Finite Group Databasebeta

← #13178657

Subgroups — #13178657

Order 1728.

1708 conjugacy classes of subgroups.

The subgroup lattice has 1330 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×#64148C211yesmaximal, characteristic, complemented
4C3×#64147C211yesmaximal, characteristic, complemented
5C3×#64146C211yesmaximal, characteristic, complemented
6#11723729C211yesmaximal, characteristic, complemented
7#11723726C211yesmaximal, characteristic, complemented
8#11723725C211yesmaximal, characteristic, complemented
9#11723724C211yesmaximal, characteristic, complemented
10#11723723C211yesmaximal, characteristic, complemented
11#11723718C211yesmaximal, characteristic, complemented
12#11723700C211yesmaximal, characteristic, complemented
13#11723692C211yesmaximal, characteristic, complemented
14#11723690C211yesmaximal, characteristic, complemented
15#11723684C211yesmaximal, characteristic, complemented
16#10595296—31nomaximal
17#10595294—31nomaximal
18#10595290—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×#1113C2211yescharacteristic
21C2×C33×D4C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C3×#638C2211yescharacteristic
25C2×C3×#638C2211yescharacteristic, complemented
26C2×C3×#638C2211yescharacteristic, complemented
27C2×C3×#638C2211yescharacteristic, complemented
28C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
29C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
30#89049—24no—
31C2×#6296C2211yescharacteristic, complemented
32C2×#6295C2211yescharacteristic
33C2×#6295C2211yescharacteristic
34#89046—24no—
35C2×#6294C2211yescharacteristic
36C2×#6294C2211yescharacteristic, complemented
37C2×#6294C2211yescharacteristic, complemented
38C2×#6294C2211yescharacteristic, complemented
39C3×#3757C2211yescharacteristic, complemented
40C3×#3757C2211yescharacteristic, complemented
41C3×#3757C2211yescharacteristic, complemented
42C3×#3757C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic
44C3×#3752C2211yescharacteristic, complemented
45C3×#3752C2211yescharacteristic, complemented
46C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47C3×#3750C2211yescharacteristic, complemented
48#88815C2211yescharacteristic, complemented
49#88815C2211yescharacteristic, complemented
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88814C2211yescharacteristic, complemented
53#88814C2211yescharacteristic, complemented
54#88814C2211yescharacteristic, complemented
55#88813C2211yescharacteristic, complemented
56C2×#3811—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×#3805—31no—
60C2×#3804—31no—
61C2×#3804—31no—
62#64148D311yescharacteristic, complemented
63#64147D311yescharacteristic, complemented
64#64146D311yescharacteristic, complemented
65C3×#939—31no—
66C3×#939—31no—
67C3×#939—61no—
68C3×#938—31no—
69C3×#938—31no—
70C3×#938—61no—
71C3×#937—31no—
72C3×#937—31no—
73C3×#937—61no—
74#63983—31no—
75#63983—31no—
76#63983—31no—
77#63975—31no—
78#63974—31no—
79#67⋊Dic3—31no—
80Dic3×#67—31no—
81#63971—31no—
82#63970—31no—
83#63969—31no—
84#63969—31no—
85D3×#217—31no—
86D3×#217—31no—
87#63959—31no—
88#63959—31no—
89#63958—31no—
90#63953—31no—
91#63952—31no—
92#63921—31no—
93D3×(C2×D3)⋊C4—31no—
94D3×(C2×D3)⋊C4—31no—
95#63904—31no—
96#63899—31no—
97#63895—31no—
98#63893—31no—
99#63891—31no—
100#63890—31no—
101#63881—31no—
102#63879—31no—
103#63854—31no—
104C23×C33C2311yescharacteristic
105C23×C33C2311yescharacteristic
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—22no—
108C22×C3×C3⋊D3—41no—
