Finite Group Databasebeta

← #13178241

Subgroups — #13178241

Order 1728.

1448 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89046C211yesmaximal, characteristic, complemented
2C2×#89041C211yesmaximal, characteristic, complemented
3C3×#64093C211yesmaximal, characteristic, complemented
4C3×#64092C211yesmaximal, characteristic, complemented
5C3×#64087C211yesmaximal, characteristic, complemented
6#11723726C211yesmaximal, characteristic, complemented
7#11723725C211yesmaximal, characteristic, complemented
8#11723724C211yesmaximal, characteristic, complemented
9#11723692C211yesmaximal, characteristic, complemented
10#11723690C211yesmaximal, characteristic, complemented
11#11723689C211yesmaximal, characteristic, complemented
12#11723686C211yesmaximal, characteristic, complemented
13#11723684C211yesmaximal, characteristic, complemented
14#11723682C211yesmaximal, characteristic, complemented
15#11723666C211yesmaximal, characteristic, complemented
16#10594065—31nomaximal
17#10594064—31nomaximal
18#10594062—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C3×C4×C3⋊D3C2211yescharacteristic
25C2×C3×C4×C3⋊D3C2211yescharacteristic
26C2×C3×#634C2211yescharacteristic
27C2×#6296C2211yescharacteristic
28C2×#6295C2211yescharacteristic
29C2×#6295C2211yescharacteristic
30#89046—24no—
31C2×#6294C2211yescharacteristic
32C2×#6294C2211yescharacteristic
33C2×#6294C2211yescharacteristic
34C2×#6294C2211yescharacteristic
35C2×#6294C2211yescharacteristic
36#89041—24no—
37C33×C22⋊C4C2211yescharacteristic
38C3×#3757C2211yescharacteristic
39C3×#3757C2211yescharacteristic
40C3×#3752C2211yescharacteristic
41C3×#3752C2211yescharacteristic
42C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
43C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
44C3×#3750C2211yescharacteristic
45C3×#3750C2211yescharacteristic
46C3×#3750C2211yescharacteristic
47C3×#3750C2211yescharacteristic
48#88815C2211yescharacteristic
49#88815C2211yescharacteristic
50#88815C2211yescharacteristic
51#88815C2211yescharacteristic
52#88814C2211yescharacteristic
53#88814C2211yescharacteristic
54#88814C2211yescharacteristic
55#88813C2211yescharacteristic
56C2×#3805—31no—
57C2×#3804—31no—
58C2×#3804—31no—
59C2×#3799—31no—
60C2×#3796—31no—
61C2×#3795—31no—
62#64093D311yescharacteristic, complemented
63#64092D311yescharacteristic, complemented
64#64087D311yescharacteristic, complemented
65C3×#884—31no—
66C3×#884—31no—
67C3×#884—61no—
68C3×#883—31no—
69C3×#883—31no—
70C3×#883—61no—
71C3×#878—31no—
72C3×#878—31no—
73C3×#878—61no—
74#63975—31no—
75#67⋊Dic3—31no—
76Dic3×#67—31no—
77#63971—31no—
78#63970—31no—
79#63969—31no—
80#63969—31no—
81#63958—31no—
82#63952—31no—
83#63904—31no—
84#63900—31no—
85#63899—31no—
86#63897—31no—
87#63895—31no—
88#63893—31no—
89#63891—31no—
90#63890—31no—
91D3×C4⋊Dic3—31no—
92D3×C4⋊Dic3—31no—
93#63884—31no—
94#63884—31no—
95#63883—31no—
96#63881—31no—
97#63879—31no—
