Finite Group Databasebeta

← C2×C3×C3⋊#5935 #72242725

Subgroups — C2×C3×C3⋊#5935 #72242725

Order 3456.

1889 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 1889 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#997C211yesmaximal, characteristic, complemented
2C3×C3⋊#5935C212yesmaximal, direct product factor
3C2×C3⋊#5935C311yesmaximal, characteristic, direct product factor
4C2×C3×#5935—33nomaximal
5C2×C3×#5241—31nomaximal
6C22×C3×C3⋊S4—41nomaximal
7C32×#997C2211yescharacteristic, complemented
8C2×C3×C3⋊GL(2,𝔽3)—42nomaximal
9C2×C32×H(5,𝔽2)D311yescharacteristic, complemented
10C2×C3×#997—21no—
11C2×C3×#997—23no—
12C2×C3×#997D313yescomplemented
13C2×C3×#997C2×C311yescharacteristic, complemented
14C3⋊#5935C2×C312yesdirect product factor
15C3×#5935—36no—
16C2×C3×#949—32no—
17C2×C3×#940—31no—
18C3×#5241—32no—
19C3×#5241—34no—
20C3×#5241—32no—
21C2×C3×#837—32no—
22C2×C3×#833—31no—
23C22×C32×A4—41no—
24C22×C32×A4—81no—
25C2×C3×C3⋊S4—42no—
26C2×C3×C3⋊S4—44no—
27C2×C32×SL(2,𝔽3)—42no—
28C3×C3⋊GL(2,𝔽3)—44no—
29C2×#5935—33no—
30C2×C3×#453—91no—
31C2×#5241—31no—
32C22×C3⋊S4—41no—
33C22×C3×S4—123no—
34C32×H(5,𝔽2)—31no—
35C32×H(5,𝔽2)—32no—
36C32×H(5,𝔽2)—61no—
37C32×H(5,𝔽2)C2×D311yescharacteristic, complemented
38C2×C32×#41—32no—
39C22×C32×D4—31no—
40C22×C32×D4—61no—
41C22×C3×#67—61no—
42C22×C3×#67—61no—
43C22×C3×D12—31no—
44C3×#997—21no—
45C3×#997—23no—
46C3×#997C2×D313yescomplemented
47C3×#997C22×C311yescharacteristic, complemented
48C2×C3⋊GL(2,𝔽3)—42no—
49C2×C3×GL(2,𝔽3)—126no—
50C3×#949—34no—
51C3×#949—34no—
52C3×#949—62no—
53C3×#949—62no—
54C2×C3×#215—62no—
55C3×#940—32no—
56C3×#940—32no—
57C3×#940—61no—
58C3×#940—61no—
59C2×C3×#213—62no—
60C2×C3×C4×Dic3—31no—
61C2×C3×#208—32no—
62C3×#837—34no—
63C3×#837—34no—
64C3×#833—32no—
65C3×#833—32no—
66C22×C3×C3⋊D3—161no—
67C2×C32×A4—42no—
68C2×C32×A4—41no—
69C2×C32×A4—81no—
70C2×C32×A4—82no—
71C3×C3⋊S4—44no—
72C32×SL(2,𝔽3)—42no—
73C2×C3×H(5,𝔽2)—21no—
74C2×C3×H(5,𝔽2)C3×D311yescharacteristic, complemented
75C2×C3×H(5,𝔽2)C3⋊D311yescharacteristic, complemented
76C2×#997—23no—
77C2×#997C3×D313yescomplemented
78#5935—36no—
79C2×C3×AGL(1,ℤ/8)—92no—
80C2×C3×#127—91no—
81C2×#949—32no—
82C2×#940—31no—
83C3×#453—92no—
84C3×#453—94no—
85C3×#453—92no—
86C2×C3×#104—92no—
87C2×C3×#100—91no—
88#5241—32no—
89#5241—34no—
90#5241—32no—
91C2×#837—32no—
92C2×#833—31no—
93C24×C32—21no—
94C24×C32—31no—
95C24×C32S411yescharacteristic
96C23×C3×D3—61no—
97C22×C3×A4—41no—
98C22×C3×A4—43no—