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—
116C33×D4—41no—
117C2×C33×C4C2311yescharacteristic
118C3×#638—22no—
119C3×#638—22no—
120C3×#638—22no—
121C3×#638—22no—
122C3×#638—22no—
123C3×#638—41no—
124C2×C3×C3⋊Dic3—22no—
125C2×C3×C3⋊Dic3C2311yescharacteristic
126C2×C3×C3⋊Dic3C2311yescharacteristic
127C2×C3×C3⋊Dic3C2311yescharacteristic
128C2×C3×C3⋊Dic3C2311yescharacteristic
129C2×C3×C3⋊Dic3C2311yescharacteristic
130C2×C3×C3⋊Dic3C2311yescharacteristic
131C2×C3×C3⋊Dic3C2311yescharacteristic
132C2×C3×C3⋊Dic3C2311yescharacteristic
133C3×C4×C3⋊D3—41no—
134#6296—22no—
135#6295—22no—
136#6295D414yescomplemented
137#6294—22no—
138#6294—22no—
139#6294—22no—
140#6294—41no—
141#5612—91no—
142#5610—91no—
143#5591—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×C32×D4—21no—
152C2×C32×D4—21no—
153C2×C32×D4—21no—
154C2×C32×D4—41no—
155C2×C32×D4C2×D311yescharacteristic, complemented
156C2×C32×D4C2×D311yescharacteristic, complemented
157C2×C32×D4C2×D311yescharacteristic, complemented
158C2×#638C2×D311yescharacteristic
159C2×#638C2×D311yescharacteristic
160C2×#638C2×D311yescharacteristic
161C2×#638C2×D311yescharacteristic, complemented
162C2×#638C2×D311yescharacteristic, complemented
163C2×#638C2×D311yescharacteristic, complemented
164C22×C3⋊Dic3C2×D311yescharacteristic, complemented
165C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
166C2×C3×#67—31no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67—31no—
175C2×C3×#67—31no—
176C2×C3×#67—31no—
177C2×C3×#67—31no—
178C2×C3×#67—61no—
179C2×C3×#67—61no—
180C2×C3×#67—61no—
181C2×C3×#67—61no—
182C2×C3×#67—61no—
183C2×C3×#67—61no—
184C22×C3×Dic3—31no—
185C22×C3×Dic3—31no—
186C22×C3×Dic3—61no—
187C2×C3×C4×D3—31no—
188C2×C3×C4×D3—31no—
189C2×C3×C4×D3—61no—
190#3811—64no—
191D3×#67—64no—
192D3×#67—64no—
193C2×#627—31no—
194C2×#627—31no—
195C2×#627—31no—
196C2×#626—31no—
197C2×#626—31no—
198C2×#626—31no—
199C2×#626—31no—
200C2×#625—31no—
201C2×#625—31no—
202C2×#624—31no—
203C2×#624—31no—
204C2×#624—31no—
205C2×#624—31no—
206#3805—64no—
207#3804—64no—
208#3804—64no—
209C2×D3×Dic3—31no—
210C2×D3×Dic3—31no—
211C2×D3×Dic3—31no—
212C2×D3×Dic3—31no—
213C2×D3×Dic3—31no—
214C2×D3×Dic3—31no—
215C2×D3×Dic3—31no—
216C2×D3×Dic3—31no—
217#3757C2×D311yescharacteristic, complemented
218#3757C2×D311yescharacteristic, complemented
219#3757C2×D311yescharacteristic, complemented
220#3757C2×D311yescharacteristic, complemented
221#3752C2×D311yescharacteristic
222#3752C2×D311yescharacteristic, complemented
223#3752C2×D311yescharacteristic, complemented
224C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
225#3750C2×D311yescharacteristic, complemented
226C3×#217—31no—
227C3×#217—31no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—31no—
234C3×#217—61no—
235C3×#217—61no—
236C3×#217—61no—
237C3×#217—61no—
238C3×(C2×D3)⋊C4—31no—
239C3×(C2×D3)⋊C4—31no—
240C3×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—31no—
242C3×(C2×D3)⋊C4—31no—
243C3×(C2×D3)⋊C4—31no—
244C3×(C2×D3)⋊C4—61no—
245C3×(C2×D3)⋊C4—61no—
246C3×(C2×D3)⋊C4—61no—
247C3×C4⋊Dic3—31no—
248C3×C4⋊Dic3—31no—
249C3×C4⋊Dic3—61no—
250C3×Dic3⋊C4—31no—
251C3×Dic3⋊C4—31no—
252C3×Dic3⋊C4—61no—
253#3724—31no—
254#3724—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—31no—
257Dic3⋊Dic3—31no—
258Dic3⋊Dic3—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—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—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—31no—
272(C2×D3)⋊Dic3—31no—
273(C2×D3)⋊Dic3—31no—
