Finite Group Databasebeta

← C2×(C3⋊#5935)⋊C3 #72242726

Subgroups — C2×(C3⋊#5935)⋊C3 #72242726

Order 3456.

1473 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 1473 conjugacy classes of subgroups — too many to draw. Only its 49 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
2(C3⋊#5935)⋊C3C212yesmaximal, direct product factor
3C2×C3⋊#5935C311yesmaximal, characteristic, complemented
4C2×C3×#5241—31nomaximal
5C22×(C3⋊S4)⋊C3—41nomaximal
6C32⋊#997C2211yescharacteristic, complemented
7C2×(C3⋊GL(2,𝔽3))⋊C3—42nomaximal
8C2×C32×H(5,𝔽2)D311yescharacteristic, complemented
9C2×C3×#997—21no—
10C2×C3×#997C2×C311yescharacteristic, complemented
11C3⋊#5935C2×C312yescomplemented
12C2×C3×#949—32no—
13C2×C3×#940—31no—
14C3×#5241—32no—
15C3×#5241—34no—
16C3×#5241—32no—
17C2×C3×#837—32no—
18C2×C3×#833—31no—
19C22×C22⋊H(3,𝔽3)—41no—
20C22×C22⋊H(3,𝔽3)—81no—
21C2×(C3⋊S4)⋊C3—42no—
22C2×(C3⋊S4)⋊C3—44no—
23C2×Q8⋊H(3,𝔽3)—42no—
24(C3⋊GL(2,𝔽3))⋊C3—44no—
25C2×#5935—91no—
26C2×C3×#453—91no—
27C2×#5241—31no—
28C22×C3⋊S4—41no—
29C32×H(5,𝔽2)—31no—
30C32×H(5,𝔽2)—32no—
31C32×H(5,𝔽2)—61no—
32C32×H(5,𝔽2)C2×D311yescharacteristic, complemented
33C2×C32×#41—32no—
34C22×C32×D4—31no—
35C22×C32×D4—61no—
36C22×C3×#67—61no—
37C22×C3×#67—61no—
38C22×C3×D12—31no—
39C3×#997—21no—
40C3×#997C22×C311yescharacteristic, complemented
41C2×C3⋊GL(2,𝔽3)—42no—
42C3×#949—34no—
43C3×#949—34no—
44C3×#949—62no—
45C3×#949—62no—
46C2×C3×#215—62no—
47C3×#940—32no—
48C3×#940—32no—
49C3×#940—61no—
50C3×#940—61no—
51C2×C3×#213—62no—
52C2×C3×C4×Dic3—31no—
53C2×C3×#208—32no—
54C3×#837—34no—
55C3×#837—34no—
56C3×#833—32no—
57C3×#833—32no—
58C22×(C3⋊D3)⋊C3—161no—
59C2×C22⋊H(3,𝔽3)—42no—
60C2×C22⋊H(3,𝔽3)—41no—
61C2×C22⋊H(3,𝔽3)—81no—
62C2×C22⋊H(3,𝔽3)—82no—
63(C3⋊S4)⋊C3—44no—
64Q8⋊H(3,𝔽3)—42no—
65C2×C3×H(5,𝔽2)—31no—
66C2×C3×H(5,𝔽2)C3×D311yescharacteristic
67C2×#997—31no—
68C2×#997—61no—
69#5935—92no—
70C2×C3×AGL(1,ℤ/8)—92no—
71C2×C3×#127—91no—
72C2×#949—32no—
73C2×#940—31no—
74C3×#453—92no—
75C3×#453—94no—
76C3×#453—92no—
77C2×C3×#104—92no—
78C2×C3×#100—91no—
79#5241—32no—
80#5241—34no—
81#5241—32no—
82C2×#837—32no—
83C2×#833—31no—
84C24×C32—21no—
85C24×C32—31no—
86C24×C32S411yescharacteristic
87C23×C3×D3—61no—
88C22×C3×A4—41no—
89C22×C3×A4—81no—
90C22×C3×A4—82no—
91C22×C3×A4—81no—
92C2×C3⋊S4—42no—
93C2×C3⋊S4—44no—
94C32×#41—32no—
95C32×#41—32no—
96C32×#41—32no—
97C32×#41—32no—
98C32×#41—62no—
99C32×#41—62no—
100C2×C32×Q8S412yescomplemented
101C2×C32×D4—32no—
102C2×C32×D4—31no—
103C2×C32×D4—31no—
104C2×C32×D4—31no—
105C2×C32×D4—31no—
106C2×C32×D4—62no—
107C2×C32×D4—62no—
108C2×C32×D4—61no—
109C2×C32×D4—61no—
