Finite Group Databasebeta

← C109×#25144 #42143138

Subgroups — C109×#25144 #42143138

Order 27904.

1114 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#471×C109C211yesmaximal, characteristic, complemented
2C109×#3056C211yesmaximal, characteristic, complemented
3C109×#3003C211yesmaximal, characteristic
4C2×#450×C109C211yesmaximal, characteristic, complemented
5C109×#2933C211yesmaximal, characteristic, complemented
6C22×#100×C109C211yesmaximal, characteristic, complemented
7C109×#2063C211yesmaximal, characteristic, complemented
8C109×#2051C211yesmaximal, characteristic, complemented
9C109×#2046C211yesmaximal, characteristic, complemented
10C109×#2019C211yesmaximal, characteristic, complemented
11C109×#1977C211yesmaximal, characteristic, complemented
12C109×#1931C211yesmaximal, characteristic, complemented
13C109×#1907C211yesmaximal, characteristic, complemented
14C109×#1901C211yesmaximal, characteristic, complemented
15C109×#1855C211yesmaximal, characteristic, complemented
16C23×D4×C109C2211yescharacteristic
17C2×#137×C109C2211yescharacteristic, complemented
18C2×AGL(1,ℤ/8)×C109C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C109C2211yescharacteristic
20C22×SD16×C109C2211yescharacteristic
21C22×SD16×C109C2211yescharacteristic
22C2×#131×C109C2211yescharacteristic, complemented
23C22×M16×C109C2211yescharacteristic
24C22×M16×C109C2211yescharacteristic
25#525×C109C2211yescharacteristic
26C2×C22⋊Q8×C109C2211yescharacteristic
27#471×C109—24no—
28#470×C109—21no—
29#468×C109—21no—
30#467×C109—21no—
31#465×C109—21no—
32#450×C109—21no—
33#450×C109—21no—
34#450×C109—21no—
35#450×C109—21no—
36#450×C109—21no—
37#450×C109—21no—
38#447×C109—21no—
39#447×C109—21no—
40#436×C109—21no—
41#435×C109—21no—
42#435×C109—21no—
43C8×D4×C109—21no—
44C2×#108×C109C2211yescharacteristic, complemented
45C2×#108×C109C2211yescharacteristic, complemented
46#428×C109C2211yescharacteristic, complemented
47#424×C109C2211yescharacteristic, complemented
48#419×C109C2211yescharacteristic, complemented
49#418×C109C2211yescharacteristic
50#418×C109C2211yescharacteristic
51#417×C109C2211yescharacteristic, complemented
52C2×#102×C109C2211yescharacteristic
53C2×#102×C109C2211yescharacteristic
54C2×#101×C109C2211yescharacteristic, complemented
55C2×#101×C109C2211yescharacteristic, complemented
56C2×#100×C109—24no—
57C2×#100×C109C2211yescharacteristic
58C2×#100×C109C2211yescharacteristic
59C2×#100×C109C2211yescharacteristic
60C2×#100×C109C2211yescharacteristic
61#408×C109C2211yescharacteristic, complemented
62#407×C109C2211yescharacteristic
63C2×C22⋊C8×C109C2211yescharacteristic
64#405×C109C2211yescharacteristic, complemented
65#343×C109C2211yescharacteristic, complemented
66#343×C109C2211yescharacteristic, complemented
67#341×C109C2211yescharacteristic, complemented
68#341×C109C2211yescharacteristic, complemented
69C25×C109—21no—
70C2×#41×C109C2311yescharacteristic
71C22×Q8×C109C2311yescharacteristic
72C22×D4×C109—22no—
73C22×D4×C109—22no—
74C22×D4×C109—21no—