274Dic32—31no—
275Dic32—31no—
276Dic32—31no—
277C22×C33—21no—
278C22×C33—21no—
279C22×C33—21no—
280C22×C33—21no—
281C22×C33—21no—
282C22×C33—21no—
283C22×C33C2411yescharacteristic
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—44no—
294C2×C3×C3⋊D3C2×D412yes—
295C2×C3×C3⋊D3C2×D412yes—
296C2×C3×C3⋊D3#4112yescomplemented
297#1113—44no—
298C33×C4—21no—
299C3×C3⋊Dic3—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×#121—91no—
314C3×#121—91no—
315C3×#120—91no—
316C2×#217—91no—
317#939—31no—
318#939—31no—
319#939—61no—
320#939—91no—
321#938—31no—
322#938—31no—
323#938—61no—
324#938—91no—
325#937—31no—
326#937—31no—
327#937—61no—
328#937—91no—
329#937—91no—
330#937—91no—
331#936—91no—
332#935—91no—
333D4×Dic3—91no—
334C4×#67—91no—
335C4×#67—91no—
336C2×(C2×D3)⋊C4—91no—
337#897—91no—
338#896—91no—
339#894—91no—
340#893—91no—
341#886—91no—
342#885—91no—
343#885—91no—
344#884—91no—
345#883—91no—
346#883—91no—
347#883—91no—
348#67⋊C4—91no—
349#67⋊C4—91no—
350D3×C22⋊C4—91no—
351D3×C22⋊C4—91no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
354#878—91no—
355C23×C32—21no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—21no—
360C23×C32—21no—
361C23×C32—41no—
362C23×C32—41no—
363C23×C32C22×D311yescharacteristic
364C23×C32C22×D311yescharacteristic
365C23×C32C22×D311yescharacteristic
366C23×C32C22×D311yescharacteristic
367C23×C32C22×D311yescharacteristic
368C23×C32C22×D311yescharacteristic
369C22×C3⋊D3—22no—
370C22×C3⋊D3—22no—
371C22×C3⋊D3—41no—
372C22×C3⋊D3C22×D311yescharacteristic
373C22×C3⋊D3C22×D311yescharacteristic
374C22×C3⋊D3C22×D311yescharacteristic
375C22×C3⋊D3C22×D311yescharacteristic
376C22×C3×D3—31no—
377C22×C3×D3—31no—
378C22×C3×D3—31no—
379C22×C3×D3—31no—
380C22×C3×D3—31no—
381C22×C3×D3—31no—
382C22×C3×D3—31no—
383C22×C3×D3—31no—
384C22×C3×D3—61no—
385C22×C3×D3—61no—
386C22×C3×D3—61no—
387C22×C3×D3—61no—
388C22×C3×D3—62no—
389C22×C3×D3—62no—
390C22×C3×D3—62no—
391C22×C3×D3—62no—
392C22×C3×D3—122no—
393C22×C3×D3—122no—
394C22×C3×D3—121no—
395C22×C3×D3—121no—
396C22×C3×D3—122no—
397C2×D32—62no—
398C2×D32—62no—
399C2×D32—62no—
400C2×D32—62no—
401C2×D32—62no—
402C2×D32—62no—
403C2×D32—121no—
404C2×D32—121no—
405C2×D32—121no—
406C32×D4—41no—
407C32×D4—41no—
408C32×D4—41no—
409C32×D4—42no—
410C32×D4—42no—
411C32×D4—42no—
412C32×D4—44no—
413C2×C32×C4—21no—
414C2×C32×C4—21no—
415C2×C32×C4—21no—
416C2×C32×C4—41no—
417C2×C32×C4C22×D311yescharacteristic
418C2×C32×C4C22×D311yescharacteristic
419C2×C32×C4C22×D311yescharacteristic
420#638—22no—
421#638—22no—
422#638—22no—
423#638—22no—
424#638—22no—
425#638—41no—
426C2×C3⋊Dic3—22no—
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
434C2×C3⋊Dic3C22×D311yescharacteristic
435C4×C3⋊D3—41no—
436C3×#67—62no—
437C3×#67—62no—
438C3×#67—62no—
439C3×#67—62no—
440C3×#67—62no—
441C3×#67—62no—
442C3×#67—62no—
443C3×#67—62no—
444C3×#67—62no—
445C3×#67—62no—
446C3×#67—122no—
447C3×#67—122no—
448C3×#67—122no—
449C3×#67—122no—
450C3×#67—122no—
451C3×#67—121no—
452C3×#67—121no—
453C3×#67—122no—
454C2×C3×Dic3—31no—
455C2×C3×Dic3—31no—
456C2×C3×Dic3—31no—
457C2×C3×Dic3—31no—
458C2×C3×Dic3—31no—
459C2×C3×Dic3—31no—
460C2×C3×Dic3—31no—
461C2×C3×Dic3—31no—
462C2×C3×Dic3—31no—
463C2×C3×Dic3—31no—
464C2×C3×Dic3—31no—
465C2×C3×Dic3—31no—
466C2×C3×Dic3—31no—
467C2×C3×Dic3—31no—
468C2×C3×Dic3—31no—
469C2×C3×Dic3—31no—
470C2×C3×Dic3—61no—
471C2×C3×Dic3—61no—
472C2×C3×Dic3—61no—
473C2×C3×Dic3—61no—
474C2×C3×Dic3—61no—
475C2×C3×Dic3—61no—
476C2×C3×Dic3—61no—
