Finite Group Databasebeta

← #13172934

Subgroups — #13172934

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×#88965C211yesmaximal, characteristic, complemented
3#11723636C211yesmaximal, characteristic, complemented
4#11723624C211yesmaximal, characteristic, complemented
5#11723623C211yesmaximal, characteristic, complemented
6C3×#63975C211yesmaximal, characteristic, complemented
7C3×#63974C211yesmaximal, characteristic, complemented
8C3×#63953C211yesmaximal, characteristic, complemented
9#11722995C211yesmaximal, characteristic, complemented
10#11722979C211yesmaximal, characteristic, complemented
11#11722961C211yesmaximal, characteristic, complemented
12#11722952C211yesmaximal, characteristic, complemented
13#11722937C211yesmaximal, characteristic, complemented
14#11722934C211yesmaximal, characteristic, complemented
15#11722905C211yesmaximal, characteristic, complemented
16#10594282—31nomaximal
17#10594280—31nomaximal
18#10594272—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×#1113C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24#89049—24no—
25C2×#6295C2211yescharacteristic
26C2×#6295C2211yescharacteristic
27C2×#6294C2211yescharacteristic
28C2×#6292C2211yescharacteristic
29C2×#6292C2211yescharacteristic, complemented
30C2×#6292C2211yescharacteristic, complemented
31C2×#6292C2211yescharacteristic, complemented
32C2×#6289C2211yescharacteristic, complemented
33C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
34C2×C3×#627C2211yescharacteristic, complemented
35C2×C3×#624C2211yescharacteristic, complemented
36C2×C3×#624C2211yescharacteristic, complemented
37C2×C3×#624C2211yescharacteristic, complemented
38#88965—24no—
39C32×#217C2211yescharacteristic, complemented
40C32×#217C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic, complemented
42#88807C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44#88804C2211yescharacteristic, complemented
45#88803C2211yescharacteristic
46#88803C2211yescharacteristic, complemented
47#88803C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic, complemented
54C3×#3722C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×#3811—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×#3799—31no—
60C2×#3799—31no—
61C2×#3798—31no—
62#64093—31no—
63#64093—31no—
64#64091—31no—
65C3×#885—31no—
66C3×#885—31no—
67C3×#883—31no—
68C3×#883—31no—
69C3×D3×C22⋊C4—31no—
70C3×D3×C22⋊C4—31no—
71#63977—31no—
72#63977—31no—
73#63977—61no—
74#63975D311yescharacteristic, complemented
75#63974D311yescharacteristic, complemented
76#63971—31no—
77#63971—31no—
78#63971—61no—
79#63958—31no—
80#63958—31no—
81#63958—61no—
82#63953D311yescharacteristic, complemented
83#63923—31no—
84#63923—31no—
85#63923—31no—
86#63921—31no—
87D3×(C2×D3)⋊C4—31no—
88D3×(C2×D3)⋊C4—31no—
89#63910—31no—
90#63909—31no—
91#63906—31no—
92#63905—31no—
93C4×#626—31no—
94#63899—31no—
95#63894—31no—
96#63888—31no—
97#63887—31no—
98#63881—31no—
99#63880—31no—
100#63880—31no—
101#63879—31no—
102#63854—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