98D3×Dic3⋊C4—31no—
99D3×Dic3⋊C4—31no—
100#63854—31no—
101#63840—31no—
102#63839—31no—
103#63839—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C2×C33×C4C2311yescharacteristic
109C2×C33×C4C2311yescharacteristic
110C3×#638—22no—
111C3×#638—22no—
112C3×#638—22no—
113C2×C3×C3⋊Dic3—22no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C3×C4⋊(C3⋊D3)—22no—
124C3×C4×C3⋊D3—22no—
125C3×C4×C3⋊D3—22no—
126C3×#634—22no—
127#6296—22no—
128#6295—22no—
129#6295D414yescomplemented
130#6294—22no—
131#6294—22no—
132#6294—22no—
133#6294—22no—
134#6294—22no—
135#5655—91no—
136#5631—91no—
137#5611—91no—
138C2×#638C2×D311yescharacteristic
139C2×#638C2×D311yescharacteristic
140C2×#638C2×D311yescharacteristic
141C22×C3⋊Dic3C2×D311yescharacteristic
142C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
143C2×C4×C3⋊D3C2×D311yescharacteristic
144C2×C4×C3⋊D3C2×D311yescharacteristic
145C2×#634C2×D311yescharacteristic
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—61no—
153C2×C3×#67—61no—
154C2×C3×#67—61no—
155C22×C3×Dic3—31no—
156C22×C3×Dic3—31no—
157C22×C3×Dic3—61no—
158C2×C3×D12—31no—
159C2×C3×D12—31no—
160C2×C3×D12—61no—
161C2×C3×C4×D3—31no—
162C2×C3×C4×D3—31no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—61no—
166C2×C3×C4×D3—61no—
167C2×C3×Dic6—31no—
168C2×C3×Dic6—31no—
169C2×C3×Dic6—61no—
170C2×#627—31no—
171C2×#627—31no—
172C2×#627—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#625—31no—
178C2×#625—31no—
179C2×#624—31no—
180C2×#624—31no—
181C2×#624—31no—
182C2×#624—31no—
183C2×#624—31no—
184#3805—64no—
185#3804—64no—
186#3804—64no—
187C2×D3×Dic3—31no—
188C2×D3×Dic3—31no—
189C2×D3×Dic3—31no—
190C2×D3×Dic3—31no—
191C2×D3×Dic3—31no—
192C2×D3×Dic3—31no—
193C2×D3×Dic3—31no—
194C2×D3×Dic3—31no—
195C2×D3×Dic3—31no—
196C2×D3×Dic3—31no—
197#3799—64no—
198#3796—64no—
199#3795—64no—
200C32×C22⋊C4—21no—
201C32×C22⋊C4—21no—
202C32×C22⋊C4—21no—
203C32×C22⋊C4—41no—
204C32×C22⋊C4C2×D311yescharacteristic
205C32×C22⋊C4C2×D311yescharacteristic
206C32×C22⋊C4C2×D311yescharacteristic
207#3757C2×D311yescharacteristic
208#3757C2×D311yescharacteristic
209#3752C2×D311yescharacteristic
210#3752C2×D311yescharacteristic
211C4⋊(C3⋊Dic3)C2×D311yescharacteristic
212C4⋊(C3⋊Dic3)C2×D311yescharacteristic
213#3750C2×D311yescharacteristic
214#3750C2×D311yescharacteristic
215#3750C2×D311yescharacteristic
216#3750C2×D311yescharacteristic
217C3×#217—31no—
218C3×#217—31no—
219C3×#217—31no—
220C3×#217—31no—
221C3×#217—61no—
222C3×#217—61no—
223C3×(C2×D3)⋊C4—31no—
224C3×(C2×D3)⋊C4—31no—
225C3×(C2×D3)⋊C4—31no—
226C3×(C2×D3)⋊C4—31no—
227C3×(C2×D3)⋊C4—61no—
228C3×(C2×D3)⋊C4—61no—
229C3×C4⋊Dic3—31no—
230C3×C4⋊Dic3—31no—
231C3×C4⋊Dic3—31no—
232C3×C4⋊Dic3—31no—
233C3×C4⋊Dic3—61no—
234C3×C4⋊Dic3—61no—
235C3×Dic3⋊C4—31no—
236C3×Dic3⋊C4—31no—
237C3×Dic3⋊C4—31no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—61no—
244C3×Dic3⋊C4—61no—
245C3×Dic3⋊C4—61no—
246C3×Dic3⋊C4—61no—
