Finite Group Databasebeta

← #13172249

Subgroups — #13172249

Order 1728.

1226 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723726C211yesmaximal, characteristic
2#11723642C211yesmaximal, characteristic, complemented
3#11723626C211yesmaximal, characteristic
4C2×#88807C211yesmaximal, characteristic, complemented
5C3×#63982C211yesmaximal, characteristic, complemented
6C3×#63964C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic
8#11723034C211yesmaximal, characteristic, complemented
9#11723015C211yesmaximal, characteristic, complemented
10#11723014C211yesmaximal, characteristic, complemented
11#11722979C211yesmaximal, characteristic, complemented
12#11722974C211yesmaximal, characteristic, complemented
13#11722972C211yesmaximal, characteristic, complemented
14#11722940C211yesmaximal, characteristic, complemented
15#11722910C211yesmaximal, characteristic, complemented
16#10594959—31nomaximal
17#10594141—31nomaximal
18#10594133—31nomaximal
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×#6294C2211yescharacteristic
24C2×#6293C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic
27C2×C3×#627C2211yescharacteristic
28C2×C3×#624C2211yescharacteristic
29C3×#3757C2211yescharacteristic
30C32×#217C2211yescharacteristic
31C32×#217C2211yescharacteristic
32#88815C2211yescharacteristic
33#88814C2211yescharacteristic
34#88813C2211yescharacteristic
35#88807C2211yescharacteristic
36#88807C2211yescharacteristic
37#88807C2211yescharacteristic
38#88807C2211yescharacteristic
39#88807C2211yescharacteristic
40#88807C2211yescharacteristic
41#88806C2211yescharacteristic
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic
43#88803C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×#3724C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×Dic3⋊Dic3C2211yescharacteristic
52C3×#3722C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C2×#3750—31no—
55#64090—31no—
56#64087—31no—
57C3×C4×#67—31no—
58C3×#924—31no—
59C3×#67⋊C4—31no—
60C3×#878—31no—
61C3×#878—31no—
62C3×#878—31no—
63#63982—31no—
64#63982—31no—
65#63982—61no—
66#63982D311yescharacteristic, complemented
67#67⋊Dic3—31no—
68#67⋊Dic3—31no—
69#67⋊Dic3—31no—
70#67⋊Dic3—61no—
71Dic3×#67—31no—
72C2×Dic3⋊Dic3—31no—
73C2×Dic3⋊Dic3—31no—
74C2×Dic3⋊Dic3—61no—
75#63964D311yescharacteristic, complemented
76#63952—31no—
77#63952D311yescharacteristic
78#63899—31no—
79#63895—31no—
80#63893—31no—
81#63888—31no—
82#63887—31no—
83#63887—31no—
84#63883—31no—
85D3×Dic3⋊C4—31no—
86D3×Dic3⋊C4—31no—
87#63871—31no—
88#63870—31no—
89#63867—31no—
90#63867—31no—
91#63857—31no—
92#63851—31no—
93#63847—31no—
