Finite Group Databasebeta

← C3×#10595132 #13174697

Subgroups — C3×#10595132 #13174697

Order 1728.

1512 conjugacy classes of subgroups.

The subgroup lattice has 1254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3805C211yesmaximal, characteristic, complemented
2C2×C3×#3804C211yesmaximal, characteristic, complemented
3C3×#64148C211yesmaximal, characteristic, complemented
4C32×#939C211yesmaximal, characteristic, complemented
5C32×#938C211yesmaximal, characteristic, complemented
6C3×#63982C211yesmaximal, characteristic, complemented
7C3×#63971C211yesmaximal, characteristic, complemented
8C3×#63971C211yesmaximal, characteristic, complemented
9C3×#63970C211yesmaximal, characteristic, complemented
10C3×#63964C211yesmaximal, characteristic, complemented
11C3×#63958C211yesmaximal, characteristic, complemented
12C3×#63906C211yesmaximal, characteristic, complemented
13C3×#63899C211yesmaximal, characteristic, complemented
14C3×#63895C211yesmaximal, characteristic, complemented
15C3×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
16C3×#5608—31nomaximal
17C3×#5597—31nomaximal
18#10595132C311yesmaximal, characteristic, direct product factor
19C2×C33×D4C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic
27C22×C32×Dic3C2211yescharacteristic
28C2×C32×C4×D3C2211yescharacteristic
29C2×C3×#627C2211yescharacteristic
30C2×C3×#627C2211yescharacteristic
31C2×C3×#626C2211yescharacteristic
32C2×C3×#626C2211yescharacteristic
33C2×C3×#625C2211yescharacteristic
34C2×C3×#624C2211yescharacteristic
35C3×#3805—24no—
36C3×#3804—24no—
37C2×C3×D3×Dic3C2211yescharacteristic
38C2×C3×D3×Dic3C2211yescharacteristic
39C2×C3×D3×Dic3C2211yescharacteristic
40C3×#3757C2211yescharacteristic
41C3×#3752C2211yescharacteristic
42C3×#3750C2211yescharacteristic
43C32×#217C2211yescharacteristic
44C32×#217C2211yescharacteristic
45C32×#217C2211yescharacteristic
46C32×(C2×D3)⋊C4C2211yescharacteristic
47C32×C4⋊Dic3C2211yescharacteristic
48C32×Dic3⋊C4C2211yescharacteristic
49C3×#3724C2211yescharacteristic
50C3×#3724C2211yescharacteristic
51C3×Dic3⋊Dic3C2211yescharacteristic
52C3×Dic3⋊Dic3C2211yescharacteristic
53C3×Dic3⋊Dic3C2211yescharacteristic
54C3×#3722C2211yescharacteristic
55C3×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×C3×#237—31no—
57C2×C3×#237—31no—
58C2×C3×#237—31no—
59C2×C3×#235—31no—
60C2×#3805C2×C311yescharacteristic, complemented
61C2×#3804C2×C311yescharacteristic, complemented
62C32×#121—31no—
63C32×#121—31no—
64#64148C2×C311yescharacteristic, complemented
65C3×#939—21no—
66C3×#939—31no—
67C3×#939—31no—
68C3×#939—31no—
69C3×#939—31no—
70C3×#939—31no—
71C3×#939—61no—
72C3×#939D311yescharacteristic, complemented
73C3×#939C2×C311yescharacteristic, complemented
74C3×#938—21no—
75C3×#938—31no—
76C3×#938—31no—
77C3×#938D311yescharacteristic, complemented
78C3×#938C2×C311yescharacteristic, complemented
79C3×#930—31no—
80C3×#924—31no—
81C2×C3×Dic3⋊C4—31no—
82C3×#897—31no—
83C3×#896—31no—
84C3×#896—31no—
85C3×D3×C4⋊C4—31no—
86C3×#884—31no—
87C3×#884—31no—
88C3×#884—31no—
89C3×#884—31no—
90C3×#878—31no—
91C3×#878—31no—
92C3×#878—31no—
93C3×#878—31no—
94#63982C2×C311yescharacteristic, complemented
95#63971C2×C311yescharacteristic, complemented
96#63971C2×C311yescharacteristic, complemented
97#63970C2×C311yescharacteristic, complemented
98#63964C2×C311yescharacteristic, complemented
99#63958C2×C311yescharacteristic, complemented
100#63906C2×C311yescharacteristic, complemented
101#63899C2×C311yescharacteristic, complemented
