Finite Group Databasebeta

← C3×#30482 #10649089

Subgroups — C3×#30482 #10649089

Order 768.

1010 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3156C211yesmaximal, characteristic, complemented
2C2×C3×#471C211yesmaximal, characteristic, complemented
3C3×#3063C211yesmaximal, characteristic, complemented
4C2×C3×#455C211yesmaximal, characteristic, complemented
5C3×#3012C211yesmaximal, characteristic
6C3×#3009C211yesmaximal, characteristic, complemented
7C3×#2052C211yesmaximal, characteristic, complemented
8C3×#2038C211yesmaximal, characteristic, complemented
9C3×#2020C211yesmaximal, characteristic, complemented
10C3×#2015C211yesmaximal, characteristic, complemented
11C3×#2007C211yesmaximal, characteristic, complemented
12C3×#2003C211yesmaximal, characteristic, complemented
13C3×#1931C211yesmaximal, characteristic, complemented
14C3×#1929C211yesmaximal, characteristic, complemented
15C3×#1876C211yesmaximal, characteristic, complemented
16#30482C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×H(5,𝔽2)C2211yescharacteristic
18C2×C3×#137C2211yescharacteristic
19C2×C3×#137C2211yescharacteristic
20C2×C3×#137C2211yescharacteristic
21C2×C3×#137C2211yescharacteristic, complemented
22C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
23C2×C3×#135C2211yescharacteristic
24C22×C3×Q16C2211yescharacteristic, complemented
25C22×C3×SD16C2211yescharacteristic
26C2×C3×#131C2211yescharacteristic, complemented
27C3×#537C2211yescharacteristic
28C3×#536C2211yescharacteristic
29C3×#536C2211yescharacteristic, complemented
30C2×C3×#124C2211yescharacteristic
31C3×#497—21no—
32C3×#497—21no—
33C3×#495—21no—
34C3×#494—21no—
35C3×#471—24no—
36C3×#470—21no—
37C3×#468—21no—
38C3×#467—21no—
39C3×#465—21no—
40C3×#455—24no—
41C3×#452—21no—
42C3×#452—21no—
43C3×#452—21no—
44C3×#450—21no—
45C3×#450—21no—
46C3×#450—21no—
47C3×#449—21no—
48C3×#447—21no—
49C2×C3×#108C2211yescharacteristic, complemented
50C3×#428C2211yescharacteristic, complemented
51C2×C3×#104C2211yescharacteristic
52C2×C3×#104C2211yescharacteristic
53C2×C3×#104C2211yescharacteristic, complemented
54C3×#418C2211yescharacteristic
55C3×#417C2211yescharacteristic
56C3×#416C2211yescharacteristic
57C2×C3×#103C2211yescharacteristic, complemented
58C2×C3×#102C2211yescharacteristic
59C2×C3×#101C2211yescharacteristic, complemented
60C2×C3×#101C2211yescharacteristic, complemented
61C2×C3×#100C2211yescharacteristic
62C3×#408C2211yescharacteristic
63C3×#408C2211yescharacteristic
64C3×#405C2211yescharacteristic, complemented
65C3×#391C2211yescharacteristic, complemented
66C3×#343C2211yescharacteristic, complemented
67C3×#341C2211yescharacteristic, complemented
68C3×#339C2211yescharacteristic, complemented
69C3×#336C2211yescharacteristic, complemented
70#3156C2×C311yescharacteristic, complemented
71C2×#471C2×C311yescharacteristic, complemented
72#3063C2×C311yescharacteristic, complemented
73C2×#455C2×C311yescharacteristic, complemented
74#3012C2×C311yescharacteristic
75#3009C2×C311yescharacteristic, complemented
76#2052C2×C311yescharacteristic, complemented
77#2038C2×C311yescharacteristic, complemented
78#2020C2×C311yescharacteristic, complemented
