Finite Group Databasebeta

← #13178631

Subgroups — #13178631

Order 1728.

1558 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3830C211yesmaximal, characteristic, complemented
2C2×#89046C211yesmaximal, characteristic, complemented
3C3×#64148C211yesmaximal, characteristic, complemented
4C3×#64144C211yesmaximal, characteristic, complemented
5#11723726C211yesmaximal, characteristic, complemented
6#11723726C211yesmaximal, characteristic, complemented
7#11723725C211yesmaximal, characteristic, complemented
8#11723724C211yesmaximal, characteristic, complemented
9C2×#88815C211yesmaximal, characteristic, complemented
10#11723721C211yesmaximal, characteristic, complemented
11#11723720C211yesmaximal, characteristic, complemented
12#11723694C211yesmaximal, characteristic, complemented
13#11723688C211yesmaximal, characteristic, complemented
14#11723682C211yesmaximal, characteristic, complemented
15#11723666C211yesmaximal, characteristic, complemented
16#10595162—31nomaximal
17#10595151—31nomaximal
18#10595149—31nomaximal
19C2×C33×D4C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C22×C3×C3⋊Dic3C2211yescharacteristic
25C22×C3×C3⋊Dic3C2211yescharacteristic
26C22×C3×C3⋊Dic3C2211yescharacteristic
27C22×C3×C3⋊Dic3C2211yescharacteristic
28C3×#3830—24no—
29C2×C3×C4×C3⋊D3C2211yescharacteristic
30C2×C3×#634C2211yescharacteristic
31C2×#6296C2211yescharacteristic
32C2×#6295C2211yescharacteristic
33#89046—24no—
34C2×#6294C2211yescharacteristic
35C2×#6294C2211yescharacteristic
36C2×#6294C2211yescharacteristic
37C3×#3757C2211yescharacteristic
38C3×#3757C2211yescharacteristic
39C3×#3757C2211yescharacteristic
40C3×#3757C2211yescharacteristic
41C3×#3752C2211yescharacteristic
42C3×#3750C2211yescharacteristic
43C3×#3750C2211yescharacteristic
44C3×#3750C2211yescharacteristic
45#88815C2211yescharacteristic
46#88815C2211yescharacteristic
47#88815C2211yescharacteristic
48#88815C2211yescharacteristic
49#88815C2211yescharacteristic
50#88815C2211yescharacteristic
51#88815C2211yescharacteristic
52#88814C2211yescharacteristic
53#88814C2211yescharacteristic
54#88814C2211yescharacteristic
55#88813C2211yescharacteristic
56C2×#3830D311yescharacteristic, complemented
57C2×C3×#237—31no—
58C2×C3×#237—31no—
59C2×C3×#237—61no—
60C2×#3805—31no—
61C2×#3804—31no—
62C2×#3804—31no—
63#64148D311yescharacteristic, complemented
64#64144D311yescharacteristic, complemented
65C3×#939—31no—
66C3×#939—31no—
67C3×#939—61no—
68C3×#935—31no—
69C3×#935—31no—
70C3×#935—61no—
71#63982—31no—
72#63975—31no—
73#67⋊Dic3—31no—
74#67⋊Dic3—31no—
75Dic3×#67—31no—
76Dic3×#67—31no—
77#63971—31no—
78#63970—31no—
79#63969—31no—
80#63969—31no—
81C2×#3724—31no—
82#63966—31no—
83C2×Dic3⋊Dic3—31no—
84C2×Dic3⋊Dic3—31no—
85#63964—31no—
86#63964—31no—
87#63962—31no—
88#63961—31no—
89#63958—31no—
90#63952—31no—
91#63952—31no—
92#63905—31no—
93#63896—31no—
94#63888—31no—
95#63887—31no—
96#63883—31no—
97D3×Dic3⋊C4—31no—
98D3×Dic3⋊C4—31no—
99#63853—31no—
100#63850—31no—
