Finite Group Databasebeta

← C3×#24325 #10642932

Subgroups — C3×#24325 #10642932

Order 768.

960 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3504C211yesmaximal, characteristic
2C3×#3078C211yesmaximal, characteristic, complemented
3C3×C4×#137C211yesmaximal, characteristic
4C3×#2565C211yesmaximal, characteristic, complemented
5C3×#2061C211yesmaximal, characteristic, complemented
6C3×#2060C211yesmaximal, characteristic, complemented
7C3×#2028C211yesmaximal, characteristic, complemented
8C3×#2028C211yesmaximal, characteristic, complemented
9C3×#1998C211yesmaximal, characteristic, complemented
10C3×#1986C211yesmaximal, characteristic, complemented
11C3×#1882C211yesmaximal, characteristic
12C3×#1882C211yesmaximal, characteristic
13C3×#1860C211yesmaximal, characteristic
14C3×#1859C211yesmaximal, characteristic
15C3×#1806C211yesmaximal, characteristic
16#24325C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#137C2211yescharacteristic
18C3×#557—21no—
19C3×#557—21no—
20C3×#554—21no—
21C3×#554—21no—
22C3×#554—22no—
23C3×#554—22no—
24C3×#544—21no—
25C3×#544—21no—
26C3×#544C2211yescharacteristic
27C3×#544C2211yescharacteristic
28C3×#533—21no—
29C3×#533C2211yescharacteristic
30C2×C3×#125—21no—
31C2×C3×#125C2211yescharacteristic
32C3×#520C2211yescharacteristic
33C3×#520C2211yescharacteristic
34C3×C4×#41C2211yescharacteristic
35C2×C3×C4×Q8C2211yescharacteristic
36C3×#479—21no—
37C3×#479—21no—
38C3×#477—21no—
39C3×#475—21no—
40C3×#441—21no—
41C3×#440—21no—
42C3×C4×Q16—21no—
43C3×C4×SD16—21no—
44C3×#428C2211yescharacteristic
45C3×#428C2211yescharacteristic
46C3×#428C2211yescharacteristic
47C3×#423C2211yescharacteristic
48C2×C3×#104C2211yescharacteristic
49C2×C3×#104C2211yescharacteristic
50C3×#419C2211yescharacteristic
51C3×#419C2211yescharacteristic
52C3×#419C2211yescharacteristic
53C3×#417C2211yescharacteristic
54C3×C4×M16C2211yescharacteristic
55C3×#398—22no—
56C3×#391C2211yescharacteristic
57C3×#391C2211yescharacteristic
58C3×#387—22no—
59C3×#384C2211yescharacteristic
60C3×#382C2211yescharacteristic
61C3×C4×C4⋊C4C2211yescharacteristic
62C3×#343C2211yescharacteristic
63C3×#343C2211yescharacteristic
64C3×#343C2211yescharacteristic
65C3×#343C2211yescharacteristic
66C3×#339C2211yescharacteristic
67C3×#339C2211yescharacteristic
68C3×#339C2211yescharacteristic
69C3×#339C2211yescharacteristic
70C3×#339C2211yescharacteristic
71C3×#339C2211yescharacteristic
72#3504C2×C311yescharacteristic
73#3078C2×C311yescharacteristic, complemented
74C4×#137C2×C311yescharacteristic
75#2565C2×C311yescharacteristic, complemented
76#2061C2×C311yescharacteristic, complemented
77#2060C2×C311yescharacteristic, complemented
78#2028C2×C311yescharacteristic, complemented
79#2028C2×C311yescharacteristic, complemented
80#1998C2×C311yescharacteristic, complemented
81#1986C2×C311yescharacteristic, complemented
82#1882C2×C311yescharacteristic
83#1882C2×C311yescharacteristic
84#1860C2×C311yescharacteristic
85#1859C2×C311yescharacteristic
86#1806C2×C311yescharacteristic
87C2×C3×#41C2311yescharacteristic
88C22×C3×Q8C2311yescharacteristic