477C2×C3×Dic3—61no—
478C2×C3×Dic3—62no—
479C2×C3×Dic3—62no—
480C2×C3×Dic3—122no—
481C3×C4×D3—121no—
482C3×C4×D3—121no—
483C3×C4×D3—122no—
484#627—62no—
485#627—62no—
486#627—62no—
487#626—34no—
488#626—34no—
489#626—62no—
490#626—62no—
491#625—34no—
492#625—62no—
493#624—62no—
494#624—62no—
495#624—62no—
496#624—121no—
497D3×Dic3—62no—
498D3×Dic3—62no—
499D3×Dic3—62no—
500D3×Dic3—62no—
501D3×Dic3—62no—
502D3×Dic3—62no—
503D3×Dic3—121no—
504D3×Dic3—121no—
505#546—271noSylow
506C2×C33—41no—
507C2×C33—41no—
508C2×C33C22×D411yescharacteristic
509C2×C33C2×#4111yescharacteristic
510C2×C33H(5,𝔽2)11yescharacteristic
511C3×C3⋊D3—22no—
512C3×C3⋊D3—22no—
513C3×C3⋊D3—22no—
514C3×C3⋊D3—41no—
515C24×C3—91no—
516C23×D3—31no—
517C23×D3—31no—
518C23×D3—61no—
519C23×D3—91no—
520C23×D3—91no—
521C23×D3—91no—
522C2×C3×D4—21no—
523C2×C3×D4—21no—
524C2×C3×D4—21no—
525C2×C3×D4—41no—
526C2×C3×D4—91no—
527C2×C3×D4—91no—
528C2×C3×D4—91no—
529C2×C3×D4—91no—
530C2×C3×D4—91no—
531C2×C3×D4—91no—
532C2×C3×D4D3211yescharacteristic, complemented
533C2×C3×D4D3211yescharacteristic, complemented
534C2×C3×D4D3211yescharacteristic, complemented
535C22×C3×C4—91no—
536C22×C3×C4—91no—
537C2×#67—31no—
538C2×#67—31no—
539C2×#67—31no—
540C2×#67—31no—
541C2×#67—31no—
542C2×#67—31no—
543C2×#67—31no—
544C2×#67—31no—
545C2×#67—31no—
546C2×#67—31no—
547C2×#67—31no—
548C2×#67—31no—
549C2×#67—61no—
550C2×#67—61no—
551C2×#67—61no—
552C2×#67—61no—
553C2×#67—61no—
554C2×#67—61no—
555C2×#67—91no—
556C2×#67—91no—
557C2×#67—91no—
558C2×#67—91no—
559C2×#67—184no—
560C22×Dic3—31no—
561C22×Dic3—31no—
562C22×Dic3—61no—
563C22×Dic3—91no—
564C22×Dic3—91no—
565C22×Dic3—91no—
566C22×Dic3—91no—
567#237—184no—
568#237—184no—
569D3×D4—184no—
570D3×D4—184no—
571#235—184no—
572C2×D12—91no—
573C2×D12—91no—
574C2×C4×D3—31no—
575C2×C4×D3—31no—
576C2×C4×D3—61no—
577C2×C4×D3—91no—
578C2×C4×D3—91no—
579C2×C4×D3—91no—
580C2×C4×D3—91no—
581C2×C4×D3—91no—
582C2×C4×D3—91no—
583C2×C4×D3—91no—
584C2×C4×D3—91no—
585C2×Dic6—91no—
586C2×Dic6—91no—
587C2×Dic6—91no—
588C3×C4⋊C4—91no—
589C3×C4⋊C4—91no—
590C3×C22⋊C4—91no—
591C3×C22⋊C4—91no—
592C3×C22⋊C4—91no—
593C3×C22⋊C4—91no—
594C3×C22⋊C4—91no—
595C3×C22⋊C4—91no—
596C3×C22⋊C4—91no—
597#217—31no—
598#217—31no—
599#217—31no—
600#217—31no—
601#217—31no—
602#217—31no—
603#217—31no—
604#217—31no—
605#217—61no—
606#217—61no—
607#217—61no—
608#217—61no—
609#217—91no—
610#217—91no—
611#217—91no—
612#217—91no—
613#217—91no—
614(C2×D3)⋊C4—31no—
615(C2×D3)⋊C4—31no—
616(C2×D3)⋊C4—31no—
617(C2×D3)⋊C4—31no—
618(C2×D3)⋊C4—31no—
619(C2×D3)⋊C4—31no—
620(C2×D3)⋊C4—61no—
621(C2×D3)⋊C4—61no—
622(C2×D3)⋊C4—61no—
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—
629(C2×D3)⋊C4—91no—
630(C2×D3)⋊C4—91no—
631(C2×D3)⋊C4—91no—
632(C2×D3)⋊C4—91no—
633C4⋊Dic3—31no—
634C4⋊Dic3—31no—
635C4⋊Dic3—61no—
636C4⋊Dic3—91no—
637C4⋊Dic3—91no—
638Dic3⋊C4—31no—
639Dic3⋊C4—31no—
640Dic3⋊C4—61no—
641Dic3⋊C4—91no—
642Dic3⋊C4—91no—
643Dic3⋊C4—91no—
644Dic3⋊C4—91no—
645C4×Dic3—91no—
646C4×Dic3—91no—
647C4×Dic3—91no—
648C22×C32—21no—
649C22×C32—21no—
650C22×C32—22no—
651C22×C32—22no—
652C22×C32—21no—
653C22×C32—21no—
654C22×C32—21no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—21no—
658C22×C32—21no—
659C22×C32—21no—
660C22×C32—21no—
661C22×C32—21no—
662C22×C32—21no—
663C22×C32—21no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—21no—
667C22×C32—21no—
668C22×C32—21no—
669C22×C32—21no—
670C22×C32—21no—
671C22×C32—41no—
672C22×C32—41no—
673C22×C32—41no—
674C22×C32—41no—