110C2×C32×D4—62no—
111C2×C32×D4—62no—
112C2×C32×D4—61no—
113C2×C32×D4—61no—
114C22×C32×C4—31no—
115C22×C32×C4—61no—
116C2×C3×#67—62no—
117C2×C3×#67—62no—
118C2×C3×#67—62no—
119C2×C3×#67—62no—
120C2×C3×#67—124no—
121C2×C3×#67—124no—
122C22×C3×Dic3—61no—
123C2×C3×D12—32no—
124C2×C3×D12—62no—
125C2×C3×D12—62no—
126C2×C3×D12—61no—
127C2×C3×SL(2,𝔽3)—42no—
128C2×C3×SL(2,𝔽3)—82no—
129C3⋊GL(2,𝔽3)—44no—
130C3×#215—64no—
131C3×#215—64no—
132C3×#213—64no—
133C3×#213—64no—
134C3×C4×Dic3—32no—
135C3×C4×Dic3—61no—
136C3×#208—34no—
137C3×#208—62no—
138C2×C3×C3⋊C8—62no—
139C2×#453—91noSylow
140C22×H(3,𝔽3)—161no—
141C2×(C3⋊D3)⋊C3—162no—
142C2×(C3⋊D3)⋊C3—164no—
143C22⋊H(3,𝔽3)—41no—
144C22⋊H(3,𝔽3)—81no—
145C22×S4—361no—
146C3×H(5,𝔽2)—31no—
147C3×H(5,𝔽2)—32no—
148C3×H(5,𝔽2)—31no—
149C3×H(5,𝔽2)—32no—
150C3×H(5,𝔽2)—31no—
151C3×H(5,𝔽2)—61no—
152C3×H(5,𝔽2)—62no—
153C3×H(5,𝔽2)—61no—
154C3×H(5,𝔽2)—61no—
155C3×H(5,𝔽2)—62no—
156C3×H(5,𝔽2)C2×C3×D311yescharacteristic
157C2×C3×#41—32no—
158C2×C3×#41—32no—
159C2×C3×#41—62no—
160C22×C3×D4—31no—
161C22×C3×D4—31no—
162C22×C3×D4—61no—
163C22×C3×D4—61no—
164C22×C3×D4—62no—
165C22×C3×D4—61no—
166C22×C3×D4—91no—
167C22×C3×D4—181no—
168C22×C3×D4—181no—
169C22×#67—61no—
170C22×#67—61no—
171C22×D12—31no—
172#997—31no—
173#997—61no—
174C2×GL(2,𝔽3)—362no—
175C3×AGL(1,ℤ/8)—94no—
176C3×AGL(1,ℤ/8)—94no—
177C3×AGL(1,ℤ/8)—182no—
178C3×AGL(1,ℤ/8)—182no—
179C2×C3×SD16—182no—
180C2×C3×D8—182no—
181C2×C3×M16—92no—
182C3×#127—92no—
183C3×#127—92no—
184C3×#127—181no—
185C3×#127—181no—
186C2×C3×C42—91no—
187#949—34no—
188#949—34no—
189#949—62no—
190#949—62no—
191C2×#215—62no—
192#940—32no—
193#940—32no—
194#940—61no—
195#940—61no—
196C2×#213—62no—
197C2×C4×Dic3—31no—
198C2×#208—32no—
199C3×#104—94no—
200C3×#104—94no—
201C3×#100—92no—
202C3×#100—92no—
203#837—34no—
204#837—34no—
205#833—32no—
206#833—32no—
207C23×C32—21no—
208C23×C32—31no—
209C23×C32—31no—
210C23×C32—31no—
211C23×C32—31no—
212C23×C32—42no—
213C23×C32—61no—
214C23×C32—61no—
215C23×C32—61no—
216C23×C32—82no—
217C23×C32—122no—
218C23×C32C2×S411yescharacteristic
219C22×C3⋊D3—161no—
220C22×C3×D3—62no—
221C22×C3×D3—121no—
222C22×C3×D3—122no—
223C22×C3×D3—122no—
224C22×C3×D3—121no—
225C2×C3×A4—42no—
226C2×C3×A4—41no—
227C2×C3×A4—81no—
228C2×C3×A4—82no—
229C2×C3×A4—82no—
230C2×C3×A4—82no—
231C2×C3×A4—84no—
232C2×C3×A4—81no—
233C3⋊S4—44no—
234C32×Q8—32no—
235C32×Q8C2×S412yescomplemented
236C32×D4—32no—
237C32×D4—32no—
238C32×D4—62no—
239C32×D4—62no—
240C32×D4—62no—
241C32×D4—62no—
242C32×D4—62no—
243C2×C32×C4—31no—
244C2×C32×C4—32no—
245C2×C32×C4—31no—
246C2×C32×C4—32no—
