Finite Group Databasebeta

← C2×#11736207 #14230334

Subgroups — C2×#11736207 #14230334

Order 1792.

2578 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊D7C211yesmaximal, characteristic
2C2×#90204C211yesmaximal, characteristic, complemented
3C22×C7×#102C211yesmaximal, characteristic, complemented
4C2×#89990C211yesmaximal, characteristic, complemented
5C2×#89886C211yesmaximal, characteristic, complemented
6C2×#89883C211yesmaximal, characteristic, complemented
7C2×#89739C211yesmaximal, characteristic, complemented
8C2×#89534C211yesmaximal, characteristic, complemented
9#11736207C2116yesmaximal, direct product factor
10C2×#89552C211yesmaximal, characteristic, complemented
11C2×#89548C211yesmaximal, characteristic, complemented
12C2×#89542C211yesmaximal, characteristic, complemented
13C2×#89536C211yesmaximal, characteristic, complemented
14C2×#89551C211yesmaximal, characteristic, complemented
15C2×#89535C211yesmaximal, characteristic, complemented
16C2×#89529C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C22⋊D7—21no—
19C22×D4×D7C2211yescharacteristic
20C23×C7×C8C2211yescharacteristic, complemented
21C22×C7×C4⋊C4C2211yescharacteristic, complemented
22C2×#6516—21no—
23C2×#6503C2211yescharacteristic
24C2×#6502—21no—
25D4×C22⋊D7—24no—
26D4×C22⋊D7C2218yes—
27C2×#6501C2211yescharacteristic
28C2×#6500—21no—
29C2×D4×Dic7C2211yescharacteristic
30C22×#1142C2211yescharacteristic
31C22×#1142C2211yescharacteristic, complemented
32C2×#6493C2211yescharacteristic
33C2×#6492—21no—
34C2×C4×C22⋊D7C2211yescharacteristic
35C2×#6489—21no—
36C2×#6487C2211yescharacteristic, complemented
37C22×#1132C2211yescharacteristic, complemented
38C22×#1131C2211yescharacteristic, complemented
39#90204—24no—
40#90204C2218yescomplemented
41C2×#6461—21no—
42C2×#6460C2211yescharacteristic, complemented
43C2×#6455C2211yescharacteristic, complemented
44C2×#6453C2211yescharacteristic, complemented
45C2×#6452—21no—
46C2×#6450C2211yescharacteristic, complemented
47C2×C7×#102C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×#102C2218yescomplemented
50C2×C7×#102C2211yescharacteristic, complemented
51C2×C7×#102C2211yescharacteristic, complemented
52#89990C2218yescomplemented
53C2×#6406C2211yescharacteristic
54C2×#6406C2211yescharacteristic, complemented
55C2×C22⋊(C7⋊C8)C2211yescharacteristic, complemented
56#89886C2218yescomplemented
57C2×#6395C2211yescharacteristic, complemented
58#89883C2218yescomplemented
59C2×(C2×D7)⋊C8C2211yescharacteristic, complemented
60C2×#6391C2211yescharacteristic, complemented
61C2×#6390C2211yescharacteristic, complemented
62C2×#6389C2211yescharacteristic, complemented
63C2×Dic7⋊C8C2211yescharacteristic, complemented
64#89739C2218yescomplemented
65C2×#6383C2211yescharacteristic, complemented
66C2×#6383C2211yescharacteristic, complemented
67C2×#6381C2211yescharacteristic, complemented
68C2×#6381C2211yescharacteristic, complemented
69#89552C2218yescomplemented