94#63846—31no—
95#63846—31no—
96#63843—31no—
97Dic3×Dic6—31no—
98#63840—31no—
99#63839—31no—
100#63839—31no—
101#63837—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)—41no—
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C3×#638Q814yescomplemented
108C2×C3×C3⋊Dic3—22no—
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C32×Dic3—41no—
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6294—22no—
122#6293—41no—
123Dic3×C3⋊D3—41no—
124C3×#627—22no—
125C3×#627—41no—
126C3×#624—41no—
127#5636—91no—
128#5635—91no—
129#5539—91no—
130C22×C32×C4—31no—
131C2×#638C2×D311yescharacteristic
132C22×C3⋊Dic3—31no—
133C22×C3⋊Dic3—31no—
134C22×C3⋊Dic3—31no—
135C22×C3⋊Dic3—61no—
136C22×C3⋊Dic3—61no—
137C22×C3⋊Dic3—61no—
138C22×C3⋊Dic3—121no—
139C22×C3⋊Dic3C2×D311yescharacteristic
140C2×C4×C3⋊D3—31no—
141C2×#634—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—61no—
145C22×C3×Dic3—21no—
146C22×C3×Dic3—31no—
147C22×C3×Dic3—31no—
148C22×C3×Dic3—61no—
149C22×C3×Dic3C2×D311yescharacteristic
150C22×C3×Dic3C2×D311yescharacteristic
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—31no—
153C2×C3×Dic6—31no—
154C2×C3×Dic6—31no—
155C2×C3×Dic6—31no—
156C2×C3×Dic6—31no—
157C2×#627—31no—
158C2×#627—31no—
159C2×#627—61no—
160C2×#627C2×D311yescharacteristic
161C2×#627C2×D311yescharacteristic
162C2×#624—31no—
163C2×#624C2×D311yescharacteristic
164C2×D3×Dic3—31no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—31no—
167C2×D3×Dic3—31no—
168C2×D3×Dic3—61no—
169C32×C22⋊C4—31no—
170C32×C22⋊C4—31no—
171#3757C2×D311yescharacteristic
172#3752—31no—
173C4⋊(C3⋊Dic3)—31no—
174#3750—31no—
175#3750—31no—
176#3750—31no—
177#3750—31no—
178#3750—31no—
179#3750—31no—
180#3750—31no—
181C4×C3⋊Dic3—31no—
182C3×#217—21no—
183C3×#217—21no—
184C3×#217—31no—
185C3×#217—31no—
186C3×#217—61no—
187C3×#217C2×D311yescharacteristic
188C3×#217C2×D311yescharacteristic
189C3×#217C2×D311yescharacteristic
190C3×#217C2×D311yescharacteristic
191C3×(C2×D3)⋊C4—31no—
192C3×(C2×D3)⋊C4—31no—
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×C4×Dic3—31no—
208C3×C4×Dic3—31no—
209#3724—31no—
210#3724—31no—
211#3724—31no—
212#3724—61no—
213#3724C2×D311yescharacteristic
214#3724C2×D311yescharacteristic
215#3724C2×D311yescharacteristic
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—61no—
233Dic3⋊Dic3—61no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3—61no—
236Dic3⋊Dic3—61no—
237Dic3⋊Dic3—61no—
238Dic3⋊Dic3—61no—
239Dic3⋊Dic3C2×D311yescharacteristic
240Dic3⋊Dic3C2×D311yescharacteristic
241Dic3⋊Dic3C2×D311yescharacteristic
242Dic3⋊Dic3C2×D311yescharacteristic
243#3722—31no—
