Finite Group Databasebeta

← C3×#82541 #11872102

Subgroups — C3×#82541 #11872102

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#518C211yesmaximal, characteristic, complemented
2C3×#5534C211yesmaximal, characteristic, complemented
3C3×#5218C211yesmaximal, characteristic, complemented
4C3×#5217C211yesmaximal, characteristic
5C3×#5018C211yesmaximal, characteristic, complemented
6C3×C4×#214C211yesmaximal, characteristic, complemented
7C3×#5016C211yesmaximal, characteristic, complemented
8C3×#5016C211yesmaximal, characteristic, complemented
9C3×#5014C211yesmaximal, characteristic, complemented
10C3×C4×#213C211yesmaximal, characteristic, complemented
11C3×#5008C211yesmaximal, characteristic, complemented
12C3×#5007C211yesmaximal, characteristic, complemented
13C3×#5003C211yesmaximal, characteristic, complemented
14C3×#5000C211yesmaximal, characteristic, complemented
15C3×#4996C211yesmaximal, characteristic, complemented
16C3×#3118—31nomaximal
17#82541C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C32×C4×D4—21no—
20C32×C4×D4—21no—
21C32×C4×D4C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C32×C4×D4C2211yescharacteristic
24C32×C4×D4C2211yescharacteristic
25C32×#117C2211yescharacteristic
26C32×#117C2211yescharacteristic
27C2×C32×C22⋊C4—21no—
28C2×C32×C22⋊C4—21no—
29C2×C3×#214C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C3×#930C2211yescharacteristic
34C3×#924C2211yescharacteristic
35C3×#898—21no—
36C3×#896—21no—
37C3×#885—21no—
38C3×#883—21no—
39C3×#875C2211yescharacteristic, complemented
40C3×C4×D12C2211yescharacteristic, complemented
41C3×#869C2211yescharacteristic, complemented
42C3×C4×Dic6C2211yescharacteristic, complemented
43C3×#832C2211yescharacteristic
44C3×#832C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#830C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#810C2211yescharacteristic, complemented
50C3×#810C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53C3×#808C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56C3×#807C2211yescharacteristic, complemented
57C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59C3×#803C2211yescharacteristic, complemented
60C3×C4×C3⋊C8C2211yescharacteristic, complemented
61C3×#542—31no—
62C3×#518—21no—
63C3×#518D311yescharacteristic, complemented
64C3×#518C2×C311yescharacteristic, complemented
65#5534C2×C311yescharacteristic, complemented
66C3×#485—31no—
67C3×#482—31no—
68C3×#476—31no—
69C3×#474—31no—
70C3×#463—31no—
71C3×#463—31no—
72C3×#450—31no—
73C3×#447—31no—
74C3×#442—31no—
75C3×#440—31no—
76C3×C4×SD16—31no—
77C3×C4×D8—31no—
78C3×#433—31no—
79#5218C2×C311yescharacteristic, complemented
80#5217C2×C311yescharacteristic
81#5018C2×C311yescharacteristic, complemented
82C4×#214C2×C311yescharacteristic, complemented
83#5016C2×C311yescharacteristic, complemented
84#5016C2×C311yescharacteristic, complemented
85#5014C2×C311yescharacteristic, complemented
86C4×#213C2×C311yescharacteristic, complemented
87#5008C2×C311yescharacteristic, complemented
88#5007C2×C311yescharacteristic, complemented
89#5003C2×C311yescharacteristic, complemented
90#5000C2×C311yescharacteristic, complemented
91#4996C2×C311yescharacteristic, complemented
92C24×C32—21no—
93C2×C32×D4—22no—
94C2×C32×D4—22no—
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4—21no—
100C22×C32×C4—21no—
101C22×C32×C4—21no—
102C22×C32×C4C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C32×C4⋊C4D411yescharacteristic
109C32×C4⋊C4D411yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C22⋊C4—21no—
114C32×C22⋊C4—21no—
115C32×C22⋊C4—21no—
116C32×C22⋊C4—21no—
117C32×C22⋊C4D411yescharacteristic
118C32×C22⋊C4D411yescharacteristic
119C32×C42—21no—
120C32×C42C2311yescharacteristic
121C32×C42C2311yescharacteristic
122C3×#217—21no—
123C3×#214—22no—
124C3×#214—22no—
125C3×#213—22no—
126C3×#213—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3—21no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3118—31noSylow
142C22×C3×D4—21no—
143C22×C3×D4C2×D311yescharacteristic
144C22×C3×D4C22×C311yescharacteristic
