Finite Group Databasebeta

← C2×#11740871 #14224499

Subgroups — C2×#11740871 #14224499

Order 1792.

2250 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#537C211yesmaximal, characteristic, complemented
2C2×#90524C211yesmaximal, characteristic, complemented
3C2×#90011C211yesmaximal, characteristic, complemented
4C2×#90010C211yesmaximal, characteristic, complemented
5C2×#90006C211yesmaximal, characteristic, complemented
6#11740871C2116yesmaximal, direct product factor
7C2×#89819C211yesmaximal, characteristic, complemented
8C2×#89821C211yesmaximal, characteristic, complemented
9C2×#89823C211yesmaximal, characteristic, complemented
10C2×#89816C211yesmaximal, characteristic, complemented
11C2×#89809C211yesmaximal, characteristic, complemented
12C2×#89814C211yesmaximal, characteristic, complemented
13C2×#89810C211yesmaximal, characteristic, complemented
14C2×#89805C211yesmaximal, characteristic, complemented
15C2×#89742C211yesmaximal, characteristic, complemented
16C2×#89739C211yesmaximal, characteristic, complemented
17C22×C7×#41C2211yescharacteristic
18C22×C7×#41C2211yescharacteristic
19C22×#1157C2211yescharacteristic
20C7×#537—24no—
21C7×#537C2218yescomplemented
22C2×C7×C22⋊Q8—21no—
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C7×C22⋊Q8C2211yescharacteristic
25C2×C7×#121—21no—
26C2×C7×#121—21no—
27C2×C7×#121—21no—
28C2×C7×#121C2211yescharacteristic
29C2×C7×#121C2211yescharacteristic
30C22×C7×C4⋊C4C2211yescharacteristic
31#90524—24no—
32#90524C2218yescomplemented
33C2×#6509—21no—
34C22×#1144C2211yescharacteristic
35C22×#1143C2211yescharacteristic
36C2×#6502—21no—
37C2×#6502—21no—
38C2×#6501—21no—
39C22×#1142C2211yescharacteristic
40C22×#1141C2211yescharacteristic
41C2×#6493C2211yescharacteristic
42C2×#6493C2211yescharacteristic
43C22×C4⋊Dic7C2211yescharacteristic
44C2×#6487C2211yescharacteristic
45C2×#6487C2211yescharacteristic
46C22×#1136C2211yescharacteristic
47C23×C7⋊C8C2211yescharacteristic
48#90011C2218yescomplemented
49#90010C2218yescomplemented
50#90006C2218yescomplemented
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55C2×C22⋊(C7⋊C8)C2211yescharacteristic
56C2×C22⋊(C7⋊C8)C2211yescharacteristic
57C2×C22⋊(C7⋊C8)C2211yescharacteristic
58C2×C22⋊(C7⋊C8)C2211yescharacteristic
59#89823C2218yescomplemented
60#89821C2218yescomplemented
61#89819C2218yescomplemented
62#89816C2218yescomplemented
63#89814C2218yescomplemented
64#89810C2218yescomplemented
65#89809C2218yescomplemented
66#89805C2218yescomplemented
67#89742C2218yescomplemented
68C2×#6384C2211yescharacteristic
69C2×#6384C2211yescharacteristic