89C3×#137—22no—
90C3×#137Q814yescomplemented
91C2×C3×Q16—21no—
92C2×C3×SD16—21no—
93C2×C3×M16C2311yescharacteristic
94C2×C3×M16C2311yescharacteristic
95C2×C3×M16C2311yescharacteristic
96C2×C3×M16C2311yescharacteristic
97C3×C4⋊Q8—22no—
98C3×C4⋊Q8—22no—
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8—21no—
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8D411yescharacteristic
104C3×C4⋊Q8D411yescharacteristic
105C3×#125—22no—
106C3×#125—22no—
107C3×#125—22no—
108C3×#125—22no—
109C3×#125—21no—
110C3×#125—21no—
111C3×#125—21no—
112C3×#125—21no—
113C3×#125—21no—
114C3×#125—21no—
115C3×#125—21no—
116C3×#125—21no—
117C3×#125D411yescharacteristic
118C3×#125D411yescharacteristic
119C3×C22⋊Q8—22no—
120C3×C22⋊Q8—22no—
121C3×C22⋊Q8—22no—
122C3×C22⋊Q8—22no—
123C3×C22⋊Q8—22no—
124C3×C22⋊Q8—22no—
125C3×C22⋊Q8—21no—
126C3×C22⋊Q8—21no—
127C3×C22⋊Q8—22no—
128C3×C22⋊Q8—22no—
129C3×C4×Q8—22no—
130C3×C4×Q8—22no—
131C3×C4×Q8—21no—
132C3×C4×Q8—21no—
133C3×C4×Q8—21no—
134C3×C4×Q8—21no—
135C3×C4×Q8—21no—
136C3×C4×Q8—21no—
137C3×C4×Q8—21no—
138C3×C4×Q8—21no—
139C3×C4×Q8D411yescharacteristic
140C3×C4×Q8D411yescharacteristic
141C3×C4×D4—21no—
142C3×C4×D4—21no—
143C3×C4×D4—21no—
144C3×C4×D4—21no—
145C3×C4×D4—22no—
146C3×C4×D4—22no—
147C3×C4×D4D411yescharacteristic
148C3×C4×D4D411yescharacteristic
149C3×#117—21no—
150C3×#117—21no—
151C3×#117—21no—
152C3×#117C2311yescharacteristic
153C3×#117C2311yescharacteristic
154C3×#117C2311yescharacteristic
155C2×C3×C4⋊C4—22no—
156C2×C3×C4⋊C4—22no—
157C2×C3×C4⋊C4—21no—
158C2×C3×C4⋊C4—21no—
159C2×C3×C4⋊C4—21no—
160C2×C3×C4⋊C4—22no—
161C2×C3×C4⋊C4—21no—
162C2×C3×C4⋊C4D412yes—
163C2×C3×C4⋊C4D412yes—
164C2×C3×C4⋊C4C2311yescharacteristic
165C2×C3×C4⋊C4C2311yescharacteristic
166C2×C3×C4⋊C4C2311yescharacteristic
167C2×C3×C42—21no—
168C2×C3×C42—21no—
169C2×C3×C42C2311yescharacteristic
170C2×C3×C42C2311yescharacteristic
171C2×C3×C42C2311yescharacteristic
172C3×#107—21no—
173C3×#107—21no—
174C3×#107—21no—
175C3×#106—21no—
176C3×#106—21no—
177C3×#106—21no—
178C3×C4⋊C8—21no—
179C3×C4⋊C8—21no—
180C3×#104—22no—
181C3×#104—22no—
182C3×#103—21no—
183C3×#103—21no—
184C3×#103—21no—
185C3×#103—21no—
186C3×#103—21no—
187C3×#103—21no—
188C3×#103—21no—
189C3×#102—21no—
190C3×#97—21no—
191C3×C4×C8—21no—
192C3×#95—21no—
193C3×#95—22no—
194C3×#95—22no—
195C3×#95—22no—
196C2×#137C22×C311yescharacteristic
197#557—21no—
198#557—21no—
199#554—21no—
200#554—21no—
201#554—22no—
202#554—22no—
203#544—21no—
204#544—21no—
205#544C22×C311yescharacteristic
206#544C22×C311yescharacteristic
207#533—21no—
208#533C22×C311yescharacteristic
209C2×#125—21no—
210C2×#125C22×C311yescharacteristic
211#520C22×C311yescharacteristic
212#520C22×C311yescharacteristic
213C4×#41C22×C311yescharacteristic
214C2×C4×Q8C22×C311yescharacteristic
215#479—21no—
216#479—21no—
217#477—21no—
218#475—21no—
219#441—21no—
220#440—21no—
221C4×Q16—21no—
222C4×SD16—21no—
223#428C22×C311yescharacteristic
224#428C22×C311yescharacteristic
225#428C22×C311yescharacteristic
226#423C22×C311yescharacteristic
227C2×#104C22×C311yescharacteristic
228C2×#104C22×C311yescharacteristic
