Finite Group Databasebeta

← #13178218

Subgroups — #13178218

Order 1728.

1188 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64090C211yesmaximal, characteristic
2C3×#64087C211yesmaximal, characteristic, complemented
3C3×#64087C211yesmaximal, characteristic, complemented
4#11723726C211yesmaximal, characteristic
5#11723726C211yesmaximal, characteristic
6C2×#88815C211yesmaximal, characteristic, complemented
7#11723721C211yesmaximal, characteristic, complemented
8#11723692C211yesmaximal, characteristic, complemented
9#11723688C211yesmaximal, characteristic, complemented
10#11723682C211yesmaximal, characteristic, complemented
11#11723679C211yesmaximal, characteristic, complemented
12#11723674C211yesmaximal, characteristic, complemented
13#11723669C211yesmaximal, characteristic, complemented
14#11723668C211yesmaximal, characteristic, complemented
15#11723666C211yesmaximal, characteristic, complemented
16#10594156—31nomaximal
17#10594141—31nomaximal
18#10594133—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2211yescharacteristic
24C2×C3×#634C2211yescharacteristic
25C2×C3×#634C2211yescharacteristic
26C2×#6296C2211yescharacteristic
27C2×#6294C2211yescharacteristic
28C2×#6294C2211yescharacteristic
29C33×C22⋊C4C2211yescharacteristic
30C3×#3757C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
34C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C3×#3750C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C3×#3750C2211yescharacteristic
39C3×#3750C2211yescharacteristic
40C3×C4×C3⋊Dic3C2211yescharacteristic
41#88815C2211yescharacteristic
42#88815C2211yescharacteristic
43#88815C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88815C2211yescharacteristic
47#88815C2211yescharacteristic
48#88815C2211yescharacteristic
49#88815C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88813C2211yescharacteristic
53#88813C2211yescharacteristic
54#64090D311yescharacteristic
55#64087D311yescharacteristic, complemented
56#64087D311yescharacteristic, complemented
57C3×#67⋊C4—31no—
58C3×#67⋊C4—31no—
59C3×#67⋊C4—61no—
60C3×#878—31no—
61C3×#878—31no—
62C3×#878—31no—
63C3×#878—31no—
64C3×#878—61no—
65C3×#878—61no—
66#63982—31no—
67#67⋊Dic3—31no—
68#67⋊Dic3—31no—
69Dic3×#67—31no—
70Dic3×#67—31no—
71C2×#3724—31no—
72C2×Dic3⋊Dic3—31no—
73C2×Dic3⋊Dic3—31no—
74#63964—31no—
75#63964—31no—
76#63952—31no—
77#63952—31no—
78#63899—31no—
79#63896—31no—
80#63895—31no—
81#63893—31no—
82#63888—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#63856—31no—
93#63847—31no—
94#63846—31no—
95#63845—31no—
96#63844—31no—
97#63843—31no—
98Dic3×Dic6—31no—
99#63840—31no—
100#63839—31no—
101#63839—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C3×#638Q814yescomplemented
107C2×C3×C3⋊Dic3—22no—
108C2×C3×C3⋊Dic3—41no—
109C2×C3×C3⋊Dic3—41no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