79#2015C2×C311yescharacteristic, complemented
80#2007C2×C311yescharacteristic, complemented
81#2003C2×C311yescharacteristic, complemented
82#1931C2×C311yescharacteristic, complemented
83#1929C2×C311yescharacteristic, complemented
84#1876C2×C311yescharacteristic, complemented
85C3×H(5,𝔽2)—22no—
86C3×H(5,𝔽2)—41no—
87C3×H(5,𝔽2)—41no—
88C3×H(5,𝔽2)—41no—
89C2×C3×#41—21no—
90C2×C3×#41—21no—
91C2×C3×#41C2311yescharacteristic
92C2×C3×#41C2311yescharacteristic
93C2×C3×#41C2311yescharacteristic
94C22×C3×Q8C2311yescharacteristic
95C22×C3×Q8C2311yescharacteristic
96C22×C3×D4—21no—
97C22×C3×D4—21no—
98C22×C3×D4—41no—
99C22×C3×D4C2311yescharacteristic
100C3×#137—22no—
101C3×#137—22no—
102C3×#137—22no—
103C3×#137—41no—
104C3×#137—41no—
105C3×#137—41no—
106C3×#137—41no—
107C3×#137—41no—
108C3×AGL(1,ℤ/8)—22no—
109C3×AGL(1,ℤ/8)—41no—
110C3×#135—41no—
111C3×#135—41no—
112C2×C3×Q16—21no—
113C2×C3×Q16—21no—
114C2×C3×Q16—21no—
115C2×C3×Q16—21no—
116C2×C3×Q16—21no—
117C2×C3×Q16—21no—
118C2×C3×Q16—41no—
119C2×C3×Q16—41no—
120C2×C3×Q16D411yescharacteristic
121C2×C3×SD16—21no—
122C2×C3×SD16—22no—
123C2×C3×SD16—21no—
124C2×C3×SD16—21no—
125C2×C3×SD16—21no—
126C2×C3×SD16—21no—
127C2×C3×SD16—21no—
128C2×C3×SD16—21no—
129C2×C3×SD16—41no—
130C2×C3×SD16D411yescharacteristic
131C2×C3×SD16D411yescharacteristic
132C2×C3×D8—21no—
133C2×C3×D8D411yescharacteristic
134C3×#131—22no—
135C3×#131—41no—
136C2×C3×M16—21no—
137C2×C3×M16C2311yescharacteristic
138C2×C3×M16C2311yescharacteristic
139C2×C3×M16C2311yescharacteristic
140C2×C3×M16C2311yescharacteristic
141C22×C3×C8—21no—
142C22×C3×C8C2311yescharacteristic
143C22×C3×C8C2311yescharacteristic
144C3×C4⋊Q8—21no—
145C3×C4⋊Q8—21no—
146C3×#124—22no—
147C3×#124—21no—
148C3×#124—21no—
149C3×#124—41no—
150C3×#123—41no—
151C3×#123—41no—
152C3×C22⋊Q8—21no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8—21no—
155C3×C22⋊Q8—21no—
156C3×C22⋊Q8—21no—
157C3×C22⋊Q8—21no—
158C3×#121—21no—
159C3×#121—21no—
160C3×#121—41no—
161C3×#117C2311yescharacteristic
162C2×C3×C4⋊C4C2311yescharacteristic
163C2×C3×C22⋊C4—41no—
164C2×C3×C42C2311yescharacteristic
165C3×#108—22no—
166C3×#107—21no—
167C3×#106—21no—
168C3×#104—22no—
169C3×#104—22no—
170C3×#104—41no—
171C3×#103—21no—
172C3×#103—21no—
173C3×#103—21no—
174C3×#103D411yescharacteristic
175C3×#103D411yescharacteristic
176C3×#102—21no—
177C3×#102—21no—
178C3×#102—21no—
179C3×#102—21no—
180C3×#102—21no—
181C3×#102D411yescharacteristic
182C3×#102D411yescharacteristic
183C3×#101—22no—
184C3×#101—41no—
185C3×#100D414yescomplemented
186C3×C22⋊C8—21no—
187C3×C22⋊C8—21no—
188C3×C22⋊C8—21no—
189C3×C22⋊C8—21no—
190C3×#97—21no—
191C3×C4×C8—21no—
192C3×#95—41no—
193C2×H(5,𝔽2)C22×C311yescharacteristic
194C2×#137C22×C311yescharacteristic
195C2×#137C22×C311yescharacteristic
196C2×#137C22×C311yescharacteristic
197C2×#137C22×C311yescharacteristic, complemented
198C2×AGL(1,ℤ/8)C22×C311yescharacteristic
199C2×#135C22×C311yescharacteristic
200C22×Q16C22×C311yescharacteristic, complemented
201C22×SD16C22×C311yescharacteristic
202C2×#131C22×C311yescharacteristic, complemented
203#537C22×C311yescharacteristic
204#536C22×C311yescharacteristic
