Finite Group Databasebeta

← C109×#24897 #42142891

Subgroups — C109×#24897 #42142891

Order 27904.

1204 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C109C211yesmaximal, characteristic
2C2×C4×D8×C109C211yesmaximal, characteristic, complemented
3C109×#2420C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C109C211yesmaximal, characteristic, complemented
5C109×#2092C211yesmaximal, characteristic, complemented
6C109×#2076C211yesmaximal, characteristic, complemented
7C109×#2054C211yesmaximal, characteristic, complemented
8C109×#2034C211yesmaximal, characteristic, complemented
9C109×#1934C211yesmaximal, characteristic, complemented
10C109×#1923C211yesmaximal, characteristic, complemented
11C109×#1879C211yesmaximal, characteristic, complemented
12C109×#1879C211yesmaximal, characteristic, complemented
13C109×#1864C211yesmaximal, characteristic, complemented
14C109×#1804C211yesmaximal, characteristic, complemented
15C109×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C109C2211yescharacteristic
17C22×D8×C109C2211yescharacteristic
18C22×D8×C109C2211yescharacteristic
19C2×#121×C109C2211yescharacteristic
20C2×C4×D4×C109C2211yescharacteristic
21C2×C4×D4×C109C2211yescharacteristic
22C2×C4×D4×C109C2211yescharacteristic, complemented
23C22×C22⋊C4×C109—21no—
24#447×C109—24no—
25C4×D8×C109—24no—
26C2×#107×C109C2211yescharacteristic, complemented
27C2×#106×C109C2211yescharacteristic, complemented
28C2×C4⋊C8×C109C2211yescharacteristic, complemented
29C2×#102×C109C2211yescharacteristic
30C2×#102×C109C2211yescharacteristic
31C2×#102×C109C2211yescharacteristic
32C2×#102×C109C2211yescharacteristic
33C2×#102×C109C2211yescharacteristic
34C2×#102×C109C2211yescharacteristic
35C2×#102×C109C2211yescharacteristic, complemented
36C2×#102×C109C2211yescharacteristic, complemented
37C2×C22⋊C8×C109C2211yescharacteristic
38C2×C22⋊C8×C109C2211yescharacteristic
39C2×C4×C8×C109C2211yescharacteristic, complemented
40#397×C109—21no—
41#394×C109—21no—
42#390×C109C2211yescharacteristic
43#390×C109C2211yescharacteristic
44#390×C109C2211yescharacteristic, complemented
45#389×C109C2211yescharacteristic, complemented
46#386×C109—21no—
47#386×C109—21no—
48#386×C109—21no—
49#382×C109C2211yescharacteristic, complemented
50#381×C109—21no—
51#380×C109C2211yescharacteristic
52#380×C109C2211yescharacteristic
53#379×C109—21no—
54C4×C22⋊C4×C109C2211yescharacteristic
55#340×C109C2211yescharacteristic, complemented
56#340×C109C2211yescharacteristic, complemented
57#340×C109C2211yescharacteristic, complemented
58#340×C109C2211yescharacteristic, complemented
59#336×C109C2211yescharacteristic, complemented
60#336×C109C2211yescharacteristic, complemented
61C25×C109—21no—
62C22×D4×C109—22no—
63C22×D4×C109—22no—
64C22×D4×C109—22no—
65C22×D4×C109—22no—
66C22×D4×C109—21no—
67C22×D4×C109—21no—
68C22×D4×C109—41no—
69C22×D4×C109—41no—
70C22×D4×C109C2311yescharacteristic
71C22×D4×C109C2311yescharacteristic
72C22×D4×C109C2311yescharacteristic
73C23×C4×C109—21no—
74C23×C4×C109—21no—
75C23×C4×C109—21no—
76C23×C4×C109C2311yescharacteristic
77C2×D8×C109—22no—
78C2×D8×C109—22no—
79C2×D8×C109—22no—
80C2×D8×C109—22no—
