Finite Group Databasebeta

← C3×#80240 #11878552

Subgroups — C3×#80240 #11878552

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5833C211yesmaximal, characteristic, complemented
2C3×#5629C211yesmaximal, characteristic, complemented
3C32×#452C211yesmaximal, characteristic, complemented
4C3×#5238C211yesmaximal, characteristic, complemented
5C3×#5189C211yesmaximal, characteristic, complemented
6C3×#5187C211yesmaximal, characteristic, complemented
7C3×#5172C211yesmaximal, characteristic, complemented
8C3×#5171C211yesmaximal, characteristic, complemented
9C3×#5043C211yesmaximal, characteristic, complemented
10C3×#4807C211yesmaximal, characteristic, complemented
11C3×#4805C211yesmaximal, characteristic, complemented
12C3×#4782C211yesmaximal, characteristic, complemented
13C3×#4777C211yesmaximal, characteristic, complemented
14C3×#4735C211yesmaximal, characteristic, complemented
15C3×#4727C211yesmaximal, characteristic, complemented
16C3×#3204—31nomaximal
17#80240C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C32×C22⋊Q8C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic
28C3×#939—21no—
29C3×#939—21no—
30C3×#938C2211yescharacteristic
31C3×#938C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C3×#930—21no—
34C3×#930C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C3×#924—21no—
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
38C2×C3×D3×C8C2211yescharacteristic
39C3×#896—21no—
40C3×#895—21no—
41C3×#895C2211yescharacteristic
42C3×D3×C4⋊C4C2211yescharacteristic
43C3×#884—21no—
44C3×#884—21no—
45C32×#103C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C32×C22⋊C8C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#830C2211yescharacteristic
53C3×#821C2211yescharacteristic
54C3×#821C2211yescharacteristic
55C3×(C2×D3)⋊C8C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×#817C2211yescharacteristic
58C3×#817C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#808C2211yescharacteristic
61C3×#537—31no—
62C3×#537—31no—
63#5833C2×C311yescharacteristic, complemented
64#5629C2×C311yescharacteristic, complemented
65C3×#483—31no—
66C3×#483—31no—
67C3×#481—31no—
68C3×#481—31no—
69C3×#470—31no—
70C3×#469—31no—
71C3×#465—31no—
72C3×#465—31no—
73C3×#452—21no—
74C3×#452—31no—
75C3×#452D311yescharacteristic, complemented
76C3×#452C2×C311yescharacteristic, complemented
77C3×#449—31no—
78C3×#449—31no—
79C3×#408—31no—
80#5238C2×C311yescharacteristic, complemented
81#5189C2×C311yescharacteristic, complemented
82#5187C2×C311yescharacteristic, complemented
83#5172C2×C311yescharacteristic, complemented
84#5171C2×C311yescharacteristic, complemented
85#5043C2×C311yescharacteristic, complemented
86#4807C2×C311yescharacteristic, complemented
87#4805C2×C311yescharacteristic, complemented
88#4782C2×C311yescharacteristic, complemented
89#4777C2×C311yescharacteristic, complemented
90#4735C2×C311yescharacteristic, complemented
91#4727C2×C311yescharacteristic, complemented
92C32×#41—41no—
93C32×#41—41no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67D411yescharacteristic
104C2×C3×#67D411yescharacteristic
105C22×C3×Dic3—21no—
106C3×#239—41no—
107C3×#239—41no—
108C3×#235—41no—
109C3×#235—41no—
110C2×C3×D12—21no—
111C2×C3×D12—21no—
112C2×C3×D12D411yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6D411yescharacteristic
119C32×Q16—41no—
120C32×SD16—41no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123C32×C4⋊C4—21no—
124C32×C4⋊C4C2311yescharacteristic
125C32×C22⋊C4—21no—
126C3×#217—21no—
127C3×#217—21no—
128C3×#215—41no—
129C3×#213—41no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4—21no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C3×ΓL(1,𝔽25)—41no—
146C3×D3×C8—41no—
147#3204—31noSylow
148C2×C3×#41—21no—
149C2×C3×#41—31no—
150C2×C3×#41—31no—
151C2×C3×#41C2×D311yescharacteristic
152C2×C3×#41C22×C311yescharacteristic
153C2×#239C22×C311yescharacteristic
154C2×#235C22×C311yescharacteristic
155C2×C3×Q16—21no—
156C2×C3×Q16C2×D311yescharacteristic