205#536C22×C311yescharacteristic, complemented
206C2×#124C22×C311yescharacteristic
207#497—21no—
208#497—21no—
209#495—21no—
210#494—21no—
211#471—24no—
212#470—21no—
213#468—21no—
214#467—21no—
215#465—21no—
216#455—24no—
217#452—21no—
218#452—21no—
219#452—21no—
220#450—21no—
221#450—21no—
222#450—21no—
223#449—21no—
224#447—21no—
225C2×#108C22×C311yescharacteristic, complemented
226#428C22×C311yescharacteristic, complemented
227C2×#104C22×C311yescharacteristic
228C2×#104C22×C311yescharacteristic
229C2×#104C22×C311yescharacteristic, complemented
230#418C22×C311yescharacteristic
231#417C22×C311yescharacteristic
232#416C22×C311yescharacteristic
233C2×#103C22×C311yescharacteristic, complemented
234C2×#102C22×C311yescharacteristic
235C2×#101C22×C311yescharacteristic, complemented
236C2×#101C22×C311yescharacteristic, complemented
237C2×#100C22×C311yescharacteristic
238#408C22×C311yescharacteristic
239#408C22×C311yescharacteristic
240#405C22×C311yescharacteristic, complemented
241#391C22×C311yescharacteristic, complemented
242#343C22×C311yescharacteristic, complemented
243#341C22×C311yescharacteristic, complemented
244#339C22×C311yescharacteristic, complemented
245#336C22×C311yescharacteristic, complemented
246C24×C3—21no—
247C24×C3—41no—
248C3×#41—21no—
249C3×#41—21no—
250C3×#41—21no—
251C3×#41—21no—
252C3×#41—21no—
253C3×#41—21no—
254C3×#41—21no—
255C3×#41—21no—
256C3×#41—21no—
257C3×#41—21no—
258C3×#41—21no—
259C3×#41—21no—
260C3×#41—42no—
261C3×#41—42no—
262C3×#41—42no—
263C3×#41—42no—
264C2×C3×Q8—21no—
265C2×C3×Q8—21no—
266C2×C3×Q8—21no—
267C2×C3×Q8—21no—
268C2×C3×Q8—21no—
269C2×C3×Q8—21no—
270C2×C3×Q8—21no—
271C2×C3×Q8—21no—
272C2×C3×Q8—21no—
273C2×C3×Q8—21no—
274C2×C3×Q8—21no—
275C2×C3×Q8—21no—
276C2×C3×Q8C2×D411yescharacteristic
277C2×C3×Q8C2×D411yescharacteristic
278C2×C3×Q8C2×D411yescharacteristic
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—41no—
288C2×C3×D4—41no—
289C2×C3×D4—42no—
290C2×C3×D4—42no—
291C2×C3×D4—42no—
292C2×C3×D4—42no—
293C2×C3×D4—44no—
294C2×C3×D4—44no—
295C2×C3×D4—41no—
296C2×C3×D4C2×D412yes—
297C2×C3×D4C2×D411yescharacteristic
298C2×C3×D4C2×D411yescharacteristic
299C2×C3×D4C2×D411yescharacteristic
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—41no—
308C22×C3×C4C2411yescharacteristic
309C3×Q16—41no—
310C3×Q16—42no—
311C3×Q16—42no—
312C3×Q16—42no—
313C3×Q16—42no—
314C3×Q16—42no—
315C3×Q16—42no—
316C3×SD16—41no—
317C3×SD16—41no—
318C3×SD16—42no—
319C3×SD16—42no—
320C3×SD16—42no—
321C3×SD16—42no—
322C3×SD16—42no—
323C3×SD16—42no—
324C3×SD16—42no—
325C3×D8—41no—
326C3×D8—42no—
327C3×M16—21no—
328C3×M16—21no—
329C3×M16—21no—
330C3×M16—21no—
331C3×M16—21no—
332C3×M16—21no—
333C3×M16—42no—
334C3×M16C2×D412yes—
335C3×M16C2×D412yes—
336C2×C3×C8—21no—
337C2×C3×C8—21no—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8—21no—
344C2×C3×C8—42no—
345C2×C3×C8C2×D411yescharacteristic
346C2×C3×C8C2×D411yescharacteristic
347C2×C3×C8C2×D411yescharacteristic
348C2×C3×C8C2×D411yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—41no—
352C3×C4⋊C4—41no—
353C3×C4⋊C4—41no—
354C3×C4⋊C4—41no—
355C3×C4⋊C4—41no—
356C3×C4⋊C4C2×D411yescharacteristic
