Finite Group Databasebeta

← #13168576

Subgroups — #13168576

Order 1728.

1094 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723694C211yesmaximal, characteristic
2#11723466C211yesmaximal, characteristic, complemented
3#11723448C211yesmaximal, characteristic, complemented
4#11723437C211yesmaximal, characteristic, complemented
5C3×#63883C211yesmaximal, characteristic, complemented
6C3×#63868C211yesmaximal, characteristic, complemented
7C3×#63837C211yesmaximal, characteristic, complemented
8#11723024C211yesmaximal, characteristic, complemented
9#11723015C211yesmaximal, characteristic, complemented
10#11723012C211yesmaximal, characteristic, complemented
11#11722995C211yesmaximal, characteristic
12#11722974C211yesmaximal, characteristic, complemented
13#11722970C211yesmaximal, characteristic, complemented
14#11722934C211yesmaximal, characteristic
15#11722915C211yesmaximal, characteristic, complemented
16#10594543—31nomaximal
17#10594333—31nomaximal
18#10593933—31nomaximal
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×#6295C2211yescharacteristic
21C2×Dic3×C3⋊D3C2211yescharacteristic
22C2×C3×#627C2211yescharacteristic
23C2×C3×#624C2211yescharacteristic
24C2×C3×#624C2211yescharacteristic
25C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
26C3×#3752C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C32×Dic3⋊C4C2211yescharacteristic
29C32×Dic3⋊C4C2211yescharacteristic
30C32×C4×Dic3C2211yescharacteristic
31#88815C2211yescharacteristic
32#88814C2211yescharacteristic
33#88814C2211yescharacteristic
34#88807C2211yescharacteristic
35#88807C2211yescharacteristic
36#88807C2211yescharacteristic
37#88806C2211yescharacteristic
38#88806C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64101—31no—
55#64098—31no—
56#64081—31no—
57C3×#898—31no—
58C3×D3×C4⋊C4—31no—
59C3×D3×C4⋊C4—31no—
60C3×#887—31no—
61C3×#876—31no—
62C3×C4×Dic6—31no—
63#63905—31no—
64#63905—31no—
65C4×#626—31no—
66#63893—31no—
67#63888—31no—
68#63887—31no—
69#63883D311yescharacteristic, complemented
70#63880—31no—
71#63879—31no—
72#63878—31no—
73#63878—31no—
74#63878—61no—
75#63871—31no—
76#63870—31no—
77#63870—31no—
78#63870—31no—
79#63870—61no—
80#63869—31no—
81#63868—31no—
82#63868D311yescharacteristic, complemented
83#63867—31no—
84#63859—31no—
85#63858—31no—
86#63856—31no—
87#63855—31no—
88#63855—31no—
89#63855—31no—
90#63855—61no—
91#63854—31no—
92#63853—31no—
93#63851—31no—
94#63850—31no—
95#63850—31no—
96#63846—31no—
97#63846—31no—
98#63846—31no—
99#63841—31no—
100#63837D311yescharacteristic, complemented
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C3×C4×C3⋊D3—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6295—22no—
119Dic3×C3⋊D3—22no—
