Finite Group Databasebeta

← C3×#25528 #10644135

Subgroups — C3×#25528 #10644135

Order 768.

1148 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3494C211yesmaximal, characteristic, complemented
2C3×#3094C211yesmaximal, characteristic, complemented
3C3×#3055C211yesmaximal, characteristic, complemented
4C3×#2619C211yesmaximal, characteristic, complemented
5C3×#2061C211yesmaximal, characteristic, complemented
6C3×#2037C211yesmaximal, characteristic, complemented
7C3×#2027C211yesmaximal, characteristic, complemented
8C3×#2002C211yesmaximal, characteristic, complemented
9C3×#1900C211yesmaximal, characteristic, complemented
10C3×#1897C211yesmaximal, characteristic, complemented
11C3×#1887C211yesmaximal, characteristic, complemented
12C3×#1883C211yesmaximal, characteristic, complemented
13C3×#1860C211yesmaximal, characteristic, complemented
14C3×#1856C211yesmaximal, characteristic, complemented
15C3×#1733C211yesmaximal, characteristic, complemented
16#25528C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C3×#555—21no—
20C3×#553—21no—
21C3×#553—21no—
22C3×#551—22no—
23C3×#547—21no—
24C3×#546—22no—
25C3×#544C2211yescharacteristic
26C3×#542—21no—
27C3×#540—21no—
28C3×#535C2211yescharacteristic
29C3×#532—21no—
30C2×C3×#127C2211yescharacteristic
31C3×#529—21no—
32C3×#525C2211yescharacteristic
33C2×C3×#121C2211yescharacteristic
34C2×C3×#121C2211yescharacteristic
35C3×#520C2211yescharacteristic
36C3×#518C2211yescharacteristic
37C2×C3×#117C2211yescharacteristic
38C2×C3×#117C2211yescharacteristic
39C3×#482—21no—
40C3×#482—21no—
41C3×#481—21no—
42C3×#480—21no—
43C3×#469—21no—
44C3×#468—21no—
45C3×#466—21no—
46C3×#465—21no—
47C3×#428C2211yescharacteristic
48C3×#428C2211yescharacteristic
49C3×#428C2211yescharacteristic
50C2×C3×#104C2211yescharacteristic
51C2×C3×#104C2211yescharacteristic
52C3×#418C2211yescharacteristic
53C3×#418C2211yescharacteristic
54C3×#418C2211yescharacteristic
55C3×#417C2211yescharacteristic
56C2×C3×#100C2211yescharacteristic
57C2×C3×#100C2211yescharacteristic
58C3×#407C2211yescharacteristic
59C3×#394—22no—
60C3×#392—22no—
61C3×#390C2211yescharacteristic
62C3×#390C2211yescharacteristic
63C3×#382C2211yescharacteristic
64C3×#343C2211yescharacteristic
65C3×#343C2211yescharacteristic
66C3×#339C2211yescharacteristic
67C3×#339C2211yescharacteristic
68C3×#339C2211yescharacteristic
69C3×#339C2211yescharacteristic
70C3×#339C2211yescharacteristic
71C3×#339C2211yescharacteristic
72#3494C2×C311yescharacteristic, complemented
73#3094C2×C311yescharacteristic, complemented
74#3055C2×C311yescharacteristic, complemented
75#2619C2×C311yescharacteristic, complemented
76#2061C2×C311yescharacteristic, complemented
77#2037C2×C311yescharacteristic, complemented
78#2027C2×C311yescharacteristic, complemented
79#2002C2×C311yescharacteristic, complemented
80#1900C2×C311yescharacteristic, complemented
81#1897C2×C311yescharacteristic, complemented
82#1887C2×C311yescharacteristic, complemented
83#1883C2×C311yescharacteristic, complemented
84#1860C2×C311yescharacteristic, complemented
85#1856C2×C311yescharacteristic, complemented
