Finite Group Databasebeta

← #13172167

Subgroups — #13172167

Order 1728.

1354 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
1#11723727C211yesmaximal, characteristic, complemented
2#11723636C211yesmaximal, characteristic, complemented
3#11723623C211yesmaximal, characteristic, complemented
4#11723592C211yesmaximal, characteristic, complemented
5C3×#63975C211yesmaximal, characteristic, complemented
6C3×#63974C211yesmaximal, characteristic, complemented
7C3×#63956C211yesmaximal, characteristic, complemented
8#11723025C211yesmaximal, characteristic, complemented
9#11723010C211yesmaximal, characteristic, complemented
10#11723000C211yesmaximal, characteristic, complemented
11#11722972C211yesmaximal, characteristic, complemented
12#11722961C211yesmaximal, characteristic, complemented
13#11722961C211yesmaximal, characteristic, complemented
14#11722933C211yesmaximal, characteristic, complemented
15#11722931C211yesmaximal, characteristic, complemented
16#10594232—31nomaximal
17#10594199—31nomaximal
18#10594194—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×#6295C2211yescharacteristic
23C2×#6295C2211yescharacteristic
24C2×#6293C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6292C2211yescharacteristic, complemented
28C2×#6289C2211yescharacteristic, complemented
29C2×C3×#624C2211yescharacteristic
30C2×C3×#624C2211yescharacteristic
31C2×C3×#624C2211yescharacteristic, complemented
32C3×#3757C2211yescharacteristic
33C32×#217C2211yescharacteristic
34C32×#217C2211yescharacteristic
35C32×#217C2211yescharacteristic
36#88814C2211yescharacteristic
37#88814C2211yescharacteristic
38#88807C2211yescharacteristic, complemented
39#88804C2211yescharacteristic, complemented
40#88804C2211yescharacteristic, complemented
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic, complemented
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45C3×#3724C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64094—31no—
55#64093—31no—
56#64091—31no—
57C3×#883—31no—
58C3×#883—31no—
59C3×D3×C22⋊C4—31no—
60C3×D3×C22⋊C4—31no—
61C3×#879—31no—
62C3×#879—31no—
63#63981—31no—
64#63977—31no—
65#63977—31no—
66#63977—31no—
67#63977—61no—
68#63976—31no—
69#63975D311yescharacteristic, complemented
70#63974D311yescharacteristic, complemented
71#63958—31no—
72#63958—31no—
73#63958—61no—
74#63956D311yescharacteristic, complemented
75#63953—31no—
76#63953—31no—
77#63953—61no—
78#63913—31no—
79#63910—31no—
80#63910—31no—
81#63909—31no—
82#63909—31no—
83#63906—31no—
84#63906—31no—
85#63904—31no—
86#63904—31no—
87#63904—31no—
88C4×#626—31no—
89C4×#625—31no—
90#63897—31no—
91#63895—31no—
92#63894—31no—
93#63862—31no—
94#63858—31no—
95#63857—31no—
96#63854—31no—
97#63853—31no—
98#63852—31no—
99#63852—31no—
100#63851—31no—
101#63848—31no—
102C23×C33C2311yescharacteristic
103C22×C3⋊(C3⋊D3)C2311yescharacteristic
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
110#6312—41no—
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C3×#638—41no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6295—22no—
