Finite Group Databasebeta

← C3×#29702 #10648309

Subgroups — C3×#29702 #10648309

Order 768.

1004 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#542C211yesmaximal, characteristic
2C2×C3×#479C211yesmaximal, characteristic, complemented
3C2×C3×#478C211yesmaximal, characteristic, complemented
4C3×#2629C211yesmaximal, characteristic, complemented
5C3×#2058C211yesmaximal, characteristic, complemented
6C3×#2057C211yesmaximal, characteristic, complemented
7C3×#2042C211yesmaximal, characteristic, complemented
8C3×#2042C211yesmaximal, characteristic, complemented
9C3×#2036C211yesmaximal, characteristic, complemented
10C3×#2035C211yesmaximal, characteristic, complemented
11C3×#2034C211yesmaximal, characteristic
12C3×#2033C211yesmaximal, characteristic
13C3×#1803C211yesmaximal, characteristic, complemented
14C3×#1802C211yesmaximal, characteristic, complemented
15C3×#1798C211yesmaximal, characteristic, complemented
16#29702C311yesmaximal, characteristic, direct product factor, Sylow
17C3×#542—24no—
18C3×#542—24no—
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×#126—21no—
21C2×C3×#125C2211yescharacteristic
22C2×C3×#124—21no—
23C2×C3×#124C2211yescharacteristic
24C2×C3×#123—21no—
25C2×C3×C22⋊Q8—21no—
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×#121C2211yescharacteristic
28C2×C3×C4×Q8C2211yescharacteristic
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×#117C2211yescharacteristic
31C3×#479—24no—
32C3×#478—24no—
33C2×C3×#107C2211yescharacteristic
34C2×C3×#107C2211yescharacteristic
35C2×C3×#106C2211yescharacteristic
36C2×C3×#106C2211yescharacteristic
37C2×C3×C4⋊C8C2211yescharacteristic
38C2×C3×C4⋊C8C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C3×#398—21no—
50C3×#398—21no—
51C3×#396—21no—
52C3×#396—21no—
53C3×#389C2211yescharacteristic
54C3×#389C2211yescharacteristic
55C3×#384C2211yescharacteristic
56C3×#380C2211yescharacteristic
57C3×#380C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#542C2×C311yescharacteristic
65C2×#479C2×C311yescharacteristic, complemented
66C2×#478C2×C311yescharacteristic, complemented
67#2629C2×C311yescharacteristic, complemented
68#2058C2×C311yescharacteristic, complemented
69#2057C2×C311yescharacteristic, complemented
70#2042C2×C311yescharacteristic, complemented
71#2042C2×C311yescharacteristic, complemented
72#2036C2×C311yescharacteristic, complemented
73#2035C2×C311yescharacteristic, complemented
74#2034C2×C311yescharacteristic
75#2033C2×C311yescharacteristic
76#1803C2×C311yescharacteristic, complemented
77#1802C2×C311yescharacteristic, complemented
78#1798C2×C311yescharacteristic, complemented
79C22×C3×Q8—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4C2311yescharacteristic
85C22×C3×C8C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C3×C4⋊Q8—22no—
90C3×C4⋊Q8—22no—
91C3×#126—28no—
92C3×#125—22no—
93C3×#125—22no—
94C3×#124—28no—
95C3×#124—22no—
96C3×#124—22no—
97C3×#123—28no—
98C3×C22⋊Q8—28no—
99C3×C22⋊Q8—22no—
100C3×C22⋊Q8—22no—
101C3×#121—22no—
102C3×#121—22no—
103C3×C4×Q8—22no—
104C3×C4×Q8D414yes—
105C3×C4×D4—22no—
106C3×C4×D4D414yes—
107C3×#117—22no—
108C3×#117—22no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4D411yescharacteristic
119C2×C3×C4⋊C4D411yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C22⋊C4—21no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4D411yescharacteristic