86#1733C2×C311yescharacteristic, complemented
87C2×C3×#41—22no—
88C2×C3×#41C2311yescharacteristic
89C22×C3×D4—21no—
90C22×C3×D4—22no—
91C22×C3×D4D412yes—
92C22×C3×D4C2311yescharacteristic
93C22×C3×D4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C3×AGL(1,ℤ/8)—22no—
96C3×AGL(1,ℤ/8)—41no—
97C2×C3×SD16—21no—
98C2×C3×D8—21no—
99C2×C3×M16—21no—
100C2×C3×M16—22no—
101C2×C3×M16—41no—
102C2×C3×M16C2311yescharacteristic
103C2×C3×M16C2311yescharacteristic
104C2×C3×M16C2311yescharacteristic
105C2×C3×M16C2311yescharacteristic
106C22×C3×C8—21no—
107C3×C4⋊Q8—21no—
108C3×C4⋊Q8—21no—
109C3×#127—21no—
110C3×#127—22no—
111C3×#127—41no—
112C3×#126—22no—
113C3×#126—22no—
114C3×#125—21no—
115C3×#125—21no—
116C3×#124—22no—
117C3×#124—22no—
118C3×#124—21no—
119C3×#123—22no—
120C3×#123—22no—
121C3×#123—22no—
122C3×#123—22no—
123C3×#123—21no—
124C3×C22⋊Q8—22no—
125C3×C22⋊Q8—22no—
126C3×C22⋊Q8D411yescharacteristic, complemented
127C3×C22⋊Q8D411yescharacteristic, complemented
128C3×#121—22no—
129C3×#121—22no—
130C3×#121—22no—
131C3×#121—21no—
132C3×#121—21no—
133C3×#121—21no—
134C3×#121—21no—
135C3×#121—21no—
136C3×#121—21no—
137C3×#121—21no—
138C3×#121—21no—
139C3×#121—21no—
140C3×#121—21no—
141C3×#121D411yescharacteristic, complemented
142C3×#121D411yescharacteristic, complemented
143C3×#120—21no—
144C3×#120—22no—
145C3×C4×Q8—21no—
146C3×C4×D4—22no—
147C3×C4×D4—22no—
148C3×C4×D4—21no—
149C3×C4×D4—22no—
150C3×C4×D4—21no—
151C3×C4×D4—21no—
152C3×C4×D4—21no—
153C3×C4×D4—21no—
154C3×C4×D4—21no—
155C3×C4×D4—21no—
156C3×#117—22no—
157C3×#117—21no—
158C3×#117—21no—
159C3×#117—21no—
160C3×#117—22no—
161C3×#117—41no—
162C3×#117D411yescharacteristic, complemented
163C3×#117D411yescharacteristic, complemented
164C3×#117C2311yescharacteristic
165C3×#117C2311yescharacteristic
166C3×#117C2311yescharacteristic
167C2×C3×C4⋊C4—21no—
168C2×C3×C4⋊C4—21no—
169C2×C3×C4⋊C4D411yescharacteristic, complemented
170C2×C3×C4⋊C4D411yescharacteristic, complemented
171C2×C3×C4⋊C4C2311yescharacteristic
172C2×C3×C4⋊C4C2311yescharacteristic
173C2×C3×C22⋊C4—21no—
174C2×C3×C22⋊C4—22no—
175C2×C3×C22⋊C4—21no—
176C2×C3×C22⋊C4—21no—
177C2×C3×C22⋊C4—22no—
178C2×C3×C22⋊C4—22no—
179C2×C3×C22⋊C4D412yes—
180C2×C3×C42—21no—
181C2×C3×C42C2311yescharacteristic
182C2×C3×C42C2311yescharacteristic
183C3×#107—21no—
184C3×#107—21no—
185C3×#107—21no—
186C3×#106—21no—
187C3×#106—21no—
188C3×#106—21no—
189C3×#104—22no—
190C3×#104—41no—
191C3×#103—21no—
192C3×#102—21no—
193C3×#102—21no—
194C3×#102—21no—
195C3×#102—21no—
196C3×#102—21no—
197C3×#102—21no—
198C3×#102—21no—
199C3×#100—22no—
200C3×#100—41no—
201C3×C22⋊C8—21no—
202C3×C22⋊C8—21no—
203C3×#95—22no—
204C2×AGL(1,ℤ/8)C22×C311yescharacteristic
205C22×M16C22×C311yescharacteristic
206#555—21no—
207#553—21no—
208#553—21no—
209#551—22no—
210#547—21no—
211#546—22no—
212#544C22×C311yescharacteristic
213#542—21no—
214#540—21no—
215#535C22×C311yescharacteristic
216#532—21no—
217C2×#127C22×C311yescharacteristic
218#529—21no—
219#525C22×C311yescharacteristic
220C2×#121C22×C311yescharacteristic
221C2×#121C22×C311yescharacteristic
222#520C22×C311yescharacteristic
223#518C22×C311yescharacteristic