229#419C22×C311yescharacteristic
230#419C22×C311yescharacteristic
231#419C22×C311yescharacteristic
232#417C22×C311yescharacteristic
233C4×M16C22×C311yescharacteristic
234#398—22no—
235#391C22×C311yescharacteristic
236#391C22×C311yescharacteristic
237#387—22no—
238#384C22×C311yescharacteristic
239#382C22×C311yescharacteristic
240C4×C4⋊C4C22×C311yescharacteristic
241#343C22×C311yescharacteristic
242#343C22×C311yescharacteristic
243#343C22×C311yescharacteristic
244#343C22×C311yescharacteristic
245#339C22×C311yescharacteristic
246#339C22×C311yescharacteristic
247#339C22×C311yescharacteristic
248#339C22×C311yescharacteristic
249#339C22×C311yescharacteristic
250#339C22×C311yescharacteristic
251C3×#41—21no—
252C3×#41—21no—
253C3×#41C2×Q812yes—
254C3×#41#4112yes—
255C2×C3×Q8—22no—
256C2×C3×Q8—22no—
257C2×C3×Q8—21no—
258C2×C3×Q8—21no—
259C2×C3×Q8—21no—
260C2×C3×Q8—21no—
261C2×C3×Q8—21no—
262C2×C3×Q8—21no—
263C2×C3×Q8—21no—
264C2×C3×Q8C2×D411yescharacteristic
265C2×C3×Q8C2×Q812yes—
266C2×C3×D4—21no—
267C2×C3×D4C2×D411yescharacteristic
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4C2×D412yes—
278C22×C3×C4C2×D412yes—
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2×D411yescharacteristic
281C22×C3×C4C2411yescharacteristic
282C3×Q16—24no—
283C3×SD16—24no—
284C3×M16—21no—
285C3×M16—21no—
286C3×M16—21no—
287C3×M16—21no—
288C3×M16—21no—
289C3×M16—21no—
290C3×M16—21no—
291C3×M16C2×Q812yes—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C3×C4⋊C4—22no—
297C3×C4⋊C4—22no—
298C3×C4⋊C4—22no—
299C3×C4⋊C4—22no—
300C3×C4⋊C4—22no—
301C3×C4⋊C4—22no—
302C3×C4⋊C4—22no—
303C3×C4⋊C4—22no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—22no—
307C3×C4⋊C4—22no—
308C3×C4⋊C4—22no—
309C3×C4⋊C4—22no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—42no—
323C3×C4⋊C4—44no—
324C3×C4⋊C4—41no—
325C3×C4⋊C4—41no—
326C3×C4⋊C4C2×D411yescharacteristic
327C3×C4⋊C4C2×D411yescharacteristic
328C3×C4⋊C4C2×D411yescharacteristic
329C3×C4⋊C4C2×D411yescharacteristic
330C3×C4⋊C4C2×D411yescharacteristic
331C3×C4⋊C4C2×D411yescharacteristic
332C3×C22⋊C4—22no—
333C3×C22⋊C4—22no—
334C3×C22⋊C4—21no—
335C3×C22⋊C4—21no—
336C3×C22⋊C4—21no—
337C3×C22⋊C4—21no—
338C3×C22⋊C4—21no—
339C3×C42—22no—
340C3×C42—22no—
341C3×C42—21no—
342C3×C42—21no—
343C3×C42—21no—
344C3×C42—21no—
345C3×C42—21no—
346C3×C42—21no—
347C3×C42—21no—
348C3×C42—21no—
349C3×C42—21no—
350C3×C42—41no—
351C3×C42—41no—
352C3×C42C2×D411yescharacteristic
353C3×C42C2×D411yescharacteristic
354C3×C42C2×D411yescharacteristic
355C3×C42C2×D411yescharacteristic
356C2×#41C23×C311yescharacteristic
357C22×Q8C23×C311yescharacteristic
358#137—22no—
359#137C3×Q814yescomplemented
360C2×Q16—21no—
361C2×SD16—21no—
362C2×M16C23×C311yescharacteristic
363C2×M16C23×C311yescharacteristic
364C2×M16C23×C311yescharacteristic
365C2×M16C23×C311yescharacteristic
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8C3×D411yescharacteristic
373C4⋊Q8C3×D411yescharacteristic
374#125—22no—
375#125—22no—
376#125—22no—
377#125—22no—
378#125—21no—
379#125—21no—
380#125—21no—
381#125—21no—
382#125—21no—