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—
116#6312—41no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#638—22no—
119C3×#638—22no—
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128#6295—22no—
129#6295D414yescomplemented
130#6294—22no—
131#6292—22no—
132#6292—22no—
133#6292—22no—
134#6292—41no—
135#6289—22no—
136Dic3×C3⋊D3—41no—
137C3×#627—22no—
138C3×#624—22no—
139C3×#624—22no—
140C3×#624—41no—
141#5676—91no—
142#5654—91no—
143#5490—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×#638—31no—
152C2×#638—31no—
153C2×#638—31no—
154C2×#638—61no—
155C2×#638—61no—
156C2×#638—61no—
157C2×#638—121no—
158C2×#638C2×D311yescharacteristic
159C2×#638C2×D311yescharacteristic
160C2×C4⋊(C3⋊D3)—31no—
161C2×C4⋊(C3⋊D3)—31no—
162C2×C4⋊(C3⋊D3)—31no—
163C2×C4⋊(C3⋊D3)—31no—
164C2×C4×C3⋊D3—31no—
165C2×C4×C3⋊D3—31no—
166C2×C3×#67—31no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—61no—
171C2×C3×#67—61no—
172C2×C3×C4×D3—31no—
173C2×C3×C4×D3—31no—
174C2×C3×C4×D3—31no—
175C2×C3×C4×D3—31no—
176C2×C3×C4×D3—31no—
177C2×C3×C4×D3—31no—
178C2×C3×Dic6—31no—
179C2×C3×Dic6—31no—
180#3811—64no—
181D3×#67—64no—
182D3×#67—64no—
183C2×#627C2×D311yescharacteristic, complemented
184C2×#626—31no—
185C2×#626—31no—
186C2×#626—31no—
187C2×#626—31no—
188C2×#626—31no—
189C2×#626—31no—
190C2×#626—31no—
191C2×#626—31no—
192C2×#626—31no—
193C2×#626—31no—
194C2×#626—31no—
195C2×#626—31no—
196C2×#626—61no—
197C2×#626—61no—
198C2×#626—61no—
199C2×#626—61no—
200C2×#625—31no—
201C2×#625—31no—
202C2×#624—31no—
203C2×#624—31no—
204C2×#624—31no—
205C2×#624—61no—
206C2×#624C2×D311yescharacteristic, complemented
207C2×#624C2×D311yescharacteristic, complemented
208C2×#624C2×D311yescharacteristic, complemented
209C2×D3×Dic3—31no—
210C2×D3×Dic3—31no—
211C2×D3×Dic3—31no—
212C2×D3×Dic3—31no—
213C2×D3×Dic3—61no—
214#3799—64no—
215#3799—64no—
216#3798—64no—
217C32×C22⋊C4—31no—
218C32×C22⋊C4—31no—
219C32×C22⋊C4—31no—
220#3752—31no—
221#3752—31no—
222#3752—31no—
223#3752—31no—
224#3750—31no—
225#3750—31no—
226C3×#217—21no—
227C3×#217—21no—
228C3×#217—21no—
229C3×#217C2×D311yescharacteristic, complemented
230C3×#217C2×D311yescharacteristic, complemented
231C3×#217C2×D311yescharacteristic, complemented
232C3×#217C2×D311yescharacteristic, complemented
233C3×#217C2×D311yescharacteristic, complemented
234C3×#217C2×D311yescharacteristic, complemented
235C3×(C2×D3)⋊C4—31no—
236C3×(C2×D3)⋊C4—31no—
237C3×(C2×D3)⋊C4—31no—
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—31no—
245C3×C4⋊Dic3—31no—
246C3×C4⋊Dic3—31no—
247C3×Dic3⋊C4—31no—
248C3×Dic3⋊C4—31no—
249C3×C4×Dic3—31no—
250C3×C4×Dic3—31no—
251#3724—31no—
252#3724—31no—
253#3724—61no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—61no—
257Dic3⋊Dic3C2×D311yescharacteristic, complemented
258Dic3⋊Dic3C2×D311yescharacteristic, complemented
259#3722—31no—
260#3722—31no—
261#3722—61no—
262#3722C2×D311yescharacteristic
263#3722C2×D311yescharacteristic
264#3722C2×D311yescharacteristic, complemented
265#3722C2×D311yescharacteristic, complemented
266#3722C2×D311yescharacteristic, complemented