157C2×C3×Q16C22×C311yescharacteristic
158C2×C3×SD16—21no—
159C2×C3×SD16—31no—
160C2×C3×SD16C2×D311yescharacteristic
161C2×C3×SD16C22×C311yescharacteristic
162C2×C3×D8—31no—
163C2×C3×M16—31no—
164C22×C3×C8—31no—
165C3×C22⋊Q8—21no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8—31no—
169C3×C22⋊Q8—61no—
170C3×C22⋊Q8—61no—
171C3×C22⋊Q8C2×D311yescharacteristic
172C3×C22⋊Q8C22×C311yescharacteristic
173C3×#121—31no—
174C3×#121—31no—
175C3×#121—31no—
176C3×#121—31no—
177C3×#121—61no—
178C3×#121—61no—
179C3×#121—61no—
180C3×#121—61no—
181C3×#121—61no—
182C3×#121—61no—
183C2×C3×C4⋊C4—31no—
184C2×C3×C4⋊C4—31no—
185#946C22×C311yescharacteristic
186#946C22×C311yescharacteristic
187#946C22×C311yescharacteristic
188C2×#215C22×C311yescharacteristic
189#939—21no—
190#939—21no—
191#938C22×C311yescharacteristic
192#938C22×C311yescharacteristic
193C2×#213C22×C311yescharacteristic
194#930—21no—
195#930C22×C311yescharacteristic
196C2×C4⋊Dic3C22×C311yescharacteristic
197#924—21no—
198C2×ΓL(1,𝔽25)C22×C311yescharacteristic
199C2×D3×C8C22×C311yescharacteristic
200#896—21no—
201#895—21no—
202#895C22×C311yescharacteristic
203D3×C4⋊C4C22×C311yescharacteristic
204#884—21no—
205#884—21no—
206C3×#106—31no—
207C3×#106—31no—
208C3×#106—31no—
209C3×#106—31no—
210C3×#103—21no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103C2×D311yescharacteristic
215C3×#103C22×C311yescharacteristic
216C3×#102—21no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102C2×D311yescharacteristic
221C3×#102C22×C311yescharacteristic
222C3×C22⋊C8—21no—
223C3×C22⋊C8—31no—
224C3×C22⋊C8—31no—
225C3×C22⋊C8—31no—
226C3×C22⋊C8C2×D311yescharacteristic
227C3×C22⋊C8C22×C311yescharacteristic
228#835C22×C311yescharacteristic
229#835C22×C311yescharacteristic
230#835C22×C311yescharacteristic
231#832C22×C311yescharacteristic
232#830C22×C311yescharacteristic
233#821C22×C311yescharacteristic
234#821C22×C311yescharacteristic
235(C2×D3)⋊C8C22×C311yescharacteristic
236(C2×D3)⋊C8C22×C311yescharacteristic
237#817C22×C311yescharacteristic
238#817C22×C311yescharacteristic
239#808C22×C311yescharacteristic
240#808C22×C311yescharacteristic
241C23×C32—21no—
242C23×C32C2×D411yescharacteristic
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×Q8—21no—
247C32×Q8—21no—
248C32×Q8—21no—
249C32×Q8—21no—
250C32×D4—21no—
251C32×D4—21no—
252C32×D4—42no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—42no—
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261C3×#67—41no—
262C3×#67—41no—
263C3×#67—81no—
264C3×#67—81no—
265C3×#67—81no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—81no—
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—41no—
275C3×D12—42no—
276C3×D12—81no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×C4×D3—21no—
280C3×C4×D3—21no—
281C3×C4×D3—42no—
282C3×C4×D3—81no—
283C3×Dic6—41no—
284C32×C8—21no—
285C32×C8—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288#537—31no—
289#537—31no—
290#483—31no—
291#483—31no—
292#481—31no—
293#481—31no—
294#470—31no—
295#469—31no—
296#465—31no—
297#465—31no—
298#452—31no—
299#452C3×D311yescharacteristic, complemented
300#449—31no—
301#449—31no—
302#408—31no—
303C3×#41—41no—
304C3×#41—41no—
305C3×#41—41no—
306C3×#41—41no—
307C3×#41—42no—
308C3×#41—42no—
309C3×#41—121no—
310C3×#41—121no—
311C3×#41—121no—
312C3×#41—121no—
313C2×C3×Q8—21no—
314C2×C3×Q8—21no—
315C2×C3×Q8—31no—
316C2×C3×Q8C22×D311yescharacteristic
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×Q8C23×C311yescharacteristic
319C2×C3×Q8C23×C311yescharacteristic
320C2×C3×D4—21no—
321C2×C3×D4—21no—
322C2×C3×D4—21no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—41no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C23×C311yescharacteristic
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—41no—
341C22×C3×C4—61no—
342C22×C3×C4—61no—
343C22×C3×C4—61no—
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C23×C311yescharacteristic
346C2×#67—21no—
347C2×#67—21no—
348C2×#67—21no—
349C2×#67C3×D411yescharacteristic