120C3×#627—22no—
121C3×#624—22no—
122C3×#624—22no—
123#5708—91no—
124#5581—91no—
125#5513—91no—
126C2×C4×C3⋊D3—31no—
127C2×C4×C3⋊D3C2×D311yescharacteristic
128C2×C3×C4×D3—31no—
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3—31no—
134C2×C3×C4×D3—61no—
135C2×C3×Dic6—31no—
136C2×C3×Dic6—31no—
137C2×#627C2×D311yescharacteristic
138C2×#626—31no—
139C2×#626—31no—
140C2×#625—31no—
141C2×#624C2×D311yescharacteristic
142C2×#624C2×D311yescharacteristic
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—61no—
146C32×C4⋊C4—31no—
147C32×C4⋊C4—31no—
148C32×C42—31no—
149#3752—31no—
150#3752—31no—
151#3752—31no—
152#3752C2×D311yescharacteristic
153C4⋊(C3⋊Dic3)—31no—
154C4⋊(C3⋊Dic3)—31no—
155#3750—31no—
156#3750—31no—
157#3750—31no—
158#3750—31no—
159#3750—31no—
160#3750C2×D311yescharacteristic
161C4×C3⋊Dic3—31no—
162C4×C3⋊Dic3—31no—
163C4×C3⋊Dic3—31no—
164C4×C3⋊Dic3—31no—
165C4×C3⋊Dic3—61no—
166C4×C3⋊Dic3—61no—
167C4×C3⋊Dic3—61no—
168C4×C3⋊Dic3—121no—
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4—31no—
171C3×(C2×D3)⋊C4—31no—
172C3×(C2×D3)⋊C4—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4—61no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—31no—
180C3×Dic3⋊C4—21no—
181C3×Dic3⋊C4—21no—
182C3×Dic3⋊C4—31no—
183C3×Dic3⋊C4—31no—
184C3×Dic3⋊C4—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—61no—
191C3×Dic3⋊C4C2×D311yescharacteristic
192C3×Dic3⋊C4C2×D311yescharacteristic
193C3×Dic3⋊C4C2×D311yescharacteristic
194C3×Dic3⋊C4C2×D311yescharacteristic
195C3×C4×Dic3—21no—
196C3×C4×Dic3—31no—
197C3×C4×Dic3—31no—
198C3×C4×Dic3—31no—
199C3×C4×Dic3—31no—
200C3×C4×Dic3C2×D311yescharacteristic
201C3×C4×Dic3C2×D311yescharacteristic
202#3724—31no—
203#3724—31no—
204#3724—31no—
205#3724—31no—
206#3724—31no—
207#3724—61no—
208#3724—61no—
209#3724C2×D311yescharacteristic
210Dic3⋊Dic3—31no—
211Dic3⋊Dic3—31no—
212Dic3⋊Dic3—31no—
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3C2×D311yescharacteristic
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231#3722—31no—
232#3722—31no—
233#3722C2×D311yescharacteristic
234#3722C2×D311yescharacteristic
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—61no—
246(C2×D3)⋊Dic3—61no—
247(C2×D3)⋊Dic3—61no—
248Dic32—31no—
249Dic32—31no—
250Dic32—61no—
251Dic32C2×D311yescharacteristic
252Dic32C2×D311yescharacteristic
253C22×C33C2411yescharacteristic
254C2×C3×C3⋊D3—21no—
255C2×C3×C3⋊D3—21no—
256C2×C3×C3⋊D3—21no—
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3#4112yes—
260C33×C4—21no—
261C3⋊(C3⋊Dic3)—21no—
262C3⋊(C3⋊Dic3)—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3#4112yes—
273C3×#126—91no—
274C3×C4×Q8—91no—
275C2×C3×C4⋊C4—91no—
276#946—91no—
277#946—91no—
278#929—91no—