101#63840—31no—
102#63839—31no—
103#63839—31no—
104C23×C33C2311yescharacteristic
105C23×C33C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C33×D4—22no—
109C2×C33×C4C2311yescharacteristic
110C3×#638—22no—
111C3×#638—22no—
112C3×#638—22no—
113C3×#638D414yescomplemented
114C2×C3×C3⋊Dic3—22no—
115C2×C3×C3⋊Dic3—22no—
116C2×C3×C3⋊Dic3—22no—
117C2×C3×C3⋊Dic3—22no—
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C2×C3×C3⋊Dic3C2311yescharacteristic
126C2×C3×C3⋊Dic3C2311yescharacteristic
127C2×C3×C3⋊Dic3C2311yescharacteristic
128C3×C4×C3⋊D3—22no—
129C3×#634—22no—
130#6296—22no—
131#6295—22no—
132#6294—22no—
133#6294—22no—
134#6294—22no—
135#5824—91no—
136#5655—91no—
137#5611—91no—
138C2×C32×D4—21no—
139C2×C32×D4—21no—
140C2×C32×D4—21no—
141C2×C32×D4—41no—
142C2×C32×D4C2×D311yescharacteristic
143C2×C32×D4C2×D311yescharacteristic
144C2×C32×D4C2×D311yescharacteristic
145C2×#638C2×D311yescharacteristic
146C2×#638C2×D311yescharacteristic
147C2×#638C2×D311yescharacteristic
148C2×#638C2×D311yescharacteristic
149C22×C3⋊Dic3C2×D311yescharacteristic
150C22×C3⋊Dic3C2×D311yescharacteristic
151C22×C3⋊Dic3C2×D311yescharacteristic
152C22×C3⋊Dic3C2×D311yescharacteristic
153#3830—24no—
154C2×C4×C3⋊D3C2×D311yescharacteristic
155C2×#634C2×D311yescharacteristic
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—61no—
165C2×C3×#67—61no—
166C2×C3×#67—61no—
167C2×C3×#67—61no—
168C22×C3×Dic3—31no—
169C22×C3×Dic3—31no—
170C22×C3×Dic3—31no—
171C22×C3×Dic3—31no—
172C22×C3×Dic3—31no—
173C22×C3×Dic3—31no—
174C22×C3×Dic3—31no—
175C22×C3×Dic3—31no—
176C22×C3×Dic3—61no—
177C22×C3×Dic3—61no—
178C22×C3×Dic3—61no—
179C22×C3×Dic3—61no—
180C3×#237—64no—
181C3×#237—64no—
182C3×#237—68no—
183C2×C3×C4×D3—31no—
184C2×C3×C4×D3—31no—
185C2×C3×C4×D3—61no—
186C2×C3×Dic6—31no—
187C2×C3×Dic6—31no—
188C2×C3×Dic6—61no—
189C2×#627—31no—
190C2×#627—31no—
191C2×#627—31no—
192C2×#626—31no—
193C2×#626—31no—
194C2×#625—31no—
195C2×#624—31no—
196C2×#624—31no—
197C2×#624—31no—
198#3805—64no—
199#3804—64no—
200#3804—64no—
201C2×D3×Dic3—31no—
202C2×D3×Dic3—31no—
203C2×D3×Dic3—31no—
204C2×D3×Dic3—31no—
205C2×D3×Dic3—31no—
206C2×D3×Dic3—31no—
207#3757C2×D311yescharacteristic
208#3757C2×D311yescharacteristic
209#3757C2×D311yescharacteristic
210#3757C2×D311yescharacteristic
211#3752C2×D311yescharacteristic
212#3750C2×D311yescharacteristic
213#3750C2×D311yescharacteristic
214#3750C2×D311yescharacteristic
215C3×#217—31no—
216C3×#217—31no—
217C3×#217—31no—
218C3×#217—31no—
219C3×#217—31no—
220C3×#217—31no—
221C3×#217—31no—
222C3×#217—31no—
223C3×#217—61no—
224C3×#217—61no—
225C3×#217—61no—
226C3×#217—61no—
227C3×(C2×D3)⋊C4—31no—
228C3×(C2×D3)⋊C4—31no—
229C3×(C2×D3)⋊C4—61no—
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—61no—
237C3×Dic3⋊C4—61no—
238C3×Dic3⋊C4—61no—
239#3724—31no—
240#3724—31no—
241#3724—31no—
242#3724—31no—
243#3724—31no—
244#3724—31no—
245#3724—31no—
246Dic3⋊Dic3—31no—
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—31no—