247#3724—31no—
248#3724—31no—
249#3724—31no—
250#3724—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—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262(C2×D3)⋊Dic3—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—
268Dic32—31no—
269Dic32—31no—
270Dic32—31no—
271C22×C33—21no—
272C22×C33—21no—
273C22×C33—21no—
274C22×C33C2411yescharacteristic
275C2×C3×C3⋊D3—21no—
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3—21no—
278C2×C3×C3⋊D3—21no—
279C2×C3×C3⋊D3—21no—
280C2×C3×C3⋊D3—21no—
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3C2×D412yes—
283C2×C3×C3⋊D3C2×D412yes—
284C33×C4—21no—
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⋊Dic3C2×D412yes—
294C3×C3⋊Dic3#4112yescomplemented
295C2×#239—91no—
296C2×#237—91no—
297C2×#237—91no—
298C2×#237—91no—
299C2×#235—91no—
300C2×#235—91no—
301C3×#123—91no—
302C3×C22⋊Q8—91no—
303C3×#121—91no—
304#944—91no—
305#939—91no—
306#938—91no—
307#935—91no—
308#935—91no—
309D4×Dic3—91no—
310C4×#67—91no—
311C4×#67—91no—
312C2×C4⋊Dic3—91no—
313C2×Dic3⋊C4—91no—
314#897—91no—
315#896—91no—
316#894—91no—
317#894—91no—
318#894—91no—
319#893—91no—
320D3×C4⋊C4—91no—
321D3×C4⋊C4—91no—
322D3×C4⋊C4—91no—
323D3×C4⋊C4—91no—
324#888—91no—
325#888—91no—
326#886—91no—
327#884—31no—
328#884—31no—
329#884—61no—
330#884—91no—
331#883—31no—
332#883—31no—
333#883—61no—
334#883—91no—
335#883—91no—
336#883—91no—
337#67⋊C4—91no—
338#67⋊C4—91no—
339#878—31no—
340#878—31no—
341#878—61no—
342#878—91no—
343C23×C32—21no—
344C23×C32—21no—
345C23×C32—21no—
346C23×C32—41no—
347C23×C32C22×D311yescharacteristic
348C23×C32C22×D311yescharacteristic
349C23×C32C22×D311yescharacteristic
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3⋊D3C22×D311yescharacteristic
352C22×C3⋊D3C22×D311yescharacteristic
353C22×C3×D3—31no—
354C22×C3×D3—31no—
355C22×C3×D3—31no—
356C22×C3×D3—31no—
357C22×C3×D3—31no—
358C22×C3×D3—31no—
359C22×C3×D3—61no—
360C22×C3×D3—61no—
361C22×C3×D3—61no—
362C2×C32×C4—21no—
363C2×C32×C4—21no—
364C2×C32×C4—21no—
365C2×C32×C4—21no—
366C2×C32×C4—21no—
367C2×C32×C4—21no—
368C2×C32×C4—41no—
369C2×C32×C4—41no—
370C2×C32×C4C22×D311yescharacteristic
371C2×C32×C4C22×D311yescharacteristic
372C2×C32×C4C22×D311yescharacteristic
373C2×C32×C4C22×D311yescharacteristic
374C2×C32×C4C22×D311yescharacteristic
375C2×C32×C4C22×D311yescharacteristic
376#638—22no—
377#638—22no—
378#638—22no—
379C2×C3⋊Dic3—22no—
380C2×C3⋊Dic3C22×D311yescharacteristic
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C2×C3⋊Dic3C22×D311yescharacteristic
388C2×C3⋊Dic3C22×D311yescharacteristic
389C4⋊(C3⋊D3)—22no—
390C4×C3⋊D3—22no—
391C4×C3⋊D3—22no—
392#634—22no—
393C3×#67—62no—
394C3×#67—62no—
395C3×#67—62no—
396C3×#67—62no—
397C3×#67—62no—
398C3×#67—62no—
399C3×#67—122no—
400C3×#67—122no—
401C3×#67—122no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
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—61no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3—61no—
