Finite Group Databasebeta

← #13178289

Subgroups — #13178289

Order 1728.

1672 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic, complemented
2C2×#89046C211yesmaximal, characteristic, complemented
3C3×#64095C211yesmaximal, characteristic, complemented
4C3×#64091C211yesmaximal, characteristic, complemented
5C3×#64090C211yesmaximal, characteristic, complemented
6C2×#88814C211yesmaximal, characteristic, complemented
7#11723717C211yesmaximal, characteristic, complemented
8#11723701C211yesmaximal, characteristic, complemented
9#11723700C211yesmaximal, characteristic, complemented
10#11723696C211yesmaximal, characteristic, complemented
11#11723692C211yesmaximal, characteristic, complemented
12#11723691C211yesmaximal, characteristic, complemented
13#11723690C211yesmaximal, characteristic, complemented
14#11723687C211yesmaximal, characteristic, complemented
15#11723672C211yesmaximal, characteristic, complemented
16#10594294—31nomaximal
17#10594293—31nomaximal
18#10594292—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×#1113C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
25C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
26C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
27C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
28C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
29#89049—24no—
30C2×#6296C2211yescharacteristic, complemented
31C2×#6295C2211yescharacteristic
32C2×#6295C2211yescharacteristic
33C2×#6295C2211yescharacteristic, complemented
34C2×#6295C2211yescharacteristic, complemented
35#89046—24no—
36C2×#6294C2211yescharacteristic
37C2×#6294C2211yescharacteristic, complemented
38C2×#6294C2211yescharacteristic, complemented
39C33×C22⋊C4C2211yescharacteristic, complemented
40C3×#3752C2211yescharacteristic
41C3×#3752C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic, complemented
44C3×#3752C2211yescharacteristic, complemented
45C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47C3×#3750C2211yescharacteristic, complemented
48C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
49#88815C2211yescharacteristic, complemented
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88814C2211yescharacteristic, complemented
53#88814C2211yescharacteristic, complemented
54#88814C2211yescharacteristic, complemented
55#88814C2211yescharacteristic, complemented
56C2×#3811—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×#3805—31no—
60C2×#3804—31no—
61C2×#3804—31no—
62#64095D311yescharacteristic, complemented
63#64091D311yescharacteristic, complemented
64#64090D311yescharacteristic, complemented
65C3×#886—31no—
66C3×#886—31no—
67C3×#886—61no—
68C3×#882—31no—
69C3×#882—31no—
70C3×#882—61no—
71C3×#67⋊C4—31no—
72C3×#67⋊C4—31no—
73C3×#67⋊C4—61no—
74#63980—31no—
75#63978—31no—
76#63978—31no—
77C2×#3722—31no—
78C2×(C2×D3)⋊Dic3—31no—
79C2×(C2×D3)⋊Dic3—31no—
80#63923—31no—
81#63922—31no—
82#63922—31no—
83#63921—31no—
84D3×(C2×D3)⋊C4—31no—
85D3×(C2×D3)⋊C4—31no—
86#63916—31no—
87#63915—31no—
88#63910—31no—
89#63909—31no—
90#63908—31no—
91#63899—31no—
92#63898—31no—
93#63895—31no—
94#63894—31no—
95#63893—31no—
96Dic3×D12—31no—
97#63891—31no—
98#63890—31no—
99#63886—31no—
100#63885—31no—
101#63854—31no—
102#63852—31no—
103#63852—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3—22no—
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—41no—
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C3×C3⋊D3C2311yescharacteristic
112C22×C3×C3⋊D3C2311yescharacteristic
113C2×#1113—22no—
114C2×#1113—22no—
115C2×#1113—41no—