256Dic3⋊Dic3—31no—
257Dic3⋊Dic3—31no—
258Dic3⋊Dic3—31no—
259Dic3⋊Dic3—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
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—
269Dic32—31no—
270Dic32—31no—
271Dic32—31no—
272C22×C33—21no—
273C22×C33—21no—
274C22×C33—21no—
275C22×C33—21no—
276C22×C33—21no—
277C22×C33C2×D412yes—
278C22×C33C2411yescharacteristic
279C2×C3×C3⋊D3—21no—
280C2×C3×C3⋊D3—21no—
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3—21no—
284C2×C3×C3⋊D3C2×D412yes—
285C33×C4—21no—
286C3×C3⋊Dic3—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×C3⋊Dic3—21no—
290C3×C3⋊Dic3—21no—
291C3×C3⋊Dic3—21no—
292C3×C3⋊Dic3—21no—
293C3×C3⋊Dic3—21no—
294C3×C3⋊Dic3C2×D412yes—
295C3×C3⋊Dic3#4112yescomplemented
296C2×C3×#41—91no—
297C2×#237—31no—
298C2×#237—31no—
299C2×#237—61no—
300C2×#237—91no—
301C2×#237—91no—
302C2×#235—91no—
303C3×#123—91no—
304C3×#121—91no—
305#946—91no—
306#944—91no—
307#939—31no—
308#939—31no—
309#939—61no—
310#939—91no—
311#938—91no—
312#935—31no—
313#935—31no—
314#935—61no—
315#935—91no—
316#935—91no—
317D4×Dic3—91no—
318D4×Dic3—91no—
319#929—91no—
320#929—91no—
321C4×#67—91no—
322C4×#67—91no—
323C2×C4⋊Dic3—91no—
324#924—91no—
325C2×Dic3⋊C4—91no—
326C2×Dic3⋊C4—91no—
327C2×Dic3⋊C4—91no—
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—21no—
348C23×C32—21no—
349C23×C32—21no—
350C23×C32—41no—
351C23×C32—41no—
352C23×C32C22×D311yescharacteristic
353C23×C32C22×D311yescharacteristic
354C23×C32C22×D311yescharacteristic
355C23×C32C22×D311yescharacteristic
356C23×C32C22×D311yescharacteristic
357C23×C32C22×D311yescharacteristic
358C22×C3⋊D3C22×D311yescharacteristic
359C22×C3⋊D3C22×D311yescharacteristic
360C22×C3×D3—31no—
361C22×C3×D3—31no—
362C22×C3×D3—31no—
363C22×C3×D3—31no—
364C22×C3×D3—61no—
365C22×C3×D3—61no—
366C32×D4—22no—
367C32×D4—24no—
368C32×D4—22no—
369C32×D4—22no—
370C32×D4—42no—
371C32×D4—42no—
372C32×D4—44no—
373C2×C32×C4—21no—
374C2×C32×C4—21no—
375C2×C32×C4—21no—
376C2×C32×C4—41no—
377C2×C32×C4C22×D311yescharacteristic
378C2×C32×C4C22×D311yescharacteristic
379C2×C32×C4C22×D311yescharacteristic
380#638—22no—
381#638—22no—
382#638—22no—
383#638#6714yescomplemented
384C2×C3⋊Dic3—22no—
385C2×C3⋊Dic3—22no—
386C2×C3⋊Dic3—22no—
387C2×C3⋊Dic3—22no—
388C2×C3⋊Dic3C22×D311yescharacteristic
389C2×C3⋊Dic3C22×D311yescharacteristic
390C2×C3⋊Dic3C22×D311yescharacteristic
391C2×C3⋊Dic3C22×D311yescharacteristic
392C2×C3⋊Dic3C22×D311yescharacteristic
393C2×C3⋊Dic3C22×D311yescharacteristic
394C2×C3⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C4×C3⋊D3—22no—
399#634—22no—
400C3×#67—34no—
401C3×#67—34no—
402C3×#67—64no—
403C3×#67—62no—
404C3×#67—62no—
405C3×#67—62no—
406C3×#67—62no—
407C3×#67—64no—
408C3×#67—62no—
409C3×#67—62no—
410C3×#67—122no—
411C3×#67—122no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
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—31no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—31no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—61no—