423C2×C3×Dic3—61no—
424C2×C3×Dic3—61no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—61no—
427C2×C3×Dic3—61no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—62no—
430C2×C3×Dic3—62no—
431C2×C3×Dic3—122no—
432C3×D12—62no—
433C3×D12—62no—
434C3×D12—122no—
435C3×C4×D3—62no—
436C3×C4×D3—62no—
437C3×C4×D3—62no—
438C3×C4×D3—62no—
439C3×C4×D3—122no—
440C3×C4×D3—122no—
441C3×Dic6—62no—
442C3×Dic6—62no—
443C3×Dic6—122no—
444#627—62no—
445#627—62no—
446#627—62no—
447#626—34no—
448#626—34no—
449#626—62no—
450#626—62no—
451#625—34no—
452#625—62no—
453#624—62no—
454#624—62no—
455#624—62no—
456#624—62no—
457#624—62no—
458D3×Dic3—62no—
459D3×Dic3—62no—
460D3×Dic3—62no—
461D3×Dic3—62no—
462D3×Dic3—62no—
463D3×Dic3—62no—
464D3×Dic3—62no—
465D3×Dic3—62no—
466D3×Dic3—62no—
467D3×Dic3—62no—
468#547—271noSylow
469C2×C33—41no—
470C2×C33C22×D411yescharacteristic
471C2×C33C2×#4111yescharacteristic
472C2×C332−1+411yescharacteristic
473C3×C3⋊D3—22no—
474C3×C3⋊D3—22no—
475C3×C3⋊D3—41no—
476C2×C3×Q8—91no—
477C2×C3×D4—91no—
478C2×C3×D4—91no—
479C2×C3×D4—91no—
480C2×C3×D4—91no—
481C22×C3×C4—91no—
482C22×C3×C4—91no—
483C22×C3×C4—91no—
484C2×#67—31no—
485C2×#67—31no—
486C2×#67—31no—
487C2×#67—31no—
488C2×#67—31no—
489C2×#67—31no—
490C2×#67—61no—
491C2×#67—61no—
492C2×#67—61no—
493C2×#67—91no—
494C2×#67—91no—
495C2×#67—91no—
496C2×#67—91no—
497C22×Dic3—31no—
498C22×Dic3—31no—
499C22×Dic3—61no—
500C22×Dic3—91no—
501C22×Dic3—91no—
502C22×Dic3—91no—
503C22×Dic3—91no—
504C22×Dic3—91no—
505#239—184no—
506#237—184no—
507#237—184no—
508#237—184no—
509#235—184no—
510#235—184no—
511C2×D12—31no—
512C2×D12—31no—
513C2×D12—61no—
514C2×D12—91no—
515C2×D12—91no—
516C2×C4×D3—31no—
517C2×C4×D3—31no—
518C2×C4×D3—31no—
519C2×C4×D3—31no—
520C2×C4×D3—61no—
521C2×C4×D3—61no—
522C2×C4×D3—91no—
523C2×C4×D3—91no—
524C2×C4×D3—91no—
525C2×C4×D3—91no—
526C2×C4×D3—91no—
527C2×C4×D3—91no—
528C2×C4×D3—91no—
529C2×C4×D3—91no—
530C2×C4×D3—91no—
531C2×C4×D3—91no—
532C2×Dic6—31no—
533C2×Dic6—31no—
534C2×Dic6—61no—
535C2×Dic6—91no—
536C2×Dic6—91no—
537C2×Dic6—91no—
538C3×C4⋊C4—91no—
539C3×C4⋊C4—91no—
540C3×C4⋊C4—91no—
541C3×C4⋊C4—91no—
542C3×C4⋊C4—91no—
543C3×C4⋊C4—91no—
544C3×C22⋊C4—21no—
545C3×C22⋊C4—21no—
546C3×C22⋊C4—21no—
547C3×C22⋊C4—41no—
548C3×C22⋊C4—91no—
549C3×C22⋊C4—91no—
550C3×C22⋊C4—91no—
551C3×C22⋊C4—91no—
552C3×C22⋊C4D3211yescharacteristic
553C3×C22⋊C4D3211yescharacteristic
554C3×C22⋊C4D3211yescharacteristic
555#217—31no—
556#217—31no—
557#217—31no—
558#217—31no—
559#217—61no—
560#217—61no—
561#217—91no—
562#217—91no—
563#217—91no—
564(C2×D3)⋊C4—31no—
565(C2×D3)⋊C4—31no—
566(C2×D3)⋊C4—31no—
567(C2×D3)⋊C4—31no—
568(C2×D3)⋊C4—61no—
569(C2×D3)⋊C4—61no—
570(C2×D3)⋊C4—91no—
571(C2×D3)⋊C4—91no—
572(C2×D3)⋊C4—91no—
573(C2×D3)⋊C4—91no—
574(C2×D3)⋊C4—91no—
575(C2×D3)⋊C4—91no—
576C4⋊Dic3—31no—
577C4⋊Dic3—31no—
578C4⋊Dic3—31no—
579C4⋊Dic3—31no—