102#63895C2×C311yescharacteristic, complemented
103D3×Dic3⋊C4C2×C311yescharacteristic, complemented
104C23×C33C2311yescharacteristic
105C23×C33C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C33×D4—41no—
110C2×C33×C4C2311yescharacteristic
111C3×#638—22no—
112C3×#638—41no—
113C2×C3×C3⋊Dic3—22no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C32×#67—22no—
118C32×#67—22no—
119C32×#67—22no—
120C32×#67—41no—
121C2×C32×Dic3—22no—
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128C32×C4×D3—41no—
129C3×#627—22no—
130C3×#627—22no—
131C3×#626—22no—
132C3×#626—41no—
133C3×#625—22no—
134C3×#624—22no—
135C3×D3×Dic3—22no—
136C3×D3×Dic3—41no—
137C3×D3×Dic3D414yescomplemented
138C3×#537—91no—
139#5608—31no—
140#5597—31no—
141C2×C32×D4—21no—
142C2×C32×D4—21no—
143C2×C32×D4—21no—
144C2×C32×D4—31no—
145C2×C32×D4—31no—
146C2×C32×D4—31no—
147C2×C32×D4—31no—
148C2×C32×D4—41no—
149C2×C32×D4C2×D311yescharacteristic
150C2×C32×D4C2×D311yescharacteristic
151C2×C32×D4C22×C311yescharacteristic
152C22×C32×C4—31no—
153C22×C32×C4—31no—
154C2×#638C22×C311yescharacteristic
155C2×#638C22×C311yescharacteristic
156C22×C3⋊Dic3C22×C311yescharacteristic
157C2×C3×#67—21no—
158C2×C3×#67—21no—
159C2×C3×#67—21no—
160C2×C3×#67—21no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—31no—
165C2×C3×#67—31no—
166C2×C3×#67—31no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
169C2×C3×#67—61no—
170C2×C3×#67—61no—
171C2×C3×#67C2×D311yescharacteristic
172C2×C3×#67C2×D311yescharacteristic
173C2×C3×#67C2×D311yescharacteristic
174C2×C3×#67C2×D311yescharacteristic
175C2×C3×#67C22×C311yescharacteristic
176C2×C3×#67C22×C311yescharacteristic
177C2×C3×#67C22×C311yescharacteristic
178C2×C3×#67C22×C311yescharacteristic
179C22×C3×Dic3—21no—
180C22×C3×Dic3—31no—
181C22×C3×Dic3—31no—
182C22×C3×Dic3—31no—
183C22×C3×Dic3—31no—
184C22×C3×Dic3—31no—
185C22×C3×Dic3—61no—
186C22×C3×Dic3C2×D311yescharacteristic
187C22×C3×Dic3C22×C311yescharacteristic
188C3×#237—64no—
189C3×#237—64no—
190C3×#237—64no—
191C3×#235—64no—
192C2×C3×D12—31no—
193C2×C3×D12—31no—
194C2×C3×C4×D3—21no—
195C2×C3×C4×D3—31no—
196C2×C3×C4×D3—31no—
197C2×C3×C4×D3—31no—
198C2×C3×C4×D3—31no—
199C2×C3×C4×D3—31no—
200C2×C3×C4×D3C2×D311yescharacteristic
201C2×C3×C4×D3C22×C311yescharacteristic
202C2×C3×Dic6—31no—
203C2×C3×Dic6—31no—
204C2×C3×Dic6—31no—
205C2×C3×Dic6—31no—
206C2×#627C22×C311yescharacteristic
207C2×#627C22×C311yescharacteristic
208C2×#626C22×C311yescharacteristic
209C2×#626C22×C311yescharacteristic
210C2×#625C22×C311yescharacteristic
211C2×#624C22×C311yescharacteristic
212#3805—24no—
213#3804—24no—
214C2×D3×Dic3C22×C311yescharacteristic
215C2×D3×Dic3C22×C311yescharacteristic
216C2×D3×Dic3C22×C311yescharacteristic
217C32×C4⋊C4—31no—
218C32×C4⋊C4—31no—
219C32×C22⋊C4—31no—
220C32×C22⋊C4—31no—
221C32×C22⋊C4—31no—
222C32×C22⋊C4—31no—
223#3757C22×C311yescharacteristic
224#3752C22×C311yescharacteristic
225#3750C22×C311yescharacteristic
226C3×#217—21no—
227C3×#217—21no—
228C3×#217—21no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—61no—
233C3×#217C2×D311yescharacteristic
234C3×#217C2×D311yescharacteristic
235C3×#217C2×D311yescharacteristic
236C3×#217C22×C311yescharacteristic
237C3×#217C22×C311yescharacteristic
238C3×#217C22×C311yescharacteristic
239C3×(C2×D3)⋊C4—21no—
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×(C2×D3)⋊C4—61no—
246C3×(C2×D3)⋊C4C2×D311yescharacteristic
247C3×(C2×D3)⋊C4C22×C311yescharacteristic
248C3×C4⋊Dic3—21no—