116C2×C33×C4C2311yescharacteristic
117C2×C33×C4C2311yescharacteristic
118C3×#638—22no—
119C3×#638—22no—
120C3×#638D414yescomplemented
121C2×C3×C3⋊Dic3—22no—
122C2×C3×C3⋊Dic3—41no—
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C2×C3×C3⋊Dic3C2311yescharacteristic
126C2×C3×C3⋊Dic3C2311yescharacteristic
127C2×C3×C3⋊Dic3C2311yescharacteristic
128C2×C3×C3⋊Dic3C2311yescharacteristic
129C2×C3×C3⋊Dic3C2311yescharacteristic
130C3×C4⋊(C3⋊D3)—22no—
131C3×C4⋊(C3⋊D3)—41no—
132C3×C4×C3⋊D3—41no—
133#6296—22no—
134#6295—22no—
135#6295—22no—
136#6295—22no—
137#6295—41no—
138#6294—22no—
139#6294—22no—
140#6294—22no—
141#5654—91no—
142#5591—91no—
143#5554—91no—
144C23×C3⋊D3C2×D311yescharacteristic
145C23×C3×D3—31no—
146C23×C3×D3—31no—
147C23×C3×D3—61no—
148C22×D32—31no—
149C22×D32—31no—
150C22×D32—31no—
151C2×#638C2×D311yescharacteristic
152C2×#638C2×D311yescharacteristic
153C2×#638C2×D311yescharacteristic, complemented
154C22×C3⋊Dic3C2×D311yescharacteristic, complemented
155C22×C3⋊Dic3C2×D311yescharacteristic, complemented
156C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
157C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
158C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—31no—
165C2×C3×#67—61no—
166C2×C3×#67—61no—
167C2×C3×#67—61no—
168C22×C3×Dic3—31no—
169C22×C3×Dic3—31no—
170C22×C3×Dic3—31no—
171C22×C3×Dic3—31no—
172C22×C3×Dic3—61no—
173C22×C3×Dic3—61no—
174C2×C3×D12—31no—
175C2×C3×D12—31no—
176C2×C3×D12—31no—
177C2×C3×D12—31no—
178C2×C3×D12—61no—
179C2×C3×D12—61no—
180C2×C3×C4×D3—31no—
181C2×C3×C4×D3—31no—
182C2×C3×C4×D3—61no—
183#3811—64no—
184D3×#67—64no—
185D3×#67—64no—
186C2×#627—31no—
187C2×#627—31no—
188C2×#627—31no—
189C2×#626—31no—
190C2×#626—31no—
191C2×#626—31no—
192C2×#626—31no—
193C2×#626—31no—
194C2×#626—31no—
195C2×#626—31no—
196C2×#626—31no—
197C2×#625—31no—
198C2×#625—31no—
199C2×#625—31no—
200C2×#625—31no—
201C2×#624—31no—
202C2×#624—31no—
203C2×#624—31no—
204#3805—64no—
205#3804—64no—
206#3804—64no—
207C2×D3×Dic3—31no—
208C2×D3×Dic3—31no—
209C2×D3×Dic3—31no—
210C2×D3×Dic3—31no—
211C2×D3×Dic3—31no—
212C2×D3×Dic3—31no—
213C32×C22⋊C4—21no—
214C32×C22⋊C4—21no—
215C32×C22⋊C4—21no—
216C32×C22⋊C4—41no—
217C32×C22⋊C4C2×D311yescharacteristic, complemented
218C32×C22⋊C4C2×D311yescharacteristic, complemented
219C32×C22⋊C4C2×D311yescharacteristic, complemented
220#3752C2×D311yescharacteristic
221#3752C2×D311yescharacteristic, complemented
222#3752C2×D311yescharacteristic, complemented
223#3752C2×D311yescharacteristic, complemented
224#3752C2×D311yescharacteristic, complemented
225C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
226C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
227#3750C2×D311yescharacteristic, complemented
228C4×C3⋊Dic3C2×D311yescharacteristic, complemented
229C3×(C2×D3)⋊C4—31no—
230C3×(C2×D3)⋊C4—31no—
231C3×(C2×D3)⋊C4—31no—
232C3×(C2×D3)⋊C4—31no—
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4—31no—
235C3×(C2×D3)⋊C4—31no—
236C3×(C2×D3)⋊C4—31no—
237C3×(C2×D3)⋊C4—31no—
238C3×(C2×D3)⋊C4—31no—
239C3×(C2×D3)⋊C4—61no—
240C3×(C2×D3)⋊C4—61no—
241C3×(C2×D3)⋊C4—61no—
242C3×(C2×D3)⋊C4—61no—
243C3×(C2×D3)⋊C4—61no—
244C3×C4⋊Dic3—31no—
245C3×C4⋊Dic3—31no—
246C3×C4⋊Dic3—31no—
247C3×C4⋊Dic3—31no—
248C3×C4⋊Dic3—61no—
249C3×C4⋊Dic3—61no—
250C3×Dic3⋊C4—31no—
251C3×Dic3⋊C4—31no—
252C3×Dic3⋊C4—61no—
253C3×C4×Dic3—31no—
254C3×C4×Dic3—31no—
255C3×C4×Dic3—61no—
256#3724—31no—
257Dic3⋊Dic3—31no—
258Dic3⋊Dic3—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—31no—
