Finite Group Databasebeta

← C3×#30481 #10649088

Subgroups — C3×#30481 #10649088

Order 768.

984 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3156C211yesmaximal, characteristic, complemented
2C2×C3×#473C211yesmaximal, characteristic, complemented
3C3×#3063C211yesmaximal, characteristic, complemented
4C2×C3×#456C211yesmaximal, characteristic, complemented
5C3×#3013C211yesmaximal, characteristic
6C3×#3011C211yesmaximal, characteristic, complemented
7C3×#2052C211yesmaximal, characteristic, complemented
8C3×#2038C211yesmaximal, characteristic, complemented
9C3×#2020C211yesmaximal, characteristic, complemented
10C3×#2016C211yesmaximal, characteristic, complemented
11C3×#2007C211yesmaximal, characteristic, complemented
12C3×#2005C211yesmaximal, characteristic, complemented
13C3×#1930C211yesmaximal, characteristic, complemented
14C3×#1929C211yesmaximal, characteristic, complemented
15C3×#1876C211yesmaximal, characteristic, complemented
16#30481C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×2−1+4C2211yescharacteristic
18C2×C3×#137C2211yescharacteristic
19C2×C3×#137C2211yescharacteristic
20C2×C3×#137C2211yescharacteristic
21C2×C3×#137C2211yescharacteristic
22C2×C3×#137C2211yescharacteristic
23C2×C3×#135C2211yescharacteristic
24C22×C3×Q16C2211yescharacteristic
25C22×C3×Q16C2211yescharacteristic
26C2×C3×#131C2211yescharacteristic
27C3×#537C2211yescharacteristic
28C3×#536C2211yescharacteristic
29C3×#536C2211yescharacteristic
30C2×C3×C4⋊Q8C2211yescharacteristic
31C3×#497—21no—
32C3×#497—21no—
33C3×#495—21no—
34C3×#494—21no—
35C3×#473—24no—
36C3×#470—21no—
37C3×#468—21no—
38C3×#467—21no—
39C3×#465—21no—
40C3×#456—24no—
41C3×#452—21no—
42C3×#452—21no—
43C3×#452—21no—
44C3×#451—21no—
45C3×#451—21no—
46C3×#451—21no—
47C3×#449—21no—
48C3×#448—21no—
49C2×C3×#108C2211yescharacteristic
50C3×#428C2211yescharacteristic
51C2×C3×#104C2211yescharacteristic
52C2×C3×#104C2211yescharacteristic
53C2×C3×#104C2211yescharacteristic
54C3×#419C2211yescharacteristic
55C3×#417C2211yescharacteristic
56C3×#416C2211yescharacteristic
57C2×C3×#103C2211yescharacteristic
58C2×C3×#103C2211yescharacteristic
59C2×C3×#101C2211yescharacteristic
60C2×C3×#101C2211yescharacteristic
61C2×C3×#101C2211yescharacteristic
62C3×#408C2211yescharacteristic
63C3×#408C2211yescharacteristic
64C3×#405C2211yescharacteristic
65C3×#391C2211yescharacteristic
66C3×#343C2211yescharacteristic
67C3×#341C2211yescharacteristic
68C3×#339C2211yescharacteristic
69C3×#336C2211yescharacteristic
70#3156C2×C311yescharacteristic, complemented
71C2×#473C2×C311yescharacteristic, complemented
72#3063C2×C311yescharacteristic, complemented
73C2×#456C2×C311yescharacteristic, complemented
74#3013C2×C311yescharacteristic
75#3011C2×C311yescharacteristic, complemented
76#2052C2×C311yescharacteristic, complemented
77#2038C2×C311yescharacteristic, complemented
78#2020C2×C311yescharacteristic, complemented
79#2016C2×C311yescharacteristic, complemented
80#2007C2×C311yescharacteristic, complemented
81#2005C2×C311yescharacteristic, complemented