249C3×C4⋊Dic3—31no—
250C3×C4⋊Dic3—31no—
251C3×C4⋊Dic3—31no—
252C3×C4⋊Dic3C2×D311yescharacteristic
253C3×C4⋊Dic3C22×C311yescharacteristic
254C3×Dic3⋊C4—21no—
255C3×Dic3⋊C4—31no—
256C3×Dic3⋊C4—31no—
257C3×Dic3⋊C4—31no—
258C3×Dic3⋊C4—31no—
259C3×Dic3⋊C4—31no—
260C3×Dic3⋊C4—31no—
261C3×Dic3⋊C4—31no—
262C3×Dic3⋊C4—31no—
263C3×Dic3⋊C4—31no—
264C3×Dic3⋊C4—61no—
265C3×Dic3⋊C4C2×D311yescharacteristic
266C3×Dic3⋊C4C22×C311yescharacteristic
267#3724C22×C311yescharacteristic
268#3724C22×C311yescharacteristic
269Dic3⋊Dic3C22×C311yescharacteristic
270Dic3⋊Dic3C22×C311yescharacteristic
271Dic3⋊Dic3C22×C311yescharacteristic
272#3722C22×C311yescharacteristic
273(C2×D3)⋊Dic3C22×C311yescharacteristic
274C22×C33—21no—
275C22×C33—21no—
276C22×C33—21no—
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×C32×D3—21no—
285C2×C32×D3—21no—
286C2×C32×D3—21no—
287C2×C32×D3—21no—
288C2×C32×D3—21no—
289C2×C32×D3C2×D412yes—
290C33×C4—21no—
291C3×C3⋊Dic3—21no—
292C3×C3⋊Dic3—21no—
293C3×C3⋊Dic3C2×D412yes—
294C32×Dic3—21no—
295C32×Dic3—21no—
296C32×Dic3—21no—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3C2×D412yes—
300C2×C3×#41—91no—
301C2×C3×#41—91no—
302C2×#237—31no—
303C2×#237—31no—
304C2×#237—31no—
305C2×#235—31no—
306C3×C22⋊Q8—91no—
307C3×C22⋊Q8—91no—
308C3×C22⋊Q8—91no—
309C3×C22⋊Q8—91no—
310C3×#121—31no—
311C3×#121—31no—
312C3×#121—31no—
313C3×#121—31no—
314C3×#121—61no—
315C3×#121—61no—
316C3×#121—91no—
317C3×#121—91no—
318C3×#121—91no—
319C3×#121—91no—
320C3×#121—91no—
321C3×#121—91no—
322C2×C3×C4⋊C4—91no—
323#939—31no—
324#939—31no—
325#939—31no—
326#939—31no—
327#939—31no—
328#939—61no—
329#939C3×D311yescharacteristic, complemented
330#938—31no—
331#938—31no—
332#938C3×D311yescharacteristic, complemented
333#930—31no—
334#924—31no—
335C2×Dic3⋊C4—31no—
336#897—31no—
337#896—31no—
338#896—31no—
339D3×C4⋊C4—31no—
340#884—31no—
341#884—31no—
342#884—31no—
343#884—31no—
344#878—31no—
345#878—31no—
346#878—31no—
347#878—31no—
348C23×C32—21no—
349C23×C32—21no—
350C23×C32—21no—
351C23×C32—21no—
352C23×C32—21no—
353C23×C32—21no—
354C23×C32—31no—
355C23×C32—31no—
356C23×C32—41no—
357C23×C32—41no—
358C23×C32C22×D311yescharacteristic
359C23×C32C22×D311yescharacteristic
360C23×C32C22×D311yescharacteristic
361C23×C32C22×D311yescharacteristic
362C23×C32C23×C311yescharacteristic
363C23×C32C23×C311yescharacteristic
364C22×C3⋊D3C23×C311yescharacteristic
365C22×C3×D3—21no—
366C22×C3×D3—21no—
367C22×C3×D3—31no—
368C22×C3×D3—31no—
369C22×C3×D3—61no—
370C22×C3×D3C22×D311yescharacteristic
371C22×C3×D3C22×D311yescharacteristic
372C22×C3×D3C23×C311yescharacteristic
373C22×C3×D3C23×C311yescharacteristic
374C32×D4—41no—
375C32×D4—41no—
376C32×D4—41no—
377C32×D4—42no—
378C32×D4—42no—
379C32×D4—42no—
380C32×D4—44no—
381C32×D4—62no—
382C32×D4—62no—
383C32×D4—62no—
384C32×D4—121no—
385C2×C32×C4—21no—
386C2×C32×C4—21no—
387C2×C32×C4—21no—
388C2×C32×C4—31no—
389C2×C32×C4—31no—
390C2×C32×C4—31no—
391C2×C32×C4—31no—
392C2×C32×C4—31no—
393C2×C32×C4—31no—
394C2×C32×C4—41no—
395C2×C32×C4—62no—
396C2×C32×C4—121no—
397C2×C32×C4C22×D311yescharacteristic
398C2×C32×C4C22×D311yescharacteristic
399C2×C32×C4C23×C311yescharacteristic
400#638—22no—
401#638—41no—
402C2×C3⋊Dic3—22no—
403C2×C3⋊Dic3C23×C311yescharacteristic
404C2×C3⋊Dic3C23×C311yescharacteristic
405C2×C3⋊Dic3C23×C311yescharacteristic
406C3×#67—22no—
407C3×#67—22no—
408C3×#67—22no—
409C3×#67—22no—
410C3×#67—22no—
411C3×#67—22no—
412C3×#67—42no—
413C3×#67—42no—
414C3×#67—42no—
415C3×#67—41no—