224C2×#117C22×C311yescharacteristic
225C2×#117C22×C311yescharacteristic
226#482—21no—
227#482—21no—
228#481—21no—
229#480—21no—
230#469—21no—
231#468—21no—
232#466—21no—
233#465—21no—
234#428C22×C311yescharacteristic
235#428C22×C311yescharacteristic
236#428C22×C311yescharacteristic
237C2×#104C22×C311yescharacteristic
238C2×#104C22×C311yescharacteristic
239#418C22×C311yescharacteristic
240#418C22×C311yescharacteristic
241#418C22×C311yescharacteristic
242#417C22×C311yescharacteristic
243C2×#100C22×C311yescharacteristic
244C2×#100C22×C311yescharacteristic
245#407C22×C311yescharacteristic
246#394—22no—
247#392—22no—
248#390C22×C311yescharacteristic
249#390C22×C311yescharacteristic
250#382C22×C311yescharacteristic
251#343C22×C311yescharacteristic
252#343C22×C311yescharacteristic
253#339C22×C311yescharacteristic
254#339C22×C311yescharacteristic
255#339C22×C311yescharacteristic
256#339C22×C311yescharacteristic
257#339C22×C311yescharacteristic
258#339C22×C311yescharacteristic
259C24×C3—21no—
260C24×C3C2×D412yes—
261C24×C3C2×D411yescharacteristic
262C3×#41—21no—
263C3×#41—21no—
264C3×#41—21no—
265C3×#41—21no—
266C3×#41—84no—
267C2×C3×Q8—22no—
268C2×C3×Q8C2×D411yescharacteristic
269C2×C3×D4—21no—
270C2×C3×D4—22no—
271C2×C3×D4—21no—
272C2×C3×D4—22no—
273C2×C3×D4—22no—
274C2×C3×D4—21no—
275C2×C3×D4—22no—
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—21no—
283C2×C3×D4—21no—
284C2×C3×D4—21no—
285C2×C3×D4—21no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—44no—
289C2×C3×D4—41no—
290C2×C3×D4—41no—
291C2×C3×D4—82no—
292C2×C3×D4—82no—
293C2×C3×D4—82no—
294C2×C3×D4—82no—
295C2×C3×D4C2×D411yescharacteristic
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—22no—
303C22×C3×C4—22no—
304C22×C3×C4—22no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4C2×D411yescharacteristic
310C22×C3×C4C2×D411yescharacteristic
311C22×C3×C4C2×D411yescharacteristic
312C22×C3×C4C2×D411yescharacteristic
313C22×C3×C4C2×D411yescharacteristic
314C22×C3×C4C2×D412yes—
315C22×C3×C4C2411yescharacteristic
316C3×SD16—42no—
317C3×D8—42no—
318C3×M16—21no—
319C3×M16—21no—
320C3×M16—21no—
321C3×M16—21no—
322C3×M16—21no—
323C3×M16—21no—
324C3×M16—21no—
325C3×M16—42no—
326C3×M16#4112yescomplemented
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8—42no—
332C3×C4⋊C4—22no—
333C3×C4⋊C4—22no—
334C3×C4⋊C4—22no—
335C3×C4⋊C4—22no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—42no—
345C3×C4⋊C4C2×D411yescharacteristic
346C3×C4⋊C4C2×D411yescharacteristic
347C3×C4⋊C4C2×D411yescharacteristic
348C3×C4⋊C4C2×D411yescharacteristic
349C3×C4⋊C4C2×D411yescharacteristic
350C3×C4⋊C4C2×D411yescharacteristic
351C3×C22⋊C4—22no—
352C3×C22⋊C4—22no—
353C3×C22⋊C4—22no—
354C3×C22⋊C4—22no—
355C3×C22⋊C4—22no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—22no—
364C3×C22⋊C4—22no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—42no—
368C3×C22⋊C4—41no—
369C3×C22⋊C4—41no—
370C3×C22⋊C4—82no—
371C3×C22⋊C4—82no—
372C3×C42—22no—
373C3×C42—21no—
374C3×C42—21no—
375C3×C42—21no—
376C3×C42—21no—
377C3×C42—21no—
378C3×C42—21no—
379C3×C42—21no—
380C3×C42—21no—
381C3×C42#4112yescomplemented