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C2×C3×D8—31no—
148C2×C3×D8—31no—
149C3×C4⋊Q8—31no—
150C3×#126—61no—
151C3×#124—31no—
152C3×#124—61no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—61no—
156C3×#121—31no—
157C3×C4×Q8—31no—
158C3×C4×D4—22no—
159C3×C4×D4—22no—
160C3×C4×D4—21no—
161C3×C4×D4—21no—
162C3×C4×D4—21no—
163C3×C4×D4—21no—
164C3×C4×D4—21no—
165C3×C4×D4—21no—
166C3×C4×D4—21no—
167C3×C4×D4—21no—
168C3×C4×D4—31no—
169C3×C4×D4C2×D311yescharacteristic
170C3×C4×D4C2×D311yescharacteristic
171C3×C4×D4C2×D311yescharacteristic
172C3×C4×D4C2×D311yescharacteristic
173C3×C4×D4C22×C311yescharacteristic
174C3×C4×D4C22×C311yescharacteristic
175C3×C4×D4C22×C311yescharacteristic
176C3×C4×D4C22×C311yescharacteristic
177C3×#117—21no—
178C3×#117—21no—
179C3×#117C2×D311yescharacteristic
180C3×#117C2×D311yescharacteristic
181C3×#117C22×C311yescharacteristic
182C3×#117C22×C311yescharacteristic
183C2×C3×C22⋊C4—22no—
184C2×C3×C22⋊C4—22no—
185C2×C3×C22⋊C4—21no—
186C2×C3×C22⋊C4—21no—
187C2×C3×C22⋊C4—21no—
188C2×C3×C22⋊C4—21no—
189C2×#214C22×C311yescharacteristic
190C2×#214C22×C311yescharacteristic
191C2×#213C22×C311yescharacteristic
192C2×#213C22×C311yescharacteristic
193#930C22×C311yescharacteristic
194#924C22×C311yescharacteristic
195#898—21no—
196#896—21no—
197#885—21no—
198#883—21no—
199#875C22×C311yescharacteristic, complemented
200C4×D12C22×C311yescharacteristic, complemented
201#869C22×C311yescharacteristic, complemented
202C4×Dic6C22×C311yescharacteristic, complemented
203C3×#107—31no—
204C3×#107—31no—
205C3×#106—31no—
206C3×#106—31no—
207C3×C4⋊C8—31no—
208C3×C4⋊C8—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×C22⋊C8—31no—
218C3×C22⋊C8—31no—
219C3×#97—31no—
220C3×C4×C8—31no—
221#832C22×C311yescharacteristic
222#832C22×C311yescharacteristic
223#832C22×C311yescharacteristic
224#832C22×C311yescharacteristic
225#830C22×C311yescharacteristic
226#830C22×C311yescharacteristic
227#810C22×C311yescharacteristic, complemented
228#810C22×C311yescharacteristic, complemented
229#809C22×C311yescharacteristic, complemented
230#809C22×C311yescharacteristic, complemented
231#808C22×C311yescharacteristic, complemented
232#808C22×C311yescharacteristic, complemented
233#807C22×C311yescharacteristic, complemented
234#807C22×C311yescharacteristic, complemented
235C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
236C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
237#803C22×C311yescharacteristic, complemented
238C4×C3⋊C8C22×C311yescharacteristic, complemented
239C23×C32—24no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—81no—
243C23×C32—81no—
244C23×C32C2×D411yescharacteristic
245C22×C3×D3—21no—
246C32×D4—24no—
247C32×D4—21no—
248C32×D4—21no—
249C32×D4#4112yes—
250C32×D4#4112yes—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—81no—
256C2×C32×C4—81no—
257C2×C32×C4—81no—
258C2×C32×C4—81no—
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2×D411yescharacteristic
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C3×#67—81no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×C4×D3—81no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—81no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#542—31no—
280#518C3×D311yescharacteristic, complemented
281#485—31no—
282#482—31no—
283#476—31no—
284#474—31no—
285#463—31no—
286#463—31no—
287#450—31no—
288#447—31no—
289#442—31no—
290#440—31no—
291C4×SD16—31no—
292C4×D8—31no—
293#433—31no—
294C24×C3—22no—
295C24×C3—21no—
296C24×C3—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C2×C3×D4—22no—
300C2×C3×D4—24no—
301C2×C3×D4—24no—
302C2×C3×D4—22no—
303C2×C3×D4—22no—
304C2×C3×D4—22no—
305C2×C3×D4—22no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—31no—
311C2×C3×D4—61no—
312C2×C3×D4C22×D311yescharacteristic
313C2×C3×D4C22×D311yescharacteristic
314C2×C3×D4C23×C311yescharacteristic
315C2×C3×D4C23×C311yescharacteristic
316C22×C3×C4—22no—
317C22×C3×C4—22no—
318C22×C3×C4—22no—
319C22×C3×C4—22no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—61no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C23×C311yescharacteristic