70#89739C2218yescomplemented
71C2×#6383C2211yescharacteristic
72C2×#6383C2211yescharacteristic
73C2×#6381C2211yescharacteristic
74C2×#6381C2211yescharacteristic
75C2×#6381C2211yescharacteristic
76C2×#6381C2211yescharacteristic
77C2×#3203—71nomaximal, Sylow
78C2×C7×#41—22no—
79C2×C7×#41—42no—
80C2×C7×#41—42no—
81C2×C7×#41—42no—
82C2×C7×#41—42no—
83C2×C7×#41D414yes—
84C2×C7×#41C2314yes—
85C2×C7×#41C2314yes—
86C22×C7×Q8D411yescharacteristic
87C22×C7×Q8C2311yescharacteristic
88C22×C7×D4—21no—
89C22×C7×D4—21no—
90C22×C7×D4—21no—
91C22×C7×D4D411yescharacteristic
92C22×C7×D4D411yescharacteristic
93C22×C7×D4D411yescharacteristic
94C22×C7×D4C2311yescharacteristic
95C23×C4×C7—21no—
96C23×C4×C7—21no—
97C23×C4×C7C2311yescharacteristic
98C23×C4×C7C2311yescharacteristic
99C23×C4×C7C2311yescharacteristic
100C22×C22⋊D7—21no—
101C22×C22⋊D7—21no—
102C22×C22⋊D7—21no—
103C23×Dic7—21no—
104C2×#1157—22no—
105C2×#1157—42no—
106C2×#1157—42no—
107C2×#1157C2314yes—
108C22×D28C2311yescharacteristic
109C22×C4×D7—21no—
110C22×Dic14C2311yescharacteristic
111C7×C22⋊Q8—28no—
112C7×C22⋊Q8—22no—
113C7×C22⋊Q8—22no—
114C7×C22⋊Q8C2314yes—
115C7×C22⋊Q8C2314yes—
116C7×#121—28no—
117C7×#121—28no—
118C7×#121—28no—
119C7×#121—22no—
120C7×#121—22no—
121C7×#121C2314yes—
122C7×#121C2314yes—
123C2×C7×C4⋊C4—21no—
124C2×C7×C4⋊C4—22no—
125C2×C7×C4⋊C4—21no—
126C2×C7×C4⋊C4—21no—
127C2×C7×C4⋊C4C2311yescharacteristic
128C2×C7×C4⋊C4C2311yescharacteristic
129C2×C7×C4⋊C4C2314yes—
130C2×C7×C22⋊C4—21no—
131C2×C7×C22⋊C4—21no—
132C2×C7×C22⋊C4—21no—
133C2×C7×C22⋊C4—21no—
134C2×C22⋊Dic7—21no—
135C2×C22⋊Dic7—21no—
136#6509—28no—
137C2×#1144—42no—
138C2×#1144C2314yes—
139C2×#1143—42no—
140C2×#1143C2314yes—
141#6502—28no—
142#6502—28no—
143#6501—28no—
144C2×#1142—42no—
145C2×#1142C2314yes—
146C2×#1141—42no—
147C2×#1141C2314yes—
148#6493—22no—
149#6493—22no—
150#6493C2314yes—
151#6493C2314yes—
152C2×(C2×D7)⋊C4—21no—
153C2×(C2×D7)⋊C4—21no—
154C2×C4⋊Dic7—21no—
155C2×C4⋊Dic7—22no—
156C2×C4⋊Dic7C2311yescharacteristic
157C2×C4⋊Dic7C2311yescharacteristic
158C2×C4⋊Dic7C2314yes—
159#6487—22no—
160#6487—22no—
161#6487C2314yes—
162#6487C2314yes—
163C2×Dic7⋊C4—21no—
164C2×Dic7⋊C4—21no—
165C2×#1136—42no—
166C2×#1136C2314yes—
167C22×C7⋊C8—42no—
168C22×C7⋊C8C2311yescharacteristic
169C22×C7⋊C8C2311yescharacteristic
170C22×C7⋊C8C2311yescharacteristic
171C22×C7⋊C8C2311yescharacteristic
172C22×C7⋊C8C2314yes—
173#6409C2314yes—
174#6409C2314yes—
175#6406C2314yes—
176#6406C2314yes—
177C22⋊(C7⋊C8)C2314yes—
178C22⋊(C7⋊C8)C2314yes—
179C22⋊(C7⋊C8)C2314yes—
180C22⋊(C7⋊C8)C2314yes—
181#6384C2314yes—