383#125—21no—
384#125—21no—
385#125—21no—
386#125C3×D411yescharacteristic
387#125C3×D411yescharacteristic
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C4×Q8—22no—
399C4×Q8—22no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8C3×D411yescharacteristic
409C4×Q8C3×D411yescharacteristic
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4C3×D411yescharacteristic
417C4×D4C3×D411yescharacteristic
418#117—21no—
419#117—21no—
420#117—21no—
421#117C23×C311yescharacteristic
422#117C23×C311yescharacteristic
423#117C23×C311yescharacteristic
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4C3×D412yes—
432C2×C4⋊C4C3×D412yes—
433C2×C4⋊C4C23×C311yescharacteristic
434C2×C4⋊C4C23×C311yescharacteristic
435C2×C4⋊C4C23×C311yescharacteristic
436C2×C42—21no—
437C2×C42—21no—
438C2×C42C23×C311yescharacteristic
439C2×C42C23×C311yescharacteristic
440C2×C42C23×C311yescharacteristic
441#107—21no—
442#107—21no—
443#107—21no—
444#106—21no—
445#106—21no—
446#106—21no—
447C4⋊C8—21no—
448C4⋊C8—21no—
449#104—22no—
450#104—22no—
451#103—21no—
452#103—21no—
453#103—21no—
454#103—21no—
455#103—21no—
456#103—21no—
457#103—21no—
458#102—21no—
459#97—21no—
460C4×C8—21no—
461#95—21no—
462#95—22no—
463#95—22no—
464#95—22no—
465C23×C3—21no—
466C23×C3C22×D411yescharacteristic
467C3×Q8—21no—
468C3×Q8—22no—
469C3×Q8—22no—
470C3×Q8—41no—
471C3×Q8—41no—
472C3×Q8—81no—
473C3×Q8—81no—
474C3×Q8—82no—
475C3×Q8—82no—
476C3×Q8C22⋊Q812yes—
477C3×D4—22no—
478C3×D4—22no—
479C3×D4—21no—
480C3×D4C22⋊Q812yes—
481C2×C3×C4—21no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—42no—
501C2×C3×C4—42no—
502C2×C3×C4—41no—
503C2×C3×C4—42no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—81no—
508C2×C3×C4—81no—
509C2×C3×C4—82no—
510C2×C3×C4—82no—
511C2×C3×C4#12011yescharacteristic
512C2×C3×C4#12011yescharacteristic
513C2×C3×C4#12011yescharacteristic
514C2×C3×C4#12011yescharacteristic
515C2×C3×C4C22×D411yescharacteristic
516C2×C3×C4C22×D411yescharacteristic
517C2×C3×C4C22×Q811yescharacteristic
518C2×C3×C4C2×#4111yescharacteristic
519C2×C3×C42−1+411yescharacteristic
520C2×C3×C42−1+411yescharacteristic
521C3×C8—22no—
522C3×C8—41no—
523C3×C8—41no—
524C3×C8—41no—
525#41—21no—
526#41—21no—
527#41C2×C3×Q812yes—
528#41C3×#4112yes—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8C2×C3×D411yescharacteristic
539C2×Q8C2×C3×Q812yes—
540C2×D4—21no—
541C2×D4C2×C3×D411yescharacteristic
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4C2×C3×D412yes—
552C22×C4C2×C3×D412yes—
553C22×C4C2×C3×D411yescharacteristic
554C22×C4C2×C3×D411yescharacteristic
555C22×C4C24×C311yescharacteristic
556Q16—24no—
557SD16—24no—
558M16—21no—
559M16—21no—
560M16—21no—
561M16—21no—
562M16—21no—
563M16—21no—
564M16—21no—
565M16C2×C3×Q812yes—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—42no—
597C4⋊C4—44no—
598C4⋊C4—41no—
599C4⋊C4—41no—
600C4⋊C4C2×C3×D411yescharacteristic
601C4⋊C4C2×C3×D411yescharacteristic
602C4⋊C4C2×C3×D411yescharacteristic
603C4⋊C4C2×C3×D411yescharacteristic
604C4⋊C4C2×C3×D411yescharacteristic
605C4⋊C4C2×C3×D411yescharacteristic