350C2×#67C3×D411yescharacteristic
351C22×Dic3—21no—
352#239—41no—
353#239—41no—
354#235—41no—
355#235—41no—
356C2×D12—21no—
357C2×D12—21no—
358C2×D12C3×D411yescharacteristic
359C2×D12C23×C311yescharacteristic
360C2×C4×D3—21no—
361C2×C4×D3—21no—
362C2×C4×D3C23×C311yescharacteristic
363C2×C4×D3C23×C311yescharacteristic
364C2×Dic6C3×D411yescharacteristic
365C3×Q16—41no—
366C3×Q16—41no—
367C3×Q16—42no—
368C3×SD16—41no—
369C3×SD16—41no—
370C3×SD16—42no—
371C3×SD16—121no—
372C3×D8—121no—
373C3×M16—121no—
374C2×C3×C8—21no—
375C2×C3×C8—21no—
376C2×C3×C8—31no—
377C2×C3×C8—31no—
378C2×C3×C8—121no—
379C2×C3×C8C22×D311yescharacteristic
380C2×C3×C8C22×D311yescharacteristic
381C2×C3×C8C23×C311yescharacteristic
382C2×C3×C8C23×C311yescharacteristic
383C3×C4⋊C4—21no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—41no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4—61no—
395C3×C4⋊C4C22×D311yescharacteristic
396C3×C4⋊C4C23×C311yescharacteristic
397C3×C22⋊C4—21no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—41no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407#217—21no—
408#217—21no—
409#215—41no—
410#213—41no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
415(C2×D3)⋊C4—21no—
416C4⋊Dic3—21no—
417C4⋊Dic3C23×C311yescharacteristic
418C4⋊Dic3C23×C311yescharacteristic
419C4⋊Dic3C23×C311yescharacteristic
420Dic3⋊C4—21no—
421Dic3⋊C4—21no—
422Dic3⋊C4—21no—
423Dic3⋊C4—21no—
424C2×C3⋊C8C23×C311yescharacteristic
425C2×C3⋊C8C23×C311yescharacteristic
426ΓL(1,𝔽25)—41no—
427D3×C8—41no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32C22×D411yescharacteristic
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C32×C4—21no—
445C32×C4—41no—
446C32×C4—41no—
447C32×C4—41no—
448C32×C4H(5,𝔽2)11yescharacteristic
449C32×C4H(5,𝔽2)11yescharacteristic
450C3×Dic3—21no—
451C3×Dic3—21no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C2×#41—31no—
456C2×#41—31no—
457C2×#41C2×C3×D311yescharacteristic
458C2×Q16C2×C3×D311yescharacteristic
459C2×SD16—31no—
460C2×SD16C2×C3×D311yescharacteristic
461C2×D8—31no—
462C2×M16—31no—
463C22×C8—31no—
464C22⋊Q8—31no—
465C22⋊Q8—31no—
466C22⋊Q8—31no—
467C22⋊Q8—61no—
468C22⋊Q8—61no—
469C22⋊Q8C2×C3×D311yescharacteristic
470#121—31no—
471#121—31no—
472#121—31no—
473#121—31no—
474#121—61no—
475#121—61no—
476#121—61no—
477#121—61no—
478#121—61no—
479#121—61no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—31no—
482#106—31no—
483#106—31no—
484#106—31no—
485#106—31no—
486#103—31no—
487#103—31no—
488#103—31no—
489#103C2×C3×D311yescharacteristic
490#102—31no—
491#102—31no—
492#102—31no—
493#102C2×C3×D311yescharacteristic
494C22⋊C8—31no—
495C22⋊C8—31no—
496C22⋊C8—31no—
497C22⋊C8C2×C3×D311yescharacteristic
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—31no—
502C23×C3—31no—
503C23×C3—41no—
504C23×C3—61no—
505C23×C3D3×D411yescharacteristic
506C23×C3C2×C3×D411yescharacteristic
507C22×D3—21no—
508C22×D3C2×C3×D411yescharacteristic
509C22×D3C2×C3×D411yescharacteristic
510C3×Q8—22no—
511C3×Q8—21no—
512C3×Q8—21no—
513C3×Q8—21no—
514C3×Q8—21no—
515C3×Q8—21no—
516C3×Q8—21no—
517C3×Q8—21no—
518C3×Q8—21no—
519C3×Q8—41no—
520C3×Q8—41no—
521C3×Q8—41no—
522C3×Q8—121no—
523C3×D4—22no—
524C3×D4—21no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—41no—
529C3×D4—42no—
530C3×D4—42no—
531C3×D4—44no—
532C3×D4—61no—
533C3×D4—61no—
534C3×D4—121no—
535C3×D4—122no—
536C3×D4—121no—
537C3×D4—121no—
538C3×D4—241no—
539C3×D4—241no—
540C3×D4—241no—
541C3×D4—241no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—31no—
555C2×C3×C4—31no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—42no—
562C2×C3×C4—42no—
563C2×C3×C4—44no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—122no—
572C2×C3×C4—241no—
573C2×C3×C4—241no—
574C2×C3×C4D3×D411yescharacteristic
575C2×C3×C4C2×C3×D411yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C24×C311yescharacteristic
578#67—41no—
579#67—41no—
580#67—81no—
581#67—81no—
582#67—81no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—81no—