436C2×C3×Dic3—61no—
437C2×C3×Dic3—61no—
438C2×C3×Dic3—61no—
439C2×C3×Dic3—61no—
440C2×C3×Dic3—61no—
441C2×C3×Dic3—61no—
442C2×C3×Dic3—62no—
443C2×C3×Dic3—62no—
444C2×C3×Dic3—62no—
445C2×C3×Dic3—62no—
446C2×C3×Dic3—64no—
447C2×C3×Dic3—64no—
448C2×C3×Dic3—62no—
449C2×C3×Dic3—62no—
450C2×C3×Dic3—62no—
451C2×C3×Dic3—62no—
452C2×C3×Dic3—122no—
453C2×C3×Dic3—122no—
454C3×C4×D3—62no—
455C3×C4×D3—62no—
456C3×C4×D3—64no—
457C3×Dic6—62no—
458C3×Dic6—62no—
459C3×Dic6—64no—
460#627—62no—
461#627—62no—
462#627—62no—
463#626—62no—
464#626—62no—
465#625—62no—
466#624—62no—
467#624—62no—
468#624—62no—
469D3×Dic3—62no—
470D3×Dic3—62no—
471D3×Dic3—62no—
472D3×Dic3—62no—
473D3×Dic3—62no—
474D3×Dic3—62no—
475#547—271noSylow
476C2×C33—22no—
477C2×C33—41no—
478C2×C33C22×D411yescharacteristic
479C2×C33C2×#4111yescharacteristic
480C2×C332−1+411yescharacteristic
481C3×C3⋊D3—22no—
482C3×C3⋊D3—41no—
483C3×#41—184no—
484C2×C3×Q8—91no—
485C2×C3×D4—21no—
486C2×C3×D4—21no—
487C2×C3×D4—21no—
488C2×C3×D4—41no—
489C2×C3×D4—91no—
490C2×C3×D4—91no—
491C2×C3×D4—91no—
492C2×C3×D4—91no—
493C2×C3×D4D3211yescharacteristic
494C2×C3×D4D3211yescharacteristic
495C2×C3×D4D3211yescharacteristic
496C22×C3×C4—91no—
497C22×C3×C4—91no—
498C22×C3×C4—91no—
499C22×C3×C4—91no—
500C22×C3×C4—91no—
501C2×#67—31no—
502C2×#67—31no—
503C2×#67—31no—
504C2×#67—31no—
505C2×#67—31no—
506C2×#67—31no—
507C2×#67—31no—
508C2×#67—31no—
509C2×#67—61no—
510C2×#67—61no—
511C2×#67—61no—
512C2×#67—61no—
513C2×#67—91no—
514C2×#67—91no—
515C22×Dic3—31no—
516C22×Dic3—31no—
517C22×Dic3—31no—
518C22×Dic3—31no—
519C22×Dic3—31no—
520C22×Dic3—31no—
521C22×Dic3—31no—
522C22×Dic3—31no—
523C22×Dic3—61no—
524C22×Dic3—61no—
525C22×Dic3—61no—
526C22×Dic3—61no—
527C22×Dic3—91no—
528C22×Dic3—91no—
529C22×Dic3—91no—
530#237—64no—
531#237—64no—
532#237—68no—
533#237—184no—
534#237—184no—
535#235—184no—
536C2×D12—91no—
537C2×C4×D3—31no—
538C2×C4×D3—31no—
539C2×C4×D3—61no—
540C2×C4×D3—91no—
541C2×C4×D3—91no—
542C2×C4×D3—91no—
543C2×C4×D3—91no—
544C2×C4×D3—91no—
545C2×C4×D3—91no—
546C2×Dic6—31no—
547C2×Dic6—31no—
548C2×Dic6—61no—
549C2×Dic6—91no—
550C2×Dic6—91no—
551C2×Dic6—91no—
552C3×C4⋊C4—91no—
553C3×C4⋊C4—91no—
554C3×C4⋊C4—91no—
555C3×C22⋊C4—91no—
556C3×C22⋊C4—91no—
557C3×C22⋊C4—91no—
558C3×C22⋊C4—91no—
559C3×C22⋊C4—91no—
560#217—31no—
561#217—31no—
562#217—31no—
563#217—31no—
564#217—31no—
565#217—31no—
566#217—31no—
567#217—31no—
568#217—61no—
569#217—61no—
570#217—61no—
571#217—61no—
572#217—91no—
573#217—91no—
574#217—91no—
575(C2×D3)⋊C4—31no—
576(C2×D3)⋊C4—31no—
577(C2×D3)⋊C4—61no—
578(C2×D3)⋊C4—91no—
579(C2×D3)⋊C4—91no—
580(C2×D3)⋊C4—91no—
581(C2×D3)⋊C4—91no—
582(C2×D3)⋊C4—91no—
583(C2×D3)⋊C4—91no—
584C4⋊Dic3—91no—
585C4⋊Dic3—91no—
586C4⋊Dic3—91no—
587C4⋊Dic3—91no—
588C4⋊Dic3—91no—
589C4⋊Dic3—91no—
590C4⋊Dic3—91no—
591Dic3⋊C4—31no—
592Dic3⋊C4—31no—
593Dic3⋊C4—31no—
594Dic3⋊C4—31no—
595Dic3⋊C4—31no—
596Dic3⋊C4—31no—
597Dic3⋊C4—61no—
598Dic3⋊C4—61no—
599Dic3⋊C4—61no—