382C2×#41—22no—
383C2×#41C23×C311yescharacteristic
384C22×D4—21no—
385C22×D4—22no—
386C22×D4C3×D412yes—
387C22×D4C23×C311yescharacteristic
388C22×D4C23×C311yescharacteristic
389C23×C4C23×C311yescharacteristic
390AGL(1,ℤ/8)—22no—
391AGL(1,ℤ/8)—41no—
392C2×SD16—21no—
393C2×D8—21no—
394C2×M16—21no—
395C2×M16—22no—
396C2×M16—41no—
397C2×M16C23×C311yescharacteristic
398C2×M16C23×C311yescharacteristic
399C2×M16C23×C311yescharacteristic
400C2×M16C23×C311yescharacteristic
401C22×C8—21no—
402C4⋊Q8—21no—
403C4⋊Q8—21no—
404#127—21no—
405#127—22no—
406#127—41no—
407#126—22no—
408#126—22no—
409#125—21no—
410#125—21no—
411#124—22no—
412#124—22no—
413#124—21no—
414#123—22no—
415#123—22no—
416#123—22no—
417#123—22no—
418#123—21no—
419C22⋊Q8—22no—
420C22⋊Q8—22no—
421C22⋊Q8C3×D411yescharacteristic, complemented
422C22⋊Q8C3×D411yescharacteristic, complemented
423#121—22no—
424#121—22no—
425#121—22no—
426#121—21no—
427#121—21no—
428#121—21no—
429#121—21no—
430#121—21no—
431#121—21no—
432#121—21no—
433#121—21no—
434#121—21no—
435#121—21no—
436#121C3×D411yescharacteristic, complemented
437#121C3×D411yescharacteristic, complemented
438#120—21no—
439#120—22no—
440C4×Q8—21no—
441C4×D4—22no—
442C4×D4—22no—
443C4×D4—21no—
444C4×D4—22no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4—21no—
451#117—22no—
452#117—21no—
453#117—21no—
454#117—21no—
455#117—22no—
456#117—41no—
457#117C3×D411yescharacteristic, complemented
458#117C3×D411yescharacteristic, complemented
459#117C23×C311yescharacteristic
460#117C23×C311yescharacteristic
461#117C23×C311yescharacteristic
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4C3×D411yescharacteristic, complemented
465C2×C4⋊C4C3×D411yescharacteristic, complemented
466C2×C4⋊C4C23×C311yescharacteristic
467C2×C4⋊C4C23×C311yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4C3×D412yes—
475C2×C42—21no—
476C2×C42C23×C311yescharacteristic
477C2×C42C23×C311yescharacteristic
478#107—21no—
479#107—21no—
480#107—21no—
481#106—21no—
482#106—21no—
483#106—21no—
484#104—22no—
485#104—41no—
486#103—21no—
487#102—21no—
488#102—21no—
489#102—21no—
490#102—21no—
491#102—21no—
492#102—21no—
493#102—21no—
494#100—22no—
495#100—41no—
496C22⋊C8—21no—
497C22⋊C8—21no—
498#95—22no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—22no—
502C23×C3—21no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—42no—
508C23×C3—42no—
509C23×C3—42no—
510C23×C3—42no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3#12011yescharacteristic
515C23×C3#12011yescharacteristic
516C23×C3C22×D411yescharacteristic
517C3×Q8—21no—
518C3×Q8—21no—
519C3×Q8—82no—
520C3×D4—21no—
521C3×D4—21no—
522C3×D4—44no—
523C3×D4—42no—
524C3×D4—41no—
525C3×D4—41no—
526C3×D4—41no—
527C3×D4—41no—
528C3×D4—41no—
529C3×D4—41no—
530C3×D4—41no—
531C3×D4—41no—
532C3×D4—41no—
533C3×D4—41no—
534C3×D4—81no—
535C3×D4—82no—
536C3×D4—82no—
537C3×D4—82no—
538C3×D4—88no—
539C3×D4—82no—
540C3×D4—82no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—42no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—42no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—42no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—81no—
