Finite Group Databasebeta

← C109×#24402 #42142396

Subgroups — C109×#24402 #42142396

Order 27904.

1358 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C109C211yesmaximal, characteristic, complemented
2C2×#472×C109C211yesmaximal, characteristic, complemented
3C2×#471×C109C211yesmaximal, characteristic, complemented
4C109×#3006C211yesmaximal, characteristic, complemented
5C2×#449×C109C211yesmaximal, characteristic, complemented
6C109×#2880C211yesmaximal, characteristic, complemented
7C109×#2052C211yesmaximal, characteristic, complemented
8C109×#2051C211yesmaximal, characteristic, complemented
9C109×#2019C211yesmaximal, characteristic, complemented
10C109×#2018C211yesmaximal, characteristic, complemented
11C109×#1908C211yesmaximal, characteristic, complemented
12C109×#1907C211yesmaximal, characteristic, complemented
13C109×#1900C211yesmaximal, characteristic, complemented
14C109×#1855C211yesmaximal, characteristic, complemented
15C109×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C22×#41×C109C2211yescharacteristic
18#575×C109—24no—
19#575×C109—24no—
20C2×#137×C109—21no—
21C2×#137×C109C2211yescharacteristic
22C2×#137×C109C2211yescharacteristic
23C2×AGL(1,ℤ/8)×C109—21no—
24C2×AGL(1,ℤ/8)×C109C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C109C2211yescharacteristic
26C2×AGL(1,ℤ/8)×C109C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C109C2211yescharacteristic
28C2×#135×C109—21no—
29C2×#135×C109—21no—
30C22×SD16×C109C2211yescharacteristic, complemented
31C22×D8×C109C2211yescharacteristic, complemented
32C2×#131×C109C2211yescharacteristic
33C2×#131×C109C2211yescharacteristic
34C22×M16×C109C2211yescharacteristic
35C2×#121×C109C2211yescharacteristic
36#472×C109—24no—
37#471×C109—24no—
38#449×C109—21no—
39#449×C109—21no—
40#449×C109—21no—
41#449×C109—21no—
42#449×C109—21no—
43#449×C109—21no—
44#448×C109—21no—
45#447×C109—21no—
46C2×#108×C109C2211yescharacteristic, complemented
47C2×#108×C109C2211yescharacteristic, complemented
48#417×C109C2211yescharacteristic
49#417×C109C2211yescharacteristic
50C2×#103×C109C2211yescharacteristic, complemented
51C2×#102×C109C2211yescharacteristic, complemented
52C2×#101×C109C2211yescharacteristic, complemented
53C2×#101×C109C2211yescharacteristic, complemented
54C2×#100×C109C2211yescharacteristic, complemented
55C2×#100×C109C2211yescharacteristic, complemented
56C2×#100×C109C2211yescharacteristic, complemented
57C2×#100×C109C2211yescharacteristic, complemented
58#408×C109—21no—
59#408×C109—21no—
60#408×C109C2211yescharacteristic
61#408×C109C2211yescharacteristic
62#407×C109—21no—
63#407×C109C2211yescharacteristic
64#407×C109C2211yescharacteristic
65C2×C22⋊C8×C109—21no—
66C2×C22⋊C8×C109C2211yescharacteristic
67#343×C109C2211yescharacteristic, complemented
68#343×C109C2211yescharacteristic, complemented
69#341×C109C2211yescharacteristic, complemented
70#341×C109C2211yescharacteristic, complemented