75C22×D4×C109—21no—
76C22×D4×C109—21no—
77C22×D4×C109—21no—
78C22×D4×C109—21no—
79C22×D4×C109—41no—
80C22×D4×C109—41no—
81C22×D4×C109C2311yescharacteristic
82C22×D4×C109C2311yescharacteristic
83C23×C4×C109C2311yescharacteristic
84#137×C109—22no—
85#137×C109—41no—
86AGL(1,ℤ/8)×C109—22no—
87AGL(1,ℤ/8)×C109—22no—
88AGL(1,ℤ/8)×C109—41no—
89AGL(1,ℤ/8)×C109—41no—
90C2×Q16×C109—21no—
91C2×SD16×C109—21no—
92C2×SD16×C109—21no—
93C2×SD16×C109—22no—
94C2×SD16×C109—21no—
95C2×SD16×C109—22no—
96C2×SD16×C109—21no—
97C2×SD16×C109—21no—
98C2×SD16×C109—21no—
99C2×SD16×C109—21no—
100C2×SD16×C109—41no—
101C2×SD16×C109—41no—
102C2×D8×C109—21no—
103C2×D8×C109—21no—
104#131×C109—22no—
105#131×C109—41no—
106C2×M16×C109—21no—
107C2×M16×C109—21no—
108C2×M16×C109—21no—
109C2×M16×C109—22no—
110C2×M16×C109—22no—
111C2×M16×C109—41no—
112C2×M16×C109—41no—
113C2×M16×C109C2311yescharacteristic
114C2×M16×C109C2311yescharacteristic
115C2×M16×C109C2311yescharacteristic
116C2×M16×C109C2311yescharacteristic
117C2×M16×C109C2311yescharacteristic
118C2×M16×C109C2311yescharacteristic
119C22×C8×C109—21no—
120C22×C8×C109—21no—
121C22×C8×C109—21no—
122C22×C8×C109C2311yescharacteristic
123C22×C8×C109C2311yescharacteristic
124#123×C109—21no—
125C22⋊Q8×C109—21no—
126C22⋊Q8×C109—21no—
127C22⋊Q8×C109—21no—
128C22⋊Q8×C109—21no—
129C22⋊Q8×C109D411yescharacteristic
130C22⋊Q8×C109D411yescharacteristic
131#121×C109D411yescharacteristic
132#121×C109D411yescharacteristic
133#120×C109—21no—
134C4×D4×C109—21no—
135C4×D4×C109—21no—
136#117×C109C2311yescharacteristic
137C2×C4⋊C4×C109—21no—
138C2×C4⋊C4×C109C2311yescharacteristic
139C2×C22⋊C4×C109—21no—
140#108×C109—22no—
141#108×C109—41no—
142#107×C109—21no—
143#106×C109—21no—
144C4⋊C8×C109—21no—
145C4⋊C8×C109—21no—
146#103×C109—21no—
147#103×C109—21no—
148#103×C109—21no—
149#102×C109—21no—
150#102×C109—21no—
151#102×C109—21no—
152#102×C109—21no—
153#102×C109—21no—
154#102×C109—21no—
155#102×C109—21no—
156#102×C109—21no—
157#102×C109—21no—
158#101×C109—22no—
159#101×C109—41no—
160#100×C109—22no—
161#100×C109—22no—
162#100×C109—22no—
163#100×C109D414yescomplemented
164C22⋊C8×C109—21no—
165C22⋊C8×C109—21no—
166C22⋊C8×C109—21no—
167C22⋊C8×C109—21no—
168C22⋊C8×C109D411yescharacteristic
169C22⋊C8×C109D411yescharacteristic
170C22⋊C8×C109D411yescharacteristic
171C22⋊C8×C109D411yescharacteristic
172#97×C109—21no—
173C4×C8×C109—21no—
174C24×C109—24no—
175C24×C109—21no—
176C24×C109—21no—
177C24×C109—42no—
178C24×C109—41no—
179C24×C109—41no—
180C24×C109—82no—
181C24×C109—82no—
182C24×C109#4111yescharacteristic
183#41×C109—21no—
184#41×C109—21no—
185#41×C109—21no—
186#41×C109—21no—
187C2×Q8×C109—21no—
188C2×Q8×C109—21no—
189C2×Q8×C109—21no—
190C2×Q8×C109—21no—
191C2×Q8×C109—21no—
192C2×Q8×C109—21no—
193C2×Q8×C109C2×D411yescharacteristic
194C2×D4×C109—24no—
195C2×D4×C109—21no—
196C2×D4×C109—21no—
197C2×D4×C109—21no—
198C2×D4×C109—21no—
199C2×D4×C109—21no—
200C2×D4×C109—21no—
201C2×D4×C109—21no—
202C2×D4×C109—21no—
203C2×D4×C109—21no—