70#89551C2218yescomplemented
71#89548C2218yescomplemented
72#89542C2218yescomplemented
73#89536C2218yescomplemented
74#89535C2218yescomplemented
75#89534C2218yescomplemented
76#89529C2218yescomplemented
77C2×#3310—71nomaximal, Sylow
78C25×C7—21no—
79C24×D7—21no—
80C22×C7×D4—24no—
81C22×C7×D4—21no—
82C22×C7×D4—22no—
83C22×C7×D4—42no—
84C22×C7×D4C2311yescharacteristic
85C22×C7×D4C2314yes—
86C22×C7×D4C2311yescharacteristic
87C23×C4×C7—21no—
88C23×C4×C7C2311yescharacteristic
89C22×C22⋊D7—21no—
90C22×C22⋊D7—21no—
91C22×C22⋊D7—28no—
92C22×C22⋊D7—21no—
93C22×C22⋊D7—21no—
94C22×C22⋊D7—21no—
95C22×C22⋊D7—48no—
96C22×C22⋊D7D411yescharacteristic
97C23×Dic7—21no—
98C2×D4×D7—24no—
99C2×D4×D7—22no—
100C2×D4×D7—42no—
101C2×D4×D7C2314yes—
102C22×D28C2311yescharacteristic
103C22×C4×D7C2311yescharacteristic
104C22×Dic14C2311yescharacteristic
105C22×C7×C8—42no—
106C22×C7×C8C2311yescharacteristic
107C22×C7×C8C2311yescharacteristic
108C22×C7×C8C2314yescomplemented
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4—22no—
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C4⋊C4C2314yescomplemented
114#6516—28no—
115C2×C22⋊Dic7—21no—
116C2×C22⋊Dic7—21no—
117C2×C22⋊Dic7—21no—
118C2×C22⋊Dic7D411yescharacteristic
119#6503—22no—
120#6503C2314yes—
121#6502—28no—
122#6501—22no—
123#6501C2314yes—
124#6500—28no—
125D4×Dic7—22no—
126D4×Dic7C2314yes—
127C2×#1142—24no—
128C2×#1142—42no—
129C2×#1142C2314yes—
130C2×#1142C2314yescomplemented
131#6493—22no—
132#6493C2314yes—
133#6492—28no—
134C4×C22⋊D7D414yes—
135C4×C22⋊D7C2314yes—
136C2×(C2×D7)⋊C4—21no—
137C2×(C2×D7)⋊C4—21no—
138C2×(C2×D7)⋊C4—21no—
139C2×(C2×D7)⋊C4D411yescharacteristic
140#6489—28no—
141C2×C4⋊Dic7—21no—
142C2×C4⋊Dic7—21no—
143C2×C4⋊Dic7C2311yescharacteristic
144C2×C4⋊Dic7C2311yescharacteristic
145#6487—22no—
146#6487C2314yescomplemented
147C2×Dic7⋊C4—21no—
148C2×Dic7⋊C4—21no—
149C2×Dic7⋊C4—21no—
150C2×Dic7⋊C4D411yescharacteristic
151C2×C4×Dic7—21no—
152C2×C4×Dic7—21no—
153C2×C4×Dic7C2311yescharacteristic
154C22×C7⋊C8C2311yescharacteristic
155C22×C7⋊C8C2311yescharacteristic
156C2×#1132—42no—
157C2×#1132C2314yescomplemented
158C2×#1131—42no—
159C2×#1131C2314yescomplemented
160#6461—28no—
161#6460—22no—
162#6460C2314yescomplemented
163#6455—22no—
164#6455C2314yescomplemented
165#6453—22no—
166#6453C2314yescomplemented
167#6452—28no—
168#6450—22no—
169#6450C2314yescomplemented
170C7×#102C2314yes—
171C7×#102C2314yes—
172C7×#102C2314yescomplemented
173C7×#102C2314yescomplemented
174#6406C2314yes—
175#6406C2314yescomplemented
176C22⋊(C7⋊C8)C2314yescomplemented
177#6395C2314yescomplemented
178(C2×D7)⋊C8C2314yescomplemented
179#6391C2314yescomplemented
180#6390C2314yescomplemented
181#6389C2314yescomplemented
182Dic7⋊C8C2314yescomplemented
183#6383C2314yescomplemented
184#6383C2314yescomplemented
185#6381C2314yescomplemented
186#6381C2314yescomplemented
187C2×#552—71no—
188C2×D42—71no—
189#3310—716no—
190C2×#490—71no—