81C2×D8×C109—41no—
82C2×D8×C109D414yes—
83C22×C8×C109C2311yescharacteristic
84C22×C8×C109C2311yescharacteristic
85C22×C8×C109C2311yescharacteristic
86C22×C8×C109C2311yescharacteristic
87#121×C109—22no—
88#121×C109—41no—
89C4×D4×C109—22no—
90C4×D4×C109—22no—
91C4×D4×C109—22no—
92C4×D4×C109—41no—
93C4×D4×C109—41no—
94C4×D4×C109—41no—
95C2×C4⋊C4×C109—21no—
96C2×C4⋊C4×C109C2311yescharacteristic
97C2×C4⋊C4×C109C2311yescharacteristic
98C2×C4⋊C4×C109C2311yescharacteristic
99C2×C4⋊C4×C109C2311yescharacteristic
100C2×C4⋊C4×C109C2311yescharacteristic
101C2×C22⋊C4×C109—21no—
102C2×C22⋊C4×C109—21no—
103C2×C22⋊C4×C109—21no—
104C2×C22⋊C4×C109—21no—
105C2×C22⋊C4×C109—21no—
106C2×C22⋊C4×C109—21no—
107C2×C22⋊C4×C109—21no—
108C2×C22⋊C4×C109—21no—
109C2×C22⋊C4×C109—21no—
110C2×C22⋊C4×C109—21no—
111C2×C22⋊C4×C109—21no—
112C2×C22⋊C4×C109—21no—
113C2×C22⋊C4×C109—44no—
114C2×C22⋊C4×C109D411yescharacteristic
115C2×C22⋊C4×C109D411yescharacteristic
116C2×C42×C109C2311yescharacteristic
117C2×C42×C109C2311yescharacteristic
118#107×C109—22no—
119#106×C109—41no—
120C4⋊C8×C109—41no—
121#102×C109—22no—
122#102×C109—22no—
123#102×C109—22no—
124#102×C109—22no—
125#102×C109—22no—
126#102×C109—22no—
127#102×C109—41no—
128#102×C109—41no—
129C22⋊C8×C109—22no—
130C22⋊C8×C109—41no—
131C4×C8×C109—22no—
132#95×C109—21no—
133#95×C109—21no—
134#95×C109—21no—
135#95×C109—21no—
136#95×C109—21no—
137#95×C109D411yescharacteristic
138#95×C109D411yescharacteristic
139C24×C109—21no—
140C24×C109—24no—
141C24×C109—21no—
142C24×C109—21no—
143C24×C109—42no—
144C24×C109—42no—
145C24×C109—42no—
146C24×C109—42no—
147C24×C109—81no—
148C24×C109—81no—
149C24×C109C2×D411yescharacteristic
150C2×D4×C109—24no—
151C2×D4×C109—21no—
152C2×D4×C109—21no—
153C2×D4×C109—21no—
154C2×D4×C109—21no—
155C2×D4×C109—21no—
156C2×D4×C109—21no—
157C2×D4×C109—21no—
158C2×D4×C109—21no—
159C2×D4×C109—21no—
160C2×D4×C109—21no—
161C2×D4×C109—21no—
162C2×D4×C109—21no—
163C2×D4×C109—21no—
164C2×D4×C109—42no—
165C2×D4×C109—42no—
166C2×D4×C109—44no—
167C2×D4×C109—44no—
168C2×D4×C109—44no—
169C2×D4×C109—44no—
170C2×D4×C109—42no—
171C2×D4×C109—42no—
172C2×D4×C109—81no—
173C2×D4×C109C2×D412yes—
174C2×D4×C109C2×D412yes—
175C2×D4×C109#4112yes—
176C2×D4×C109#4112yes—
177C2×D4×C109#4112yes—
178C22×C4×C109—21no—
179C22×C4×C109—21no—
180C22×C4×C109—21no—
181C22×C4×C109—21no—
182C22×C4×C109—21no—
183C22×C4×C109—21no—
184C22×C4×C109—21no—
185C22×C4×C109—21no—
186C22×C4×C109—21no—
187C22×C4×C109—21no—
188C22×C4×C109—21no—
189C22×C4×C109—42no—
190C22×C4×C109—42no—
191C22×C4×C109—42no—
192C22×C4×C109—42no—
193C22×C4×C109—42no—
194C22×C4×C109—42no—
195C22×C4×C109—81no—
196C22×C4×C109—81no—
197C22×C4×C109—81no—
198C22×C4×C109C2×D411yescharacteristic
199C22×C4×C109C2×D411yescharacteristic
200C22×C4×C109C2×D411yescharacteristic
201C22×C4×C109C2×D411yescharacteristic
202C22×C4×C109C2×D411yescharacteristic
203C22×C4×C109C2411yescharacteristic
204D8×C109—28no—
205D8×C109—44no—
206C2×C8×C109—21no—
207C2×C8×C109—21no—
208C2×C8×C109—21no—
209C2×C8×C109—21no—
210C2×C8×C109—21no—
211C2×C8×C109—21no—
212C2×C8×C109—21no—
213C2×C8×C109—21no—
214C2×C8×C109—21no—