99C22×C3×A4—83no—
100C22×C3×A4—81no—
101C22×C3×A4—83no—
102C22×C3×A4—86no—
103C22×C3×A4—82no—
104C22×C3×A4—81no—
105C2×C3⋊S4—42no—
106C2×C3⋊S4—44no—
107C2×C3×S4—126no—
108C2×C3×S4—1212no—
109C32×#41—32no—
110C32×#41—32no—
111C32×#41—32no—
112C32×#41—32no—
113C32×#41—62no—
114C32×#41—62no—
115C2×C32×Q8S412yescomplemented
116C2×C32×D4—32no—
117C2×C32×D4—31no—
118C2×C32×D4—31no—
119C2×C32×D4—31no—
120C2×C32×D4—31no—
121C2×C32×D4—62no—
122C2×C32×D4—62no—
123C2×C32×D4—61no—
124C2×C32×D4—61no—
125C2×C32×D4—62no—
126C2×C32×D4—62no—
127C2×C32×D4—61no—
128C2×C32×D4—61no—
129C22×C32×C4—31no—
130C22×C32×C4—61no—
131C2×C3×#67—62no—
132C2×C3×#67—62no—
133C2×C3×#67—62no—
134C2×C3×#67—62no—
135C2×C3×#67—124no—
136C2×C3×#67—124no—
137C22×C3×Dic3—61no—
138C2×C3×D12—32no—
139C2×C3×D12—62no—
140C2×C3×D12—62no—
141C2×C3×D12—61no—
142C2×C3×SL(2,𝔽3)—42no—
143C2×C3×SL(2,𝔽3)—46no—
144C2×C3×SL(2,𝔽3)—86no—
145C2×C3×SL(2,𝔽3)—82no—
146C3⋊GL(2,𝔽3)—44no—
147C3×GL(2,𝔽3)—1212no—
148C3×#215—64no—
149C3×#215—64no—
150C3×#213—64no—
151C3×#213—64no—
152C3×C4×Dic3—32no—
153C3×C4×Dic3—61no—
154C3×#208—34no—
155C3×#208—62no—
156C2×C3×C3⋊C8—62no—
157C2×#453—91noSylow
158C22×C33—161no—
159C2×C3×C3⋊D3—162no—
160C2×C3×C3⋊D3—164no—
161C32×A4—41no—
162C32×A4—81no—
163C22×S4—123no—
164C3×H(5,𝔽2)—21no—
165C3×H(5,𝔽2)—31no—
166C3×H(5,𝔽2)—31no—
167C3×H(5,𝔽2)—32no—
168C3×H(5,𝔽2)—32no—
169C3×H(5,𝔽2)—62no—
170C3×H(5,𝔽2)—61no—
171C3×H(5,𝔽2)—61no—
172C3×H(5,𝔽2)—61no—
173C3×H(5,𝔽2)—62no—
174C3×H(5,𝔽2)C2×C3×D311yescharacteristic, complemented
175C3×H(5,𝔽2)C2×C3⋊D311yescharacteristic, complemented
176C2×C3×#41—32no—
177C2×C3×#41—32no—
178C2×C3×#41—62no—
179C22×C3×D4—31no—
180C22×C3×D4—31no—
181C22×C3×D4—61no—
182C22×C3×D4—61no—
183C22×C3×D4—61no—
184C22×C3×D4—62no—
185C22×C3×D4—91no—
186C22×C3×D4—181no—
187C22×C3×D4—181no—
188C22×#67—61no—
189C22×#67—61no—
190C22×D12—31no—
191#997—23no—
192#997C2×C3×D313yescomplemented
193C2×GL(2,𝔽3)—126no—
194C3×AGL(1,ℤ/8)—94no—
195C3×AGL(1,ℤ/8)—94no—
196C3×AGL(1,ℤ/8)—182no—
197C3×AGL(1,ℤ/8)—182no—
198C2×C3×SD16—182no—
199C2×C3×D8—182no—
200C2×C3×M16—92no—
201C3×#127—92no—
202C3×#127—92no—
203C3×#127—181no—
204C3×#127—181no—
205C2×C3×C42—91no—
206#949—34no—
207#949—34no—
208#949—62no—
209#949—62no—
210C2×#215—62no—
211#940—32no—
212#940—32no—
213#940—61no—
214#940—61no—
215C2×#213—62no—
216C2×C4×Dic3—31no—
217C2×#208—32no—
218C3×#104—94no—
219C3×#104—94no—
220C3×#100—92no—
221C3×#100—92no—
222#837—34no—
223#837—34no—
224#833—32no—
225#833—32no—