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—61no—
274(C2×D3)⋊Dic3—61no—
275(C2×D3)⋊Dic3—61no—
276Dic32C2×D311yescharacteristic, complemented
277C22×C33—21no—
278C22×C33—21no—
279C22×C33—21no—
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—44no—
294C2×C3×C3⋊D3C2×D412yes—
295C2×C3×C3⋊D3C2×D412yes—
296C2×C3×C3⋊D3#4112yescomplemented
297#1113—44no—
298C3⋊(C3⋊Dic3)—21no—
299C3×C3⋊Dic3—21no—
300C3×C3⋊Dic3C2×D412yes—
301C32×Dic3—21no—
302C32×Dic3—21no—
303C32×Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C22×#67—91no—
308C2×#239—91no—
309C2×D3×D4—91no—
310C2×D3×D4—91no—
311C2×#235—91no—
312C2×#235—91no—
313C3×#124—91no—
314C3×#123—91no—
315C2×C3×C22⋊C4—91no—
316#953—91no—
317#946—91no—
318#939—91no—
319#938—91no—
320#930—91no—
321#929—91no—
322C4×#67—91no—
323C2×(C2×D3)⋊C4—91no—
324#896—91no—
325#895—91no—
326#894—91no—
327#893—91no—
328#885—31no—
329#885—31no—
330#884—91no—
331#884—91no—
332#884—91no—
333#884—91no—
334#884—91no—
335#884—181no—
336#884—181no—
337#883—31no—
338#883—31no—
339#883—91no—
340#882—91no—
341#882—91no—
342#882—91no—
343#882—91no—
344#882—91no—
345#882—181no—
346#67⋊C4—91no—
347#67⋊C4—91no—
348D3×C22⋊C4—31no—
349D3×C22⋊C4—31no—
350D3×C22⋊C4—91no—
351D3×C22⋊C4—91no—
352#878—91no—
353C4×D12—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—31no—
365C22×C3⋊D3—31no—
366C22×C3⋊D3—31no—
367C22×C3⋊D3—41no—
368C22×C3⋊D3—61no—
369C22×C3⋊D3—61no—
370C22×C3⋊D3—61no—
371C22×C3⋊D3—121no—
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—
406C2×C32×C4—31no—
407C2×C32×C4—31no—
408C2×C32×C4—31no—
409C2×C32×C4—31no—
410C2×C32×C4—31no—
411C2×C32×C4—31no—
412#638—22no—
413#638—22no—
414#638—121no—
415#638—121no—
416#638—121no—
417#638—122no—
418#638—122no—
419#638—122no—
420#638—124no—
421C2×C3⋊Dic3—31no—
422C2×C3⋊Dic3—31no—
423C2×C3⋊Dic3—31no—
424C2×C3⋊Dic3—61no—
425C2×C3⋊Dic3—61no—
426C2×C3⋊Dic3—61no—
427C2×C3⋊Dic3—121no—
428C2×C3⋊Dic3C22×D311yescharacteristic
429C2×C3⋊Dic3C22×D311yescharacteristic
430C4⋊(C3⋊D3)—62no—
431C4⋊(C3⋊D3)—62no—
432C4⋊(C3⋊D3)—62no—
433C4⋊(C3⋊D3)—121no—
434C4×C3⋊D3—62no—
435C4×C3⋊D3—121no—
436C3×#67—62no—
437C3×#67—62no—
438C3×#67—62no—
439C3×#67—62no—
440C3×#67—122no—
441C3×#67—122no—
442C2×C3×Dic3—21no—
443C2×C3×Dic3—21no—
444C2×C3×Dic3—21no—
445C2×C3×Dic3—21no—
446C2×C3×Dic3—21no—
447C2×C3×Dic3—21no—
448C2×C3×Dic3—31no—
449C2×C3×Dic3—31no—
450C2×C3×Dic3—31no—
451C2×C3×Dic3—31no—
452C2×C3×Dic3—61no—
453C2×C3×Dic3—61no—
454C2×C3×Dic3C22×D311yescharacteristic
455C2×C3×Dic3C22×D311yescharacteristic
456C2×C3×Dic3C22×D311yescharacteristic
457C2×C3×Dic3C22×D311yescharacteristic
458C2×C3×Dic3C22×D311yescharacteristic
459C2×C3×Dic3C22×D311yescharacteristic
460C2×C3×Dic3C22×D311yescharacteristic
461C2×C3×Dic3C22×D311yescharacteristic
462C2×C3×Dic3C22×D311yescharacteristic
463C2×C3×Dic3C22×D311yescharacteristic
464C2×C3×Dic3C22×D311yescharacteristic
465C2×C3×Dic3C22×D311yescharacteristic
466C3×C4×D3—62no—
467C3×C4×D3—62no—
468C3×C4×D3—62no—
469C3×C4×D3—62no—
470C3×C4×D3—121no—
471C3×C4×D3—121no—
472C3×Dic6—62no—
