Finite Group Databasebeta

← #13172099

Subgroups — #13172099

Order 1728.

1556 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89029C211yesmaximal, characteristic, complemented
2C2×C3×#3804C211yesmaximal, characteristic, complemented
3#11723726C211yesmaximal, characteristic, complemented
4C2×#88807C211yesmaximal, characteristic, complemented
5#11723603C211yesmaximal, characteristic, complemented
6C3×#63980C211yesmaximal, characteristic, complemented
7C3×#63961C211yesmaximal, characteristic, complemented
8#11723034C211yesmaximal, characteristic, complemented
9#11722992C211yesmaximal, characteristic, complemented
10#11722991C211yesmaximal, characteristic, complemented
11#11722976C211yesmaximal, characteristic, complemented
12#11722975C211yesmaximal, characteristic, complemented
13#11722965C211yesmaximal, characteristic, complemented
14#11722924C211yesmaximal, characteristic, complemented
15#11722910C211yesmaximal, characteristic, complemented
16#10595162—31nomaximal
17#10595151—31nomaximal
18#10594888—31nomaximal
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C2×#6294C2211yescharacteristic
26C2×#6293C2211yescharacteristic
27C2×#6290C2211yescharacteristic
28C2×Dic3×C3⋊D3C2211yescharacteristic
29#89029—24no—
30C2×D3×C3⋊Dic3C2211yescharacteristic
31C2×C3×#627C2211yescharacteristic
32C2×C3×#626C2211yescharacteristic
33C2×C3×#625C2211yescharacteristic
34C2×C3×#624C2211yescharacteristic
35C3×#3804—24no—
36C2×C3×D3×Dic3C2211yescharacteristic
37C3×#3757C2211yescharacteristic
38#88815C2211yescharacteristic
39#88814C2211yescharacteristic
40#88813C2211yescharacteristic
41#88807C2211yescharacteristic
42#88807C2211yescharacteristic
43#88807C2211yescharacteristic
44#88807C2211yescharacteristic
45#88807C2211yescharacteristic
46#88807C2211yescharacteristic
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49C3×#3724C2211yescharacteristic
50C3×#3724C2211yescharacteristic
51C3×#3724C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×#3830—31no—
57C2×C3×#237—31no—
58C2×C3×#235—31no—
59C2×#3805—31no—
60C2×#3805—31no—
61C2×#3805—61no—
62C2×#3804D311yescharacteristic, complemented
63#64144—31no—
64C2×#3750—31no—
65C3×#939—31no—
66C3×#939—31no—
67C3×#935—31no—
68C3×#929—31no—
69#63982—31no—
70#63980D311yescharacteristic, complemented
71#63975—31no—
72#67⋊Dic3—31no—
73#67⋊Dic3—31no—
74Dic3×#67—31no—
75Dic3×#67—31no—
76#63970—31no—
77#63969—31no—
78C2×Dic3⋊Dic3—31no—
79C2×Dic3⋊Dic3—31no—
80C2×Dic3⋊Dic3—61no—
81#63964—31no—
82#63962—31no—
83#63962—31no—
84#63962—61no—
85#63961D311yescharacteristic, complemented
86#63958—31no—
87#63952—31no—
88#63905—31no—
89#63905—31no—
90#63896—31no—
91#63887—31no—
92#63887—31no—
93#63885—31no—
94#63884—31no—
95#63883—31no—
96#63879—31no—
97D3×Dic3⋊C4—31no—
98D3×Dic3⋊C4—31no—
99#63853—31no—
100#63851—31no—
101#63840—31no—
102#63839—31no—
103#63839—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C2×C3⋊(C3⋊Dic3)—22no—
109C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C3×#638D414yescomplemented