191C2×#482—71no—
192C2×#480—71no—
193C2×#478—71no—
194C2×#468—71no—
195C2×#465—71no—
196C2×#460—71no—
197C2×#450—71no—
198C2×#450—71no—
199C2×#440—71no—
200C2×#435—71no—
201C2×#418—71no—
202C22×#102D711yescharacteristic, complemented
203C24×C7—21no—
204C24×C7—21no—
205C24×C7—24no—
206C24×C7—44no—
207C24×C7—44no—
208C24×C7—82no—
209C24×C7C2×D411yescharacteristic
210C23×D7—21no—
211C23×D7—24no—
212C23×D7—44no—
213C23×D7—44no—
214C23×D7—82no—
215C23×D7C2×D411yescharacteristic
216C2×C7×D4—28no—
217C2×C7×D4—21no—
218C2×C7×D4—24no—
219C2×C7×D4—21no—
220C2×C7×D4—22no—
221C2×C7×D4—22no—
222C2×C7×D4—22no—
223C2×C7×D4—44no—
224C2×C7×D4—48no—
225C2×C7×D4—44no—
226C2×C7×D4#4114yes—
227C2×C7×D4C2412yes—
228C2×C7×D4C2412yes—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—24no—
234C22×C4×C7—44no—
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2×D412yes—
237C22×C4×C7C2412yes—
238C22×C4×C7C2411yescharacteristic
239C2×C22⋊D7—24no—
240C2×C22⋊D7—24no—
241C2×C22⋊D7—24no—
242C2×C22⋊D7—24no—
243C2×C22⋊D7—24no—
244C2×C22⋊D7—24no—
245C2×C22⋊D7—44no—
246C2×C22⋊D7—44no—
247C2×C22⋊D7—432no—
248C2×C22⋊D7—44no—
249C2×C22⋊D7—44no—
250C2×C22⋊D7—82no—
251C2×C22⋊D7C2×D414yes—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—24no—
256C22×Dic7—44no—
257C22×Dic7C2×D411yescharacteristic
258C22×Dic7C2×D411yescharacteristic
259C22×Dic7C2×D411yescharacteristic
260D4×D7—28no—
261D4×D7—44no—
262D4×D7—48no—
263C2×D28—22no—
264C2×D28—22no—
265C2×D28—21no—
266C2×D28C2412yes—
267C2×C4×D7—22no—
268C2×C4×D7—22no—
269C2×C4×D7C2×D412yes—
270C2×C4×D7C2412yes—
271C2×Dic14—22no—
272C2×Dic14—22no—
273C2×Dic14—21no—
274C2×Dic14C2412yes—
275C2×C7×C8—22no—
276C2×C7×C8—22no—
277C2×C7×C8—44no—
278C2×C7×C8C2412yes—
279C2×C7×C8C2412yes—
280C7×C4⋊C4—21no—
281C7×C4⋊C4—24no—
282C7×C4⋊C4—21no—
283C7×C4⋊C4C2412yes—
284C7×C4⋊C4C2412yes—
285C22⋊Dic7—24no—
286C22⋊Dic7—24no—
287C22⋊Dic7—24no—
288C22⋊Dic7C2×D414yes—
289#1142—28no—
290#1142—44no—
291(C2×D7)⋊C4—24no—
292(C2×D7)⋊C4—24no—
293(C2×D7)⋊C4—24no—
294(C2×D7)⋊C4C2×D414yes—
295C4⋊Dic7—21no—
296C4⋊Dic7—21no—
297C4⋊Dic7—24no—
298C4⋊Dic7—24no—
299C4⋊Dic7C2412yes—
300C4⋊Dic7C2412yes—
301Dic7⋊C4—24no—
302Dic7⋊C4—24no—
303Dic7⋊C4—24no—
304Dic7⋊C4C2×D414yes—
305C4×Dic7—24no—
306C4×Dic7—24no—
307C4×Dic7C2×D412yes—
308C4×Dic7C2412yes—
309C2×C7⋊C8—22no—
310C2×C7⋊C8—22no—
311C2×C7⋊C8C2412yes—
312C2×C7⋊C8C2412yes—
313#1132—44no—
314#1131—44no—
315C23×D4—71no—
316C23×D4—141no—
317C23×D4C2×D711yescharacteristic
318C22×SD16—71no—
319C22×SD16—71no—
320C22×SD16—71no—
321C22×M16—71no—
322C23×C8C2×D711yescharacteristic, complemented
323#552—78no—
324#552—144no—
325D42—78no—
326D42—144no—
327C2×#127—71no—
328C2×#126—141no—
329C2×#125—71no—
330C2×#125—141no—
331C2×#123—141no—
332C2×C22⋊Q8—71no—
333C2×C22⋊Q8—71no—
334C2×#121—71no—
335C2×#121—71no—
336C2×#121—141no—
337C2×#120—141no—
338C2×#120—141no—
339C2×C4×Q8—71no—
340C2×C4×D4—71no—
341C2×C4×D4—71no—
342C2×#117—71no—
343C2×#117—141no—