600Dic3⋊C4—91no—
601Dic3⋊C4—91no—
602Dic3⋊C4—91no—
603Dic3⋊C4—91no—
604Dic3⋊C4—91no—
605Dic3⋊C4—91no—
606Dic3⋊C4—91no—
607Dic3⋊C4—91no—
608Dic3⋊C4—91no—
609Dic3⋊C4—91no—
610Dic3⋊C4—91no—
611Dic3⋊C4—91no—
612Dic3⋊C4—91no—
613Dic3⋊C4—91no—
614C4×Dic3—91no—
615C4×Dic3—91no—
616C4×Dic3—91no—
617C22×C32—21no—
618C22×C32—21no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—21no—
622C22×C32—21no—
623C22×C32—21no—
624C22×C32—22no—
625C22×C32—21no—
626C22×C32—21no—
627C22×C32—21no—
628C22×C32—21no—
629C22×C32—21no—
630C22×C32—21no—
631C22×C32—21no—
632C22×C32—21no—
633C22×C32—21no—
634C22×C32—21no—
635C22×C32—21no—
636C22×C32—22no—
637C22×C32—22no—
638C22×C32—22no—
639C22×C32—41no—
640C22×C32—42no—
641C22×C32—41no—
642C22×C32—41no—
643C22×C32—42no—
644C22×C32—41no—
645C22×C32—41no—
646C22×C32—41no—
647C22×C32—41no—
648C22×C32—41no—
649C22×C32—41no—
650C22×C32—41no—
651C22×C32—41no—
652C22×C32—41no—
653C22×C32—41no—
654C22×C32—41no—
655C22×C32—41no—
656C22×C32—81no—
657C22×C32—81no—
658C22×C32—81no—
659C22×C32—81no—
660C22×C32D3×D412yes—
661C22×C32D3×D412yes—
662C22×C32C2×#6712yes—
663C22×C32C23×D311yescharacteristic
664C22×C32C23×D311yescharacteristic
665C22×C32C23×D311yescharacteristic
666C2×C3⋊D3—21no—
667C2×C3⋊D3—21no—
668C2×C3⋊D3—21no—
669C2×C3⋊D3—21no—
670C2×C3⋊D3—21no—
671C2×C3⋊D3C2×#6712yes—
672C2×C3×D3—32no—
673C2×C3×D3—32no—
674C2×C3×D3—62no—
675C2×C3×D3—61no—
676C2×C3×D3—61no—
677C2×C3×D3—61no—
678C2×C3×D3—61no—
679C2×C3×D3—61no—
680C2×C3×D3—61no—
681C2×C3×D3—61no—
682C2×C3×D3—61no—
683C2×C3×D3—61no—
684C2×C3×D3—61no—
685C2×C3×D3—121no—
686C2×C3×D3—121no—
687C2×C3×D3—121no—
688C2×C3×D3—121no—
689C2×C3×D3—121no—
690C32×C4—21no—
691C32×C4—22no—
692C32×C4—21no—
693C32×C4—21no—
694C32×C4—41no—
695C32×C4—41no—
696C32×C4—42no—
697C3⋊Dic3—21no—
698C3⋊Dic3—21no—
699C3⋊Dic3—21no—
700C3⋊Dic3—21no—
701C3⋊Dic3—21no—
702C3⋊Dic3—21no—
703C3⋊Dic3—21no—
704C3⋊Dic3—21no—
705C3⋊Dic3#23712yescomplemented
706C3⋊Dic3C2×#6712yes—
707C3×Dic3—32no—
708C3×Dic3—32no—
709C3×Dic3—32no—
710C3×Dic3—32no—
711C3×Dic3—62no—
712C3×Dic3—62no—
713C3×Dic3—62no—
714C3×Dic3—62no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—61no—
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—61no—
728C3×Dic3—61no—
729C3×Dic3—61no—
730C3×Dic3—61no—
731C3×Dic3—121no—
732C3×Dic3—121no—
733C3×Dic3—121no—
734C3×Dic3—121no—
735C3×Dic3—121no—
736C3×Dic3—121no—
737C2×#41—91no—
738C2×#41—271no—
739C4⋊Q8—271no—
740#123—91no—
741#123—271no—
742#123—271no—
743#123—271no—
744C22⋊Q8—271no—
745C22⋊Q8—271no—
746#121—91no—
747#121—271no—
748C4×D4—271no—
749C4×D4—271no—
750C2×C4⋊C4—271no—
751C2×C4⋊C4—271no—
752C33#54711yescharacteristic, complemented, Sylow
753C23×C3—21no—
754C23×C3—21no—
755C23×C3—21no—
756C23×C3—21no—
757C23×C3—21no—
758C23×C3—21no—
759C23×C3—41no—
760C23×C3—41no—
761C23×C3—91no—
762C23×C3—91no—
763C23×C3C2×D3211yescharacteristic
764C23×C3C2×D3211yescharacteristic
765C23×C3C2×D3211yescharacteristic
766C23×C3C2×D3211yescharacteristic