247C2×C32×C4—61no—
248C2×C32×C4—62no—
249C2×C32×C4—61no—
250C3×#67—124no—
251C3×#67—124no—
252C3×#67—124no—
253C3×#67—124no—
254C2×C3×Dic3—62no—
255C2×C3×Dic3—64no—
256C3×D12—64no—
257C3×D12—122no—
258C3×SL(2,𝔽3)—42no—
259C3×SL(2,𝔽3)—82no—
260C3×C3⋊C8—64no—
261C2×H(5,𝔽2)(C3⋊D3)⋊C311yescharacteristic, complemented
262C2×AGL(1,ℤ/8)—92no—
263C2×#127—91no—
264#453—92no—
265#453—94no—
266#453—92no—
267C2×#104—92no—
268C2×#100—91no—
269C2×H(3,𝔽3)—162no—
270C2×H(3,𝔽3)—161no—
271(C3⋊D3)⋊C3—164no—
272C24×C3—21no—
273C24×C3—31no—
274C24×C3—31no—
275C24×C3—31no—
276C24×C3—61no—
277C24×C3—61no—
278C24×C3—181no—
279C24×C3C3×S411yescharacteristic
280C23×D3—61no—
281C22×A4—121no—
282C22×A4—241no—
283C22×A4—242no—
284C22×A4—241no—
285C2×S4—362no—
286C2×S4—364no—
287C3×#41—32no—
288C3×#41—32no—
289C3×#41—32no—
290C3×#41—32no—
291C3×#41—32no—
292C3×#41—32no—
293C3×#41—32no—
294C3×#41—32no—
295C3×#41—62no—
296C3×#41—62no—
297C3×#41—62no—
298C3×#41—62no—
299C3×#41—62no—
300C3×#41—62no—
301C3×#41—62no—
302C3×#41—62no—
303C3×#41—62no—
304C3×#41—62no—
305C3×#41—62no—
306C3×#41—62no—
307C2×C3×Q8—32no—
308C2×C3×Q8C3×S412yes—
309C2×C3×D4—32no—
310C2×C3×D4—32no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C2×C3×D4—31no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—61no—
320C2×C3×D4—61no—
321C2×C3×D4—62no—
322C2×C3×D4—61no—
323C2×C3×D4—61no—
324C2×C3×D4—62no—
325C2×C3×D4—62no—
326C2×C3×D4—62no—
327C2×C3×D4—62no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4—62no—
331C2×C3×D4—62no—
332C2×C3×D4—62no—
333C2×C3×D4—62no—
334C2×C3×D4—62no—
335C2×C3×D4—62no—
336C2×C3×D4—61no—
337C2×C3×D4—62no—
338C2×C3×D4—62no—
339C2×C3×D4—61no—
340C2×C3×D4—62no—
341C2×C3×D4—61no—
342C2×C3×D4—61no—
343C2×C3×D4—62no—
344C2×C3×D4—62no—
345C2×C3×D4—61no—
346C2×C3×D4—62no—
347C2×C3×D4—62no—
348C2×C3×D4—62no—
349C2×C3×D4—62no—
350C2×C3×D4—61no—
351C2×C3×D4—62no—
352C2×C3×D4—92no—
353C2×C3×D4—182no—
354C2×C3×D4—182no—
355C2×C3×D4—181no—
356C2×C3×D4—182no—
357C2×C3×D4—182no—
358C2×C3×D4—182no—
359C2×C3×D4—182no—
360C2×C3×D4—364no—
361C2×C3×D4—364no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—61no—
365C22×C3×C4—61no—
366C22×C3×C4—62no—
367C22×C3×C4—61no—
368C22×C3×C4—181no—
369C2×#67—62no—
370C2×#67—62no—
371C2×#67—62no—
372C2×#67—62no—
373C2×#67—124no—
374C2×#67—124no—
375C22×Dic3—61no—
376C2×D12—32no—
377C2×D12—62no—
378C2×D12—62no—
379C2×D12—61no—
380C2×SL(2,𝔽3)—122no—
381C2×SL(2,𝔽3)—242no—
382GL(2,𝔽3)—364no—
383C3×SD16—184no—
384C3×SD16—184no—
385C3×D8—184no—
386C3×D8—184no—
387C3×M16—94no—
388C3×M16—182no—
389C2×C3×C8—182no—
390C3×C42—92no—
391C3×C42—181no—
392#215—64no—