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
121C3×C4×C3⋊D3—41no—
122C3×#634—22no—
123C3×#634—41no—
124#6296—41no—
125#6294—22no—
126#6294—41no—
127#5636—91no—
128#5635—91no—
129#5539—91no—
130C2×#638C2×D311yescharacteristic
131C22×C3⋊Dic3C2×D311yescharacteristic
132C22×C3⋊Dic3C2×D311yescharacteristic
133C22×C3⋊Dic3C2×D311yescharacteristic
134C2×C4×C3⋊D3C2×D311yescharacteristic
135C2×#634C2×D311yescharacteristic
136C2×#634C2×D311yescharacteristic
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C2×C3×#67—61no—
140C22×C3×Dic3—31no—
141C22×C3×Dic3—31no—
142C22×C3×Dic3—31no—
143C22×C3×Dic3—31no—
144C22×C3×Dic3—31no—
145C22×C3×Dic3—31no—
146C22×C3×Dic3—61no—
147C22×C3×Dic3—61no—
148C22×C3×Dic3—61no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C2×C3×C4×D3—61no—
152C2×C3×Dic6—31no—
153C2×C3×Dic6—31no—
154C2×C3×Dic6—31no—
155C2×C3×Dic6—31no—
156C2×C3×Dic6—61no—
157C2×C3×Dic6—61no—
158C2×#627—31no—
159C2×#627—31no—
160C2×#627—31no—
161C2×#624—31no—
162C2×#624—31no—
163C2×D3×Dic3—31no—
164C2×D3×Dic3—31no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—31no—
167C32×C22⋊C4—21no—
168C32×C22⋊C4—21no—
169C32×C22⋊C4—21no—
170C32×C22⋊C4—41no—
171C32×C22⋊C4C2×D311yescharacteristic
172C32×C22⋊C4C2×D311yescharacteristic
173C32×C22⋊C4C2×D311yescharacteristic
174#3757C2×D311yescharacteristic
175#3757C2×D311yescharacteristic
176#3752C2×D311yescharacteristic
177C4⋊(C3⋊Dic3)C2×D311yescharacteristic
178C4⋊(C3⋊Dic3)C2×D311yescharacteristic
179#3750C2×D311yescharacteristic
180#3750C2×D311yescharacteristic
181#3750C2×D311yescharacteristic
182#3750C2×D311yescharacteristic
183#3750C2×D311yescharacteristic
184C4×C3⋊Dic3C2×D311yescharacteristic
185C3×#217—31no—
186C3×#217—31no—
187C3×#217—31no—
188C3×#217—31no—
189C3×#217—61no—
190C3×#217—61no—
191C3×(C2×D3)⋊C4—31no—
192C3×(C2×D3)⋊C4—31no—
193C3×(C2×D3)⋊C4—61no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—31no—
198C3×C4⋊Dic3—61no—
199C3×C4⋊Dic3—61no—
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×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—61no—
211C3×Dic3⋊C4—61no—
212C3×Dic3⋊C4—61no—
213C3×Dic3⋊C4—61no—
214C3×Dic3⋊C4—61no—
215C3×C4×Dic3—31no—
216C3×C4×Dic3—31no—
217C3×C4×Dic3—61no—
218#3724—31no—
219#3724—31no—
220#3724—31no—
221#3724—31no—
222#3724—31no—
223#3724—31no—
224#3724—31no—
225#3724—31no—
226#3724—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238Dic3⋊Dic3—31no—
239Dic3⋊Dic3—31no—
240Dic3⋊Dic3—31no—
241Dic3⋊Dic3—31no—
242Dic3⋊Dic3—31no—
243Dic3⋊Dic3—31no—
244Dic3⋊Dic3—31no—
245#3722—31no—
246#3722—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—31no—
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—
264C33×C4—21no—
265C33×C4—21no—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3—21no—
273C3×C3⋊Dic3—21no—
