Finite Group Databasebeta

← C109×#24893 #42142887

Subgroups — C109×#24893 #42142887

Order 27904.

1232 conjugacy classes of subgroups.

The subgroup lattice has 818 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×#2422C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C109C211yesmaximal, characteristic, complemented
5C109×#2093C211yesmaximal, characteristic, complemented
6C109×#2075C211yesmaximal, characteristic, complemented
7C109×#2054C211yesmaximal, characteristic, complemented
8C109×#2033C211yesmaximal, characteristic, complemented
9C109×#1934C211yesmaximal, characteristic, complemented
10C109×#1923C211yesmaximal, characteristic, complemented
11C109×#1879C211yesmaximal, characteristic, complemented
12C109×#1879C211yesmaximal, characteristic, complemented
13C109×#1862C211yesmaximal, characteristic, complemented
14C109×#1802C211yesmaximal, characteristic, complemented
15C109×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C109C2211yescharacteristic
17C22×D8×C109C2211yescharacteristic
18C22×D8×C109C2211yescharacteristic
19C2×#123×C109—21no—
20C2×#121×C109C2211yescharacteristic
21C2×C4×D4×C109C2211yescharacteristic
22C2×C4×D4×C109C2211yescharacteristic
23C2×C4×D4×C109C2211yescharacteristic, complemented
24C22×C22⋊C4×C109—21no—
25#447×C109—24no—
26C4×D8×C109—24no—
27C2×#107×C109C2211yescharacteristic, complemented
28C2×#107×C109C2211yescharacteristic, complemented
29C2×C4⋊C8×C109C2211yescharacteristic, complemented
30C2×#102×C109C2211yescharacteristic
31C2×#102×C109C2211yescharacteristic
32C2×#102×C109C2211yescharacteristic
33C2×#102×C109C2211yescharacteristic
34C2×#102×C109C2211yescharacteristic
35C2×#102×C109C2211yescharacteristic
36C2×#102×C109C2211yescharacteristic, complemented
37C2×#102×C109C2211yescharacteristic, complemented
38C2×C22⋊C8×C109C2211yescharacteristic
39C2×C22⋊C8×C109C2211yescharacteristic
40C2×C4×C8×C109C2211yescharacteristic, complemented
41#397×C109—21no—
42#394×C109—21no—
43#390×C109C2211yescharacteristic
44#390×C109C2211yescharacteristic
45#390×C109C2211yescharacteristic, complemented
46#389×C109C2211yescharacteristic, complemented
47#386×C109—21no—
48#386×C109—21no—
49#385×C109—21no—
50#384×C109C2211yescharacteristic, complemented
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#123×C109—44no—
88#121×C109—22no—
89#121×C109—41no—
90C4×D4×C109—22no—
91C4×D4×C109—22no—
92C4×D4×C109—22no—
93C4×D4×C109—41no—
94C4×D4×C109—41no—
95C4×D4×C109—41no—
96C2×C4⋊C4×C109—21no—
97C2×C4⋊C4×C109—21no—
98C2×C4⋊C4×C109—21no—
99C2×C4⋊C4×C109C2311yescharacteristic
100C2×C4⋊C4×C109C2311yescharacteristic
101C2×C4⋊C4×C109C2311yescharacteristic
102C2×C4⋊C4×C109C2311yescharacteristic
103C2×C4⋊C4×C109C2311yescharacteristic
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—21no—
114C2×C22⋊C4×C109—21no—
115C2×C22⋊C4×C109—21no—
116C2×C22⋊C4×C109—44no—
117C2×C22⋊C4×C109D411yescharacteristic
118C2×C22⋊C4×C109D411yescharacteristic
119C2×C42×C109C2311yescharacteristic
120C2×C42×C109C2311yescharacteristic
121#107×C109—22no—
122#107×C109—41no—
123C4⋊C8×C109—41no—
124#102×C109—22no—
125#102×C109—22no—
126#102×C109—22no—
127#102×C109—22no—
128#102×C109—22no—
129#102×C109—22no—
130#102×C109—41no—
131#102×C109—41no—
132C22⋊C8×C109—22no—
133C22⋊C8×C109—41no—
134C4×C8×C109—22no—
135#95×C109—21no—
136#95×C109—21no—
137#95×C109—21no—
138#95×C109D411yescharacteristic