473C3×Dic6—62no—
474#627—22no—
475#626—34no—
476#626—34no—
477#626—62no—
478#626—62no—
479#626—62no—
480#626—62no—
481#626—62no—
482#626—62no—
483#626—62no—
484#626—62no—
485#626—122no—
486#626—122no—
487#626—122no—
488#626—121no—
489#626—121no—
490#626—122no—
491#625—34no—
492#625—62no—
493#624—22no—
494#624—22no—
495#624—41no—
496#624—62no—
497#624—62no—
498#624—62no—
499#624—122no—
500D3×Dic3—62no—
501D3×Dic3—62no—
502D3×Dic3—121no—
503D3×Dic3—121no—
504D3×Dic3—122no—
505#546—271noSylow
506C2×C33—41no—
507C2×C33C22×D411yescharacteristic
508C2×C33C2×#4111yescharacteristic
509C2×C33H(5,𝔽2)11yescharacteristic
510C3⋊(C3⋊D3)—41no—
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×Q8—91no—
523C2×C3×D4—91no—
524C2×C3×D4—91no—
525C22×C3×C4—91no—
526C22×C3×C4—91no—
527C22×C3×C4—91no—
528C2×#67—31no—
529C2×#67—31no—
530C2×#67—31no—
531C2×#67—31no—
532C2×#67—61no—
533C2×#67—61no—
534C2×#67—91no—
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—91no—
544C2×#67—91no—
545C2×#67—181no—
546C2×#67—181no—
547C2×#67—181no—
548C2×#67—184no—
549C2×#67—361no—
550C22×Dic3—91no—
551C22×Dic3—91no—
552#239—184no—
553D3×D4—184no—
554D3×D4—184no—
555#235—184no—
556#235—184no—
557C2×D12—91no—
558C2×D12—91no—
559C2×D12—91no—
560C2×D12—91no—
561C2×D12—91no—
562C2×D12—91no—
563C2×D12—91no—
564C2×D12—91no—
565C2×D12—91no—
566C2×D12—91no—
567C2×D12—181no—
568C2×D12—181no—
569C2×D12—181no—
570C2×D12—181no—
571C2×C4×D3—31no—
572C2×C4×D3—31no—
573C2×C4×D3—31no—
574C2×C4×D3—31no—
575C2×C4×D3—31no—
576C2×C4×D3—31no—
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—181no—
585C2×C4×D3—181no—
586C2×Dic6—31no—
587C2×Dic6—31no—
588C3×C4⋊C4—91no—
589C3×C4⋊C4—91no—
590C3×C22⋊C4—31no—
591C3×C22⋊C4—31no—
592C3×C22⋊C4—31no—
593C3×C22⋊C4—31no—
594C3×C22⋊C4—31no—
595C3×C22⋊C4—31no—
596C3×C22⋊C4—61no—
597C3×C22⋊C4—61no—
598C3×C22⋊C4—61no—
599C3×C22⋊C4—91no—
600C3×C22⋊C4—91no—
601C3×C22⋊C4—91no—
602C3×C22⋊C4—91no—
603C3×C22⋊C4—91no—
604C3×C42—91no—
605#217—91no—
606#217—91no—
607#217—91no—
608#217D3211yescharacteristic, complemented
609#217D3211yescharacteristic, complemented
610#217D3211yescharacteristic, complemented
611(C2×D3)⋊C4—31no—
612(C2×D3)⋊C4—31no—
613(C2×D3)⋊C4—31no—
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—31no—
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—
629(C2×D3)⋊C4—91no—
630(C2×D3)⋊C4—181no—
631(C2×D3)⋊C4—181no—
632(C2×D3)⋊C4—181no—
633(C2×D3)⋊C4—181no—
634C4⋊Dic3—31no—
635C4⋊Dic3—31no—
636C4⋊Dic3—91no—
637Dic3⋊C4—31no—
638Dic3⋊C4—31no—
639Dic3⋊C4—91no—
640Dic3⋊C4—91no—
641Dic3⋊C4—91no—
642Dic3⋊C4—91no—
643Dic3⋊C4—91no—
644Dic3⋊C4—181no—
645Dic3⋊C4—181no—
646C4×Dic3—31no—
647C4×Dic3—31no—
648C22×C32—21no—
649C22×C32—22no—
650C22×C32—21no—
651C22×C32—21no—
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—41no—
662C22×C32—41no—
663C22×C32—41no—
664C22×C32—42no—
665C22×C32—41no—
666C22×C32—41no—
667C22×C32—41no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—41no—
671C22×C32—81no—
672C22×C32—81no—
673C22×C32C23×D311yescharacteristic
674C22×C32C23×D311yescharacteristic