134C2×C3×C22⋊C4D411yescharacteristic
135C2×C3×C42—21no—
136C2×C3×C42C2311yescharacteristic
137C2×C3×C42C2311yescharacteristic
138C3×#107—22no—
139C3×#107—22no—
140C3×#106—22no—
141C3×#106—22no—
142C3×C4⋊C8—22no—
143C3×C4⋊C8—22no—
144C3×#103—22no—
145C3×#103—22no—
146C3×#103—41no—
147C3×#103—41no—
148C3×#102—22no—
149C3×#102—22no—
150C3×#102—41no—
151C3×#102—41no—
152C3×C22⋊C8—41no—
153C3×C22⋊C8—41no—
154C3×#95—21no—
155C3×#95—21no—
156C3×#95—21no—
157C3×#95—21no—
158#542—24no—
159#542—24no—
160C2×C4⋊Q8C22×C311yescharacteristic
161C2×#126—21no—
162C2×#125C22×C311yescharacteristic
163C2×#124—21no—
164C2×#124C22×C311yescharacteristic
165C2×#123—21no—
166C2×C22⋊Q8—21no—
167C2×C22⋊Q8C22×C311yescharacteristic
168C2×#121C22×C311yescharacteristic
169C2×C4×Q8C22×C311yescharacteristic
170C2×C4×D4C22×C311yescharacteristic
171C2×#117C22×C311yescharacteristic
172#479—24no—
173#478—24no—
174C2×#107C22×C311yescharacteristic
175C2×#107C22×C311yescharacteristic
176C2×#106C22×C311yescharacteristic
177C2×#106C22×C311yescharacteristic
178C2×C4⋊C8C22×C311yescharacteristic
179C2×C4⋊C8C22×C311yescharacteristic
180C2×#103C22×C311yescharacteristic
181C2×#103C22×C311yescharacteristic
182C2×#103C22×C311yescharacteristic
183C2×#103C22×C311yescharacteristic
184C2×#102C22×C311yescharacteristic
185C2×#102C22×C311yescharacteristic
186C2×#102C22×C311yescharacteristic
187C2×#102C22×C311yescharacteristic
188C2×C22⋊C8C22×C311yescharacteristic
189C2×C22⋊C8C22×C311yescharacteristic
190#398—21no—
191#398—21no—
192#396—21no—
193#396—21no—
194#389C22×C311yescharacteristic
195#389C22×C311yescharacteristic
196#384C22×C311yescharacteristic
197#380C22×C311yescharacteristic
198#380C22×C311yescharacteristic
199#340C22×C311yescharacteristic
200#340C22×C311yescharacteristic
201#340C22×C311yescharacteristic
202#340C22×C311yescharacteristic
203#336C22×C311yescharacteristic
204#336C22×C311yescharacteristic
205C24×C3—21no—
206C24×C3C2×D411yescharacteristic
207C2×C3×Q8—24no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8—81no—
214C2×C3×Q8—81no—
215C2×C3×Q8C2×D412yes—
216C2×C3×D4—24no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—81no—
223C2×C3×D4—81no—
224C2×C3×D4C2×D412yes—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—24no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—81no—
240C22×C3×C4—81no—
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2411yescharacteristic
247C2×C3×C8—21no—
248C2×C3×C8—21no—
249C2×C3×C8—21no—
250C2×C3×C8—21no—
251C2×C3×C8—21no—
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C3×C4⋊C4—24no—
260C3×C4⋊C4—24no—
261C3×C4⋊C4—24no—
262C3×C4⋊C4—22no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—42no—
275C3×C4⋊C4—42no—
276C3×C4⋊C4—81no—
277C3×C4⋊C4—81no—
278C3×C4⋊C4—81no—
279C3×C4⋊C4—81no—
280C3×C4⋊C4C2×D412yes—
281C3×C4⋊C4C2×D412yes—
282C3×C22⋊C4—24no—
283C3×C22⋊C4—24no—
284C3×C22⋊C4—24no—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—22no—
288C3×C22⋊C4—22no—
289C3×C22⋊C4—81no—
290C3×C22⋊C4—81no—
291C3×C42—24no—
292C3×C42—21no—
293C3×C42—21no—
294C3×C42C2×D412yes—
295C3×C42C2×D412yes—
296C22×Q8—21no—
297C22×Q8C23×C311yescharacteristic
298C22×D4—21no—
299C22×D4C23×C311yescharacteristic
300C23×C4—21no—
301C23×C4C23×C311yescharacteristic
302C22×C8C23×C311yescharacteristic
