Finite Group Databasebeta

← C3×#27794 #10646401

Subgroups — C3×#27794 #10646401

Order 768.

880 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#501C211yesmaximal, characteristic, complemented
2C2×C3×#469C211yesmaximal, characteristic
3C3×#2491C211yesmaximal, characteristic, complemented
4C3×#2490C211yesmaximal, characteristic, complemented
5C3×#2034C211yesmaximal, characteristic, complemented
6C3×#2033C211yesmaximal, characteristic, complemented
7C3×#2025C211yesmaximal, characteristic, complemented
8C3×#2023C211yesmaximal, characteristic, complemented
9C3×#1972C211yesmaximal, characteristic, complemented
10C3×#1970C211yesmaximal, characteristic, complemented
11C3×#1926C211yesmaximal, characteristic, complemented
12C3×#1925C211yesmaximal, characteristic, complemented
13C3×#1809C211yesmaximal, characteristic, complemented
14C3×C4×#106C211yesmaximal, characteristic, complemented
15C3×#1753C211yesmaximal, characteristic, complemented
16#27794C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×#125C2211yescharacteristic
21C2×C3×#124—21no—
22C2×C3×#121C2211yescharacteristic
23C2×C3×#121C2211yescharacteristic
24C3×#501—24no—
25C3×#469—24no—
26C2×C3×#107C2211yescharacteristic
27C2×C3×#107C2211yescharacteristic
28C2×C3×#106C2211yescharacteristic
29C2×C3×#106C2211yescharacteristic
30C2×C3×#106C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×C3×#97C2211yescharacteristic
39C2×C3×C4×C8C2211yescharacteristic
40C3×#397—21no—
41C3×#394—21no—
42C3×#394—21no—
43C3×#393—21no—
44C3×#390—21no—
45C3×#390C2211yescharacteristic
46C3×#390C2211yescharacteristic
47C3×#390C2211yescharacteristic
48C3×#390C2211yescharacteristic
49C3×#388—21no—
50C3×#388—21no—
51C3×#380C2211yescharacteristic
52C3×#380C2211yescharacteristic
53C3×C4×C4⋊C4C2211yescharacteristic
54C3×C4×C4⋊C4C2211yescharacteristic
55C3×C4×C22⋊C4C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#501C2×C311yescharacteristic, complemented
63C2×#469C2×C311yescharacteristic
64#2491C2×C311yescharacteristic, complemented
65#2490C2×C311yescharacteristic, complemented
66#2034C2×C311yescharacteristic, complemented
67#2033C2×C311yescharacteristic, complemented
68#2025C2×C311yescharacteristic, complemented
69#2023C2×C311yescharacteristic, complemented
70#1972C2×C311yescharacteristic, complemented
71#1970C2×C311yescharacteristic, complemented
72#1926C2×C311yescharacteristic, complemented
73#1925C2×C311yescharacteristic, complemented
74#1809C2×C311yescharacteristic, complemented
75C4×#106C2×C311yescharacteristic, complemented
76#1753C2×C311yescharacteristic, complemented
77C22×C3×Q8—21no—
78C22×C3×D4—21no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C2×C3×D8—22no—
84C2×C3×D8—22no—
85C2×C3×D8—22no—
86C2×C3×M16—22no—
87C2×C3×M16—22no—
88C2×C3×M16—22no—
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×C4⋊Q8—22no—
94C3×C4⋊Q8—41no—
95C3×#125—22no—
96C3×#125—41no—
97C3×#124—44no—
98C3×#121—22no—
99C3×#121—22no—
100C3×#121—41no—
101C3×#121—41no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4D411yescharacteristic
124C2×C3×C22⋊C4D411yescharacteristic
125C2×C3×C42—21no—
126C2×C3×C42—21no—
127C2×C3×C42C2311yescharacteristic
128C2×C3×C42C2311yescharacteristic
129C3×#107—22no—
130C3×#107—22no—