580C4⋊Dic3—61no—
581C4⋊Dic3—61no—
582C4⋊Dic3—91no—
583C4⋊Dic3—91no—
584C4⋊Dic3—91no—
585C4⋊Dic3—91no—
586Dic3⋊C4—31no—
587Dic3⋊C4—31no—
588Dic3⋊C4—31no—
589Dic3⋊C4—31no—
590Dic3⋊C4—31no—
591Dic3⋊C4—31no—
592Dic3⋊C4—31no—
593Dic3⋊C4—31no—
594Dic3⋊C4—61no—
595Dic3⋊C4—61no—
596Dic3⋊C4—61no—
597Dic3⋊C4—61no—
598Dic3⋊C4—91no—
599Dic3⋊C4—91no—
600Dic3⋊C4—91no—
601Dic3⋊C4—91no—
602Dic3⋊C4—91no—
603Dic3⋊C4—91no—
604Dic3⋊C4—91no—
605Dic3⋊C4—91no—
606C4×Dic3—91no—
607C4×Dic3—91no—
608C4×Dic3—91no—
609C22×C32—21no—
610C22×C32—22no—
611C22×C32—21no—
612C22×C32—21no—
613C22×C32—21no—
614C22×C32—21no—
615C22×C32—21no—
616C22×C32—21no—
617C22×C32—21no—
618C22×C32—21no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—21no—
622C22×C32—41no—
623C22×C32—41no—
624C22×C32—41no—
625C22×C32—42no—
626C22×C32—41no—
627C22×C32—41no—
628C22×C32—41no—
629C22×C32—41no—
630C22×C32—41no—
631C22×C32—41no—
632C22×C32—81no—
633C22×C32—81no—
634C22×C32C23×D311yescharacteristic
635C22×C32C23×D311yescharacteristic
636C22×C32C23×D311yescharacteristic
637C2×C3⋊D3—21no—
638C2×C3⋊D3—21no—
639C2×C3⋊D3—21no—
640C2×C3⋊D3—21no—
641C2×C3⋊D3—21no—
642C2×C3⋊D3—21no—
643C2×C3⋊D3—21no—
644C2×C3⋊D3D3×D412yes—
645C2×C3⋊D3D3×D412yes—
646C2×C3×D3—32no—
647C2×C3×D3—32no—
648C2×C3×D3—32no—
649C2×C3×D3—32no—
650C2×C3×D3—62no—
651C2×C3×D3—62no—
652C2×C3×D3—61no—
653C2×C3×D3—61no—
654C2×C3×D3—61no—
655C2×C3×D3—61no—
656C2×C3×D3—61no—
657C2×C3×D3—61no—
658C2×C3×D3—61no—
659C2×C3×D3—61no—
660C2×C3×D3—61no—
661C2×C3×D3—61no—
662C2×C3×D3—61no—
663C2×C3×D3—61no—
664C2×C3×D3—61no—
665C2×C3×D3—61no—
666C2×C3×D3—121no—
667C2×C3×D3—121no—
668C2×C3×D3—121no—
669C2×C3×D3—121no—
670C2×C3×D3—121no—
671C2×C3×D3—121no—
672C2×C3×D3—121no—
673C32×C4—21no—
674C32×C4—21no—
675C32×C4—21no—
676C32×C4—21no—
677C32×C4—21no—
678C32×C4—21no—
679C32×C4—41no—
680C32×C4—41no—
681C32×C4—41no—
682C32×C4—41no—
683C32×C4—41no—
684C32×C4—41no—
685C32×C4—81no—
686C32×C4—81no—
687C3⋊Dic3—21no—
688C3⋊Dic3—21no—
689C3⋊Dic3—21no—
690C3⋊Dic3—21no—
691C3⋊Dic3—21no—
692C3⋊Dic3—21no—
693C3⋊Dic3—21no—
694C3⋊Dic3D3×D412yes—
695C3⋊Dic3#23712yescomplemented
696C3×Dic3—32no—
697C3×Dic3—32no—
698C3×Dic3—32no—
699C3×Dic3—32no—
700C3×Dic3—62no—
701C3×Dic3—62no—
702C3×Dic3—61no—
703C3×Dic3—61no—
704C3×Dic3—61no—
705C3×Dic3—61no—
706C3×Dic3—61no—
707C3×Dic3—61no—
708C3×Dic3—61no—
709C3×Dic3—61no—
710C3×Dic3—61no—
711C3×Dic3—61no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—121no—
717C3×Dic3—121no—
718C3×Dic3—121no—
719C3×Dic3—121no—
720C3×Dic3—121no—
721C3×Dic3—121no—
722C3×Dic3—121no—
723C2×#41—271no—
724C2×#41—271no—
725C4⋊Q8—271no—
726#123—91no—
727#123—271no—
728#123—271no—
729#123—271no—
730C22⋊Q8—91no—
731C22⋊Q8—271no—
732#121—91no—
733#121—271no—
734C4×D4—271no—
735C4×D4—271no—
736C2×C4⋊C4—271no—
737C2×C4⋊C4—271no—
738C33#54711yescharacteristic, complemented, Sylow
739C23×C3—21no—
740C23×C3—21no—
741C23×C3—21no—
742C23×C3—41no—