123#6295—41no—
124#6293—41no—
125#6292—22no—
126#6292—41no—
127#6292—41no—
128#6289—41no—
129C3×#624—41no—
130C3×#624—41no—
131C3×#624—41no—
132#5704—91no—
133#5657—91no—
134#5494—91no—
135C23×C3⋊D3C2×D311yescharacteristic
136C23×C3×D3—31no—
137C23×C3×D3—31no—
138C23×C3×D3—61no—
139C2×#638—31no—
140C2×#638—31no—
141C2×#638—31no—
142C2×#638—61no—
143C2×#638—61no—
144C2×#638—61no—
145C2×#638—121no—
146C2×#638C2×D311yescharacteristic
147C2×C4⋊(C3⋊D3)—31no—
148C2×C4⋊(C3⋊D3)—31no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4×C3⋊D3—31no—
151C2×#634—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—61no—
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—31no—
157C2×C3×C4×D3—31no—
158C2×C3×C4×D3—31no—
159C2×C3×C4×D3—31no—
160C2×C3×C4×D3—31no—
161C2×#627—31no—
162C2×#627—31no—
163C2×#627—61no—
164C2×#626—31no—
165C2×#626—31no—
166C2×#626—31no—
167C2×#626—31no—
168C2×#626—31no—
169C2×#626—31no—
170C2×#626—31no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626—61no—
175C2×#626—61no—
176C2×#626—61no—
177C2×#625—31no—
178C2×#625—31no—
179C2×#624—31no—
180C2×#624—31no—
181C2×#624—61no—
182C2×#624C2×D311yescharacteristic
183C2×#624C2×D311yescharacteristic
184C2×#624C2×D311yescharacteristic, complemented
185C32×C22⋊C4—31no—
186C32×C22⋊C4—31no—
187C32×C22⋊C4—31no—
188#3757C2×D311yescharacteristic
189#3752—31no—
190#3752—31no—
191#3752—31no—
192#3752—31no—
193#3752—31no—
194#3750—31no—
195C4×C3⋊Dic3—31no—
196C3×#217—21no—
197C3×#217—21no—
198C3×#217—21no—
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—61no—
202C3×#217C2×D311yescharacteristic
203C3×#217C2×D311yescharacteristic
204C3×#217C2×D311yescharacteristic
205C3×#217C2×D311yescharacteristic
206C3×#217C2×D311yescharacteristic
207C3×#217C2×D311yescharacteristic
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×C4⋊Dic3—31no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4—31no—
224C3×C4×Dic3—31no—
225C3×C4×Dic3—31no—
226#3724C2×D311yescharacteristic, complemented
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—61no—
230Dic3⋊Dic3C2×D311yescharacteristic, complemented
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—31no—
240#3722—61no—
241#3722—61no—
242#3722C2×D311yescharacteristic
243#3722C2×D311yescharacteristic
244#3722C2×D311yescharacteristic, complemented
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—61no—
256(C2×D3)⋊Dic3—61no—
257(C2×D3)⋊Dic3—61no—
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)—21no—
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—
279C3⋊(C3⋊Dic3)—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C32×Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#126—91no—
290C3×#123—91no—
291C2×C3×C22⋊C4—91no—
292#953—91no—
293#953—91no—
294#938—91no—
295#937—91no—
296#930—91no—
297#930—91no—
298C4×#67—91no—
299C4×#67—91no—
300C4×#67—91no—
301#924—91no—
302#898—91no—
303#898—91no—
304#897—91no—
305#896—91no—
306#895—91no—
307#895—91no—
308#894—91no—
309#894—91no—
310#893—91no—
311#893—91no—
312#885—91no—
313#885—91no—
314#885—91no—