71C2×#41×C109—21no—
72C2×#41×C109—21no—
73C2×#41×C109—22no—
74C2×#41×C109—22no—
75C2×#41×C109—22no—
76C2×#41×C109—22no—
77C2×#41×C109—21no—
78C2×#41×C109—21no—
79C2×#41×C109—21no—
80C2×#41×C109—21no—
81C2×#41×C109—41no—
82C2×#41×C109—41no—
83C2×#41×C109—41no—
84C2×#41×C109—41no—
85C2×#41×C109D411yescharacteristic
86C2×#41×C109D411yescharacteristic
87C2×#41×C109C2311yescharacteristic
88C2×#41×C109C2311yescharacteristic
89C22×Q8×C109D411yescharacteristic
90C22×Q8×C109C2311yescharacteristic
91C22×D4×C109—21no—
92C22×D4×C109—21no—
93C22×D4×C109—21no—
94C22×D4×C109D411yescharacteristic
95C22×D4×C109C2311yescharacteristic
96C22×D4×C109C2311yescharacteristic
97C23×C4×C109—21no—
98C23×C4×C109—21no—
99C23×C4×C109C2311yescharacteristic
100#137×C109—28no—
101#137×C109—22no—
102#137×C109—22no—
103#137×C109—22no—
104#137×C109D414yescomplemented
105AGL(1,ℤ/8)×C109—28no—
106AGL(1,ℤ/8)×C109—22no—
107AGL(1,ℤ/8)×C109—22no—
108AGL(1,ℤ/8)×C109—22no—
109AGL(1,ℤ/8)×C109—22no—
110AGL(1,ℤ/8)×C109—22no—
111AGL(1,ℤ/8)×C109—41no—
112AGL(1,ℤ/8)×C109—41no—
113AGL(1,ℤ/8)×C109D414yescomplemented
114#135×C109—28no—
115#135×C109—28no—
116C2×Q16×C109—21no—
117C2×Q16×C109—21no—
118C2×SD16×C109—21no—
119C2×SD16×C109—21no—
120C2×SD16×C109—21no—
121C2×SD16×C109—21no—
122C2×SD16×C109—22no—
123C2×SD16×C109—21no—
124C2×SD16×C109—21no—
125C2×SD16×C109—21no—
126C2×SD16×C109—21no—
127C2×SD16×C109—41no—
128C2×D8×C109—21no—
129C2×D8×C109—21no—
130C2×D8×C109—22no—
131C2×D8×C109—21no—
132C2×D8×C109—21no—
133C2×D8×C109—21no—
134C2×D8×C109—21no—
135C2×D8×C109—41no—
136#131×C109—22no—
137#131×C109—22no—
138#131×C109—41no—
139#131×C109—41no—
140C2×M16×C109—21no—
141C2×M16×C109—22no—
142C2×M16×C109—22no—
143C2×M16×C109—21no—
144C2×M16×C109—21no—
145C2×M16×C109C2311yescharacteristic
146C2×M16×C109C2311yescharacteristic
147C2×M16×C109C2311yescharacteristic
148C2×M16×C109C2311yescharacteristic
149C2×M16×C109C2311yescharacteristic
150C2×M16×C109C2311yescharacteristic
151C22×C8×C109—21no—
152C22×C8×C109—21no—
153C22×C8×C109—21no—
154C22×C8×C109C2311yescharacteristic
155C22×C8×C109C2311yescharacteristic
156#121×C109—21no—
157#121×C109—21no—
158#121×C109—21no—
159#121×C109—21no—
160C2×C4⋊C4×C109C2311yescharacteristic
161C2×C22⋊C4×C109—21no—
162#108×C109—22no—
163#108×C109—22no—
164#103×C109—21no—
165#103×C109—21no—
166#103×C109—21no—
167#103×C109—21no—
168#102×C109—21no—
169#102×C109—21no—
170#102×C109—21no—
171#102×C109—21no—
172#101×C109—22no—
173#101×C109—41no—
174#100×C109—22no—
175#100×C109—22no—
176#100×C109—22no—
177#100×C109—41no—
178C22⋊C8×C109—21no—
179C22⋊C8×C109—21no—
180C22⋊C8×C109—21no—
181C22⋊C8×C109—21no—
182C22⋊C8×C109—21no—
183C22⋊C8×C109—21no—
184C22⋊C8×C109—21no—
185C22⋊C8×C109—21no—
186C22⋊C8×C109D411yescharacteristic
187C22⋊C8×C109D411yescharacteristic
188C22⋊C8×C109D411yescharacteristic
189C22⋊C8×C109D411yescharacteristic
190C24×C109—21no—
191C24×C109—21no—