344C22×C4⋊C4C2×D711yescharacteristic, complemented
345#490—78no—
346#482—78no—
347#480—78no—
348#478—78no—
349#468—78no—
350#465—78no—
351#460—78no—
352#450—78no—
353#450—78no—
354#440—78no—
355#435—78no—
356C2×#107—71no—
357C2×#107—71no—
358C2×#106—71no—
359C2×C4⋊C8—71no—
360#418—78no—
361C2×#103—71no—
362C2×#102—71no—
363C2×#102—71no—
364C2×#102—71no—
365C2×#102—71no—
366C2×#102—71no—
367C2×#102C2×D711yescharacteristic
368C2×#102C2×D711yescharacteristic
369C2×#102C2×D718yescomplemented
370C2×#102C2×D711yescharacteristic, complemented
371C2×#102C2×D711yescharacteristic, complemented
372C2×C22⋊C8—71no—
373C2×C22⋊C8—71no—
374C2×#97—71no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—24no—
378C23×C7—22no—
379C23×C7—22no—
380C23×C7—48no—
381C23×C7—42no—
382C23×C7—42no—
383C23×C7—42no—
384C23×C7—48no—
385C23×C7—42no—
386C23×C7—42no—
387C23×C7—84no—
388C23×C7—816no—
389C23×C7AGL(1,ℤ/8)14yes—
390C23×C7C22×D412yes—
391C23×C7C22×D411yescharacteristic
392C22×D7—22no—
393C22×D7—22no—
394C22×D7—22no—
395C22×D7—22no—
396C22×D7—48no—
397C22×D7—48no—
398C22×D7—42no—
399C22×D7—42no—
400C22×D7—42no—
401C22×D7—84no—
402C22×D7—816no—
403C22×D7C22×D412yes—
404C7×D4—24no—
405C7×D4—22no—
406C7×D4—22no—
407C7×D4—22no—
408C7×D4—48no—
409C7×D4—42no—
410C7×D4C2×#4114yes—
411C2×C4×C7—22no—
412C2×C4×C7—24no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—48no—
418C2×C4×C7—42no—
419C2×C4×C7—42no—
420C2×C4×C7C22×D412yes—
421C2×C4×C7C22×D411yescharacteristic
422C2×C4×C7C2×#4112yes—
423C2×C4×C7H(5,𝔽2)12yes—
424C2×C4×C7C2511yescharacteristic
425C22⋊D7—28no—
426C22⋊D7—48no—
427C22⋊D7—48no—
428C22⋊D7—48no—
429C22⋊D7—48no—
430C22⋊D7—84no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—48no—
438C2×Dic7—42no—
439C2×Dic7—42no—
440C2×Dic7—42no—
441C2×Dic7C22×D412yes—
442C2×Dic7C22×D412yes—
443C2×Dic7C22×D412yes—
444D28—22no—
445D28—22no—
446D28—42no—
447C4×D7—24no—
448C4×D7—22no—
449C4×D7—22no—
450Dic14—22no—
451Dic14—22no—
452Dic14—42no—
453C7×C8—22no—
454C7×C8—22no—
455C7⋊C8—22no—
456C7⋊C8—22no—
457C25—21no—
458C25—141no—
459C22×Q8—71no—
460C22×D4—24no—
461C22×D4—21no—
462C22×D4—22no—
463C22×D4—42no—
464C22×D4—71no—
465C22×D4—74no—
466C22×D4—71no—
467C22×D4—142no—
468C22×D4—141no—
469C22×D4—141no—
470C22×D4—141no—
471C22×D4—148no—
472C22×D4—144no—
473C22×D4—141no—
474C22×D4—141no—
475C22×D4—282no—
476C22×D4—288no—
477C22×D4C22×D711yescharacteristic
478C22×D4C22×D714yes—
479C22×D4C22×D711yescharacteristic
480C23×C4—21no—
481C23×C4—71no—
482C23×C4—141no—
483C23×C4C22×D711yescharacteristic
484C2×SD16—74no—
485C2×SD16—74no—
486C2×SD16—74no—
487C2×SD16—144no—
488C2×SD16—282no—
489C2×SD16—282no—
490C2×M16—74no—
491C2×M16—282no—
492C22×C8—42no—
493C22×C8—71no—
494C22×C8—71no—
495C22×C8C22×D711yescharacteristic
496C22×C8C22×D711yescharacteristic
497C22×C8C22×D714yescomplemented
498#127—74no—
499#127—142no—
500#126—148no—
501#125—74no—
502#125—142no—
503#125—148no—
504#123—148no—
