982C22×C3—62no—
983C22×C3—61no—
984C22×C3—61no—
985C22×C3—61no—
986C22×C3—61no—
987C22×C3—61no—
988C22×C3—61no—
989C22×C3—81no—
990C22×C3—81no—
991C22×C3—121no—
992C22×C3—121no—
993C22×C3—181no—
994C22×C3—181no—
995C22×C3—181no—
996C22×C3—181no—
997C22×C3—181no—
998C22×C3—181no—
999C22×C3C22×D3211yescharacteristic
1000C22×C3C22×D3211yescharacteristic
1001C22×C3C22×D3211yescharacteristic
1002C2×D3—21no—
1003C2×D3—21no—
1004C2×D3—21no—
1005C2×D3—62no—
1006C2×D3—61no—
1007C2×D3—61no—
1008C2×D3—61no—
1009C2×D3—61no—
1010C2×D3—61no—
1011C2×D3—61no—
1012C2×D3—61no—
1013C2×D3—61no—
1014C2×D3—61no—
1015C2×D3—61no—
1016C2×D3—61no—
1017C2×D3—61no—
1018C2×D3—92no—
1019C2×D3—92no—
1020C2×D3—92no—
1021C2×D3—121no—
1022C2×D3—121no—
1023C2×D3—121no—
1024C2×D3—121no—
1025C2×D3—121no—
1026C2×D3—182no—
1027C2×D3—182no—
1028C2×D3—182no—
1029C2×D3—181no—
1030C2×D3—181no—
1031C2×D3—181no—
1032C2×D3—181no—
1033C2×D3—181no—
1034C2×D3—181no—
1035C2×D3—362no—
1036C2×D3—361no—
1037C2×D3—361no—
1038C2×D3—361no—
1039C2×D3—361no—
1040C2×D3—361no—
1041C2×D3—361no—
1042C2×D3—364no—
1043C2×D3—364no—
1044C2×D3—364no—
1045C2×D3—368no—
1046C2×D3—721no—
1047C2×D3—721no—
1048C3×C4—62no—
1049C3×C4—61no—
1050C3×C4—61no—
1051C3×C4—61no—
1052C3×C4—61no—
1053C3×C4—61no—
1054C3×C4—61no—
1055C3×C4—61no—
1056C3×C4—61no—
1057C3×C4—61no—
1058C3×C4—61no—
1059C3×C4—121no—
1060C3×C4—121no—
1061C3×C4—121no—
1062C3×C4—121no—
1063C3×C4—181no—
1064C3×C4—181no—
1065C3×C4—181no—
1066C3×C4—181no—
1067Dic3—21no—
1068Dic3—21no—
1069Dic3—21no—
1070Dic3—21no—
1071Dic3—21no—
1072Dic3—62no—
1073Dic3—61no—
1074Dic3—61no—
1075Dic3—61no—
1076Dic3—61no—
1077Dic3—61no—
1078Dic3—61no—
1079Dic3—61no—
1080Dic3—61no—
1081Dic3—121no—
1082Dic3—121no—
1083Dic3—121no—
1084Dic3—182no—
1085Dic3—181no—
1086Dic3—181no—
1087Dic3—181no—
1088Dic3—361no—
1089Dic3—361no—
1090Dic3—362no—
1091C32—21no—
1092C32—21no—
1093C32—21no—
1094C32—41no—
1095C32#561311yescharacteristic, complemented
1096C32#565711yescharacteristic, complemented
1097C32#567811yescharacteristic, complemented
1098C23—31no—
1099C23—91no—
1100C23—91no—
1101C23—271no—
1102C23—542no—
1103C23—1081no—
1104C23—1081no—
1105C23D3311yescharacteristic
1106Q8—361no—
1107D4—121no—
1108D4—361no—
1109D4—361no—
1110D4—361no—
1111D4—542no—
1112D4—542no—
1113D4—1081no—
1114C2×C4—31no—
1115C2×C4—31no—
1116C2×C4—31no—
1117C2×C4—31no—
1118C2×C4—31no—
1119C2×C4—91no—
1120C2×C4—91no—
1121C2×C4—91no—
1122C2×C4—91no—
1123C2×C4—121no—
1124C2×C4—271no—
1125C2×C4—1081no—
1126C2×C4—1081no—
1127C2×C4—1081no—
1128C2×C3—21no—
1129C2×C3—21no—
1130C2×C3—21no—
1131C2×C3—21no—
1132C2×C3—21no—
1133C2×C3—21no—
1134C2×C3—21no—
1135C2×C3—21no—
1136C2×C3—21no—
1137C2×C3—42no—
1138C2×C3—41no—
1139C2×C3—41no—
1140C2×C3—41no—
1141C2×C3—41no—
1142C2×C3—41no—
1143C2×C3—41no—
1144C2×C3—81no—
1145C2×C3—81no—
1146C2×C3—82no—
1147C2×C3—122no—
1148C2×C3—121no—
1149C2×C3—121no—
1150C2×C3—361no—
1151C2×C3—361no—
1152C2×C3#6430611yescharacteristic
1153C2×C3#6430711yescharacteristic