767C23×C3C2×D3211yescharacteristic
768C23×C3C2×D3211yescharacteristic
769C22×D3—31no—
770C22×D3—31no—
771C22×D3—31no—
772C22×D3—31no—
773C22×D3—61no—
774C22×D3—61no—
775C3×Q8—182no—
776C3×D4—24no—
777C3×D4—22no—
778C3×D4—22no—
779C3×D4—22no—
780C3×D4—42no—
781C3×D4—42no—
782C3×D4—44no—
783C3×D4—94no—
784C3×D4—182no—
785C3×D4—182no—
786C3×D4—182no—
787C2×C3×C4—21no—
788C2×C3×C4—21no—
789C2×C3×C4—21no—
790C2×C3×C4—41no—
791C2×C3×C4—91no—
792C2×C3×C4—91no—
793C2×C3×C4—91no—
794C2×C3×C4—91no—
795C2×C3×C4—91no—
796C2×C3×C4—91no—
797C2×C3×C4—91no—
798C2×C3×C4—91no—
799C2×C3×C4—91no—
800C2×C3×C4—91no—
801C2×C3×C4—182no—
802C2×C3×C4—182no—
803C2×C3×C4—182no—
804C2×C3×C4—182no—
805C2×C3×C4—182no—
806C2×C3×C4C2×D3211yescharacteristic
807C2×C3×C4C2×D3211yescharacteristic
808C2×C3×C4C2×D3211yescharacteristic
809#67—34no—
810#67—34no—
811#67—64no—
812#67—62no—
813#67—62no—
814#67—62no—
815#67—62no—
816#67—64no—
817#67—62no—
818#67—62no—
819#67—122no—
820#67—122no—
821#67—182no—
822#67—182no—
823C2×Dic3—31no—
824C2×Dic3—31no—
825C2×Dic3—31no—
826C2×Dic3—31no—
827C2×Dic3—31no—
828C2×Dic3—31no—
829C2×Dic3—31no—
830C2×Dic3—31no—
831C2×Dic3—31no—
832C2×Dic3—31no—
833C2×Dic3—31no—
834C2×Dic3—31no—
835C2×Dic3—31no—
836C2×Dic3—31no—
837C2×Dic3—31no—
838C2×Dic3—31no—
839C2×Dic3—31no—
840C2×Dic3—31no—
841C2×Dic3—31no—
842C2×Dic3—31no—
843C2×Dic3—61no—
844C2×Dic3—61no—
845C2×Dic3—61no—
846C2×Dic3—61no—
847C2×Dic3—61no—
848C2×Dic3—61no—
849C2×Dic3—61no—
850C2×Dic3—61no—
851C2×Dic3—61no—
852C2×Dic3—61no—
853C2×Dic3—62no—
854C2×Dic3—62no—
855C2×Dic3—62no—
856C2×Dic3—62no—
857C2×Dic3—64no—
858C2×Dic3—64no—
859C2×Dic3—62no—
860C2×Dic3—62no—
861C2×Dic3—62no—
862C2×Dic3—62no—
863C2×Dic3—122no—
864C2×Dic3—122no—
865C2×Dic3—182no—
866C2×Dic3—182no—
867C2×Dic3—182no—
868D12—182no—
869C4×D3—62no—
870C4×D3—62no—
871C4×D3—64no—
872C4×D3—182no—
873C4×D3—182no—
874C4×D3—182no—
875C4×D3—182no—
876C4×D3—182no—
877C4×D3—182no—
878Dic6—62no—
879Dic6—62no—
880Dic6—64no—
881Dic6—182no—
882Dic6—182no—
883Dic6—182no—
884C2×C32—22no—
885C2×C32—22no—
886C2×C32—22no—
887C2×C32—21no—
888C2×C32—21no—
889C2×C32—21no—
890C2×C32—21no—
891C2×C32—21no—
892C2×C32—21no—
893C2×C32—21no—
894C2×C32—21no—
895C2×C32—21no—
896C2×C32—41no—
897C2×C32—41no—
898C2×C32—41no—
899C2×C32—42no—
900C2×C32—42no—
901C2×C32—42no—
902C2×C32—41no—
903C2×C32—42no—
904C2×C32—41no—
905C2×C32—41no—
906C2×C32—82no—
907C2×C32—81no—
908C2×C32—81no—
909C2×C32—82no—
910C2×C32C2×D3×D411yescharacteristic
911C2×C32C2×D3×D411yescharacteristic
912C2×C32C2×#23711yescharacteristic
913C2×C32D3×#4111yescharacteristic
914C2×C32D3×#4111yescharacteristic
915C2×C32#101011yescharacteristic
916C2×C32#101011yescharacteristic
917C2×C32#101011yescharacteristic
918C2×C32C22×#6711yescharacteristic
919C3⋊D3—22no—
920C3⋊D3—41no—
921C3×D3—62no—
922C3×D3—62no—
923C3×D3—122no—
924C3×D3—121no—
925C3×D3—121no—
926C3×D3—241no—
927#41—184no—
928#41—544no—
929C2×Q8—91no—
930C2×Q8—271no—
931C2×D4—91no—