264#3722—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—31no—
272(C2×D3)⋊Dic3—31no—
273(C2×D3)⋊Dic3—31no—
274(C2×D3)⋊Dic3—31no—
275(C2×D3)⋊Dic3—31no—
276(C2×D3)⋊Dic3—31no—
277C22×C33—21no—
278C22×C33—21no—
279C22×C33C2×D412yes—
280C22×C33C2411yescharacteristic
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3—21no—
284C2×C3×C3⋊D3—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3—21no—
292C2×C3×C3⋊D3—21no—
293C2×C3×C3⋊D3—21no—
294C2×C3×C3⋊D3—44no—
295C2×C3×C3⋊D3C2×D412yes—
296C2×C3×C3⋊D3#4112yescomplemented
297#1113—44no—
298C33×C4—21no—
299C33×C4—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C3×C3⋊Dic3—21no—
305C3×C3⋊Dic3—21no—
306C3×C3⋊Dic3C2×D412yes—
307C22×#67—91no—
308C2×#237—91no—
309C2×#237—91no—
310C2×D3×D4—91no—
311C2×D3×D4—91no—
312C2×#235—91no—
313C3×#123—91no—
314C3×#120—91no—
315C3×C4×D4—91no—
316C2×#217—91no—
317#939—91no—
318#939—91no—
319#939—91no—
320#938—91no—
321#937—91no—
322D4×Dic3—91no—
323#930—91no—
324#930—91no—
325C2×(C2×D3)⋊C4—91no—
326C2×(C2×D3)⋊C4—91no—
327C2×(C2×D3)⋊C4—91no—
328#897—91no—
329#896—91no—
330#895—91no—
331#895—91no—
332#894—91no—
333#893—91no—
334#886—31no—
335#886—31no—
336#886—61no—
337#886—91no—
338#885—91no—
339#885—91no—
340#884—91no—
341#883—91no—
342#882—31no—
343#882—31no—
344#882—61no—
345#882—91no—
346#882—91no—
347#67⋊C4—31no—
348#67⋊C4—31no—
349#67⋊C4—61no—
350D3×C22⋊C4—91no—
351D3×C22⋊C4—91no—
352#878—91no—
353#875—91no—
354C4×D12—91no—
355C23×C32—21no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—41no—
359C23×C32C22×D311yescharacteristic
360C23×C32C22×D311yescharacteristic
361C23×C32C22×D311yescharacteristic
362C22×C3⋊D3—22no—
363C22×C3⋊D3—22no—
364C22×C3⋊D3—41no—
365C22×C3⋊D3C22×D311yescharacteristic
366C22×C3⋊D3C22×D311yescharacteristic
367C22×C3⋊D3C22×D311yescharacteristic
368C22×C3⋊D3C22×D311yescharacteristic
369C22×C3⋊D3C22×D311yescharacteristic
370C22×C3×D3—31no—
371C22×C3×D3—31no—
372C22×C3×D3—31no—
373C22×C3×D3—31no—
374C22×C3×D3—31no—
375C22×C3×D3—31no—
376C22×C3×D3—31no—
377C22×C3×D3—31no—
378C22×C3×D3—31no—
379C22×C3×D3—31no—
380C22×C3×D3—61no—
381C22×C3×D3—61no—
382C22×C3×D3—61no—
383C22×C3×D3—61no—
384C22×C3×D3—61no—
385C22×C3×D3—62no—
386C22×C3×D3—62no—
387C22×C3×D3—62no—
388C22×C3×D3—62no—
389C22×C3×D3—122no—
390C22×C3×D3—122no—
391C22×C3×D3—121no—
392C22×C3×D3—121no—
393C22×C3×D3—122no—
394C2×D32—62no—
395C2×D32—62no—
396C2×D32—62no—
397C2×D32—62no—
398C2×D32—62no—
399C2×D32—62no—
400C2×D32—121no—
401C2×D32—121no—
402C2×D32—121no—
403C2×C32×C4—21no—
404C2×C32×C4—21no—
405C2×C32×C4—21no—
406C2×C32×C4—21no—
407C2×C32×C4—21no—
408C2×C32×C4—21no—
409C2×C32×C4—41no—
410C2×C32×C4—41no—
411C2×C32×C4C22×D311yescharacteristic
412C2×C32×C4C22×D311yescharacteristic
413C2×C32×C4C22×D311yescharacteristic
414C2×C32×C4C22×D311yescharacteristic
415C2×C32×C4C22×D311yescharacteristic
416C2×C32×C4C22×D311yescharacteristic
417#638—22no—
418#638—22no—
419#638D1214yescomplemented
420C2×C3⋊Dic3—22no—
421C2×C3⋊Dic3—41no—
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
429C4⋊(C3⋊D3)—22no—
430C4⋊(C3⋊D3)—41no—
431C4×C3⋊D3—41no—
432C3×#67—34no—
433C3×#67—34no—
434C3×#67—64no—
435C3×#67—62no—
436C3×#67—62no—
437C3×#67—62no—
438C3×#67—62no—
439C3×#67—122no—
440C3×#67—122no—
441C2×C3×Dic3—31no—
442C2×C3×Dic3—31no—
443C2×C3×Dic3—31no—
444C2×C3×Dic3—31no—
445C2×C3×Dic3—31no—
446C2×C3×Dic3—31no—
447C2×C3×Dic3—31no—
448C2×C3×Dic3—31no—
449C2×C3×Dic3—31no—
450C2×C3×Dic3—31no—
451C2×C3×Dic3—31no—
452C2×C3×Dic3—31no—
453C2×C3×Dic3—31no—
454C2×C3×Dic3—31no—
455C2×C3×Dic3—61no—
456C2×C3×Dic3—61no—