505C22⋊Q8—74no—
506C22⋊Q8—74no—
507C22⋊Q8—142no—
508C22⋊Q8—142no—
509#121—74no—
510#121—74no—
511#121—148no—
512#121—142no—
513#121—142no—
514#120—148no—
515#120—148no—
516C4×Q8—74no—
517C4×Q8—142no—
518C4×D4—74no—
519C4×D4—74no—
520C4×D4—74no—
521C4×D4—142no—
522#117—74no—
523#117—148no—
524#117—142no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—71no—
528C2×C4⋊C4—71no—
529C2×C4⋊C4—71no—
530C2×C4⋊C4—141no—
531C2×C4⋊C4—141no—
532C2×C4⋊C4—141no—
533C2×C4⋊C4—141no—
534C2×C4⋊C4—141no—
535C2×C4⋊C4C22×D711yescharacteristic
536C2×C4⋊C4C22×D711yescharacteristic
537C2×C4⋊C4C22×D714yescomplemented
538C2×C22⋊C4—71no—
539C2×C22⋊C4—71no—
540C2×C22⋊C4—141no—
541C2×C22⋊C4—141no—
542C2×C22⋊C4—141no—
543C2×C22⋊C4—141no—
544C2×C22⋊C4—141no—
545C2×C22⋊C4—141no—
546C2×C42—71no—
547C2×C42—141no—
548C2×C42—141no—
549#107—74no—
550#107—74no—
551#106—74no—
552C4⋊C8—74no—
553#103—74no—
554#102—74no—
555#102—74no—
556#102—74no—
557#102—74no—
558#102—74no—
559#102C22×D714yes—
560#102C22×D714yes—
561#102C22×D714yescomplemented
562#102C22×D714yescomplemented
563C22⋊C8—74no—
564C22⋊C8—74no—
565#97—74no—
566C22×C7—22no—
567C22×C7—28no—
568C22×C7—22no—
569C22×C7—24no—
570C22×C7—48no—
571C22×C7—42no—
572C22×C7—42no—
573C22×C7—42no—
574C22×C7—42no—
575C22×C7—42no—
576C22×C7—816no—
577C22×C7—84no—
578C22×C7#54612yes—
579C22×C7C2×AGL(1,ℤ/8)14yes—
580C22×C7C2×AGL(1,ℤ/8)12yes—
581C22×C7#57712yes—
582C22×C7C23×D411yescharacteristic
583C2×D7—22no—
584C2×D7—22no—
585C2×D7—22no—
586C2×D7—44no—
587C2×D7—42no—
588C2×D7—42no—
589C2×D7—42no—
590C2×D7—816no—
591C2×D7—84no—
592C4×C7—22no—
593C4×C7—42no—
594C4×C7—42no—
595C4×C7#54612yes—
596C4×C7C22×#4111yescharacteristic
597C4×C7C2×H(5,𝔽2)11yescharacteristic
598Dic7—22no—
599Dic7—22no—
600Dic7—22no—
601Dic7—42no—
602Dic7—42no—
603Dic7—42no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—44no—
608C24—44no—
609C24—71no—
610C24—82no—
611C24—144no—
612C24—141no—
613C24—284no—
614C24—284no—
615C24—562no—
616C24D4×D711yescharacteristic
617C2×Q8—72no—
618C2×Q8—141no—
619C2×Q8—142no—
620C2×Q8—142no—
621C2×D4—28no—
622C2×D4—22no—
623C2×D4—21no—
624C2×D4—24no—
625C2×D4—21no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—44no—
629C2×D4—48no—
630C2×D4—44no—
631C2×D4—74no—
632C2×D4—72no—
633C2×D4—144no—
634C2×D4—144no—
635C2×D4—144no—
636C2×D4—144no—
637C2×D4—148no—
638C2×D4—144no—
639C2×D4—144no—
640C2×D4—142no—
641C2×D4—141no—
642C2×D4—142no—
643C2×D4—284no—
644C2×D4—288no—
645C2×D4—284no—
646C2×D4—284no—
647C2×D4—2832no—
648C2×D4—284no—
649C2×D4—284no—
650C2×D4—562no—
651C2×D4#115714yes—
652C2×D4C23×D712yes—
653C2×D4C23×D712yes—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—24no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—44no—
660C22×C4—71no—
661C22×C4—71no—
662C22×C4—71no—
663C22×C4—72no—
664C22×C4—72no—
665C22×C4—144no—
666C22×C4—142no—
667C22×C4—142no—
668C22×C4—141no—
669C22×C4—141no—
670C22×C4—141no—
671C22×C4—284no—