204C2×D4×C109—21no—
205C2×D4×C109—21no—
206C2×D4×C109—21no—
207C2×D4×C109—21no—
208C2×D4×C109—42no—
209C2×D4×C109—42no—
210C2×D4×C109—42no—
211C2×D4×C109—42no—
212C2×D4×C109—42no—
213C2×D4×C109—42no—
214C2×D4×C109—42no—
215C2×D4×C109—42no—
216C2×D4×C109—42no—
217C2×D4×C109—41no—
218C2×D4×C109—41no—
219C2×D4×C109C2×D412yes—
220C2×D4×C109C2×D411yescharacteristic
221C2×D4×C109#4112yes—
222C22×C4×C109—21no—
223C22×C4×C109—21no—
224C22×C4×C109—21no—
225C22×C4×C109—21no—
226C22×C4×C109—21no—
227C22×C4×C109—21no—
228C22×C4×C109—21no—
229C22×C4×C109C2×D411yescharacteristic
230C22×C4×C109C2×D411yescharacteristic
231C22×C4×C109C2×D411yescharacteristic
232C22×C4×C109C2×D411yescharacteristic
233C22×C4×C109#4111yescharacteristic
234C22×C4×C109C2411yescharacteristic
235Q16×C109—42no—
236SD16×C109—42no—
237SD16×C109—42no—
238SD16×C109—42no—
239SD16×C109—42no—
240SD16×C109—42no—
241SD16×C109—42no—
242SD16×C109—42no—
243D8×C109—42no—
244D8×C109—42no—
245M16×C109—21no—
246M16×C109—21no—
247M16×C109—21no—
248M16×C109—21no—
249M16×C109—21no—
250M16×C109—21no—
251M16×C109—21no—
252M16×C109—21no—
253M16×C109—21no—
254M16×C109—21no—
255M16×C109—42no—
256M16×C109—42no—
257M16×C109—42no—
258M16×C109C2×D412yes—
259M16×C109C2×D412yes—
260C2×C8×C109—21no—
261C2×C8×C109—21no—
262C2×C8×C109—21no—
263C2×C8×C109—21no—
264C2×C8×C109—21no—
265C2×C8×C109—21no—
266C2×C8×C109—21no—
267C2×C8×C109—21no—
268C2×C8×C109—21no—
269C2×C8×C109—21no—
270C2×C8×C109—42no—
271C2×C8×C109—42no—
272C2×C8×C109—42no—
273C2×C8×C109C2×D411yescharacteristic
274C2×C8×C109C2×D411yescharacteristic
275C2×C8×C109C2×D411yescharacteristic
276C2×C8×C109C2×D411yescharacteristic
277C4⋊C4×C109—21no—
278C4⋊C4×C109—21no—
279C4⋊C4×C109—21no—
280C4⋊C4×C109—21no—
281C4⋊C4×C109—41no—
282C4⋊C4×C109—41no—
283C4⋊C4×C109C2×D411yescharacteristic
284C4⋊C4×C109C2×D411yescharacteristic
285C22⋊C4×C109—21no—
286C22⋊C4×C109—21no—
287C22⋊C4×C109—21no—
288C22⋊C4×C109—21no—
289C22⋊C4×C109—21no—
290C22⋊C4×C109—41no—
291C22⋊C4×C109—41no—
292C42×C109—21no—
293C23×C109—21no—
294C23×C109—21no—
295C23×C109—22no—
296C23×C109—21no—
297C23×C109—22no—
298C23×C109—22no—
299C23×C109—41no—
300C23×C109—44no—
301C23×C109—44no—
302C23×C109—41no—
303C23×C109—41no—
304C23×C109—41no—
305C23×C109—41no—
306C23×C109—81no—
307C23×C109—81no—
308C23×C109—81no—
309C23×C109—81no—
310C23×C109—82no—
311C23×C109—82no—
312C23×C109—82no—
313C23×C109—88no—
314C23×C109—88no—
315C23×C109—82no—
316C23×C109#12111yescharacteristic
317C23×C109#12111yescharacteristic
318C23×C109C2×#4111yescharacteristic
319Q8×C109—21no—
320Q8×C109—21no—
321Q8×C109—41no—
322Q8×C109—41no—
323Q8×C109—41no—
324Q8×C109—41no—
325D4×C109—21no—
326D4×C109—22no—
327D4×C109—22no—
328D4×C109—21no—
329D4×C109—22no—
330D4×C109—22no—
331D4×C109—44no—
332D4×C109—44no—
333D4×C109—41no—
334D4×C109—41no—
335D4×C109—42no—
336D4×C109—41no—
337D4×C109—41no—
338D4×C109—41no—
339D4×C109—41no—
340D4×C109—81no—
341C2×C4×C109—21no—
342C2×C4×C109—21no—
343C2×C4×C109—21no—
344C2×C4×C109—21no—