743C23×C3—91no—
744C23×C3—91no—
745C23×C3—91no—
746C23×C3C2×D3211yescharacteristic
747C23×C3C2×D3211yescharacteristic
748C23×C3C2×D3211yescharacteristic
749C22×D3—31no—
750C22×D3—31no—
751C22×D3—31no—
752C22×D3—31no—
753C22×D3—31no—
754C22×D3—31no—
755C22×D3—61no—
756C22×D3—61no—
757C22×D3—61no—
758C3×Q8—182no—
759C3×D4—182no—
760C3×D4—182no—
761C3×D4—182no—
762C3×D4—182no—
763C2×C3×C4—21no—
764C2×C3×C4—21no—
765C2×C3×C4—21no—
766C2×C3×C4—21no—
767C2×C3×C4—21no—
768C2×C3×C4—21no—
769C2×C3×C4—41no—
770C2×C3×C4—41no—
771C2×C3×C4—91no—
772C2×C3×C4—91no—
773C2×C3×C4—91no—
774C2×C3×C4—91no—
775C2×C3×C4—91no—
776C2×C3×C4—91no—
777C2×C3×C4—91no—
778C2×C3×C4—91no—
779C2×C3×C4—91no—
780C2×C3×C4—182no—
781C2×C3×C4—182no—
782C2×C3×C4—182no—
783C2×C3×C4C2×D3211yescharacteristic
784C2×C3×C4C2×D3211yescharacteristic
785C2×C3×C4C2×D3211yescharacteristic
786C2×C3×C4C2×D3211yescharacteristic
787C2×C3×C4C2×D3211yescharacteristic
788C2×C3×C4C2×D3211yescharacteristic
789#67—62no—
790#67—62no—
791#67—62no—
792#67—62no—
793#67—62no—
794#67—62no—
795#67—94no—
796#67—94no—
797#67—122no—
798#67—122no—
799#67—122no—
800#67—182no—
801#67—182no—
802C2×Dic3—31no—
803C2×Dic3—31no—
804C2×Dic3—31no—
805C2×Dic3—31no—
806C2×Dic3—31no—
807C2×Dic3—31no—
808C2×Dic3—31no—
809C2×Dic3—31no—
810C2×Dic3—31no—
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—61no—
821C2×Dic3—61no—
822C2×Dic3—61no—
823C2×Dic3—61no—
824C2×Dic3—61no—
825C2×Dic3—61no—
826C2×Dic3—61no—
827C2×Dic3—61no—
828C2×Dic3—61no—
829C2×Dic3—62no—
830C2×Dic3—62no—
831C2×Dic3—122no—
832C2×Dic3—182no—
833C2×Dic3—182no—
834C2×Dic3—182no—
835C2×Dic3—182no—
836C2×Dic3—182no—
837D12—62no—
838D12—62no—
839D12—94no—
840D12—122no—
841D12—182no—
842C4×D3—62no—
843C4×D3—62no—
844C4×D3—62no—
845C4×D3—62no—
846C4×D3—122no—
847C4×D3—122no—
848C4×D3—182no—
849C4×D3—182no—
850C4×D3—182no—
851C4×D3—182no—
852C4×D3—182no—
853C4×D3—182no—
854C4×D3—182no—
855C4×D3—182no—
856C4×D3—182no—
857C4×D3—182no—
858Dic6—62no—
859Dic6—62no—
860Dic6—122no—
861Dic6—182no—
862Dic6—182no—
863Dic6—182no—
864C2×C32—21no—
865C2×C32—21no—
866C2×C32—21no—
867C2×C32—21no—
868C2×C32—21no—
869C2×C32—21no—
870C2×C32—21no—
871C2×C32—21no—
872C2×C32—21no—
873C2×C32—41no—
874C2×C32—41no—
875C2×C32—41no—
876C2×C32—41no—
877C2×C32—42no—
878C2×C32—41no—
879C2×C32—41no—
880C2×C32—81no—
881C2×C32—81no—
882C2×C32—82no—
883C2×C32C2×D3×D411yescharacteristic
884C2×C32C2×D3×D411yescharacteristic
885C2×C32C2×D3×D411yescharacteristic
886C2×C32C2×#23711yescharacteristic
887C2×C32#100711yescharacteristic
888C2×C32D3×#4111yescharacteristic
889C2×C32D3×#4111yescharacteristic
890C2×C32#101011yescharacteristic
891C2×C32#101011yescharacteristic
892C3⋊D3—22no—
893C3⋊D3—22no—
894C3⋊D3—41no—
895C3×D3—62no—
896C3×D3—62no—
897C3×D3—62no—
898C3×D3—62no—
899C3×D3—122no—
900C3×D3—122no—
901C3×D3—121no—
902C3×D3—121no—
903C3×D3—241no—
904#41—544no—
905#41—544no—
906C2×Q8—91no—