112C2×C3×C3⋊Dic3—22no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C32×#67—22no—
119C32×#67—22no—
120C2×C32×Dic3—22no—
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125#6294—22no—
126#6293—22no—
127#6290—22no—
128Dic3×C3⋊D3—22no—
129D3×C3⋊Dic3—22no—
130C3×#627—22no—
131C3×#626—22no—
132C3×#625—22no—
133C3×#624—22no—
134C3×D3×Dic3—22no—
135#5824—91no—
136#5655—91no—
137#5611—91no—
138C2×C32×D4—31no—
139C2×C32×D4—31no—
140C22×C32×C4—31no—
141C2×#638—31no—
142C2×#638C2×D311yescharacteristic
143C22×C3⋊Dic3—31no—
144C22×C3⋊Dic3—31no—
145C22×C3⋊Dic3—31no—
146C22×C3⋊Dic3—31no—
147C22×C3⋊Dic3—61no—
148C22×C3⋊Dic3—61no—
149C22×C3⋊Dic3—61no—
150C22×C3⋊Dic3—121no—
151C22×C3⋊Dic3C2×D311yescharacteristic
152#3830—64no—
153C2×C4×C3⋊D3—31no—
154C2×#634—31no—
155C2×C3×#67—21no—
156C2×C3×#67—21no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—61no—
163C2×C3×#67C2×D311yescharacteristic
164C2×C3×#67C2×D311yescharacteristic
165C2×C3×#67C2×D311yescharacteristic
166C2×C3×#67C2×D311yescharacteristic
167C22×C3×Dic3—21no—
168C22×C3×Dic3—31no—
169C22×C3×Dic3—31no—
170C22×C3×Dic3—31no—
171C22×C3×Dic3—61no—
172C22×C3×Dic3C2×D311yescharacteristic
173C22×C3×Dic3C2×D311yescharacteristic
174C3×#237—64no—
175C3×#235—64no—
176C2×C3×D12—31no—
177C2×C3×C4×D3—31no—
178C2×C3×C4×D3—31no—
179C2×C3×C4×D3—31no—
180C2×C3×Dic6—31no—
181C2×C3×Dic6—31no—
182C2×#627—31no—
183C2×#627—31no—
184C2×#627—61no—
185C2×#627C2×D311yescharacteristic
186C2×#626C2×D311yescharacteristic
187C2×#625—31no—
188C2×#625—31no—
189C2×#625—61no—
190C2×#625C2×D311yescharacteristic
191C2×#624—31no—
192C2×#624C2×D311yescharacteristic
193#3805—64no—
194#3805—64no—
195#3805—68no—
196#3804—24no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3—31no—
199C2×D3×Dic3—31no—
200C2×D3×Dic3—31no—
201C2×D3×Dic3—31no—
202C2×D3×Dic3—31no—
203C2×D3×Dic3—61no—
204C2×D3×Dic3—61no—
205C2×D3×Dic3C2×D311yescharacteristic
206#3757—31no—
207#3757—31no—
208#3757C2×D311yescharacteristic
209#3750—31no—
210#3750—31no—
211#3750—31no—
212#3750—31no—
213#3750—31no—
214#3750—31no—
215C3×#217—31no—
216C3×#217—31no—
217C3×#217—31no—
218C3×#217—31no—
219C3×#217—31no—
220C3×#217—31no—
221C3×#217—61no—
222C3×(C2×D3)⋊C4—31no—
223C3×(C2×D3)⋊C4—31no—
224C3×(C2×D3)⋊C4—31no—
225C3×(C2×D3)⋊C4—31no—
226C3×Dic3⋊C4—31no—
227C3×Dic3⋊C4—31no—
228C3×Dic3⋊C4—31no—
229C3×Dic3⋊C4—31no—
230C3×Dic3⋊C4—31no—
231C3×Dic3⋊C4—31no—
232#3724—31no—
233#3724C2×D311yescharacteristic
234#3724C2×D311yescharacteristic
235#3724C2×D311yescharacteristic
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238Dic3⋊Dic3—31no—
239Dic3⋊Dic3—31no—
240Dic3⋊Dic3—31no—
241Dic3⋊Dic3—31no—
242Dic3⋊Dic3—31no—
243Dic3⋊Dic3—31no—
244Dic3⋊Dic3—31no—
245Dic3⋊Dic3—31no—
246Dic3⋊Dic3—31no—
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—61no—
251Dic3⋊Dic3—61no—
252Dic3⋊Dic3—61no—
253Dic3⋊Dic3—61no—
254Dic3⋊Dic3—61no—
255Dic3⋊Dic3—61no—
256#3722—31no—
257(C2×D3)⋊Dic3—31no—
258(C2×D3)⋊Dic3—31no—
259(C2×D3)⋊Dic3—31no—