315#885—91no—
316#885—91no—
317#885—181no—
318#884—91no—
319#884—91no—
320#884—91no—
321#884—91no—
322#884—181no—
323#883—31no—
324#883—31no—
325#883—91no—
326#882—91no—
327#882—91no—
328#882—91no—
329#882—181no—
330D3×C22⋊C4—31no—
331D3×C22⋊C4—31no—
332#879—31no—
333#879—31no—
334#879—91no—
335#875—91no—
336C4×D12—91no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—41no—
341C23×C32C22×D311yescharacteristic
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C22×C3⋊D3—22no—
345C22×C3⋊D3—31no—
346C22×C3⋊D3—31no—
347C22×C3⋊D3—31no—
348C22×C3⋊D3—41no—
349C22×C3⋊D3—41no—
350C22×C3⋊D3—61no—
351C22×C3⋊D3—61no—
352C22×C3⋊D3—61no—
353C22×C3⋊D3—121no—
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—
375C2×C32×C4—31no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—31no—
379C2×C32×C4—31no—
380C2×C32×C4—31no—
381#638—41no—
382#638—121no—
383#638—121no—
384#638—121no—
385#638—122no—
386#638—122no—
387#638—122no—
388#638—124no—
389C2×C3⋊Dic3—31no—
390C2×C3⋊Dic3—31no—
391C2×C3⋊Dic3—31no—
392C2×C3⋊Dic3—61no—
393C2×C3⋊Dic3—61no—
394C2×C3⋊Dic3—61no—
395C2×C3⋊Dic3—121no—
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C2×C3⋊Dic3C22×D311yescharacteristic
399C4⋊(C3⋊D3)—62no—
400C4⋊(C3⋊D3)—121no—
401C4⋊(C3⋊D3)—121no—
402C4×C3⋊D3—121no—
403#634—121no—
404C3×#67—121no—
405C3×#67—121no—
406C3×#67—122no—
407C2×C3×Dic3—21no—
408C2×C3×Dic3—21no—
409C2×C3×Dic3—21no—
410C2×C3×Dic3—21no—
411C2×C3×Dic3—21no—
412C2×C3×Dic3—21no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—31no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—61no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C3×C4×D3—121no—
435C3×C4×D3—121no—
436C3×C4×D3—121no—
437C3×C4×D3—121no—
438C3×C4×D3—121no—
439C3×C4×D3—121no—
440#627—121no—
441#627—121no—
442#627—122no—
443#626—62no—
444#626—62no—
445#626—62no—
446#626—62no—
447#626—122no—
448#626—121no—
449#626—121no—
450#626—121no—
451#626—121no—
452#626—122no—
453#626—122no—
454#626—121no—
455#626—121no—
456#625—62no—
457#625—121no—
458#624—41no—
459#624—41no—
460#624—41no—
461#624—121no—
462#624—121no—
463#624—122no—
464#538—271noSylow
465C2×C33—41no—
466C2×C33C2×#4111yescharacteristic
467C2×C33H(5,𝔽2)11yescharacteristic
468C2×C33H(5,𝔽2)11yescharacteristic
469C3⋊(C3⋊D3)—41no—
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—91no—
478C22×C3×C4—91no—
479C22×C3×C4—91no—
480C22×C3×C4—91no—
481C2×#67—31no—
482C2×#67—31no—
483C2×#67—61no—
484C2×#67—91no—
485C2×#67—91no—
486C2×#67—91no—
487C2×#67—91no—
488C2×#67—91no—
489C2×#67—91no—
490C2×#67—91no—
491C2×#67—91no—
492C2×#67—91no—
493C2×#67—91no—
494C2×#67—181no—
495C2×#67—181no—
496C2×#67—181no—
497C2×#67—361no—
498C2×D12—91no—
499C2×D12—91no—
500C2×D12—91no—
501C2×D12—91no—
502C2×D12—91no—
503C2×D12—91no—
504C2×D12—91no—
505C2×D12—91no—
506C2×D12—181no—
507C2×D12—181no—
508C2×D12—181no—
509C2×C4×D3—31no—
510C2×C4×D3—31no—
511C2×C4×D3—31no—
512C2×C4×D3—31no—
513C2×C4×D3—31no—
514C2×C4×D3—31no—
515C2×C4×D3—91no—
516C2×C4×D3—91no—
517C2×C4×D3—91no—
518C2×C4×D3—181no—
519C2×Dic6—91no—
520C2×Dic6—91no—