182#6384C2314yes—
183#6383C2314yes—
184#6383C2314yes—
185#6381C2314yes—
186#6381C2314yes—
187#6381C2314yes—
188#6381C2314yes—
189C2×#537—71no—
190C2×#537D711yescharacteristic, complemented
191#3203—716no—
192C2×#484—71no—
193C2×#484—71no—
194C2×#480—71no—
195C2×#480—71no—
196C2×#468—71no—
197C2×#468—71no—
198C2×#467—71no—
199C2×#466—71no—
200C2×#452—71no—
201C2×#452—71no—
202C2×#449—71no—
203C2×#449—71no—
204C2×#408—71no—
205C24×C7—21no—
206C24×C7C2×D411yescharacteristic
207C24×C7C2×D411yescharacteristic
208C24×C7C2×D411yescharacteristic
209C23×D7—21no—
210C7×#41—48no—
211C7×#41—44no—
212C7×#41—44no—
213C7×#41—44no—
214C7×#41—44no—
215C7×#41—48no—
216C2×C7×Q8—21no—
217C2×C7×Q8—22no—
218C2×C7×Q8—22no—
219C2×C7×Q8—42no—
220C2×C7×Q8C2×D414yes—
221C2×C7×Q8C2412yes—
222C2×C7×D4—24no—
223C2×C7×D4—24no—
224C2×C7×D4—24no—
225C2×C7×D4—21no—
226C2×C7×D4—22no—
227C2×C7×D4—22no—
228C2×C7×D4—42no—
229C2×C7×D4—42no—
230C2×C7×D4—42no—
231C2×C7×D4—44no—
232C2×C7×D4—82no—
233C2×C7×D4—82no—
234C2×C7×D4C2×D414yes—
235C2×C7×D4C2×D414yes—
236C2×C7×D4C2×D414yes—
237C2×C7×D4C2412yes—
238C22×C4×C7—22no—
239C22×C4×C7—22no—
240C22×C4×C7—22no—
241C22×C4×C7—22no—
242C22×C4×C7—22no—
243C22×C4×C7—22no—
244C22×C4×C7—21no—
245C22×C4×C7—21no—
246C22×C4×C7—21no—
247C22×C4×C7—24no—
248C22×C4×C7—24no—
249C22×C4×C7—44no—
250C22×C4×C7—82no—
251C22×C4×C7C2×D411yescharacteristic
252C22×C4×C7C2×D411yescharacteristic
253C22×C4×C7C2×D412yes—
254C22×C4×C7C2×D412yes—
255C22×C4×C7C2×D411yescharacteristic
256C22×C4×C7C2×D412yes—
257C22×C4×C7C2412yes—
258C22×C4×C7C2412yes—
259C22×C4×C7C2412yes—
260C22×C4×C7C2411yescharacteristic
261C2×C22⋊D7—24no—
262C2×C22⋊D7—24no—
263C2×C22⋊D7—24no—
264C2×C22⋊D7—44no—
265C2×C22⋊D7—82no—
266C2×C22⋊D7—82no—
267C22×Dic7—21no—
268C22×Dic7—21no—
269C22×Dic7—21no—
270C22×Dic7—24no—
271C22×Dic7—82no—
272#1157—44no—
273#1157—44no—
274#1157—48no—
275C2×D28—22no—
276C2×D28—22no—
277C2×D28—21no—
278C2×D28C2412yes—
279C2×C4×D7—24no—
280C2×C4×D7—44no—
281C2×Dic14—22no—
282C2×Dic14—22no—
283C2×Dic14—21no—
284C2×Dic14C2412yes—
285C7×C4⋊C4—24no—
286C7×C4⋊C4—21no—
287C7×C4⋊C4—21no—
288C7×C4⋊C4—24no—
289C7×C4⋊C4—24no—
290C7×C4⋊C4C2412yes—
291C7×C4⋊C4C2412yes—
292C7×C22⋊C4—24no—
293C7×C22⋊C4—24no—
294C7×C22⋊C4—24no—
295C7×C22⋊C4—24no—
296C22⋊Dic7—24no—
297C22⋊Dic7—24no—
298#1144—44no—
299#1143—44no—
300#1142—44no—
301#1141—44no—
302(C2×D7)⋊C4—24no—
303(C2×D7)⋊C4—24no—
304C4⋊Dic7—21no—
305C4⋊Dic7—21no—
306C4⋊Dic7—24no—
307C4⋊Dic7C2412yes—
308C4⋊Dic7C2412yes—
309Dic7⋊C4—24no—
310Dic7⋊C4—24no—
311#1136—44no—
312C2×C7⋊C8—22no—
313C2×C7⋊C8—22no—