192C24×C109—21no—
193C24×C109#4111yescharacteristic
194#41×C109—21no—
195#41×C109—21no—
196#41×C109—24no—
197#41×C109—24no—
198#41×C109—22no—
199#41×C109—22no—
200#41×C109—21no—
201#41×C109—21no—
202#41×C109—21no—
203#41×C109—21no—
204#41×C109—42no—
205#41×C109—42no—
206#41×C109—41no—
207#41×C109—41no—
208#41×C109—42no—
209#41×C109—42no—
210#41×C109—42no—
211#41×C109—42no—
212#41×C109—42no—
213#41×C109—42no—
214#41×C109—42no—
215#41×C109—42no—
216#41×C109C2×D412yes—
217#41×C109C2×D412yes—
218C2×Q8×C109—21no—
219C2×Q8×C109—21no—
220C2×Q8×C109—22no—
221C2×Q8×C109—21no—
222C2×Q8×C109—21no—
223C2×Q8×C109—21no—
224C2×Q8×C109—21no—
225C2×Q8×C109—41no—
226C2×Q8×C109C2×D412yes—
227C2×Q8×C109C2×D411yescharacteristic
228C2×Q8×C109C2×D411yescharacteristic
229C2×D4×C109—21no—
230C2×D4×C109—22no—
231C2×D4×C109—21no—
232C2×D4×C109—21no—
233C2×D4×C109—21no—
234C2×D4×C109—21no—
235C2×D4×C109—21no—
236C2×D4×C109—21no—
237C2×D4×C109—21no—
238C2×D4×C109—21no—
239C2×D4×C109—21no—
240C2×D4×C109—21no—
241C2×D4×C109—21no—
242C2×D4×C109—21no—
243C2×D4×C109—21no—
244C2×D4×C109—21no—
245C2×D4×C109—21no—
246C2×D4×C109—41no—
247C2×D4×C109—42no—
248C2×D4×C109—42no—
249C2×D4×C109—42no—
250C2×D4×C109—42no—
251C2×D4×C109—41no—
252C2×D4×C109—41no—
253C2×D4×C109—41no—
254C2×D4×C109—41no—
255C2×D4×C109—82no—
256C2×D4×C109C2×D412yes—
257C2×D4×C109C2×D411yescharacteristic
258C2×D4×C109C2×D411yescharacteristic
259C22×C4×C109—21no—
260C22×C4×C109—21no—
261C22×C4×C109—21no—
262C22×C4×C109—21no—
263C22×C4×C109—21no—
264C22×C4×C109—21no—
265C22×C4×C109—21no—
266C22×C4×C109—21no—
267C22×C4×C109—21no—
268C22×C4×C109—21no—
269C22×C4×C109—21no—
270C22×C4×C109—42no—
271C22×C4×C109—42no—
272C22×C4×C109—42no—
273C22×C4×C109—42no—
274C22×C4×C109—41no—
275C22×C4×C109—41no—
276C22×C4×C109C2×D411yescharacteristic
277C22×C4×C109C2×D411yescharacteristic
278C22×C4×C109C2×D411yescharacteristic
279C22×C4×C109C2×D411yescharacteristic
280C22×C4×C109#4111yescharacteristic
281C22×C4×C109C2411yescharacteristic
282Q16×C109—24no—
283Q16×C109—24no—
284SD16×C109—24no—
285SD16×C109—24no—
286SD16×C109—24no—
287SD16×C109—24no—
288SD16×C109—42no—
289SD16×C109—42no—
290SD16×C109—42no—
291SD16×C109—42no—
292D8×C109—24no—
293D8×C109—24no—
294D8×C109—42no—
295D8×C109—42no—
296D8×C109—42no—
297D8×C109—42no—
298M16×C109—24no—
299M16×C109—21no—
300M16×C109—21no—
301M16×C109—21no—
302M16×C109—21no—
303M16×C109—21no—
304M16×C109—21no—
305M16×C109—21no—
306M16×C109—21no—
307M16×C109—21no—
308M16×C109—21no—
309M16×C109—42no—
310M16×C109—42no—
311M16×C109C2×D412yes—
312M16×C109C2×D412yes—
313C2×C8×C109—24no—
314C2×C8×C109—21no—
315C2×C8×C109—21no—
316C2×C8×C109—21no—
317C2×C8×C109—21no—
318C2×C8×C109—21no—
319C2×C8×C109—21no—
320C2×C8×C109—21no—
321C2×C8×C109—21no—
322C2×C8×C109—21no—
323C2×C8×C109—21no—
324C2×C8×C109—42no—
325C2×C8×C109—42no—
326C2×C8×C109C2×D411yescharacteristic
327C2×C8×C109C2×D411yescharacteristic
