Finite Group Databasebeta

← #13170767

Subgroups — #13170767

Order 1728.

1722 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89019C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic
3#11723688C211yesmaximal, characteristic, complemented
4#11723539C211yesmaximal, characteristic
5#11723470C211yesmaximal, characteristic, complemented
6C3×#63896C211yesmaximal, characteristic, complemented
7C3×#63888C211yesmaximal, characteristic, complemented
8C3×#63887C211yesmaximal, characteristic, complemented
9#11722984C211yesmaximal, characteristic, complemented
10#11722975C211yesmaximal, characteristic, complemented
11#11722972C211yesmaximal, characteristic, complemented
12#11722971C211yesmaximal, characteristic, complemented
13#11722912C211yesmaximal, characteristic, complemented
14#11722912C211yesmaximal, characteristic, complemented
15#11722906C211yesmaximal, characteristic
16#10595429—31nomaximal
17#10594624—31nomaximal
18#10594067—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×#634C2211yescharacteristic, complemented
22C2×C32×Dic6C2211yescharacteristic, complemented
23C2×#6294C2211yescharacteristic
24C2×#6293C2211yescharacteristic, complemented
25C2×#6293C2211yescharacteristic, complemented
26C2×#6289C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29C2×#6289C2211yescharacteristic
30C2×#6289C2211yescharacteristic
31#89019—24no—
32C2×C3×#624C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34C2×C3×D3×Dic3C2211yescharacteristic
35D3×#624—24no—
36C3×#3752C2211yescharacteristic
37C3×#3750C2211yescharacteristic, complemented
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×Dic3⋊C4C2211yescharacteristic, complemented
40#88815C2211yescharacteristic, complemented
41#88815C2211yescharacteristic, complemented
42#88814C2211yescharacteristic
43#88807C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88803C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47C3×#3724C2211yescharacteristic, complemented
48C3×#3724C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×Dic3⋊Dic3C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×Q8×C3⋊D3—31no—
57C22×#624—31no—
58C2×C4×D32—31no—
59C2×C4×D32—31no—
60C2×#3797—31no—
61C2×#3797—31no—
62C2×#3797—61no—
63C4⋊C4×C3⋊D3—31no—
64C22⋊C4×C3⋊D3—31no—
65C3×#946—31no—
66C3×#946—31no—
67C3×#896—31no—
68C3×#896—31no—
69C3×#878—31no—
70C3×#878—31no—
71#63974—31no—
72#63964—31no—
73#63964—31no—
74#63921—31no—
75#63921—31no—
76#63921—31no—
77#63921—31no—
78#63921—61no—
79#63900—31no—
80#63900—31no—
81#63896—31no—
82#63896—31no—
83#63896—31no—
84#63896D311yescharacteristic, complemented
85#63895—31no—
86#63895—31no—
87#63893—31no—
88#63893—31no—
89#63888—31no—
90#63888D311yescharacteristic, complemented
91#63887—31no—
92#63887D311yescharacteristic, complemented
93#63883—31no—
94#63883—31no—
95#63883—31no—
96#63883—31no—
97#63883—31no—
98#63883—31no—
99#63883—61no—
100#63857—31no—
101#63857—31no—
102#63851—31no—
103#63851—31no—
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×D3×C3⋊D3—22no—
108C2×D3×C3⋊D3—22no—
109C2×D3×C3⋊D3Q814yescomplemented