345C2×C4×C109—21no—
346C2×C4×C109—21no—
347C2×C4×C109—21no—
348C2×C4×C109—21no—
349C2×C4×C109—21no—
350C2×C4×C109—21no—
351C2×C4×C109—21no—
352C2×C4×C109—21no—
353C2×C4×C109—21no—
354C2×C4×C109—41no—
355C2×C4×C109—41no—
356C2×C4×C109—41no—
357C2×C4×C109—41no—
358C2×C4×C109—41no—
359C2×C4×C109—41no—
360C2×C4×C109—81no—
361C2×C4×C109#12111yescharacteristic
362C2×C4×C109#12111yescharacteristic
363C2×C4×C109C22×D411yescharacteristic
364C2×C4×C109C22×D411yescharacteristic
365C2×C4×C109C22×D411yescharacteristic
366C2×C4×C109C2×#4111yescharacteristic
367C2×C4×C109H(5,𝔽2)11yescharacteristic
368C2×C4×C109H(5,𝔽2)11yescharacteristic
369C8×C109—21no—
370C8×C109—21no—
371C8×C109—22no—
372C8×C109—22no—
373C8×C109—21no—
374C8×C109—21no—
375C8×C109—41no—
376C8×C109—41no—
377C8×C109—41no—
378C8×C109—41no—
379C22×C109—21no—
380C22×C109—21no—
381C22×C109—21no—
382C22×C109—21no—
383C22×C109—21no—
384C22×C109—21no—
385C22×C109—21no—
386C22×C109—42no—
387C22×C109—42no—
388C22×C109—41no—
389C22×C109—42no—
390C22×C109—42no—
391C22×C109—41no—
392C22×C109—41no—
393C22×C109—82no—
394C22×C109—82no—
395C22×C109—88no—
396C22×C109—82no—
397C22×C109—82no—
398C22×C109—88no—
399C22×C109—81no—
400C22×C109—81no—
401C22×C109—81no—
402C22×C109—81no—
403C22×C109#47112yescomplemented
404C22×C109C2×#12111yescharacteristic
405C22×C109#52511yescharacteristic
406C22×C109#53811yescharacteristic
407C4×C109—21no—
408C4×C109—21no—
409C4×C109—41no—
410C4×C109—41no—
411C4×C109—41no—
412C4×C109—81no—
413C4×C109—81no—
414C4×C109D4211yescharacteristic
415C4×C109D4211yescharacteristic
416C4×C109#54611yescharacteristic
417C4×C109#54611yescharacteristic
418#25144C10911yesmaximal, characteristic, direct product factor, Sylow
419C2×C109—21no—
420C2×C109—21no—
421C2×C109—22no—
422C2×C109—41no—
423C2×C109—81no—
424C2×C109—82no—
425C2×C109—82no—
426C2×C109#242411yescharacteristic
427C2×C109C2×#47111yescharacteristic
428C2×C109#306811yescharacteristic
429C2×#471C2×C10911yescharacteristic, complemented
430#3056C2×C10911yescharacteristic, complemented
431#3003C2×C10911yescharacteristic
432C2×#450C2×C10911yescharacteristic, complemented
433#2933C2×C10911yescharacteristic, complemented
434C22×#100C2×C10911yescharacteristic, complemented
435#2063C2×C10911yescharacteristic, complemented
436#2051C2×C10911yescharacteristic, complemented
437#2046C2×C10911yescharacteristic, complemented
438#2019C2×C10911yescharacteristic, complemented
439#1977C2×C10911yescharacteristic, complemented
440#1931C2×C10911yescharacteristic, complemented
441#1907C2×C10911yescharacteristic, complemented
442#1901C2×C10911yescharacteristic, complemented
443#1855C2×C10911yescharacteristic, complemented
444C109#2514411yescharacteristic, direct product factor, Sylow
445C23×D4C22×C10911yescharacteristic
446C2×#137C22×C10911yescharacteristic, complemented
447C2×AGL(1,ℤ/8)C22×C10911yescharacteristic
448C2×AGL(1,ℤ/8)C22×C10911yescharacteristic
449C22×SD16C22×C10911yescharacteristic
450C22×SD16C22×C10911yescharacteristic