215C2×C8×C109—21no—
216C2×C8×C109—21no—
217C2×C8×C109C2×D412yes—
218C4⋊C4×C109—21no—
219C4⋊C4×C109—21no—
220C4⋊C4×C109—21no—
221C4⋊C4×C109—21no—
222C4⋊C4×C109—21no—
223C4⋊C4×C109—21no—
224C4⋊C4×C109—21no—
225C4⋊C4×C109—21no—
226C4⋊C4×C109—21no—
227C4⋊C4×C109—21no—
228C4⋊C4×C109—81no—
229C22⋊C4×C109—22no—
230C22⋊C4×C109—22no—
231C22⋊C4×C109—42no—
232C22⋊C4×C109—42no—
233C22⋊C4×C109—42no—
234C22⋊C4×C109—42no—
235C22⋊C4×C109—42no—
236C22⋊C4×C109—42no—
237C22⋊C4×C109—42no—
238C22⋊C4×C109—81no—
239C22⋊C4×C109—81no—
240C22⋊C4×C109—81no—
241C22⋊C4×C109—81no—
242C22⋊C4×C109—81no—
243C42×C109—21no—
244C42×C109—21no—
245C42×C109—21no—
246C42×C109—21no—
247C23×C109—21no—
248C23×C109—22no—
249C23×C109—22no—
250C23×C109—21no—
251C23×C109—22no—
252C23×C109—21no—
253C23×C109—21no—
254C23×C109—21no—
255C23×C109—21no—
256C23×C109—22no—
257C23×C109—22no—
258C23×C109—48no—
259C23×C109—48no—
260C23×C109—41no—
261C23×C109—41no—
262C23×C109—41no—
263C23×C109—41no—
264C23×C109—41no—
265C23×C109—41no—
266C23×C109—41no—
267C23×C109—41no—
268C23×C109—41no—
269C23×C109—41no—
270C23×C109—41no—
271C23×C109—41no—
272C23×C109—41no—
273C23×C109—41no—
274C23×C109—41no—
275C23×C109—41no—
276C23×C109—84no—
277C23×C109—84no—
278C23×C109—84no—
279C23×C109—84no—
280C23×C109—84no—
281C23×C109#13512yes—
282C23×C109C22×D411yescharacteristic
283D4×C109—22no—
284D4×C109—22no—
285D4×C109—22no—
286D4×C109—22no—
287D4×C109—22no—
288D4×C109—22no—
289D4×C109—22no—
290D4×C109—48no—
291D4×C109—41no—
292D4×C109—41no—
293D4×C109—41no—
294D4×C109—41no—
295D4×C109—84no—
296D4×C109#12314yes—
297C2×C4×C109—21no—
298C2×C4×C109—21no—
299C2×C4×C109—21no—
300C2×C4×C109—21no—
301C2×C4×C109—21no—
302C2×C4×C109—21no—
303C2×C4×C109—21no—
304C2×C4×C109—21no—
305C2×C4×C109—21no—
306C2×C4×C109—21no—
307C2×C4×C109—21no—
308C2×C4×C109—21no—
309C2×C4×C109—21no—
310C2×C4×C109—21no—
311C2×C4×C109—41no—
312C2×C4×C109—41no—
313C2×C4×C109—41no—
314C2×C4×C109—41no—
315C2×C4×C109—41no—
316C2×C4×C109—41no—
317C2×C4×C109—41no—
318C2×C4×C109—41no—
319C2×C4×C109—41no—
320C2×C4×C109—41no—
321C2×C4×C109—41no—
322C2×C4×C109—41no—
323C2×C4×C109—41no—
324C2×C4×C109—41no—
325C2×C4×C109—41no—
326C2×C4×C109—41no—
327C2×C4×C109—41no—
328C2×C4×C109—41no—
329C2×C4×C109—41no—
330C2×C4×C109—84no—
331C2×C4×C109—84no—
332C2×C4×C109—84no—
333C2×C4×C109AGL(1,ℤ/8)12yes—
334C2×C4×C109C22×D411yescharacteristic
335C2×C4×C109C2×#4111yescharacteristic
336C2×C4×C109C2×#4111yescharacteristic
337C2×C4×C109C2×#4111yescharacteristic
338C2×C4×C109H(5,𝔽2)11yescharacteristic
339C2×C4×C109H(5,𝔽2)11yescharacteristic
340C8×C109—22no—
341C8×C109—41no—
342C8×C109—41no—
343C8×C109—41no—
344C22×C109—22no—
345C22×C109—24no—
346C22×C109—22no—
347C22×C109—22no—
348C22×C109—42no—
349C22×C109—41no—
350C22×C109—42no—
351C22×C109—41no—
352C22×C109—42no—
353C22×C109—41no—
354C22×C109—42no—
355C22×C109—42no—
356C22×C109—42no—
357C22×C109—41no—
358C22×C109—42no—
359C22×C109—42no—
360C22×C109—42no—
361C22×C109—42no—
362C22×C109—42no—
363C22×C109—42no—
364C22×C109—816no—
365C22×C109—81no—
366C22×C109—81no—
367C22×C109—81no—
368C22×C109—81no—
369C22×C109—81no—
370C22×C109—81no—
371C22×C109—81no—