244#3722C2×D311yescharacteristic
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—61no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—61no—
256Dic32C2×D311yescharacteristic
257C22×C33—21no—
258C22×C33—21no—
259C22×C33C2×Q812yes—
260C22×C33C2411yescharacteristic
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3—21no—
263C2×C3×C3⋊D3C2×Q812yes—
264C3⋊(C3⋊Dic3)—21no—
265C3⋊(C3⋊Dic3)—21no—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3C2×Q812yes—
270C3×C3⋊Dic3#4112yes—
271C32×Dic3—21no—
272C32×Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C3×C22⋊Q8—91no—
278C3×C22⋊Q8—91no—
279C3×C4×D4—91no—
280#946—91no—
281#946—91no—
282Q8×Dic3—91no—
283#944—91no—
284D4×Dic3—91no—
285D4×Dic3—91no—
286C4×#67—31no—
287C4×#67—91no—
288C2×C4⋊Dic3—91no—
289#924—31no—
290#924—91no—
291C2×Dic3⋊C4—91no—
292C2×Dic3⋊C4—91no—
293C2×Dic3⋊C4—91no—
294C2×Dic3⋊C4—181no—
295#897—91no—
296#897—91no—
297#896—91no—
298#896—91no—
299D3×C4⋊C4—91no—
300D3×C4⋊C4—91no—
301#890—91no—
302#889—91no—
303#889—91no—
304#889—91no—
305#889—91no—
306#888—91no—
307#888—91no—
308#887—91no—
309#67⋊C4—31no—
310#67⋊C4—91no—
311#67⋊C4—91no—
312#67⋊C4—91no—
313#67⋊C4—181no—
314#878—31no—
315#878—31no—
316#878—31no—
317#878—91no—
318#878—91no—
319#878—91no—
320#878—91no—
321#878—91no—
322#878—181no—
323#870—91no—
324C4×Dic6—91no—
325C23×C32—21no—
326C23×C32—21no—
327C23×C32—21no—
328C23×C32—41no—
329C23×C32C22×D311yescharacteristic
330C23×C32C22×D311yescharacteristic
331C23×C32C22×D311yescharacteristic
332C22×C3⋊D3C22×D311yescharacteristic
333C22×C3×D3—31no—
334C22×C3×D3—31no—
335C22×C3×D3—61no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338C2×C32×C4—31no—
339C2×C32×C4—31no—
340C2×C32×C4—31no—
341C2×C32×C4—31no—
342C2×C32×C4—121no—
343#638Dic614yescomplemented
344C2×C3⋊Dic3—22no—
345C2×C3⋊Dic3—31no—
346C2×C3⋊Dic3—31no—
347C2×C3⋊Dic3—31no—
348C2×C3⋊Dic3—31no—
349C2×C3⋊Dic3—31no—
350C2×C3⋊Dic3—31no—
351C2×C3⋊Dic3—61no—
352C2×C3⋊Dic3—61no—
353C2×C3⋊Dic3—61no—
354C2×C3⋊Dic3—61no—
355C2×C3⋊Dic3—61no—
356C2×C3⋊Dic3—61no—
357C2×C3⋊Dic3—121no—
358C2×C3⋊Dic3—121no—
359C2×C3⋊Dic3—121no—
360C2×C3⋊Dic3—121no—
361C2×C3⋊Dic3—121no—
362C2×C3⋊Dic3—122no—
363C2×C3⋊Dic3—122no—
364C2×C3⋊Dic3—122no—
365C2×C3⋊Dic3—124no—
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C2×C3⋊Dic3C22×D311yescharacteristic
369C2×C3⋊Dic3C22×D311yescharacteristic
370C2×C3⋊Dic3C22×D311yescharacteristic
371C4×C3⋊D3—121no—
372#634—121no—
373C3×#67—34no—
374C3×#67—34no—
375C3×#67—64no—
376C2×C3×Dic3—21no—
377C2×C3×Dic3—21no—
378C2×C3×Dic3—21no—
379C2×C3×Dic3—21no—
380C2×C3×Dic3—21no—