279#929—91no—
280C4×#67—91no—
281#926—91no—
282#926—91no—
283#924—91no—
284#898—31no—
285#898—91no—
286#897—91no—
287#896—91no—
288#894—91no—
289#894—91no—
290#892—91no—
291#892—91no—
292#892—91no—
293#892—181no—
294D3×C4⋊C4—31no—
295D3×C4⋊C4—31no—
296#890—91no—
297#890—91no—
298#889—91no—
299#889—91no—
300#889—91no—
301#889—91no—
302#889—91no—
303#889—91no—
304#889—181no—
305#887—31no—
306#883—91no—
307#883—91no—
308#67⋊C4—91no—
309#879—91no—
310#878—91no—
311#877—91no—
312#876—31no—
313#876—91no—
314C4×D12—91no—
315#872—91no—
316#872—91no—
317#872—91no—
318#872—181no—
319#870—91no—
320C4×Dic6—31no—
321C22×C3⋊D3C22×D311yescharacteristic
322C22×C3⋊D3C22×D311yescharacteristic
323C22×C3×D3—31no—
324C22×C3×D3—31no—
325C22×C3×D3—31no—
326C22×C3×D3—31no—
327C22×C3×D3—61no—
328C22×C3×D3—61no—
329C2×C32×C4—21no—
330C2×C32×C4—21no—
331C2×C32×C4—21no—
332C2×C32×C4—31no—
333C2×C32×C4—31no—
334C2×C32×C4—31no—
335C2×C32×C4—31no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338C2×C32×C4—41no—
339C2×C32×C4C22×D311yescharacteristic
340C2×C32×C4C22×D311yescharacteristic
341C2×C32×C4C22×D311yescharacteristic
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—31no—
344C2×C3⋊Dic3—31no—
345C2×C3⋊Dic3—31no—
346C2×C3⋊Dic3—31no—
347C2×C3⋊Dic3—31no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—61no—
350C2×C3⋊Dic3—61no—
351C2×C3⋊Dic3—61no—
352C2×C3⋊Dic3—61no—
353C2×C3⋊Dic3—61no—
354C2×C3⋊Dic3—121no—
355C2×C3⋊Dic3—121no—
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360C4×C3⋊D3—22no—
361C4×C3⋊D3—62no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—21no—
365C2×C3×Dic3—21no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—31no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—31no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—61no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—61no—
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
389C2×C3×Dic3C22×D311yescharacteristic
390C2×C3×Dic3C22×D311yescharacteristic
391C2×C3×Dic3C22×D311yescharacteristic
392C3×C4×D3—62no—
393C3×C4×D3—62no—
394C3×C4×D3—62no—
395C3×C4×D3—62no—
396C3×C4×D3—62no—
397C3×C4×D3—64no—
398C3×C4×D3—62no—
399C3×Dic6—62no—
400C3×Dic6—62no—
401#627—22no—
402#626—62no—
403#626—62no—
404#625—62no—
405#624—22no—
406#624—22no—
407D3×Dic3—64no—
408D3×Dic3—62no—
409D3×Dic3—62no—
410#552—271noSylow
411C2×C33C2×#4111yescharacteristic
412C2×C33C2×#4111yescharacteristic
413C2×C332−1+411yescharacteristic
414C3×C3⋊D3—22no—
415C3×C3⋊D3—41no—
416C2×C3×Q8—91no—
417C22×C3×C4—91no—
418C22×C3×C4—91no—
419C22×C3×C4—91no—
420C2×#67—91no—
421C2×#67—91no—
422C22×Dic3—91no—
423C2×D12—91no—
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—61no—