110C2×C33×C4C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C4×C3⋊(C3⋊D3)—22no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C3×#634—22no—
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C32×Dic6—22no—
125#6294—22no—
126#6293—22no—
127#6293—22no—
128#6289—22no—
129#6289—22no—
130#6289—22no—
131#6289—22no—
132#6289D414yes—
133C3×#624—22no—
134C3×D3×Dic3—22no—
135C3×D3×Dic3—22no—
136D3×C22⋊Q8—91no—
137D3×C22⋊Q8—91no—
138D3×C22⋊Q8—91no—
139C23×C3⋊D3—31no—
140C22×D32—31no—
141C22×D32—31no—
142C22×D32—61no—
143C2×C32×Q8—31no—
144Q8×C3⋊D3—64no—
145C2×C4×C3⋊D3—31no—
146C2×C4×C3⋊D3—31no—
147C2×C4×C3⋊D3—31no—
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—31no—
153C2×C4×C3⋊D3—61no—
154C2×C4×C3⋊D3—61no—
155C2×C4×C3⋊D3—61no—
156C2×C4×C3⋊D3—121no—
157C2×#634—31no—
158C2×#634—31no—
159C2×#634C2×D311yescharacteristic, complemented
160C22×C3×Dic3—31no—
161C22×C3×Dic3—31no—
162C2×C3×C4×D3—31no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×Dic6—21no—
167C2×C3×Dic6—31no—
168C2×C3×Dic6—31no—
169C2×C3×Dic6—61no—
170C2×C3×Dic6C2×D311yescharacteristic, complemented
171C2×C3×Dic6C2×D311yescharacteristic, complemented
172C2×#627—31no—
173C2×#627—31no—
174C2×#627—31no—
175C2×#627—31no—
176C2×#627—61no—
177C2×#627—61no—
178C2×#624—31no—
179C2×#624—31no—
180C2×#624—31no—
181C2×#624—31no—
182C2×#624—31no—
183C2×#624—31no—
184C2×#624—31no—
185C2×#624—31no—
186C2×#624—31no—
187C2×#624—31no—
188C2×#624—31no—
189C2×#624—64no—
190C2×#624—61no—
191C2×#624—61no—
192C2×#624—61no—
193C2×#624—61no—
194C2×#624—61no—
195C2×#624C2×D311yescharacteristic
196C2×D3×Dic3—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3C2×D311yescharacteristic
199C2×D3×Dic3C2×D311yescharacteristic
200C4×D32—64no—
201C4×D32—64no—
202#3797—64no—
203#3797—64no—
204#3797—68no—
205C32×C4⋊C4—31no—
206C32×C22⋊C4—31no—
207#3757—31no—
208#3752—31no—
209#3752C2×D311yescharacteristic
210C4⋊(C3⋊Dic3)—31no—
211#3750—31no—
212#3750C2×D311yescharacteristic, complemented
213C3×#217—31no—
214C3×#217—31no—
215C3×(C2×D3)⋊C4—21no—
216C3×(C2×D3)⋊C4—31no—
217C3×(C2×D3)⋊C4—31no—
218C3×(C2×D3)⋊C4—31no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×(C2×D3)⋊C4—31no—
222C3×(C2×D3)⋊C4—61no—
223C3×(C2×D3)⋊C4C2×D311yescharacteristic
224C3×(C2×D3)⋊C4C2×D311yescharacteristic
225C3×C4⋊Dic3—31no—
226C3×C4⋊Dic3—31no—
227C3×C4⋊Dic3—31no—
228C3×C4⋊Dic3—31no—
229C3×Dic3⋊C4—21no—
230C3×Dic3⋊C4—31no—
231C3×Dic3⋊C4—31no—
232C3×Dic3⋊C4—31no—
233C3×Dic3⋊C4—31no—
234C3×Dic3⋊C4—31no—
235C3×Dic3⋊C4—31no—
236C3×Dic3⋊C4—31no—
237C3×Dic3⋊C4—31no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—61no—
241C3×Dic3⋊C4C2×D311yescharacteristic, complemented
242C3×Dic3⋊C4C2×D311yescharacteristic, complemented
243#3724—31no—
244#3724—31no—
245#3724C2×D311yescharacteristic, complemented
246#3724C2×D311yescharacteristic, complemented
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—61no—
256Dic3⋊Dic3—61no—
257Dic3⋊Dic3C2×D311yescharacteristic, complemented
258Dic3⋊Dic3C2×D311yescharacteristic, complemented
259Dic3⋊Dic3C2×D311yescharacteristic, complemented
260Dic3⋊Dic3C2×D311yescharacteristic, complemented
261#3722—31no—
262#3722C2×D311yescharacteristic