139#95×C109D411yescharacteristic
140C24×C109—21no—
141C24×C109—24no—
142C24×C109—21no—
143C24×C109—21no—
144C24×C109—42no—
145C24×C109—42no—
146C24×C109—42no—
147C24×C109—42no—
148C24×C109—81no—
149C24×C109—81no—
150C24×C109C2×D411yescharacteristic
151C2×D4×C109—24no—
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—21no—
165C2×D4×C109—42no—
166C2×D4×C109—42no—
167C2×D4×C109—44no—
168C2×D4×C109—44no—
169C2×D4×C109—44no—
170C2×D4×C109—44no—
171C2×D4×C109—42no—
172C2×D4×C109—42no—
173C2×D4×C109—81no—
174C2×D4×C109C2×D412yes—
175C2×D4×C109C2×D412yes—
176C2×D4×C109#4112yes—
177C2×D4×C109#4112yes—
178C2×D4×C109#4112yes—
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—21no—
190C22×C4×C109—42no—
191C22×C4×C109—42no—
192C22×C4×C109—42no—
193C22×C4×C109—42no—
194C22×C4×C109—42no—
195C22×C4×C109—42no—
196C22×C4×C109—81no—
197C22×C4×C109—81no—
198C22×C4×C109—81no—
199C22×C4×C109C2×D411yescharacteristic
200C22×C4×C109C2×D411yescharacteristic
201C22×C4×C109C2×D411yescharacteristic
202C22×C4×C109C2×D411yescharacteristic
203C22×C4×C109C2×D411yescharacteristic
204C22×C4×C109C2411yescharacteristic
205D8×C109—28no—
206D8×C109—44no—
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×C109—21no—
218C2×C8×C109C2×D412yes—
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—21no—
229C4⋊C4×C109—42no—
230C4⋊C4×C109—42no—
231C4⋊C4×C109—81no—
232C22⋊C4×C109—41no—
233C22⋊C4×C109—42no—
234C22⋊C4×C109—42no—
235C22⋊C4×C109—42no—
236C22⋊C4×C109—42no—
237C22⋊C4×C109—42no—
238C22⋊C4×C109—42no—
239C22⋊C4×C109—42no—
240C22⋊C4×C109—42no—
241C22⋊C4×C109—42no—
242C22⋊C4×C109—42no—
243C22⋊C4×C109—81no—
244C22⋊C4×C109—81no—
245C22⋊C4×C109D814yescomplemented
246C42×C109—21no—
247C42×C109—21no—
248C42×C109—21no—
249C42×C109—21no—
250C23×C109—21no—
251C23×C109—22no—
252C23×C109—22no—
253C23×C109—21no—
254C23×C109—22no—
255C23×C109—21no—
256C23×C109—21no—
257C23×C109—21no—
258C23×C109—21no—
259C23×C109—22no—
260C23×C109—22no—
261C23×C109—48no—
262C23×C109—48no—
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—41no—
277C23×C109—41no—
278C23×C109—41no—
279C23×C109—84no—
280C23×C109—84no—
281C23×C109—84no—
282C23×C109—84no—
283C23×C109—84no—
284C23×C109C2×D812yes—
285C23×C109C22×D411yescharacteristic
286D4×C109—22no—
287D4×C109—22no—
288D4×C109—22no—
289D4×C109—22no—
290D4×C109—22no—
291D4×C109—22no—
292D4×C109—22no—
293D4×C109—48no—
294D4×C109—41no—
295D4×C109—41no—
296D4×C109—41no—
297D4×C109—41no—
298D4×C109—84no—
299D4×C109#12314yescomplemented
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—21no—
312C2×C4×C109—21no—
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—41no—
331C2×C4×C109—41no—
332C2×C4×C109—84no—
333C2×C4×C109—84no—
334C2×C4×C109—84no—
335C2×C4×C109C2×D812yes—
336C2×C4×C109C2×D812yes—
337C2×C4×C109C22×D411yescharacteristic
338C2×C4×C109C2×#4111yescharacteristic
339C2×C4×C109C2×#4111yescharacteristic
340C2×C4×C109C2×#4111yescharacteristic
341C2×C4×C109H(5,𝔽2)11yescharacteristic
342C2×C4×C109H(5,𝔽2)11yescharacteristic
343C8×C109—22no—
344C8×C109—41no—
345C8×C109—41no—
346C8×C109—41no—
347C22×C109—22no—
348C22×C109—24no—
349C22×C109—22no—
350C22×C109—22no—
351C22×C109—42no—
352C22×C109—41no—
353C22×C109—42no—
354C22×C109—41no—
355C22×C109—41no—
356C22×C109—42no—
357C22×C109—42no—
358C22×C109—42no—
359C22×C109—41no—
360C22×C109—42no—
361C22×C109—42no—
362C22×C109—42no—