672C22×C4D4×D712yes—
673C22×C4D4×D711yescharacteristic
674C22×C4C23×D712yes—
675C22×C4C23×D711yescharacteristic
676SD16—148no—
677SD16—284no—
678SD16—284no—
679M16—284no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—44no—
683C2×C8—72no—
684C2×C8—72no—
685C2×C8—142no—
686C2×C8—142no—
687C2×C8C23×D712yes—
688C2×C8C23×D712yes—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—24no—
692C4⋊C4—74no—
693C4⋊C4—72no—
694C4⋊C4—72no—
695C4⋊C4—144no—
696C4⋊C4—144no—
697C4⋊C4—144no—
698C4⋊C4—144no—
699C4⋊C4—144no—
700C4⋊C4—141no—
701C4⋊C4—141no—
702C4⋊C4C23×D712yes—
703C4⋊C4C23×D712yes—
704C22⋊C4—74no—
705C22⋊C4—74no—
706C22⋊C4—144no—
707C22⋊C4—144no—
708C22⋊C4—144no—
709C22⋊C4—144no—
710C22⋊C4—144no—
711C22⋊C4—144no—
712C42—72no—
713C42—72no—
714C42—144no—
715C42—144no—
716C2×C7—24no—
717C2×C7—44no—
718C2×C7—82no—
719C2×C7#331014yescomplemented
720C2×C7C2×#54611yescharacteristic
721C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
722C2×C7C2×#57711yescharacteristic
723D7—42no—
724D7—82no—
725C23—22no—
726C23—22no—
727C23—24no—
728C23—22no—
729C23—22no—
730C23—48no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—48no—
735C23—42no—
736C23—42no—
737C23—72no—
738C23—84no—
739C23—816no—
740C23—142no—
741C23—142no—
742C23—142no—
743C23—142no—
744C23—288no—
745C23—288no—
746C23—282no—
747C23—282no—
748C23—282no—
749C23—564no—
750C23—5616no—
751C23#647414yes—
752C23C2×D4×D712yes—
753C23C2×D4×D711yescharacteristic
754Q8—142no—
755Q8—142no—
756Q8—282no—
757D4—24no—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—48no—
762D4—42no—
763D4—148no—
764D4—142no—
765D4—142no—
766D4—288no—
767D4—288no—
768D4—288no—
769D4—288no—
770D4—282no—
771D4—564no—
772D4C2×#115714yes—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—48no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—72no—
783C2×C4—72no—
784C2×C4—72no—
785C2×C4—142no—
786C2×C4—142no—
787C2×C4—142no—
788C2×C4—144no—
789C2×C4—142no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—288no—
795C2×C4—282no—
796C2×C4—282no—
797C2×C4—282no—
798C2×C4C2×#115712yes—
799C2×C4C2×D4×D712yes—
800C2×C4C2×D4×D711yescharacteristic
801C2×C4#654812yes—
802C2×C4C24×D711yescharacteristic
803C8—22no—
804C8—22no—
805C8—142no—
806C8—142no—
807C7C2×#331011yescharacteristic, complemented, Sylow
808C22—22no—
809C22—28no—
810C22—22no—
811C22—24no—
812C22—48no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—816no—
819C22—84no—
820C22—142no—
821C22—142no—
822C22—142no—
823C22—284no—
824C22—282no—
825C22—282no—
826C22—282no—
827C22—5616no—
828C22—564no—
829C22#9018112yes—
830C22C2×#647414yes—
831C22C2×#647412yes—
832C22#9045312yes—
833C22C22×D4×D711yescharacteristic
834C4—22no—
835C4—42no—
836C4—42no—
837C4—142no—
838C4—142no—
839C4—142no—
840C4—282no—
841C4—282no—
842C4—282no—
843C4#9018112yes—
844C4C22×#115711yescharacteristic
845C4C2×#654811yescharacteristic
846C2—24no—
847C2—44no—
848C2—82no—
849C2—282no—
850C2—562no—