357C3×C4⋊C4C2×D411yescharacteristic
358C3×C22⋊C4—21no—
359C3×C22⋊C4—41no—
360C3×C22⋊C4—41no—
361C3×C22⋊C4—41no—
362C3×C22⋊C4—41no—
363C3×C22⋊C4—41no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—44no—
366C3×C42—21no—
367C3×C42—21no—
368C3×C42—21no—
369H(5,𝔽2)—22no—
370H(5,𝔽2)—41no—
371H(5,𝔽2)—41no—
372H(5,𝔽2)—41no—
373C2×#41—21no—
374C2×#41—21no—
375C2×#41C23×C311yescharacteristic
376C2×#41C23×C311yescharacteristic
377C2×#41C23×C311yescharacteristic
378C22×Q8C23×C311yescharacteristic
379C22×Q8C23×C311yescharacteristic
380C22×D4—21no—
381C22×D4—21no—
382C22×D4—41no—
383C22×D4C23×C311yescharacteristic
384#137—22no—
385#137—22no—
386#137—22no—
387#137—41no—
388#137—41no—
389#137—41no—
390#137—41no—
391#137—41no—
392AGL(1,ℤ/8)—22no—
393AGL(1,ℤ/8)—41no—
394#135—41no—
395#135—41no—
396C2×Q16—21no—
397C2×Q16—21no—
398C2×Q16—21no—
399C2×Q16—21no—
400C2×Q16—21no—
401C2×Q16—21no—
402C2×Q16—41no—
403C2×Q16—41no—
404C2×Q16C3×D411yescharacteristic
405C2×SD16—21no—
406C2×SD16—22no—
407C2×SD16—21no—
408C2×SD16—21no—
409C2×SD16—21no—
410C2×SD16—21no—
411C2×SD16—21no—
412C2×SD16—21no—
413C2×SD16—41no—
414C2×SD16C3×D411yescharacteristic
415C2×SD16C3×D411yescharacteristic
416C2×D8—21no—
417C2×D8C3×D411yescharacteristic
418#131—22no—
419#131—41no—
420C2×M16—21no—
421C2×M16C23×C311yescharacteristic
422C2×M16C23×C311yescharacteristic
423C2×M16C23×C311yescharacteristic
424C2×M16C23×C311yescharacteristic
425C22×C8—21no—
426C22×C8C23×C311yescharacteristic
427C22×C8C23×C311yescharacteristic
428C4⋊Q8—21no—
429C4⋊Q8—21no—
430#124—22no—
431#124—21no—
432#124—21no—
433#124—41no—
434#123—41no—
435#123—41no—
436C22⋊Q8—21no—
437C22⋊Q8—21no—
438C22⋊Q8—21no—
439C22⋊Q8—21no—
440C22⋊Q8—21no—
441C22⋊Q8—21no—
442#121—21no—
443#121—21no—
444#121—41no—
445#117C23×C311yescharacteristic
446C2×C4⋊C4C23×C311yescharacteristic
447C2×C22⋊C4—41no—
448C2×C42C23×C311yescharacteristic
449#108—22no—
450#107—21no—
451#106—21no—
452#104—22no—
453#104—22no—
454#104—41no—
455#103—21no—
456#103—21no—
457#103—21no—
458#103C3×D411yescharacteristic
459#103C3×D411yescharacteristic
460#102—21no—
461#102—21no—
462#102—21no—
463#102—21no—
464#102—21no—
465#102C3×D411yescharacteristic
466#102C3×D411yescharacteristic
467#101—22no—
468#101—41no—
469#100C3×D414yescomplemented
470C22⋊C8—21no—
471C22⋊C8—21no—
472C22⋊C8—21no—
473C22⋊C8—21no—
474#97—21no—
475C4×C8—21no—
476#95—41no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—22no—
481C23×C3—44no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—81no—
485C23×C3—81no—
486C23×C3—161no—
487C23×C3—161no—
488C23×C3H(5,𝔽2)11yescharacteristic
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—41no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×Q8—41no—
499C3×Q8—41no—
500C3×Q8—41no—
501C3×Q8—41no—
502C3×Q8—41no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—22no—
508C3×D4—22no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—44no—
512C3×D4—44no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—41no—
518C3×D4—41no—
519C3×D4—41no—
520C3×D4—41no—
521C3×D4—161no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—44no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—81no—