451C2×#131C22×C10911yescharacteristic, complemented
452C22×M16C22×C10911yescharacteristic
453C22×M16C22×C10911yescharacteristic
454#525C22×C10911yescharacteristic
455C2×C22⋊Q8C22×C10911yescharacteristic
456#471—24no—
457#470—21no—
458#468—21no—
459#467—21no—
460#465—21no—
461#450—21no—
462#450—21no—
463#450—21no—
464#450—21no—
465#450—21no—
466#450—21no—
467#447—21no—
468#447—21no—
469#436—21no—
470#435—21no—
471#435—21no—
472C8×D4—21no—
473C2×#108C22×C10911yescharacteristic, complemented
474C2×#108C22×C10911yescharacteristic, complemented
475#428C22×C10911yescharacteristic, complemented
476#424C22×C10911yescharacteristic, complemented
477#419C22×C10911yescharacteristic, complemented
478#418C22×C10911yescharacteristic
479#418C22×C10911yescharacteristic
480#417C22×C10911yescharacteristic, complemented
481C2×#102C22×C10911yescharacteristic
482C2×#102C22×C10911yescharacteristic
483C2×#101C22×C10911yescharacteristic, complemented
484C2×#101C22×C10911yescharacteristic, complemented
485C2×#100—24no—
486C2×#100C22×C10911yescharacteristic
487C2×#100C22×C10911yescharacteristic
488C2×#100C22×C10911yescharacteristic
489C2×#100C22×C10911yescharacteristic
490#408C22×C10911yescharacteristic, complemented
491#407C22×C10911yescharacteristic
492C2×C22⋊C8C22×C10911yescharacteristic
493#405C22×C10911yescharacteristic, complemented
494#343C22×C10911yescharacteristic, complemented
495#343C22×C10911yescharacteristic, complemented
496#341C22×C10911yescharacteristic, complemented
497#341C22×C10911yescharacteristic, complemented
498C25—21no—
499C2×#41C23×C10911yescharacteristic
500C22×Q8C23×C10911yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C23×C10911yescharacteristic
511C22×D4C23×C10911yescharacteristic
512C23×C4C23×C10911yescharacteristic
513#137—22no—
514#137—41no—
515AGL(1,ℤ/8)—22no—
516AGL(1,ℤ/8)—22no—
517AGL(1,ℤ/8)—41no—
518AGL(1,ℤ/8)—41no—
519C2×Q16—21no—
520C2×SD16—21no—
521C2×SD16—21no—
522C2×SD16—22no—
523C2×SD16—21no—
524C2×SD16—22no—
525C2×SD16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×D8—21no—
532C2×D8—21no—
533#131—22no—
534#131—41no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16C23×C10911yescharacteristic
543C2×M16C23×C10911yescharacteristic
544C2×M16C23×C10911yescharacteristic
545C2×M16C23×C10911yescharacteristic
546C2×M16C23×C10911yescharacteristic
547C2×M16C23×C10911yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—21no—
551C22×C8C23×C10911yescharacteristic
552C22×C8C23×C10911yescharacteristic
553#123—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8D4×C10911yescharacteristic
559C22⋊Q8D4×C10911yescharacteristic
560#121D4×C10911yescharacteristic
561#121D4×C10911yescharacteristic
562#120—21no—
563C4×D4—21no—
564C4×D4—21no—
565#117C23×C10911yescharacteristic
566C2×C4⋊C4—21no—
567C2×C4⋊C4C23×C10911yescharacteristic
568C2×C22⋊C4—21no—
569#108—22no—
570#108—41no—
571#107—21no—
572#106—21no—
573C4⋊C8—21no—
574C4⋊C8—21no—
575#103—21no—
576#103—21no—
577#103—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581#102—21no—