226C23×C32—21no—
227C23×C32—31no—
228C23×C32—31no—
229C23×C32—31no—
230C23×C32—31no—
231C23×C32—42no—
232C23×C32—61no—
233C23×C32—61no—
234C23×C32—61no—
235C23×C32—82no—
236C23×C32—122no—
237C23×C32C2×S411yescharacteristic
238C22×C3⋊D3—161no—
239C22×C3×D3—62no—
240C22×C3×D3—121no—
241C22×C3×D3—122no—
242C22×C3×D3—122no—
243C22×C3×D3—121no—
244C22×C3×D3—483no—
245C2×C3×A4—42no—
246C2×C3×A4—41no—
247C2×C3×A4—46no—
248C2×C3×A4—43no—
249C2×C3×A4—83no—
250C2×C3×A4—81no—
251C2×C3×A4—82no—
252C2×C3×A4—86no—
253C2×C3×A4—83no—
254C2×C3×A4—86no—
255C2×C3×A4—86no—
256C2×C3×A4—82no—
257C2×C3×A4—82no—
258C2×C3×A4—812no—
259C2×C3×A4—84no—
260C2×C3×A4—81no—
261C3⋊S4—44no—
262C3×S4—1212no—
263C32×Q8—32no—
264C32×Q8C2×S412yescomplemented
265C32×D4—32no—
266C32×D4—32no—
267C32×D4—62no—
268C32×D4—62no—
269C32×D4—62no—
270C32×D4—62no—
271C32×D4—62no—
272C2×C32×C4—31no—
273C2×C32×C4—32no—
274C2×C32×C4—31no—
275C2×C32×C4—32no—
276C2×C32×C4—61no—
277C2×C32×C4—62no—
278C2×C32×C4—61no—
279C3×#67—124no—
280C3×#67—124no—
281C3×#67—124no—
282C3×#67—124no—
283C2×C3×Dic3—62no—
284C2×C3×Dic3—64no—
285C3×D12—64no—
286C3×D12—122no—
287C3×SL(2,𝔽3)—42no—
288C3×SL(2,𝔽3)—46no—
289C3×SL(2,𝔽3)—86no—
290C3×SL(2,𝔽3)—82no—
291C3×C3⋊C8—64no—
292C2×H(5,𝔽2)C3×C3⋊D311yescharacteristic, complemented
293C2×AGL(1,ℤ/8)—92no—
294C2×#127—91no—
295#453—92no—
296#453—94no—
297#453—92no—
298C2×#104—92no—
299C2×#100—91no—
300C2×C33—162no—
301C2×C33—161no—
302C3×C3⋊D3—164no—
303C24×C3—22no—
304C24×C3—21no—
305C24×C3—21no—
306C24×C3—21no—
307C24×C3—31no—
308C24×C3—31no—
309C24×C3—61no—
310C24×C3—181no—
311C24×C3C3×S411yescharacteristic
312C24×C3C3⋊S411yescharacteristic
313C23×D3—61no—
314C22×A4—43no—
315C22×A4—83no—
316C22×A4—86no—
317C22×A4—83no—
318C2×S4—126no—
319C2×S4—1212no—
320C3×#41—32no—
321C3×#41—32no—
322C3×#41—32no—
323C3×#41—32no—
324C3×#41—32no—
325C3×#41—32no—
326C3×#41—32no—
327C3×#41—32no—
328C3×#41—62no—
329C3×#41—62no—
330C3×#41—62no—
331C3×#41—62no—
332C3×#41—62no—
333C3×#41—62no—
334C3×#41—62no—
335C3×#41—62no—
336C3×#41—64no—
337C3×#41—64no—
338C2×C3×Q8—22no—
339C2×C3×Q8C3×S412yescomplemented
340C2×C3×Q8C3⋊S412yescomplemented
341C2×C3×D4—32no—
342C2×C3×D4—32no—
343C2×C3×D4—31no—
344C2×C3×D4—31no—
345C2×C3×D4—31no—
346C2×C3×D4—31no—
347C2×C3×D4—31no—
348C2×C3×D4—31no—
349C2×C3×D4—31no—
350C2×C3×D4—31no—
351C2×C3×D4—61no—
352C2×C3×D4—61no—
353C2×C3×D4—62no—
354C2×C3×D4—61no—
355C2×C3×D4—61no—
356C2×C3×D4—62no—
357C2×C3×D4—62no—
358C2×C3×D4—62no—