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—61no—
264(C2×D3)⋊Dic3—61no—
265(C2×D3)⋊Dic3C2×D311yescharacteristic
266(C2×D3)⋊Dic3C2×D311yescharacteristic
267(C2×D3)⋊Dic3C2×D311yescharacteristic
268(C2×D3)⋊Dic3C2×D311yescharacteristic
269Dic32—31no—
270Dic32—31no—
271Dic32—31no—
272C22×C33—21no—
273C22×C33—21no—
274C22×C33C2×D412yes—
275C22×C33C2411yescharacteristic
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3—21no—
278C2×C3×C3⋊D3C2×D412yes—
279C2×C32×D3—21no—
280C2×C32×D3—21no—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284C2×C32×D3—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—
291C3×C3⋊Dic3#4112yescomplemented
292C32×Dic3—21no—
293C32×Dic3—21no—
294C32×Dic3—21no—
295C32×Dic3—21no—
296C2×C3×#41—91no—
297C2×#237—31no—
298C2×#237—91no—
299C2×#237—91no—
300C2×#237—91no—
301C2×#237—181no—
302C2×#235—31no—
303C3×#123—91no—
304C3×#121—91no—
305#946—91no—
306#944—91no—
307#939—31no—
308#939—31no—
309#939—91no—
310#938—91no—
311#935—31no—
312#935—91no—
313#935—91no—
314#935—91no—
315#935—181no—
316D4×Dic3—91no—
317D4×Dic3—91no—
318#929—31no—
319#929—91no—
320C4×#67—91no—
321C4×#67—91no—
322C2×C4⋊Dic3—91no—
323#924—91no—
324C2×Dic3⋊C4—91no—
325C2×Dic3⋊C4—91no—
326C2×Dic3⋊C4—91no—
327C2×Dic3⋊C4—181no—
328#896—91no—
329#894—91no—
330D3×C4⋊C4—91no—
331D3×C4⋊C4—91no—
332#888—91no—
333#888—91no—
334#886—91no—
335#884—91no—
336#883—91no—
337#883—91no—
338#883—91no—
339#67⋊C4—91no—
340#67⋊C4—91no—
341#878—91no—
342#878—91no—
343#878—91no—
344C23×C32—21no—
345C23×C32—21no—
346C23×C32—21no—
347C23×C32—31no—
348C23×C32—31no—
349C23×C32—41no—
350C23×C32C22×D311yescharacteristic
351C23×C32C22×D311yescharacteristic
352C23×C32C22×D311yescharacteristic
353C22×C3⋊D3C22×D311yescharacteristic
354C22×C3×D3—21no—
355C22×C3×D3—21no—
356C22×C3×D3—31no—
357C22×C3×D3—31no—
358C22×C3×D3—61no—
359C22×C3×D3C22×D311yescharacteristic
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C22×D311yescharacteristic
362C22×C3×D3C22×D311yescharacteristic
363C32×D4—62no—
364C32×D4—62no—
365C2×C32×C4—31no—
366C2×C32×C4—31no—
367C2×C32×C4—31no—
368C2×C32×C4—31no—
369C2×C32×C4—62no—
370#638—62no—
371#638#6714yescomplemented
372C2×C3⋊Dic3—22no—
373C2×C3⋊Dic3—31no—
374C2×C3⋊Dic3—31no—
375C2×C3⋊Dic3—31no—
376C2×C3⋊Dic3—31no—
377C2×C3⋊Dic3—31no—
378C2×C3⋊Dic3—31no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—61no—
381C2×C3⋊Dic3—61no—
382C2×C3⋊Dic3—61no—
383C2×C3⋊Dic3—61no—
384C2×C3⋊Dic3—61no—
385C2×C3⋊Dic3—62no—
386C2×C3⋊Dic3—62no—
387C2×C3⋊Dic3—64no—
388C2×C3⋊Dic3—62no—
389C2×C3⋊Dic3—62no—
390C2×C3⋊Dic3—121no—
391C2×C3⋊Dic3—121no—
392C2×C3⋊Dic3—122no—
393C2×C3⋊Dic3—122no—
394C2×C3⋊Dic3—124no—
395C2×C3⋊Dic3C22×D311yescharacteristic
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C2×C3⋊Dic3C22×D311yescharacteristic
399C2×C3⋊Dic3C22×D311yescharacteristic
400C4×C3⋊D3—62no—
401#634—62no—
402C3×#67—24no—
403C3×#67—22no—
404C3×#67—22no—
405C3×#67—22no—
406C3×#67—22no—
407C3×#67—34no—
408C3×#67—34no—
409C3×#67—42no—