521C2×Dic6—91no—
522C2×Dic6—181no—
523C3×C4⋊C4—91no—
524C3×C4⋊C4—91no—
525C3×C4⋊C4—91no—
526C3×C4⋊C4—91no—
527C3×C4⋊C4—91no—
528C3×C22⋊C4—31no—
529C3×C22⋊C4—31no—
530C3×C22⋊C4—31no—
531C3×C22⋊C4—31no—
532C3×C22⋊C4—31no—
533C3×C22⋊C4—31no—
534C3×C22⋊C4—61no—
535C3×C22⋊C4—61no—
536C3×C22⋊C4—61no—
537C3×C22⋊C4—91no—
538C3×C22⋊C4—91no—
539C3×C22⋊C4—91no—
540C3×C22⋊C4—91no—
541C3×C42—91no—
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#217D3211yescharacteristic
551#217D3211yescharacteristic
552#217D3211yescharacteristic
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—91no—
560(C2×D3)⋊C4—91no—
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—91no—
575(C2×D3)⋊C4—181no—
576(C2×D3)⋊C4—181no—
577(C2×D3)⋊C4—181no—
578(C2×D3)⋊C4—181no—
579(C2×D3)⋊C4—181no—
580C4⋊Dic3—31no—
581C4⋊Dic3—31no—
582C4⋊Dic3—31no—
583C4⋊Dic3—31no—
584C4⋊Dic3—91no—
585Dic3⋊C4—31no—
586Dic3⋊C4—31no—
587Dic3⋊C4—31no—
588Dic3⋊C4—31no—
589Dic3⋊C4—31no—
590Dic3⋊C4—31no—
591Dic3⋊C4—91no—
592Dic3⋊C4—91no—
593Dic3⋊C4—181no—
594C4×Dic3—31no—
595C4×Dic3—31no—
596C4×Dic3—91no—
597C4×Dic3—91no—
598C4×Dic3—91no—
599C4×Dic3—181no—
600C22×C32—21no—
601C22×C32—22no—
602C22×C32—21no—
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—41no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—42no—
617C22×C32—41no—
618C22×C32—41no—
619C22×C32—41no—
620C22×C32—41no—
621C22×C32—41no—
622C22×C32—41no—
623C22×C32—81no—
624C22×C32—81no—
625C22×C32C23×D311yescharacteristic
626C22×C32C23×D311yescharacteristic
627C22×C32C23×D311yescharacteristic
628C2×C3⋊D3—21no—
629C2×C3⋊D3—21no—
630C2×C3⋊D3—21no—
631C2×C3⋊D3—21no—
632C2×C3⋊D3—21no—
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—44no—
637C2×C3⋊D3—61no—
638C2×C3⋊D3—62no—
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—121no—
648C2×C3⋊D3—121no—
649C2×C3⋊D3—122no—
650C2×C3⋊D3—121no—
651C2×C3⋊D3—121no—
652C2×C3⋊D3—121no—
653C2×C3⋊D3—121no—
654C2×C3⋊D3—121no—
655C2×C3⋊D3—121no—
656C2×C3⋊D3—241no—
657C2×C3⋊D3—241no—
658C2×C3⋊D3#23512yes—
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—61no—
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—121no—
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—61no—
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—61no—
699C3⋊Dic3—62no—
700C3⋊Dic3—61no—
701C3⋊Dic3—61no—
702C3⋊Dic3—121no—
703C3⋊Dic3—121no—
704C3⋊Dic3—122no—
705C3×Dic3—21no—
706C3×Dic3—21no—
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—41no—
722C3×Dic3—41no—
723C3×Dic3—62no—
724C3×Dic3—61no—
725C3×Dic3—61no—
726C3×Dic3—61no—
727C3×Dic3—61no—
728C3×Dic3—61no—
729C3×Dic3—61no—
730C3×Dic3—121no—
731C3×Dic3—121no—
732#126—91no—
733#126—271no—
734#124—271no—
735#124—271no—
736#123—91no—
737#123—271no—
738C22⋊Q8—271no—
739#121—271no—
740#121—271no—
741#121—271no—
742#120—271no—
743#120—271no—
744C4×D4—271no—
745C4×D4—271no—
746C2×C22⋊C4—91no—
747C33#53811yescharacteristic, complemented, Sylow
748C23×C3—21no—
749C23×C3—21no—
750C23×C3—21no—
751C23×C3—41no—
752C23×C3—91no—
753C23×C3—91no—
754C23×C3—91no—
755C23×C3—182no—