381C2×C3×Dic3—21no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—31no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—31no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—31no—
391C2×C3×Dic3—31no—
392C2×C3×Dic3—41no—
393C2×C3×Dic3—41no—
394C2×C3×Dic3—42no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—61no—
397C2×C3×Dic3—61no—
398C2×C3×Dic3—61no—
399C2×C3×Dic3—61no—
400C2×C3×Dic3—62no—
401C2×C3×Dic3—62no—
402C2×C3×Dic3—64no—
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C2×C3×Dic3C22×D311yescharacteristic
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C3×C4×D3—121no—
416C3×C4×D3—121no—
417C3×Dic6—62no—
418C3×Dic6—62no—
419C3×Dic6—121no—
420C3×Dic6—121no—
421#627—22no—
422#627—41no—
423#627—121no—
424#627—121no—
425#627—122no—
426#624—41no—
427#624—62no—
428D3×Dic3—62no—
429D3×Dic3—62no—
430D3×Dic3—121no—
431D3×Dic3—121no—
432D3×Dic3—122no—
433#554—271noSylow
434C2×C33—22no—
435C2×C33C22×Q811yescharacteristic
436C2×C33C2×#4111yescharacteristic
437C2×C33H(5,𝔽2)11yescharacteristic
438C3×C3⋊D3—22no—
439C2×C3×Q8—91no—
440C2×C3×Q8—91no—
441C2×C3×D4—91no—
442C22×C3×C4—31no—
443C22×C3×C4—31no—
444C22×C3×C4—61no—
445C22×C3×C4—91no—
446C22×C3×C4—91no—
447C2×#67—31no—
448C2×#67—31no—
449C2×#67—61no—
450C22×Dic3—31no—
451C22×Dic3—31no—
452C22×Dic3—61no—
453C22×Dic3—91no—
454C22×Dic3—91no—
455C22×Dic3—91no—
456C22×Dic3—91no—
457C22×Dic3—91no—
458C22×Dic3—181no—
459C22×Dic3—181no—
460C22×Dic3—181no—
461C22×Dic3—361no—
462C22×Dic3D3211yescharacteristic
463C2×C4×D3—31no—
464C2×C4×D3—31no—
465C2×C4×D3—91no—
466C2×C4×D3—91no—
467C2×C4×D3—91no—
468C2×C4×D3—91no—
469C2×C4×D3—181no—
470C2×Dic6—31no—
471C2×Dic6—31no—
472C2×Dic6—31no—
473C2×Dic6—31no—
474C2×Dic6—91no—
475C2×Dic6—91no—
476C2×Dic6—91no—
477C2×Dic6—181no—
478C3×C4⋊C4—91no—
479C3×C4⋊C4—91no—
480C3×C4⋊C4—91no—
481C3×C4⋊C4—91no—
482C3×C4⋊C4—91no—
483C3×C4⋊C4—91no—
484C3×C4⋊C4—91no—
485C3×C22⋊C4—31no—
486C3×C22⋊C4—31no—
487C3×C22⋊C4—31no—
488C3×C22⋊C4—31no—
489C3×C22⋊C4—61no—
490C3×C22⋊C4—61no—
491C3×C22⋊C4—91no—
492C3×C22⋊C4—91no—
493C3×C42—91no—
494#217—31no—
495#217—31no—
496#217—61no—
497#217—91no—
498#217—91no—
499#217D3211yescharacteristic
500#217D3211yescharacteristic
501(C2×D3)⋊C4—31no—
502(C2×D3)⋊C4—31no—
503(C2×D3)⋊C4—91no—
504(C2×D3)⋊C4—91no—
505(C2×D3)⋊C4—91no—
506(C2×D3)⋊C4—91no—
507(C2×D3)⋊C4—181no—
508C4⋊Dic3—31no—
509C4⋊Dic3—31no—
510C4⋊Dic3—31no—
511C4⋊Dic3—31no—
512C4⋊Dic3—91no—
513C4⋊Dic3—91no—
514C4⋊Dic3—91no—
515C4⋊Dic3—91no—
516C4⋊Dic3—91no—
517C4⋊Dic3—91no—
518C4⋊Dic3—91no—
519C4⋊Dic3—91no—
520C4⋊Dic3—91no—
521C4⋊Dic3—181no—
522Dic3⋊C4—31no—
523Dic3⋊C4—31no—