587C2×Dic3C2×C3×D411yescharacteristic
588C2×Dic3C2×C3×D411yescharacteristic
589D12—21no—
590D12—21no—
591D12—41no—
592D12—42no—
593D12—81no—
594C4×D3—21no—
595C4×D3—21no—
596C4×D3—21no—
597C4×D3—21no—
598C4×D3—42no—
599C4×D3—81no—
600Dic6—41no—
601C3×C8—21no—
602C3×C8—21no—
603C3×C8—21no—
604C3×C8—21no—
605C3×C8—41no—
606C3×C8—41no—
607C3×C8—61no—
608C3×C8—61no—
609C3⋊C8—21no—
610C3⋊C8—21no—
611C2×C32—41no—
612C2×C32—81no—
613C2×C32#53411yescharacteristic
614C2×C32#57711yescharacteristic
615C2×C32#57711yescharacteristic
616C3×D3—41no—
617C3×D3—41no—
618C3×D3—81no—
619#41—41no—
620#41—41no—
621#41—121no—
622#41—121no—
623#41—121no—
624#41—121no—
625C2×Q8—31no—
626C2×Q8C22×C3×D311yescharacteristic
627C2×Q8C22×C3×D311yescharacteristic
628C2×D4—21no—
629C2×D4—31no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—31no—
633C2×D4—61no—
634C2×D4—61no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—61no—
638C2×D4C22×C3×D311yescharacteristic
639C22×C4—21no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4C22×C3×D311yescharacteristic
646Q16—41no—
647SD16—41no—
648SD16—121no—
649D8—121no—
650M16—121no—
651C2×C8—31no—
652C2×C8—31no—
653C2×C8—121no—
654C2×C8C22×C3×D311yescharacteristic
655C2×C8C22×C3×D311yescharacteristic
656C4⋊C4—21no—
657C4⋊C4—31no—
658C4⋊C4—31no—
659C4⋊C4—31no—
660C4⋊C4—61no—
661C4⋊C4—61no—
662C4⋊C4—61no—
663C4⋊C4—61no—
664C4⋊C4—61no—
665C4⋊C4C22×C3×D311yescharacteristic
666C22⋊C4—21no—
667C22⋊C4—61no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—42no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C22×C3×D411yescharacteristic
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—21no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—41no—
718C3×C4—42no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—61no—
726C3×C4—61no—
727C3×C4—81no—
728C3×C4—81no—
729C3×C4—121no—
730C3×C4—121no—
731C3×C4—121no—
732C3×C4#100411yescharacteristic
733C3×C4#100411yescharacteristic
734C3×C4C3×H(5,𝔽2)11yescharacteristic
735C3×C4C3×H(5,𝔽2)11yescharacteristic
736Dic3—21no—
737Dic3—21no—
738Dic3—41no—
739Dic3—41no—
740Dic3—41no—
741C32#320411yescharacteristic, complemented, Sylow
742C23—21no—
743C23—31no—
744C23—31no—
745C23—61no—
746C23C3×D3×D411yescharacteristic
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—121no—
752D4—21no—
753D4—21no—
754D4—42no—
755D4—61no—
756D4—61no—
757D4—121no—
758D4—122no—
759D4—121no—
760D4—121no—
761D4—241no—
762D4—241no—
763D4—241no—
764D4—241no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—42no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—122no—
781C2×C4—241no—
782C2×C4—241no—
783C2×C4C3×D3×D411yescharacteristic
784C2×C4C23×C3×D311yescharacteristic
785C8—21no—
786C8—21no—
787C8—61no—
788C8—61no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—41no—
793C2×C3—41no—
794C2×C3—81no—
795C2×C3—82no—
796C2×C3—81no—
797C2×C3—81no—
798C2×C3—121no—
799C2×C3—121no—
800C2×C3—241no—
801C2×C3#558911yescharacteristic
802C2×C3#577011yescharacteristic
803C2×C3#577811yescharacteristic
804C2×C3C3×#53411yescharacteristic
805C2×C3C3×#57711yescharacteristic
806C2×C3C3×#57711yescharacteristic
807D3—41no—
808D3—41no—
809D3—81no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—61no—
817C22—61no—
818C22—61no—
819C22—61no—
820C22—61no—
821C22—61no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22C2×C3×D3×D411yescharacteristic
826C4—21no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—61no—
831C4—61no—
832C4—121no—
833C4—121no—
834C4—121no—
835C4C3×#100411yescharacteristic
836C4C3×#100411yescharacteristic
837C3—21no—
838C3#8024011yescharacteristic, direct product factor
839C3C3×#320411yescharacteristic, complemented
840C2—41no—
841C2—81no—
842C2—121no—
843C2—121no—
844C2—241no—
845C2C3×#558911yescharacteristic
846C2C3×#577011yescharacteristic
847C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#452C2
socleC22×C32C22×D4
hypercenterC3×#452D3
hypocenterC3C3×#3204
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#452