1154C2×C3#6430711yescharacteristic
1155C2×C3#6431211yescharacteristic
1156C2×C3#6431211yescharacteristic
1157C2×C3#6431411yescharacteristic
1158C2×C3#6431411yescharacteristic
1159C2×C3#6433011yescharacteristic
1160C2×C3#6433011yescharacteristic
1161D3—41no—
1162D3—122no—
1163D3—121no—
1164D3—121no—
1165D3—121no—
1166D3—121no—
1167D3—182no—
1168D3—182no—
1169D3—182no—
1170D3—241no—
1171D3—362no—
1172D3—362no—
1173D3—362no—
1174D3—722no—
1175C22—21no—
1176C22—21no—
1177C22—21no—
1178C22—61no—
1179C22—61no—
1180C22—61no—
1181C22—181no—
1182C22—181no—
1183C22—181no—
1184C22—181no—
1185C22—181no—
1186C22—181no—
1187C22—272no—
1188C22—541no—
1189C22—541no—
1190C22—1084no—
1191C22C2×D3311yescharacteristic
1192C4—61no—
1193C4—61no—
1194C4—61no—
1195C4—61no—
1196C4—61no—
1197C4—181no—
1198C4—181no—
1199C4—181no—
1200C4—181no—
1201C4—541no—
1202C3—21no—
1203C3—21no—
1204C3—21no—
1205C3—41no—
1206C3#1059430711yescharacteristic, complemented
1207C3#1059508911yescharacteristic, complemented
1208C3#1059520711yescharacteristic, complemented
1209C2—41no—
1210C2—121no—
1211C2—361no—
1212C2—361no—
1213C2—542no—
1214C2#1172441111yescharacteristic
1215C2#1172441811yescharacteristic
1216C2#1172441811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723725C2semidirect
2. #11723643C2semidirect
3. #11723623C2semidirect
4. #11723618C2semidirect
5. C3×#63978C2semidirect
6. C3×#63966C2semidirect
7. C3×#63959C2semidirect
8. #11723024C2semidirect
9. #11723019C2semidirect
10. #11723007C2semidirect
11. #11722994C2semidirect
12. #11722973C2semidirect
13. #11722950C2semidirect
14. #11722937C2semidirect
15. #11722906C2semidirect
22. C2×C3×#638C22semidirect
24. C22×C32×Dic3C22semidirect
26. C2×#6294C22semidirect
30. C2×C3×#627C22semidirect
32. C3×#3757C22semidirect
33. C32×#217C22semidirect
34. #88815C22semidirect
36. #88807C22semidirect
37. #88806C22semidirect
41. #88803C22semidirect
43. Dic3×C3⋊Dic3C22semidirect
44. C3×Dic3⋊Dic3C22semidirect
45. C3×Dic3⋊Dic3C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
49. C3×#3722C22semidirect
53. C3×Dic32C22semidirect
67. #63978D3semidirect
72. #63966D3semidirect
73. #63959D3semidirect
149. C2×#638C2×D3semidirect
164. C22×C3×Dic3C2×D3semidirect
165. C22×C3×Dic3C2×D3semidirect
169. C2×#627C2×D3semidirect
188. #3757C2×D3semidirect
203. C3×#217C2×D3semidirect
204. C3×#217C2×D3semidirect
231. Dic3⋊Dic3C2×D3semidirect
232. Dic3⋊Dic3C2×D3semidirect
233. Dic3⋊Dic3C2×D3semidirect
243. #3722C2×D3semidirect
261. Dic32C2×D3semidirect
507. C22×Dic3D32semidirect
551. #217D32semidirect
748. C33#538semidirect
1095. C32#5613semidirect
1096. C32#5657semidirect
1097. C32#5678semidirect
1206. C3#10594307semidirect
1207. C3#10595089semidirect
1208. C3#10595207semidirect

Maximal subgroups

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

subgroupindex
#117237252
#117236432
#117236232
#117236182
C3×#639782
C3×#639662
C3×#639592
#117230242
#117230192
#117230072
#117229942
#117229732
#117229502
#117229372
#117229062
#105952073
#105950893
#105943073