431C2×C4×D3—91no—
432C2×C4×D3—91no—
433C2×C4×D3—181no—
434C2×Dic6—31no—
435C2×Dic6—31no—
436C3×C4⋊C4—31no—
437C3×C4⋊C4—31no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—31no—
440C3×C4⋊C4—61no—
441C3×C4⋊C4—61no—
442C3×C4⋊C4—91no—
443C3×C4⋊C4—91no—
444C3×C4⋊C4—91no—
445C3×C4⋊C4—91no—
446C3×C4⋊C4—91no—
447C3×C4⋊C4—91no—
448C3×C22⋊C4—91no—
449C3×C22⋊C4—91no—
450C3×C22⋊C4—91no—
451C3×C42—31no—
452C3×C42—31no—
453C3×C42—61no—
454C3×C42—91no—
455C3×C42—91no—
456#217—91no—
457#217—91no—
458#217—91no—
459#217—91no—
460#217—91no—
461(C2×D3)⋊C4—31no—
462(C2×D3)⋊C4—31no—
463(C2×D3)⋊C4—31no—
464(C2×D3)⋊C4—31no—
465(C2×D3)⋊C4—31no—
466(C2×D3)⋊C4—31no—
467(C2×D3)⋊C4—61no—
468(C2×D3)⋊C4—91no—
469(C2×D3)⋊C4—91no—
470(C2×D3)⋊C4—91no—
471(C2×D3)⋊C4—91no—
472(C2×D3)⋊C4—91no—
473(C2×D3)⋊C4—91no—
474(C2×D3)⋊C4—91no—
475(C2×D3)⋊C4—91no—
476(C2×D3)⋊C4—91no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—181no—
479(C2×D3)⋊C4—181no—
480(C2×D3)⋊C4—181no—
481C4⋊Dic3—31no—
482C4⋊Dic3—31no—
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—91no—
486C4⋊Dic3—91no—
487C4⋊Dic3—91no—
488C4⋊Dic3—91no—
489C4⋊Dic3—91no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—181no—
494C4⋊Dic3—181no—
495Dic3⋊C4—31no—
496Dic3⋊C4—31no—
497Dic3⋊C4—31no—
498Dic3⋊C4—31no—
499Dic3⋊C4—31no—
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—61no—
504Dic3⋊C4—91no—
505Dic3⋊C4—91no—
506Dic3⋊C4—91no—
507Dic3⋊C4—91no—
508Dic3⋊C4—91no—
509Dic3⋊C4—91no—
510Dic3⋊C4—91no—
511Dic3⋊C4—91no—
512Dic3⋊C4—91no—
513Dic3⋊C4—91no—
514Dic3⋊C4—91no—
515Dic3⋊C4—91no—
516Dic3⋊C4—91no—
517Dic3⋊C4—91no—
518Dic3⋊C4—91no—
519Dic3⋊C4—91no—
520Dic3⋊C4—181no—
521Dic3⋊C4—181no—
522Dic3⋊C4—181no—
523Dic3⋊C4—181no—
524Dic3⋊C4—181no—
525Dic3⋊C4D3211yescharacteristic
526Dic3⋊C4D3211yescharacteristic
527C4×Dic3—31no—
528C4×Dic3—31no—
529C4×Dic3—31no—
530C4×Dic3—31no—
531C4×Dic3—91no—
532C4×Dic3—91no—
533C4×Dic3—91no—
534C4×Dic3—91no—
535C4×Dic3—91no—
536C4×Dic3—91no—
537C4×Dic3—181no—
538C4×Dic3—181no—
539C4×Dic3—181no—
540C4×Dic3—181no—
541C4×Dic3—361no—
542C4×Dic3D3211yescharacteristic
543C22×C32—21no—
544C22×C32—21no—
545C22×C32—21no—
546C22×C32—41no—
547C22×C32C23×D311yescharacteristic
548C22×C32C23×D311yescharacteristic
549C22×C32C23×D311yescharacteristic
550C2×C3⋊D3—21no—
551C2×C3⋊D3—21no—
552C2×C3⋊D3—21no—
553C2×C3⋊D3—21no—
554C2×C3⋊D3—21no—
555C2×C3⋊D3#23712yes—
556C2×C3×D3—32no—
557C2×C3×D3—32no—
558C2×C3×D3—62no—
559C2×C3×D3—61no—
560C2×C3×D3—61no—
561C2×C3×D3—61no—
562C2×C3×D3—61no—
563C2×C3×D3—62no—
564C2×C3×D3—61no—
565C2×C3×D3—61no—
566C2×C3×D3—61no—
567C2×C3×D3—61no—
568C2×C3×D3—61no—
569C2×C3×D3—61no—
570C2×C3×D3—121no—
571C2×C3×D3—121no—
572C2×C3×D3—121no—
573C2×C3×D3—121no—