328C2×C8×C109C2×D411yescharacteristic
329C2×C8×C109C2×D411yescharacteristic
330C4⋊C4×C109—21no—
331C4⋊C4×C109—21no—
332C22⋊C4×C109—41no—
333C22⋊C4×C109—41no—
334C23×C109—21no—
335C23×C109—21no—
336C23×C109—21no—
337C23×C109—21no—
338C23×C109—22no—
339C23×C109—41no—
340C23×C109—41no—
341C23×C109—42no—
342C23×C109—42no—
343C23×C109—41no—
344C23×C109—41no—
345C23×C109—41no—
346C23×C109—41no—
347C23×C109—41no—
348C23×C109—81no—
349C23×C109—81no—
350C23×C109—81no—
351C23×C109—81no—
352C23×C109—81no—
353C23×C109#12111yescharacteristic
354C23×C109#12111yescharacteristic
355C23×C109C2×#4111yescharacteristic
356Q8×C109—21no—
357Q8×C109—21no—
358Q8×C109—22no—
359Q8×C109—21no—
360Q8×C109—22no—
361Q8×C109—42no—
362Q8×C109—41no—
363Q8×C109—41no—
364Q8×C109#12012yes—
365D4×C109—22no—
366D4×C109—22no—
367D4×C109—21no—
368D4×C109—22no—
369D4×C109—21no—
370D4×C109—21no—
371D4×C109—22no—
372D4×C109—42no—
373D4×C109—42no—
374D4×C109—42no—
375D4×C109—44no—
376D4×C109—44no—
377D4×C109—41no—
378D4×C109—41no—
379D4×C109—41no—
380D4×C109—41no—
381D4×C109—41no—
382D4×C109—41no—
383D4×C109—41no—
384D4×C109—41no—
385D4×C109—82no—
386D4×C109—82no—
387D4×C109#12012yes—
388C2×C4×C109—21no—
389C2×C4×C109—21no—
390C2×C4×C109—21no—
391C2×C4×C109—21no—
392C2×C4×C109—21no—
393C2×C4×C109—21no—
394C2×C4×C109—21no—
395C2×C4×C109—22no—
396C2×C4×C109—22no—
397C2×C4×C109—21no—
398C2×C4×C109—21no—
399C2×C4×C109—21no—
400C2×C4×C109—21no—
401C2×C4×C109—21no—
402C2×C4×C109—22no—
403C2×C4×C109—42no—
404C2×C4×C109—42no—
405C2×C4×C109—42no—
406C2×C4×C109—44no—
407C2×C4×C109—44no—
408C2×C4×C109—41no—
409C2×C4×C109—41no—
410C2×C4×C109—41no—
411C2×C4×C109—41no—
412C2×C4×C109—41no—
413C2×C4×C109—81no—
414C2×C4×C109#12111yescharacteristic
415C2×C4×C109#12111yescharacteristic
416C2×C4×C109C22×D411yescharacteristic
417C2×C4×C109C22×D411yescharacteristic
418C2×C4×C109C22×D411yescharacteristic
419C2×C4×C109C22×D411yescharacteristic
420C2×C4×C109H(5,𝔽2)11yescharacteristic
421C2×C4×C109H(5,𝔽2)11yescharacteristic
422C8×C109—22no—
423C8×C109—22no—
424C8×C109—21no—
425C8×C109—21no—
426C8×C109—21no—
427C8×C109—21no—
428C8×C109—41no—
429C8×C109—41no—
430C8×C109—41no—
431C8×C109—41no—
432C22×C109—21no—
433C22×C109—21no—
434C22×C109—21no—
435C22×C109—21no—
436C22×C109—22no—
437C22×C109—21no—
438C22×C109—21no—
439C22×C109—21no—
440C22×C109—21no—
441C22×C109—41no—
442C22×C109—41no—
443C22×C109—41no—
444C22×C109—42no—
445C22×C109—41no—
446C22×C109—41no—
447C22×C109—81no—
448C22×C109—81no—
449C22×C109—82no—
450C22×C109—82no—
451C22×C109—84no—
452C22×C109—81no—
453C22×C109—81no—
454C22×C109—81no—
455C22×C109—81no—
456C22×C109—81no—
457C22×C109—161no—
458C22×C109—161no—
459C22×C109C2×#12111yescharacteristic
460C22×C109#54611yescharacteristic
461C22×C109#54611yescharacteristic
462C4×C109—21no—
463C4×C109—21no—
464C4×C109—22no—
465C4×C109—41no—
466C4×C109—42no—
467C4×C109—81no—
468C4×C109C2×#12011yescharacteristic