82#1930C2×C311yescharacteristic, complemented
83#1929C2×C311yescharacteristic, complemented
84#1876C2×C311yescharacteristic, complemented
85C3×2−1+4—22no—
86C3×2−1+4—41no—
87C3×2−1+4—41no—
88C3×2−1+4—41no—
89C2×C3×#41—21no—
90C2×C3×#41—21no—
91C2×C3×#41—41no—
92C2×C3×#41C2311yescharacteristic
93C2×C3×#41C2311yescharacteristic
94C2×C3×#41C2311yescharacteristic
95C22×C3×Q8—21no—
96C22×C3×Q8—21no—
97C22×C3×Q8C2311yescharacteristic
98C22×C3×Q8C2311yescharacteristic
99C22×C3×Q8C2311yescharacteristic
100C3×#137—22no—
101C3×#137—22no—
102C3×#137—22no—
103C3×#137—22no—
104C3×#137—41no—
105C3×#137—41no—
106C3×#137—41no—
107C3×#137—41no—
108C3×#137—41no—
109C3×#137—41no—
110C3×#135—41no—
111C3×#135—41no—
112C2×C3×Q16—22no—
113C2×C3×Q16—21no—
114C2×C3×Q16—21no—
115C2×C3×Q16—21no—
116C2×C3×Q16—21no—
117C2×C3×Q16—21no—
118C2×C3×Q16—21no—
119C2×C3×Q16—21no—
120C2×C3×Q16—21no—
121C2×C3×Q16—21no—
122C2×C3×Q16—41no—
123C2×C3×Q16—41no—
124C2×C3×Q16—41no—
125C2×C3×Q16D411yescharacteristic
126C2×C3×SD16—21no—
127C2×C3×SD16—21no—
128C2×C3×SD16—21no—
129C2×C3×SD16—21no—
130C2×C3×SD16—21no—
131C2×C3×SD16D411yescharacteristic
132C2×C3×SD16D411yescharacteristic
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—22no—
145C3×C4⋊Q8—21no—
146C3×C4⋊Q8—21no—
147C3×C4⋊Q8—41no—
148C3×#124—21no—
149C3×#124—21no—
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⋊C4—41no—
163C2×C3×C4⋊C4C2311yescharacteristic
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×#103—21no—
175C3×#103—21no—
176C3×#103—21no—
177C3×#103—21no—
178C3×#103D411yescharacteristic
179C3×#103D411yescharacteristic
180C3×#102—21no—
181C3×#102D411yescharacteristic
182C3×#102D411yescharacteristic
183C3×#101—22no—
184C3×#101—41no—
185C3×#101D414yescomplemented
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—
193C2×2−1+4C22×C311yescharacteristic
194C2×#137C22×C311yescharacteristic
195C2×#137C22×C311yescharacteristic
196C2×#137C22×C311yescharacteristic
197C2×#137C22×C311yescharacteristic
198C2×#137C22×C311yescharacteristic
199C2×#135C22×C311yescharacteristic
200C22×Q16C22×C311yescharacteristic
201C22×Q16C22×C311yescharacteristic
202C2×#131C22×C311yescharacteristic
203#537C22×C311yescharacteristic
204#536C22×C311yescharacteristic
205#536C22×C311yescharacteristic
206C2×C4⋊Q8C22×C311yescharacteristic
207#497—21no—
208#497—21no—
209#495—21no—
210#494—21no—
211#473—24no—
212#470—21no—
213#468—21no—
214#467—21no—
215#465—21no—
216#456—24no—
217#452—21no—
218#452—21no—
219#452—21no—
220#451—21no—
221#451—21no—
222#451—21no—
223#449—21no—
224#448—21no—
225C2×#108C22×C311yescharacteristic
226#428C22×C311yescharacteristic
227C2×#104C22×C311yescharacteristic
228C2×#104C22×C311yescharacteristic
229C2×#104C22×C311yescharacteristic
230#419C22×C311yescharacteristic
231#417C22×C311yescharacteristic
232#416C22×C311yescharacteristic
233C2×#103C22×C311yescharacteristic
234C2×#103C22×C311yescharacteristic
235C2×#101C22×C311yescharacteristic
236C2×#101C22×C311yescharacteristic
237C2×#101C22×C311yescharacteristic
238#408C22×C311yescharacteristic