932C2×D4—91no—
933C2×D4—91no—
934C2×D4—91no—
935C2×D4—271no—
936C2×D4#111311yescharacteristic
937C22×C4—91no—
938C22×C4—91no—
939C22×C4—91no—
940C22×C4—91no—
941C22×C4—91no—
942C22×C4—271no—
943C22×C4—271no—
944C22×C4—271no—
945C4⋊C4—91no—
946C4⋊C4—91no—
947C4⋊C4—91no—
948C4⋊C4—271no—
949C4⋊C4—271no—
950C4⋊C4—271no—
951C4⋊C4—271no—
952C4⋊C4—271no—
953C4⋊C4—271no—
954C4⋊C4—271no—
955C22⋊C4—91no—
956C22⋊C4—91no—
957C22⋊C4—91no—
958C22⋊C4—91no—
959C22⋊C4—91no—
960C22⋊C4—271no—
961C22⋊C4—271no—
962C22⋊C4—271no—
963C42—271no—
964C22×C3—21no—
965C22×C3—21no—
966C22×C3—21no—
967C22×C3—21no—
968C22×C3—21no—
969C22×C3—21no—
970C22×C3—22no—
971C22×C3—21no—
972C22×C3—21no—
973C22×C3—21no—
974C22×C3—21no—
975C22×C3—21no—
976C22×C3—21no—
977C22×C3—21no—
978C22×C3—21no—
979C22×C3—21no—
980C22×C3—21no—
981C22×C3—21no—
982C22×C3—21no—
983C22×C3—22no—
984C22×C3—22no—
985C22×C3—22no—
986C22×C3—41no—
987C22×C3—41no—
988C22×C3—41no—
989C22×C3—41no—
990C22×C3—41no—
991C22×C3—41no—
992C22×C3—41no—
993C22×C3—41no—
994C22×C3—41no—
995C22×C3—41no—
996C22×C3—41no—
997C22×C3—41no—
998C22×C3—41no—
999C22×C3—41no—
1000C22×C3—42no—
1001C22×C3—41no—
1002C22×C3—42no—
1003C22×C3—81no—
1004C22×C3—81no—
1005C22×C3—81no—
1006C22×C3—81no—
1007C22×C3—92no—
1008C22×C3—181no—
1009C22×C3—181no—
1010C22×C3—181no—
1011C22×C3—181no—
1012C22×C3—181no—
1013C22×C3D3×#6712yes—
1014C22×C3D3×#6712yes—
1015C22×C3#381112yes—
1016C22×C3C22×D3211yescharacteristic
1017C22×C3C22×D3211yescharacteristic
1018C22×C3C22×D3211yescharacteristic
1019C2×D3—32no—
1020C2×D3—32no—
1021C2×D3—62no—
1022C2×D3—61no—
1023C2×D3—61no—
1024C2×D3—61no—
1025C2×D3—61no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—61no—
1030C2×D3—61no—
1031C2×D3—61no—
1032C2×D3—121no—
1033C2×D3—121no—
1034C2×D3—121no—
1035C2×D3—121no—
1036C2×D3—121no—
1037C3×C4—22no—
1038C3×C4—21no—
1039C3×C4—21no—
1040C3×C4—21no—
1041C3×C4—41no—
1042C3×C4—41no—
1043C3×C4—42no—
1044C3×C4—92no—
1045C3×C4—92no—
1046C3×C4—181no—
1047C3×C4—181no—
1048C3×C4—181no—
1049C3×C4—181no—
1050C3×C4—181no—
1051C3×C4—181no—
1052C3×C4—181no—
1053C3×C4—181no—
1054Dic3—32no—
1055Dic3—32no—
1056Dic3—32no—
1057Dic3—32no—
1058Dic3—62no—
1059Dic3—62no—
1060Dic3—62no—
1061Dic3—62no—
1062Dic3—61no—
1063Dic3—61no—
1064Dic3—61no—
1065Dic3—61no—
1066Dic3—61no—
1067Dic3—61no—
1068Dic3—61no—
1069Dic3—61no—
1070Dic3—61no—
1071Dic3—61no—
1072Dic3—61no—
1073Dic3—61no—
1074Dic3—61no—
1075Dic3—61no—
1076Dic3—61no—
1077Dic3—61no—
1078Dic3—121no—
1079Dic3—121no—
1080Dic3—121no—
1081Dic3—121no—
1082Dic3—121no—
1083Dic3—121no—
1084C32—21no—
1085C32—21no—
1086C32—21no—
1087C32—41no—
1088C32#561111yescharacteristic, complemented
1089C32#565511yescharacteristic, complemented
1090C32#582411yescharacteristic, complemented
1091C23—91no—
1092C23—91no—
1093C23C2×#111311yescharacteristic
1094C23C2×#111311yescharacteristic
1095Q8—182no—
1096Q8—542no—
1097D4—22no—
1098D4—94no—
1099D4—182no—
1100D4—182no—
1101D4—182no—
1102D4—542no—
1103C2×C4—91no—