572C2×C3×C4—82no—
573C2×C3×C4—82no—
574C2×C3×C4—82no—
575C2×C3×C4#12011yescharacteristic
576C2×C3×C4#12011yescharacteristic
577C2×C3×C4C22×D411yescharacteristic
578C2×C3×C4C22×D411yescharacteristic
579C2×C3×C4C2×#4111yescharacteristic
580C2×C3×C4C2×#4111yescharacteristic
581C2×C3×C4H(5,𝔽2)11yescharacteristic
582C2×C3×C42−1+411yescharacteristic
583C3×C8—22no—
584C3×C8—41no—
585C3×C8—41no—
586C3×C8—41no—
587C24—21no—
588C24C2×C3×D412yes—
589C24C2×C3×D411yescharacteristic
590#41—21no—
591#41—21no—
592#41—21no—
593#41—21no—
594#41—84no—
595C2×Q8—22no—
596C2×Q8C2×C3×D411yescharacteristic
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—44no—
617C2×D4—41no—
618C2×D4—41no—
619C2×D4—82no—
620C2×D4—82no—
621C2×D4—82no—
622C2×D4—82no—
623C2×D4C2×C3×D411yescharacteristic
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4C2×C3×D411yescharacteristic
638C22×C4C2×C3×D411yescharacteristic
639C22×C4C2×C3×D411yescharacteristic
640C22×C4C2×C3×D411yescharacteristic
641C22×C4C2×C3×D411yescharacteristic
642C22×C4C2×C3×D412yes—
643C22×C4C24×C311yescharacteristic
644SD16—42no—
645D8—42no—
646M16—21no—
647M16—21no—
648M16—21no—
649M16—21no—
650M16—21no—
651M16—21no—
652M16—21no—
653M16—42no—
654M16C3×#4112yescomplemented
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—42no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—42no—
673C4⋊C4C2×C3×D411yescharacteristic
674C4⋊C4C2×C3×D411yescharacteristic
675C4⋊C4C2×C3×D411yescharacteristic
676C4⋊C4C2×C3×D411yescharacteristic
677C4⋊C4C2×C3×D411yescharacteristic
678C4⋊C4C2×C3×D411yescharacteristic
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—42no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C22⋊C4—82no—
699C22⋊C4—82no—
700C42—22no—
701C42—21no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—21no—
706C42—21no—
707C42—21no—
708C42—21no—
709C42C3×#4112yescomplemented
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—41no—
719C22×C3—42no—
720C22×C3—41no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—41no—
724C22×C3—81no—
725C22×C3—81no—
726C22×C3—82no—
727C22×C3—82no—
728C22×C3—82no—
729C22×C3—82no—
730C22×C3—81no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3C2×#12011yescharacteristic
734C22×C3#54611yescharacteristic
735C22×C3#54711yescharacteristic
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—42no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—42no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—41no—
746C3×C4—41no—
747C3×C4—81no—
748C3×C4—81no—
749C3×C4#53211yescharacteristic
750C3×C4#53711yescharacteristic
751C3×C4#54611yescharacteristic
752C3×C4#54711yescharacteristic
753C23—21no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—22no—
758C23—22no—
759C23—41no—
760C23—41no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23C3×#12011yescharacteristic
769C23C3×#12011yescharacteristic
770C23C22×C3×D411yescharacteristic
771Q8—21no—
772Q8—21no—
773Q8—82no—
774D4—21no—
775D4—21no—
776D4—44no—
777D4—42no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—82no—
789D4—81no—
790D4—82no—