457C2×C3×Dic3—61no—
458C2×C3×Dic3—61no—
459C2×C3×Dic3—61no—
460C2×C3×Dic3—61no—
461C2×C3×Dic3—61no—
462C2×C3×Dic3—62no—
463C2×C3×Dic3—62no—
464C2×C3×Dic3—122no—
465C2×C3×Dic3—121no—
466C2×C3×Dic3—121no—
467C2×C3×Dic3—122no—
468C3×D12—62no—
469C3×D12—62no—
470C3×D12—122no—
471C3×D12—121no—
472C3×D12—121no—
473C3×D12—122no—
474C3×C4×D3—121no—
475C3×C4×D3—121no—
476C3×C4×D3—122no—
477#627—62no—
478#627—62no—
479#627—62no—
480#626—62no—
481#626—62no—
482#626—62no—
483#626—62no—
484#626—62no—
485#626—62no—
486#626—121no—
487#626—121no—
488#625—62no—
489#625—62no—
490#625—62no—
491#625—121no—
492#624—62no—
493#624—62no—
494#624—62no—
495D3×Dic3—62no—
496D3×Dic3—62no—
497D3×Dic3—62no—
498D3×Dic3—62no—
499D3×Dic3—62no—
500D3×Dic3—62no—
501#546—271noSylow
502C2×C33—22no—
503C2×C33C22×D411yescharacteristic
504C2×C33C2×#4111yescharacteristic
505C2×C33H(5,𝔽2)11yescharacteristic
506C3×C3⋊D3—22no—
507C3×C3⋊D3—22no—
508C3×C3⋊D3—41no—
509C3×C3⋊D3—41no—
510C3×C3⋊D3—41no—
511C24×C3—91no—
512C23×D3—31no—
513C23×D3—31no—
514C23×D3—61no—
515C23×D3—91no—
516C23×D3—91no—
517C23×D3—91no—
518C2×C3×D4—91no—
519C2×C3×D4—91no—
520C2×C3×D4—91no—
521C2×C3×D4—91no—
522C2×C3×D4—91no—
523C22×C3×C4—91no—
524C22×C3×C4—91no—
525C22×C3×C4—91no—
526C2×#67—31no—
527C2×#67—31no—
528C2×#67—31no—
529C2×#67—31no—
530C2×#67—31no—
531C2×#67—31no—
532C2×#67—61no—
533C2×#67—61no—
534C2×#67—61no—
535C2×#67—91no—
536C2×#67—91no—
537C2×#67—91no—
538C2×#67—91no—
539C2×#67—91no—
540C2×#67—91no—
541C2×#67—91no—
542C2×#67—91no—
543C2×#67—184no—
544C22×Dic3—31no—
545C22×Dic3—31no—
546C22×Dic3—31no—
547C22×Dic3—31no—
548C22×Dic3—61no—
549C22×Dic3—61no—
550C22×Dic3—91no—
551C22×Dic3—91no—
552C22×Dic3—91no—
553#237—184no—
554#237—184no—
555D3×D4—184no—
556D3×D4—184no—
557#235—184no—
558C2×D12—31no—
559C2×D12—31no—
560C2×D12—31no—
561C2×D12—31no—
562C2×D12—61no—
563C2×D12—61no—
564C2×D12—91no—
565C2×D12—91no—
566C2×D12—91no—
567C2×D12—91no—
568C2×C4×D3—31no—
569C2×C4×D3—31no—
570C2×C4×D3—61no—
571C2×C4×D3—91no—
572C2×C4×D3—91no—
573C2×C4×D3—91no—
574C2×C4×D3—91no—
575C2×C4×D3—91no—
576C2×C4×D3—91no—
577C2×Dic6—91no—
578C2×Dic6—91no—
579C2×Dic6—91no—
580C3×C4⋊C4—91no—
581C3×C4⋊C4—91no—
582C3×C4⋊C4—91no—
583C3×C22⋊C4—21no—
584C3×C22⋊C4—21no—
585C3×C22⋊C4—21no—
586C3×C22⋊C4—41no—
587C3×C22⋊C4—91no—
588C3×C22⋊C4—91no—
589C3×C22⋊C4—91no—
590C3×C22⋊C4—91no—
591C3×C22⋊C4—91no—
592C3×C22⋊C4D3211yescharacteristic, complemented
593C3×C22⋊C4D3211yescharacteristic, complemented
594C3×C22⋊C4D3211yescharacteristic, complemented
595C3×C42—91no—
596#217—91no—
597#217—91no—
598#217—91no—
599#217—91no—
600#217—91no—
601#217—91no—
602(C2×D3)⋊C4—31no—
603(C2×D3)⋊C4—31no—
604(C2×D3)⋊C4—31no—
605(C2×D3)⋊C4—31no—
606(C2×D3)⋊C4—31no—
607(C2×D3)⋊C4—31no—
608(C2×D3)⋊C4—31no—
609(C2×D3)⋊C4—31no—
610(C2×D3)⋊C4—31no—
611(C2×D3)⋊C4—31no—
612(C2×D3)⋊C4—61no—
613(C2×D3)⋊C4—61no—
614(C2×D3)⋊C4—61no—
615(C2×D3)⋊C4—61no—
616(C2×D3)⋊C4—61no—
617(C2×D3)⋊C4—91no—
618(C2×D3)⋊C4—91no—
619(C2×D3)⋊C4—91no—
620(C2×D3)⋊C4—91no—
621(C2×D3)⋊C4—91no—
622(C2×D3)⋊C4—91no—
623(C2×D3)⋊C4—91no—
624(C2×D3)⋊C4—91no—
625(C2×D3)⋊C4—91no—
626(C2×D3)⋊C4—91no—
627(C2×D3)⋊C4—91no—
628(C2×D3)⋊C4—91no—
629C4⋊Dic3—31no—
630C4⋊Dic3—31no—
631C4⋊Dic3—31no—
632C4⋊Dic3—31no—
633C4⋊Dic3—61no—
634C4⋊Dic3—61no—
635C4⋊Dic3—91no—
636Dic3⋊C4—31no—
637Dic3⋊C4—31no—
638Dic3⋊C4—61no—
639Dic3⋊C4—91no—
640Dic3⋊C4—91no—
641C4×Dic3—31no—
642C4×Dic3—31no—
643C4×Dic3—61no—
644C22×C32—21no—
645C22×C32—21no—
646C22×C32—21no—
647C22×C32—21no—
648C22×C32—21no—
649C22×C32—21no—
650C22×C32—21no—