363C22×C109—42no—
364C22×C109—42no—
365C22×C109—42no—
366C22×C109—42no—
367C22×C109—816no—
368C22×C109—81no—
369C22×C109—81no—
370C22×C109—81no—
371C22×C109—81no—
372C22×C109—81no—
373C22×C109—81no—
374C22×C109—81no—
375C22×C109—81no—
376C22×C109#52511yescharacteristic
377C22×C109D4211yescharacteristic
378C22×C109#54611yescharacteristic
379C22×C109C22×D811yescharacteristic
380C22×C109#57511yescharacteristic
381C22×C109#57611yescharacteristic
382C22×C109#57711yescharacteristic
383C4×C109—22no—
384C4×C109—22no—
385C4×C109—41no—
386C4×C109—41no—
387C4×C109—41no—
388C4×C109—81no—
389C4×C109—81no—
390C4×C109—81no—
391C4×C109—81no—
392C4×C109—81no—
393C4×C109C2×#12311yescharacteristic
394C4×C109#53811yescharacteristic
395C4×C109#54611yescharacteristic
396C4×C109#55111yescharacteristic
397#24893C10911yesmaximal, characteristic, direct product factor, Sylow
398C2×C109—42no—
399C2×C109—44no—
400C2×C109—82no—
401C2×C109—82no—
402C2×C109#241811yescharacteristic
403C2×C109#310011yescharacteristic
404C2×C109#311811yescharacteristic
405C2×C109#326711yescharacteristic
406C2×C109D4×D811yescharacteristic
407C2×C109#329411yescharacteristic
408C2×C109#332211yescharacteristic
409C2×#447C2×C10911yescharacteristic
410C2×C4×D8C2×C10911yescharacteristic, complemented
411#2422C2×C10911yescharacteristic, complemented
412D4×C22⋊C4C2×C10911yescharacteristic, complemented
413#2093C2×C10911yescharacteristic, complemented
414#2075C2×C10911yescharacteristic, complemented
415#2054C2×C10911yescharacteristic, complemented
416#2033C2×C10911yescharacteristic, complemented
417#1934C2×C10911yescharacteristic, complemented
418#1923C2×C10911yescharacteristic, complemented
419#1879C2×C10911yescharacteristic, complemented
420#1879C2×C10911yescharacteristic, complemented
421#1862C2×C10911yescharacteristic, complemented
422#1802C2×C10911yescharacteristic, complemented
423#1786C2×C10911yescharacteristic, complemented
424C109#2489311yescharacteristic, direct product factor, Sylow
425C23×D4C22×C10911yescharacteristic
426C22×D8C22×C10911yescharacteristic
427C22×D8C22×C10911yescharacteristic
428C2×#123—21no—
429C2×#121C22×C10911yescharacteristic
430C2×C4×D4C22×C10911yescharacteristic
431C2×C4×D4C22×C10911yescharacteristic
432C2×C4×D4C22×C10911yescharacteristic, complemented
433C22×C22⋊C4—21no—
434#447—24no—
435C4×D8—24no—
436C2×#107C22×C10911yescharacteristic, complemented
437C2×#107C22×C10911yescharacteristic, complemented
438C2×C4⋊C8C22×C10911yescharacteristic, complemented
439C2×#102C22×C10911yescharacteristic
440C2×#102C22×C10911yescharacteristic
441C2×#102C22×C10911yescharacteristic
442C2×#102C22×C10911yescharacteristic
443C2×#102C22×C10911yescharacteristic
444C2×#102C22×C10911yescharacteristic
445C2×#102C22×C10911yescharacteristic, complemented
446C2×#102C22×C10911yescharacteristic, complemented
447C2×C22⋊C8C22×C10911yescharacteristic
448C2×C22⋊C8C22×C10911yescharacteristic
449C2×C4×C8C22×C10911yescharacteristic, complemented
450#397—21no—
451#394—21no—
452#390C22×C10911yescharacteristic
453#390C22×C10911yescharacteristic
454#390C22×C10911yescharacteristic, complemented
455#389C22×C10911yescharacteristic, complemented
456#386—21no—
457#386—21no—
458#385—21no—
459#384C22×C10911yescharacteristic, complemented
460#380C22×C10911yescharacteristic
461#380C22×C10911yescharacteristic
462#379—21no—
463C4×C22⋊C4C22×C10911yescharacteristic