574C32×C4—21no—
575C32×C4—22no—
576C32×C4—21no—
577C32×C4—21no—
578C32×C4—32no—
579C32×C4—41no—
580C32×C4—41no—
581C32×C4—42no—
582C32×C4—61no—
583C32×C4—61no—
584C32×C4—61no—
585C32×C4—61no—
586C32×C4—61no—
587C3⋊Dic3—21no—
588C3⋊Dic3—21no—
589C3⋊Dic3—21no—
590C3⋊Dic3—21no—
591C3⋊Dic3—61no—
592C3⋊Dic3—61no—
593C3⋊Dic3—62no—
594C3⋊Dic3—62no—
595C3⋊Dic3—61no—
596C3⋊Dic3—61no—
597C3⋊Dic3—61no—
598C3⋊Dic3—61no—
599C3⋊Dic3—121no—
600C3⋊Dic3—121no—
601C3⋊Dic3—121no—
602C3⋊Dic3—121no—
603C3⋊Dic3—122no—
604C3⋊Dic3—122no—
605C3×Dic3—21no—
606C3×Dic3—21no—
607C3×Dic3—21no—
608C3×Dic3—21no—
609C3×Dic3—21no—
610C3×Dic3—21no—
611C3×Dic3—21no—
612C3×Dic3—21no—
613C3×Dic3—21no—
614C3×Dic3—21no—
615C3×Dic3—22no—
616C3×Dic3—41no—
617C3×Dic3—41no—
618C3×Dic3—41no—
619C3×Dic3—41no—
620C3×Dic3—41no—
621C3×Dic3—62no—
622C3×Dic3—61no—
623C3×Dic3—61no—
624C3×Dic3—61no—
625C3×Dic3—61no—
626C3×Dic3—61no—
627C3×Dic3—61no—
628C3×Dic3—61no—
629C3×Dic3—61no—
630C3×Dic3—121no—
631C3×Dic3—121no—
632C3×Dic3—121no—
633C3×Dic3#23512yes—
634C3×Dic3#23512yes—
635#126—91no—
636#126—271no—
637#125—271no—
638#125—271no—
639#125—271no—
640#123—271no—
641#123—271no—
642C22⋊Q8—271no—
643C22⋊Q8—271no—
644C4×Q8—91no—
645C4×D4—271no—
646#117—271no—
647#117—271no—
648#117—271no—
649C2×C4⋊C4—91no—
650C33#55211yescharacteristic, complemented, Sylow
651C23×C3—91no—
652C23×C3—91no—
653C22×D3—31no—
654C22×D3—31no—
655C22×D3—31no—
656C22×D3—31no—
657C22×D3—61no—
658C22×D3—61no—
659C3×Q8—182no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—31no—
664C2×C3×C4—31no—
665C2×C3×C4—31no—
666C2×C3×C4—31no—
667C2×C3×C4—31no—
668C2×C3×C4—31no—
669C2×C3×C4—31no—
670C2×C3×C4—31no—
671C2×C3×C4—31no—
672C2×C3×C4—31no—
673C2×C3×C4—31no—
674C2×C3×C4—31no—
675C2×C3×C4—41no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—91no—
683C2×C3×C4—91no—
684C2×C3×C4—91no—
685C2×C3×C4—91no—
686C2×C3×C4—182no—
687C2×C3×C4—182no—
688C2×C3×C4—182no—
689C2×C3×C4C2×D3211yescharacteristic
690C2×C3×C4C2×D3211yescharacteristic
691C2×C3×C4C2×D3211yescharacteristic
692#67—182no—
693#67—182no—
694C2×Dic3—31no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—31no—
698C2×Dic3—31no—
699C2×Dic3—31no—
700C2×Dic3—31no—
701C2×Dic3—31no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—91no—
707C2×Dic3—91no—
708C2×Dic3—91no—
709C2×Dic3—91no—
710C2×Dic3—91no—
711C2×Dic3—91no—
712C2×Dic3—181no—
713C2×Dic3—181no—
714C2×Dic3—181no—
715C2×Dic3—181no—
716C2×Dic3—181no—
717C2×Dic3—181no—
718C2×Dic3—182no—
719C2×Dic3—361no—
720C2×Dic3—361no—
721C2×Dic3C2×D3211yescharacteristic
722C2×Dic3C2×D3211yescharacteristic
723C2×Dic3C2×D3211yescharacteristic
724C2×Dic3C2×D3211yescharacteristic
725C2×Dic3C2×D3211yescharacteristic