582#102—21no—
583#102—21no—
584#102—21no—
585#102—21no—
586#102—21no—
587#101—22no—
588#101—41no—
589#100—22no—
590#100—22no—
591#100—22no—
592#100D4×C10914yescomplemented
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—21no—
596C22⋊C8—21no—
597C22⋊C8D4×C10911yescharacteristic
598C22⋊C8D4×C10911yescharacteristic
599C22⋊C8D4×C10911yescharacteristic
600C22⋊C8D4×C10911yescharacteristic
601#97—21no—
602C4×C8—21no—
603C24—24no—
604C24—21no—
605C24—21no—
606C24—42no—
607C24—41no—
608C24—41no—
609C24—82no—
610C24—82no—
611C24#41×C10911yescharacteristic
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8C2×D4×C10911yescharacteristic
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—41no—
647C2×D4—41no—
648C2×D4C2×D4×C10912yes—
649C2×D4C2×D4×C10911yescharacteristic
650C2×D4#41×C10912yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4C2×D4×C10911yescharacteristic
659C22×C4C2×D4×C10911yescharacteristic
660C22×C4C2×D4×C10911yescharacteristic
661C22×C4C2×D4×C10911yescharacteristic
662C22×C4#41×C10911yescharacteristic
663C22×C4C24×C10911yescharacteristic
664Q16—42no—
665SD16—42no—
666SD16—42no—
667SD16—42no—
668SD16—42no—
669SD16—42no—
670SD16—42no—
671SD16—42no—
672D8—42no—
673D8—42no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C10912yes—
688M16C2×D4×C10912yes—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—42no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8C2×D4×C10911yescharacteristic
703C2×C8C2×D4×C10911yescharacteristic
704C2×C8C2×D4×C10911yescharacteristic
705C2×C8C2×D4×C10911yescharacteristic
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—41no—
711C4⋊C4—41no—
712C4⋊C4C2×D4×C10911yescharacteristic
713C4⋊C4C2×D4×C10911yescharacteristic
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—41no—
720C22⋊C4—41no—
721C42—21no—
722C23—21no—
723C23—21no—
724C23—22no—
725C23—21no—
726C23—22no—
727C23—22no—
728C23—41no—
729C23—44no—
730C23—44no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—81no—
736C23—81no—
737C23—81no—
738C23—81no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—88no—
743C23—88no—
744C23—82no—
745C23#121×C10911yescharacteristic
746C23#121×C10911yescharacteristic
747C23C2×#41×C10911yescharacteristic
748Q8—21no—
749Q8—21no—
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754D4—21no—
755D4—22no—
756D4—22no—
757D4—21no—
758D4—22no—
759D4—22no—
760D4—44no—
761D4—44no—
762D4—41no—
763D4—41no—
764D4—42no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—81no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—81no—
790C2×C4#121×C10911yescharacteristic
791C2×C4#121×C10911yescharacteristic
792C2×C4C22×D4×C10911yescharacteristic
793C2×C4C22×D4×C10911yescharacteristic
794C2×C4C22×D4×C10911yescharacteristic
795C2×C4C2×#41×C10911yescharacteristic
796C2×C4H(5,𝔽2)×C10911yescharacteristic
797C2×C4H(5,𝔽2)×C10911yescharacteristic
798C8—21no—
799C8—21no—
800C8—22no—
801C8—22no—
802C8—21no—
803C8—21no—
804C8—41no—
805C8—41no—
806C8—41no—