416C3×#67—41no—
417C3×#67—42no—
418C3×#67—62no—
419C3×#67—62no—
420C3×#67—62no—
421C3×#67—62no—
422C3×#67—62no—
423C3×#67—122no—
424C3×#67—121no—
425C3×#67—121no—
426C3×#67—121no—
427C3×#67—122no—
428C2×C3×Dic3—22no—
429C2×C3×Dic3—22no—
430C2×C3×Dic3—21no—
431C2×C3×Dic3—21no—
432C2×C3×Dic3—21no—
433C2×C3×Dic3—21no—
434C2×C3×Dic3—21no—
435C2×C3×Dic3—21no—
436C2×C3×Dic3—31no—
437C2×C3×Dic3—31no—
438C2×C3×Dic3—34no—
439C2×C3×Dic3—31no—
440C2×C3×Dic3—31no—
441C2×C3×Dic3—31no—
442C2×C3×Dic3—31no—
443C2×C3×Dic3—42no—
444C2×C3×Dic3—61no—
445C2×C3×Dic3—61no—
446C2×C3×Dic3—61no—
447C2×C3×Dic3—62no—
448C2×C3×Dic3—62no—
449C2×C3×Dic3—62no—
450C2×C3×Dic3—122no—
451C2×C3×Dic3—121no—
452C2×C3×Dic3C22×D311yescharacteristic
453C2×C3×Dic3C22×D311yescharacteristic
454C2×C3×Dic3C22×D311yescharacteristic
455C2×C3×Dic3C22×D311yescharacteristic
456C2×C3×Dic3C22×D311yescharacteristic
457C2×C3×Dic3C22×D311yescharacteristic
458C2×C3×Dic3C23×C311yescharacteristic
459C2×C3×Dic3C23×C311yescharacteristic
460C2×C3×Dic3C23×C311yescharacteristic
461C2×C3×Dic3C23×C311yescharacteristic
462C2×C3×Dic3C23×C311yescharacteristic
463C2×C3×Dic3C23×C311yescharacteristic
464C3×D12—62no—
465C3×D12—121no—
466C3×C4×D3—34no—
467C3×C4×D3—41no—
468C3×C4×D3—41no—
469C3×C4×D3—42no—
470C3×C4×D3—62no—
471C3×C4×D3—62no—
472C3×C4×D3—62no—
473C3×C4×D3—121no—
474C3×Dic6—62no—
475C3×Dic6—62no—
476C3×Dic6—62no—
477C3×Dic6—62no—
478#627—22no—
479#627—22no—
480#626—22no—
481#626—41no—
482#625—22no—
483#624—22no—
484D3×Dic3—22no—
485D3×Dic3—41no—
486D3×Dic3C3×D414yescomplemented
487#537—91noSylow
488C2×C33—41no—
489C2×C33—41no—
490C2×C33C22×D411yescharacteristic
491C2×C33H(5,𝔽2)11yescharacteristic
492C2×C332−1+411yescharacteristic
493C3×C3⋊D3—41no—
494C32×D3—22no—
495C32×D3—41no—
496C3×#41—184no—
497C3×#41—184no—
498C2×C3×Q8—91no—
499C2×C3×Q8—91no—
500C2×C3×D4—21no—
501C2×C3×D4—21no—
502C2×C3×D4—21no—
503C2×C3×D4—31no—
504C2×C3×D4—31no—
505C2×C3×D4—31no—
506C2×C3×D4—31no—
507C2×C3×D4—31no—
508C2×C3×D4—31no—
509C2×C3×D4—31no—
510C2×C3×D4—31no—
511C2×C3×D4—41no—
512C2×C3×D4—61no—
513C2×C3×D4—61no—
514C2×C3×D4—61no—
515C2×C3×D4—61no—
516C2×C3×D4—91no—
517C2×C3×D4—91no—
518C2×C3×D4—91no—
519C2×C3×D4—91no—
520C2×C3×D4—91no—
521C2×C3×D4D3211yescharacteristic
522C2×C3×D4C2×C3×D311yescharacteristic
523C2×C3×D4C2×C3×D311yescharacteristic
524C22×C3×C4—31no—
525C22×C3×C4—31no—
526C22×C3×C4—31no—
527C22×C3×C4—31no—
528C22×C3×C4—61no—
529C22×C3×C4—61no—
530C22×C3×C4—91no—
531C22×C3×C4—91no—
532C22×C3×C4—91no—
533C22×C3×C4—91no—
534C22×C3×C4—91no—
535C2×#67—31no—
536C2×#67—31no—
537C2×#67—31no—
538C2×#67—31no—
539C2×#67—31no—
540C2×#67—31no—
541C2×#67—31no—
542C2×#67—31no—
543C2×#67—61no—
544C2×#67—61no—
545C2×#67C2×C3×D311yescharacteristic
546C2×#67C2×C3×D311yescharacteristic
547C2×#67C2×C3×D311yescharacteristic
548C2×#67C2×C3×D311yescharacteristic
549C22×Dic3—31no—
550C22×Dic3—31no—
551C22×Dic3—31no—
552C22×Dic3—31no—
553C22×Dic3—31no—
554C22×Dic3—61no—
555C22×Dic3C2×C3×D311yescharacteristic
556#237—64no—
557#237—64no—
558#237—64no—
559#235—64no—
560C2×D12—31no—
561C2×D12—31no—
562C2×C4×D3—31no—
563C2×C4×D3—31no—
564C2×C4×D3—31no—
565C2×C4×D3—31no—
566C2×C4×D3—31no—
567C2×C4×D3C2×C3×D311yescharacteristic
568C2×Dic6—31no—
569C2×Dic6—31no—
570C2×Dic6—31no—
571C2×Dic6—31no—
572C3×C4⋊C4—31no—
573C3×C4⋊C4—31no—
574C3×C4⋊C4—31no—
575C3×C4⋊C4—31no—
576C3×C4⋊C4—61no—
577C3×C4⋊C4—61no—
578C3×C4⋊C4—91no—
579C3×C4⋊C4—91no—
580C3×C4⋊C4—91no—
581C3×C4⋊C4—91no—