726C2×Dic3C2×D3211yescharacteristic
727D12—182no—
728C4×D3—62no—
729C4×D3—62no—
730C4×D3—62no—
731C4×D3—62no—
732C4×D3—62no—
733C4×D3—64no—
734C4×D3—62no—
735C4×D3—182no—
736C4×D3—182no—
737C4×D3—184no—
738Dic6—62no—
739Dic6—62no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—21no—
748C2×C32—21no—
749C2×C32—41no—
750C2×C32—41no—
751C2×C32—41no—
752C2×C32C2×#23511yescharacteristic
753C2×C32C2×#23511yescharacteristic
754C2×C32C2×#23711yescharacteristic
755C2×C32#100711yescharacteristic
756C2×C32#100711yescharacteristic
757C2×C32D3×#4111yescharacteristic
758C2×C32D3×#4111yescharacteristic
759C2×C32D3×#4111yescharacteristic
760C2×C32#101011yescharacteristic
761C3⋊D3—22no—
762C3⋊D3—41no—
763C3×D3—62no—
764C3×D3—62no—
765C3×D3—122no—
766C3×D3—122no—
767C3×D3—121no—
768C3×D3—121no—
769C2×Q8—91no—
770C2×D4—271no—
771C22×C4—91no—
772C22×C4—91no—
773C22×C4—91no—
774C22×C4—271no—
775C4⋊C4—31no—
776C4⋊C4—31no—
777C4⋊C4—91no—
778C4⋊C4—91no—
779C4⋊C4—91no—
780C4⋊C4—91no—
781C4⋊C4—91no—
782C4⋊C4—91no—
783C4⋊C4—271no—
784C4⋊C4—271no—
785C4⋊C4—271no—
786C4⋊C4—271no—
787C4⋊C4—271no—
788C4⋊C4—271no—
789C4⋊C4—271no—
790C4⋊C4—271no—
791C22⋊C4—91no—
792C22⋊C4—91no—
793C22⋊C4—91no—
794C22⋊C4—271no—
795C22⋊C4—271no—
796C22⋊C4—271no—
797C22⋊C4—271no—
798C22⋊C4—271no—
799C42—31no—
800C42—91no—
801C42—91no—
802C42—271no—
803C42—271no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—41no—
808C22×C3—92no—
809C22×C3—181no—
810C22×C3—181no—
811C22×C3—181no—
812C22×C3—181no—
813C22×C3—181no—
814C22×C3C22×D3211yescharacteristic
815C22×C3C22×D3211yescharacteristic
816C22×C3C22×D3211yescharacteristic
817C2×D3—32no—
818C2×D3—32no—
819C2×D3—62no—
820C2×D3—61no—
821C2×D3—61no—
822C2×D3—61no—
823C2×D3—61no—
824C2×D3—62no—
825C2×D3—61no—
826C2×D3—61no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—61no—
831C2×D3—121no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3—121no—
835C3×C4—22no—
836C3×C4—21no—
837C3×C4—21no—
838C3×C4—21no—
839C3×C4—32no—
840C3×C4—32no—
841C3×C4—41no—
842C3×C4—41no—
843C3×C4—42no—
844C3×C4—62no—
845C3×C4—61no—
846C3×C4—61no—
847C3×C4—61no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—61no—
853C3×C4—61no—
854C3×C4—61no—
855C3×C4—121no—
856C3×C4—121no—
857C3×C4—121no—
858C3×C4—121no—
859C3×C4—121no—
860C3×C4—181no—
861C3×C4—181no—
862C3×C4—181no—
863C3×C4—181no—
864Dic3—21no—
865Dic3—21no—
866Dic3—21no—
867Dic3—21no—
868Dic3—21no—
869Dic3—62no—
870Dic3—61no—
871Dic3—61no—
872Dic3—61no—
873Dic3—61no—
874Dic3—61no—
875Dic3—61no—
876Dic3—61no—
877Dic3—61no—
878Dic3—121no—
879Dic3—121no—
880Dic3—121no—
881Dic3—182no—
882Dic3—182no—
883Dic3—181no—
884Dic3—181no—
885Dic3—181no—
886Dic3—181no—
887Dic3—181no—
888Dic3—181no—