469C4×C109#53411yescharacteristic
470C4×C109D4211yescharacteristic
471C4×C109D4211yescharacteristic
472#24402C10911yesmaximal, characteristic, direct product factor, Sylow
473C2×C109—21no—
474C2×C109—21no—
475C2×C109—41no—
476C2×C109—41no—
477C2×C109—42no—
478C2×C109—81no—
479C2×C109—82no—
480C2×C109—161no—
481C2×C109#241011yescharacteristic
482C2×C109#306711yescharacteristic
483C2×C109#306811yescharacteristic
484C2×#575C2×C10911yescharacteristic, complemented
485C2×#472C2×C10911yescharacteristic, complemented
486C2×#471C2×C10911yescharacteristic, complemented
487#3006C2×C10911yescharacteristic, complemented
488C2×#449C2×C10911yescharacteristic, complemented
489#2880C2×C10911yescharacteristic, complemented
490#2052C2×C10911yescharacteristic, complemented
491#2051C2×C10911yescharacteristic, complemented
492#2019C2×C10911yescharacteristic, complemented
493#2018C2×C10911yescharacteristic, complemented
494#1908C2×C10911yescharacteristic, complemented
495#1907C2×C10911yescharacteristic, complemented
496#1900C2×C10911yescharacteristic, complemented
497#1855C2×C10911yescharacteristic, complemented
498#1785C2×C10911yescharacteristic, complemented
499C109#2440211yescharacteristic, direct product factor, Sylow
500C22×#41C22×C10911yescharacteristic
501C22×#41C22×C10911yescharacteristic
502#575—24no—
503#575—24no—
504C2×#137—21no—
505C2×#137C22×C10911yescharacteristic
506C2×#137C22×C10911yescharacteristic
507C2×AGL(1,ℤ/8)—21no—
508C2×AGL(1,ℤ/8)C22×C10911yescharacteristic
509C2×AGL(1,ℤ/8)C22×C10911yescharacteristic
510C2×AGL(1,ℤ/8)C22×C10911yescharacteristic
511C2×AGL(1,ℤ/8)C22×C10911yescharacteristic
512C2×#135—21no—
513C2×#135—21no—
514C22×SD16C22×C10911yescharacteristic, complemented
515C22×D8C22×C10911yescharacteristic, complemented
516C2×#131C22×C10911yescharacteristic
517C2×#131C22×C10911yescharacteristic
518C22×M16C22×C10911yescharacteristic
519C2×#121C22×C10911yescharacteristic
520#472—24no—
521#471—24no—
522#449—21no—
523#449—21no—
524#449—21no—
525#449—21no—
526#449—21no—
527#449—21no—
528#448—21no—
529#447—21no—
530C2×#108C22×C10911yescharacteristic, complemented
531C2×#108C22×C10911yescharacteristic, complemented
532#417C22×C10911yescharacteristic
533#417C22×C10911yescharacteristic
534C2×#103C22×C10911yescharacteristic, complemented
535C2×#102C22×C10911yescharacteristic, complemented
536C2×#101C22×C10911yescharacteristic, complemented
537C2×#101C22×C10911yescharacteristic, complemented
538C2×#100C22×C10911yescharacteristic, complemented
539C2×#100C22×C10911yescharacteristic, complemented
540C2×#100C22×C10911yescharacteristic, complemented
541C2×#100C22×C10911yescharacteristic, complemented
542#408—21no—
543#408—21no—
544#408C22×C10911yescharacteristic
545#408C22×C10911yescharacteristic
546#407—21no—
547#407C22×C10911yescharacteristic
548#407C22×C10911yescharacteristic
549C2×C22⋊C8—21no—
550C2×C22⋊C8C22×C10911yescharacteristic