524Dic3⋊C4—31no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—31no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—31no—
531Dic3⋊C4—31no—
532Dic3⋊C4—91no—
533Dic3⋊C4—91no—
534Dic3⋊C4—91no—
535Dic3⋊C4—91no—
536Dic3⋊C4—91no—
537Dic3⋊C4—91no—
538Dic3⋊C4—91no—
539Dic3⋊C4—91no—
540Dic3⋊C4—91no—
541Dic3⋊C4—91no—
542Dic3⋊C4—91no—
543Dic3⋊C4—91no—
544Dic3⋊C4—91no—
545Dic3⋊C4—91no—
546Dic3⋊C4—91no—
547Dic3⋊C4—91no—
548Dic3⋊C4—91no—
549Dic3⋊C4—91no—
550Dic3⋊C4—181no—
551Dic3⋊C4—181no—
552Dic3⋊C4—181no—
553Dic3⋊C4—181no—
554Dic3⋊C4—181no—
555Dic3⋊C4—181no—
556Dic3⋊C4—181no—
557C4×Dic3—31no—
558C4×Dic3—31no—
559C4×Dic3—91no—
560C4×Dic3—91no—
561C4×Dic3—91no—
562C4×Dic3—91no—
563C4×Dic3—91no—
564C4×Dic3—91no—
565C4×Dic3—181no—
566C22×C32—21no—
567C22×C32—21no—
568C22×C32—22no—
569C22×C32—22no—
570C22×C32—21no—
571C22×C32—21no—
572C22×C32—21no—
573C22×C32—21no—
574C22×C32—21no—
575C22×C32—21no—
576C22×C32—21no—
577C22×C32—22no—
578C22×C32—22no—
579C22×C32—22no—
580C22×C32—42no—
581C22×C32—41no—
582C22×C32—41no—
583C22×C32—41no—
584C22×C32—41no—
585C22×C32—41no—
586C22×C32—42no—
587C22×C32—42no—
588C22×C32C2×Dic612yes—
589C22×C32D3×Q812yes—
590C22×C32D3×Q812yes—
591C22×C32C23×D311yescharacteristic
592C22×C32C23×D311yescharacteristic
593C22×C32C23×D311yescharacteristic
594C2×C3⋊D3—21no—
595C2×C3⋊D3—21no—
596C2×C3⋊D3C2×Dic612yes—
597C2×C3×D3—32no—
598C2×C3×D3—32no—
599C2×C3×D3—62no—
600C2×C3×D3—61no—
601C2×C3×D3—61no—
602C2×C3×D3—61no—
603C2×C3×D3—61no—
604C2×C3×D3—121no—
605C2×C3×D3—121no—
606C32×C4—61no—
607C32×C4—61no—
608C32×C4—61no—
609C32×C4—61no—
610C32×C4—61no—
611C32×C4—61no—
612C3⋊Dic3—21no—
613C3⋊Dic3—21no—
614C3⋊Dic3—21no—
615C3⋊Dic3—61no—
616C3⋊Dic3—61no—
617C3⋊Dic3—62no—
618C3⋊Dic3—62no—
619C3⋊Dic3—61no—
620C3⋊Dic3—61no—
621C3⋊Dic3—61no—
622C3⋊Dic3—61no—
623C3⋊Dic3—121no—
624C3⋊Dic3—121no—
625C3⋊Dic3—121no—
626C3⋊Dic3—121no—
627C3⋊Dic3—122no—
628C3⋊Dic3—122no—
629C3⋊Dic3C2×Dic612yes—
630C3⋊Dic3#23712yes—
631C3×Dic3—21no—
632C3×Dic3—21no—
633C3×Dic3—21no—
634C3×Dic3—21no—
635C3×Dic3—21no—
636C3×Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—32no—
644C3×Dic3—32no—
645C3×Dic3—32no—
646C3×Dic3—32no—
647C3×Dic3—41no—
648C3×Dic3—41no—
649C3×Dic3—41no—
650C3×Dic3—41no—
651C3×Dic3—41no—
652C3×Dic3—41no—
653C3×Dic3—62no—
654C3×Dic3—62no—
655C3×Dic3—62no—
656C3×Dic3—61no—
657C3×Dic3—61no—
658C3×Dic3—61no—
659C3×Dic3—61no—
660C3×Dic3—61no—
661C3×Dic3—61no—
662C3×Dic3—121no—
663C3×Dic3—121no—
664C4⋊Q8—271no—
665#125—271no—
666#125—271no—
667C22⋊Q8—91no—
668C22⋊Q8—91no—
669C22⋊Q8—271no—
670C22⋊Q8—271no—
671C22⋊Q8—271no—
672C22⋊Q8—271no—