582C3×C4⋊C4—91no—
583C3×C4⋊C4—91no—
584C3×C22⋊C4—31no—
585C3×C22⋊C4—31no—
586C3×C22⋊C4—31no—
587C3×C22⋊C4—31no—
588C3×C22⋊C4—31no—
589C3×C22⋊C4—31no—
590C3×C22⋊C4—31no—
591C3×C22⋊C4—31no—
592C3×C22⋊C4—61no—
593C3×C22⋊C4—61no—
594C3×C22⋊C4—61no—
595C3×C22⋊C4—61no—
596C3×C22⋊C4—91no—
597C3×C22⋊C4—91no—
598C3×C22⋊C4—91no—
599C3×C22⋊C4—91no—
600#217—31no—
601#217—31no—
602#217—31no—
603#217—61no—
604#217C2×C3×D311yescharacteristic
605#217C2×C3×D311yescharacteristic
606#217C2×C3×D311yescharacteristic
607(C2×D3)⋊C4—31no—
608(C2×D3)⋊C4—31no—
609(C2×D3)⋊C4—31no—
610(C2×D3)⋊C4—31no—
611(C2×D3)⋊C4—31no—
612(C2×D3)⋊C4—61no—
613(C2×D3)⋊C4C2×C3×D311yescharacteristic
614C4⋊Dic3—31no—
615C4⋊Dic3—31no—
616C4⋊Dic3—31no—
617C4⋊Dic3C2×C3×D311yescharacteristic
618Dic3⋊C4—31no—
619Dic3⋊C4—31no—
620Dic3⋊C4—31no—
621Dic3⋊C4—31no—
622Dic3⋊C4—31no—
623Dic3⋊C4—31no—
624Dic3⋊C4—31no—
625Dic3⋊C4—31no—
626Dic3⋊C4—31no—
627Dic3⋊C4—61no—
628Dic3⋊C4C2×C3×D311yescharacteristic
629C22×C32—21no—
630C22×C32—21no—
631C22×C32—22no—
632C22×C32—22no—
633C22×C32—21no—
634C22×C32—21no—
635C22×C32—21no—
636C22×C32—21no—
637C22×C32—21no—
638C22×C32—21no—
639C22×C32—21no—
640C22×C32—21no—
641C22×C32—21no—
642C22×C32—21no—
643C22×C32—21no—
644C22×C32—21no—
645C22×C32—21no—
646C22×C32—21no—
647C22×C32—21no—
648C22×C32—21no—
649C22×C32—21no—
650C22×C32—21no—
651C22×C32—21no—
652C22×C32—32no—
653C22×C32—41no—
654C22×C32—41no—
655C22×C32—41no—
656C22×C32—41no—
657C22×C32—41no—
658C22×C32—42no—
659C22×C32—42no—
660C22×C32—41no—
661C22×C32—41no—
662C22×C32—41no—
663C22×C32—41no—
664C22×C32—41no—
665C22×C32—41no—
666C22×C32—41no—
667C22×C32—41no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—41no—
671C22×C32—41no—
672C22×C32—61no—
673C22×C32—61no—
674C22×C32—61no—
675C22×C32—61no—
676C22×C32—61no—
677C22×C32—81no—
678C22×C32—81no—
679C22×C32—81no—
680C22×C32—81no—
681C22×C32C23×D311yescharacteristic
682C22×C32C23×D311yescharacteristic
683C22×C32C24×C311yescharacteristic
684C2×C3⋊D3—21no—
685C2×C3⋊D3—21no—
686C2×C3⋊D3—21no—
687C2×C3×D3—21no—
688C2×C3×D3—21no—
689C2×C3×D3—21no—
690C2×C3×D3—21no—
691C2×C3×D3—21no—
692C2×C3×D3—21no—
693C2×C3×D3—21no—
694C2×C3×D3—21no—
695C2×C3×D3—21no—
696C2×C3×D3—21no—
697C2×C3×D3—22no—
698C2×C3×D3—41no—
699C2×C3×D3—41no—
700C2×C3×D3—41no—
701C2×C3×D3—41no—
702C2×C3×D3—41no—
703C2×C3×D3—61no—
704C2×C3×D3—61no—
705C2×C3×D3—61no—
706C2×C3×D3—61no—
707C2×C3×D3—61no—
708C2×C3×D3—61no—
709C2×C3×D3—121no—
710C2×C3×D3—121no—
711C2×C3×D3—121no—
712C2×C3×D3D3×D412yes—
713C2×C3×D3C2×C3×D412yes—
714C32×C4—21no—
715C32×C4—22no—
716C32×C4—21no—
717C32×C4—21no—
718C32×C4—32no—
719C32×C4—41no—
720C32×C4—41no—
721C32×C4—42no—
722C32×C4—61no—
723C32×C4—61no—
724C32×C4—61no—
725C32×C4—61no—
726C32×C4—61no—
727C3⋊Dic3—21no—
728C3⋊Dic3—21no—
729C3⋊Dic3C2×C3×D412yes—
730C3×Dic3—21no—
731C3×Dic3—21no—
732C3×Dic3—21no—
733C3×Dic3—21no—
734C3×Dic3—21no—
735C3×Dic3—21no—
736C3×Dic3—21no—
737C3×Dic3—21no—
738C3×Dic3—21no—
739C3×Dic3—21no—
740C3×Dic3—22no—
741C3×Dic3—32no—
742C3×Dic3—32no—
743C3×Dic3—41no—
744C3×Dic3—41no—
745C3×Dic3—41no—
746C3×Dic3—41no—
747C3×Dic3—41no—
748C3×Dic3—62no—
749C3×Dic3—61no—
750C3×Dic3—61no—
751C3×Dic3—61no—
752C3×Dic3—61no—
753C3×Dic3—121no—
754C3×Dic3—121no—
755C3×Dic3D3×D412yes—
756C3×Dic3C2×C3×D412yes—
757C2×#41—91no—
758C2×#41—91no—
759C22⋊Q8—91no—
760C22⋊Q8—91no—
761C22⋊Q8—91no—
762C22⋊Q8—91no—
763#121—31no—
764#121—31no—
765#121—91no—
766#121—91no—
767#121—91no—
768#121—91no—
769#121—91no—
770#121—91no—