651C22×C32—21no—
652C22×C32—21no—
653C22×C32—22no—
654C22×C32—22no—
655C22×C32—22no—
656C22×C32—41no—
657C22×C32—42no—
658C22×C32—41no—
659C22×C32—41no—
660C22×C32—41no—
661C22×C32—41no—
662C22×C32—41no—
663C22×C32—41no—
664C22×C32—81no—
665C22×C32—81no—
666C22×C32C2×D1212yes—
667C22×C32D3×D412yes—
668C22×C32D3×D412yes—
669C22×C32C23×D311yescharacteristic
670C22×C32C23×D311yescharacteristic
671C22×C32C23×D311yescharacteristic
672C2×C3⋊D3—21no—
673C2×C3⋊D3—21no—
674C2×C3⋊D3—21no—
675C2×C3⋊D3—21no—
676C2×C3⋊D3—21no—
677C2×C3⋊D3—21no—
678C2×C3⋊D3—21no—
679C2×C3⋊D3—21no—
680C2×C3⋊D3—21no—
681C2×C3⋊D3—21no—
682C2×C3⋊D3—21no—
683C2×C3⋊D3—21no—
684C2×C3⋊D3—21no—
685C2×C3⋊D3—44no—
686C2×C3⋊D3C2×D1212yes—
687C2×C3⋊D3#23712yescomplemented
688C2×C3×D3—32no—
689C2×C3×D3—32no—
690C2×C3×D3—32no—
691C2×C3×D3—32no—
692C2×C3×D3—62no—
693C2×C3×D3—62no—
694C2×C3×D3—61no—
695C2×C3×D3—61no—
696C2×C3×D3—61no—
697C2×C3×D3—61no—
698C2×C3×D3—61no—
699C2×C3×D3—61no—
700C2×C3×D3—61no—
701C2×C3×D3—61no—
702C2×C3×D3—62no—
703C2×C3×D3—61no—
704C2×C3×D3—61no—
705C2×C3×D3—61no—
706C2×C3×D3—61no—
707C2×C3×D3—61no—
708C2×C3×D3—61no—
709C2×C3×D3—61no—
710C2×C3×D3—61no—
711C2×C3×D3—61no—
712C2×C3×D3—61no—
713C2×C3×D3—61no—
714C2×C3×D3—61no—
715C2×C3×D3—61no—
716C2×C3×D3—61no—
717C2×C3×D3—61no—
718C2×C3×D3—61no—
719C2×C3×D3—61no—
720C2×C3×D3—61no—
721C2×C3×D3—121no—
722C2×C3×D3—121no—
723C2×C3×D3—121no—
724C2×C3×D3—121no—
725C2×C3×D3—121no—
726C2×C3×D3—121no—
727C2×C3×D3—121no—
728C2×C3×D3—121no—
729C2×C3×D3—121no—
730C2×C3×D3—121no—
731C2×C3×D3—121no—
732C2×C3×D3—121no—
733C2×C3×D3—124no—
734C2×C3×D3—124no—
735C2×C3×D3—128no—
736D32—124no—
737D32—124no—
738D32—124no—
739C32×C4—21no—
740C32×C4—21no—
741C32×C4—21no—
742C32×C4—21no—
743C32×C4—21no—
744C32×C4—21no—
745C32×C4—41no—
746C32×C4—41no—
747C32×C4—41no—
748C32×C4—41no—
749C32×C4—41no—
750C32×C4—41no—
751C32×C4—81no—
752C32×C4—81no—
753C3⋊Dic3—21no—
754C3⋊Dic3—21no—
755C3⋊Dic3—21no—
756C3⋊Dic3—21no—
757C3⋊Dic3—21no—
758C3⋊Dic3—21no—
759C3⋊Dic3C2×D1212yes—
760C3×Dic3—32no—
761C3×Dic3—32no—
762C3×Dic3—62no—
763C3×Dic3—62no—
764C3×Dic3—61no—
765C3×Dic3—61no—
766C3×Dic3—61no—
767C3×Dic3—61no—
768C3×Dic3—61no—
769C3×Dic3—61no—
770C3×Dic3—61no—
771C3×Dic3—61no—
772C3×Dic3—61no—
773C3×Dic3—61no—
774C3×Dic3—61no—
775C3×Dic3—61no—
776C3×Dic3—121no—
777C3×Dic3—121no—
778C3×Dic3—121no—
779C3×Dic3—121no—
780C3×Dic3—121no—
781C2×#41—271no—
782C22×D4—271no—
783#124—271no—
784#123—91no—
785#123—271no—
786C22⋊Q8—271no—
787#121—271no—
788#121—271no—
789#121—271no—
790#120—91no—
791#120—271no—
792C4×D4—91no—
793C4×D4—271no—
794C2×C22⋊C4—271no—
795C2×C22⋊C4—271no—
796C33#54611yescharacteristic, complemented, Sylow
797C23×C3—21no—
798C23×C3—21no—
799C23×C3—21no—
800C23×C3—41no—
801C23×C3—91no—
802C23×C3—91no—
803C23×C3—91no—
804C23×C3—91no—
805C23×C3—91no—
806C23×C3—182no—
807C23×C3—182no—
808C23×C3—361no—
809C23×C3C2×D3211yescharacteristic
810C23×C3C2×D3211yescharacteristic
811C23×C3C2×D3211yescharacteristic
812C22×D3—31no—
813C22×D3—31no—
814C22×D3—31no—
815C22×D3—31no—
816C22×D3—31no—
817C22×D3—31no—
818C22×D3—31no—
819C22×D3—31no—
820C22×D3—31no—
821C22×D3—31no—
822C22×D3—61no—
823C22×D3—61no—
824C22×D3—61no—
825C22×D3—61no—
826C22×D3—61no—
827C22×D3—62no—
828C22×D3—62no—
829C22×D3—62no—
830C22×D3—62no—
831C22×D3—122no—
832C22×D3—122no—
833C22×D3—121no—
834C22×D3—121no—
835C22×D3—122no—
836C22×D3—182no—
837C22×D3—182no—
838C22×D3—182no—
839C22×D3—182no—
840C22×D3—182no—
841C22×D3—182no—
842C22×D3—361no—
843C22×D3—361no—
844C22×D3—361no—