274C3×C3⋊Dic3—21no—
275C3×C3⋊Dic3C2×Q812yes—
276C3×C3⋊Dic3#4112yes—
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—91no—
287C4×#67—91no—
288C2×C4⋊Dic3—91no—
289#924—91no—
290#924—91no—
291C2×Dic3⋊C4—91no—
292C2×Dic3⋊C4—91no—
293C2×Dic3⋊C4—91no—
294#897—91no—
295#897—91no—
296#896—91no—
297#896—91no—
298D3×C4⋊C4—91no—
299D3×C4⋊C4—91no—
300#890—91no—
301#889—91no—
302#889—91no—
303#889—91no—
304#889—91no—
305#888—91no—
306#888—91no—
307#887—91no—
308#67⋊C4—31no—
309#67⋊C4—31no—
310#67⋊C4—61no—
311#67⋊C4—91no—
312#67⋊C4—91no—
313#878—31no—
314#878—31no—
315#878—31no—
316#878—31no—
317#878—61no—
318#878—61no—
319#878—91no—
320#878—91no—
321#878—91no—
322#878—91no—
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—21no—
337C2×C32×C4—21no—
338C2×C32×C4—21no—
339C2×C32×C4—21no—
340C2×C32×C4—21no—
341C2×C32×C4—21no—
342C2×C32×C4—41no—
343C2×C32×C4—41no—
344C2×C32×C4C22×D311yescharacteristic
345C2×C32×C4C22×D311yescharacteristic
346C2×C32×C4C22×D311yescharacteristic
347C2×C32×C4C22×D311yescharacteristic
348C2×C32×C4C22×D311yescharacteristic
349C2×C32×C4C22×D311yescharacteristic
350#638Dic614yescomplemented
351C2×C3⋊Dic3—22no—
352C2×C3⋊Dic3—41no—
353C2×C3⋊Dic3—41no—
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360C2×C3⋊Dic3C22×D311yescharacteristic
361C2×C3⋊Dic3C22×D311yescharacteristic
362C2×C3⋊Dic3C22×D311yescharacteristic
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C4×C3⋊D3—41no—
366#634—22no—
367#634—41no—
368C3×#67—34no—
369C3×#67—34no—
370C3×#67—64no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
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—31no—
393C2×C3×Dic3—61no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—61no—
397C2×C3×Dic3—61no—
398C2×C3×Dic3—61no—
399C2×C3×Dic3—61no—
400C2×C3×Dic3—61no—
401C2×C3×Dic3—61no—
402C2×C3×Dic3—61no—
403C2×C3×Dic3—61no—
404C2×C3×Dic3—62no—
405C2×C3×Dic3—62no—
406C2×C3×Dic3—122no—
407C2×C3×Dic3—121no—
408C2×C3×Dic3—121no—
409C2×C3×Dic3—121no—
410C2×C3×Dic3—121no—
411C2×C3×Dic3—122no—
412C2×C3×Dic3—122no—
413C3×C4×D3—121no—
414C3×C4×D3—121no—
415C3×C4×D3—122no—
416C3×Dic6—62no—
417C3×Dic6—62no—
418C3×Dic6—122no—
419C3×Dic6—121no—
420C3×Dic6—121no—
421C3×Dic6—122no—
422#627—121no—
423#627—121no—
424#627—121no—
425#624—62no—
426#624—121no—
427D3×Dic3—62no—
428D3×Dic3—62no—
429D3×Dic3—121no—
430D3×Dic3—121no—
431#554—271noSylow
432C2×C33—22no—
433C2×C33C22×Q811yescharacteristic
434C2×C33C2×#4111yescharacteristic
435C2×C33H(5,𝔽2)11yescharacteristic
436C3×C3⋊D3—22no—
437C2×C3×Q8—91no—
438C2×C3×Q8—91no—
439C2×C3×D4—91no—
440C22×C3×C4—91no—
441C22×C3×C4—91no—
442C22×C3×C4—91no—
443C22×C3×C4—91no—
444C2×#67—31no—
445C2×#67—31no—
446C2×#67—61no—
447C22×Dic3—31no—
448C22×Dic3—31no—
449C22×Dic3—31no—
450C22×Dic3—31no—
451C22×Dic3—31no—
452C22×Dic3—31no—
453C22×Dic3—61no—