359C2×C3×D4—62no—
360C2×C3×D4—61no—
361C2×C3×D4—61no—
362C2×C3×D4—61no—
363C2×C3×D4—61no—
364C2×C3×D4—62no—
365C2×C3×D4—62no—
366C2×C3×D4—62no—
367C2×C3×D4—62no—
368C2×C3×D4—62no—
369C2×C3×D4—61no—
370C2×C3×D4—61no—
371C2×C3×D4—62no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C2×C3×D4—64no—
375C2×C3×D4—64no—
376C2×C3×D4—62no—
377C2×C3×D4—64no—
378C2×C3×D4—64no—
379C2×C3×D4—62no—
380C2×C3×D4—92no—
381C2×C3×D4—182no—
382C2×C3×D4—182no—
383C2×C3×D4—181no—
384C2×C3×D4—182no—
385C2×C3×D4—182no—
386C2×C3×D4—182no—
387C2×C3×D4—182no—
388C2×C3×D4—364no—
389C2×C3×D4—364no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—61no—
393C22×C3×C4—61no—
394C22×C3×C4—61no—
395C22×C3×C4—62no—
396C22×C3×C4—181no—
397C2×#67—62no—
398C2×#67—62no—
399C2×#67—62no—
400C2×#67—62no—
401C2×#67—124no—
402C2×#67—124no—
403C22×Dic3—61no—
404C2×D12—32no—
405C2×D12—62no—
406C2×D12—62no—
407C2×D12—61no—
408C2×SL(2,𝔽3)—46no—
409C2×SL(2,𝔽3)—86no—
410GL(2,𝔽3)—1212no—
411C3×SD16—184no—
412C3×SD16—184no—
413C3×D8—184no—
414C3×D8—184no—
415C3×M16—94no—
416C3×M16—182no—
417C2×C3×C8—182no—
418C3×C42—92no—
419C3×C42—181no—
420#215—64no—
421#215—64no—
422#213—64no—
423#213—64no—
424C4×Dic3—32no—
425C4×Dic3—61no—
426#208—34no—
427#208—62no—
428C2×C3⋊C8—62no—
429C22×C32—31no—
430C22×C32—31no—
431C22×C32—41no—
432C22×C32—61no—
433C22×C32—61no—
434C22×C32—62no—
435C22×C32—81no—
436C22×C32—122no—
437C22×C32—121no—
438C22×C32—121no—
439C22×C32—121no—
440C22×C32—161no—
441C22×C32—163no—
442C22×C32—241no—
443C22×C32—241no—
444C22×C32—323no—
445C22×C32—321no—
446C22×C32#102011yescharacteristic
447C2×C3⋊D3—162no—
448C2×C3⋊D3—164no—
449C2×C3×D3—122no—
450C2×C3×D3—122no—
451C2×C3×D3—122no—
452C2×C3×D3—242no—
453C2×C3×D3—242no—
454C2×C3×D3—486no—
455C2×C3×D3—4812no—
456C3×A4—41no—
457C3×A4—43no—
458C3×A4—81no—
459C3×A4—83no—
460C3×A4—83no—
461C3×A4—81no—
462C3×A4—86no—
463C3×A4—82no—
464C32×C4—32no—
465C32×C4—32no—
466C3×Dic3—64no—
467H(5,𝔽2)—31no—
468H(5,𝔽2)—32no—
469H(5,𝔽2)—61no—
470H(5,𝔽2)C2×C3×C3⋊D311yescharacteristic, complemented
471C2×#41—32no—
472C22×D4—31no—
473C22×D4—61no—
474C22×D4—91no—
475C22×D4—181no—
476C22×D4—181no—
477AGL(1,ℤ/8)—94no—
478AGL(1,ℤ/8)—94no—
479AGL(1,ℤ/8)—182no—
480AGL(1,ℤ/8)—182no—
481C2×SD16—182no—
482C2×D8—182no—
483C2×M16—92no—
484#127—92no—
485#127—92no—
486#127—181no—
487#127—181no—
488C2×C42—91no—
489#104—94no—
490#104—94no—
491#100—92no—
492#100—92no—
493C33—161noSylow
494C23×C3—22no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—31no—