756C23×C3—361no—
757C23×C3—361no—
758C23×C3C2×D3211yescharacteristic
759C23×C3C2×D3211yescharacteristic
760C23×C3C2×D3211yescharacteristic
761C22×D3—31no—
762C22×D3—31no—
763C22×D3—31no—
764C22×D3—31no—
765C22×D3—31no—
766C22×D3—31no—
767C22×D3—61no—
768C22×D3—61no—
769C22×D3—61no—
770C22×D3—62no—
771C22×D3—62no—
772C22×D3—91no—
773C22×D3—91no—
774C22×D3—91no—
775C22×D3—122no—
776C22×D3—121no—
777C22×D3—121no—
778C22×D3—121no—
779C22×D3—121no—
780C22×D3—122no—
781C22×D3—122no—
782C22×D3—181no—
783C22×D3—181no—
784C22×D3—181no—
785C22×D3—361no—
786C3×D4—361no—
787C2×C3×C4—31no—
788C2×C3×C4—31no—
789C2×C3×C4—31no—
790C2×C3×C4—31no—
791C2×C3×C4—31no—
792C2×C3×C4—31no—
793C2×C3×C4—31no—
794C2×C3×C4—31no—
795C2×C3×C4—31no—
796C2×C3×C4—31no—
797C2×C3×C4—31no—
798C2×C3×C4—31no—
799C2×C3×C4—61no—
800C2×C3×C4—61no—
801C2×C3×C4—61no—
802C2×C3×C4—61no—
803C2×C3×C4—61no—
804C2×C3×C4—61no—
805C2×C3×C4—91no—
806C2×C3×C4—91no—
807C2×C3×C4—91no—
808C2×C3×C4—361no—
809C2×C3×C4—361no—
810C2×C3×C4—361no—
811#67—121no—
812#67—121no—
813#67—122no—
814#67—182no—
815#67—182no—
816#67—182no—
817#67—361no—
818#67—361no—
819#67—361no—
820#67—361no—
821#67—361no—
822#67—361no—
823#67—361no—
824#67—362no—
825#67—362no—
826#67—362no—
827#67—364no—
828C2×Dic3—31no—
829C2×Dic3—31no—
830C2×Dic3—31no—
831C2×Dic3—31no—
832C2×Dic3—31no—
833C2×Dic3—31no—
834C2×Dic3—61no—
835C2×Dic3—61no—
836C2×Dic3—61no—
837C2×Dic3—91no—
838C2×Dic3—91no—
839C2×Dic3—91no—
840C2×Dic3—181no—
841C2×Dic3—181no—
842C2×Dic3—181no—
843C2×Dic3—361no—
844C2×Dic3C2×D3211yescharacteristic
845C2×Dic3C2×D3211yescharacteristic
846C2×Dic3C2×D3211yescharacteristic
847C2×Dic3C2×D3211yescharacteristic
848C2×Dic3C2×D3211yescharacteristic
849C2×Dic3C2×D3211yescharacteristic
850D12—182no—
851D12—182no—
852D12—182no—
853D12—362no—
854D12—361no—
855D12—361no—
856D12—361no—
857D12—361no—
858D12—362no—
859D12—362no—
860D12—361no—
861C4×D3—121no—
862C4×D3—121no—
863C4×D3—121no—
864C4×D3—121no—
865C4×D3—121no—
866C4×D3—121no—
867C4×D3—361no—
868C4×D3—361no—
869C4×D3—361no—
870C4×D3—362no—
871Dic6—361no—
872Dic6—361no—
873Dic6—361no—
874Dic6—362no—
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—42no—
889C2×C32—41no—
890C2×C32—41no—
891C2×C32—81no—
892C2×C32—81no—
893C2×C32—82no—
894C2×C32C2×#23511yescharacteristic
895C2×C32#100411yescharacteristic
896C2×C32#100411yescharacteristic
897C2×C32#100411yescharacteristic
898C2×C32D3×#4111yescharacteristic
899C2×C32D3×#4111yescharacteristic
900C2×C32#100911yescharacteristic
901C2×C32#100911yescharacteristic
902C2×C32#100911yescharacteristic
903C3⋊D3—22no—
904C3⋊D3—41no—
905C3⋊D3—41no—
906C3⋊D3—121no—
907C3⋊D3—122no—
908C3⋊D3—121no—
909C3⋊D3—121no—
910C3⋊D3—241no—
911C3⋊D3—241no—
912C3⋊D3—242no—
913C3×D3—62no—
914C3×D3—62no—
915C3×D3—122no—
916C3×D3—122no—
917C3×D3—121no—
918C3×D3—121no—
919C3×D3—121no—
920C3×D3—121no—
921C3×D3—241no—
922C24—91no—
923C2×Q8—271no—
924C2×D4—91no—
925C2×D4—271no—
926C2×D4—271no—
927C2×D4—271no—
928C2×D4—271no—
929C2×D4—271no—
930C2×D4—271no—
931C22×C4—91no—
932C22×C4—91no—