454C22×Dic3—61no—
455C22×Dic3—61no—
456C22×Dic3—91no—
457C22×Dic3—91no—
458C2×C4×D3—31no—
459C2×C4×D3—31no—
460C2×C4×D3—61no—
461C2×C4×D3—91no—
462C2×C4×D3—91no—
463C2×C4×D3—91no—
464C2×C4×D3—91no—
465C2×Dic6—31no—
466C2×Dic6—31no—
467C2×Dic6—31no—
468C2×Dic6—31no—
469C2×Dic6—61no—
470C2×Dic6—61no—
471C2×Dic6—91no—
472C2×Dic6—91no—
473C2×Dic6—91no—
474C3×C4⋊C4—91no—
475C3×C4⋊C4—91no—
476C3×C4⋊C4—91no—
477C3×C4⋊C4—91no—
478C3×C4⋊C4—91no—
479C3×C4⋊C4—91no—
480C3×C4⋊C4—91no—
481C3×C22⋊C4—21no—
482C3×C22⋊C4—21no—
483C3×C22⋊C4—21no—
484C3×C22⋊C4—41no—
485C3×C22⋊C4—91no—
486C3×C22⋊C4—91no—
487C3×C22⋊C4—91no—
488C3×C22⋊C4D3211yescharacteristic
489C3×C22⋊C4D3211yescharacteristic
490C3×C22⋊C4D3211yescharacteristic
491C3×C42—91no—
492#217—31no—
493#217—31no—
494#217—31no—
495#217—31no—
496#217—61no—
497#217—61no—
498#217—91no—
499#217—91no—
500(C2×D3)⋊C4—31no—
501(C2×D3)⋊C4—31no—
502(C2×D3)⋊C4—61no—
503(C2×D3)⋊C4—91no—
504(C2×D3)⋊C4—91no—
505(C2×D3)⋊C4—91no—
506(C2×D3)⋊C4—91no—
507C4⋊Dic3—31no—
508C4⋊Dic3—31no—
509C4⋊Dic3—31no—
510C4⋊Dic3—31no—
511C4⋊Dic3—61no—
512C4⋊Dic3—61no—
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—91no—
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—61no—
533Dic3⋊C4—61no—
534Dic3⋊C4—61no—
535Dic3⋊C4—61no—
536Dic3⋊C4—61no—
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—91no—
551Dic3⋊C4—91no—
552Dic3⋊C4—91no—
553Dic3⋊C4—91no—
554Dic3⋊C4—91no—
555C4×Dic3—31no—
556C4×Dic3—31no—
557C4×Dic3—61no—
558C4×Dic3—91no—
559C4×Dic3—91no—
560C4×Dic3—91no—
561C4×Dic3—91no—
562C4×Dic3—91no—
563C4×Dic3—91no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—21no—
567C22×C32—21no—
568C22×C32—21no—
569C22×C32—21no—
570C22×C32—21no—
571C22×C32—21no—
572C22×C32—21no—
573C22×C32—22no—
574C22×C32—22no—
575C22×C32—22no—
576C22×C32—41no—
577C22×C32—42no—
578C22×C32—41no—
579C22×C32—41no—
580C22×C32—41no—
581C22×C32—41no—
582C22×C32—41no—
583C22×C32—41no—
584C22×C32—81no—
585C22×C32—81no—
586C22×C32C2×Dic612yes—
587C22×C32D3×Q812yes—
588C22×C32D3×Q812yes—
589C22×C32C23×D311yescharacteristic
590C22×C32C23×D311yescharacteristic
591C22×C32C23×D311yescharacteristic
592C2×C3⋊D3—21no—
593C2×C3⋊D3—21no—
594C2×C3⋊D3C2×Dic612yes—
595C2×C3×D3—32no—
596C2×C3×D3—32no—
597C2×C3×D3—62no—
598C2×C3×D3—61no—
599C2×C3×D3—61no—
600C2×C3×D3—61no—
601C2×C3×D3—61no—
602C2×C3×D3—121no—
603C2×C3×D3—121no—
604C32×C4—21no—
605C32×C4—21no—
606C32×C4—21no—
607C32×C4—21no—
608C32×C4—21no—
609C32×C4—21no—
610C32×C4—41no—
611C32×C4—41no—
612C32×C4—41no—
613C32×C4—41no—
614C32×C4—41no—
615C32×C4—41no—
616C32×C4—81no—
617C32×C4—81no—
618C3⋊Dic3—21no—
619C3⋊Dic3—21no—
620C3⋊Dic3—21no—
621C3⋊Dic3—21no—
622C3⋊Dic3—21no—
623C3⋊Dic3—21no—
624C3⋊Dic3—21no—
625C3⋊Dic3—21no—
626C3⋊Dic3—21no—
627C3⋊Dic3C2×Dic612yes—
628C3⋊Dic3#23712yes—
629C3×Dic3—32no—