675C22×C32—41no—
676C22×C32—42no—
677C22×C32—42no—
678C22×C32—41no—
679C22×C32—41no—
680C22×C32—41no—
681C22×C32—41no—
682C22×C32—41no—
683C22×C32—41no—
684C22×C32—41no—
685C22×C32—41no—
686C22×C32—41no—
687C22×C32—41no—
688C22×C32—41no—
689C22×C32—41no—
690C22×C32—81no—
691C22×C32—81no—
692C22×C32—81no—
693C22×C32—81no—
694C22×C32C23×D311yescharacteristic
695C22×C32C23×D311yescharacteristic
696C22×C32C23×D311yescharacteristic
697C2×C3⋊D3—21no—
698C2×C3⋊D3—21no—
699C2×C3⋊D3—21no—
700C2×C3⋊D3—21no—
701C2×C3⋊D3—21no—
702C2×C3⋊D3—21no—
703C2×C3⋊D3—21no—
704C2×C3⋊D3—21no—
705C2×C3⋊D3—21no—
706C2×C3⋊D3—44no—
707C2×C3⋊D3D3×D412yes—
708C2×C3⋊D3D3×D412yes—
709C2×C3⋊D3#23712yescomplemented
710C2×C3×D3—32no—
711C2×C3×D3—32no—
712C2×C3×D3—32no—
713C2×C3×D3—32no—
714C2×C3×D3—32no—
715C2×C3×D3—32no—
716C2×C3×D3—62no—
717C2×C3×D3—62no—
718C2×C3×D3—62no—
719C2×C3×D3—61no—
720C2×C3×D3—61no—
721C2×C3×D3—61no—
722C2×C3×D3—61no—
723C2×C3×D3—61no—
724C2×C3×D3—61no—
725C2×C3×D3—61no—
726C2×C3×D3—61no—
727C2×C3×D3—61no—
728C2×C3×D3—61no—
729C2×C3×D3—61no—
730C2×C3×D3—61no—
731C2×C3×D3—61no—
732C2×C3×D3—61no—
733C2×C3×D3—61no—
734C2×C3×D3—61no—
735C2×C3×D3—61no—
736C2×C3×D3—61no—
737C2×C3×D3—121no—
738C2×C3×D3—121no—
739C2×C3×D3—121no—
740C2×C3×D3—121no—
741C2×C3×D3—121no—
742C2×C3×D3—121no—
743C2×C3×D3—121no—
744C2×C3×D3—121no—
745C2×C3×D3—121no—
746C2×C3×D3—124no—
747C2×C3×D3—124no—
748C2×C3×D3—128no—
749D32—124no—
750D32—124no—
751D32—124no—
752C32×C4—21no—
753C32×C4—22no—
754C32×C4—21no—
755C32×C4—21no—
756C32×C4—41no—
757C32×C4—41no—
758C32×C4—42no—
759C3⋊Dic3—21no—
760C3⋊Dic3—21no—
761C3⋊Dic3—21no—
762C3⋊Dic3—21no—
763C3⋊Dic3—21no—
764C3⋊Dic3—21no—
765C3⋊Dic3—21no—
766C3⋊Dic3D3×D412yes—
767C3×Dic3—32no—
768C3×Dic3—32no—
769C3×Dic3—62no—
770C3×Dic3—61no—
771C3×Dic3—61no—
772C3×Dic3—61no—
773C3×Dic3—61no—
774C3×Dic3—61no—
775C3×Dic3—61no—
776C3×Dic3—61no—
777C3×Dic3—61no—
778C3×Dic3—61no—
779C3×Dic3—61no—
780C3×Dic3—61no—
781C3×Dic3—61no—
782C3×Dic3—61no—
783C3×Dic3—61no—
784C3×Dic3—121no—
785C3×Dic3—121no—
786C3×Dic3—121no—
787C3×Dic3—121no—
788C3×Dic3—121no—
789C3×Dic3—121no—
790C3×Dic3—121no—
791C2×#41—271no—
792C22×D4—271no—
793#124—271no—
794#123—271no—
795#123—271no—
796C22⋊Q8—271no—
797#121—91no—
798#121—91no—
799#121—271no—
800#120—91no—
801#120—271no—
802C4×D4—271no—
803C4×D4—271no—
804C2×C22⋊C4—271no—
805C2×C22⋊C4—271no—
806C33#54611yescharacteristic, complemented, Sylow
807C23×C3—21no—
808C23×C3—21no—
809C23×C3—21no—
810C23×C3—21no—
811C23×C3—21no—
812C23×C3—21no—
813C23×C3—41no—
814C23×C3—41no—
815C23×C3—91no—
816C23×C3—91no—
817C23×C3—91no—
818C23×C3—91no—
819C23×C3—182no—
820C23×C3—182no—
821C23×C3—361no—
822C23×C3C2×D3211yescharacteristic
823C23×C3C2×D3211yescharacteristic
824C23×C3C2×D3211yescharacteristic
825C23×C3C2×D3211yescharacteristic
826C23×C3C2×D3211yescharacteristic
827C23×C3C2×D3211yescharacteristic
828C22×D3—31no—
829C22×D3—31no—
830C22×D3—31no—
831C22×D3—31no—
832C22×D3—31no—
833C22×D3—31no—
834C22×D3—31no—
835C22×D3—31no—
836C22×D3—61no—
837C22×D3—61no—
838C22×D3—61no—
839C22×D3—61no—
840C22×D3—62no—
841C22×D3—62no—
842C22×D3—62no—
843C22×D3—62no—
844C22×D3—122no—
845C22×D3—122no—
846C22×D3—121no—
847C22×D3—121no—
848C22×D3—122no—
849C22×D3—182no—
850C22×D3—182no—
851C22×D3—182no—
852C22×D3—182no—
853C22×D3—182no—
854C22×D3—182no—
855C22×D3—361no—
856C22×D3—361no—
857C22×D3—361no—
858C3×D4—41no—
859C3×D4—41no—
860C3×D4—41no—
861C3×D4—42no—
862C3×D4—42no—
863C3×D4—42no—
864C3×D4—44no—