303C22×C8C23×C311yescharacteristic
304C22×C8C23×C311yescharacteristic
305C22×C8C23×C311yescharacteristic
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308#126—28no—
309#125—22no—
310#125—22no—
311#124—28no—
312#124—22no—
313#124—22no—
314#123—28no—
315C22⋊Q8—28no—
316C22⋊Q8—22no—
317C22⋊Q8—22no—
318#121—22no—
319#121—22no—
320C4×Q8—22no—
321C4×Q8C3×D414yes—
322C4×D4—22no—
323C4×D4C3×D414yes—
324#117—22no—
325#117—22no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4C3×D411yescharacteristic
336C2×C4⋊C4C3×D411yescharacteristic
337C2×C4⋊C4C23×C311yescharacteristic
338C2×C4⋊C4C23×C311yescharacteristic
339C2×C4⋊C4C23×C311yescharacteristic
340C2×C4⋊C4C23×C311yescharacteristic
341C2×C4⋊C4C23×C311yescharacteristic
342C2×C4⋊C4C23×C311yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4C3×D411yescharacteristic
351C2×C22⋊C4C3×D411yescharacteristic
352C2×C42—21no—
353C2×C42C23×C311yescharacteristic
354C2×C42C23×C311yescharacteristic
355#107—22no—
356#107—22no—
357#106—22no—
358#106—22no—
359C4⋊C8—22no—
360C4⋊C8—22no—
361#103—22no—
362#103—22no—
363#103—41no—
364#103—41no—
365#102—22no—
366#102—22no—
367#102—41no—
368#102—41no—
369C22⋊C8—41no—
370C22⋊C8—41no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375C23×C3—21no—
376C23×C3—22no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3C22×D411yescharacteristic
390C3×Q8—22no—
391C3×Q8—22no—
392C3×Q8—41no—
393C3×Q8—41no—
394C3×Q8—84no—
395C3×D4—22no—
396C3×D4—22no—
397C3×D4—41no—
398C3×D4—41no—
399C3×D4—84no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—22no—
406C2×C3×C4—21no—
407C2×C3×C4—22no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—84no—
439C2×C3×C4#12012yes—
440C2×C3×C4#12012yes—
441C2×C3×C4C22×D411yescharacteristic
442C2×C3×C4C22×D411yescharacteristic
443C2×C3×C4H(5,𝔽2)11yescharacteristic
444C2×C3×C42−1+411yescharacteristic
445C2×C3×C42−1+411yescharacteristic
446C2×C3×C42−1+411yescharacteristic
447C3×C8—41no—
448C3×C8—41no—
449C3×C8—41no—
450C3×C8—41no—
451C24—21no—
452C24C2×C3×D411yescharacteristic
453C2×Q8—24no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—81no—
460C2×Q8—81no—
461C2×Q8C2×C3×D412yes—
462C2×D4—24no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—81no—
469C2×D4—81no—
470C2×D4C2×C3×D412yes—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—24no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4C2×C3×D411yescharacteristic
488C22×C4C2×C3×D411yescharacteristic
489C22×C4C2×C3×D411yescharacteristic
490C22×C4C2×C3×D411yescharacteristic
491C22×C4C2×C3×D411yescharacteristic
492C22×C4C24×C311yescharacteristic
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—24no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—81no—
523C4⋊C4—81no—
524C4⋊C4—81no—
525C4⋊C4—81no—
526C4⋊C4C2×C3×D412yes—
527C4⋊C4C2×C3×D412yes—
528C22⋊C4—24no—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C22⋊C4—24no—
532C22⋊C4—24no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—81no—
536C22⋊C4—81no—
537C42—24no—
538C42—21no—
539C42—21no—
540C42C2×C3×D412yes—
541C42C2×C3×D412yes—
542C22×C3—41no—
543C22×C3—42no—
544C22×C3—41no—
545C22×C3—41no—
546C22×C3—41no—
547C22×C3—41no—
548C22×C3—42no—
549C22×C3—41no—
550C22×C3—41no—
551C22×C3—42no—
552C22×C3—81no—
553C22×C3—81no—
554C22×C3—81no—
555C22×C3—81no—
556C22×C3C2×#12011yescharacteristic