372C22×C109—81no—
373C22×C109#52511yescharacteristic
374C22×C109D4211yescharacteristic
375C22×C109#54611yescharacteristic
376C22×C109C2×#13511yescharacteristic
377C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C109#57611yescharacteristic
379C22×C109#57611yescharacteristic
380C4×C109—22no—
381C4×C109—41no—
382C4×C109—41no—
383C4×C109—41no—
384C4×C109—41no—
385C4×C109—81no—
386C4×C109—81no—
387C4×C109—81no—
388C4×C109—81no—
389C4×C109—81no—
390C4×C109C2×#12311yescharacteristic
391C4×C109#53811yescharacteristic
392C4×C109#54611yescharacteristic
393C4×C109#55111yescharacteristic
394#24897C10911yesmaximal, characteristic, direct product factor, Sylow
395C2×C109—42no—
396C2×C109—44no—
397C2×C109—82no—
398C2×C109—82no—
399C2×C109#241811yescharacteristic
400C2×C109#310511yescharacteristic
401C2×C109#312211yescharacteristic
402C2×C109#326411yescharacteristic
403C2×C109#328011yescharacteristic
404C2×C109#329711yescharacteristic
405C2×C109#332511yescharacteristic
406C2×#447C2×C10911yescharacteristic
407C2×C4×D8C2×C10911yescharacteristic, complemented
408#2420C2×C10911yescharacteristic, complemented
409D4×C22⋊C4C2×C10911yescharacteristic, complemented
410#2092C2×C10911yescharacteristic, complemented
411#2076C2×C10911yescharacteristic, complemented
412#2054C2×C10911yescharacteristic, complemented
413#2034C2×C10911yescharacteristic, complemented
414#1934C2×C10911yescharacteristic, complemented
415#1923C2×C10911yescharacteristic, complemented
416#1879C2×C10911yescharacteristic, complemented
417#1879C2×C10911yescharacteristic, complemented
418#1864C2×C10911yescharacteristic, complemented
419#1804C2×C10911yescharacteristic, complemented
420#1786C2×C10911yescharacteristic, complemented
421C109#2489711yescharacteristic, direct product factor, Sylow
422C23×D4C22×C10911yescharacteristic
423C22×D8C22×C10911yescharacteristic
424C22×D8C22×C10911yescharacteristic
425C2×#121C22×C10911yescharacteristic
426C2×C4×D4C22×C10911yescharacteristic
427C2×C4×D4C22×C10911yescharacteristic
428C2×C4×D4C22×C10911yescharacteristic, complemented
429C22×C22⋊C4—21no—
430#447—24no—
431C4×D8—24no—
432C2×#107C22×C10911yescharacteristic, complemented
433C2×#106C22×C10911yescharacteristic, complemented
434C2×C4⋊C8C22×C10911yescharacteristic, complemented
435C2×#102C22×C10911yescharacteristic
436C2×#102C22×C10911yescharacteristic
437C2×#102C22×C10911yescharacteristic
438C2×#102C22×C10911yescharacteristic
439C2×#102C22×C10911yescharacteristic
440C2×#102C22×C10911yescharacteristic
441C2×#102C22×C10911yescharacteristic, complemented
442C2×#102C22×C10911yescharacteristic, complemented
443C2×C22⋊C8C22×C10911yescharacteristic
444C2×C22⋊C8C22×C10911yescharacteristic
445C2×C4×C8C22×C10911yescharacteristic, complemented
446#397—21no—
447#394—21no—
448#390C22×C10911yescharacteristic
449#390C22×C10911yescharacteristic
450#390C22×C10911yescharacteristic, complemented
451#389C22×C10911yescharacteristic, complemented
452#386—21no—
453#386—21no—
454#386—21no—
455#382C22×C10911yescharacteristic, complemented
456#381—21no—
457#380C22×C10911yescharacteristic
458#380C22×C10911yescharacteristic
459#379—21no—