791D4—82no—
792D4—88no—
793D4—82no—
794D4—82no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—81no—
826C2×C4—82no—
827C2×C4—82no—
828C2×C4—82no—
829C2×C4C3×#12011yescharacteristic
830C2×C4C3×#12011yescharacteristic
831C2×C4C22×C3×D411yescharacteristic
832C2×C4C22×C3×D411yescharacteristic
833C2×C4C2×C3×#4111yescharacteristic
834C2×C4C2×C3×#4111yescharacteristic
835C2×C4C3×H(5,𝔽2)11yescharacteristic
836C2×C4C3×2−1+411yescharacteristic
837C8—22no—
838C8—41no—
839C8—41no—
840C8—41no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—41no—
844C2×C3—41no—
845C2×C3—81no—
846C2×C3—82no—
847C2×C3—161no—
848C2×C3#243011yescharacteristic
849C2×C3#301911yescharacteristic
850C2×C3#302111yescharacteristic
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—41no—
860C22—42no—
861C22—41no—
862C22—42no—
863C22—42no—
864C22—41no—
865C22—81no—
866C22—81no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22C2×C3×#12011yescharacteristic
875C22C3×#54611yescharacteristic
876C22C3×#54711yescharacteristic
877C4—21no—
878C4—21no—
879C4—42no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—42no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—81no—
889C4—81no—
890C4C3×#53211yescharacteristic
891C4C3×#53711yescharacteristic
892C4C3×#54611yescharacteristic
893C4C3×#54711yescharacteristic
894C3#2552811yescharacteristic, direct product factor, Sylow
895C2—21no—
896C2—21no—
897C2—41no—
898C2—41no—
899C2—82no—
900C2—81no—
901C2—161no—
902C2C3×#243011yescharacteristic
903C2C3×#301911yescharacteristic
904C2C3×#302111yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3494C2semidirect
2. C3×#3094C2semidirect
3. C3×#3055C2semidirect
4. C3×#2619C2semidirect
5. C3×#2061C2semidirect
6. C3×#2037C2semidirect
7. C3×#2027C2semidirect
8. C3×#2002C2semidirect
9. C3×#1900C2semidirect
10. C3×#1897C2semidirect
11. C3×#1887C2semidirect
12. C3×#1883C2semidirect
13. C3×#1860C2semidirect
14. C3×#1856C2semidirect
15. C3×#1733C2semidirect
16. #25528C3direct (N × H)
72. #3494C2×C3semidirect
73. #3094C2×C3semidirect
74. #3055C2×C3semidirect
75. #2619C2×C3semidirect
76. #2061C2×C3semidirect
77. #2037C2×C3semidirect
78. #2027C2×C3semidirect
79. #2002C2×C3semidirect
80. #1900C2×C3semidirect
81. #1897C2×C3semidirect
82. #1887C2×C3semidirect
83. #1883C2×C3semidirect
84. #1860C2×C3semidirect
85. #1856C2×C3semidirect
86. #1733C2×C3semidirect
126. C3×C22⋊Q8D4semidirect
127. C3×C22⋊Q8D4semidirect
141. C3×#121D4semidirect
142. C3×#121D4semidirect
162. C3×#117D4semidirect
163. C3×#117D4semidirect
169. C2×C3×C4⋊C4D4semidirect
170. C2×C3×C4⋊C4D4semidirect
326. C3×M16#41semidirect
381. C3×C42#41semidirect
421. C22⋊Q8C3×D4semidirect
422. C22⋊Q8C3×D4semidirect
436. #121C3×D4semidirect
437. #121C3×D4semidirect
457. #117C3×D4semidirect
458. #117C3×D4semidirect
464. C2×C4⋊C4C3×D4semidirect
465. C2×C4⋊C4C3×D4semidirect
654. M16C3×#41semidirect
709. C42C3×#41semidirect
894. C3#25528direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#34942
C3×#30942
C3×#30552
C3×#26192
C3×#20612
C3×#20372
C3×#20272
C3×#20022
C3×#19002
C3×#18972
C3×#18872
C3×#18832
C3×#18602
C3×#18562
C3×#17332
#255283