131C3×#106—22no—
132C3×#106—22no—
133C3×#106D414yes—
134C3×#102—22no—
135C3×#102—22no—
136C3×#102—22no—
137C3×#102—22no—
138C3×#102—41no—
139C3×#102—41no—
140C3×C22⋊C8—22no—
141C3×#97—22no—
142C3×C4×C8—22no—
143C3×#95—21no—
144C3×#95—21no—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95D411yescharacteristic
148C3×#95D411yescharacteristic
149C22×D8C22×C311yescharacteristic
150C22×M16C22×C311yescharacteristic
151C2×C4⋊Q8C22×C311yescharacteristic
152C2×#125C22×C311yescharacteristic
153C2×#124—21no—
154C2×#121C22×C311yescharacteristic
155C2×#121C22×C311yescharacteristic
156#501—24no—
157#469—24no—
158C2×#107C22×C311yescharacteristic
159C2×#107C22×C311yescharacteristic
160C2×#106C22×C311yescharacteristic
161C2×#106C22×C311yescharacteristic
162C2×#106C22×C311yescharacteristic
163C2×#102C22×C311yescharacteristic
164C2×#102C22×C311yescharacteristic
165C2×#102C22×C311yescharacteristic
166C2×#102C22×C311yescharacteristic
167C2×#102C22×C311yescharacteristic
168C2×#102C22×C311yescharacteristic
169C2×C22⋊C8C22×C311yescharacteristic
170C2×#97C22×C311yescharacteristic
171C2×C4×C8C22×C311yescharacteristic
172#397—21no—
173#394—21no—
174#394—21no—
175#393—21no—
176#390—21no—
177#390C22×C311yescharacteristic
178#390C22×C311yescharacteristic
179#390C22×C311yescharacteristic
180#390C22×C311yescharacteristic
181#388—21no—
182#388—21no—
183#380C22×C311yescharacteristic
184#380C22×C311yescharacteristic
185C4×C4⋊C4C22×C311yescharacteristic
186C4×C4⋊C4C22×C311yescharacteristic
187C4×C22⋊C4C22×C311yescharacteristic
188#340C22×C311yescharacteristic
189#340C22×C311yescharacteristic
190#340C22×C311yescharacteristic
191#340C22×C311yescharacteristic
192#336C22×C311yescharacteristic
193#336C22×C311yescharacteristic
194C24×C3—21no—
195C24×C3—21no—
196C24×C3C2×D411yescharacteristic
197C2×C3×Q8—42no—
198C2×C3×Q8—42no—
199C2×C3×Q8—81no—
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—42no—
213C2×C3×D4—42no—
214C2×C3×D4—42no—
215C2×C3×D4—42no—
216C2×C3×D4—81no—
217C2×C3×D4—81no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2411yescharacteristic
236C3×D8—44no—
237C3×M16—44no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8C2×D412yes—
247C2×C3×C8#4112yes—
248C2×C3×C8#4112yes—
249C2×C3×C8#4112yes—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—42no—
261C3×C4⋊C4—42no—
262C3×C4⋊C4—42no—
263C3×C4⋊C4C2×D412yes—
264C3×C4⋊C4C2×D412yes—
265C3×C22⋊C4—22no—
266C3×C22⋊C4—41no—
267C3×C22⋊C4—42no—
268C3×C22⋊C4—42no—
269C3×C22⋊C4—42no—
270C3×C22⋊C4—42no—
271C3×C22⋊C4—42no—
272C3×C22⋊C4—42no—
273C3×C22⋊C4—42no—
274C3×C22⋊C4—81no—
275C3×C22⋊C4—81no—
276C3×C22⋊C4—81no—
277C3×C22⋊C4—81no—
278C3×C22⋊C4—81no—
279C3×C42—21no—
280C3×C42—21no—
281C3×C42—21no—
282C3×C42—21no—
283C3×C42—42no—
284C3×C42—81no—
285C22×Q8—21no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4C23×C311yescharacteristic
289C22×D4C23×C311yescharacteristic
290C23×C4C23×C311yescharacteristic
291C2×D8—22no—
292C2×D8—22no—
293C2×D8—22no—
294C2×M16—22no—
295C2×M16—22no—
296C2×M16—22no—
297C22×C8C23×C311yescharacteristic
298C22×C8C23×C311yescharacteristic
299C22×C8C23×C311yescharacteristic
300C22×C8C23×C311yescharacteristic
301C4⋊Q8—22no—
302C4⋊Q8—41no—
303#125—22no—
304#125—41no—
305#124—44no—
306#121—22no—