807C8—41no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—42no—
821C22—42no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—88no—
827C22—88no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22#471×C10912yescomplemented
833C22C2×#121×C10911yescharacteristic
834C22#525×C10911yescharacteristic
835C22#538×C10911yescharacteristic
836C4—21no—
837C4—21no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—81no—
842C4—81no—
843C4D42×C10911yescharacteristic
844C4D42×C10911yescharacteristic
845C4#546×C10911yescharacteristic
846C4#546×C10911yescharacteristic
847C2—21no—
848C2—21no—
849C2—22no—
850C2—41no—
851C2—81no—
852C2—82no—
853C2—82no—
854C2C109×#242411yescharacteristic
855C2C2×#471×C10911yescharacteristic
856C2C109×#306811yescharacteristic
subgroupG/H
center, socleC22×C109C2×#121
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC109×#3003C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#471×C109C2semidirect
2. C109×#3056C2semidirect
4. C2×#450×C109C2semidirect
5. C109×#2933C2semidirect
6. C22×#100×C109C2semidirect
7. C109×#2063C2semidirect
8. C109×#2051C2semidirect
9. C109×#2046C2semidirect
10. C109×#2019C2semidirect
11. C109×#1977C2semidirect
12. C109×#1931C2semidirect
13. C109×#1907C2semidirect
14. C109×#1901C2semidirect
15. C109×#1855C2semidirect
17. C2×#137×C109C22semidirect
22. C2×#131×C109C22semidirect
44. C2×#108×C109C22semidirect
45. C2×#108×C109C22semidirect
46. #428×C109C22semidirect
47. #424×C109C22semidirect
48. #419×C109C22semidirect
51. #417×C109C22semidirect
54. C2×#101×C109C22semidirect
55. C2×#101×C109C22semidirect
61. #408×C109C22semidirect
64. #405×C109C22semidirect
65. #343×C109C22semidirect
66. #343×C109C22semidirect
67. #341×C109C22semidirect
68. #341×C109C22semidirect
163. #100×C109D4semidirect
403. C22×C109#471semidirect
418. #25144C109direct (N × H)
429. C2×#471C2×C109semidirect
430. #3056C2×C109semidirect
432. C2×#450C2×C109semidirect
433. #2933C2×C109semidirect
434. C22×#100C2×C109semidirect
435. #2063C2×C109semidirect
436. #2051C2×C109semidirect
437. #2046C2×C109semidirect
438. #2019C2×C109semidirect
439. #1977C2×C109semidirect
440. #1931C2×C109semidirect
441. #1907C2×C109semidirect
442. #1901C2×C109semidirect
443. #1855C2×C109semidirect
444. C109#25144direct (N × H)
446. C2×#137C22×C109semidirect
451. C2×#131C22×C109semidirect
473. C2×#108C22×C109semidirect
474. C2×#108C22×C109semidirect
475. #428C22×C109semidirect
476. #424C22×C109semidirect
477. #419C22×C109semidirect
480. #417C22×C109semidirect
483. C2×#101C22×C109semidirect
484. C2×#101C22×C109semidirect
490. #408C22×C109semidirect
493. #405C22×C109semidirect
494. #343C22×C109semidirect
495. #343C22×C109semidirect
496. #341C22×C109semidirect
497. #341C22×C109semidirect
592. #100D4×C109semidirect
832. C22#471×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#471×C1092
C109×#30562
C109×#30032
C2×#450×C1092
C109×#29332
C22×#100×C1092
C109×#20632
C109×#20512
C109×#20462
C109×#20192
C109×#19772
C109×#19312
C109×#19072
C109×#19012
C109×#18552
#25144109