239#408C22×C311yescharacteristic
240#405C22×C311yescharacteristic
241#391C22×C311yescharacteristic
242#343C22×C311yescharacteristic
243#341C22×C311yescharacteristic
244#339C22×C311yescharacteristic
245#336C22×C311yescharacteristic
246C3×#41—21no—
247C3×#41—21no—
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—44no—
259C3×#41—42no—
260C3×#41—42no—
261C3×#41—42no—
262C3×#41—42no—
263C3×#41—44no—
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×Q8—21no—
277C2×C3×Q8—21no—
278C2×C3×Q8—21no—
279C2×C3×Q8—21no—
280C2×C3×Q8—21no—
281C2×C3×Q8—41no—
282C2×C3×Q8—42no—
283C2×C3×Q8—42no—
284C2×C3×Q8—42no—
285C2×C3×Q8—42no—
286C2×C3×Q8C2×D412yes—
287C2×C3×Q8C2×D411yescharacteristic
288C2×C3×Q8C2×D411yescharacteristic
289C2×C3×Q8C2×D411yescharacteristic
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—41no—
294C2×C3×D4—41no—
295C2×C3×D4C2×D411yescharacteristic
296C2×C3×D4C2×D411yescharacteristic
297C2×C3×D4C2×D411yescharacteristic
298C22×C3×C4—21no—
299C22×C3×C4—21no—
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—41no—
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×Q16—42no—
317C3×Q16—42no—
318C3×Q16—42no—
319C3×SD16—41no—
320C3×SD16—41no—
321C3×SD16—42no—
322C3×SD16—42no—
323C3×SD16—42no—
324C3×SD16—42no—
325C3×SD16—42no—
326C3×D8—41no—
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⋊C4—44no—
357C3×C4⋊C4C2×D411yescharacteristic
358C3×C4⋊C4C2×D411yescharacteristic
359C3×C22⋊C4—21no—
360C3×C22⋊C4—41no—
361C3×C22⋊C4—41no—
362C3×C22⋊C4—41no—
363C3×C22⋊C4—41no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—41no—
366C3×C42—21no—
367C3×C42—21no—
368C3×C42—21no—
3692−1+4—22no—
3702−1+4—41no—
3712−1+4—41no—
3722−1+4—41no—
373C2×#41—21no—
374C2×#41—21no—
375C2×#41—41no—
376C2×#41C23×C311yescharacteristic
377C2×#41C23×C311yescharacteristic
378C2×#41C23×C311yescharacteristic
379C22×Q8—21no—
380C22×Q8—21no—
381C22×Q8C23×C311yescharacteristic
382C22×Q8C23×C311yescharacteristic
383C22×Q8C23×C311yescharacteristic
384#137—22no—
385#137—22no—
386#137—22no—
387#137—22no—
388#137—41no—
389#137—41no—
390#137—41no—
391#137—41no—
392#137—41no—
393#137—41no—
394#135—41no—
395#135—41no—
396C2×Q16—22no—
397C2×Q16—21no—
398C2×Q16—21no—
399C2×Q16—21no—
400C2×Q16—21no—
401C2×Q16—21no—
402C2×Q16—21no—
403C2×Q16—21no—
404C2×Q16—21no—
405C2×Q16—21no—
406C2×Q16—41no—
407C2×Q16—41no—
408C2×Q16—41no—
409C2×Q16C3×D411yescharacteristic
410C2×SD16—21no—
411C2×SD16—21no—
412C2×SD16—21no—
413C2×SD16—21no—
414C2×SD16—21no—
415C2×SD16C3×D411yescharacteristic
416C2×SD16C3×D411yescharacteristic
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—22no—
429C4⋊Q8—21no—
430C4⋊Q8—21no—
431C4⋊Q8—41no—
432#124—21no—
433#124—21no—
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⋊C4—41no—
447C2×C4⋊C4C23×C311yescharacteristic
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#103—21no—
459#103—21no—
460#103—21no—
461#103—21no—
462#103C3×D411yescharacteristic
463#103C3×D411yescharacteristic
464#102—21no—
465#102C3×D411yescharacteristic
466#102C3×D411yescharacteristic
467#101—22no—