410C3×#67—64no—
411C3×#67—62no—
412C3×#67—62no—
413C3×#67—62no—
414C2×C3×Dic3—22no—
415C2×C3×Dic3—22no—
416C2×C3×Dic3—21no—
417C2×C3×Dic3—21no—
418C2×C3×Dic3—21no—
419C2×C3×Dic3—21no—
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—31no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—42no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—61no—
436C2×C3×Dic3—62no—
437C2×C3×Dic3—62no—
438C2×C3×Dic3—62no—
439C2×C3×Dic3—64no—
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C2×C3×Dic3C22×D311yescharacteristic
447C2×C3×Dic3C22×D311yescharacteristic
448C3×D12—62no—
449C3×C4×D3—62no—
450C3×C4×D3—62no—
451C3×C4×D3—62no—
452C3×Dic6—62no—
453C3×Dic6—62no—
454#627—22no—
455#627—62no—
456#627—62no—
457#627—64no—
458#626—22no—
459#625—22no—
460#625—62no—
461#625—62no—
462#625—64no—
463#624—22no—
464#624—62no—
465D3×Dic3—22no—
466D3×Dic3—62no—
467D3×Dic3—62no—
468D3×Dic3—64no—
469D3×Dic3—62no—
470D3×Dic3—62no—
471D3×Dic3—62no—
472D3×Dic3—64no—
473D3×Dic3—62no—
474#547—271noSylow
475C2×C33—22no—
476C2×C33C22×D411yescharacteristic
477C2×C33C2×#4111yescharacteristic
478C2×C332−1+411yescharacteristic
479C3×C3⋊D3—22no—
480C32×D3—41no—
481C32×D3—41no—
482C3×#41—184no—
483C2×C3×Q8—91no—
484C2×C3×D4—31no—
485C2×C3×D4—31no—
486C2×C3×D4—31no—
487C2×C3×D4—31no—
488C2×C3×D4—61no—
489C2×C3×D4—61no—
490C2×C3×D4—91no—
491C2×C3×D4—91no—
492C2×C3×D4—91no—
493C22×C3×C4—31no—
494C22×C3×C4—31no—
495C22×C3×C4—61no—
496C22×C3×C4—91no—
497C22×C3×C4—91no—
498C22×C3×C4—91no—
499C2×#67—31no—
500C2×#67—31no—
501C2×#67—31no—
502C2×#67—31no—
503C2×#67—31no—
504C2×#67—61no—
505C2×#67—91no—
506C2×#67—91no—
507C2×#67—91no—
508C2×#67—181no—
509C2×#67D3211yescharacteristic
510C2×#67D3211yescharacteristic
511C22×Dic3—31no—
512C22×Dic3—31no—
513C22×Dic3—31no—
514C22×Dic3—61no—
515C22×Dic3—91no—
516C22×Dic3—91no—
517C22×Dic3—91no—
518C22×Dic3—91no—
519C22×Dic3—91no—
520C22×Dic3—91no—
521C22×Dic3—91no—
522C22×Dic3—181no—
523C22×Dic3—181no—
524C22×Dic3—181no—
525C22×Dic3—181no—
526C22×Dic3—361no—
527C22×Dic3D3211yescharacteristic
528#237—64no—
529#237—184no—
530#237—184no—
531#237—184no—
532#237—188no—
533#235—64no—
534C2×D12—31no—
535C2×C4×D3—31no—
536C2×C4×D3—31no—
537C2×C4×D3—31no—
538C2×C4×D3—91no—
539C2×C4×D3—91no—
540C2×C4×D3—91no—
541C2×C4×D3—91no—
542C2×C4×D3—91no—
543C2×C4×D3—181no—
544C2×Dic6—31no—
545C2×Dic6—31no—
546C2×Dic6—91no—
547C2×Dic6—91no—
548C2×Dic6—91no—
549C2×Dic6—181no—
550C3×C4⋊C4—91no—
551C3×C4⋊C4—91no—
552C3×C4⋊C4—91no—
553C3×C22⋊C4—91no—
554C3×C22⋊C4—91no—
555C3×C22⋊C4—91no—
556C3×C22⋊C4—91no—
557C3×C22⋊C4—91no—
558#217—31no—
559#217—31no—
560#217—31no—
561#217—31no—
562#217—31no—
563#217—31no—
564#217—61no—
565#217—91no—
566#217—91no—
567#217—91no—
568#217—91no—
569#217—91no—
570#217—181no—
571#217—181no—
572(C2×D3)⋊C4—31no—
573(C2×D3)⋊C4—31no—
574(C2×D3)⋊C4—31no—
575(C2×D3)⋊C4—31no—
576(C2×D3)⋊C4—91no—
577(C2×D3)⋊C4—91no—
578(C2×D3)⋊C4—91no—
579(C2×D3)⋊C4—91no—
580C4⋊Dic3—91no—
581C4⋊Dic3—91no—
582C4⋊Dic3—91no—
583C4⋊Dic3—91no—