865C3×D4—182no—
866C3×D4—182no—
867C3×D4—182no—
868C3×D4—182no—
869C3×D4—182no—
870C3×D4—361no—
871C2×C3×C4—21no—
872C2×C3×C4—21no—
873C2×C3×C4—21no—
874C2×C3×C4—41no—
875C2×C3×C4—91no—
876C2×C3×C4—91no—
877C2×C3×C4—91no—
878C2×C3×C4—91no—
879C2×C3×C4—91no—
880C2×C3×C4—91no—
881C2×C3×C4—91no—
882C2×C3×C4—91no—
883C2×C3×C4—182no—
884C2×C3×C4—361no—
885C2×C3×C4C2×D3211yescharacteristic
886C2×C3×C4C2×D3211yescharacteristic
887C2×C3×C4C2×D3211yescharacteristic
888#67—62no—
889#67—62no—
890#67—62no—
891#67—62no—
892#67—62no—
893#67—62no—
894#67—62no—
895#67—62no—
896#67—62no—
897#67—62no—
898#67—94no—
899#67—94no—
900#67—122no—
901#67—122no—
902#67—122no—
903#67—122no—
904#67—122no—
905#67—121no—
906#67—121no—
907#67—122no—
908#67—182no—
909#67—182no—
910C2×Dic3—31no—
911C2×Dic3—31no—
912C2×Dic3—31no—
913C2×Dic3—31no—
914C2×Dic3—31no—
915C2×Dic3—31no—
916C2×Dic3—31no—
917C2×Dic3—31no—
918C2×Dic3—31no—
919C2×Dic3—31no—
920C2×Dic3—31no—
921C2×Dic3—31no—
922C2×Dic3—31no—
923C2×Dic3—31no—
924C2×Dic3—31no—
925C2×Dic3—31no—
926C2×Dic3—61no—
927C2×Dic3—61no—
928C2×Dic3—61no—
929C2×Dic3—61no—
930C2×Dic3—61no—
931C2×Dic3—61no—
932C2×Dic3—61no—
933C2×Dic3—61no—
934C2×Dic3—62no—
935C2×Dic3—62no—
936C2×Dic3—122no—
937C2×Dic3—182no—
938C2×Dic3—182no—
939C2×Dic3—182no—
940C2×Dic3—361no—
941D12—94no—
942D12—182no—
943C4×D3—121no—
944C4×D3—121no—
945C4×D3—122no—
946C4×D3—182no—
947C4×D3—182no—
948C4×D3—182no—
949C4×D3—182no—
950C4×D3—182no—
951C4×D3—182no—
952C4×D3—361no—
953C4×D3—361no—
954Dic6—182no—
955Dic6—182no—
956Dic6—182no—
957C2×C32—21no—
958C2×C32—21no—
959C2×C32—21no—
960C2×C32—21no—
961C2×C32—21no—
962C2×C32—21no—
963C2×C32—21no—
964C2×C32—21no—
965C2×C32—21no—
966C2×C32—41no—
967C2×C32—41no—
968C2×C32—41no—
969C2×C32—41no—
970C2×C32—41no—
971C2×C32—42no—
972C2×C32—42no—
973C2×C32—41no—
974C2×C32—41no—
975C2×C32—41no—
976C2×C32—41no—
977C2×C32—81no—
978C2×C32—81no—
979C2×C32—81no—
980C2×C32—81no—
981C2×C32—82no—
982C2×C32—82no—
983C2×C32C2×D3×D411yescharacteristic
984C2×C32C2×D3×D411yescharacteristic
985C2×C32C2×D3×D411yescharacteristic
986C2×C32C2×#23711yescharacteristic
987C2×C32#100411yescharacteristic
988C2×C32#100411yescharacteristic
989C2×C32#100411yescharacteristic
990C2×C32D3×#4111yescharacteristic
991C2×C32D3×#4111yescharacteristic
992C3⋊D3—22no—
993C3⋊D3—22no—
994C3⋊D3—22no—
995C3⋊D3—41no—
996C3×D3—62no—
997C3×D3—62no—
998C3×D3—62no—
999C3×D3—62no—
1000C3×D3—62no—
1001C3×D3—62no—
1002C3×D3—122no—
1003C3×D3—122no—
1004C3×D3—122no—
1005C3×D3—121no—
1006C3×D3—121no—
1007C3×D3—241no—
1008C24—91no—
1009C24—271no—
1010#41—544no—
1011C2×Q8—271no—
1012C2×D4—91no—
1013C2×D4—91no—
1014C2×D4—91no—
1015C2×D4—91no—
1016C2×D4—91no—
1017C2×D4—91no—
1018C2×D4—271no—
1019C2×D4—271no—
1020C2×D4—544no—
1021C2×D4#111311yescharacteristic, complemented
1022C22×C4—91no—
1023C22×C4—91no—
1024C22×C4—271no—
1025C22×C4—271no—
1026C22×C4—271no—
1027C22×C4—271no—
1028C4⋊C4—91no—
1029C4⋊C4—91no—
1030C4⋊C4—271no—
1031C4⋊C4—271no—
1032C22⋊C4—91no—
1033C22⋊C4—91no—
1034C22⋊C4—91no—
1035C22⋊C4—91no—
1036C22⋊C4—91no—
1037C22⋊C4—91no—
1038C22⋊C4—91no—
1039C22⋊C4—271no—
1040C22⋊C4—271no—
1041C22⋊C4—271no—
1042C22⋊C4—271no—
1043C22⋊C4—271no—
1044C42—271no—
1045C22×C3—22no—
1046C22×C3—22no—
1047C22×C3—21no—
1048C22×C3—21no—
1049C22×C3—21no—
1050C22×C3—21no—
1051C22×C3—21no—
1052C22×C3—21no—
1053C22×C3—21no—
1054C22×C3—21no—
1055C22×C3—21no—
1056C22×C3—21no—
1057C22×C3—21no—
1058C22×C3—21no—
1059C22×C3—21no—
1060C22×C3—21no—
1061C22×C3—21no—