314C2×C7⋊C8—22no—
315C2×C7⋊C8—22no—
316C2×C7⋊C8—44no—
317C2×C7⋊C8C2412yes—
318C2×C7⋊C8C2412yes—
319C2×C7⋊C8C2412yes—
320C2×C7⋊C8C2412yes—
321C22×#41—71no—
322C22×#41C2×D711yescharacteristic
323C22×#41C2×D711yescharacteristic
324C22×Q16—71no—
325C22×SD16—71no—
326C22×SD16—71no—
327C22×D8—71no—
328C22×M16—71no—
329C23×C8—71no—
330#537—24no—
331#537—78no—
332#537—144no—
333#537C2×D718yescomplemented
334C2×C22⋊Q8—21no—
335C2×C22⋊Q8—71no—
336C2×C22⋊Q8—71no—
337C2×C22⋊Q8—141no—
338C2×C22⋊Q8C2×D711yescharacteristic
339C2×C22⋊Q8C2×D711yescharacteristic
340C2×#121—21no—
341C2×#121—21no—
342C2×#121—21no—
343C2×#121—71no—
344C2×#121—71no—
345C2×#121—141no—
346C2×#121—141no—
347C2×#121—141no—
348C2×#121C2×D711yescharacteristic
349C2×#121C2×D711yescharacteristic
350C22×C4⋊C4—71no—
351C22×C4⋊C4C2×D711yescharacteristic
352#484—78no—
353#484—78no—
354#480—78no—
355#480—78no—
356#468—78no—
357#468—78no—
358#467—78no—
359#466—78no—
360#452—78no—
361#452—78no—
362#449—78no—
363#449—78no—
364C2×#107—71no—
365C2×#107—71no—
366C2×#107—71no—
367C2×#107—71no—
368C2×#103—71no—
369C2×#103—71no—
370C2×#103—71no—
371C2×#103—71no—
372C2×#102—71no—
373C2×#102—71no—
374C2×#102—71no—
375C2×#102—71no—
376#408—78no—
377C2×C22⋊C8—71no—
378C2×C22⋊C8—71no—
379C2×C22⋊C8—71no—
380C2×C22⋊C8—71no—
381C23×C7—22no—
382C23×C7—22no—
383C23×C7—22no—
384C23×C7—22no—
385C23×C7—22no—
386C23×C7—22no—
387C23×C7—22no—
388C23×C7—22no—
389C23×C7—22no—
390C23×C7—22no—
391C23×C7—42no—
392C23×C7—42no—
393C23×C7—42no—
394C23×C7C22×D412yes—
395C23×C7C22×D412yes—
396C23×C7C22×D412yes—
397C23×C7C22×D411yescharacteristic
398C22×D7—22no—
399C22×D7—42no—
400C22×D7—42no—
401C22×D7—42no—
402C7×Q8—22no—
403C7×Q8—22no—
404C7×Q8—44no—
405C7×Q8—42no—
406C7×D4—22no—
407C7×D4—22no—
408C7×D4—44no—
409C7×D4—44no—
410C7×D4—44no—
411C7×D4—48no—
412C7×D4—42no—
413C7×D4—84no—
414C7×D4—84no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—24no—
419C2×C4×C7—24no—
420C2×C4×C7—24no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
430C2×C4×C7—48no—
431C2×C4×C7—42no—
432C2×C4×C7—42no—
433C2×C4×C7—42no—
434C2×C4×C7—84no—
435C2×C4×C7C22×D412yes—
436C2×C4×C7C22×D412yes—
437C2×C4×C7C22×D412yes—
438C2×C4×C7C22×D411yescharacteristic
439C2×C4×C7H(5,𝔽2)12yes—
440C2×C4×C7H(5,𝔽2)12yes—
441C2×C4×C7C2511yescharacteristic
442C22⋊D7—48no—
443C22⋊D7—84no—
444C22⋊D7—84no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—42no—
449C2×Dic7—42no—
450C2×Dic7—42no—
451C2×Dic7—84no—
452D28—22no—
453D28—22no—
454D28—42no—
455C4×D7—48no—
456Dic14—22no—
457Dic14—22no—
458Dic14—42no—
459C7⋊C8—22no—
460C7⋊C8—22no—