332C2×#67—21no—
333C2×D12C23×C311yescharacteristic
334C2×C4×D3—21no—
335C2×Dic6—21no—
336C2×Dic6C23×C311yescharacteristic
337C3×SD16—62no—
338C3×SD16—62no—
339C3×D8—62no—
340C3×D8—62no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4#6711yescharacteristic
355C3×C4⋊C4#6711yescharacteristic
356C3×C4⋊C4C3×D411yescharacteristic
357C3×C4⋊C4C3×D411yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C23×C311yescharacteristic
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C22⋊C4—22no—
363C3×C22⋊C4—22no—
364C3×C22⋊C4—22no—
365C3×C22⋊C4—22no—
366C3×C22⋊C4—22no—
367C3×C22⋊C4—21no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—21no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—21no—
377C3×C22⋊C4—21no—
378C3×C22⋊C4—21no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C22⋊C4#6711yescharacteristic
385C3×C22⋊C4#6711yescharacteristic
386C3×C22⋊C4C3×D411yescharacteristic
387C3×C22⋊C4C3×D411yescharacteristic
388C3×C42—22no—
389C3×C42—21no—
390C3×C42—21no—
391C3×C42—21no—
392C3×C42—21no—
393C3×C42—61no—
394C3×C42C22×D311yescharacteristic
395C3×C42C22×D311yescharacteristic
396C3×C42C23×C311yescharacteristic
397C3×C42C23×C311yescharacteristic
398#217—21no—
399#214—22no—
400#214—22no—
401#213—22no—
402#213—22no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—21no—
407C4⋊Dic3—21no—
408C4⋊Dic3C23×C311yescharacteristic
409C4⋊Dic3C23×C311yescharacteristic
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412C4×Dic3—21no—
413C2×C3⋊C8C23×C311yescharacteristic
414C2×C3⋊C8C23×C311yescharacteristic
415C2×C3⋊C8C23×C311yescharacteristic
416C2×C3⋊C8C23×C311yescharacteristic
417C22×C32—21no—
418C22×C32—22no—
419C22×C32—22no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32—41no—
426C22×C32—84no—
427C22×C32C22×D411yescharacteristic
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4—21no—
436C32×C4—41no—
437C32×C4—41no—
438C32×C4C2×#4111yescharacteristic
439C32×C4C2×#4111yescharacteristic
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C22×D4C2×C3×D311yescharacteristic
444C2×SD16—31no—
445C2×SD16—31no—
446C2×D8—31no—
447C2×D8—31no—
448C4⋊Q8—31no—
449#126—61no—
450#124—31no—
451#124—61no—
452#123—61no—
453C22⋊Q8—31no—
454C22⋊Q8—61no—
455#121—31no—
456C4×Q8—31no—
457C4×D4—21no—
458C4×D4—21no—
459C4×D4—31no—
460C4×D4C2×C3×D311yescharacteristic
461C4×D4C2×C3×D311yescharacteristic
462C4×D4C2×C3×D311yescharacteristic
463C4×D4C2×C3×D311yescharacteristic
464#117C2×C3×D311yescharacteristic
465#117C2×C3×D311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468#107—31no—
469#107—31no—
470#106—31no—
471#106—31no—
472C4⋊C8—31no—
473C4⋊C8—31no—
474#103—31no—
475#103—31no—
476#102—31no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—31no—
481#102—31no—
482C22⋊C8—31no—
483C22⋊C8—31no—
484#97—31no—
485C4×C8—31no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—28no—
489C23×C3—24no—
490C23×C3—24no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—61no—
497C23×C3—81no—
498C23×C3—81no—
499C23×C3—81no—
500C23×C3—81no—
501C23×C3—82no—
502C23×C3—82no—
503C23×C3C2×#6711yescharacteristic
504C23×C3C2×C3×D411yescharacteristic
505C22×D3—21no—
506C3×Q8—61no—
507C3×Q8—61no—
508C3×Q8—241no—
509C3×D4—28no—
510C3×D4—24no—
511C3×D4—24no—
512C3×D4—22no—
513C3×D4—22no—
514C3×D4—21no—
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—22no—
519C3×D4—22no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—241no—
523C3×D4#23512yes—
524C3×D4#23512yes—
525C3×D4C3×#4112yes—
526C3×D4C3×#4112yes—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—81no—
549C2×C3×C4—81no—
550C2×C3×C4—81no—
551C2×C3×C4—81no—
552C2×C3×C4—81no—
553C2×C3×C4—81no—
554C2×C3×C4—81no—
555C2×C3×C4—81no—
556C2×C3×C4—82no—
557C2×C3×C4—82no—
558C2×C3×C4—82no—
559C2×C3×C4—82no—
560C2×C3×C4—241no—
561C2×C3×C4C2×#6711yescharacteristic
562C2×C3×C4C2×#6711yescharacteristic
563C2×C3×C4C2×#6711yescharacteristic
564C2×C3×C4C2×#6711yescharacteristic
565C2×C3×C4C2×#6711yescharacteristic
566C2×C3×C4C2×C3×D411yescharacteristic
567C2×C3×C4C2×C3×D411yescharacteristic
568C2×C3×C4C2×C3×D411yescharacteristic