771C2×C4⋊C4—91no—
772C33#53711yescharacteristic, complemented, Sylow
773C23×C3—21no—
774C23×C3—21no—
775C23×C3—21no—
776C23×C3—21no—
777C23×C3—21no—
778C23×C3—21no—
779C23×C3—31no—
780C23×C3—31no—
781C23×C3—31no—
782C23×C3—31no—
783C23×C3—41no—
784C23×C3—41no—
785C23×C3—61no—
786C23×C3—61no—
787C23×C3—91no—
788C23×C3C2×D3211yescharacteristic
789C23×C3C2×D3211yescharacteristic
790C23×C3C22×C3×D311yescharacteristic
791C23×C3C22×C3×D311yescharacteristic
792C23×C3C22×C3×D311yescharacteristic
793C23×C3C22×C3×D311yescharacteristic
794C22×D3—31no—
795C22×D3—31no—
796C22×D3—61no—
797C22×D3C22×C3×D311yescharacteristic
798C22×D3C22×C3×D311yescharacteristic
799C3×Q8—182no—
800C3×Q8—182no—
801C3×D4—41no—
802C3×D4—41no—
803C3×D4—41no—
804C3×D4—42no—
805C3×D4—42no—
806C3×D4—42no—
807C3×D4—44no—
808C3×D4—62no—
809C3×D4—62no—
810C3×D4—62no—
811C3×D4—62no—
812C3×D4—62no—
813C3×D4—62no—
814C3×D4—122no—
815C3×D4—122no—
816C3×D4—122no—
817C3×D4—121no—
818C3×D4—121no—
819C3×D4—122no—
820C3×D4—182no—
821C3×D4—182no—
822C3×D4—182no—
823C3×D4—361no—
824C3×D4—361no—
825C2×C3×C4—21no—
826C2×C3×C4—21no—
827C2×C3×C4—21no—
828C2×C3×C4—31no—
829C2×C3×C4—31no—
830C2×C3×C4—31no—
831C2×C3×C4—31no—
832C2×C3×C4—31no—
833C2×C3×C4—31no—
834C2×C3×C4—31no—
835C2×C3×C4—31no—
836C2×C3×C4—31no—
837C2×C3×C4—31no—
838C2×C3×C4—31no—
839C2×C3×C4—31no—
840C2×C3×C4—41no—
841C2×C3×C4—61no—
842C2×C3×C4—61no—
843C2×C3×C4—61no—
844C2×C3×C4—61no—
845C2×C3×C4—61no—
846C2×C3×C4—61no—
847C2×C3×C4—62no—
848C2×C3×C4—62no—
849C2×C3×C4—94no—
850C2×C3×C4—91no—
851C2×C3×C4—91no—
852C2×C3×C4—91no—
853C2×C3×C4—122no—
854C2×C3×C4—121no—
855C2×C3×C4—121no—
856C2×C3×C4—122no—
857C2×C3×C4—182no—
858C2×C3×C4—182no—
859C2×C3×C4—182no—
860C2×C3×C4—361no—
861C2×C3×C4C2×D3211yescharacteristic
862C2×C3×C4C22×C3×D311yescharacteristic
863C2×C3×C4C22×C3×D311yescharacteristic
864#67—22no—
865#67—22no—
866#67—22no—
867#67—41no—
868#67—62no—
869#67—62no—
870#67—62no—
871#67—62no—
872#67—62no—
873#67—122no—
874#67—121no—
875#67—121no—
876#67—121no—
877#67—122no—
878C2×Dic3—22no—
879C2×Dic3—31no—
880C2×Dic3—31no—
881C2×Dic3—34no—
882C2×Dic3—31no—
883C2×Dic3—31no—
884C2×Dic3—31no—
885C2×Dic3—31no—
886C2×Dic3—61no—
887C2×Dic3—61no—
888C2×Dic3—61no—
889C2×Dic3—62no—
890C2×Dic3—62no—
891C2×Dic3—62no—
892C2×Dic3—122no—
893C2×Dic3—121no—
894C2×Dic3C22×C3×D311yescharacteristic
895C2×Dic3C22×C3×D311yescharacteristic
896C2×Dic3C22×C3×D311yescharacteristic
897C2×Dic3C22×C3×D311yescharacteristic
898C2×Dic3C22×C3×D311yescharacteristic
899C2×Dic3C22×C3×D311yescharacteristic
900D12—62no—
901D12—121no—
902C4×D3—34no—
903C4×D3—41no—
904C4×D3—62no—
905C4×D3—62no—
906C4×D3—62no—
907C4×D3—121no—
908Dic6—62no—
909Dic6—62no—
910Dic6—62no—
911Dic6—62no—
912C2×C32—21no—
913C2×C32—21no—
914C2×C32—21no—
915C2×C32—21no—
916C2×C32—21no—
917C2×C32—21no—
918C2×C32—21no—
919C2×C32—21no—
920C2×C32—21no—
921C2×C32—41no—
922C2×C32—41no—
923C2×C32—41no—
924C2×C32—41no—
925C2×C32—41no—
926C2×C32—42no—
927C2×C32—42no—
928C2×C32—41no—
929C2×C32—41no—
930C2×C32—41no—
931C2×C32—41no—
932C2×C32—62no—
933C2×C32—81no—
934C2×C32—81no—
935C2×C32—81no—
936C2×C32—81no—
937C2×C32—82no—
938C2×C32—82no—
939C2×C32—121no—
940C2×C32C2×D3×D411yescharacteristic
941C2×C32C2×D3×D411yescharacteristic
942C2×C32#100411yescharacteristic
943C2×C32#100411yescharacteristic
944C2×C32#101011yescharacteristic
945C2×C32#101011yescharacteristic
946C2×C32C22×C3×D411yescharacteristic
947C2×C32C3×H(5,𝔽2)11yescharacteristic