551#343C22×C10911yescharacteristic, complemented
552#343C22×C10911yescharacteristic, complemented
553#341C22×C10911yescharacteristic, complemented
554#341C22×C10911yescharacteristic, complemented
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—22no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41—41no—
569C2×#41D4×C10911yescharacteristic
570C2×#41D4×C10911yescharacteristic
571C2×#41C23×C10911yescharacteristic
572C2×#41C23×C10911yescharacteristic
573C22×Q8D4×C10911yescharacteristic
574C22×Q8C23×C10911yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4D4×C10911yescharacteristic
579C22×D4C23×C10911yescharacteristic
580C22×D4C23×C10911yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4C23×C10911yescharacteristic
584#137—28no—
585#137—22no—
586#137—22no—
587#137—22no—
588#137D4×C10914yescomplemented
589AGL(1,ℤ/8)—28no—
590AGL(1,ℤ/8)—22no—
591AGL(1,ℤ/8)—22no—
592AGL(1,ℤ/8)—22no—
593AGL(1,ℤ/8)—22no—
594AGL(1,ℤ/8)—22no—
595AGL(1,ℤ/8)—41no—
596AGL(1,ℤ/8)—41no—
597AGL(1,ℤ/8)D4×C10914yescomplemented
598#135—28no—
599#135—28no—
600C2×Q16—21no—
601C2×Q16—21no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—22no—
607C2×SD16—21no—
608C2×SD16—21no—
609C2×SD16—21no—
610C2×SD16—21no—
611C2×SD16—41no—
612C2×D8—21no—
613C2×D8—21no—
614C2×D8—22no—
615C2×D8—21no—
616C2×D8—21no—
617C2×D8—21no—
618C2×D8—21no—
619C2×D8—41no—
620#131—22no—
621#131—22no—
622#131—41no—
623#131—41no—
624C2×M16—21no—
625C2×M16—22no—
626C2×M16—22no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16C23×C10911yescharacteristic
630C2×M16C23×C10911yescharacteristic
631C2×M16C23×C10911yescharacteristic
632C2×M16C23×C10911yescharacteristic
633C2×M16C23×C10911yescharacteristic
634C2×M16C23×C10911yescharacteristic
635C22×C8—21no—
636C22×C8—21no—
637C22×C8—21no—
638C22×C8C23×C10911yescharacteristic
639C22×C8C23×C10911yescharacteristic
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644C2×C4⋊C4C23×C10911yescharacteristic
645C2×C22⋊C4—21no—
646#108—22no—
647#108—22no—
648#103—21no—
649#103—21no—
650#103—21no—
651#103—21no—
652#102—21no—
653#102—21no—
654#102—21no—
655#102—21no—
656#101—22no—
657#101—41no—
658#100—22no—
659#100—22no—
660#100—22no—
661#100—41no—
662C22⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—21no—
668C22⋊C8—21no—
669C22⋊C8—21no—
670C22⋊C8D4×C10911yescharacteristic
671C22⋊C8D4×C10911yescharacteristic
672C22⋊C8D4×C10911yescharacteristic
673C22⋊C8D4×C10911yescharacteristic
674C24—21no—
675C24—21no—
676C24—21no—
677C24#41×C10911yescharacteristic
678#41—21no—
679#41—21no—
680#41—24no—
681#41—24no—
682#41—22no—
683#41—22no—
684#41—21no—
685#41—21no—
686#41—21no—
687#41—21no—
688#41—42no—
689#41—42no—
690#41—41no—
691#41—41no—
692#41—42no—
693#41—42no—
694#41—42no—
695#41—42no—
696#41—42no—
697#41—42no—
698#41—42no—
699#41—42no—
700#41C2×D4×C10912yes—
701#41C2×D4×C10912yes—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—22no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8—41no—