845C3×D4—94no—
846C3×D4—182no—
847C3×D4—182no—
848C3×D4—182no—
849C3×D4—361no—
850C2×C3×C4—21no—
851C2×C3×C4—21no—
852C2×C3×C4—21no—
853C2×C3×C4—21no—
854C2×C3×C4—21no—
855C2×C3×C4—21no—
856C2×C3×C4—41no—
857C2×C3×C4—41no—
858C2×C3×C4—91no—
859C2×C3×C4—91no—
860C2×C3×C4—91no—
861C2×C3×C4—91no—
862C2×C3×C4—91no—
863C2×C3×C4—91no—
864C2×C3×C4—91no—
865C2×C3×C4—182no—
866C2×C3×C4—361no—
867C2×C3×C4—361no—
868C2×C3×C4C2×D3211yescharacteristic
869C2×C3×C4C2×D3211yescharacteristic
870C2×C3×C4C2×D3211yescharacteristic
871C2×C3×C4C2×D3211yescharacteristic
872C2×C3×C4C2×D3211yescharacteristic
873C2×C3×C4C2×D3211yescharacteristic
874#67—34no—
875#67—34no—
876#67—64no—
877#67—62no—
878#67—62no—
879#67—62no—
880#67—62no—
881#67—122no—
882#67—122no—
883#67—182no—
884#67—182no—
885#67—182no—
886#67—182no—
887#67—182no—
888#67—182no—
889#67—361no—
890#67—361no—
891C2×Dic3—31no—
892C2×Dic3—31no—
893C2×Dic3—31no—
894C2×Dic3—31no—
895C2×Dic3—31no—
896C2×Dic3—31no—
897C2×Dic3—31no—
898C2×Dic3—31no—
899C2×Dic3—31no—
900C2×Dic3—31no—
901C2×Dic3—31no—
902C2×Dic3—31no—
903C2×Dic3—31no—
904C2×Dic3—31no—
905C2×Dic3—61no—
906C2×Dic3—61no—
907C2×Dic3—61no—
908C2×Dic3—61no—
909C2×Dic3—61no—
910C2×Dic3—61no—
911C2×Dic3—61no—
912C2×Dic3—62no—
913C2×Dic3—62no—
914C2×Dic3—122no—
915C2×Dic3—121no—
916C2×Dic3—121no—
917C2×Dic3—122no—
918C2×Dic3—182no—
919C2×Dic3—182no—
920C2×Dic3—182no—
921D12—62no—
922D12—62no—
923D12—122no—
924D12—121no—
925D12—121no—
926D12—122no—
927D12—182no—
928D12—182no—
929D12—182no—
930D12—361no—
931C4×D3—121no—
932C4×D3—121no—
933C4×D3—122no—
934C4×D3—182no—
935C4×D3—182no—
936C4×D3—182no—
937C4×D3—182no—
938C4×D3—182no—
939C4×D3—182no—
940Dic6—182no—
941Dic6—182no—
942Dic6—182no—
943C2×C32—22no—
944C2×C32—22no—
945C2×C32—22no—
946C2×C32—21no—
947C2×C32—21no—
948C2×C32—21no—
949C2×C32—21no—
950C2×C32—21no—
951C2×C32—21no—
952C2×C32—21no—
953C2×C32—21no—
954C2×C32—21no—
955C2×C32—41no—
956C2×C32—41no—
957C2×C32—41no—
958C2×C32—42no—
959C2×C32—42no—
960C2×C32—42no—
961C2×C32—82no—
962C2×C32C22×D1211yescharacteristic
963C2×C32C2×D3×D411yescharacteristic
964C2×C32C2×D3×D411yescharacteristic
965C2×C32C2×#23711yescharacteristic
966C2×C32#100411yescharacteristic
967C2×C32#100411yescharacteristic
968C2×C32D3×#4111yescharacteristic
969C2×C32D3×#4111yescharacteristic
970C2×C32#100911yescharacteristic
971C3⋊D3—22no—
972C3⋊D3—22no—
973C3⋊D3—41no—
974C3⋊D3—41no—
975C3⋊D3—41no—
976C3×D3—62no—
977C3×D3—62no—
978C3×D3—62no—
979C3×D3—62no—
980C3×D3—122no—
981C3×D3—122no—
982C3×D3—122no—
983C3×D3—121no—
984C3×D3—121no—
985C3×D3—121no—
986C3×D3—121no—
987C3×D3—121no—
988C3×D3—121no—
989C3×D3—241no—
990C3×D3—241no—
991C24—91no—
992C24—271no—
993#41—544no—
994C2×Q8—271no—
995C2×D4—91no—
996C2×D4—91no—
997C2×D4—91no—
998C2×D4—91no—
999C2×D4—91no—
1000C2×D4—271no—
1001C2×D4—271no—
1002C2×D4—271no—
1003C2×D4—271no—
1004C2×D4—544no—
1005C22×C4—91no—
1006C22×C4—91no—
1007C22×C4—91no—
1008C22×C4—271no—
1009C22×C4—271no—
1010C22×C4—271no—
1011C4⋊C4—91no—
1012C4⋊C4—91no—
1013C4⋊C4—91no—
1014C4⋊C4—271no—
1015C22⋊C4—91no—
1016C22⋊C4—91no—
1017C22⋊C4—91no—
1018C22⋊C4—91no—
1019C22⋊C4—91no—
1020C22⋊C4—271no—
1021C22⋊C4—271no—
1022C22⋊C4—271no—
1023C22⋊C4—271no—
1024C22⋊C4—271no—
1025C22⋊C4—271no—
1026C22⋊C4#111311yescharacteristic, complemented
1027C42—91no—
1028C22×C3—21no—
1029C22×C3—21no—
1030C22×C3—21no—
1031C22×C3—21no—
1032C22×C3—21no—
1033C22×C3—21no—
1034C22×C3—21no—
1035C22×C3—21no—
1036C22×C3—21no—
1037C22×C3—22no—
1038C22×C3—22no—
1039C22×C3—22no—
1040C22×C3—41no—