461C7⋊C8—22no—
462C7⋊C8—22no—
463C2×#41—22no—
464C2×#41—42no—
465C2×#41—42no—
466C2×#41—42no—
467C2×#41—42no—
468C2×#41—74no—
469C2×#41—142no—
470C2×#41—282no—
471C2×#41—282no—
472C2×#41C22⋊D714yes—
473C2×#41C22×D714yes—
474C2×#41C22×D714yes—
475C22×Q8—71no—
476C22×Q8C22⋊D711yescharacteristic
477C22×Q8C22×D711yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—71no—
482C22×D4—141no—
483C22×D4—141no—
484C22×D4—141no—
485C22×D4C22⋊D711yescharacteristic
486C22×D4C22⋊D711yescharacteristic
487C22×D4C22⋊D711yescharacteristic
488C22×D4C22×D711yescharacteristic
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—141no—
492C23×C4—141no—
493C23×C4C22×D711yescharacteristic
494C23×C4C22×D711yescharacteristic
495C23×C4C22×D711yescharacteristic
496C2×Q16—74no—
497C2×Q16—282no—
498C2×SD16—74no—
499C2×SD16—74no—
500C2×SD16—282no—
501C2×SD16—282no—
502C2×D8—74no—
503C2×D8—282no—
504C2×M16—74no—
505C2×M16—282no—
506C22×C8—71no—
507C22×C8—71no—
508C22×C8—71no—
509C22×C8—71no—
510C22×C8—74no—
511C22×C8—282no—
512C22⋊Q8—28no—
513C22⋊Q8—22no—
514C22⋊Q8—22no—
515C22⋊Q8—74no—
516C22⋊Q8—74no—
517C22⋊Q8—148no—
518C22⋊Q8—142no—
519C22⋊Q8—142no—
520C22⋊Q8C22×D714yes—
521C22⋊Q8C22×D714yes—
522#121—28no—
523#121—28no—
524#121—28no—
525#121—22no—
526#121—22no—
527#121—74no—
528#121—74no—
529#121—148no—
530#121—148no—
531#121—148no—
532#121—142no—
533#121—142no—
534#121C22×D714yes—
535#121C22×D714yes—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—71no—
541C2×C4⋊C4—71no—
542C2×C4⋊C4—74no—
543C2×C4⋊C4—141no—
544C2×C4⋊C4—142no—
545C2×C4⋊C4—141no—
546C2×C4⋊C4—141no—
547C2×C4⋊C4C22×D711yescharacteristic
548C2×C4⋊C4C22×D711yescharacteristic
549C2×C4⋊C4C22×D714yes—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—141no—
555C2×C22⋊C4—141no—
556C2×C22⋊C4—141no—
557C2×C22⋊C4—141no—
558#107—74no—
559#107—74no—
560#107—74no—
561#107—74no—
562#103—74no—
563#103—74no—
564#103—74no—
565#103—74no—
566#102—74no—
567#102—74no—
568#102—74no—
569#102—74no—
570C22⋊C8—74no—
571C22⋊C8—74no—
572C22⋊C8—74no—
573C22⋊C8—74no—
574C22×C7—22no—
575C22×C7—22no—
576C22×C7—22no—
577C22×C7—22no—
578C22×C7—22no—
579C22×C7—22no—
580C22×C7—22no—
581C22×C7—22no—
582C22×C7—22no—
583C22×C7—44no—
584C22×C7—44no—
585C22×C7—44no—
586C22×C7—42no—
587C22×C7—42no—
588C22×C7—42no—
589C22×C7—84no—
590C22×C7#53412yes—
591C22×C7#57612yes—
592C22×C7#57812yes—
593C22×C7C23×D411yescharacteristic
594C2×D7—42no—
595C2×D7—42no—
596C2×D7—42no—
597C2×D7—84no—
598C4×C7—22no—
599C4×C7—22no—
600C4×C7—22no—
601C4×C7—42no—
602C4×C7—42no—
603C4×C7—42no—
604C4×C7#53412yes—