673C4×Q8—271no—
674C4×D4—91no—
675C4×D4—271no—
676C4×D4—271no—
677C2×C4⋊C4—271no—
678C2×C4⋊C4—271no—
679C33#55411yescharacteristic, complemented, Sylow
680C23×C3—21no—
681C23×C3—21no—
682C23×C3—21no—
683C23×C3—41no—
684C23×C3—91no—
685C23×C3C2×D3211yescharacteristic
686C23×C3C2×D3211yescharacteristic
687C23×C3C2×D3211yescharacteristic
688C22×D3—31no—
689C22×D3—31no—
690C22×D3—61no—
691C3×Q8—182no—
692C3×Q8—361no—
693C3×D4—94no—
694C2×C3×C4—31no—
695C2×C3×C4—31no—
696C2×C3×C4—31no—
697C2×C3×C4—31no—
698C2×C3×C4—31no—
699C2×C3×C4—31no—
700C2×C3×C4—31no—
701C2×C3×C4—31no—
702C2×C3×C4—31no—
703C2×C3×C4—31no—
704C2×C3×C4—31no—
705C2×C3×C4—31no—
706C2×C3×C4—61no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—61no—
711C2×C3×C4—61no—
712C2×C3×C4—91no—
713C2×C3×C4—91no—
714C2×C3×C4—91no—
715C2×C3×C4—91no—
716C2×C3×C4—91no—
717C2×C3×C4—121no—
718C2×C3×C4—121no—
719C2×C3×C4—122no—
720C2×C3×C4—182no—
721C2×C3×C4—361no—
722#67—34no—
723#67—34no—
724#67—64no—
725C2×Dic3—31no—
726C2×Dic3—31no—
727C2×Dic3—31no—
728C2×Dic3—31no—
729C2×Dic3—31no—
730C2×Dic3—31no—
731C2×Dic3—31no—
732C2×Dic3—31no—
733C2×Dic3—31no—
734C2×Dic3—31no—
735C2×Dic3—41no—
736C2×Dic3—61no—
737C2×Dic3—61no—
738C2×Dic3—61no—
739C2×Dic3—61no—
740C2×Dic3—61no—
741C2×Dic3—62no—
742C2×Dic3—62no—
743C2×Dic3—64no—
744C2×Dic3—91no—
745C2×Dic3—91no—
746C2×Dic3—91no—
747C2×Dic3—91no—
748C2×Dic3—91no—
749C2×Dic3—91no—
750C2×Dic3—181no—
751C2×Dic3—181no—
752C2×Dic3—181no—
753C2×Dic3—181no—
754C2×Dic3—181no—
755C2×Dic3—181no—
756C2×Dic3—182no—
757C2×Dic3—361no—
758C2×Dic3—361no—
759C2×Dic3—361no—
760C2×Dic3—361no—
761C2×Dic3—361no—
762C2×Dic3—361no—
763C2×Dic3—362no—
764C2×Dic3—362no—
765C2×Dic3—362no—
766C2×Dic3—364no—
767C2×Dic3C2×D3211yescharacteristic
768C2×Dic3C2×D3211yescharacteristic
769C2×Dic3C2×D3211yescharacteristic
770C2×Dic3C2×D3211yescharacteristic
771C2×Dic3C2×D3211yescharacteristic
772C2×Dic3C2×D3211yescharacteristic
773C4×D3—121no—
774C4×D3—121no—
775C4×D3—182no—
776C4×D3—182no—
777C4×D3—361no—
778C4×D3—361no—
779C4×D3—362no—
780Dic6—62no—
781Dic6—62no—
782Dic6—121no—
783Dic6—121no—
784Dic6—361no—
785Dic6—361no—
786Dic6—361no—
787Dic6—362no—
788C2×C32—22no—
789C2×C32—24no—
790C2×C32—22no—
791C2×C32—22no—
792C2×C32—21no—
793C2×C32—21no—
794C2×C32—21no—
795C2×C32—21no—
796C2×C32—21no—
797C2×C32—21no—
798C2×C32—21no—
799C2×C32—21no—
800C2×C32—21no—
801C2×C32—41no—
802C2×C32—41no—
803C2×C32—41no—
804C2×C32—42no—
805C2×C32—42no—
806C2×C32—44no—
807C2×C32C22×Dic611yescharacteristic
808C2×C32C2×#23711yescharacteristic
809C2×C32#100411yescharacteristic
810C2×C32#100411yescharacteristic