675C22×C32C23×D311yescharacteristic
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⋊D3—61no—
687C2×C3⋊D3—62no—
688C2×C3⋊D3—61no—
689C2×C3⋊D3—61no—
690C2×C3⋊D3—61no—
691C2×C3⋊D3—61no—
692C2×C3⋊D3—61no—
693C2×C3⋊D3—61no—
694C2×C3⋊D3—61no—
695C2×C3⋊D3—61no—
696C2×C3⋊D3—121no—
697C2×C3⋊D3—121no—
698C2×C3⋊D3—122no—
699C2×C3⋊D3—121no—
700C2×C3⋊D3—121no—
701C2×C3⋊D3—121no—
702C2×C3⋊D3—121no—
703C2×C3⋊D3—121no—
704C2×C3⋊D3—121no—
705C2×C3⋊D3—241no—
706C2×C3⋊D3—241no—
707C2×C3⋊D3#23512yescomplemented
708C2×C3⋊D3D3×D412yes—
709C2×C3⋊D3D3×D412yes—
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—61no—
753C32×C4—61no—
754C32×C4—61no—
755C32×C4—61no—
756C32×C4—61no—
757C32×C4—61no—
758C3⋊Dic3—21no—
759C3⋊Dic3—61no—
760C3⋊Dic3—62no—
761C3⋊Dic3—61no—
762C3⋊Dic3—61no—
763C3⋊Dic3—121no—
764C3⋊Dic3—121no—
765C3⋊Dic3—122no—
766C3⋊Dic3D3×D412yes—
767C3×Dic3—21no—
768C3×Dic3—21no—
769C3×Dic3—21no—
770C3×Dic3—21no—
771C3×Dic3—21no—
772C3×Dic3—21no—
773C3×Dic3—21no—
774C3×Dic3—21no—
775C3×Dic3—21no—
776C3×Dic3—21no—
777C3×Dic3—21no—
778C3×Dic3—21no—
779C3×Dic3—32no—
780C3×Dic3—32no—
781C3×Dic3—41no—
782C3×Dic3—41no—
783C3×Dic3—41no—
784C3×Dic3—41no—
785C3×Dic3—41no—
786C3×Dic3—41no—
787C3×Dic3—62no—
788C3×Dic3—61no—
789C3×Dic3—61no—
790C3×Dic3—121no—
791C2×#41—271no—
792C22×D4—271no—
793#124—91no—
794#123—91no—
795#123—271no—
796C22⋊Q8—271no—
797#121—271no—
798#121—271no—
799#121—271no—
800#120—271no—
801#120—271no—
802C4×D4—271no—
803C4×D4—271no—
804C2×C22⋊C4—91no—
805C2×C22⋊C4—271no—
806C33#54611yescharacteristic, complemented, Sylow
807C23×C3—21no—
808C23×C3—21no—
809C23×C3—21no—
810C23×C3—41no—
811C23×C3—91no—
812C23×C3—91no—
813C23×C3—91no—
814C23×C3—91no—
815C23×C3—182no—
816C23×C3—182no—
817C23×C3—361no—
818C23×C3C2×D3211yescharacteristic
819C23×C3C2×D3211yescharacteristic
820C23×C3C2×D3211yescharacteristic
821C22×D3—31no—
822C22×D3—31no—
823C22×D3—31no—
824C22×D3—31no—
825C22×D3—31no—
826C22×D3—31no—
827C22×D3—31no—
828C22×D3—31no—
829C22×D3—61no—
830C22×D3—61no—
831C22×D3—61no—
832C22×D3—61no—
833C22×D3—62no—
834C22×D3—62no—
835C22×D3—62no—
836C22×D3—62no—
837C22×D3—91no—
838C22×D3—91no—
839C22×D3—91no—
840C22×D3—122no—
841C22×D3—122no—
842C22×D3—121no—
843C22×D3—121no—
844C22×D3—122no—
845C22×D3—181no—
846C22×D3—181no—
847C22×D3—181no—
848C22×D3—182no—
849C22×D3—182no—
850C22×D3—182no—
851C22×D3—182no—
852C22×D3—182no—
853C22×D3—182no—
854C22×D3—361no—
855C22×D3—361no—
856C22×D3—361no—
857C22×D3—361no—
858C3×Q8—182no—
859C3×D4—182no—
860C3×D4—182no—
861C2×C3×C4—31no—
862C2×C3×C4—31no—
863C2×C3×C4—31no—
864C2×C3×C4—31no—
865C2×C3×C4—31no—
866C2×C3×C4—31no—
867C2×C3×C4—31no—
868C2×C3×C4—31no—
869C2×C3×C4—31no—
870C2×C3×C4—31no—
871C2×C3×C4—31no—
872C2×C3×C4—31no—
873C2×C3×C4—61no—
874C2×C3×C4—61no—
875C2×C3×C4—61no—
876C2×C3×C4—61no—
877C2×C3×C4—61no—
878C2×C3×C4—61no—
879C2×C3×C4—91no—
880C2×C3×C4—91no—
881C2×C3×C4—182no—
882C2×C3×C4—182no—
883C2×C3×C4—361no—
884#67—62no—
885#67—62no—
886#67—62no—
887#67—62no—
888#67—94no—
889#67—94no—
890#67—122no—
891#67—122no—