1062C22×C3—21no—
1063C22×C3—21no—
1064C22×C3—21no—
1065C22×C3—21no—
1066C22×C3—21no—
1067C22×C3—21no—
1068C22×C3—41no—
1069C22×C3—41no—
1070C22×C3—41no—
1071C22×C3—41no—
1072C22×C3—41no—
1073C22×C3—41no—
1074C22×C3—41no—
1075C22×C3—41no—
1076C22×C3—41no—
1077C22×C3—41no—
1078C22×C3—41no—
1079C22×C3—41no—
1080C22×C3—41no—
1081C22×C3—41no—
1082C22×C3—41no—
1083C22×C3—41no—
1084C22×C3—42no—
1085C22×C3—42no—
1086C22×C3—41no—
1087C22×C3—81no—
1088C22×C3—81no—
1089C22×C3—81no—
1090C22×C3—81no—
1091C22×C3—92no—
1092C22×C3—92no—
1093C22×C3—92no—
1094C22×C3—181no—
1095C22×C3—181no—
1096C22×C3—181no—
1097C22×C3—181no—
1098C22×C3—181no—
1099C22×C3—181no—
1100C22×C3—181no—
1101C22×C3—181no—
1102C22×C3—181no—
1103C22×C3—364no—
1104C22×C3C22×D3211yescharacteristic
1105C22×C3C22×D3211yescharacteristic
1106C22×C3C22×D3211yescharacteristic
1107C2×D3—32no—
1108C2×D3—32no—
1109C2×D3—32no—
1110C2×D3—32no—
1111C2×D3—32no—
1112C2×D3—32no—
1113C2×D3—62no—
1114C2×D3—62no—
1115C2×D3—62no—
1116C2×D3—61no—
1117C2×D3—61no—
1118C2×D3—61no—
1119C2×D3—61no—
1120C2×D3—61no—
1121C2×D3—61no—
1122C2×D3—61no—
1123C2×D3—61no—
1124C2×D3—61no—
1125C2×D3—61no—
1126C2×D3—61no—
1127C2×D3—61no—
1128C2×D3—61no—
1129C2×D3—61no—
1130C2×D3—61no—
1131C2×D3—61no—
1132C2×D3—61no—
1133C2×D3—61no—
1134C2×D3—121no—
1135C2×D3—121no—
1136C2×D3—121no—
1137C2×D3—121no—
1138C2×D3—121no—
1139C2×D3—121no—
1140C2×D3—121no—
1141C2×D3—121no—
1142C2×D3—121no—
1143C2×D3—124no—
1144C2×D3—124no—
1145C2×D3—128no—
1146C2×D3—364no—
1147C2×D3—364no—
1148C2×D3—364no—
1149C3×C4—22no—
1150C3×C4—21no—
1151C3×C4—21no—
1152C3×C4—21no—
1153C3×C4—41no—
1154C3×C4—41no—
1155C3×C4—42no—
1156C3×C4—92no—
1157C3×C4—181no—
1158C3×C4—181no—
1159C3×C4—181no—
1160C3×C4—181no—
1161C3×C4—181no—
1162C3×C4—181no—
1163C3×C4—181no—
1164Dic3—32no—
1165Dic3—32no—
1166Dic3—62no—
1167Dic3—61no—
1168Dic3—61no—
1169Dic3—61no—
1170Dic3—61no—
1171Dic3—61no—
1172Dic3—61no—
1173Dic3—61no—
1174Dic3—61no—
1175Dic3—61no—
1176Dic3—61no—
1177Dic3—61no—
1178Dic3—61no—
1179Dic3—61no—
1180Dic3—61no—
1181Dic3—121no—
1182Dic3—121no—
1183Dic3—121no—
1184Dic3—121no—
1185Dic3—121no—
1186Dic3—121no—
1187Dic3—121no—
1188C32—21no—
1189C32—21no—
1190C32—21no—
1191C32—41no—
1192C32#559111yescharacteristic, complemented
1193C32#561011yescharacteristic, complemented
1194C32#561211yescharacteristic, complemented
1195C23—91no—
1196C23—91no—
1197C23—91no—
1198C23—91no—
1199C23—182no—
1200C23—182no—
1201C23—361no—
1202C23—542no—
1203C23—542no—
1204C23—1081no—
1205C23C2×#111311yescharacteristic
1206C23C2×#111311yescharacteristic
1207Q8—542no—
1208D4—41no—
1209D4—182no—
1210D4—182no—
1211D4—182no—
1212D4—182no—
1213D4—182no—
1214D4—274no—
1215D4—361no—
1216D4—542no—
1217C2×C4—91no—
1218C2×C4—91no—
1219C2×C4—91no—
1220C2×C4—91no—
1221C2×C4—91no—
1222C2×C4—91no—
1223C2×C4—91no—
1224C2×C4—91no—
1225C2×C4—182no—
1226C2×C4—361no—
1227C2×C4—542no—
1228C2×C4—542no—
1229C2×C4—542no—
1230C2×C4—1081no—
1231C2×C4C2×#111311yescharacteristic
1232C2×C3—21no—
1233C2×C3—21no—
1234C2×C3—21no—
1235C2×C3—21no—
1236C2×C3—21no—
1237C2×C3—21no—
1238C2×C3—21no—
1239C2×C3—21no—
1240C2×C3—21no—
1241C2×C3—42no—
1242C2×C3—42no—
1243C2×C3—41no—
1244C2×C3—41no—
1245C2×C3—41no—
1246C2×C3—41no—
1247C2×C3—41no—
1248C2×C3—41no—
1249C2×C3—41no—
1250C2×C3—41no—
1251C2×C3—41no—
1252C2×C3—81no—
1253C2×C3—81no—
1254C2×C3—81no—
1255C2×C3—81no—
1256C2×C3—82no—
1257C2×C3—82no—
1258C2×C3—182no—
1259C2×C3—182no—
1260C2×C3—182no—
1261C2×C3—361no—
1262C2×C3D32×D411yescharacteristic