464#340C22×C10911yescharacteristic, complemented
465#340C22×C10911yescharacteristic, complemented
466#340C22×C10911yescharacteristic, complemented
467#340C22×C10911yescharacteristic, complemented
468#336C22×C10911yescharacteristic, complemented
469#336C22×C10911yescharacteristic, complemented
470C25—21no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—41no—
478C22×D4—41no—
479C22×D4C23×C10911yescharacteristic
480C22×D4C23×C10911yescharacteristic
481C22×D4C23×C10911yescharacteristic
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C10911yescharacteristic
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—41no—
491C2×D8D4×C10914yes—
492C22×C8C23×C10911yescharacteristic
493C22×C8C23×C10911yescharacteristic
494C22×C8C23×C10911yescharacteristic
495C22×C8C23×C10911yescharacteristic
496#123—44no—
497#121—22no—
498#121—41no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—41no—
503C4×D4—41no—
504C4×D4—41no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4C23×C10911yescharacteristic
509C2×C4⋊C4C23×C10911yescharacteristic
510C2×C4⋊C4C23×C10911yescharacteristic
511C2×C4⋊C4C23×C10911yescharacteristic
512C2×C4⋊C4C23×C10911yescharacteristic
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—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—44no—
526C2×C22⋊C4D4×C10911yescharacteristic
527C2×C22⋊C4D4×C10911yescharacteristic
528C2×C42C23×C10911yescharacteristic
529C2×C42C23×C10911yescharacteristic
530#107—22no—
531#107—41no—
532C4⋊C8—41no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—22no—
538#102—22no—
539#102—41no—
540#102—41no—
541C22⋊C8—22no—
542C22⋊C8—41no—
543C4×C8—22no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95D4×C10911yescharacteristic
548#95D4×C10911yescharacteristic
549C24—21no—
550C24—24no—
551C24—21no—
552C24—21no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—81no—
558C24—81no—
559C24C2×D4×C10911yescharacteristic
560C2×D4—24no—
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—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—44no—
579C2×D4—44no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—81no—
583C2×D4C2×D4×C10912yes—
584C2×D4C2×D4×C10912yes—
585C2×D4#41×C10912yes—
586C2×D4#41×C10912yes—
587C2×D4#41×C10912yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4C2×D4×C10911yescharacteristic
609C22×C4C2×D4×C10911yescharacteristic
610C22×C4C2×D4×C10911yescharacteristic
611C22×C4C2×D4×C10911yescharacteristic
612C22×C4C2×D4×C10911yescharacteristic
613C22×C4C24×C10911yescharacteristic
614D8—28no—
615D8—44no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8C2×D4×C10912yes—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—81no—
641C22⋊C4—41no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—81no—
653C22⋊C4—81no—
654C22⋊C4D8×C10914yescomplemented
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—22no—
670C23—48no—
671C23—48no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—84no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23C2×D8×C10912yes—
694C23C22×D4×C10911yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4#123×C10914yescomplemented
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—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
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—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4C2×D8×C10912yes—
745C2×C4C2×D8×C10912yes—