584C4⋊Dic3—91no—
585C4⋊Dic3—91no—
586C4⋊Dic3—91no—
587Dic3⋊C4—31no—
588Dic3⋊C4—31no—
589Dic3⋊C4—31no—
590Dic3⋊C4—31no—
591Dic3⋊C4—31no—
592Dic3⋊C4—31no—
593Dic3⋊C4—91no—
594Dic3⋊C4—91no—
595Dic3⋊C4—91no—
596Dic3⋊C4—91no—
597Dic3⋊C4—91no—
598Dic3⋊C4—91no—
599Dic3⋊C4—91no—
600Dic3⋊C4—91no—
601Dic3⋊C4—91no—
602Dic3⋊C4—91no—
603Dic3⋊C4—91no—
604Dic3⋊C4—91no—
605Dic3⋊C4—91no—
606Dic3⋊C4—91no—
607Dic3⋊C4—181no—
608Dic3⋊C4—181no—
609Dic3⋊C4—181no—
610Dic3⋊C4—181no—
611Dic3⋊C4—181no—
612Dic3⋊C4—181no—
613C4×Dic3—91no—
614C4×Dic3—91no—
615C4×Dic3—91no—
616C22×C32—21no—
617C22×C32—21no—
618C22×C32—22no—
619C22×C32—22no—
620C22×C32—21no—
621C22×C32—21no—
622C22×C32—21no—
623C22×C32—21no—
624C22×C32—21no—
625C22×C32—21no—
626C22×C32—21no—
627C22×C32—22no—
628C22×C32—22no—
629C22×C32—22no—
630C22×C32—42no—
631C22×C32—41no—
632C22×C32—41no—
633C22×C32—41no—
634C22×C32—41no—
635C22×C32—41no—
636C22×C32—42no—
637C22×C32—42no—
638C22×C32—61no—
639C22×C32—61no—
640C22×C32—61no—
641C22×C32—61no—
642C22×C32—61no—
643C22×C32—61no—
644C22×C32D3×D412yes—
645C22×C32D3×D412yes—
646C22×C32C2×#6712yes—
647C22×C32C23×D311yescharacteristic
648C22×C32C23×D311yescharacteristic
649C22×C32C23×D311yescharacteristic
650C2×C3⋊D3—21no—
651C2×C3⋊D3—21no—
652C2×C3⋊D3C2×#6712yes—
653C2×C3×D3—22no—
654C2×C3×D3—21no—
655C2×C3×D3—21no—
656C2×C3×D3—21no—
657C2×C3×D3—21no—
658C2×C3×D3—21no—
659C2×C3×D3—21no—
660C2×C3×D3—21no—
661C2×C3×D3—21no—
662C2×C3×D3—21no—
663C2×C3×D3—21no—
664C2×C3×D3—21no—
665C2×C3×D3—21no—
666C2×C3×D3—32no—
667C2×C3×D3—32no—
668C2×C3×D3—41no—
669C2×C3×D3—41no—
670C2×C3×D3—41no—
671C2×C3×D3—41no—
672C2×C3×D3—41no—
673C2×C3×D3—62no—
674C2×C3×D3—61no—
675C2×C3×D3—61no—
676C2×C3×D3—61no—
677C2×C3×D3—61no—
678C2×C3×D3—121no—
679C2×C3×D3—121no—
680C32×C4—61no—
681C32×C4—61no—
682C32×C4—61no—
683C32×C4—61no—
684C3⋊Dic3—21no—
685C3⋊Dic3—21no—
686C3⋊Dic3—21no—
687C3⋊Dic3—61no—
688C3⋊Dic3—61no—
689C3⋊Dic3—62no—
690C3⋊Dic3—62no—
691C3⋊Dic3—61no—
692C3⋊Dic3—61no—
693C3⋊Dic3—61no—
694C3⋊Dic3—61no—
695C3⋊Dic3—121no—
696C3⋊Dic3—121no—
697C3⋊Dic3—121no—
698C3⋊Dic3—121no—
699C3⋊Dic3—122no—
700C3⋊Dic3—122no—
701C3⋊Dic3#23712yescomplemented
702C3⋊Dic3C2×#6712yes—
703C3×Dic3—22no—
704C3×Dic3—21no—
705C3×Dic3—21no—
706C3×Dic3—21no—
707C3×Dic3—21no—
708C3×Dic3—21no—
709C3×Dic3—21no—
710C3×Dic3—21no—
711C3×Dic3—21no—
712C3×Dic3—32no—
713C3×Dic3—32no—
714C3×Dic3—32no—
715C3×Dic3—32no—
716C3×Dic3—41no—
717C3×Dic3—41no—
718C3×Dic3—41no—
719C3×Dic3—62no—
720C3×Dic3—62no—
721C3×Dic3—62no—
722C3×Dic3—61no—
723C3×Dic3—61no—
724C3×Dic3—61no—
725C3×Dic3—61no—
726C3×Dic3—61no—
727C3×Dic3—61no—
728C3×Dic3—121no—
729C3×Dic3—121no—
730C2×#41—91no—
731C2×#41—271no—
732C4⋊Q8—271no—
733#123—91no—
734#123—271no—
735#123—271no—
736#123—271no—
737C22⋊Q8—271no—
738C22⋊Q8—271no—
739#121—91no—
740#121—271no—
741C4×D4—271no—
742C4×D4—271no—
743C2×C4⋊C4—271no—
744C2×C4⋊C4—271no—
745C33#54711yescharacteristic, complemented, Sylow
746C23×C3—21no—
747C23×C3—21no—
748C23×C3—21no—