1263C2×C3D32×D411yescharacteristic
1264C2×C3D32×D411yescharacteristic
1265C2×C3D3×#23711yescharacteristic
1266C2×C3D3×#23711yescharacteristic
1267C2×C3#6431211yescharacteristic
1268C2×C3#6433011yescharacteristic
1269C2×C3#6433011yescharacteristic
1270C2×C3#6433011yescharacteristic
1271D3—62no—
1272D3—62no—
1273D3—62no—
1274D3—62no—
1275D3—62no—
1276D3—62no—
1277D3—122no—
1278D3—122no—
1279D3—122no—
1280D3—121no—
1281D3—121no—
1282D3—241no—
1283C22—21no—
1284C22—21no—
1285C22—21no—
1286C22—21no—
1287C22—21no—
1288C22—21no—
1289C22—92no—
1290C22—92no—
1291C22—92no—
1292C22—181no—
1293C22—181no—
1294C22—181no—
1295C22—181no—
1296C22—181no—
1297C22—181no—
1298C22—181no—
1299C22—181no—
1300C22—181no—
1301C22—364no—
1302C22—1084no—
1303C22C22×#111311yescharacteristic
1304C4—21no—
1305C4—92no—
1306C4—181no—
1307C4—181no—
1308C4—181no—
1309C4—181no—
1310C4—181no—
1311C4—181no—
1312C4—181no—
1313C3—21no—
1314C3—21no—
1315C3—21no—
1316C3—41no—
1317C3#1059529011yescharacteristic, complemented
1318C3#1059529411yescharacteristic, complemented
1319C3#1059529611yescharacteristic, complemented
1320C2—41no—
1321C2—41no—
1322C2—182no—
1323C2—182no—
1324C2—182no—
1325C2—361no—
1326C2D4×#111311yescharacteristic
1327C2#1172462211yescharacteristic
1328C2#1172463311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#89049C2semidirect
2. C2×#89046C2semidirect
3. C3×#64148C2semidirect
4. C3×#64147C2semidirect
5. C3×#64146C2semidirect
6. #11723729C2semidirect
7. #11723726C2semidirect
8. #11723725C2semidirect
9. #11723724C2semidirect
10. #11723723C2semidirect
11. #11723718C2semidirect
12. #11723700C2semidirect
13. #11723692C2semidirect
14. #11723690C2semidirect
15. #11723684C2semidirect
21. C2×C33×D4C22semidirect
25. C2×C3×#638C22semidirect
26. C2×C3×#638C22semidirect
27. C2×C3×#638C22semidirect
28. C22×C3×C3⋊Dic3C22semidirect
29. C2×C3×C4×C3⋊D3C22semidirect
31. C2×#6296C22semidirect
36. C2×#6294C22semidirect
37. C2×#6294C22semidirect
38. C2×#6294C22semidirect
39. C3×#3757C22semidirect
40. C3×#3757C22semidirect
41. C3×#3757C22semidirect
42. C3×#3757C22semidirect
44. C3×#3752C22semidirect
45. C3×#3752C22semidirect
46. C3×C4⋊(C3⋊Dic3)C22semidirect
47. C3×#3750C22semidirect
48. #88815C22semidirect
49. #88815C22semidirect
52. #88814C22semidirect
53. #88814C22semidirect
54. #88814C22semidirect
55. #88813C22semidirect
62. #64148D3semidirect
63. #64147D3semidirect
64. #64146D3semidirect
136. #6295D4semidirect
155. C2×C32×D4C2×D3semidirect
156. C2×C32×D4C2×D3semidirect
157. C2×C32×D4C2×D3semidirect
161. C2×#638C2×D3semidirect
162. C2×#638C2×D3semidirect
163. C2×#638C2×D3semidirect
164. C22×C3⋊Dic3C2×D3semidirect
165. C2×C4×C3⋊D3C2×D3semidirect
217. #3757C2×D3semidirect
218. #3757C2×D3semidirect
219. #3757C2×D3semidirect
220. #3757C2×D3semidirect
222. #3752C2×D3semidirect
223. #3752C2×D3semidirect
224. C4⋊(C3⋊Dic3)C2×D3semidirect
225. #3750C2×D3semidirect
296. C2×C3×C3⋊D3#41semidirect
532. C2×C3×D4D32semidirect
533. C2×C3×D4D32semidirect
534. C2×C3×D4D32semidirect
709. C2×C3⋊D3#237semidirect
806. C33#546semidirect
1021. C2×D4#1113semidirect
1192. C32#5591semidirect
1193. C32#5610semidirect
1194. C32#5612semidirect
1317. C3#10595290semidirect
1318. C3#10595294semidirect
1319. C3#10595296semidirect

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×#641482
C3×#641472
C3×#641462
#117237292
#117237262
#117237252
#117237242
#117237232
#117237182
#117237002
#117236922
#117236902
#117236842
#105952963
#105952943
#105952903