892#67—182no—
893#67—182no—
894#67—182no—
895#67—182no—
896#67—182no—
897#67—361no—
898#67—361no—
899#67—361no—
900#67—361no—
901#67—362no—
902#67—362no—
903#67—362no—
904#67—364no—
905C2×Dic3—31no—
906C2×Dic3—31no—
907C2×Dic3—31no—
908C2×Dic3—31no—
909C2×Dic3—61no—
910C2×Dic3—61no—
911C2×Dic3—91no—
912C2×Dic3—91no—
913C2×Dic3—91no—
914C2×Dic3—181no—
915C2×Dic3—181no—
916C2×Dic3—181no—
917C2×Dic3—182no—
918C2×Dic3—361no—
919C2×Dic3—361no—
920C2×Dic3C2×D3211yescharacteristic
921C2×Dic3C2×D3211yescharacteristic
922C2×Dic3C2×D3211yescharacteristic
923C2×Dic3C2×D3211yescharacteristic
924C2×Dic3C2×D3211yescharacteristic
925C2×Dic3C2×D3211yescharacteristic
926D12—94no—
927D12—182no—
928D12—182no—
929D12—182no—
930D12—182no—
931D12—182no—
932D12—182no—
933D12—182no—
934D12—362no—
935D12—362no—
936D12—362no—
937D12—361no—
938D12—361no—
939D12—362no—
940C4×D3—62no—
941C4×D3—62no—
942C4×D3—62no—
943C4×D3—62no—
944C4×D3—121no—
945C4×D3—121no—
946C4×D3—182no—
947C4×D3—182no—
948C4×D3—182no—
949C4×D3—182no—
950C4×D3—182no—
951C4×D3—362no—
952C4×D3—361no—
953C4×D3—361no—
954C4×D3—362no—
955Dic6—62no—
956Dic6—62no—
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—42no—
971C2×C32—41no—
972C2×C32—41no—
973C2×C32—81no—
974C2×C32—81no—
975C2×C32—82no—
976C2×C32C2×#23511yescharacteristic
977C2×C32C2×D3×D411yescharacteristic
978C2×C32C2×D3×D411yescharacteristic
979C2×C32C2×D3×D411yescharacteristic
980C2×C32#100411yescharacteristic
981C2×C32D3×#4111yescharacteristic
982C2×C32D3×#4111yescharacteristic
983C2×C32#100911yescharacteristic
984C2×C32#100911yescharacteristic
985C3⋊D3—22no—
986C3⋊D3—22no—
987C3⋊D3—22no—
988C3⋊D3—41no—
989C3⋊D3—121no—
990C3⋊D3—122no—
991C3⋊D3—121no—
992C3⋊D3—121no—
993C3⋊D3—241no—
994C3⋊D3—241no—
995C3⋊D3—242no—
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—91no—
1012C2×D4—91no—
1013C2×D4—91no—
1014C2×D4—271no—
1015C2×D4—271no—
1016C2×D4—271no—
1017C2×D4—271no—
1018C2×D4—271no—
1019C2×D4—271no—
1020C2×D4—271no—
1021C2×D4—544no—
1022C22×C4—91no—
1023C22×C4—91no—
1024C22×C4—91no—
1025C22×C4—271no—
1026C22×C4—271no—
1027C22×C4—271no—
1028C4⋊C4—91no—
1029C4⋊C4—91no—
1030C4⋊C4—271no—
1031C4⋊C4—271no—
1032C22⋊C4—31no—
1033C22⋊C4—31no—
1034C22⋊C4—31no—
1035C22⋊C4—91no—
1036C22⋊C4—91no—
1037C22⋊C4—91no—
1038C22⋊C4—91no—
1039C22⋊C4—91no—
1040C22⋊C4—271no—
1041C22⋊C4—271no—
1042C22⋊C4—271no—
1043C22⋊C4—271no—
1044C42—91no—
1045C22×C3—22no—
1046C22×C3—21no—
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—41no—
1059C22×C3—41no—
1060C22×C3—41no—
1061C22×C3—41no—
1062C22×C3—41no—
1063C22×C3—41no—
1064C22×C3—41no—
1065C22×C3—41no—
1066C22×C3—42no—
1067C22×C3—41no—
1068C22×C3—81no—
1069C22×C3—81no—
1070C22×C3—92no—
1071C22×C3—92no—
1072C22×C3—92no—
1073C22×C3—181no—
1074C22×C3—181no—
1075C22×C3—181no—
1076C22×C3—181no—
1077C22×C3—181no—
1078C22×C3—181no—
1079C22×C3—181no—
1080C22×C3—181no—
1081C22×C3—181no—
1082C22×C3—364no—
1083C22×C3C22×D3211yescharacteristic
1084C22×C3C22×D3211yescharacteristic
1085C22×C3C22×D3211yescharacteristic
1086C2×D3—32no—
1087C2×D3—32no—