393#215—64no—
394#213—64no—
395#213—64no—
396C4×Dic3—32no—
397C4×Dic3—61no—
398#208—34no—
399#208—62no—
400C2×C3⋊C8—62no—
401C22×C32—31no—
402C22×C32—31no—
403C22×C32—41no—
404C22×C32—61no—
405C22×C32—61no—
406C22×C32—62no—
407C22×C32—81no—
408C22×C32—122no—
409C22×C32—121no—
410C22×C32—121no—
411C22×C32—121no—
412C22×C32—161no—
413C22×C32—241no—
414C22×C32—241no—
415C22×C32—321no—
416C22×C32#102011yescharacteristic
417C2×C3⋊D3—162no—
418C2×C3⋊D3—164no—
419C2×C3×D3—122no—
420C2×C3×D3—122no—
421C2×C3×D3—122no—
422C2×C3×D3—242no—
423C2×C3×D3—242no—
424C3×A4—41no—
425C3×A4—81no—
426C3×A4—81no—
427C3×A4—82no—
428C32×C4—32no—
429C32×C4—32no—
430C3×Dic3—64no—
431H(5,𝔽2)—31no—
432H(5,𝔽2)—32no—
433H(5,𝔽2)—61no—
434H(5,𝔽2)C2×(C3⋊D3)⋊C311yescharacteristic, complemented
435C2×#41—32no—
436C22×D4—31no—
437C22×D4—61no—
438C22×D4—91no—
439C22×D4—181no—
440C22×D4—181no—
441AGL(1,ℤ/8)—94no—
442AGL(1,ℤ/8)—94no—
443AGL(1,ℤ/8)—182no—
444AGL(1,ℤ/8)—182no—
445C2×SD16—182no—
446C2×D8—182no—
447C2×M16—92no—
448#127—92no—
449#127—92no—
450#127—181no—
451#127—181no—
452C2×C42—91no—
453#104—94no—
454#104—94no—
455#100—92no—
456#100—92no—
457H(3,𝔽3)—161noSylow
458C23×C3—21no—
459C23×C3—31no—
460C23×C3—31no—
461C23×C3—31no—
462C23×C3—31no—
463C23×C3—31no—
464C23×C3—31no—
465C23×C3—31no—
466C23×C3—31no—
467C23×C3—31no—
468C23×C3—42no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—61no—
473C23×C3—61no—
474C23×C3—62no—
475C23×C3—61no—
476C23×C3—61no—
477C23×C3—61no—
478C23×C3—62no—
479C23×C3—62no—
480C23×C3—61no—
481C23×C3—61no—
482C23×C3—61no—
483C23×C3—82no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—122no—
487C23×C3—182no—
488C23×C3—242no—
489C23×C3—242no—
490C23×C3—361no—
491C23×C3—361no—
492C23×C3—362no—
493C23×C3—362no—
494C23×C3C2×C3×S411yescharacteristic
495C22×D3—62no—
496C22×D3—121no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3—121no—
500C22×D3—1441no—
501C2×A4—122no—
502C2×A4—121no—
503C2×A4—241no—
504C2×A4—242no—
505C2×A4—242no—
506C2×A4—242no—
507C2×A4—244no—
508C2×A4—241no—
509S4—364no—
510C3×Q8—32no—
511C3×Q8—32no—
512C3×Q8—32no—
513C3×Q8—62no—
514C3×Q8C2×C3×S412yes—
515C3×D4—32no—
516C3×D4—32no—
517C3×D4—32no—
518C3×D4—32no—
519C3×D4—62no—
520C3×D4—62no—
521C3×D4—62no—
522C3×D4—62no—
523C3×D4—62no—
524C3×D4—62no—
525C3×D4—62no—
526C3×D4—62no—
527C3×D4—62no—
528C3×D4—62no—
529C3×D4—62no—
530C3×D4—62no—
531C3×D4—62no—
532C3×D4—62no—
533C3×D4—62no—
534C3×D4—62no—
535C3×D4—62no—
536C3×D4—62no—
537C3×D4—62no—
538C3×D4—62no—
539C3×D4—62no—
540C3×D4—62no—
541C3×D4—184no—
542C3×D4—362no—
543C3×D4—364no—
544C3×D4—364no—
545C3×D4—364no—