468#101—41no—
469#101C3×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×C3H(5,𝔽2)11yescharacteristic
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—22no—
485C3×Q8—21no—
486C3×Q8—22no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—44no—
490C3×Q8—41no—
491C3×Q8—41no—
492C3×Q8—41no—
493C3×Q8—41no—
494C3×Q8—41no—
495C3×Q8—41no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×Q8—41no—
499C3×Q8—41no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—44no—
507C3×D4—41no—
508C3×D4—41no—
509C3×D4—41no—
510C3×D4—41no—
511C3×D4—41no—
512C3×D4—41no—
513C3×D4—161no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—41no—
522C2×C3×C4—44no—
523C2×C3×C4—44no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
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—81no—
541C2×C3×C4C22×D411yescharacteristic
542C2×C3×C4C22×D411yescharacteristic
543C2×C3×C4C22×D411yescharacteristic
544C2×C3×C4H(5,𝔽2)11yescharacteristic
545C2×C3×C4H(5,𝔽2)11yescharacteristic
546C2×C3×C4H(5,𝔽2)11yescharacteristic
547C3×C8—21no—
548C3×C8—21no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—22no—
552C3×C8—22no—
553C3×C8—41no—
554C3×C8—41no—
555#41—21no—
556#41—21no—
557#41—21no—
558#41—21no—
559#41—21no—
560#41—21no—
561#41—21no—
562#41—21no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—44no—
568#41—42no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—44no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
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×Q8—21no—
590C2×Q8—41no—
591C2×Q8—42no—
592C2×Q8—42no—
593C2×Q8—42no—
594C2×Q8—42no—
595C2×Q8C2×C3×D412yes—
596C2×Q8C2×C3×D411yescharacteristic
597C2×Q8C2×C3×D411yescharacteristic
598C2×Q8C2×C3×D411yescharacteristic
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4C2×C3×D411yescharacteristic
605C2×D4C2×C3×D411yescharacteristic
606C2×D4C2×C3×D411yescharacteristic
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4C24×C311yescharacteristic
618Q16—41no—
619Q16—42no—
620Q16—42no—
621Q16—42no—
622Q16—42no—
623Q16—42no—
624Q16—42no—
625Q16—42no—
626Q16—42no—
627Q16—42no—
628SD16—41no—
629SD16—41no—
630SD16—42no—
631SD16—42no—
632SD16—42no—
633SD16—42no—
634SD16—42no—
635D8—41no—
636M16—21no—
637M16—21no—
638M16—21no—
639M16—21no—
640M16—21no—
641M16—21no—
642M16—42no—
643M16C2×C3×D412yes—
644M16C2×C3×D412yes—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—42no—
654C2×C8C2×C3×D411yescharacteristic
655C2×C8C2×C3×D411yescharacteristic
656C2×C8C2×C3×D411yescharacteristic
657C2×C8C2×C3×D411yescharacteristic
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—41no—
661C4⋊C4—41no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4—44no—
666C4⋊C4C2×C3×D411yescharacteristic
667C4⋊C4C2×C3×D411yescharacteristic
668C22⋊C4—21no—
669C22⋊C4—41no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C42—21no—
676C42—21no—
677C42—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3#53511yescharacteristic
690C22×C3D4211yescharacteristic
691C22×C3#56011yescharacteristic
692C3×C4—42no—