1088C2×D3—32no—
1089C2×D3—32no—
1090C2×D3—32no—
1091C2×D3—32no—
1092C2×D3—62no—
1093C2×D3—62no—
1094C2×D3—62no—
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—61no—
1106C2×D3—61no—
1107C2×D3—61no—
1108C2×D3—61no—
1109C2×D3—61no—
1110C2×D3—61no—
1111C2×D3—61no—
1112C2×D3—61no—
1113C2×D3—121no—
1114C2×D3—121no—
1115C2×D3—121no—
1116C2×D3—121no—
1117C2×D3—121no—
1118C2×D3—121no—
1119C2×D3—121no—
1120C2×D3—121no—
1121C2×D3—121no—
1122C2×D3—124no—
1123C2×D3—124no—
1124C2×D3—128no—
1125C2×D3—182no—
1126C2×D3—181no—
1127C2×D3—181no—
1128C2×D3—181no—
1129C2×D3—181no—
1130C2×D3—181no—
1131C2×D3—181no—
1132C2×D3—181no—
1133C2×D3—181no—
1134C2×D3—181no—
1135C2×D3—361no—
1136C2×D3—361no—
1137C2×D3—361no—
1138C2×D3—361no—
1139C2×D3—361no—
1140C2×D3—361no—
1141C2×D3—361no—
1142C2×D3—361no—
1143C2×D3—362no—
1144C2×D3—364no—
1145C2×D3—364no—
1146C2×D3—364no—
1147C2×D3—721no—
1148C2×D3—721no—
1149C3×C4—61no—
1150C3×C4—61no—
1151C3×C4—61no—
1152C3×C4—61no—
1153C3×C4—61no—
1154C3×C4—61no—
1155C3×C4—61no—
1156C3×C4—61no—
1157C3×C4—61no—
1158C3×C4—61no—
1159C3×C4—61no—
1160C3×C4—61no—
1161C3×C4—92no—
1162C3×C4—121no—
1163C3×C4—121no—
1164C3×C4—121no—
1165C3×C4—121no—
1166C3×C4—121no—
1167C3×C4—121no—
1168C3×C4—181no—
1169Dic3—21no—
1170Dic3—21no—
1171Dic3—21no—
1172Dic3—21no—
1173Dic3—21no—
1174Dic3—21no—
1175Dic3—32no—
1176Dic3—32no—
1177Dic3—62no—
1178Dic3—61no—
1179Dic3—61no—
1180Dic3—121no—
1181Dic3—182no—
1182Dic3—181no—
1183Dic3—181no—
1184Dic3—181no—
1185Dic3—361no—
1186Dic3—361no—
1187Dic3—362no—
1188C32—21no—
1189C32—21no—
1190C32—21no—
1191C32—41no—
1192C32#549011yescharacteristic, complemented
1193C32#565411yescharacteristic, complemented
1194C32#567611yescharacteristic, complemented
1195C23—91no—
1196C23—91no—
1197C23—91no—
1198C23—91no—
1199C23—182no—
1200C23—182no—
1201C23—271no—
1202C23—361no—
1203C23—542no—
1204C23—542no—
1205C23—1081no—
1206C23D3311yescharacteristic
1207Q8—182no—
1208D4—182no—
1209D4—182no—
1210D4—274no—
1211D4—542no—
1212D4—542no—
1213D4—542no—
1214D4—542no—
1215D4—1081no—
1216D4—1081no—
1217C2×C4—31no—
1218C2×C4—31no—
1219C2×C4—31no—
1220C2×C4—31no—
1221C2×C4—31no—
1222C2×C4—31no—
1223C2×C4—91no—
1224C2×C4—91no—
1225C2×C4—182no—
1226C2×C4—182no—
1227C2×C4—271no—
1228C2×C4—361no—
1229C2×C4—542no—
1230C2×C4—542no—
1231C2×C4—1081no—
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—41no—
1243C2×C3—41no—
1244C2×C3—41no—
1245C2×C3—41no—
1246C2×C3—41no—
1247C2×C3—41no—
1248C2×C3—81no—
1249C2×C3—81no—
1250C2×C3—82no—
1251C2×C3—182no—
1252C2×C3—182no—
1253C2×C3—182no—
1254C2×C3—361no—
1255C2×C3D3×#23511yescharacteristic
1256C2×C3D3×#23511yescharacteristic
1257C2×C3#6430811yescharacteristic
1258C2×C3D32×D411yescharacteristic
1259C2×C3D32×D411yescharacteristic
1260C2×C3D32×D411yescharacteristic
1261C2×C3#6431211yescharacteristic
1262C2×C3#6431411yescharacteristic
1263C2×C3#6431411yescharacteristic
1264D3—62no—
1265D3—62no—
1266D3—62no—
1267D3—62no—
1268D3—62no—
1269D3—62no—
1270D3—122no—
1271D3—122no—
1272D3—122no—
1273D3—121no—
1274D3—121no—
1275D3—241no—
1276D3—362no—