557C22×C3#53611yescharacteristic
558C22×C3#53711yescharacteristic
559C22×C3#57611yescharacteristic
560C22×C3#57711yescharacteristic
561C22×C3#57711yescharacteristic
562C22×C3#57811yescharacteristic
563C3×C4—22no—
564C3×C4—22no—
565C3×C4—41no—
566C3×C4—42no—
567C3×C4—41no—
568C3×C4—42no—
569C3×C4—42no—
570C3×C4—41no—
571C3×C4—81no—
572C3×C4—81no—
573C3×C4—81no—
574C3×C4—81no—
575C3×C4#53611yescharacteristic
576C3×C4#53611yescharacteristic
577C3×C4#53711yescharacteristic
578C3×C4#53711yescharacteristic
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—22no—
585C23—21no—
586C23—21no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C22×C3×D411yescharacteristic
594Q8—22no—
595Q8—22no—
596Q8—41no—
597Q8—41no—
598Q8—84no—
599D4—22no—
600D4—22no—
601D4—41no—
602D4—41no—
603D4—84no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—84no—
643C2×C4C3×#12012yes—
644C2×C4C3×#12012yes—
645C2×C4C22×C3×D411yescharacteristic
646C2×C4C22×C3×D411yescharacteristic
647C2×C4C3×H(5,𝔽2)11yescharacteristic
648C2×C4C3×2−1+411yescharacteristic
649C2×C4C3×2−1+411yescharacteristic
650C2×C4C3×2−1+411yescharacteristic
651C8—41no—
652C8—41no—
653C8—41no—
654C8—41no—
655C2×C3—81no—
656C2×C3—82no—
657C2×C3#261611yescharacteristic
658C2×C3#301211yescharacteristic
659C2×C3#301311yescharacteristic
660C2×C3#324311yescharacteristic
661C2×C3#324411yescharacteristic
662C2×C3#325711yescharacteristic
663C2×C3#325811yescharacteristic
664C22—41no—
665C22—42no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—42no—
671C22—41no—
672C22—41no—
673C22—42no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22C2×C3×#12011yescharacteristic
679C22C3×#53611yescharacteristic
680C22C3×#53711yescharacteristic
681C22C3×#57611yescharacteristic
682C22C3×#57711yescharacteristic
683C22C3×#57711yescharacteristic
684C22C3×#57811yescharacteristic
685C4—22no—
686C4—22no—
687C4—41no—
688C4—42no—
689C4—41no—
690C4—42no—
691C4—42no—
692C4—41no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4C3×#53611yescharacteristic
698C4C3×#53611yescharacteristic
699C4C3×#53711yescharacteristic
700C4C3×#53711yescharacteristic
701C3#2970211yescharacteristic, direct product factor, Sylow
702C2—81no—
703C2—82no—
704C2C3×#261611yescharacteristic
705C2C3×#301211yescharacteristic
706C2C3×#301311yescharacteristic
707C2C3×#324311yescharacteristic
708C2C3×#324411yescharacteristic
709C2C3×#325711yescharacteristic
710C2C3×#325811yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#479C2semidirect
3. C2×C3×#478C2semidirect
4. C3×#2629C2semidirect
5. C3×#2058C2semidirect
6. C3×#2057C2semidirect
7. C3×#2042C2semidirect
8. C3×#2042C2semidirect
9. C3×#2036C2semidirect
10. C3×#2035C2semidirect
13. C3×#1803C2semidirect
14. C3×#1802C2semidirect
15. C3×#1798C2semidirect
16. #29702C3direct (N × H)
65. C2×#479C2×C3semidirect
66. C2×#478C2×C3semidirect
67. #2629C2×C3semidirect
68. #2058C2×C3semidirect
69. #2057C2×C3semidirect
70. #2042C2×C3semidirect
71. #2042C2×C3semidirect
72. #2036C2×C3semidirect
73. #2035C2×C3semidirect
76. #1803C2×C3semidirect
77. #1802C2×C3semidirect
78. #1798C2×C3semidirect
701. C3#29702direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5422
C2×C3×#4792
C2×C3×#4782
C3×#26292
C3×#20582
C3×#20572
C3×#20422
C3×#20362
C3×#20352
C3×#20342
C3×#20332
C3×#18032
C3×#18022
C3×#17982
#297023