605C4×C7C2×H(5,𝔽2)11yescharacteristic
606C4×C7C2×H(5,𝔽2)11yescharacteristic
607Dic7—42no—
608Dic7—42no—
609Dic7—42no—
610C24—21no—
611C24—141no—
612C24C2×C22⋊D711yescharacteristic
613C24C2×C22⋊D711yescharacteristic
614C24C2×C22⋊D711yescharacteristic
615#41—48no—
616#41—44no—
617#41—44no—
618#41—44no—
619#41—44no—
620#41—48no—
621#41—284no—
622#41—284no—
623#41—288no—
624C2×Q8—21no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—42no—
628C2×Q8—72no—
629C2×Q8—141no—
630C2×Q8—142no—
631C2×Q8—142no—
632C2×Q8C2×C22⋊D714yes—
633C2×Q8C23×D712yes—
634C2×D4—24no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—22no—
638C2×D4—22no—
639C2×D4—21no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—44no—
644C2×D4—72no—
645C2×D4—82no—
646C2×D4—82no—
647C2×D4—144no—
648C2×D4—144no—
649C2×D4—144no—
650C2×D4—142no—
651C2×D4—142no—
652C2×D4—141no—
653C2×D4—284no—
654C2×D4—562no—
655C2×D4—562no—
656C2×D4C2×C22⋊D714yes—
657C2×D4C2×C22⋊D714yes—
658C2×D4C2×C22⋊D714yes—
659C2×D4C23×D712yes—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—44no—
672C22×C4—82no—
673C22×C4—141no—
674C22×C4—141no—
675C22×C4—141no—
676C22×C4—144no—
677C22×C4—144no—
678C22×C4—284no—
679C22×C4—562no—
680C22×C4C2×C22⋊D712yes—
681C22×C4C2×C22⋊D712yes—
682C22×C4C2×C22⋊D712yes—
683C22×C4C2×C22⋊D711yescharacteristic
684C22×C4C2×C22⋊D711yescharacteristic
685C22×C4C2×C22⋊D711yescharacteristic
686C22×C4C23×D712yes—
687C22×C4C23×D712yes—
688C22×C4C23×D712yes—
689C22×C4C23×D711yescharacteristic
690Q16—284no—
691SD16—284no—
692SD16—284no—
693D8—284no—
694M16—284no—
695C2×C8—72no—
696C2×C8—72no—
697C2×C8—72no—
698C2×C8—72no—
699C2×C8—142no—
700C2×C8—142no—
701C2×C8—142no—
702C2×C8—142no—
703C2×C8—284no—
704C4⋊C4—24no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—24no—
708C4⋊C4—24no—
709C4⋊C4—72no—
710C4⋊C4—72no—
711C4⋊C4—144no—
712C4⋊C4—144no—
713C4⋊C4—144no—
714C4⋊C4—141no—
715C4⋊C4—141no—
716C4⋊C4C23×D712yes—
717C4⋊C4C23×D712yes—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—24no—
722C22⋊C4—144no—
723C22⋊C4—144no—
724C22⋊C4—144no—
725C22⋊C4—144no—
726C2×C7—42no—
727C2×C7—42no—
728C2×C7—42no—
729C2×C7—82no—
730C2×C7#320314yescomplemented
731C2×C7C2×#53411yescharacteristic
732C2×C7C2×#57611yescharacteristic
733C2×C7C2×#57811yescharacteristic
734D7—82no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—142no—
749C23—282no—
750C23—282no—
751C23—282no—
752C23C22×C22⋊D712yes—
753C23C22×C22⋊D712yes—
754C23C22×C22⋊D712yes—
755C23C22×C22⋊D711yescharacteristic
756Q8—22no—
757Q8—22no—
758Q8—44no—
759Q8—42no—
760Q8—142no—
761Q8—142no—
762Q8—282no—
763D4—22no—