1277D3—361no—
1278D3—361no—
1279D3—361no—
1280D3—721no—
1281D3—721no—
1282D3—722no—
1283C22—21no—
1284C22—21no—
1285C22—21no—
1286C22—92no—
1287C22—92no—
1288C22—92no—
1289C22—181no—
1290C22—181no—
1291C22—181no—
1292C22—181no—
1293C22—181no—
1294C22—181no—
1295C22—181no—
1296C22—181no—
1297C22—181no—
1298C22—364no—
1299C22—541no—
1300C22—541no—
1301C22—541no—
1302C22—1084no—
1303C22C2×D3311yescharacteristic
1304C4—61no—
1305C4—61no—
1306C4—61no—
1307C4—61no—
1308C4—61no—
1309C4—61no—
1310C4—92no—
1311C4—181no—
1312C4—541no—
1313C3—21no—
1314C3—21no—
1315C3—21no—
1316C3—41no—
1317C3#1059427211yescharacteristic, complemented
1318C3#1059428011yescharacteristic, complemented
1319C3#1059428211yescharacteristic, complemented
1320C2—41no—
1321C2—182no—
1322C2—182no—
1323C2—182no—
1324C2—361no—
1325C2—1081no—
1326C2#1172441011yescharacteristic
1327C2#1172442011yescharacteristic
1328C2#1172444011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#89049C2semidirect
2. C2×#88965C2semidirect
3. #11723636C2semidirect
4. #11723624C2semidirect
5. #11723623C2semidirect
6. C3×#63975C2semidirect
7. C3×#63974C2semidirect
8. C3×#63953C2semidirect
9. #11722995C2semidirect
10. #11722979C2semidirect
11. #11722961C2semidirect
12. #11722952C2semidirect
13. #11722937C2semidirect
14. #11722934C2semidirect
15. #11722905C2semidirect
21. C2×#6312C22semidirect
29. C2×#6292C22semidirect
30. C2×#6292C22semidirect
31. C2×#6292C22semidirect
32. C2×#6289C22semidirect
33. C2×Dic3×C3⋊D3C22semidirect
34. C2×C3×#627C22semidirect
35. C2×C3×#624C22semidirect
36. C2×C3×#624C22semidirect
37. C2×C3×#624C22semidirect
39. C32×#217C22semidirect
40. C32×#217C22semidirect
41. C32×#217C22semidirect
42. #88807C22semidirect
43. #88806C22semidirect
44. #88804C22semidirect
46. #88803C22semidirect
47. #88803C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
52. C3×#3722C22semidirect
53. C3×#3722C22semidirect
54. C3×#3722C22semidirect
55. C3×Dic32C22semidirect
74. #63975D3semidirect
75. #63974D3semidirect
82. #63953D3semidirect
129. #6295D4semidirect
183. C2×#627C2×D3semidirect
206. C2×#624C2×D3semidirect
207. C2×#624C2×D3semidirect
208. C2×#624C2×D3semidirect
229. C3×#217C2×D3semidirect
230. C3×#217C2×D3semidirect
231. C3×#217C2×D3semidirect
232. C3×#217C2×D3semidirect
233. C3×#217C2×D3semidirect
234. C3×#217C2×D3semidirect
257. Dic3⋊Dic3C2×D3semidirect
258. Dic3⋊Dic3C2×D3semidirect
264. #3722C2×D3semidirect
265. #3722C2×D3semidirect
266. #3722C2×D3semidirect
276. Dic32C2×D3semidirect
296. C2×C3×C3⋊D3#41semidirect
608. #217D32semidirect
609. #217D32semidirect
610. #217D32semidirect
707. C2×C3⋊D3#235semidirect
806. C33#546semidirect
1192. C32#5490semidirect
1193. C32#5654semidirect
1194. C32#5676semidirect
1317. C3#10594272semidirect
1318. C3#10594280semidirect
1319. C3#10594282semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
C2×#889652
#117236362
#117236242
#117236232
C3×#639752
C3×#639742
C3×#639532
#117229952
#117229792
#117229612
#117229522
#117229372
#117229342
#117229052
#105942823
#105942803
#105942723