1041C22×C3—41no—
1042C22×C3—41no—
1043C22×C3—41no—
1044C22×C3—41no—
1045C22×C3—41no—
1046C22×C3—41no—
1047C22×C3—42no—
1048C22×C3—81no—
1049C22×C3—81no—
1050C22×C3—92no—
1051C22×C3—92no—
1052C22×C3—181no—
1053C22×C3—181no—
1054C22×C3—181no—
1055C22×C3—181no—
1056C22×C3—181no—
1057C22×C3—181no—
1058C22×C3—181no—
1059C22×C3—181no—
1060C22×C3—181no—
1061C22×C3—181no—
1062C22×C3—181no—
1063C22×C3—181no—
1064C22×C3—181no—
1065C22×C3—364no—
1066C22×C3D3×D1212yes—
1067C22×C3D3×D1212yes—
1068C22×C3#380212yes—
1069C22×C3C22×D3211yescharacteristic
1070C22×C3C22×D3211yescharacteristic
1071C22×C3C22×D3211yescharacteristic
1072C2×D3—32no—
1073C2×D3—32no—
1074C2×D3—32no—
1075C2×D3—32no—
1076C2×D3—62no—
1077C2×D3—62no—
1078C2×D3—61no—
1079C2×D3—61no—
1080C2×D3—61no—
1081C2×D3—61no—
1082C2×D3—61no—
1083C2×D3—61no—
1084C2×D3—61no—
1085C2×D3—61no—
1086C2×D3—62no—
1087C2×D3—61no—
1088C2×D3—61no—
1089C2×D3—61no—
1090C2×D3—61no—
1091C2×D3—61no—
1092C2×D3—61no—
1093C2×D3—61no—
1094C2×D3—61no—
1095C2×D3—61no—
1096C2×D3—61no—
1097C2×D3—61no—
1098C2×D3—61no—
1099C2×D3—61no—
1100C2×D3—61no—
1101C2×D3—61no—
1102C2×D3—61no—
1103C2×D3—61no—
1104C2×D3—61no—
1105C2×D3—121no—
1106C2×D3—121no—
1107C2×D3—121no—
1108C2×D3—121no—
1109C2×D3—121no—
1110C2×D3—121no—
1111C2×D3—121no—
1112C2×D3—121no—
1113C2×D3—121no—
1114C2×D3—121no—
1115C2×D3—121no—
1116C2×D3—121no—
1117C2×D3—124no—
1118C2×D3—124no—
1119C2×D3—128no—
1120C2×D3—364no—
1121C2×D3—364no—
1122C2×D3—364no—
1123C3×C4—21no—
1124C3×C4—21no—
1125C3×C4—21no—
1126C3×C4—21no—
1127C3×C4—21no—
1128C3×C4—21no—
1129C3×C4—41no—
1130C3×C4—41no—
1131C3×C4—41no—
1132C3×C4—41no—
1133C3×C4—41no—
1134C3×C4—41no—
1135C3×C4—81no—
1136C3×C4—81no—
1137C3×C4—92no—
1138C3×C4—181no—
1139C3×C4—181no—
1140C3×C4—181no—
1141C3×C4—181no—
1142C3×C4—181no—
1143C3×C4—181no—
1144Dic3—32no—
1145Dic3—32no—
1146Dic3—62no—
1147Dic3—62no—
1148Dic3—61no—
1149Dic3—61no—
1150Dic3—61no—
1151Dic3—61no—
1152Dic3—61no—
1153Dic3—61no—
1154Dic3—61no—
1155Dic3—61no—
1156Dic3—61no—
1157Dic3—61no—
1158Dic3—61no—
1159Dic3—61no—
1160Dic3—121no—
1161Dic3—121no—
1162Dic3—121no—
1163Dic3—121no—
1164Dic3—121no—
1165C32—21no—
1166C32—21no—
1167C32—21no—
1168C32—41no—
1169C32#555411yescharacteristic, complemented
1170C32#559111yescharacteristic, complemented
1171C32#565411yescharacteristic, complemented
1172C23—91no—
1173C23—91no—
1174C23—91no—
1175C23—91no—
1176C23—91no—
1177C23—182no—
1178C23—182no—
1179C23—361no—
1180C23—542no—
1181C23—542no—
1182C23—1081no—
1183C23C2×#111311yescharacteristic
1184Q8—542no—
1185D4—94no—
1186D4—182no—
1187D4—182no—
1188D4—182no—
1189D4—361no—
1190D4—542no—
1191D4—542no—
1192D4—542no—
1193D4—1081no—
1194C2×C4—91no—
1195C2×C4—91no—
1196C2×C4—91no—
1197C2×C4—91no—
1198C2×C4—91no—
1199C2×C4—91no—
1200C2×C4—91no—
1201C2×C4—182no—
1202C2×C4—361no—
1203C2×C4—361no—
1204C2×C4—542no—
1205C2×C4—542no—
1206C2×C4—542no—
1207C2×C4C2×#111311yescharacteristic
1208C2×C4C2×#111311yescharacteristic
1209C2×C3—22no—
1210C2×C3—22no—
1211C2×C3—22no—
1212C2×C3—21no—
1213C2×C3—21no—
1214C2×C3—21no—
1215C2×C3—21no—
1216C2×C3—21no—
1217C2×C3—21no—
1218C2×C3—21no—
1219C2×C3—21no—
1220C2×C3—21no—
1221C2×C3—42no—
1222C2×C3—42no—
1223C2×C3—42no—
1224C2×C3—41no—
1225C2×C3—41no—
1226C2×C3—41no—
1227C2×C3—82no—
1228C2×C3—182no—
1229C2×C3—182no—
1230C2×C3—361no—
1231C2×C3—361no—
1232C2×C3—361no—
1233C2×C3C2×D3×D1211yescharacteristic
1234C2×C3C2×D3×D1211yescharacteristic
1235C2×C3C2×#380211yescharacteristic
1236C2×C3D3×#23711yescharacteristic
1237C2×C3D3×#23711yescharacteristic