569C2×C3×C4C2×C3×D411yescharacteristic
570C2×C3×C4C2×C3×D411yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572C2×C3×C4C24×C311yescharacteristic
573#67—81no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577D12—21no—
578D12—21no—
579C4×D3—81no—
580Dic6—21no—
581Dic6—21no—
582Dic6—81no—
583C3×C8—61no—
584C3×C8—61no—
585C3×C8—61no—
586C3×C8—61no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C3⋊C8—21no—
590C3⋊C8—21no—
591C2×C32—41no—
592C2×C32—42no—
593C2×C32—42no—
594C2×C32#52511yescharacteristic
595C2×C32#57611yescharacteristic
596C2×C32#57711yescharacteristic
597C3×D3—81no—
598C24—21no—
599C2×Q8—31no—
600C2×Q8—61no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—21no—
604C2×D4—31no—
605C2×D4—61no—
606C2×D4C22×C3×D311yescharacteristic
607C2×D4C22×C3×D311yescharacteristic
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—61no—
613C22×C4C22×C3×D311yescharacteristic
614SD16—62no—
615SD16—62no—
616D8—62no—
617D8—62no—
618C2×C8—31no—
619C2×C8—31no—
620C2×C8—31no—
621C2×C8—31no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4C3×#6711yescharacteristic
628C4⋊C4C3×#6711yescharacteristic
629C4⋊C4C22×C3×D311yescharacteristic
630C4⋊C4C22×C3×D311yescharacteristic
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4C3×#6711yescharacteristic
642C22⋊C4C3×#6711yescharacteristic
643C42—21no—
644C42—61no—
645C42C22×C3×D311yescharacteristic
646C42C22×C3×D311yescharacteristic
647C22×C3—22no—
648C22×C3—24no—
649C22×C3—24no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—21no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—88no—
676C22×C3—84no—
677C22×C3—84no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3C22×#6711yescharacteristic
682C22×C3C22×C3×D411yescharacteristic
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C3×C4—22no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—42no—
704C3×C4—42no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4—41no—
709C3×C4—121no—
710C3×C4—121no—
711C3×C4—121no—
712C3×C4C2×#23511yescharacteristic
713C3×C4C2×#23511yescharacteristic
714C3×C4C2×C3×#4111yescharacteristic
715C3×C4C2×C3×#4111yescharacteristic
716Dic3—41no—
717Dic3—41no—
718Dic3—41no—
719C32#311811yescharacteristic, complemented, Sylow
720C23—24no—
721C23—21no—
722C23—21no—
723C23—61no—
724C23—81no—
725C23—81no—
726C23C2×C3×#6711yescharacteristic
727Q8—61no—
728Q8—61no—
729Q8—241no—
730D4—24no—
731D4—21no—
732D4—21no—
733D4—61no—
734D4—61no—
735D4—241no—
736D4C3×#23512yes—
737D4C3×#23512yes—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—241no—
750C2×C4C2×C3×#6711yescharacteristic
751C2×C4C2×C3×#6711yescharacteristic
752C2×C4C2×C3×#6711yescharacteristic
753C2×C4C2×C3×#6711yescharacteristic
754C2×C4C2×C3×#6711yescharacteristic
755C2×C4C23×C3×D311yescharacteristic
756C8—61no—
757C8—61no—
758C8—61no—
759C8—61no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—42no—
764C2×C3—44no—
765C2×C3—44no—
766C2×C3—41no—
767C2×C3—42no—
768C2×C3—42no—
769C2×C3—41no—
770C2×C3—42no—
771C2×C3—42no—
772C2×C3—241no—
773C2×C3#579111yescharacteristic
774C2×C3#583511yescharacteristic
775C2×C3#583611yescharacteristic
776C2×C3C3×#52511yescharacteristic
777C2×C3C3×#57611yescharacteristic
778C2×C3C3×#57711yescharacteristic
779D3—81no—
780C22—21no—
781C22—22no—
782C22—22no—
783C22—21no—
784C22—21no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—84no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22C22×C3×#6711yescharacteristic
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—41no—
800C4—41no—
801C4—121no—
802C4—121no—
803C4—121no—
804C4C2×C3×#23511yescharacteristic
805C4C2×C3×#23511yescharacteristic
806C3—21no—
807C3#8254111yescharacteristic, direct product factor
808C3C3×#311811yescharacteristic, complemented
809C2—41no—
810C2—42no—
811C2—42no—
812C2—241no—
813C2C3×#579111yescharacteristic
814C2C3×#583511yescharacteristic
815C2C3×#583611yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#518C2
socleC22×C32C22×D4
prime radicalC3×#5217C2
hypercenterC3×#518D3
hypocenterC3C3×#3118
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#518