630C3×Dic3—32no—
631C3×Dic3—32no—
632C3×Dic3—32no—
633C3×Dic3—62no—
634C3×Dic3—62no—
635C3×Dic3—62no—
636C3×Dic3—62no—
637C3×Dic3—61no—
638C3×Dic3—61no—
639C3×Dic3—61no—
640C3×Dic3—61no—
641C3×Dic3—61no—
642C3×Dic3—61no—
643C3×Dic3—61no—
644C3×Dic3—61no—
645C3×Dic3—61no—
646C3×Dic3—61no—
647C3×Dic3—61no—
648C3×Dic3—61no—
649C3×Dic3—61no—
650C3×Dic3—61no—
651C3×Dic3—61no—
652C3×Dic3—61no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—121no—
656C3×Dic3—121no—
657C3×Dic3—121no—
658C3×Dic3—121no—
659C3×Dic3—121no—
660C3×Dic3—121no—
661C3×Dic3—121no—
662C4⋊Q8—271no—
663#125—271no—
664#125—271no—
665C22⋊Q8—91no—
666C22⋊Q8—91no—
667C22⋊Q8—271no—
668C22⋊Q8—271no—
669C22⋊Q8—271no—
670C22⋊Q8—271no—
671C4×Q8—271no—
672C4×D4—91no—
673C4×D4—271no—
674C4×D4—271no—
675C2×C4⋊C4—271no—
676C2×C4⋊C4—271no—
677C33#55411yescharacteristic, complemented, Sylow
678C23×C3—21no—
679C23×C3—21no—
680C23×C3—21no—
681C23×C3—41no—
682C23×C3—91no—
683C23×C3C2×D3211yescharacteristic
684C23×C3C2×D3211yescharacteristic
685C23×C3C2×D3211yescharacteristic
686C22×D3—31no—
687C22×D3—31no—
688C22×D3—61no—
689C3×Q8—182no—
690C3×Q8—361no—
691C3×D4—94no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
694C2×C3×C4—21no—
695C2×C3×C4—21no—
696C2×C3×C4—21no—
697C2×C3×C4—21no—
698C2×C3×C4—41no—
699C2×C3×C4—41no—
700C2×C3×C4—91no—
701C2×C3×C4—91no—
702C2×C3×C4—91no—
703C2×C3×C4—91no—
704C2×C3×C4—91no—
705C2×C3×C4—91no—
706C2×C3×C4—91no—
707C2×C3×C4—91no—
708C2×C3×C4—91no—
709C2×C3×C4—91no—
710C2×C3×C4—91no—
711C2×C3×C4—182no—
712C2×C3×C4—361no—
713C2×C3×C4—361no—
714C2×C3×C4—361no—
715C2×C3×C4C2×D3211yescharacteristic
716C2×C3×C4C2×D3211yescharacteristic
717C2×C3×C4C2×D3211yescharacteristic
718C2×C3×C4C2×D3211yescharacteristic
719C2×C3×C4C2×D3211yescharacteristic
720C2×C3×C4C2×D3211yescharacteristic
721#67—34no—
722#67—34no—
723#67—64no—
724C2×Dic3—31no—
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—31no—
736C2×Dic3—31no—
737C2×Dic3—31no—
738C2×Dic3—31no—
739C2×Dic3—31no—
740C2×Dic3—31no—
741C2×Dic3—31no—
742C2×Dic3—31no—
743C2×Dic3—31no—
744C2×Dic3—31no—
745C2×Dic3—31no—
746C2×Dic3—61no—
747C2×Dic3—61no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—61no—
751C2×Dic3—61no—
752C2×Dic3—61no—
753C2×Dic3—61no—
754C2×Dic3—61no—
755C2×Dic3—61no—
756C2×Dic3—61no—
757C2×Dic3—62no—
758C2×Dic3—62no—
759C2×Dic3—122no—
760C2×Dic3—121no—
761C2×Dic3—121no—
762C2×Dic3—121no—
763C2×Dic3—121no—
764C2×Dic3—122no—
765C2×Dic3—122no—
766C2×Dic3—182no—
767C2×Dic3—361no—
768C4×D3—121no—
769C4×D3—121no—
770C4×D3—122no—
771C4×D3—182no—
772C4×D3—182no—
773C4×D3—361no—
774C4×D3—361no—
775Dic6—62no—
776Dic6—62no—
777Dic6—122no—
778Dic6—121no—
779Dic6—121no—
780Dic6—122no—
781Dic6—361no—
782Dic6—361no—
783Dic6—361no—
784C2×C32—22no—
785C2×C32—22no—
786C2×C32—22no—
787C2×C32—21no—