710C2×Q8C2×D4×C10912yes—
711C2×Q8C2×D4×C10911yescharacteristic
712C2×Q8C2×D4×C10911yescharacteristic
713C2×D4—21no—
714C2×D4—22no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—41no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—41no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—82no—
740C2×D4C2×D4×C10912yes—
741C2×D4C2×D4×C10911yescharacteristic
742C2×D4C2×D4×C10911yescharacteristic
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4C2×D4×C10911yescharacteristic
761C22×C4C2×D4×C10911yescharacteristic
762C22×C4C2×D4×C10911yescharacteristic
763C22×C4C2×D4×C10911yescharacteristic
764C22×C4#41×C10911yescharacteristic
765C22×C4C24×C10911yescharacteristic
766Q16—24no—
767Q16—24no—
768SD16—24no—
769SD16—24no—
770SD16—24no—
771SD16—24no—
772SD16—42no—
773SD16—42no—
774SD16—42no—
775SD16—42no—
776D8—24no—
777D8—24no—
778D8—42no—
779D8—42no—
780D8—42no—
781D8—42no—
782M16—24no—
783M16—21no—
784M16—21no—
785M16—21no—
786M16—21no—
787M16—21no—
788M16—21no—
789M16—21no—
790M16—21no—
791M16—21no—
792M16—21no—
793M16—42no—
794M16—42no—
795M16C2×D4×C10912yes—
796M16C2×D4×C10912yes—
797C2×C8—24no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—42no—
809C2×C8—42no—
810C2×C8C2×D4×C10911yescharacteristic
811C2×C8C2×D4×C10911yescharacteristic
812C2×C8C2×D4×C10911yescharacteristic
813C2×C8C2×D4×C10911yescharacteristic
814C4⋊C4—21no—
815C4⋊C4—21no—
816C22⋊C4—41no—
817C22⋊C4—41no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—22no—
823C23—41no—
824C23—41no—
825C23—42no—
826C23—42no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23—81no—
837C23#121×C10911yescharacteristic
838C23#121×C10911yescharacteristic
839C23C2×#41×C10911yescharacteristic
840Q8—21no—
841Q8—21no—
842Q8—22no—
843Q8—21no—
844Q8—22no—
845Q8—42no—
846Q8—41no—
847Q8—41no—
848Q8#120×C10912yes—
849D4—22no—
850D4—22no—
851D4—21no—
852D4—22no—
853D4—21no—
854D4—21no—
855D4—22no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—44no—
860D4—44no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865D4—41no—
866D4—41no—
867D4—41no—
868D4—41no—
869D4—82no—
870D4—82no—
871D4#120×C10912yes—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—81no—
898C2×C4#121×C10911yescharacteristic
899C2×C4#121×C10911yescharacteristic
900C2×C4C22×D4×C10911yescharacteristic
901C2×C4C22×D4×C10911yescharacteristic
902C2×C4C22×D4×C10911yescharacteristic
903C2×C4C22×D4×C10911yescharacteristic
904C2×C4H(5,𝔽2)×C10911yescharacteristic
905C2×C4H(5,𝔽2)×C10911yescharacteristic
906C8—22no—
907C8—22no—
908C8—21no—
909C8—21no—
910C8—21no—
911C8—21no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—41no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—22no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—42no—
931C22—81no—
932C22—81no—
933C22—82no—
934C22—82no—
935C22—84no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22—81no—