749C23×C3—31no—
750C23×C3—31no—
751C23×C3—31no—
752C23×C3—31no—
753C23×C3—41no—
754C23×C3—61no—
755C23×C3—61no—
756C23×C3—91no—
757C23×C3C2×D3211yescharacteristic
758C23×C3C2×D3211yescharacteristic
759C23×C3C2×D3211yescharacteristic
760C22×D3—31no—
761C22×D3—31no—
762C22×D3—61no—
763C22×D3C2×D3211yescharacteristic
764C22×D3C2×D3211yescharacteristic
765C3×Q8—182no—
766C3×D4—64no—
767C3×D4—62no—
768C3×D4—62no—
769C3×D4—62no—
770C3×D4—62no—
771C3×D4—94no—
772C3×D4—122no—
773C3×D4—182no—
774C3×D4—182no—
775C2×C3×C4—31no—
776C2×C3×C4—31no—
777C2×C3×C4—31no—
778C2×C3×C4—31no—
779C2×C3×C4—31no—
780C2×C3×C4—31no—
781C2×C3×C4—31no—
782C2×C3×C4—31no—
783C2×C3×C4—61no—
784C2×C3×C4—61no—
785C2×C3×C4—61no—
786C2×C3×C4—61no—
787C2×C3×C4—62no—
788C2×C3×C4—62no—
789C2×C3×C4—91no—
790C2×C3×C4—91no—
791C2×C3×C4—91no—
792C2×C3×C4—91no—
793C2×C3×C4—91no—
794C2×C3×C4—122no—
795C2×C3×C4—182no—
796C2×C3×C4—182no—
797C2×C3×C4—182no—
798#67—22no—
799#67—22no—
800#67—34no—
801#67—34no—
802#67—64no—
803#67—62no—
804#67—62no—
805#67—62no—
806#67—182no—
807#67—182no—
808#67—182no—
809#67—184no—
810C2×Dic3—22no—
811C2×Dic3—31no—
812C2×Dic3—31no—
813C2×Dic3—31no—
814C2×Dic3—31no—
815C2×Dic3—31no—
816C2×Dic3—31no—
817C2×Dic3—31no—
818C2×Dic3—31no—
819C2×Dic3—31no—
820C2×Dic3—31no—
821C2×Dic3—61no—
822C2×Dic3—61no—
823C2×Dic3—61no—
824C2×Dic3—61no—
825C2×Dic3—61no—
826C2×Dic3—62no—
827C2×Dic3—62no—
828C2×Dic3—62no—
829C2×Dic3—64no—
830C2×Dic3—91no—
831C2×Dic3—91no—
832C2×Dic3—91no—
833C2×Dic3—91no—
834C2×Dic3—91no—
835C2×Dic3—91no—
836C2×Dic3—181no—
837C2×Dic3—181no—
838C2×Dic3—181no—
839C2×Dic3—181no—
840C2×Dic3—181no—
841C2×Dic3—181no—
842C2×Dic3—182no—
843C2×Dic3—182no—
844C2×Dic3—182no—
845C2×Dic3—182no—
846C2×Dic3—184no—
847C2×Dic3—184no—
848C2×Dic3—182no—
849C2×Dic3—182no—
850C2×Dic3—182no—
851C2×Dic3—361no—
852C2×Dic3—361no—
853C2×Dic3—362no—
854C2×Dic3—362no—
855C2×Dic3—364no—
856C2×Dic3C2×D3211yescharacteristic
857C2×Dic3C2×D3211yescharacteristic
858C2×Dic3C2×D3211yescharacteristic
859C2×Dic3C2×D3211yescharacteristic
860D12—62no—
861C4×D3—62no—
862C4×D3—62no—
863C4×D3—62no—
864C4×D3—182no—
865C4×D3—182no—
866C4×D3—182no—
867C4×D3—182no—
868C4×D3—184no—
869C4×D3—182no—
870Dic6—62no—
871Dic6—62no—
872Dic6—182no—
873Dic6—182no—
874Dic6—182no—
875Dic6—184no—
876C2×C32—22no—
877C2×C32—24no—
878C2×C32—22no—
879C2×C32—22no—
880C2×C32—21no—
881C2×C32—21no—
882C2×C32—21no—
883C2×C32—21no—
884C2×C32—21no—
885C2×C32—21no—
886C2×C32—21no—
887C2×C32—21no—
888C2×C32—21no—
889C2×C32—41no—
890C2×C32—41no—
891C2×C32—41no—
892C2×C32—42no—
893C2×C32—42no—
894C2×C32—44no—
895C2×C32—121no—
896C2×C32—121no—
897C2×C32C2×D3×D411yescharacteristic
898C2×C32C2×D3×D411yescharacteristic
899C2×C32C2×#23711yescharacteristic
900C2×C32D3×#4111yescharacteristic
901C2×C32D3×#4111yescharacteristic
902C2×C32#101011yescharacteristic
903C2×C32#101011yescharacteristic
904C2×C32#101011yescharacteristic
905C2×C32C22×#6711yescharacteristic
906C3⋊D3—22no—
907C3×D3—42no—