811C2×C32C2×D3×Q811yescharacteristic
812C2×C32C2×D3×Q811yescharacteristic
813C2×C32D3×#4111yescharacteristic
814C2×C32D3×#4111yescharacteristic
815C2×C32#100911yescharacteristic
816C3⋊D3—22no—
817C3×D3—62no—
818C3×D3—62no—
819C3×D3—122no—
820C2×Q8—91no—
821C2×Q8—91no—
822C2×Q8—271no—
823C2×D4—91no—
824C22×C4—31no—
825C22×C4—91no—
826C22×C4—91no—
827C22×C4—271no—
828C22×C4—271no—
829C22×C4—271no—
830C4⋊C4—91no—
831C4⋊C4—91no—
832C4⋊C4—91no—
833C4⋊C4—91no—
834C4⋊C4—91no—
835C4⋊C4—91no—
836C4⋊C4—91no—
837C4⋊C4—271no—
838C4⋊C4—271no—
839C4⋊C4—271no—
840C4⋊C4—271no—
841C4⋊C4—271no—
842C4⋊C4—271no—
843C4⋊C4—271no—
844C4⋊C4—271no—
845C4⋊C4—271no—
846C22⋊C4—31no—
847C22⋊C4—31no—
848C22⋊C4—91no—
849C22⋊C4—91no—
850C22⋊C4—271no—
851C22⋊C4—271no—
852C42—91no—
853C42—271no—
854C42—271no—
855C22×C3—22no—
856C22×C3—22no—
857C22×C3—21no—
858C22×C3—21no—
859C22×C3—21no—
860C22×C3—21no—
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—22no—
869C22×C3—41no—
870C22×C3—41no—
871C22×C3—41no—
872C22×C3—41no—
873C22×C3—42no—
874C22×C3—42no—
875C22×C3—41no—
876C22×C3—42no—
877C22×C3—92no—
878C22×C3—181no—
879C22×C3—181no—
880C22×C3D3×Dic612yes—
881C22×C3D3×Dic612yes—
882C22×C3#379712yes—
883C22×C3C22×D3211yescharacteristic
884C22×C3C22×D3211yescharacteristic
885C22×C3C22×D3211yescharacteristic
886C2×D3—32no—
887C2×D3—32no—
888C2×D3—62no—
889C2×D3—61no—
890C2×D3—61no—
891C2×D3—61no—
892C2×D3—61no—
893C2×D3—121no—
894C2×D3—121no—
895C3×C4—61no—
896C3×C4—61no—
897C3×C4—61no—
898C3×C4—61no—
899C3×C4—61no—
900C3×C4—61no—
901C3×C4—61no—
902C3×C4—61no—
903C3×C4—61no—
904C3×C4—61no—
905C3×C4—61no—
906C3×C4—61no—
907C3×C4—92no—
908C3×C4—92no—
909C3×C4—121no—
910C3×C4—121no—
911C3×C4—121no—
912C3×C4—121no—
913C3×C4—121no—
914C3×C4—121no—
915C3×C4—181no—
916C3×C4—181no—
917C3×C4—181no—
918Dic3—21no—
919Dic3—21no—
920Dic3—21no—
921Dic3—21no—
922Dic3—21no—
923Dic3—21no—
924Dic3—32no—
925Dic3—32no—
926Dic3—32no—
927Dic3—32no—
928Dic3—62no—
929Dic3—62no—
930Dic3—62no—
931Dic3—61no—
932Dic3—61no—
933Dic3—61no—
934Dic3—61no—
935Dic3—61no—
936Dic3—61no—
937Dic3—121no—
938Dic3—121no—
939Dic3—182no—
940Dic3—182no—
941Dic3—181no—
942Dic3—181no—
943Dic3—181no—
944Dic3—181no—
945Dic3—181no—
946Dic3—181no—
947Dic3—361no—
948Dic3—361no—
949Dic3—361no—
950Dic3—361no—
951Dic3—362no—
952Dic3—362no—
953C32—21no—
954C32—21no—
955C32—21no—
956C32—41no—
957C32#553911yescharacteristic, complemented
958C32#563511yescharacteristic, complemented
959C32#563611yescharacteristic, complemented
960C23—91no—
961C23D3311yescharacteristic
962Q8—182no—
963Q8—361no—
964Q8—1081no—