933C22×C4—91no—
934C22×C4—271no—
935C4⋊C4—91no—
936C4⋊C4—91no—
937C4⋊C4—91no—
938C4⋊C4—91no—
939C4⋊C4—91no—
940C4⋊C4—271no—
941C22⋊C4—31no—
942C22⋊C4—31no—
943C22⋊C4—31no—
944C22⋊C4—91no—
945C22⋊C4—91no—
946C22⋊C4—91no—
947C22⋊C4—91no—
948C22⋊C4—271no—
949C22⋊C4—271no—
950C22⋊C4—271no—
951C22⋊C4—271no—
952C22⋊C4—271no—
953C22⋊C4—271no—
954C22⋊C4—271no—
955C42—91no—
956C42—271no—
957C22×C3—22no—
958C22×C3—21no—
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—41no—
971C22×C3—41no—
972C22×C3—41no—
973C22×C3—41no—
974C22×C3—41no—
975C22×C3—41no—
976C22×C3—41no—
977C22×C3—41no—
978C22×C3—42no—
979C22×C3—41no—
980C22×C3—81no—
981C22×C3—81no—
982C22×C3—92no—
983C22×C3—181no—
984C22×C3—181no—
985C22×C3—181no—
986C22×C3—181no—
987C22×C3—181no—
988C22×C3—181no—
989C22×C3—181no—
990C22×C3—181no—
991C22×C3—364no—
992C22×C3C22×D3211yescharacteristic
993C22×C3C22×D3211yescharacteristic
994C22×C3C22×D3211yescharacteristic
995C2×D3—32no—
996C2×D3—32no—
997C2×D3—62no—
998C2×D3—61no—
999C2×D3—61no—
1000C2×D3—61no—
1001C2×D3—61no—
1002C2×D3—62no—
1003C2×D3—61no—
1004C2×D3—61no—
1005C2×D3—61no—
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—121no—
1016C2×D3—121no—
1017C2×D3—121no—
1018C2×D3—121no—
1019C2×D3—121no—
1020C2×D3—121no—
1021C2×D3—121no—
1022C2×D3—124no—
1023C2×D3—124no—
1024C2×D3—128no—
1025C2×D3—182no—
1026C2×D3—181no—
1027C2×D3—181no—
1028C2×D3—181no—
1029C2×D3—181no—
1030C2×D3—181no—
1031C2×D3—181no—
1032C2×D3—181no—
1033C2×D3—181no—
1034C2×D3—181no—
1035C2×D3—361no—
1036C2×D3—361no—
1037C2×D3—361no—
1038C2×D3—361no—
1039C2×D3—361no—
1040C2×D3—361no—
1041C2×D3—361no—
1042C2×D3—361no—
1043C2×D3—362no—
1044C2×D3—721no—
1045C2×D3—721no—
1046C3×C4—61no—
1047C3×C4—61no—
1048C3×C4—61no—
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—121no—
1059C3×C4—121no—
1060C3×C4—121no—
1061C3×C4—121no—
1062C3×C4—121no—
1063C3×C4—121no—
1064C3×C4—181no—
1065C3×C4—181no—
1066C3×C4—181no—
1067Dic3—21no—
1068Dic3—21no—
1069Dic3—21no—
1070Dic3—21no—
1071Dic3—21no—
1072Dic3—21no—
1073Dic3—62no—
1074Dic3—61no—
1075Dic3—61no—
1076Dic3—61no—
1077Dic3—61no—
1078Dic3—61no—
1079Dic3—61no—
1080Dic3—121no—
1081Dic3—121no—
1082Dic3—182no—
1083Dic3—181no—
1084Dic3—181no—
1085Dic3—181no—
1086Dic3—361no—
1087Dic3—361no—
1088Dic3—362no—
1089C32—21no—
1090C32—21no—
1091C32—21no—
1092C32—41no—
1093C32#549411yescharacteristic, complemented
1094C32#565711yescharacteristic, complemented
1095C32#570411yescharacteristic, complemented
1096C23—91no—
1097C23—91no—
1098C23—91no—
1099C23—182no—
1100C23—271no—
1101C23—361no—
1102C23—361no—
1103C23D3311yescharacteristic
1104Q8—1081no—
1105D4—361no—
1106D4—542no—
1107D4—542no—
1108D4—1081no—
1109D4—1081no—
1110D4—1081no—
1111D4—1081no—
1112C2×C4—31no—
1113C2×C4—31no—
1114C2×C4—31no—
1115C2×C4—31no—
1116C2×C4—31no—
1117C2×C4—31no—
1118C2×C4—91no—
1119C2×C4—91no—
1120C2×C4—91no—
1121C2×C4—271no—
1122C2×C4—361no—
1123C2×C4—361no—
1124C2×C4—361no—
1125C2×C4—1081no—
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—41no—
1137C2×C3—41no—