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—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—61no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3C2×D311yescharacteristic
272(C2×D3)⋊Dic3C2×D311yescharacteristic
273C22×C33C2411yescharacteristic
274C2×C3⋊(C3⋊D3)C2×D412yes—
275C2×C3⋊(C3⋊D3)C2×Q812yes—
276C2×C3⋊(C3⋊D3)#4112yes—
277C2×C3×C3⋊D3—21no—
278C2×C3×C3⋊D3—21no—
279C2×C3×C3⋊D3C2×Q812yescomplemented
280C2×C32×D3—21no—
281C2×C32×D3—21no—
282C2×C32×D3C2×Q812yescomplemented
283D3×C3⋊D3—28no—
284C33×C4—21no—
285C3⋊(C3⋊Dic3)—21no—
286C3×C3⋊Dic3—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×C3⋊Dic3—21no—
290C3×C3⋊Dic3C2×D412yes—
291C32×Dic3—21no—
292C32×Dic3—21no—
293C32×Dic3—21no—
294C32×Dic3—21no—
295C32×Dic3C2×D412yes—
296C2×D3×Q8—91no—
297C2×D3×Q8—91no—
298C2×D3×Q8—91no—
299C2×D3×Q8—181no—
300C22×C4×D3—91no—
301C22×C4×D3—91no—
302C22×C4×D3—91no—
303C3×C22⋊Q8—91no—
304C3×C22⋊Q8—91no—
305C3×C22⋊Q8—91no—
306#946—31no—
307#946—31no—
308#946—91no—
309#924—91no—
310#924—91no—
311#924—91no—
312#897—91no—
313#897—91no—
314#897—91no—
315#896—31no—
316#896—31no—
317#896—91no—
318#896—91no—
319#896—91no—
320#896—91no—
321D3×C4⋊C4—91no—
322D3×C4⋊C4—91no—
323D3×C4⋊C4—91no—
324D3×C4⋊C4—91no—
325D3×C4⋊C4—91no—
326D3×C4⋊C4—91no—
327D3×C4⋊C4—91no—
328D3×C4⋊C4—91no—
329D3×C4⋊C4—91no—
330D3×C4⋊C4—181no—
331D3×C22⋊C4—91no—
332D3×C22⋊C4—91no—
333D3×C22⋊C4—91no—
334D3×C22⋊C4—91no—
335D3×C22⋊C4—91no—
336D3×C22⋊C4—91no—
337D3×C22⋊C4—181no—
338#878—31no—
339#878—31no—
340#878—91no—
341#878—91no—
342#878—91no—
343#878—91no—
344C23×C32—31no—
345C22×C3⋊D3—31no—
346C22×C3⋊D3—31no—
347C22×C3⋊D3—31no—
348C22×C3⋊D3—34no—
349C22×C3⋊D3—61no—
350C22×C3⋊D3—61no—
351C22×C3⋊D3—61no—
352C22×C3⋊D3—62no—
353C22×C3⋊D3—62no—
354C22×C3⋊D3—121no—
355C22×C3⋊D3C22×D311yescharacteristic
356C22×C3×D3—21no—
357C22×C3×D3—31no—
358C22×C3×D3—31no—
359C22×C3×D3—61no—
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C22×D311yescharacteristic
362C2×D32—34no—
363C2×D32—34no—
364C2×D32—64no—
365C2×D32—62no—
366C2×D32—62no—
367C2×D32—62no—
368C2×D32—62no—
369C2×D32—122no—
370C2×D32—122no—
371C32×Q8—62no—
372C2×C32×C4—21no—
373C2×C32×C4—21no—
374C2×C32×C4—21no—
375C2×C32×C4—31no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—31no—
379C2×C32×C4—31no—
380C2×C32×C4—41no—
381C2×C32×C4C22×D311yescharacteristic
382C2×C32×C4C22×D311yescharacteristic
383C2×C32×C4C22×D311yescharacteristic
384C2×C3⋊Dic3—31no—
385C2×C3⋊Dic3—31no—
386C2×C3⋊Dic3—31no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—61no—
390C2×C3⋊Dic3—121no—
391C2×C3⋊Dic3C22×D311yescharacteristic
392C2×C3⋊Dic3C22×D311yescharacteristic
393C2×C3⋊Dic3C22×D311yescharacteristic
394C2×C3⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
396C4×C3⋊D3—34no—
397C4×C3⋊D3—62no—
398C4×C3⋊D3—62no—
399C4×C3⋊D3—62no—
400C4×C3⋊D3—62no—
401C4×C3⋊D3—62no—
402C4×C3⋊D3—62no—
403C4×C3⋊D3—62no—
404C4×C3⋊D3—64no—
405C4×C3⋊D3—122no—
406C4×C3⋊D3—122no—
407C4×C3⋊D3—124no—
408#634—22no—
409#634—62no—
410#634—62no—
411C2×C3×Dic3—21no—
412C2×C3×Dic3—21no—
413C2×C3×Dic3—21no—
414C2×C3×Dic3—21no—
415C2×C3×Dic3—21no—