693C3×C4—42no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—81no—
700C3×C4—81no—
701C3×C4—81no—
702C3×C4#53411yescharacteristic
703C3×C4#53511yescharacteristic
704C3×C4D4211yescharacteristic
705C3×C4D4211yescharacteristic
706C23—21no—
707C23—21no—
708C23—21no—
709C23C3×H(5,𝔽2)11yescharacteristic
710Q8—21no—
711Q8—21no—
712Q8—21no—
713Q8—22no—
714Q8—21no—
715Q8—22no—
716Q8—21no—
717Q8—21no—
718Q8—44no—
719Q8—41no—
720Q8—41no—
721Q8—41no—
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726Q8—41no—
727Q8—41no—
728Q8—41no—
729D4—21no—
730D4—21no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—21no—
735D4—44no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—161no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—41no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—81no—
770C2×C4C22×C3×D411yescharacteristic
771C2×C4C22×C3×D411yescharacteristic
772C2×C4C22×C3×D411yescharacteristic
773C2×C4C3×H(5,𝔽2)11yescharacteristic
774C2×C4C3×H(5,𝔽2)11yescharacteristic
775C2×C4C3×H(5,𝔽2)11yescharacteristic
776C8—21no—
777C8—21no—
778C8—21no—
779C8—21no—
780C8—22no—
781C8—22no—
782C8—41no—
783C8—41no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—81no—
787C2×C3—81no—
788C2×C3—81no—
789C2×C3#266911yescharacteristic
790C2×C3#328911yescharacteristic
791C2×C3#329311yescharacteristic
792C22—21no—
793C22—21no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22C3×#53511yescharacteristic
804C22C3×D4211yescharacteristic
805C22C3×#56011yescharacteristic
806C4—42no—
807C4—42no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—81no—
814C4—81no—
815C4—81no—
816C4C3×#53411yescharacteristic
817C4C3×#53511yescharacteristic
818C4C3×D4211yescharacteristic
819C4C3×D4211yescharacteristic
820C3#3048111yescharacteristic, direct product factor, Sylow
821C2—21no—
822C2—21no—
823C2—81no—
824C2—81no—
825C2—81no—
826C2C3×#266911yescharacteristic
827C2C3×#328911yescharacteristic
828C2C3×#329311yescharacteristic
subgroupG/H
center, socleC22×C3D42
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#3013C2
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×#473C2semidirect
3. C3×#3063C2semidirect
4. C2×C3×#456C2semidirect
6. C3×#3011C2semidirect
7. C3×#2052C2semidirect
8. C3×#2038C2semidirect
9. C3×#2020C2semidirect
10. C3×#2016C2semidirect
11. C3×#2007C2semidirect
12. C3×#2005C2semidirect
13. C3×#1930C2semidirect
14. C3×#1929C2semidirect
15. C3×#1876C2semidirect
16. #30481C3direct (N × H)
70. #3156C2×C3semidirect
71. C2×#473C2×C3semidirect
72. #3063C2×C3semidirect
73. C2×#456C2×C3semidirect
75. #3011C2×C3semidirect
76. #2052C2×C3semidirect
77. #2038C2×C3semidirect
78. #2020C2×C3semidirect
79. #2016C2×C3semidirect
80. #2007C2×C3semidirect
81. #2005C2×C3semidirect
82. #1930C2×C3semidirect
83. #1929C2×C3semidirect
84. #1876C2×C3semidirect
185. C3×#101D4semidirect
469. #101C3×D4semidirect
820. C3#30481direct (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×#4732
C3×#30632
C2×C3×#4562
C3×#30132
C3×#30112
C3×#20522
C3×#20382
C3×#20202
C3×#20162
C3×#20072
C3×#20052
C3×#19302
C3×#19292
C3×#18762
#304813