545C2×C3×C4C22×D411yescharacteristic
546C2×C3×C4C22×D411yescharacteristic
547C2×C3×C4C22×D411yescharacteristic
548C2×C3×C4H(5,𝔽2)11yescharacteristic
549C2×C3×C4H(5,𝔽2)11yescharacteristic
550C2×C3×C4H(5,𝔽2)11yescharacteristic
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—22no—
556C3×C8—22no—
557C3×C8—41no—
558C3×C8—41no—
559C24—21no—
560C24—41no—
561#41—21no—
562#41—21no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—21no—
568#41—21no—
569#41—21no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—42no—
574#41—42no—
575#41—42no—
576#41—42no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8C2×C3×D411yescharacteristic
590C2×Q8C2×C3×D411yescharacteristic
591C2×Q8C2×C3×D411yescharacteristic
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—44no—
607C2×D4—44no—
608C2×D4—41no—
609C2×D4C2×C3×D412yes—
610C2×D4C2×C3×D411yescharacteristic
611C2×D4C2×C3×D411yescharacteristic
612C2×D4C2×C3×D411yescharacteristic
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—41no—
621C22×C4C24×C311yescharacteristic
622Q16—41no—
623Q16—42no—
624Q16—42no—
625Q16—42no—
626Q16—42no—
627Q16—42no—
628Q16—42no—
629SD16—41no—
630SD16—41no—
631SD16—42no—
632SD16—42no—
633SD16—42no—
634SD16—42no—
635SD16—42no—
636SD16—42no—
637SD16—42no—
638D8—41no—
639D8—42no—
640M16—21no—
641M16—21no—
642M16—21no—
643M16—21no—
644M16—21no—
645M16—21no—
646M16—42no—
647M16C2×C3×D412yes—
648M16C2×C3×D412yes—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—42no—
658C2×C8C2×C3×D411yescharacteristic
659C2×C8C2×C3×D411yescharacteristic
660C2×C8C2×C3×D411yescharacteristic
661C2×C8C2×C3×D411yescharacteristic
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—41no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4C2×C3×D411yescharacteristic
670C4⋊C4C2×C3×D411yescharacteristic
671C22⋊C4—21no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—44no—
679C42—21no—
680C42—21no—
681C42—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—42no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—82no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—161no—
698C22×C3—164no—
699C22×C3#53511yescharacteristic
700C22×C3D4211yescharacteristic
701C22×C3#56011yescharacteristic
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—81no—
708C3×C4—81no—
709C3×C4—81no—
710C3×C4—81no—
711C3×C4#53411yescharacteristic
712C3×C4#53511yescharacteristic
713C3×C4D4211yescharacteristic
714C3×C4D4211yescharacteristic
715C23—21no—
716C23—21no—
717C23—21no—
718C23—22no—
719C23—44no—
720C23—41no—
721C23—41no—
722C23—81no—
723C23—81no—
724C23—161no—
725C23—161no—
726C23C3×H(5,𝔽2)11yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—41no—
734Q8—41no—
735Q8—41no—
736Q8—41no—
737Q8—41no—
738Q8—41no—
739Q8—41no—
740Q8—41no—
741D4—21no—
742D4—21no—
743D4—21no—
744D4—21no—
745D4—22no—
746D4—22no—
747D4—21no—
748D4—21no—
749D4—44no—
750D4—44no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—161no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—44no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—81no—
783C2×C4C22×C3×D411yescharacteristic
784C2×C4C22×C3×D411yescharacteristic