307#121—22no—
308#121—41no—
309#121—41no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4C23×C311yescharacteristic
314C2×C4⋊C4C23×C311yescharacteristic
315C2×C4⋊C4C23×C311yescharacteristic
316C2×C4⋊C4C23×C311yescharacteristic
317C2×C4⋊C4C23×C311yescharacteristic
318C2×C4⋊C4C23×C311yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4C3×D411yescharacteristic
332C2×C22⋊C4C3×D411yescharacteristic
333C2×C42—21no—
334C2×C42—21no—
335C2×C42C23×C311yescharacteristic
336C2×C42C23×C311yescharacteristic
337#107—22no—
338#107—22no—
339#106—22no—
340#106—22no—
341#106C3×D414yes—
342#102—22no—
343#102—22no—
344#102—22no—
345#102—22no—
346#102—41no—
347#102—41no—
348C22⋊C8—22no—
349#97—22no—
350C4×C8—22no—
351#95—21no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95C3×D411yescharacteristic
356#95C3×D411yescharacteristic
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3—41no—
367C23×C3—41no—
368C23×C3—41no—
369C23×C3—41no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3—41no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3C22×D411yescharacteristic
379C3×Q8—84no—
380C3×D4—41no—
381C3×D4—41no—
382C3×D4—41no—
383C3×D4—41no—
384C3×D4—41no—
385C3×D4—41no—
386C3×D4—41no—
387C3×D4—41no—
388C3×D4—84no—
389C3×D4—84no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
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×C4AGL(1,ℤ/8)12yes—
427C2×C3×C4C22×D411yescharacteristic
428C2×C3×C4C2×#4111yescharacteristic
429C2×C3×C4C2×#4111yescharacteristic
430C2×C3×C4C2×#4111yescharacteristic
431C2×C3×C4H(5,𝔽2)11yescharacteristic
432C2×C3×C42−1+411yescharacteristic
433C3×C8—22no—
434C3×C8—41no—
435C3×C8—41no—
436C3×C8#12414yescomplemented
437C24—21no—
438C24—21no—
439C24C2×C3×D411yescharacteristic
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8—81no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—81no—
460C2×D4—81no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4C2×C3×D411yescharacteristic
474C22×C4C2×C3×D411yescharacteristic
475C22×C4C2×C3×D411yescharacteristic
476C22×C4C2×C3×D411yescharacteristic
477C22×C4C2×C3×D411yescharacteristic
478C22×C4C24×C311yescharacteristic
479D8—44no—
480M16—44no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8C2×C3×D412yes—
490C2×C8C3×#4112yes—
491C2×C8C3×#4112yes—
492C2×C8C3×#4112yes—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—42no—
506C4⋊C4C2×C3×D412yes—
507C4⋊C4C2×C3×D412yes—
508C22⋊C4—22no—
509C22⋊C4—41no—
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—81no—
518C22⋊C4—81no—
519C22⋊C4—81no—
520C22⋊C4—81no—
521C22⋊C4—81no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—42no—
527C42—81no—
528C22×C3—41no—
529C22×C3—41no—
530C22×C3—41no—
531C22×C3—41no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—41no—
535C22×C3—81no—
536C22×C3—81no—
537C22×C3—81no—
538C22×C3—81no—
539C22×C3—81no—
540C22×C3—81no—
541C22×C3—81no—
542C22×C3—81no—
543C22×C3—81no—
544C22×C3—81no—
545C22×C3—81no—
546C22×C3—81no—
547C22×C3—81no—
548C22×C3—81no—
549C22×C3#53211yescharacteristic
550C22×C3D4211yescharacteristic
551C22×C3#54711yescharacteristic
552C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
553C22×C3#57511yescharacteristic
554C22×C3#57611yescharacteristic
555C22×C3#57711yescharacteristic