948C2×C32C3×2−1+411yescharacteristic
949C3⋊D3—41no—
950C3×D3—22no—
951C3×D3—22no—
952C3×D3—42no—
953C3×D3—41no—
954C3×D3—41no—
955C3×D3—81no—
956C3×D3—121no—
957C3×D3—121no—
958C3×D3—241no—
959#41—184no—
960#41—184no—
961C2×Q8—91no—
962C2×Q8—91no—
963C2×D4—31no—
964C2×D4—31no—
965C2×D4—31no—
966C2×D4—31no—
967C2×D4—91no—
968C2×D4—91no—
969C2×D4—91no—
970C2×D4—91no—
971C2×D4—91no—
972C2×D4C3×D3211yescharacteristic
973C22×C4—31no—
974C22×C4—31no—
975C22×C4—91no—
976C22×C4—91no—
977C22×C4—91no—
978C22×C4—91no—
979C22×C4—91no—
980C4⋊C4—31no—
981C4⋊C4—31no—
982C4⋊C4—91no—
983C4⋊C4—91no—
984C4⋊C4—91no—
985C4⋊C4—91no—
986C4⋊C4—91no—
987C4⋊C4—91no—
988C22⋊C4—31no—
989C22⋊C4—31no—
990C22⋊C4—31no—
991C22⋊C4—31no—
992C22⋊C4—91no—
993C22⋊C4—91no—
994C22⋊C4—91no—
995C22⋊C4—91no—
996C22×C3—22no—
997C22×C3—22no—
998C22×C3—21no—
999C22×C3—21no—
1000C22×C3—21no—
1001C22×C3—21no—
1002C22×C3—21no—
1003C22×C3—21no—
1004C22×C3—21no—
1005C22×C3—21no—
1006C22×C3—21no—
1007C22×C3—21no—
1008C22×C3—21no—
1009C22×C3—21no—
1010C22×C3—21no—
1011C22×C3—21no—
1012C22×C3—21no—
1013C22×C3—21no—
1014C22×C3—21no—
1015C22×C3—21no—
1016C22×C3—21no—
1017C22×C3—21no—
1018C22×C3—21no—
1019C22×C3—32no—
1020C22×C3—32no—
1021C22×C3—41no—
1022C22×C3—41no—
1023C22×C3—41no—
1024C22×C3—41no—
1025C22×C3—41no—
1026C22×C3—41no—
1027C22×C3—41no—
1028C22×C3—41no—
1029C22×C3—41no—
1030C22×C3—41no—
1031C22×C3—41no—
1032C22×C3—41no—
1033C22×C3—41no—
1034C22×C3—41no—
1035C22×C3—41no—
1036C22×C3—41no—
1037C22×C3—42no—
1038C22×C3—42no—
1039C22×C3—41no—
1040C22×C3—62no—
1041C22×C3—61no—
1042C22×C3—61no—
1043C22×C3—61no—
1044C22×C3—61no—
1045C22×C3—61no—
1046C22×C3—61no—
1047C22×C3—61no—
1048C22×C3—61no—
1049C22×C3—61no—
1050C22×C3—61no—
1051C22×C3—81no—
1052C22×C3—81no—
1053C22×C3—81no—
1054C22×C3—81no—
1055C22×C3—121no—
1056C22×C3—121no—
1057C22×C3—121no—
1058C22×C3—121no—
1059C22×C3—121no—
1060C22×C3—181no—
1061C22×C3—181no—
1062C22×C3—181no—
1063C22×C3C22×D3211yescharacteristic
1064C22×C3C23×C3×D311yescharacteristic
1065C22×C3C23×C3×D311yescharacteristic
1066C2×D3—21no—
1067C2×D3—21no—
1068C2×D3—21no—
1069C2×D3—21no—
1070C2×D3—21no—
1071C2×D3—61no—
1072C2×D3—61no—
1073C2×D3—61no—
1074C2×D3—61no—
1075C2×D3—61no—
1076C2×D3—61no—
1077C2×D3—121no—
1078C2×D3—121no—
1079C2×D3—121no—
1080C2×D3C3×D3×D412yes—
1081C3×C4—22no—
1082C3×C4—21no—
1083C3×C4—21no—
1084C3×C4—21no—
1085C3×C4—32no—
1086C3×C4—32no—
1087C3×C4—41no—
1088C3×C4—41no—
1089C3×C4—42no—
1090C3×C4—62no—
1091C3×C4—61no—
1092C3×C4—61no—
1093C3×C4—61no—
1094C3×C4—61no—
1095C3×C4—61no—
1096C3×C4—61no—
1097C3×C4—61no—
1098C3×C4—61no—
1099C3×C4—61no—
1100C3×C4—61no—
1101C3×C4—92no—
1102C3×C4—121no—
1103C3×C4—121no—
1104C3×C4—121no—
1105C3×C4—121no—
1106C3×C4—121no—
1107C3×C4—181no—
1108C3×C4—181no—
1109Dic3—21no—
1110Dic3—21no—
1111Dic3—21no—
1112Dic3—21no—
1113Dic3—21no—
1114Dic3—32no—
1115Dic3—32no—
1116Dic3—62no—
1117Dic3—61no—
1118Dic3—61no—
1119Dic3—61no—
1120Dic3—61no—
1121Dic3—121no—
1122Dic3—121no—
1123Dic3C3×D3×D412yes—
1124C32—21no—
1125C32—21no—
1126C32—21no—
1127C32—41no—
1128C32#559711yescharacteristic, complemented
1129C32#560811yescharacteristic, complemented
1130C32C3×#53711yescharacteristic, complemented
1131C23—31no—
1132C23—31no—
1133C23—91no—
1134C23C2×C3×D3211yescharacteristic
1135C23C2×C3×D3211yescharacteristic
1136Q8—182no—
1137Q8—182no—
1138D4—41no—
1139D4—62no—
1140D4—62no—
1141D4—62no—
1142D4—121no—
1143D4—182no—
1144D4—182no—
1145D4—182no—
1146D4—361no—
1147D4—361no—