460C4×C22⋊C4C22×C10911yescharacteristic
461#340C22×C10911yescharacteristic, complemented
462#340C22×C10911yescharacteristic, complemented
463#340C22×C10911yescharacteristic, complemented
464#340C22×C10911yescharacteristic, complemented
465#336C22×C10911yescharacteristic, complemented
466#336C22×C10911yescharacteristic, complemented
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4C23×C10911yescharacteristic
477C22×D4C23×C10911yescharacteristic
478C22×D4C23×C10911yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C23×C10911yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—41no—
488C2×D8D4×C10914yes—
489C22×C8C23×C10911yescharacteristic
490C22×C8C23×C10911yescharacteristic
491C22×C8C23×C10911yescharacteristic
492C22×C8C23×C10911yescharacteristic
493#121—22no—
494#121—41no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—41no—
499C4×D4—41no—
500C4×D4—41no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4C23×C10911yescharacteristic
503C2×C4⋊C4C23×C10911yescharacteristic
504C2×C4⋊C4C23×C10911yescharacteristic
505C2×C4⋊C4C23×C10911yescharacteristic
506C2×C4⋊C4C23×C10911yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—44no—
520C2×C22⋊C4D4×C10911yescharacteristic
521C2×C22⋊C4D4×C10911yescharacteristic
522C2×C42C23×C10911yescharacteristic
523C2×C42C23×C10911yescharacteristic
524#107—22no—
525#106—41no—
526C4⋊C8—41no—
527#102—22no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—41no—
534#102—41no—
535C22⋊C8—22no—
536C22⋊C8—41no—
537C4×C8—22no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95D4×C10911yescharacteristic
544#95D4×C10911yescharacteristic
545C24—21no—
546C24—24no—
547C24—21no—
548C24—21no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—42no—
553C24—81no—
554C24—81no—
555C24C2×D4×C10911yescharacteristic
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—44no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4C2×D4×C10912yes—
580C2×D4C2×D4×C10912yes—
581C2×D4#41×C10912yes—
582C2×D4#41×C10912yes—
583C2×D4#41×C10912yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4C2×D4×C10911yescharacteristic
605C22×C4C2×D4×C10911yescharacteristic
606C22×C4C2×D4×C10911yescharacteristic
607C22×C4C2×D4×C10911yescharacteristic
608C22×C4C2×D4×C10911yescharacteristic
609C22×C4C24×C10911yescharacteristic
610D8—28no—
611D8—44no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8C2×D4×C10912yes—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—81no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C23—21no—
654C23—22no—
655C23—22no—
656C23—21no—
657C23—22no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—48no—
665C23—48no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23#135×C10912yes—
688C23C22×D4×C10911yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4#123×C10914yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4—84no—
739C2×C4AGL(1,ℤ/8)×C10912yes—
740C2×C4C22×D4×C10911yescharacteristic
741C2×C4C2×#41×C10911yescharacteristic
742C2×C4C2×#41×C10911yescharacteristic
743C2×C4C2×#41×C10911yescharacteristic
744C2×C4H(5,𝔽2)×C10911yescharacteristic
745C2×C4H(5,𝔽2)×C10911yescharacteristic