556C3×C4—22no—
557C3×C4—41no—
558C3×C4—41no—
559C3×C4—41no—
560C3×C4—42no—
561C3×C4—41no—
562C3×C4—42no—
563C3×C4—81no—
564C3×C4—81no—
565C3×C4—81no—
566C3×C4—81no—
567C3×C4C2×#12411yescharacteristic
568C3×C4#54211yescharacteristic
569C3×C4#54811yescharacteristic
570C3×C4#55511yescharacteristic
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23C22×C3×D411yescharacteristic
593Q8—84no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—41no—
602D4—84no—
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—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
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×C4C3×AGL(1,ℤ/8)12yes—
641C2×C4C22×C3×D411yescharacteristic
642C2×C4C2×C3×#4111yescharacteristic
643C2×C4C2×C3×#4111yescharacteristic
644C2×C4C2×C3×#4111yescharacteristic
645C2×C4C3×H(5,𝔽2)11yescharacteristic
646C2×C4C3×2−1+411yescharacteristic
647C8—22no—
648C8—41no—
649C8—41no—
650C8C3×#12414yescomplemented
651C2×C3—81no—
652C2×C3—161no—
653C2×C3—161no—
654C2×C3#249111yescharacteristic
655C2×C3#317111yescharacteristic
656C2×C3#317911yescharacteristic
657C2×C3#327411yescharacteristic
658C2×C3#327511yescharacteristic
659C2×C3#334511yescharacteristic
660C2×C3#334711yescharacteristic
661C22—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22C3×#53211yescharacteristic
683C22C3×D4211yescharacteristic
684C22C3×#54711yescharacteristic
685C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
686C22C3×#57511yescharacteristic
687C22C3×#57611yescharacteristic
688C22C3×#57711yescharacteristic
689C4—22no—
690C4—41no—
691C4—41no—
692C4—42no—
693C4—41no—
694C4—42no—
695C4—41no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4C2×C3×#12411yescharacteristic
701C4C3×#54211yescharacteristic
702C4C3×#54811yescharacteristic
703C4C3×#55511yescharacteristic
704C3#2779411yescharacteristic, direct product factor, Sylow
705C2—81no—
706C2—161no—
707C2—161no—
708C2C3×#249111yescharacteristic
709C2C3×#317111yescharacteristic
710C2C3×#317911yescharacteristic
711C2C3×#327411yescharacteristic
712C2C3×#327511yescharacteristic
713C2C3×#334511yescharacteristic
714C2C3×#334711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#469C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#501C2semidirect
3. C3×#2491C2semidirect
4. C3×#2490C2semidirect
5. C3×#2034C2semidirect
6. C3×#2033C2semidirect
7. C3×#2025C2semidirect
8. C3×#2023C2semidirect
9. C3×#1972C2semidirect
10. C3×#1970C2semidirect
11. C3×#1926C2semidirect
12. C3×#1925C2semidirect
13. C3×#1809C2semidirect
14. C3×C4×#106C2semidirect
15. C3×#1753C2semidirect
16. #27794C3direct (N × H)
62. C2×#501C2×C3semidirect
64. #2491C2×C3semidirect
65. #2490C2×C3semidirect
66. #2034C2×C3semidirect
67. #2033C2×C3semidirect
68. #2025C2×C3semidirect
69. #2023C2×C3semidirect
70. #1972C2×C3semidirect
71. #1970C2×C3semidirect
72. #1926C2×C3semidirect
73. #1925C2×C3semidirect
74. #1809C2×C3semidirect
75. C4×#106C2×C3semidirect
76. #1753C2×C3semidirect
436. C3×C8#124semidirect
650. C8C3×#124semidirect
704. C3#27794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5012
C2×C3×#4692
C3×#24912
C3×#24902
C3×#20342
C3×#20332
C3×#20252
C3×#20232
C3×#19722
C3×#19702
C3×#19262
C3×#19252
C3×#18092
C3×C4×#1062
C3×#17532
#277943