1148C2×C4—31no—
1149C2×C4—31no—
1150C2×C4—31no—
1151C2×C4—31no—
1152C2×C4—31no—
1153C2×C4—31no—
1154C2×C4—62no—
1155C2×C4—94no—
1156C2×C4—91no—
1157C2×C4—91no—
1158C2×C4—91no—
1159C2×C4—121no—
1160C2×C4—182no—
1161C2×C4—182no—
1162C2×C4—182no—
1163C2×C4—361no—
1164C2×C4C2×C3×D3211yescharacteristic
1165C2×C3—21no—
1166C2×C3—21no—
1167C2×C3—21no—
1168C2×C3—21no—
1169C2×C3—21no—
1170C2×C3—21no—
1171C2×C3—21no—
1172C2×C3—21no—
1173C2×C3—21no—
1174C2×C3—42no—
1175C2×C3—42no—
1176C2×C3—41no—
1177C2×C3—41no—
1178C2×C3—41no—
1179C2×C3—41no—
1180C2×C3—41no—
1181C2×C3—41no—
1182C2×C3—41no—
1183C2×C3—41no—
1184C2×C3—41no—
1185C2×C3—62no—
1186C2×C3—62no—
1187C2×C3—81no—
1188C2×C3—81no—
1189C2×C3—81no—
1190C2×C3—81no—
1191C2×C3—82no—
1192C2×C3—82no—
1193C2×C3—122no—
1194C2×C3—121no—
1195C2×C3—121no—
1196C2×C3—241no—
1197C2×C3—361no—
1198C2×C3#6430911yescharacteristic
1199C2×C3D32×D411yescharacteristic
1200C2×C3#6433011yescharacteristic
1201C2×C3C2×C3×D3×D411yescharacteristic
1202C2×C3C2×C3×D3×D411yescharacteristic
1203C2×C3C3×#100411yescharacteristic
1204C2×C3C3×#100411yescharacteristic
1205C2×C3C3×#101011yescharacteristic
1206C2×C3C3×#101011yescharacteristic
1207D3—22no—
1208D3—41no—
1209D3—121no—
1210D3—121no—
1211D3—241no—
1212C22—21no—
1213C22—21no—
1214C22—21no—
1215C22—21no—
1216C22—21no—
1217C22—21no—
1218C22—32no—
1219C22—61no—
1220C22—61no—
1221C22—61no—
1222C22—61no—
1223C22—61no—
1224C22—181no—
1225C22—181no—
1226C22—181no—
1227C22C22×C3×D3211yescharacteristic
1228C4—21no—
1229C4—32no—
1230C4—61no—
1231C4—61no—
1232C4—61no—
1233C4—61no—
1234C4—61no—
1235C4—92no—
1236C4—181no—
1237C4—181no—
1238C3—21no—
1239C3—21no—
1240C3—21no—
1241C3—41no—
1242C3#1059513211yescharacteristic, direct product factor
1243C3C3×#559711yescharacteristic, complemented
1244C3C3×#560811yescharacteristic, complemented
1245C2—41no—
1246C2—41no—
1247C2—62no—
1248C2—121no—
1249C2—361no—
1250C2C3×#6430911yescharacteristic
1251C2C3×D32×D411yescharacteristic
1252C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#537
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3805C2semidirect
2. C2×C3×#3804C2semidirect
3. C3×#64148C2semidirect
4. C32×#939C2semidirect
5. C32×#938C2semidirect
6. C3×#63982C2semidirect
7. C3×#63971C2semidirect
8. C3×#63971C2semidirect
9. C3×#63970C2semidirect
10. C3×#63964C2semidirect
11. C3×#63958C2semidirect
12. C3×#63906C2semidirect
13. C3×#63899C2semidirect
14. C3×#63895C2semidirect
15. C3×D3×Dic3⋊C4C2semidirect
18. #10595132C3direct (N × H)
60. C2×#3805C2×C3semidirect
61. C2×#3804C2×C3semidirect
64. #64148C2×C3semidirect
72. C3×#939D3semidirect
73. C3×#939C2×C3semidirect
77. C3×#938D3semidirect
78. C3×#938C2×C3semidirect
94. #63982C2×C3semidirect
95. #63971C2×C3semidirect
96. #63971C2×C3semidirect
97. #63970C2×C3semidirect
98. #63964C2×C3semidirect
99. #63958C2×C3semidirect
100. #63906C2×C3semidirect
101. #63899C2×C3semidirect
102. #63895C2×C3semidirect
103. D3×Dic3⋊C4C2×C3semidirect
137. C3×D3×Dic3D4semidirect
329. #939C3×D3semidirect
332. #938C3×D3semidirect
486. D3×Dic3C3×D4semidirect
772. C33#537semidirect
1128. C32#5597semidirect
1129. C32#5608semidirect
1130. C32C3×#537semidirect
1242. C3#10595132direct (N × H)
1243. C3C3×#5597semidirect
1244. C3C3×#5608semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38052
C2×C3×#38042
C3×#641482
C32×#9392
C32×#9382
C3×#639822
C3×#639712
C3×#639702
C3×#639642
C3×#639582
C3×#639062
C3×#638992
C3×#638952
C3×D3×Dic3⋊C42
C3×#56083
C3×#55973
#105951323