499C23×C3—31no—
500C23×C3—31no—
501C23×C3—31no—
502C23×C3—31no—
503C23×C3—31no—
504C23×C3—31no—
505C23×C3—31no—
506C23×C3—42no—
507C23×C3—42no—
508C23×C3—61no—
509C23×C3—61no—
510C23×C3—61no—
511C23×C3—61no—
512C23×C3—62no—
513C23×C3—61no—
514C23×C3—61no—
515C23×C3—62no—
516C23×C3—61no—
517C23×C3—61no—
518C23×C3—62no—
519C23×C3—61no—
520C23×C3—61no—
521C23×C3—82no—
522C23×C3—84no—
523C23×C3—82no—
524C23×C3—82no—
525C23×C3—122no—
526C23×C3—122no—
527C23×C3—182no—
528C23×C3—242no—
529C23×C3—361no—
530C23×C3—362no—
531C23×C3—362no—
532C23×C3—361no—
533C23×C3C2×C3×S411yescharacteristic
534C23×C3C2×C3⋊S411yescharacteristic
535C22×D3—62no—
536C22×D3—121no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—121no—
540C22×D3—483no—
541C2×A4—46no—
542C2×A4—43no—
543C2×A4—83no—
544C2×A4—86no—
545C2×A4—86no—
546C2×A4—86no—
547C2×A4—812no—
548C2×A4—83no—
549S4—1212no—
550C3×Q8—22no—
551C3×Q8—32no—
552C3×Q8—32no—
553C3×Q8—62no—
554C3×Q8C2×C3×S412yescomplemented
555C3×Q8C2×C3⋊S412yescomplemented
556C3×D4—32no—
557C3×D4—32no—
558C3×D4—32no—
559C3×D4—32no—
560C3×D4—62no—
561C3×D4—62no—
562C3×D4—62no—
563C3×D4—62no—
564C3×D4—62no—
565C3×D4—62no—
566C3×D4—62no—
567C3×D4—62no—
568C3×D4—62no—
569C3×D4—62no—
570C3×D4—62no—
571C3×D4—62no—
572C3×D4—64no—
573C3×D4—64no—
574C3×D4—64no—
575C3×D4—64no—
576C3×D4—64no—
577C3×D4—184no—
578C3×D4—362no—
579C3×D4—364no—
580C3×D4—364no—
581C3×D4—364no—
582C3×D4—364no—
583C2×C3×C4—31no—
584C2×C3×C4—32no—
585C2×C3×C4—31no—
586C2×C3×C4—31no—
587C2×C3×C4—31no—
588C2×C3×C4—32no—
589C2×C3×C4—32no—
590C2×C3×C4—32no—
591C2×C3×C4—62no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—62no—
595C2×C3×C4—61no—
596C2×C3×C4—62no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—62no—
600C2×C3×C4—61no—
601C2×C3×C4—62no—
602C2×C3×C4—64no—
603C2×C3×C4—62no—
604C2×C3×C4—182no—
605C2×C3×C4—184no—
606#67—124no—
607#67—124no—
608#67—124no—
609#67—124no—
610C2×Dic3—62no—
611C2×Dic3—64no—
612D12—64no—
613D12—122no—
614SL(2,𝔽3)—46no—
615SL(2,𝔽3)—86no—
616C3×C8—184no—
617C3⋊C8—64no—
618C2×C32—61no—
619C2×C32—61no—
620C2×C32—121no—
621C2×C32—121no—
622C2×C32—161no—
623C2×C32—162no—
624C2×C32—163no—
625C2×C32—166no—
626C2×C32—323no—
627C2×C32—326no—
628C2×C32—321no—
629C2×C32—322no—
630C2×C32#593512yescomplemented
631C2×C32C2×#102011yescharacteristic
632C3⋊D3—164no—
633C3×D3—242no—
634C3×D3—4812no—
635C24—21no—
636C24—31no—
637C24—181no—
638C24C3×C3⋊S411yescharacteristic
639#41—32no—
640#41—32no—