788C2×C32—21no—
789C2×C32—21no—
790C2×C32—21no—
791C2×C32—21no—
792C2×C32—21no—
793C2×C32—21no—
794C2×C32—21no—
795C2×C32—21no—
796C2×C32—41no—
797C2×C32—41no—
798C2×C32—41no—
799C2×C32—42no—
800C2×C32—42no—
801C2×C32—42no—
802C2×C32—82no—
803C2×C32C22×Dic611yescharacteristic
804C2×C32C2×#23711yescharacteristic
805C2×C32#100411yescharacteristic
806C2×C32#100411yescharacteristic
807C2×C32C2×D3×Q811yescharacteristic
808C2×C32C2×D3×Q811yescharacteristic
809C2×C32D3×#4111yescharacteristic
810C2×C32D3×#4111yescharacteristic
811C2×C32#100911yescharacteristic
812C3⋊D3—22no—
813C3×D3—62no—
814C3×D3—62no—
815C3×D3—122no—
816C2×Q8—91no—
817C2×Q8—91no—
818C2×Q8—271no—
819C2×D4—91no—
820C22×C4—91no—
821C22×C4—91no—
822C22×C4—91no—
823C22×C4—91no—
824C22×C4—271no—
825C22×C4—271no—
826C4⋊C4—91no—
827C4⋊C4—91no—
828C4⋊C4—91no—
829C4⋊C4—91no—
830C4⋊C4—91no—
831C4⋊C4—91no—
832C4⋊C4—91no—
833C4⋊C4—271no—
834C4⋊C4—271no—
835C4⋊C4—271no—
836C4⋊C4—271no—
837C4⋊C4—271no—
838C4⋊C4—271no—
839C4⋊C4—271no—
840C4⋊C4—271no—
841C4⋊C4—271no—
842C22⋊C4—91no—
843C22⋊C4—91no—
844C22⋊C4—91no—
845C22⋊C4—271no—
846C22⋊C4—271no—
847C22⋊C4#111311yescharacteristic
848C42—91no—
849C42—271no—
850C42—271no—
851C22×C3—21no—
852C22×C3—21no—
853C22×C3—21no—
854C22×C3—21no—
855C22×C3—21no—
856C22×C3—21no—
857C22×C3—21no—
858C22×C3—21no—
859C22×C3—21no—
860C22×C3—22no—
861C22×C3—22no—
862C22×C3—22no—
863C22×C3—41no—
864C22×C3—41no—
865C22×C3—41no—
866C22×C3—41no—
867C22×C3—41no—
868C22×C3—41no—
869C22×C3—41no—
870C22×C3—42no—
871C22×C3—81no—
872C22×C3—81no—
873C22×C3—92no—
874C22×C3—181no—
875C22×C3—181no—
876C22×C3D3×Dic612yes—
877C22×C3D3×Dic612yes—
878C22×C3#379712yes—
879C22×C3C22×D3211yescharacteristic
880C22×C3C22×D3211yescharacteristic
881C22×C3C22×D3211yescharacteristic
882C2×D3—32no—
883C2×D3—32no—
884C2×D3—62no—
885C2×D3—61no—
886C2×D3—61no—
887C2×D3—61no—
888C2×D3—61no—
889C2×D3—121no—
890C2×D3—121no—
891C3×C4—21no—
892C3×C4—21no—
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—41no—
898C3×C4—41no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4—41no—
902C3×C4—41no—
903C3×C4—81no—
904C3×C4—81no—
905C3×C4—92no—
906C3×C4—92no—
907C3×C4—181no—
908C3×C4—181no—
909C3×C4—181no—
910C3×C4—181no—
911C3×C4—181no—
912C3×C4—181no—
913C3×C4—181no—
914C3×C4—181no—
915C3×C4—181no—
916Dic3—32no—
917Dic3—32no—
918Dic3—32no—
919Dic3—32no—
920Dic3—62no—
921Dic3—62no—
922Dic3—62no—
923Dic3—62no—
924Dic3—61no—
925Dic3—61no—
926Dic3—61no—
927Dic3—61no—
928Dic3—61no—
929Dic3—61no—
930Dic3—61no—
931Dic3—61no—
932Dic3—61no—
933Dic3—61no—
934Dic3—61no—
935Dic3—61no—
936Dic3—61no—
937Dic3—61no—
938Dic3—61no—
939Dic3—61no—
940Dic3—61no—
941Dic3—61no—
942Dic3—121no—
943Dic3—121no—
944Dic3—121no—
945Dic3—121no—
946Dic3—121no—
947Dic3—121no—
948Dic3—121no—
949C32—21no—
950C32—21no—
951C32—21no—