907C2×Q8—271no—
908C2×D4—91no—
909C2×D4—91no—
910C2×D4—91no—
911C2×D4—91no—
912C2×D4—271no—
913C2×D4—271no—
914C22×C4—91no—
915C22×C4—91no—
916C22×C4—91no—
917C22×C4—271no—
918C22×C4—271no—
919C22×C4—271no—
920C22×C4—271no—
921C22×C4—271no—
922C4⋊C4—91no—
923C4⋊C4—91no—
924C4⋊C4—91no—
925C4⋊C4—91no—
926C4⋊C4—91no—
927C4⋊C4—91no—
928C4⋊C4—271no—
929C4⋊C4—271no—
930C4⋊C4—271no—
931C4⋊C4—271no—
932C22⋊C4—91no—
933C22⋊C4—91no—
934C22⋊C4—91no—
935C22⋊C4—91no—
936C22⋊C4—271no—
937C22⋊C4—271no—
938C22⋊C4—271no—
939C22⋊C4#111311yescharacteristic
940C42—271no—
941C22×C3—22no—
942C22×C3—21no—
943C22×C3—21no—
944C22×C3—21no—
945C22×C3—21no—
946C22×C3—21no—
947C22×C3—21no—
948C22×C3—21no—
949C22×C3—21no—
950C22×C3—21no—
951C22×C3—21no—
952C22×C3—21no—
953C22×C3—21no—
954C22×C3—41no—
955C22×C3—41no—
956C22×C3—41no—
957C22×C3—41no—
958C22×C3—41no—
959C22×C3—41no—
960C22×C3—41no—
961C22×C3—41no—
962C22×C3—42no—
963C22×C3—41no—
964C22×C3—81no—
965C22×C3—81no—
966C22×C3—92no—
967C22×C3—92no—
968C22×C3—181no—
969C22×C3—181no—
970C22×C3—181no—
971C22×C3—181no—
972C22×C3—181no—
973C22×C3—181no—
974C22×C3—181no—
975C22×C3C22×D3211yescharacteristic
976C22×C3C22×D3211yescharacteristic
977C22×C3C22×D3211yescharacteristic
978C2×D3—32no—
979C2×D3—32no—
980C2×D3—32no—
981C2×D3—32no—
982C2×D3—62no—
983C2×D3—62no—
984C2×D3—61no—
985C2×D3—61no—
986C2×D3—61no—
987C2×D3—61no—
988C2×D3—61no—
989C2×D3—61no—
990C2×D3—61no—
991C2×D3—61no—
992C2×D3—61no—
993C2×D3—61no—
994C2×D3—61no—
995C2×D3—61no—
996C2×D3—61no—
997C2×D3—61no—
998C2×D3—121no—
999C2×D3—121no—
1000C2×D3—121no—
1001C2×D3—121no—
1002C2×D3—121no—
1003C2×D3—121no—
1004C2×D3—121no—
1005C3×C4—21no—
1006C3×C4—21no—
1007C3×C4—21no—
1008C3×C4—21no—
1009C3×C4—21no—
1010C3×C4—21no—
1011C3×C4—41no—
1012C3×C4—41no—
1013C3×C4—41no—
1014C3×C4—41no—
1015C3×C4—41no—
1016C3×C4—41no—
1017C3×C4—81no—
1018C3×C4—81no—
1019C3×C4—92no—
1020C3×C4—92no—
1021C3×C4—181no—
1022C3×C4—181no—
1023C3×C4—181no—
1024C3×C4—181no—
1025C3×C4—181no—
1026C3×C4—181no—
1027C3×C4—181no—
1028Dic3—32no—
1029Dic3—32no—
1030Dic3—32no—
1031Dic3—32no—
1032Dic3—62no—
1033Dic3—62no—
1034Dic3—61no—
1035Dic3—61no—
1036Dic3—61no—
1037Dic3—61no—
1038Dic3—61no—
1039Dic3—61no—
1040Dic3—61no—
1041Dic3—61no—
1042Dic3—61no—
1043Dic3—61no—
1044Dic3—61no—
1045Dic3—61no—
1046Dic3—61no—
1047Dic3—61no—
1048Dic3—121no—
1049Dic3—121no—
1050Dic3—121no—
1051Dic3—121no—
1052Dic3—121no—
1053Dic3—121no—
1054Dic3—121no—
1055C32—21no—
1056C32—21no—
1057C32—21no—
1058C32—41no—
1059C32#561111yescharacteristic, complemented
1060C32#563111yescharacteristic, complemented
1061C32#565511yescharacteristic, complemented
1062C23—91no—
1063C23—91no—
1064C23—91no—
1065C23C2×#111311yescharacteristic
1066Q8—182no—
1067Q8—542no—
1068D4—182no—
1069D4—182no—
1070D4—182no—
1071D4—182no—
1072D4—274no—
1073D4—542no—
1074C2×C4—91no—
1075C2×C4—91no—
1076C2×C4—91no—
1077C2×C4—91no—
1078C2×C4—91no—