851C2#1173620714yesdirect product factor
852C2C2×#9018111yescharacteristic
853C2C22×#647411yescharacteristic
854C2C2×#9045311yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC22×C7×#102C2
socleC23×C7C22×D4
prime radicalC2×D4×C22⋊D7C2
hypercenterC22×#102D7
hypocenterC7C2×#3310
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#90204C2semidirect
3. C22×C7×#102C2semidirect
4. C2×#89990C2semidirect
5. C2×#89886C2semidirect
6. C2×#89883C2semidirect
7. C2×#89739C2semidirect
8. C2×#89534C2semidirect
9. #11736207C2direct (N × H)
10. C2×#89552C2semidirect
11. C2×#89548C2semidirect
12. C2×#89542C2semidirect
13. C2×#89536C2semidirect
14. C2×#89551C2semidirect
15. C2×#89535C2semidirect
16. C2×#89529C2semidirect
20. C23×C7×C8C22semidirect
21. C22×C7×C4⋊C4C22semidirect
31. C22×#1142C22semidirect
36. C2×#6487C22semidirect
37. C22×#1132C22semidirect
38. C22×#1131C22semidirect
40. #90204C22semidirect
42. C2×#6460C22semidirect
43. C2×#6455C22semidirect
44. C2×#6453C22semidirect
46. C2×#6450C22semidirect
49. C2×C7×#102C22semidirect
50. C2×C7×#102C22semidirect
51. C2×C7×#102C22semidirect
52. #89990C22semidirect
54. C2×#6406C22semidirect
55. C2×C22⋊(C7⋊C8)C22semidirect
56. #89886C22semidirect
57. C2×#6395C22semidirect
58. #89883C22semidirect
59. C2×(C2×D7)⋊C8C22semidirect
60. C2×#6391C22semidirect
61. C2×#6390C22semidirect
62. C2×#6389C22semidirect
63. C2×Dic7⋊C8C22semidirect
64. #89739C22semidirect
65. C2×#6383C22semidirect
66. C2×#6383C22semidirect
67. C2×#6381C22semidirect
68. C2×#6381C22semidirect
69. #89552C22semidirect
70. #89551C22semidirect
71. #89548C22semidirect
72. #89542C22semidirect
73. #89536C22semidirect
74. #89535C22semidirect
75. #89534C22semidirect
76. #89529C22semidirect
108. C22×C7×C8C23semidirect
113. C2×C7×C4⋊C4C23semidirect
130. C2×#1142C23semidirect
146. #6487C23semidirect
157. C2×#1132C23semidirect
159. C2×#1131C23semidirect
162. #6460C23semidirect
164. #6455C23semidirect
166. #6453C23semidirect
169. #6450C23semidirect
172. C7×#102C23semidirect
173. C7×#102C23semidirect
175. #6406C23semidirect
176. C22⋊(C7⋊C8)C23semidirect
177. #6395C23semidirect
178. (C2×D7)⋊C8C23semidirect
179. #6391C23semidirect
180. #6390C23semidirect
181. #6389C23semidirect
182. Dic7⋊C8C23semidirect
183. #6383C23semidirect
184. #6383C23semidirect
185. #6381C23semidirect
186. #6381C23semidirect
202. C22×#102D7semidirect
322. C23×C8C2×D7semidirect
344. C22×C4⋊C4C2×D7semidirect
369. C2×#102C2×D7semidirect
370. C2×#102C2×D7semidirect
371. C2×#102C2×D7semidirect
497. C22×C8C22×D7semidirect
537. C2×C4⋊C4C22×D7semidirect
561. #102C22×D7semidirect
562. #102C22×D7semidirect
719. C2×C7#3310semidirect
807. C7C2×#3310semidirect
851. C2#11736207direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊D72
C2×#902042
C22×C7×#1022
C2×#899902
C2×#898862
C2×#898832
C2×#897392
C2×#895342
#117362072
C2×#895522
C2×#895482
C2×#895422
C2×#895362
C2×#895512
C2×#895352
C2×#895292
C2×#33107