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—61no—
427C2×C3×Dic3—61no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3—61no—
431C2×C3×Dic3—62no—
432C2×C3×Dic3—62no—
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
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
443C3×C4×D3—62no—
444C3×C4×D3—62no—
445C3×C4×D3—62no—
446C3×C4×D3—62no—
447C3×Dic6—24no—
448C3×Dic6—22no—
449C3×Dic6—22no—
450C3×Dic6—62no—
451C3×Dic6—62no—
452C3×Dic6—64no—
453#627—62no—
454#627—62no—
455#627—64no—
456#627—64no—
457#627—62no—
458#627—62no—
459#624—22no—
460#624—34no—
461#624—34no—
462#624—64no—
463#624—62no—
464#624—62no—
465#624—62no—
466#624—62no—
467#624—62no—
468#624—62no—
469#624—62no—
470#624—62no—
471#624—64no—
472#624—64no—
473#624—62no—
474#624—122no—
475#624—122no—
476D3×Dic3—22no—
477D3×Dic3—22no—
478D3×Dic3—62no—
479D3×Dic3—62no—
480C2×C22⋊Q8—271noSylow
481C2×C33C22×D411yescharacteristic
482C2×C33C22×Q811yescharacteristic
483C2×C33C2×#4111yescharacteristic
484C3⋊(C3⋊D3)C22⋊Q814yescomplemented
485C3×C3⋊D3—22no—
486C32×D3—22no—
487C23×D3—91no—
488C23×D3—91no—
489C23×D3—91no—
490C23×D3—181no—
491C2×C3×Q8—31no—
492C2×C3×Q8—31no—
493C2×C3×Q8—61no—
494C2×C3×Q8—91no—
495C22×C3×C4—91no—
496C22×C3×C4—91no—
497C22×C3×C4—91no—
498C22×Dic3—31no—
499C22×Dic3—31no—
500C22×Dic3—91no—
501D3×Q8—184no—
502D3×Q8—184no—
503D3×Q8—184no—
504D3×Q8—188no—
505C2×C4×D3—31no—
506C2×C4×D3—31no—
507C2×C4×D3—31no—
508C2×C4×D3—31no—
509C2×C4×D3—91no—
510C2×C4×D3—91no—
511C2×C4×D3—91no—
512C2×C4×D3—91no—
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—91no—
522C2×C4×D3—91no—
523C2×C4×D3—91no—
524C2×C4×D3—91no—
525C2×C4×D3—91no—
526C2×C4×D3—91no—
527C2×C4×D3—91no—
528C2×C4×D3—91no—
529C2×C4×D3—181no—
530C2×C4×D3—181no—
531C2×C4×D3—181no—
532C2×C4×D3—181no—
533C2×C4×D3—181no—
534C2×C4×D3—181no—
535C2×C4×D3—181no—
536C2×C4×D3—181no—
537C2×C4×D3—184no—
538C2×C4×D3—184no—
539C2×C4×D3—184no—
540C2×C4×D3—361no—
541C2×Dic6—31no—
542C2×Dic6—31no—
543C2×Dic6—61no—
544C2×Dic6—91no—
545C2×Dic6—91no—
546C2×Dic6—91no—
547C2×Dic6—91no—
548C2×Dic6—91no—
549C2×Dic6—91no—
550C2×Dic6—181no—
551C2×Dic6—181no—
552C2×Dic6D3211yescharacteristic, complemented
553C3×C4⋊C4—31no—
554C3×C4⋊C4—31no—
555C3×C4⋊C4—61no—
556C3×C4⋊C4—91no—
557C3×C4⋊C4—91no—
558C3×C4⋊C4—91no—
559C3×C4⋊C4—91no—
560C3×C4⋊C4—91no—
561C3×C4⋊C4—91no—
562C3×C4⋊C4—91no—
563C3×C22⋊C4—31no—
564C3×C22⋊C4—31no—
565C3×C22⋊C4—61no—
566C3×C22⋊C4—91no—
567C3×C22⋊C4—91no—
568C3×C22⋊C4—91no—
569C3×C22⋊C4—91no—
570#217—31no—
571#217—31no—
572#217—91no—
573#217—91no—
574#217—91no—
575#217—91no—
576#217—181no—
577(C2×D3)⋊C4—31no—
578(C2×D3)⋊C4—31no—
579(C2×D3)⋊C4—31no—
580(C2×D3)⋊C4—31no—
581(C2×D3)⋊C4—31no—
582(C2×D3)⋊C4—31no—
583(C2×D3)⋊C4—61no—
584(C2×D3)⋊C4—91no—
585(C2×D3)⋊C4—91no—
586(C2×D3)⋊C4—91no—
587(C2×D3)⋊C4—91no—
588(C2×D3)⋊C4—91no—
589(C2×D3)⋊C4—181no—
590(C2×D3)⋊C4D3211yescharacteristic
591C4⋊Dic3—31no—
592C4⋊Dic3—31no—
593C4⋊Dic3—31no—
594C4⋊Dic3—31no—
595C4⋊Dic3—91no—
596C4⋊Dic3—91no—
597C4⋊Dic3—91no—
598C4⋊Dic3—91no—
599C4⋊Dic3—91no—
600C4⋊Dic3—181no—
601Dic3⋊C4—31no—
602Dic3⋊C4—31no—
603Dic3⋊C4—31no—
604Dic3⋊C4—31no—