641#41—32no—
642#41—32no—
643#41—62no—
644#41—62no—
645C2×Q8C3×C3⋊S412yescomplemented
646C2×D4—32no—
647C2×D4—31no—
648C2×D4—31no—
649C2×D4—31no—
650C2×D4—31no—
651C2×D4—62no—
652C2×D4—62no—
653C2×D4—61no—
654C2×D4—61no—
655C2×D4—62no—
656C2×D4—62no—
657C2×D4—61no—
658C2×D4—61no—
659C2×D4—92no—
660C2×D4—182no—
661C2×D4—182no—
662C2×D4—181no—
663C2×D4—182no—
664C2×D4—182no—
665C2×D4—182no—
666C2×D4—182no—
667C2×D4—364no—
668C2×D4—364no—
669C22×C4—31no—
670C22×C4—61no—
671C22×C4—181no—
672SD16—184no—
673SD16—184no—
674D8—184no—
675D8—184no—
676M16—94no—
677M16—182no—
678C2×C8—182no—
679C42—92no—
680C42—181no—
681C22×C3—21no—
682C22×C3—31no—
683C22×C3—31no—
684C22×C3—31no—
685C22×C3—31no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—61no—
689C22×C3—61no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—62no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—81no—
699C22×C3—82no—
700C22×C3—81no—
701C22×C3—81no—
702C22×C3—122no—
703C22×C3—124no—
704C22×C3—121no—
705C22×C3—121no—
706C22×C3—121no—
707C22×C3—121no—
708C22×C3—121no—
709C22×C3—121no—
710C22×C3—122no—
711C22×C3—122no—
712C22×C3—163no—
713C22×C3—241no—
714C22×C3—241no—
715C22×C3—241no—
716C22×C3—241no—
717C22×C3—241no—
718C22×C3—242no—
719C22×C3—241no—
720C22×C3—241no—
721C22×C3—242no—
722C22×C3—323no—
723C22×C3—362no—
724C22×C3—362no—
725C22×C3—362no—
726C22×C3—722no—
727C22×C3—722no—
728C22×C3C3×#102011yescharacteristic
729C22×C3C3⋊#102011yescharacteristic
730C2×D3—122no—
731C2×D3—122no—
732C2×D3—122no—
733C2×D3—242no—
734C2×D3—242no—
735C2×D3—486no—
736C2×D3—4812no—
737A4—43no—
738A4—83no—
739A4—83no—
740A4—86no—
741C3×C4—32no—
742C3×C4—32no—
743C3×C4—32no—
744C3×C4—32no—
745C3×C4—62no—
746C3×C4—62no—
747C3×C4—184no—
748Dic3—64no—
749C32—161no—
750C32—163no—
751C32—323no—
752C32—321no—
753C32C2×#593511yescharacteristic, complemented
754C23—21no—
755C23—31no—
756C23—31no—
757C23—31no—
758C23—31no—
759C23—42no—
760C23—61no—
761C23—61no—
762C23—61no—
763C23—82no—
764C23—122no—
765C23—182no—
766C23—361no—
767C23—362no—
768C23—362no—
769C23—361no—
770C23C2×C3×C3⋊S411yescharacteristic
771Q8—32no—
772Q8C2×C3×C3⋊S412yescomplemented
773D4—32no—
774D4—32no—
775D4—62no—
776D4—62no—
777D4—62no—
778D4—62no—
779D4—62no—
780D4—184no—
781D4—362no—
782D4—364no—
783D4—364no—
784D4—364no—
785D4—364no—
786C2×C4—31no—
787C2×C4—31no—
788C2×C4—32no—
789C2×C4—32no—
790C2×C4—61no—
791C2×C4—62no—
792C2×C4—61no—
793C2×C4—182no—
794C2×C4—184no—
795C8—184no—
796C2×C3—21no—