Complements

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

NH ≅ G/Ntype
1. C32×#518C2semidirect
2. C3×#5534C2semidirect
3. C3×#5218C2semidirect
5. C3×#5018C2semidirect
6. C3×C4×#214C2semidirect
7. C3×#5016C2semidirect
8. C3×#5016C2semidirect
9. C3×#5014C2semidirect
10. C3×C4×#213C2semidirect
11. C3×#5008C2semidirect
12. C3×#5007C2semidirect
13. C3×#5003C2semidirect
14. C3×#5000C2semidirect
15. C3×#4996C2semidirect
17. #82541C3direct (N × H)
39. C3×#875C22semidirect
40. C3×C4×D12C22semidirect
41. C3×#869C22semidirect
42. C3×C4×Dic6C22semidirect
49. C3×#810C22semidirect
50. C3×#810C22semidirect
51. C3×#809C22semidirect
52. C3×#809C22semidirect
53. C3×#808C22semidirect
54. C3×#808C22semidirect
55. C3×#807C22semidirect
56. C3×#807C22semidirect
57. C3×C4⋊(C3⋊C8)C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. C3×#803C22semidirect
60. C3×C4×C3⋊C8C22semidirect
63. C3×#518D3semidirect
64. C3×#518C2×C3semidirect
65. #5534C2×C3semidirect
79. #5218C2×C3semidirect
81. #5018C2×C3semidirect
82. C4×#214C2×C3semidirect
83. #5016C2×C3semidirect
84. #5016C2×C3semidirect
85. #5014C2×C3semidirect
86. C4×#213C2×C3semidirect
87. #5008C2×C3semidirect
88. #5007C2×C3semidirect
89. #5003C2×C3semidirect
90. #5000C2×C3semidirect
91. #4996C2×C3semidirect
199. #875C22×C3semidirect
200. C4×D12C22×C3semidirect
201. #869C22×C3semidirect
202. C4×Dic6C22×C3semidirect
227. #810C22×C3semidirect
228. #810C22×C3semidirect
229. #809C22×C3semidirect
230. #809C22×C3semidirect
231. #808C22×C3semidirect
232. #808C22×C3semidirect
233. #807C22×C3semidirect
234. #807C22×C3semidirect
235. C4⋊(C3⋊C8)C22×C3semidirect
236. C4⋊(C3⋊C8)C22×C3semidirect
237. #803C22×C3semidirect
238. C4×C3⋊C8C22×C3semidirect
280. #518C3×D3semidirect
719. C32#3118semidirect
807. C3#82541direct (N × H)
808. C3C3×#3118semidirect

Maximal subgroups

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

subgroupindex
C32×#5182
C3×#55342
C3×#52182
C3×#52172
C3×#50182
C3×C4×#2142
C3×#50162
C3×#50142
C3×C4×#2132
C3×#50082
C3×#50072
C3×#50032
C3×#50002
C3×#49962
C3×#31183
#825413