965D4—94no—
966C2×C4—31no—
967C2×C4—31no—
968C2×C4—31no—
969C2×C4—31no—
970C2×C4—31no—
971C2×C4—31no—
972C2×C4—91no—
973C2×C4—91no—
974C2×C4—91no—
975C2×C4—91no—
976C2×C4—91no—
977C2×C4—121no—
978C2×C4—182no—
979C2×C4—271no—
980C2×C4—271no—
981C2×C4—361no—
982C2×C4—542no—
983C2×C4—1081no—
984C2×C4—1081no—
985C2×C3—24no—
986C2×C3—22no—
987C2×C3—22no—
988C2×C3—22no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—21no—
995C2×C3—21no—
996C2×C3—21no—
997C2×C3—21no—
998C2×C3—42no—
999C2×C3—42no—
1000C2×C3—44no—
1001C2×C3—41no—
1002C2×C3—41no—
1003C2×C3—41no—
1004C2×C3—182no—
1005C2×C3C2×D3×Dic611yescharacteristic
1006C2×C3C2×D3×Dic611yescharacteristic
1007C2×C3C2×#379711yescharacteristic
1008C2×C3#6430611yescharacteristic
1009C2×C3D3×#23711yescharacteristic
1010C2×C3D3×#23711yescharacteristic
1011C2×C3#6431411yescharacteristic
1012C2×C3#6431411yescharacteristic
1013C2×C3#6433011yescharacteristic
1014D3—62no—
1015D3—62no—
1016D3—122no—
1017C22—21no—
1018C22—21no—
1019C22—92no—
1020C22—181no—
1021C22—181no—
1022C22#8895712yes—
1023C22C2×D3311yescharacteristic
1024C4—61no—
1025C4—61no—
1026C4—61no—
1027C4—61no—
1028C4—61no—
1029C4—61no—
1030C4—92no—
1031C4—92no—
1032C4—181no—
1033C4—181no—
1034C4—181no—
1035C4—541no—
1036C4—541no—
1037C3—21no—
1038C3—21no—
1039C3—21no—
1040C3—41no—
1041C3#1059413311yescharacteristic, complemented
1042C3#1059414111yescharacteristic, complemented
1043C3#1059495911yescharacteristic, complemented
1044C2—22no—
1045C2—182no—
1046C2#1172440711yescharacteristic
1047C2#1172441911yescharacteristic
1048C2C2×#8895711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radicalC2×C3×#638C22
hypercenterC23D33
hypocenterC33#554
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. #11723642C2semidirect
4. C2×#88807C2semidirect
5. C3×#63982C2semidirect
6. C3×#63964C2semidirect
8. #11723034C2semidirect
9. #11723015C2semidirect
10. #11723014C2semidirect
11. #11722979C2semidirect
12. #11722974C2semidirect
13. #11722972C2semidirect
14. #11722940C2semidirect
15. #11722910C2semidirect
66. #63982D3semidirect
75. #63964D3semidirect
107. C3×#638Q8semidirect
343. #638Dic6semidirect
679. C33#554semidirect
957. C32#5539semidirect
958. C32#5635semidirect
959. C32#5636semidirect
1041. C3#10594133semidirect
1042. C3#10594141semidirect
1043. C3#10594959semidirect

Maximal subgroups

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

subgroupindex
#117237262
#117236422
#117236262
C2×#888072
C3×#639822
C3×#639642
C3×#639522
#117230342
#117230152
#117230142
#117229792
#117229742
#117229722
#117229402
#117229102
#105949593
#105941413
#105941333