908C3×D3—41no—
909C3×D3—41no—
910C3×D3—41no—
911C3×D3—41no—
912C3×D3—62no—
913C3×D3—62no—
914C3×D3—81no—
915C3×D3—122no—
916#41—184no—
917#41—544no—
918C2×Q8—91no—
919C2×Q8—271no—
920C2×D4—31no—
921C2×D4—31no—
922C2×D4—91no—
923C2×D4—91no—
924C2×D4—91no—
925C2×D4—271no—
926C22×C4—31no—
927C22×C4—91no—
928C22×C4—91no—
929C22×C4—91no—
930C22×C4—271no—
931C22×C4—271no—
932C22×C4—271no—
933C22×C4—271no—
934C4⋊C4—91no—
935C4⋊C4—91no—
936C4⋊C4—91no—
937C4⋊C4—271no—
938C4⋊C4—271no—
939C4⋊C4—271no—
940C4⋊C4—271no—
941C4⋊C4—271no—
942C4⋊C4—271no—
943C4⋊C4—271no—
944C22⋊C4—91no—
945C22⋊C4—91no—
946C22⋊C4—91no—
947C22⋊C4—91no—
948C22⋊C4—91no—
949C22⋊C4—271no—
950C22⋊C4—271no—
951C22⋊C4—271no—
952C42—271no—
953C22×C3—22no—
954C22×C3—22no—
955C22×C3—21no—
956C22×C3—21no—
957C22×C3—21no—
958C22×C3—21no—
959C22×C3—21no—
960C22×C3—21no—
961C22×C3—21no—
962C22×C3—21no—
963C22×C3—21no—
964C22×C3—22no—
965C22×C3—22no—
966C22×C3—22no—
967C22×C3—41no—
968C22×C3—41no—
969C22×C3—41no—
970C22×C3—41no—
971C22×C3—42no—
972C22×C3—42no—
973C22×C3—41no—
974C22×C3—42no—
975C22×C3—62no—
976C22×C3—61no—
977C22×C3—61no—
978C22×C3—61no—
979C22×C3—61no—
980C22×C3—61no—
981C22×C3—61no—
982C22×C3—61no—
983C22×C3—61no—
984C22×C3—61no—
985C22×C3—61no—
986C22×C3—61no—
987C22×C3—61no—
988C22×C3—92no—
989C22×C3—121no—
990C22×C3—121no—
991C22×C3—121no—
992C22×C3—121no—
993C22×C3—121no—
994C22×C3—181no—
995C22×C3—181no—
996C22×C3D3×#6712yes—
997C22×C3D3×#6712yes—
998C22×C3#381112yes—
999C22×C3C22×D3211yescharacteristic
1000C22×C3C22×D3211yescharacteristic
1001C22×C3C22×D3211yescharacteristic
1002C2×D3—21no—
1003C2×D3—21no—
1004C2×D3—21no—
1005C2×D3—21no—
1006C2×D3—21no—
1007C2×D3—21no—
1008C2×D3—32no—
1009C2×D3—32no—
1010C2×D3—62no—
1011C2×D3—61no—
1012C2×D3—61no—
1013C2×D3—61no—
1014C2×D3—61no—
1015C2×D3—121no—
1016C2×D3—121no—
1017C3×C4—62no—
1018C3×C4—61no—
1019C3×C4—61no—
1020C3×C4—61no—
1021C3×C4—61no—
1022C3×C4—61no—
1023C3×C4—61no—
1024C3×C4—61no—
1025C3×C4—61no—
1026C3×C4—92no—
1027C3×C4—92no—
1028C3×C4—121no—
1029C3×C4—121no—
1030C3×C4—121no—
1031C3×C4—181no—
1032C3×C4—181no—
1033C3×C4—181no—
1034Dic3—21no—
1035Dic3—21no—
1036Dic3—21no—
1037Dic3—21no—
1038Dic3—32no—
1039Dic3—32no—
1040Dic3—32no—
1041Dic3—32no—
1042Dic3—62no—
1043Dic3—62no—
1044Dic3—62no—
1045Dic3—61no—
1046Dic3—61no—
1047Dic3—61no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—121no—
1052Dic3—121no—
1053Dic3—182no—
1054Dic3—182no—
1055Dic3—181no—
1056Dic3—181no—
1057Dic3—181no—
1058Dic3—181no—
1059Dic3—181no—
1060Dic3—181no—
1061Dic3—361no—
1062Dic3—361no—
1063Dic3—361no—
1064Dic3—361no—
1065Dic3—362no—
1066Dic3—362no—
1067C32—21no—
1068C32—21no—
1069C32—21no—
1070C32—41no—
1071C32#561111yescharacteristic, complemented
1072C32#565511yescharacteristic, complemented
1073C32#582411yescharacteristic, complemented
1074C23—31no—
1075C23—31no—
1076C23—91no—
1077C23D3311yescharacteristic
1078Q8—182no—
1079Q8—542no—
1080D4—62no—
1081D4—62no—
1082D4—94no—
1083D4—182no—
1084D4—182no—