605Dic3⋊C4—31no—
606Dic3⋊C4—31no—
607Dic3⋊C4—31no—
608Dic3⋊C4—31no—
609Dic3⋊C4—31no—
610Dic3⋊C4—31no—
611Dic3⋊C4—61no—
612Dic3⋊C4—91no—
613Dic3⋊C4—91no—
614Dic3⋊C4—91no—
615Dic3⋊C4—91no—
616Dic3⋊C4—91no—
617Dic3⋊C4—91no—
618Dic3⋊C4—91no—
619Dic3⋊C4—181no—
620Dic3⋊C4D3211yescharacteristic, complemented
621C22×C32—21no—
622C22×C32—21no—
623C22×C32—21no—
624C22×C32—32no—
625C22×C32—41no—
626C22×C32—61no—
627C22×C32—61no—
628C22×C32C23×D311yescharacteristic
629C22×C32C23×D311yescharacteristic
630C22×C32C23×D311yescharacteristic
631C2×C3⋊D3—21no—
632C2×C3⋊D3—21no—
633C2×C3⋊D3—32no—
634C2×C3⋊D3—32no—
635C2×C3⋊D3—32no—
636C2×C3⋊D3—32no—
637C2×C3⋊D3—32no—
638C2×C3⋊D3—32no—
639C2×C3⋊D3—32no—
640C2×C3⋊D3—32no—
641C2×C3⋊D3—32no—
642C2×C3⋊D3—62no—
643C2×C3⋊D3—62no—
644C2×C3⋊D3—62no—
645C2×C3⋊D3—62no—
646C2×C3⋊D3—62no—
647C2×C3⋊D3—62no—
648C2×C3⋊D3—62no—
649C2×C3⋊D3—62no—
650C2×C3⋊D3—62no—
651C2×C3⋊D3—68no—
652C2×C3⋊D3—122no—
653C2×C3⋊D3—122no—
654C2×C3⋊D3—122no—
655C2×C3⋊D3D3×Q812yescomplemented
656C2×C3×D3—21no—
657C2×C3×D3—21no—
658C2×C3×D3—21no—
659C2×C3×D3—21no—
660C2×C3×D3—22no—
661C2×C3×D3—32no—
662C2×C3×D3—32no—
663C2×C3×D3—41no—
664C2×C3×D3—41no—
665C2×C3×D3—62no—
666C2×C3×D3—61no—
667C2×C3×D3—61no—
668C2×C3×D3—61no—
669C2×C3×D3—61no—
670C2×C3×D3—121no—
671C2×C3×D3—121no—
672C2×C3×D3D3×Q812yescomplemented
673C2×C3×D3D3×Q812yescomplemented
674D32—68no—
675D32—68no—
676D32—128no—
677C32×C4—21no—
678C32×C4—22no—
679C32×C4—21no—
680C32×C4—21no—
681C32×C4—32no—
682C32×C4—41no—
683C32×C4—41no—
684C32×C4—42no—
685C32×C4—61no—
686C32×C4—61no—
687C32×C4—61no—
688C32×C4—61no—
689C3⋊Dic3—21no—
690C3⋊Dic3—21no—
691C3⋊Dic3—21no—
692C3⋊Dic3—21no—
693C3⋊Dic3—61no—
694C3⋊Dic3—62no—
695C3⋊Dic3—61no—
696C3⋊Dic3—61no—
697C3⋊Dic3—121no—
698C3⋊Dic3—121no—
699C3⋊Dic3—122no—
700C3⋊Dic3D3×D412yes—
701C3×Dic3—22no—
702C3×Dic3—22no—
703C3×Dic3—21no—
704C3×Dic3—21no—
705C3×Dic3—21no—
706C3×Dic3—21no—
707C3×Dic3—21no—
708C3×Dic3—21no—
709C3×Dic3—21no—
710C3×Dic3—21no—
711C3×Dic3—22no—
712C3×Dic3—32no—
713C3×Dic3—32no—
714C3×Dic3—41no—
715C3×Dic3—41no—
716C3×Dic3—62no—
717C3×Dic3—62no—
718C3×Dic3—62no—
719C3×Dic3—61no—
720C3×Dic3—61no—
721C3×Dic3—61no—
722C3×Dic3—61no—
723C3×Dic3—61no—
724C3×Dic3—61no—
725C3×Dic3—61no—
726C3×Dic3—61no—
727C3×Dic3—121no—
728C3×Dic3—121no—
729C3×Dic3D3×D412yes—
730C3×Dic3D3×D412yes—
731C22×Q8—271no—
732C23×C4—271no—
733C22⋊Q8—91no—
734C22⋊Q8—91no—
735C22⋊Q8—91no—
736C22⋊Q8—271no—
737C22⋊Q8—271no—
738C22⋊Q8—271no—
739C22⋊Q8—271no—
740C22⋊Q8—271no—
741C2×C4⋊C4—271no—
742C2×C4⋊C4—271no—
743C2×C4⋊C4—271no—
744C2×C22⋊C4—271no—
745C2×C22⋊C4—271no—
746C33C2×C22⋊Q811yescharacteristic, complemented, Sylow
747C23×C3—31no—
748C23×C3—31no—
749C23×C3—61no—
750C23×C3—91no—
751C22×D3—31no—
752C22×D3—31no—
753C22×D3—61no—
754C22×D3—94no—
755C22×D3—94no—
756C22×D3—91no—
757C22×D3—91no—
758C22×D3—91no—
759C22×D3—94no—
760C22×D3—184no—
761C22×D3—181no—
762C22×D3—181no—
763C22×D3—181no—
764C22×D3—182no—
765C22×D3—182no—
766C22×D3—182no—
767C22×D3—182no—
768C22×D3—182no—
769C22×D3—182no—
770C22×D3—361no—
771C22×D3—362no—
772C22×D3—362no—
773C22×D3C2×D3211yescharacteristic