Complements

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

NH ≅ G/Ntype
1. C3×#5833C2semidirect
2. C3×#5629C2semidirect
3. C32×#452C2semidirect
4. C3×#5238C2semidirect
5. C3×#5189C2semidirect
6. C3×#5187C2semidirect
7. C3×#5172C2semidirect
8. C3×#5171C2semidirect
9. C3×#5043C2semidirect
10. C3×#4807C2semidirect
11. C3×#4805C2semidirect
12. C3×#4782C2semidirect
13. C3×#4777C2semidirect
14. C3×#4735C2semidirect
15. C3×#4727C2semidirect
17. #80240C3direct (N × H)
63. #5833C2×C3semidirect
64. #5629C2×C3semidirect
75. C3×#452D3semidirect
76. C3×#452C2×C3semidirect
80. #5238C2×C3semidirect
81. #5189C2×C3semidirect
82. #5187C2×C3semidirect
83. #5172C2×C3semidirect
84. #5171C2×C3semidirect
85. #5043C2×C3semidirect
86. #4807C2×C3semidirect
87. #4805C2×C3semidirect
88. #4782C2×C3semidirect
89. #4777C2×C3semidirect
90. #4735C2×C3semidirect
91. #4727C2×C3semidirect
299. #452C3×D3semidirect
741. C32#3204semidirect
838. C3#80240direct (N × H)
839. C3C3×#3204semidirect

Maximal subgroups

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

subgroupindex
C3×#58332
C3×#56292
C32×#4522
C3×#52382
C3×#51892
C3×#51872
C3×#51722
C3×#51712
C3×#50432
C3×#48072
C3×#48052
C3×#47822
C3×#47772
C3×#47352
C3×#47272
C3×#32043
#802403