1079C2×C4—91no—
1080C2×C4—91no—
1081C2×C4—91no—
1082C2×C4—91no—
1083C2×C4—182no—
1084C2×C4—182no—
1085C2×C4—182no—
1086C2×C4—542no—
1087C2×C4—542no—
1088C2×C4—542no—
1089C2×C4—542no—
1090C2×C4—542no—
1091C2×C4C2×#111311yescharacteristic
1092C2×C4C2×#111311yescharacteristic
1093C2×C3—21no—
1094C2×C3—21no—
1095C2×C3—21no—
1096C2×C3—21no—
1097C2×C3—21no—
1098C2×C3—21no—
1099C2×C3—21no—
1100C2×C3—21no—
1101C2×C3—21no—
1102C2×C3—42no—
1103C2×C3—41no—
1104C2×C3—41no—
1105C2×C3—41no—
1106C2×C3—41no—
1107C2×C3—41no—
1108C2×C3—41no—
1109C2×C3—81no—
1110C2×C3—81no—
1111C2×C3—82no—
1112C2×C3—182no—
1113C2×C3—182no—
1114C2×C3—361no—
1115C2×C3#6429711yescharacteristic
1116C2×C3#6429711yescharacteristic
1117C2×C3#6429811yescharacteristic
1118C2×C3D32×D411yescharacteristic
1119C2×C3D32×D411yescharacteristic
1120C2×C3D32×D411yescharacteristic
1121C2×C3D3×#23711yescharacteristic
1122C2×C3D3×#23711yescharacteristic
1123C2×C3#6431211yescharacteristic
1124D3—62no—
1125D3—62no—
1126D3—62no—
1127D3—62no—
1128D3—122no—
1129D3—122no—
1130D3—121no—
1131D3—121no—
1132D3—241no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—92no—
1137C22—92no—
1138C22—181no—
1139C22—181no—
1140C22—181no—
1141C22—181no—
1142C22—181no—
1143C22—181no—
1144C22—181no—
1145C22C22×#111311yescharacteristic
1146C4—21no—
1147C4—21no—
1148C4—92no—
1149C4—92no—
1150C4—181no—
1151C4—181no—
1152C4—181no—
1153C4—181no—
1154C4—181no—
1155C4—181no—
1156C4—181no—
1157C3—21no—
1158C3—21no—
1159C3—21no—
1160C3—41no—
1161C3#1059406211yescharacteristic, complemented
1162C3#1059406411yescharacteristic, complemented
1163C3#1059406511yescharacteristic, complemented
1164C2—41no—
1165C2—182no—
1166C2—182no—
1167C2—361no—
1168C2#1172461411yescharacteristic
1169C2D4×#111311yescharacteristic
1170C2#1172462211yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4#1113
hypocenterC33#547
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#89046C2semidirect
2. C2×#89041C2semidirect
3. C3×#64093C2semidirect
4. C3×#64092C2semidirect
5. C3×#64087C2semidirect
6. #11723726C2semidirect
7. #11723725C2semidirect
8. #11723724C2semidirect
9. #11723692C2semidirect
10. #11723690C2semidirect
11. #11723689C2semidirect
12. #11723686C2semidirect
13. #11723684C2semidirect
14. #11723682C2semidirect
15. #11723666C2semidirect
62. #64093D3semidirect
63. #64092D3semidirect
64. #64087D3semidirect
129. #6295D4semidirect
294. C3×C3⋊Dic3#41semidirect
695. C3⋊Dic3#237semidirect
738. C33#547semidirect
1059. C32#5611semidirect
1060. C32#5631semidirect
1061. C32#5655semidirect
1161. C3#10594062semidirect
1162. C3#10594064semidirect
1163. C3#10594065semidirect

Maximal subgroups

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

subgroupindex
C2×#890462
C2×#890412
C3×#640932
C3×#640922
C3×#640872
#117237262
#117237252
#117237242
#117236922
#117236902
#117236892
#117236862
#117236842
#117236822
#117236662
#105940653
#105940643
#105940623