774C3×Q8—62no—
775C3×Q8—62no—
776C3×Q8—64no—
777C3×Q8—182no—
778C2×C3×C4—21no—
779C2×C3×C4—21no—
780C2×C3×C4—21no—
781C2×C3×C4—31no—
782C2×C3×C4—31no—
783C2×C3×C4—31no—
784C2×C3×C4—31no—
785C2×C3×C4—31no—
786C2×C3×C4—31no—
787C2×C3×C4—31no—
788C2×C3×C4—31no—
789C2×C3×C4—31no—
790C2×C3×C4—31no—
791C2×C3×C4—41no—
792C2×C3×C4—61no—
793C2×C3×C4—61no—
794C2×C3×C4—61no—
795C2×C3×C4—61no—
796C2×C3×C4—61no—
797C2×C3×C4—91no—
798C2×C3×C4—91no—
799C2×C3×C4—91no—
800C2×C3×C4—91no—
801C2×C3×C4—91no—
802C2×C3×C4—182no—
803C2×C3×C4—182no—
804C2×C3×C4—182no—
805C2×C3×C4C2×D3211yescharacteristic
806C2×C3×C4C2×D3211yescharacteristic
807C2×C3×C4C2×D3211yescharacteristic
808C2×Dic3—31no—
809C2×Dic3—31no—
810C2×Dic3—31no—
811C2×Dic3—31no—
812C2×Dic3—31no—
813C2×Dic3—31no—
814C2×Dic3—31no—
815C2×Dic3—31no—
816C2×Dic3—31no—
817C2×Dic3—31no—
818C2×Dic3—61no—
819C2×Dic3—61no—
820C2×Dic3—61no—
821C2×Dic3—61no—
822C2×Dic3—61no—
823C2×Dic3—62no—
824C2×Dic3—62no—
825C2×Dic3—91no—
826C2×Dic3—91no—
827C2×Dic3—91no—
828C2×Dic3—181no—
829C2×Dic3—181no—
830C2×Dic3—181no—
831C2×Dic3—182no—
832C2×Dic3—361no—
833C2×Dic3C2×D3211yescharacteristic
834C2×Dic3C2×D3211yescharacteristic
835C2×Dic3C2×D3211yescharacteristic
836C2×Dic3C2×D3211yescharacteristic
837C2×Dic3C2×D3211yescharacteristic
838C4×D3—62no—
839C4×D3—62no—
840C4×D3—62no—
841C4×D3—62no—
842C4×D3—94no—
843C4×D3—94no—
844C4×D3—94no—
845C4×D3—184no—
846C4×D3—182no—
847C4×D3—182no—
848C4×D3—182no—
849C4×D3—182no—
850C4×D3—182no—
851C4×D3—182no—
852C4×D3—182no—
853C4×D3—182no—
854C4×D3—182no—
855C4×D3—182no—
856C4×D3—182no—
857C4×D3—182no—
858C4×D3—182no—
859C4×D3—184no—
860C4×D3—184no—
861C4×D3—182no—
862C4×D3—182no—
863C4×D3—182no—
864C4×D3—182no—
865C4×D3—184no—
866C4×D3—362no—
867C4×D3—362no—
868C4×D3—362no—
869C4×D3—362no—
870C4×D3—364no—
871Dic6—22no—
872Dic6—62no—
873Dic6—62no—
874Dic6—64no—
875Dic6—182no—
876Dic6—182no—
877Dic6—182no—
878Dic6—182no—
879Dic6—182no—
880Dic6—184no—
881Dic6—184no—
882Dic6—182no—
883C2×C32—21no—
884C2×C32—21no—
885C2×C32—21no—
886C2×C32—21no—
887C2×C32—21no—
888C2×C32—21no—
889C2×C32—21no—
890C2×C32—21no—
891C2×C32—21no—
892C2×C32—41no—
893C2×C32—41no—
894C2×C32—41no—
895C2×C32—62no—
896C2×C32C2×D3×D411yescharacteristic
897C2×C32C2×D3×D411yescharacteristic
898C2×C32C2×D3×D411yescharacteristic
899C2×C32C2×D3×Q811yescharacteristic
900C2×C32C2×D3×Q811yescharacteristic
901C2×C32C2×D3×Q811yescharacteristic
902C2×C32D3×#4111yescharacteristic
903C2×C32D3×#4111yescharacteristic
904C2×C32D3×#4111yescharacteristic
905C3⋊D3—22no—
906C3⋊D3—34no—
907C3⋊D3—34no—
908C3⋊D3—34no—
909C3⋊D3—64no—
910C3⋊D3—64no—
911C3⋊D3—64no—
912C3⋊D3—124no—
913C3×D3—22no—
914C3×D3—22no—
915C3×D3—42no—
916C3×D3—62no—
917C3×D3—62no—
918C3×D3—122no—
919C24—271no—
920C2×Q8—31no—
921C2×Q8—91no—
922C2×Q8—271no—
923C2×Q8—271no—
924C2×Q8—544no—
925C22×C4—91no—
926C22×C4—91no—
927C22×C4—91no—
928C22×C4—271no—
929C22×C4—271no—
930C22×C4—271no—
931C22×C4—271no—
932C22×C4—271no—
933C22×C4—271no—
934C22×C4—271no—
935C22×C4—544no—
936C4⋊C4—31no—
937C4⋊C4—91no—
938C4⋊C4—91no—
939C4⋊C4—91no—
940C4⋊C4—91no—
941C4⋊C4—91no—