889Dic3—361no—
890Dic3—361no—
891Dic3—361no—
892Dic3—361no—
893Dic3—362no—
894Dic3—362no—
895Dic3#379812yes—
896C32—21no—
897C32—21no—
898C32—21no—
899C32—41no—
900C32#551311yescharacteristic, complemented
901C32#558111yescharacteristic, complemented
902C32#570811yescharacteristic, complemented
903C23—91no—
904C23—91no—
905Q8—182no—
906D4—542no—
907C2×C4—31no—
908C2×C4—31no—
909C2×C4—31no—
910C2×C4—31no—
911C2×C4—31no—
912C2×C4—31no—
913C2×C4—91no—
914C2×C4—91no—
915C2×C4—91no—
916C2×C4—91no—
917C2×C4—182no—
918C2×C4—182no—
919C2×C4—182no—
920C2×C4—271no—
921C2×C4—271no—
922C2×C4—542no—
923C2×C4D3311yescharacteristic
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—41no—
934C2×C3—41no—
935C2×C3—41no—
936C2×C3—182no—
937C2×C3—361no—
938C2×C3#6429711yescharacteristic
939C2×C3C2×#379811yescharacteristic
940C2×C3D3×#23511yescharacteristic
941C2×C3D3×#23511yescharacteristic
942C2×C3#6430611yescharacteristic
943C2×C3D3×#23711yescharacteristic
944C2×C3D3×#23711yescharacteristic
945C2×C3#6431511yescharacteristic
946C2×C3#6431611yescharacteristic
947D3—62no—
948D3—62no—
949D3—122no—
950D3—122no—
951D3—121no—
952D3—121no—
953C22—92no—
954C22—181no—
955C22—181no—
956C22—181no—
957C22—181no—
958C22—181no—
959C22C2×D3311yescharacteristic
960C4—21no—
961C4—32no—
962C4—61no—
963C4—61no—
964C4—61no—
965C4—61no—
966C4—61no—
967C4—181no—
968C4—181no—
969C4—181no—
970C4—181no—
971C4—541no—
972C4—541no—
973C3—21no—
974C3—21no—
975C3—21no—
976C3—41no—
977C3#1059393311yescharacteristic, complemented
978C3#1059433311yescharacteristic, complemented
979C3#1059454311yescharacteristic, complemented
980C2—182no—
981C2—361no—
982C2D3×#379811yescharacteristic
983C2#1172439711yescharacteristic
984C2#1172440711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6295C22
hypercenterC2×C4D33
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723466C2semidirect
3. #11723448C2semidirect
4. #11723437C2semidirect
5. C3×#63883C2semidirect
6. C3×#63868C2semidirect
7. C3×#63837C2semidirect
8. #11723024C2semidirect
9. #11723015C2semidirect
10. #11723012C2semidirect
12. #11722974C2semidirect
13. #11722970C2semidirect
15. #11722915C2semidirect
69. #63883D3semidirect
82. #63868D3semidirect
100. #63837D3semidirect
650. C33#552semidirect
900. C32#5513semidirect
901. C32#5581semidirect
902. C32#5708semidirect
977. C3#10593933semidirect
978. C3#10594333semidirect
979. C3#10594543semidirect

Maximal subgroups

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

subgroupindex
#117236942
#117234662
#117234482
#117234372
C3×#638832
C3×#638682
C3×#638372
#117230242
#117230152
#117230122
#117229952
#117229742
#117229702
#117229342
#117229152
#105945433
#105943333
#105939333