546C3×D4—364no—
547C2×C3×C4—31no—
548C2×C3×C4—32no—
549C2×C3×C4—31no—
550C2×C3×C4—31no—
551C2×C3×C4—31no—
552C2×C3×C4—32no—
553C2×C3×C4—32no—
554C2×C3×C4—32no—
555C2×C3×C4—62no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—62no—
559C2×C3×C4—61no—
560C2×C3×C4—62no—
561C2×C3×C4—61no—
562C2×C3×C4—62no—
563C2×C3×C4—62no—
564C2×C3×C4—62no—
565C2×C3×C4—62no—
566C2×C3×C4—61no—
567C2×C3×C4—62no—
568C2×C3×C4—61no—
569C2×C3×C4—182no—
570C2×C3×C4—184no—
571#67—124no—
572#67—124no—
573#67—124no—
574#67—124no—
575C2×Dic3—62no—
576C2×Dic3—64no—
577D12—64no—
578D12—122no—
579SL(2,𝔽3)—122no—
580SL(2,𝔽3)—242no—
581C3×C8—184no—
582C3⋊C8—64no—
583C2×C32—61no—
584C2×C32—61no—
585C2×C32—121no—
586C2×C32—121no—
587C2×C32—161no—
588C2×C32—162no—
589C2×C32—321no—
590C2×C32—322no—
591C2×C32#593512yescomplemented
592C2×C32C2×#102011yescharacteristic
593C3⋊D3—164no—
594C3×D3—242no—
595C24—21no—
596C24—31no—
597C24—181no—
598C24(C3⋊S4)⋊C311yescharacteristic
599#41—32no—
600#41—32no—
601#41—32no—
602#41—32no—
603#41—62no—
604#41—62no—
605C2×Q8(C3⋊S4)⋊C312yescomplemented
606C2×D4—32no—
607C2×D4—31no—
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—31no—
611C2×D4—62no—
612C2×D4—62no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—62no—
616C2×D4—62no—
617C2×D4—61no—
618C2×D4—61no—
619C2×D4—92no—
620C2×D4—182no—
621C2×D4—182no—
622C2×D4—181no—
623C2×D4—182no—
624C2×D4—182no—
625C2×D4—182no—
626C2×D4—182no—
627C2×D4—364no—
628C2×D4—364no—
629C22×C4—31no—
630C22×C4—61no—
631C22×C4—181no—
632SD16—184no—
633SD16—184no—
634D8—184no—
635D8—184no—
636M16—94no—
637M16—182no—
638C2×C8—182no—
639C42—92no—
640C42—181no—
641C22×C3—31no—
642C22×C3—31no—
643C22×C3—31no—
644C22×C3—31no—
645C22×C3—31no—
646C22×C3—41no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—62no—
650C22×C3—62no—
651C22×C3—62no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—62no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—81no—
658C22×C3—121no—
659C22×C3—122no—
660C22×C3—122no—
661C22×C3—124no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—122no—
669C22×C3—241no—
670C22×C3—241no—
671C22×C3—241no—
672C22×C3—241no—
673C22×C3—241no—
674C22×C3—241no—
675C22×C3—241no—
676C22×C3—242no—
677C22×C3—241no—
678C22×C3—242no—
679C22×C3—362no—
680C22×C3—362no—
681C22×C3—362no—
682C22×C3—481no—
683C22×C3—722no—
684C22×C3—722no—
685C22×C3—961no—
686C22×C3C3×#102011yescharacteristic
687C2×D3—122no—
688C2×D3—122no—
689C2×D3—122no—
690C2×D3—242no—
691C2×D3—242no—
692C2×D3—1442no—
693C2×D3—1444no—
694A4—121no—
695A4—241no—
696A4—241no—
697A4—242no—
698C3×C4—32no—
699C3×C4—32no—
700C3×C4—32no—