942C4⋊C4—91no—
943C4⋊C4—91no—
944C4⋊C4—271no—
945C4⋊C4—271no—
946C4⋊C4—271no—
947C4⋊C4—271no—
948C22⋊C4—31no—
949C22⋊C4—91no—
950C22⋊C4—91no—
951C22⋊C4—91no—
952C22⋊C4—91no—
953C22⋊C4—271no—
954C22⋊C4—271no—
955C22⋊C4—271no—
956C22×C3—21no—
957C22×C3—21no—
958C22×C3—21no—
959C22×C3—32no—
960C22×C3—32no—
961C22×C3—41no—
962C22×C3—62no—
963C22×C3—61no—
964C22×C3—61no—
965C22×C3—61no—
966C22×C3—61no—
967C22×C3—92no—
968C22×C3—121no—
969C22×C3—121no—
970C22×C3—181no—
971C22×C3—181no—
972C22×C3C22×D3211yescharacteristic
973C22×C3C22×D3211yescharacteristic
974C22×C3C22×D3211yescharacteristic
975C2×D3—21no—
976C2×D3—21no—
977C2×D3—32no—
978C2×D3—32no—
979C2×D3—62no—
980C2×D3—61no—
981C2×D3—61no—
982C2×D3—61no—
983C2×D3—61no—
984C2×D3—92no—
985C2×D3—92no—
986C2×D3—92no—
987C2×D3—92no—
988C2×D3—92no—
989C2×D3—92no—
990C2×D3—92no—
991C2×D3—92no—
992C2×D3—92no—
993C2×D3—121no—
994C2×D3—121no—
995C2×D3—182no—
996C2×D3—182no—
997C2×D3—182no—
998C2×D3—182no—
999C2×D3—182no—
1000C2×D3—182no—
1001C2×D3—182no—
1002C2×D3—182no—
1003C2×D3—182no—
1004C2×D3—188no—
1005C2×D3—188no—
1006C2×D3—188no—
1007C2×D3—362no—
1008C2×D3—362no—
1009C2×D3—362no—
1010C2×D3—368no—
1011C2×D3#379712yescomplemented
1012C3×C4—22no—
1013C3×C4—21no—
1014C3×C4—21no—
1015C3×C4—21no—
1016C3×C4—32no—
1017C3×C4—32no—
1018C3×C4—41no—
1019C3×C4—41no—
1020C3×C4—42no—
1021C3×C4—62no—
1022C3×C4—62no—
1023C3×C4—62no—
1024C3×C4—61no—
1025C3×C4—61no—
1026C3×C4—61no—
1027C3×C4—61no—
1028C3×C4—61no—
1029C3×C4—61no—
1030C3×C4—61no—
1031C3×C4—61no—
1032C3×C4—92no—
1033C3×C4—121no—
1034C3×C4—121no—
1035C3×C4—181no—
1036C3×C4—181no—
1037C3×C4—181no—
1038C3×C4—181no—
1039Dic3—21no—
1040Dic3—21no—
1041Dic3—21no—
1042Dic3—21no—
1043Dic3—32no—
1044Dic3—32no—
1045Dic3—62no—
1046Dic3—62no—
1047Dic3—62no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—61no—
1053Dic3—61no—
1054Dic3—61no—
1055Dic3—61no—
1056Dic3—121no—
1057Dic3—121no—
1058Dic3—182no—
1059Dic3—181no—
1060Dic3—181no—
1061Dic3—181no—
1062Dic3—361no—
1063Dic3—361no—
1064Dic3—362no—
1065Dic3#381112yes—
1066C32—21no—
1067C32—21no—
1068C32—21no—
1069C32—41no—
1070C32D3×C22⋊Q811yescharacteristic, complemented
1071C32D3×C22⋊Q811yescharacteristic, complemented
1072C32D3×C22⋊Q811yescharacteristic, complemented
1073C23—31no—
1074C23—91no—
1075C23—274no—
1076C23—271no—
1077C23—542no—
1078C23—542no—
1079Q8—62no—
1080Q8—182no—
1081Q8—542no—
1082Q8—542no—
1083C2×C4—31no—
1084C2×C4—31no—
1085C2×C4—31no—
1086C2×C4—31no—
1087C2×C4—31no—
1088C2×C4—91no—
1089C2×C4—91no—
1090C2×C4—91no—
1091C2×C4—91no—
1092C2×C4—91no—
1093C2×C4—182no—
1094C2×C4—182no—
1095C2×C4—182no—
1096C2×C4—274no—
1097C2×C4—271no—
1098C2×C4—542no—
1099C2×C4—542no—
1100C2×C4—542no—
1101C2×C4—542no—
1102C2×C4—542no—
1103C2×C4—542no—
1104C2×C4D3311yescharacteristic
1105C2×C3—21no—
1106C2×C3—21no—
1107C2×C3—21no—
1108C2×C3—21no—
1109C2×C3—21no—
1110C2×C3—21no—
1111C2×C3—21no—
1112C2×C3—21no—
1113C2×C3—21no—
1114C2×C3—41no—
1115C2×C3—41no—
1116C2×C3—41no—
1117C2×C3—62no—
1118C2×C3—62no—
1119C2×C3—122no—
1120C2×C3—182no—
1121C2×C3C2×#379711yescharacteristic
1122C2×C3#6430611yescharacteristic