1104C2×C4—91no—
1105C2×C4—91no—
1106C2×C4—91no—
1107C2×C4—91no—
1108C2×C4—91no—
1109C2×C4—91no—
1110C2×C4—91no—
1111C2×C4—91no—
1112C2×C4—91no—
1113C2×C4—182no—
1114C2×C4—182no—
1115C2×C4—182no—
1116C2×C4—182no—
1117C2×C4—182no—
1118C2×C4—542no—
1119C2×C4—542no—
1120C2×C4—542no—
1121C2×C4C2×#111311yescharacteristic
1122C2×C3—22no—
1123C2×C3—22no—
1124C2×C3—22no—
1125C2×C3—21no—
1126C2×C3—21no—
1127C2×C3—21no—
1128C2×C3—21no—
1129C2×C3—21no—
1130C2×C3—21no—
1131C2×C3—21no—
1132C2×C3—21no—
1133C2×C3—21no—
1134C2×C3—42no—
1135C2×C3—42no—
1136C2×C3—42no—
1137C2×C3—42no—
1138C2×C3—41no—
1139C2×C3—41no—
1140C2×C3—41no—
1141C2×C3—41no—
1142C2×C3—41no—
1143C2×C3—41no—
1144C2×C3—82no—
1145C2×C3—81no—
1146C2×C3—81no—
1147C2×C3—82no—
1148C2×C3—182no—
1149C2×C3—361no—
1150C2×C3#6430911yescharacteristic
1151C2×C3#6430911yescharacteristic
1152C2×C3#6430911yescharacteristic
1153C2×C3D3×#23711yescharacteristic
1154C2×C3D3×#23711yescharacteristic
1155C2×C3#6431211yescharacteristic
1156C2×C3C2×D3×#6711yescharacteristic
1157C2×C3C2×D3×#6711yescharacteristic
1158C2×C3C2×#381111yescharacteristic
1159D3—62no—
1160D3—62no—
1161D3—122no—
1162D3—121no—
1163D3—121no—
1164D3—241no—
1165C22—21no—
1166C22—21no—
1167C22—21no—
1168C22—21no—
1169C22—21no—
1170C22—92no—
1171C22—181no—
1172C22—181no—
1173C22—181no—
1174C22—181no—
1175C22—181no—
1176C22#8904912yes—
1177C22C22×#111311yescharacteristic
1178C4—21no—
1179C4—92no—
1180C4—92no—
1181C4—181no—
1182C4—181no—
1183C4—181no—
1184C4—181no—
1185C4—181no—
1186C4—181no—
1187C4—181no—
1188C4—181no—
1189C3—21no—
1190C3—21no—
1191C3—21no—
1192C3—41no—
1193C3#1059514911yescharacteristic, complemented
1194C3#1059515111yescharacteristic, complemented
1195C3#1059516211yescharacteristic, complemented
1196C2—22no—
1197C2—41no—
1198C2—182no—
1199C2—361no—
1200C2#1172462011yescharacteristic
1201C2#1172462211yescharacteristic
1202C2C2×#8904911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#547
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3830C2semidirect
2. C2×#89046C2semidirect
3. C3×#64148C2semidirect
4. C3×#64144C2semidirect
5. #11723726C2semidirect
6. #11723726C2semidirect
7. #11723725C2semidirect
8. #11723724C2semidirect
9. C2×#88815C2semidirect
10. #11723721C2semidirect
11. #11723720C2semidirect
12. #11723694C2semidirect
13. #11723688C2semidirect
14. #11723682C2semidirect
15. #11723666C2semidirect
56. C2×#3830D3semidirect
63. #64148D3semidirect
64. #64144D3semidirect
113. C3×#638D4semidirect
295. C3×C3⋊Dic3#41semidirect
383. #638#67semidirect
705. C3⋊Dic3#237semidirect
752. C33#547semidirect
1088. C32#5611semidirect
1089. C32#5655semidirect
1090. C32#5824semidirect
1193. C3#10595149semidirect
1194. C3#10595151semidirect
1195. C3#10595162semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38302
C2×#890462
C3×#641482
C3×#641442
#117237262
#117237252
#117237242
C2×#888152
#117237212
#117237202
#117236942
#117236882
#117236822
#117236662
#105951623
#105951513
#105951493