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C42—22no—
614C42—22no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—41no—
625C42—41no—
626C42C2×C3×D411yescharacteristic
627C42C2×C3×D411yescharacteristic
628C42C2×C3×D411yescharacteristic
629C42C2×C3×D411yescharacteristic
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—22no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3C2×#12011yescharacteristic
636C22×C3#54811yescharacteristic
637C22×C3D4×Q811yescharacteristic
638C3×C4—22no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—42no—
644C3×C4—42no—
645C3×C4—42no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—42no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—81no—
654C3×C4—81no—
655C3×C4C2×C22⋊Q811yescharacteristic
656C3×C4#53611yescharacteristic
657C3×C4#54811yescharacteristic
658C3×C4D4×Q811yescharacteristic
659C23—21no—
660C23C22×C3×D411yescharacteristic
661Q8—21no—
662Q8—22no—
663Q8—22no—
664Q8—41no—
665Q8—41no—
666Q8—81no—
667Q8—81no—
668Q8—82no—
669Q8—82no—
670Q8C3×C22⋊Q812yes—
671D4—22no—
672D4—22no—
673D4—21no—
674D4C3×C22⋊Q812yes—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4C3×#12011yescharacteristic
706C2×C4C3×#12011yescharacteristic
707C2×C4C3×#12011yescharacteristic
708C2×C4C3×#12011yescharacteristic
709C2×C4C22×C3×D411yescharacteristic
710C2×C4C22×C3×D411yescharacteristic
711C2×C4C22×C3×Q811yescharacteristic
712C2×C4C2×C3×#4111yescharacteristic
713C2×C4C3×2−1+411yescharacteristic
714C2×C4C3×2−1+411yescharacteristic
715C8—22no—
716C8—41no—
717C8—41no—
718C8—41no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—42no—
722C2×C3#240911yescharacteristic
723C2×C3#301811yescharacteristic
724C2×C3#302211yescharacteristic
725C22—21no—
726C22—21no—
727C22—22no—
728C22—41no—
729C22—41no—
730C22C2×C3×#12011yescharacteristic
731C22C3×#54811yescharacteristic
732C22C3×D4×Q811yescharacteristic
733C4—22no—
734C4—21no—
735C4—21no—
736C4—21no—
737C4—21no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—42no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—81no—
749C4—81no—
750C4C2×C3×C22⋊Q811yescharacteristic
751C4C3×#53611yescharacteristic
752C4C3×#54811yescharacteristic
753C4C3×D4×Q811yescharacteristic
754C3#2432511yescharacteristic, direct product factor, Sylow
755C2—21no—
756C2—21no—
757C2—42no—
758C2C3×#240911yescharacteristic
759C2C3×#301811yescharacteristic
760C2C3×#302211yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#3078C2semidirect
4. C3×#2565C2semidirect
5. C3×#2061C2semidirect
6. C3×#2060C2semidirect
7. C3×#2028C2semidirect
8. C3×#2028C2semidirect
9. C3×#1998C2semidirect
10. C3×#1986C2semidirect
16. #24325C3direct (N × H)
73. #3078C2×C3semidirect
75. #2565C2×C3semidirect
76. #2061C2×C3semidirect
77. #2060C2×C3semidirect
78. #2028C2×C3semidirect
79. #2028C2×C3semidirect
80. #1998C2×C3semidirect
81. #1986C2×C3semidirect
90. C3×#137Q8semidirect
359. #137C3×Q8semidirect
754. C3#24325direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35042
C3×#30782
C3×C4×#1372
C3×#25652
C3×#20612
C3×#20602
C3×#20282
C3×#19982
C3×#19862
C3×#18822
C3×#18602
C3×#18592
C3×#18062
#243253