701C3×C4—32no—
702C3×C4—62no—
703C3×C4—62no—
704C3×C4—184no—
705Dic3—64no—
706C32—161no—
707C32—321no—
708C32C2×#593511yescharacteristic, complemented
709C23—21no—
710C23—31no—
711C23—31no—
712C23—31no—
713C23—31no—
714C23—42no—
715C23—61no—
716C23—61no—
717C23—61no—
718C23—82no—
719C23—122no—
720C23—182no—
721C23—361no—
722C23—362no—
723C23—362no—
724C23—361no—
725C23C2×(C3⋊S4)⋊C311yescharacteristic
726Q8—32no—
727Q8C2×(C3⋊S4)⋊C312yescomplemented
728D4—32no—
729D4—32no—
730D4—62no—
731D4—62no—
732D4—62no—
733D4—62no—
734D4—62no—
735D4—184no—
736D4—362no—
737D4—364no—
738D4—364no—
739D4—364no—
740D4—364no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—32no—
744C2×C4—32no—
745C2×C4—61no—
746C2×C4—62no—
747C2×C4—61no—
748C2×C4—182no—
749C2×C4—184no—
750C8—184no—
751C2×C3—31no—
752C2×C3—32no—
753C2×C3—61no—
754C2×C3—61no—
755C2×C3—61no—
756C2×C3—61no—
757C2×C3—121no—
758C2×C3—121no—
759C2×C3—121no—
760C2×C3—121no—
761C2×C3—122no—
762C2×C3—122no—
763C2×C3—121no—
764C2×C3—121no—
765C2×C3—481no—
766C2×C3—482no—
767C2×C3—722no—
768C2×C3—961no—
769C2×C3—962no—
770C2×C3C3×#593512yes—
771C2×C3C2×C3×#102011yescharacteristic
772D3—242no—
773D3—1444no—
774C22—31no—
775C22—31no—
776C22—41no—
777C22—62no—
778C22—61no—
779C22—61no—
780C22—81no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22—122no—
785C22—241no—
786C22—241no—
787C22—362no—
788C22—362no—
789C22—362no—
790C22—722no—
791C22—722no—
792C22#1172405211yescharacteristic
793C4—32no—
794C4—32no—
795C4—184no—
796C3—31no—
797C3—481no—
798C3—961no—
799C3C2×C3×#593511yescharacteristic
800C2—61no—
801C2—61no—
802C2—121no—
803C2—121no—
804C2—722no—
805C2(C3⋊#5935)⋊C312yesdirect product factor
806C2C2×#1172405211yescharacteristic
subgroupG/H
center, hypercenterC22#11724052
commutator, cosocle, hypocenterC3×#997C22×C3
FrattiniC2×C3C2×C3×#1020
FittingC2×C32×H(5,𝔽2)D3
socleC22×C3C3×#1020
LCSG ▷ C3×#997
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×C32⋊#997C2semidirect
2. (C3⋊#5935)⋊C3C2direct (N × H)
3. C2×C3⋊#5935C3semidirect
6. C32⋊#997C22semidirect
8. C2×C32×H(5,𝔽2)D3semidirect
10. C2×C3×#997C2×C3semidirect
11. C3⋊#5935C2×C3semidirect
32. C32×H(5,𝔽2)C2×D3semidirect
40. C3×#997C22×C3semidirect
100. C2×C32×Q8S4semidirect
235. C32×Q8C2×S4semidirect
261. C2×H(5,𝔽2)(C3⋊D3)⋊C3semidirect
434. H(5,𝔽2)C2×(C3⋊D3)⋊C3semidirect
591. C2×C32#5935semidirect
605. C2×Q8(C3⋊S4)⋊C3semidirect
708. C32C2×#5935semidirect
727. Q8C2×(C3⋊S4)⋊C3semidirect
805. C2(C3⋊#5935)⋊C3direct (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⋊#5935)⋊C32
C2×C3⋊#59353
C2×C3×#52413
C22×(C3⋊S4)⋊C34
C2×(C3⋊GL(2,𝔽3))⋊C34