1238C2×C3#6431211yescharacteristic
1239C2×C3#6431311yescharacteristic
1240C2×C3#6431411yescharacteristic
1241C2×C3#6431411yescharacteristic
1242D3—62no—
1243D3—62no—
1244D3—62no—
1245D3—62no—
1246D3—122no—
1247D3—122no—
1248D3—122no—
1249D3—121no—
1250D3—121no—
1251D3—121no—
1252D3—121no—
1253D3—121no—
1254D3—121no—
1255D3—241no—
1256D3—241no—
1257C22—21no—
1258C22—21no—
1259C22—92no—
1260C22—92no—
1261C22—181no—
1262C22—181no—
1263C22—181no—
1264C22—181no—
1265C22—181no—
1266C22—181no—
1267C22—181no—
1268C22—181no—
1269C22—181no—
1270C22—181no—
1271C22—181no—
1272C22—181no—
1273C22—181no—
1274C22—364no—
1275C22—1084no—
1276C22C4⋊#111312yes—
1277C22C22×#111311yescharacteristic
1278C4—21no—
1279C4—21no—
1280C4—92no—
1281C4—181no—
1282C4—181no—
1283C4—181no—
1284C4—181no—
1285C4—181no—
1286C4—181no—
1287C3—21no—
1288C3—21no—
1289C3—21no—
1290C3—41no—
1291C3#1059429211yescharacteristic, complemented
1292C3#1059429311yescharacteristic, complemented
1293C3#1059429411yescharacteristic, complemented
1294C2—22no—
1295C2—182no—
1296C2—182no—
1297C2—361no—
1298C2—361no—
1299C2—361no—
1300C2C2×C4⋊#111311yescharacteristic
1301C2#1172462211yescharacteristic
1302C2#1172462311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4#1113
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#89049C2semidirect
2. C2×#89046C2semidirect
3. C3×#64095C2semidirect
4. C3×#64091C2semidirect
5. C3×#64090C2semidirect
6. C2×#88814C2semidirect
7. #11723717C2semidirect
8. #11723701C2semidirect
9. #11723700C2semidirect
10. #11723696C2semidirect
11. #11723692C2semidirect
12. #11723691C2semidirect
13. #11723690C2semidirect
14. #11723687C2semidirect
15. #11723672C2semidirect
23. C2×C3×#638C22semidirect
24. C22×C3×C3⋊Dic3C22semidirect
25. C22×C3×C3⋊Dic3C22semidirect
27. C2×C3×C4⋊(C3⋊D3)C22semidirect
28. C2×C3×C4×C3⋊D3C22semidirect
30. C2×#6296C22semidirect
33. C2×#6295C22semidirect
34. C2×#6295C22semidirect
37. C2×#6294C22semidirect
38. C2×#6294C22semidirect
39. C33×C22⋊C4C22semidirect
41. C3×#3752C22semidirect
42. C3×#3752C22semidirect
43. C3×#3752C22semidirect
44. C3×#3752C22semidirect
45. C3×C4⋊(C3⋊Dic3)C22semidirect
46. C3×C4⋊(C3⋊Dic3)C22semidirect
47. C3×#3750C22semidirect
48. C3×C4×C3⋊Dic3C22semidirect
49. #88815C22semidirect
52. #88814C22semidirect
53. #88814C22semidirect
54. #88814C22semidirect
55. #88814C22semidirect
62. #64095D3semidirect
63. #64091D3semidirect
64. #64090D3semidirect
120. C3×#638D4semidirect
153. C2×#638C2×D3semidirect
154. C22×C3⋊Dic3C2×D3semidirect
155. C22×C3⋊Dic3C2×D3semidirect
157. C2×C4⋊(C3⋊D3)C2×D3semidirect
158. C2×C4×C3⋊D3C2×D3semidirect
217. C32×C22⋊C4C2×D3semidirect
218. C32×C22⋊C4C2×D3semidirect
219. C32×C22⋊C4C2×D3semidirect
221. #3752C2×D3semidirect
222. #3752C2×D3semidirect
223. #3752C2×D3semidirect
224. #3752C2×D3semidirect
225. C4⋊(C3⋊Dic3)C2×D3semidirect
226. C4⋊(C3⋊Dic3)C2×D3semidirect
227. #3750C2×D3semidirect
228. C4×C3⋊Dic3C2×D3semidirect
296. C2×C3×C3⋊D3#41semidirect
419. #638D12semidirect
592. C3×C22⋊C4D32semidirect
593. C3×C22⋊C4D32semidirect
594. C3×C22⋊C4D32semidirect
687. C2×C3⋊D3#237semidirect
796. C33#546semidirect
1026. C22⋊C4#1113semidirect
1169. C32#5554semidirect
1170. C32#5591semidirect
1171. C32#5654semidirect
1291. C3#10594292semidirect
1292. C3#10594293semidirect
1293. C3#10594294semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
C2×#890462
C3×#640952
C3×#640912
C3×#640902
C2×#888142
#117237172
#117237012
#117237002
#117236962
#117236922
#117236912
#117236902
#117236872
#117236722
#105942943
#105942933
#105942923