797C2×C3—22no—
798C2×C3—61no—
799C2×C3—61no—
800C2×C3—61no—
801C2×C3—61no—
802C2×C3—121no—
803C2×C3—121no—
804C2×C3—122no—
805C2×C3—122no—
806C2×C3—121no—
807C2×C3—121no—
808C2×C3—121no—
809C2×C3—121no—
810C2×C3—163no—
811C2×C3—166no—
812C2×C3—323no—
813C2×C3—326no—
814C2×C3—722no—
815C2×C3C3×#593512yescomplemented
816C2×C3C3⋊#593512yesdirect product factor
817C2×C3C2×C3×#102011yescharacteristic
818C2×C3C2×C3⋊#102011yescharacteristic
819D3—242no—
820D3—4812no—
821C22—31no—
822C22—31no—
823C22—41no—
824C22—62no—
825C22—61no—
826C22—61no—
827C22—81no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—122no—
832C22—241no—
833C22—241no—
834C22—362no—
835C22—362no—
836C22—362no—
837C22—722no—
838C22—722no—
839C22C3×C3⋊#102011yescharacteristic
840C4—32no—
841C4—32no—
842C4—184no—
843C3—21no—
844C3—163no—
845C3—323no—
846C3C2×C3×#593511yescharacteristic, complemented
847C3C2×C3⋊#593511yescharacteristic, direct product factor
848C2—61no—
849C2—61no—
850C2—121no—
851C2—121no—
852C2—722no—
853C2C3×C3⋊#593512yesdirect product factor
854C2C2×C3×C3⋊#102011yescharacteristic
subgroupG/H
center, hypercenterC22×C3C3⋊#1020
commutator, cosocle, hypocenterC3×#997C22×C3
FrattiniC2C2×C3×C3⋊#1020
FittingC2×C32×H(5,𝔽2)D3
socleC22×C32#1020
LCSG ▷ C3×#997
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C2×C32×#997C2semidirect
2. C3×C3⋊#5935C2direct (N × H)
3. C2×C3⋊#5935C3direct (N × H)
7. C32×#997C22semidirect
9. C2×C32×H(5,𝔽2)D3semidirect
12. C2×C3×#997D3semidirect
13. C2×C3×#997C2×C3semidirect
14. C3⋊#5935C2×C3direct (N × H)
37. C32×H(5,𝔽2)C2×D3semidirect
46. C3×#997C2×D3semidirect
47. C3×#997C22×C3semidirect
74. C2×C3×H(5,𝔽2)C3×D3semidirect
75. C2×C3×H(5,𝔽2)C3⋊D3semidirect
77. C2×#997C3×D3semidirect
115. C2×C32×Q8S4semidirect
174. C3×H(5,𝔽2)C2×C3×D3semidirect
175. C3×H(5,𝔽2)C2×C3⋊D3semidirect
192. #997C2×C3×D3semidirect
264. C32×Q8C2×S4semidirect
292. C2×H(5,𝔽2)C3×C3⋊D3semidirect
339. C2×C3×Q8C3×S4semidirect
340. C2×C3×Q8C3⋊S4semidirect
470. H(5,𝔽2)C2×C3×C3⋊D3semidirect
554. C3×Q8C2×C3×S4semidirect
555. C3×Q8C2×C3⋊S4semidirect
630. C2×C32#5935semidirect
645. C2×Q8C3×C3⋊S4semidirect
753. C32C2×#5935semidirect
772. Q8C2×C3×C3⋊S4semidirect
815. C2×C3C3×#5935semidirect
816. C2×C3C3⋊#5935direct (N × H)
846. C3C2×C3×#5935semidirect
847. C3C2×C3⋊#5935direct (N × H)
853. C2C3×C3⋊#5935direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#9972
C3×C3⋊#59352
C2×C3⋊#59353
C2×C3×#59353
C2×C3×#52413
C22×C3×C3⋊S44
C2×C3×C3⋊GL(2,𝔽3)4