952C32—41no—
953C32#553911yescharacteristic, complemented
954C32#563511yescharacteristic, complemented
955C32#563611yescharacteristic, complemented
956C23—91no—
957C23C2×#111311yescharacteristic
958Q8—182no—
959Q8—361no—
960Q8—1081no—
961D4—94no—
962C2×C4—91no—
963C2×C4—91no—
964C2×C4—91no—
965C2×C4—91no—
966C2×C4—91no—
967C2×C4—91no—
968C2×C4—91no—
969C2×C4—91no—
970C2×C4—91no—
971C2×C4—91no—
972C2×C4—91no—
973C2×C4—182no—
974C2×C4—361no—
975C2×C4—361no—
976C2×C4—361no—
977C2×C4—542no—
978C2×C4—1081no—
979C2×C4C2×#111311yescharacteristic
980C2×C4C2×#111311yescharacteristic
981C2×C3—22no—
982C2×C3—22no—
983C2×C3—22no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—42no—
994C2×C3—42no—
995C2×C3—42no—
996C2×C3—41no—
997C2×C3—41no—
998C2×C3—41no—
999C2×C3—82no—
1000C2×C3—182no—
1001C2×C3C2×D3×Dic611yescharacteristic
1002C2×C3C2×D3×Dic611yescharacteristic
1003C2×C3C2×#379711yescharacteristic
1004C2×C3D3×#23711yescharacteristic
1005C2×C3D3×#23711yescharacteristic
1006C2×C3#6431211yescharacteristic
1007C2×C3#6431311yescharacteristic
1008C2×C3#6431411yescharacteristic
1009C2×C3#6431411yescharacteristic
1010D3—62no—
1011D3—62no—
1012D3—122no—
1013C22—21no—
1014C22—21no—
1015C22—92no—
1016C22—181no—
1017C22—181no—
1018C22#8904012yes—
1019C22C22×#111311yescharacteristic
1020C4—21no—
1021C4—21no—
1022C4—92no—
1023C4—92no—
1024C4—181no—
1025C4—181no—
1026C4—181no—
1027C4—181no—
1028C4—181no—
1029C4—181no—
1030C4—181no—
1031C4—181no—
1032C4—181no—
1033C3—21no—
1034C3—21no—
1035C3—21no—
1036C3—41no—
1037C3#1059413311yescharacteristic, complemented
1038C3#1059414111yescharacteristic, complemented
1039C3#1059415611yescharacteristic, complemented
1040C2—22no—
1041C2—182no—
1042C2C2×#8904011yescharacteristic
1043C2#1172462211yescharacteristic
1044C2#1172462311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radicalC2×C3×#638C22
hypercenterC22⋊C4#1113
hypocenterC33#554
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#64087C2semidirect
3. C3×#64087C2semidirect
6. C2×#88815C2semidirect
7. #11723721C2semidirect
8. #11723692C2semidirect
9. #11723688C2semidirect
10. #11723682C2semidirect
11. #11723679C2semidirect
12. #11723674C2semidirect
13. #11723669C2semidirect
14. #11723668C2semidirect
15. #11723666C2semidirect
55. #64087D3semidirect
56. #64087D3semidirect
106. C3×#638Q8semidirect
350. #638Dic6semidirect
677. C33#554semidirect
953. C32#5539semidirect
954. C32#5635semidirect
955. C32#5636semidirect
1037. C3#10594133semidirect
1038. C3#10594141semidirect
1039. C3#10594156semidirect

Maximal subgroups

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

subgroupindex
C3×#640902
C3×#640872
#117237262
C2×#888152
#117237212
#117236922
#117236882
#117236822
#117236792
#117236742
#117236692
#117236682
#117236662
#105941563
#105941413
#105941333