940C22—81no—
941C22—161no—
942C22—161no—
943C22C2×#121×C10911yescharacteristic
944C22#546×C10911yescharacteristic
945C22#546×C10911yescharacteristic
946C4—21no—
947C4—21no—
948C4—22no—
949C4—41no—
950C4—42no—
951C4—81no—
952C4C2×#120×C10911yescharacteristic
953C4#534×C10911yescharacteristic
954C4D42×C10911yescharacteristic
955C4D42×C10911yescharacteristic
956C2—21no—
957C2—21no—
958C2—41no—
959C2—41no—
960C2—42no—
961C2—81no—
962C2—82no—
963C2—161no—
964C2C109×#241011yescharacteristic
965C2C109×#306711yescharacteristic
966C2C109×#306811yescharacteristic
subgroupG/H
center, socleC22×C109C2×#121
commutator, Frattini, cosocleC22×C4C24×C109
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×#575×C109C2semidirect
2. C2×#472×C109C2semidirect
3. C2×#471×C109C2semidirect
4. C109×#3006C2semidirect
5. C2×#449×C109C2semidirect
6. C109×#2880C2semidirect
7. C109×#2052C2semidirect
8. C109×#2051C2semidirect
9. C109×#2019C2semidirect
10. C109×#2018C2semidirect
11. C109×#1908C2semidirect
12. C109×#1907C2semidirect
13. C109×#1900C2semidirect
14. C109×#1855C2semidirect
15. C109×#1785C2semidirect
30. C22×SD16×C109C22semidirect
31. C22×D8×C109C22semidirect
46. C2×#108×C109C22semidirect
47. C2×#108×C109C22semidirect
50. C2×#103×C109C22semidirect
51. C2×#102×C109C22semidirect
52. C2×#101×C109C22semidirect
53. C2×#101×C109C22semidirect
54. C2×#100×C109C22semidirect
55. C2×#100×C109C22semidirect
56. C2×#100×C109C22semidirect
57. C2×#100×C109C22semidirect
67. #343×C109C22semidirect
68. #343×C109C22semidirect
69. #341×C109C22semidirect
70. #341×C109C22semidirect
104. #137×C109D4semidirect
113. AGL(1,ℤ/8)×C109D4semidirect
472. #24402C109direct (N × H)
484. C2×#575C2×C109semidirect
485. C2×#472C2×C109semidirect
486. C2×#471C2×C109semidirect
487. #3006C2×C109semidirect
488. C2×#449C2×C109semidirect
489. #2880C2×C109semidirect
490. #2052C2×C109semidirect
491. #2051C2×C109semidirect
492. #2019C2×C109semidirect
493. #2018C2×C109semidirect
494. #1908C2×C109semidirect
495. #1907C2×C109semidirect
496. #1900C2×C109semidirect
497. #1855C2×C109semidirect
498. #1785C2×C109semidirect
499. C109#24402direct (N × H)
514. C22×SD16C22×C109semidirect
515. C22×D8C22×C109semidirect
530. C2×#108C22×C109semidirect
531. C2×#108C22×C109semidirect
534. C2×#103C22×C109semidirect
535. C2×#102C22×C109semidirect
536. C2×#101C22×C109semidirect
537. C2×#101C22×C109semidirect
538. C2×#100C22×C109semidirect
539. C2×#100C22×C109semidirect
540. C2×#100C22×C109semidirect
541. C2×#100C22×C109semidirect
551. #343C22×C109semidirect
552. #343C22×C109semidirect
553. #341C22×C109semidirect
554. #341C22×C109semidirect
588. #137D4×C109semidirect
597. AGL(1,ℤ/8)D4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1092
C2×#472×C1092
C2×#471×C1092
C109×#30062
C2×#449×C1092
C109×#28802
C109×#20522
C109×#20512
C109×#20192
C109×#20182
C109×#19082
C109×#19072
C109×#19002
C109×#18552
C109×#17852
#24402109