764D4—22no—
765D4—44no—
766D4—44no—
767D4—44no—
768D4—48no—
769D4—42no—
770D4—84no—
771D4—84no—
772D4—142no—
773D4—142no—
774D4—288no—
775D4—282no—
776D4—564no—
777D4—564no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—48no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—84no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—142no—
801C2×C4—288no—
802C2×C4—282no—
803C2×C4—282no—
804C2×C4—282no—
805C2×C4—564no—
806C2×C4#654812yes—
807C2×C4#654812yes—
808C2×C4C22×C22⋊D712yes—
809C2×C4C22×C22⋊D712yes—
810C2×C4C22×C22⋊D712yes—
811C2×C4C22×C22⋊D711yescharacteristic
812C2×C4C24×D711yescharacteristic
813C8—142no—
814C8—142no—
815C8—142no—
816C8—142no—
817C7C2×#320311yescharacteristic, complemented, Sylow
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—84no—
834C22—282no—
835C22—282no—
836C22—282no—
837C22—564no—
838C22#9049512yes—
839C22#9052612yes—
840C22#9052912yes—
841C22C23×C22⋊D711yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—282no—
849C4—282no—
850C4—282no—
851C4#9049512yes—
852C4C2×#654811yescharacteristic
853C4C2×#654811yescharacteristic
854C2—42no—
855C2—42no—
856C2—42no—
857C2—82no—
858C2—562no—
859C2#1174087114yesdirect product factor
860C2C2×#9049511yescharacteristic
861C2C2×#9052611yescharacteristic
862C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#537C2
socleC23×C7C22×D4
hypercenterC2×#537D7
hypocenterC7C2×#3203
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×C7×#537C2semidirect
2. C2×#90524C2semidirect
3. C2×#90011C2semidirect
4. C2×#90010C2semidirect
5. C2×#90006C2semidirect
6. #11740871C2direct (N × H)
7. C2×#89819C2semidirect
8. C2×#89821C2semidirect
9. C2×#89823C2semidirect
10. C2×#89816C2semidirect
11. C2×#89809C2semidirect
12. C2×#89814C2semidirect
13. C2×#89810C2semidirect
14. C2×#89805C2semidirect
15. C2×#89742C2semidirect
16. C2×#89739C2semidirect
21. C7×#537C22semidirect
32. #90524C22semidirect
48. #90011C22semidirect
49. #90010C22semidirect
50. #90006C22semidirect
59. #89823C22semidirect
60. #89821C22semidirect
61. #89819C22semidirect
62. #89816C22semidirect
63. #89814C22semidirect
64. #89810C22semidirect
65. #89809C22semidirect
66. #89805C22semidirect
67. #89742C22semidirect
70. #89739C22semidirect
190. C2×#537D7semidirect
333. #537C2×D7semidirect
730. C2×C7#3203semidirect
817. C7C2×#3203semidirect
859. C2#11740871direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5372
C2×#905242
C2×#900112
C2×#900102
C2×#900062
#117408712
C2×#898192
C2×#898212
C2×#898232
C2×#898162
C2×#898092
C2×#898142
C2×#898102
C2×#898052
C2×#897422
C2×#897392
C2×#32037