746C8—22no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—24no—
754C22—42no—
755C22—41no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—41no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—816no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22#525×C10911yescharacteristic
780C22D42×C10911yescharacteristic
781C22#546×C10911yescharacteristic
782C22C2×#135×C10911yescharacteristic
783C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
784C22#576×C10911yescharacteristic
785C22#576×C10911yescharacteristic
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C2×#123×C10911yescharacteristic
797C4#538×C10911yescharacteristic
798C4#546×C10911yescharacteristic
799C4#551×C10911yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—82no—
804C2C109×#241811yescharacteristic
805C2C109×#310511yescharacteristic
806C2C109×#312211yescharacteristic
807C2C109×#326411yescharacteristic
808C2C109×#328011yescharacteristic
809C2C109×#329711yescharacteristic
810C2C109×#332511yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC2×#447×C109C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C4×C22⋊C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×D8×C109C2semidirect
3. C109×#2420C2semidirect
4. D4×C22⋊C4×C109C2semidirect
5. C109×#2092C2semidirect
6. C109×#2076C2semidirect
7. C109×#2054C2semidirect
8. C109×#2034C2semidirect
9. C109×#1934C2semidirect
10. C109×#1923C2semidirect
11. C109×#1879C2semidirect
12. C109×#1879C2semidirect
13. C109×#1864C2semidirect
14. C109×#1804C2semidirect
15. C109×#1786C2semidirect
22. C2×C4×D4×C109C22semidirect
26. C2×#107×C109C22semidirect
27. C2×#106×C109C22semidirect
28. C2×C4⋊C8×C109C22semidirect
35. C2×#102×C109C22semidirect
36. C2×#102×C109C22semidirect
39. C2×C4×C8×C109C22semidirect
44. #390×C109C22semidirect
45. #389×C109C22semidirect
49. #382×C109C22semidirect
55. #340×C109C22semidirect
56. #340×C109C22semidirect
57. #340×C109C22semidirect
58. #340×C109C22semidirect
59. #336×C109C22semidirect
60. #336×C109C22semidirect
394. #24897C109direct (N × H)
407. C2×C4×D8C2×C109semidirect
408. #2420C2×C109semidirect
409. D4×C22⋊C4C2×C109semidirect
410. #2092C2×C109semidirect
411. #2076C2×C109semidirect
412. #2054C2×C109semidirect
413. #2034C2×C109semidirect
414. #1934C2×C109semidirect
415. #1923C2×C109semidirect
416. #1879C2×C109semidirect
417. #1879C2×C109semidirect
418. #1864C2×C109semidirect
419. #1804C2×C109semidirect
420. #1786C2×C109semidirect
421. C109#24897direct (N × H)
428. C2×C4×D4C22×C109semidirect
432. C2×#107C22×C109semidirect
433. C2×#106C22×C109semidirect
434. C2×C4⋊C8C22×C109semidirect
441. C2×#102C22×C109semidirect
442. C2×#102C22×C109semidirect
445. C2×C4×C8C22×C109semidirect
450. #390C22×C109semidirect
451. #389C22×C109semidirect
455. #382C22×C109semidirect
461. #340C22×C109semidirect
462. #340C22×C109semidirect
463. #340C22×C109semidirect
464. #340C22×C109semidirect
465. #336C22×C109semidirect
466. #336C22×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1092
C2×C4×D8×C1092
C109×#24202
D4×C22⋊C4×C1092
C109×#20922
C109×#20762
C109×#20542
C109×#20342
C109×#19342
C109×#19232
C109×#18792
C109×#18642
C109×#18042
C109×#17862
#24897109