1123C2×C3D32×D411yescharacteristic
1124C2×C3D32×D411yescharacteristic
1125C2×C3#6431211yescharacteristic
1126C2×C3D32×Q811yescharacteristic
1127C2×C3D32×Q811yescharacteristic
1128C2×C3#6431911yescharacteristic
1129C2×C3C2×#381111yescharacteristic
1130D3—22no—
1131D3—62no—
1132D3—62no—
1133D3—94no—
1134D3—94no—
1135D3—94no—
1136D3—122no—
1137D3—184no—
1138D3—184no—
1139D3—184no—
1140D3—364no—
1141C22—32no—
1142C22—61no—
1143C22—61no—
1144C22—92no—
1145C22—181no—
1146C22—181no—
1147C22—272no—
1148C22—272no—
1149C22—272no—
1150C22—548no—
1151C22C2×D3311yescharacteristic
1152C4—21no—
1153C4—32no—
1154C4—61no—
1155C4—61no—
1156C4—61no—
1157C4—61no—
1158C4—92no—
1159C4—181no—
1160C4—181no—
1161C4—181no—
1162C4—181no—
1163C4—541no—
1164C3—21no—
1165C3—21no—
1166C3—21no—
1167C3—41no—
1168C3#1059406711yescharacteristic, complemented
1169C3#1059462411yescharacteristic, complemented
1170C3#1059542911yescharacteristic, complemented
1171C2—62no—
1172C2—182no—
1173C2—274no—
1174C2D3×#379711yescharacteristic
1175C2#1172437611yescharacteristic
1176C2D3×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×D3×C3⋊D3C22
hypercenterC2×C4D33
hypocenterC33C2×C22⋊Q8
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#89019C2semidirect
3. #11723688C2semidirect
5. #11723470C2semidirect
6. C3×#63896C2semidirect
7. C3×#63888C2semidirect
8. C3×#63887C2semidirect
9. #11722984C2semidirect
10. #11722975C2semidirect
11. #11722972C2semidirect
12. #11722971C2semidirect
13. #11722912C2semidirect
14. #11722912C2semidirect
21. C2×C3×#634C22semidirect
22. C2×C32×Dic6C22semidirect
24. C2×#6293C22semidirect
25. C2×#6293C22semidirect
37. C3×#3750C22semidirect
39. C32×Dic3⋊C4C22semidirect
40. #88815C22semidirect
41. #88815C22semidirect
43. #88807C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
47. C3×#3724C22semidirect
48. C3×#3724C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
52. C3×Dic3⋊Dic3C22semidirect
84. #63896D3semidirect
90. #63888D3semidirect
92. #63887D3semidirect
109. C2×D3×C3⋊D3Q8semidirect
159. C2×#634C2×D3semidirect
170. C2×C3×Dic6C2×D3semidirect
171. C2×C3×Dic6C2×D3semidirect
212. #3750C2×D3semidirect
241. C3×Dic3⋊C4C2×D3semidirect
242. C3×Dic3⋊C4C2×D3semidirect
245. #3724C2×D3semidirect
246. #3724C2×D3semidirect
257. Dic3⋊Dic3C2×D3semidirect
258. Dic3⋊Dic3C2×D3semidirect
259. Dic3⋊Dic3C2×D3semidirect
260. Dic3⋊Dic3C2×D3semidirect
279. C2×C3×C3⋊D3C2×Q8semidirect
282. C2×C32×D3C2×Q8semidirect
484. C3⋊(C3⋊D3)C22⋊Q8semidirect
552. C2×Dic6D32semidirect
620. Dic3⋊C4D32semidirect
655. C2×C3⋊D3D3×Q8semidirect
672. C2×C3×D3D3×Q8semidirect
673. C2×C3×D3D3×Q8semidirect
746. C33C2×C22⋊Q8semidirect
1011. C2×D3#3797semidirect
1070. C32D3×C22⋊Q8semidirect
1071. C32D3×C22⋊Q8semidirect
1072. C32D3×C22⋊Q8semidirect
1168. C3#10594067semidirect
1169. C3#10594624semidirect
1170. C3#10595429semidirect

Maximal subgroups

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

subgroupindex
C2×#890192
C2×D3×#6242
#117236882
#117235392
#117234702
C3×#638962
C3×#638882
C3×#638872
#117229842
#117229752
#117229722
#117229712
#117229122
#117229062
#105954293
#105946243
#105940673