1085D4—542no—
1086C2×C4—31no—
1087C2×C4—31no—
1088C2×C4—31no—
1089C2×C4—31no—
1090C2×C4—62no—
1091C2×C4—91no—
1092C2×C4—91no—
1093C2×C4—91no—
1094C2×C4—91no—
1095C2×C4—91no—
1096C2×C4—182no—
1097C2×C4—182no—
1098C2×C4—182no—
1099C2×C4—271no—
1100C2×C4—271no—
1101C2×C4—542no—
1102C2×C4—542no—
1103C2×C4—542no—
1104C2×C4—542no—
1105C2×C3—24no—
1106C2×C3—22no—
1107C2×C3—22no—
1108C2×C3—22no—
1109C2×C3—21no—
1110C2×C3—21no—
1111C2×C3—21no—
1112C2×C3—21no—
1113C2×C3—21no—
1114C2×C3—21no—
1115C2×C3—21no—
1116C2×C3—21no—
1117C2×C3—21no—
1118C2×C3—42no—
1119C2×C3—42no—
1120C2×C3—44no—
1121C2×C3—41no—
1122C2×C3—41no—
1123C2×C3—41no—
1124C2×C3—122no—
1125C2×C3—121no—
1126C2×C3—121no—
1127C2×C3—121no—
1128C2×C3—121no—
1129C2×C3—182no—
1130C2×C3—241no—
1131C2×C3#6429811yescharacteristic
1132C2×C3#6430611yescharacteristic
1133C2×C3#6430911yescharacteristic
1134C2×C3#6430911yescharacteristic
1135C2×C3D3×#23711yescharacteristic
1136C2×C3D3×#23711yescharacteristic
1137C2×C3C2×D3×#6711yescharacteristic
1138C2×C3C2×D3×#6711yescharacteristic
1139C2×C3C2×#381111yescharacteristic
1140D3—41no—
1141D3—41no—
1142D3—62no—
1143D3—62no—
1144D3—122no—
1145C22—21no—
1146C22—21no—
1147C22—61no—
1148C22—61no—
1149C22—61no—
1150C22—61no—
1151C22—61no—
1152C22—61no—
1153C22—92no—
1154C22—181no—
1155C22—181no—
1156C22#8895212yes—
1157C22C2×D3311yescharacteristic
1158C4—61no—
1159C4—61no—
1160C4—61no—
1161C4—61no—
1162C4—92no—
1163C4—92no—
1164C4—181no—
1165C4—181no—
1166C4—181no—
1167C4—541no—
1168C4—541no—
1169C3—21no—
1170C3—21no—
1171C3—21no—
1172C3—41no—
1173C3#1059488811yescharacteristic, complemented
1174C3#1059515111yescharacteristic, complemented
1175C3#1059516211yescharacteristic, complemented
1176C2—22no—
1177C2—121no—
1178C2—121no—
1179C2—182no—
1180C2#1172440711yescharacteristic
1181C2C2×#8895211yescharacteristic
1182C2#1172442711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#547
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#89029C2semidirect
2. C2×C3×#3804C2semidirect
3. #11723726C2semidirect
4. C2×#88807C2semidirect
5. #11723603C2semidirect
6. C3×#63980C2semidirect
7. C3×#63961C2semidirect
8. #11723034C2semidirect
9. #11722992C2semidirect
10. #11722991C2semidirect
11. #11722976C2semidirect
12. #11722975C2semidirect
13. #11722965C2semidirect
14. #11722924C2semidirect
15. #11722910C2semidirect
62. C2×#3804D3semidirect
70. #63980D3semidirect
85. #63961D3semidirect
111. C3×#638D4semidirect
291. C3×C3⋊Dic3#41semidirect
371. #638#67semidirect
701. C3⋊Dic3#237semidirect
745. C33#547semidirect
1071. C32#5611semidirect
1072. C32#5655semidirect
1073. C32#5824semidirect
1173. C3#10594888semidirect
1174. C3#10595151semidirect
1175. C3#10595162semidirect

Maximal subgroups

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

subgroupindex
C2×#890292
C2×C3×#38042
#117237262
C2×#888072
#117236032
C3×#639802
C3×#639612
#117230342
#117229922
#117229912
#117229762
#117229752
#117229652
#117229242
#117229102
#105951623
#105951513
#105948883