746C2×C4C22×D4×C10911yescharacteristic
747C2×C4C2×#41×C10911yescharacteristic
748C2×C4C2×#41×C10911yescharacteristic
749C2×C4C2×#41×C10911yescharacteristic
750C2×C4H(5,𝔽2)×C10911yescharacteristic
751C2×C4H(5,𝔽2)×C10911yescharacteristic
752C8—22no—
753C8—41no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—24no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—42no—
769C22—41no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—816no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22#525×C10911yescharacteristic
786C22D42×C10911yescharacteristic
787C22#546×C10911yescharacteristic
788C22C22×D8×C10911yescharacteristic
789C22#575×C10911yescharacteristic
790C22#576×C10911yescharacteristic
791C22#577×C10911yescharacteristic
792C4—22no—
793C4—22no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4C2×#123×C10911yescharacteristic
803C4#538×C10911yescharacteristic
804C4#546×C10911yescharacteristic
805C4#551×C10911yescharacteristic
806C2—42no—
807C2—44no—
808C2—82no—
809C2—82no—
810C2C109×#241811yescharacteristic
811C2C109×#310011yescharacteristic
812C2C109×#311811yescharacteristic
813C2C109×#326711yescharacteristic
814C2D4×D8×C10911yescharacteristic
815C2C109×#329411yescharacteristic
816C2C109×#332211yescharacteristic
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×#2422C2semidirect
4. D4×C22⋊C4×C109C2semidirect
5. C109×#2093C2semidirect
6. C109×#2075C2semidirect
7. C109×#2054C2semidirect
8. C109×#2033C2semidirect
9. C109×#1934C2semidirect
10. C109×#1923C2semidirect
11. C109×#1879C2semidirect
12. C109×#1879C2semidirect
13. C109×#1862C2semidirect
14. C109×#1802C2semidirect
15. C109×#1786C2semidirect
23. C2×C4×D4×C109C22semidirect
27. C2×#107×C109C22semidirect
28. C2×#107×C109C22semidirect
29. C2×C4⋊C8×C109C22semidirect
36. C2×#102×C109C22semidirect
37. C2×#102×C109C22semidirect
40. C2×C4×C8×C109C22semidirect
45. #390×C109C22semidirect
46. #389×C109C22semidirect
50. #384×C109C22semidirect
55. #340×C109C22semidirect
56. #340×C109C22semidirect
57. #340×C109C22semidirect
58. #340×C109C22semidirect
59. #336×C109C22semidirect
60. #336×C109C22semidirect
245. C22⋊C4×C109D8semidirect
299. D4×C109#123semidirect
397. #24893C109direct (N × H)
410. C2×C4×D8C2×C109semidirect
411. #2422C2×C109semidirect
412. D4×C22⋊C4C2×C109semidirect
413. #2093C2×C109semidirect
414. #2075C2×C109semidirect
415. #2054C2×C109semidirect
416. #2033C2×C109semidirect
417. #1934C2×C109semidirect
418. #1923C2×C109semidirect
419. #1879C2×C109semidirect
420. #1879C2×C109semidirect
421. #1862C2×C109semidirect
422. #1802C2×C109semidirect
423. #1786C2×C109semidirect
424. C109#24893direct (N × H)
432. C2×C4×D4C22×C109semidirect
436. C2×#107C22×C109semidirect
437. C2×#107C22×C109semidirect
438. C2×C4⋊C8C22×C109semidirect
445. C2×#102C22×C109semidirect
446. C2×#102C22×C109semidirect
449. C2×C4×C8C22×C109semidirect
454. #390C22×C109semidirect
455. #389C22×C109semidirect
459. #384C22×C109semidirect
464. #340C22×C109semidirect
465. #340C22×C109semidirect
466. #340C22×C109semidirect
467. #340C22×C109semidirect
468. #336C22×C109semidirect
469. #336C22×C109semidirect
654. C22⋊C4D8×C109semidirect
708. D4#123×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×#24222
D4×C22⋊C4×C1092
C109×#20932
C109×#20752
C109×#20542
C109×#20332
C109×#19342
C109×#19232
C109×#18792
C109×#18622
C109×#18022
C109×#17862
#24893109