785C2×C4C22×C3×D411yescharacteristic
786C2×C4C3×H(5,𝔽2)11yescharacteristic
787C2×C4C3×H(5,𝔽2)11yescharacteristic
788C2×C4C3×H(5,𝔽2)11yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—22no—
794C8—22no—
795C8—41no—
796C8—41no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—81no—
800C2×C3—81no—
801C2×C3—81no—
802C2×C3—82no—
803C2×C3#266911yescharacteristic
804C2×C3#328911yescharacteristic
805C2×C3#329011yescharacteristic
806C22—21no—
807C22—21no—
808C22—41no—
809C22—41no—
810C22—42no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—82no—
819C22—81no—
820C22—81no—
821C22—161no—
822C22—164no—
823C22C3×#53511yescharacteristic
824C22C3×D4211yescharacteristic
825C22C3×#56011yescharacteristic
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4—81no—
835C4C3×#53411yescharacteristic
836C4C3×#53511yescharacteristic
837C4C3×D4211yescharacteristic
838C4C3×D4211yescharacteristic
839C3#3048211yescharacteristic, direct product factor, Sylow
840C2—21no—
841C2—21no—
842C2—81no—
843C2—81no—
844C2—81no—
845C2—82no—
846C2C3×#266911yescharacteristic
847C2C3×#328911yescharacteristic
848C2C3×#329011yescharacteristic
subgroupG/H
center, socleC22×C3D42
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#3012C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3156C2semidirect
2. C2×C3×#471C2semidirect
3. C3×#3063C2semidirect
4. C2×C3×#455C2semidirect
6. C3×#3009C2semidirect
7. C3×#2052C2semidirect
8. C3×#2038C2semidirect
9. C3×#2020C2semidirect
10. C3×#2015C2semidirect
11. C3×#2007C2semidirect
12. C3×#2003C2semidirect
13. C3×#1931C2semidirect
14. C3×#1929C2semidirect
15. C3×#1876C2semidirect
16. #30482C3direct (N × H)
21. C2×C3×#137C22semidirect
24. C22×C3×Q16C22semidirect
26. C2×C3×#131C22semidirect
29. C3×#536C22semidirect
49. C2×C3×#108C22semidirect
50. C3×#428C22semidirect
53. C2×C3×#104C22semidirect
57. C2×C3×#103C22semidirect
59. C2×C3×#101C22semidirect
60. C2×C3×#101C22semidirect
64. C3×#405C22semidirect
65. C3×#391C22semidirect
66. C3×#343C22semidirect
67. C3×#341C22semidirect
68. C3×#339C22semidirect
69. C3×#336C22semidirect
70. #3156C2×C3semidirect
71. C2×#471C2×C3semidirect
72. #3063C2×C3semidirect
73. C2×#455C2×C3semidirect
75. #3009C2×C3semidirect
76. #2052C2×C3semidirect
77. #2038C2×C3semidirect
78. #2020C2×C3semidirect
79. #2015C2×C3semidirect
80. #2007C2×C3semidirect
81. #2003C2×C3semidirect
82. #1931C2×C3semidirect
83. #1929C2×C3semidirect
84. #1876C2×C3semidirect
185. C3×#100D4semidirect
197. C2×#137C22×C3semidirect
200. C22×Q16C22×C3semidirect
202. C2×#131C22×C3semidirect
205. #536C22×C3semidirect
225. C2×#108C22×C3semidirect
226. #428C22×C3semidirect
229. C2×#104C22×C3semidirect
233. C2×#103C22×C3semidirect
235. C2×#101C22×C3semidirect
236. C2×#101C22×C3semidirect
240. #405C22×C3semidirect
241. #391C22×C3semidirect
242. #343C22×C3semidirect
243. #341C22×C3semidirect
244. #339C22×C3semidirect
245. #336C22×C3semidirect
469. #100C3×D4semidirect
839. C3#30482direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#31562
C2×C3×#4712
C3×#30632
C2×C3×#4552
C3×#30122
C3×#30092
C3×#20522
C3×#20382
C3×#20202
C3×#20152
C3×#20072
C3×#20032
C3×#19312
C3×#19292
C3×#18762
#304823