1138C2×C3—41no—
1139C2×C3—41no—
1140C2×C3—41no—
1141C2×C3—41no—
1142C2×C3—81no—
1143C2×C3—81no—
1144C2×C3—82no—
1145C2×C3—182no—
1146C2×C3—361no—
1147C2×C3—361no—
1148C2×C3D3×#23511yescharacteristic
1149C2×C3D3×#23511yescharacteristic
1150C2×C3#6430811yescharacteristic
1151C2×C3#6431211yescharacteristic
1152C2×C3#6431311yescharacteristic
1153C2×C3#6431411yescharacteristic
1154C2×C3#6431411yescharacteristic
1155C2×C3#6431411yescharacteristic
1156C2×C3#6431411yescharacteristic
1157D3—62no—
1158D3—62no—
1159D3—122no—
1160D3—122no—
1161D3—121no—
1162D3—121no—
1163D3—121no—
1164D3—121no—
1165D3—241no—
1166D3—362no—
1167D3—361no—
1168D3—361no—
1169D3—361no—
1170D3—721no—
1171D3—721no—
1172D3—722no—
1173C22—21no—
1174C22—21no—
1175C22—21no—
1176C22—92no—
1177C22—181no—
1178C22—181no—
1179C22—181no—
1180C22—181no—
1181C22—181no—
1182C22—181no—
1183C22—181no—
1184C22—181no—
1185C22—364no—
1186C22—541no—
1187C22—541no—
1188C22—541no—
1189C22C2×D3311yescharacteristic
1190C4—61no—
1191C4—61no—
1192C4—61no—
1193C4—61no—
1194C4—61no—
1195C4—61no—
1196C4—181no—
1197C4—181no—
1198C4—181no—
1199C4—541no—
1200C3—21no—
1201C3—21no—
1202C3—21no—
1203C3—41no—
1204C3#1059419411yescharacteristic, complemented
1205C3#1059419911yescharacteristic, complemented
1206C3#1059423211yescharacteristic, complemented
1207C2—41no—
1208C2—182no—
1209C2—361no—
1210C2—361no—
1211C2—1081no—
1212C2#1172441011yescharacteristic
1213C2#1172441611yescharacteristic
1214C2#1172442011yescharacteristic
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. #11723727C2semidirect
2. #11723636C2semidirect
3. #11723623C2semidirect
4. #11723592C2semidirect
5. C3×#63975C2semidirect
6. C3×#63974C2semidirect
7. C3×#63956C2semidirect
8. #11723025C2semidirect
9. #11723010C2semidirect
10. #11723000C2semidirect
11. #11722972C2semidirect
12. #11722961C2semidirect
13. #11722961C2semidirect
14. #11722933C2semidirect
15. #11722931C2semidirect
24. C2×#6293C22semidirect
27. C2×#6292C22semidirect
28. C2×#6289C22semidirect
31. C2×C3×#624C22semidirect
38. #88807C22semidirect
39. #88804C22semidirect
40. #88804C22semidirect
43. #88803C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. C3×#3724C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
52. C3×#3722C22semidirect
53. C3×Dic32C22semidirect
69. #63975D3semidirect
70. #63974D3semidirect
74. #63956D3semidirect
184. C2×#624C2×D3semidirect
226. #3724C2×D3semidirect
230. Dic3⋊Dic3C2×D3semidirect
231. Dic3⋊Dic3C2×D3semidirect
232. Dic3⋊Dic3C2×D3semidirect
233. Dic3⋊Dic3C2×D3semidirect
244. #3722C2×D3semidirect
261. Dic32C2×D3semidirect
747. C33#538semidirect
1093. C32#5494semidirect
1094. C32#5657semidirect
1095. C32#5704semidirect
1204. C3#10594194semidirect
1205. C3#10594199semidirect
1206. C3#10594232semidirect

Maximal subgroups

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

subgroupindex
#117237272
#117236362
#117236232
#117235922
C3×#639752
C3×#639742
C3×#639562
#117230252
#117230102
#117230002
#117229722
#117229612
#117229332
#117229312
#105942323
#105941993
#105941943