Finite Group Databasebeta

← C2×#11739790 #13520020

Subgroups — C2×#11739790 #13520020

Order 1792.

4134 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×D4C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D7C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D7C211yesmaximal, characteristic, complemented
4C22×#6489C211yesmaximal, characteristic, complemented
5C2×#89995C211yesmaximal, characteristic
6C2×#89994C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
8#11739790C2116yesmaximal, direct product factor
9C2×#89766C211yesmaximal, characteristic, complemented
10C2×#89756C211yesmaximal, characteristic, complemented
11C2×#89731C211yesmaximal, characteristic, complemented
12C2×#89724C211yesmaximal, characteristic, complemented
13C2×#89720C211yesmaximal, characteristic, complemented
14C2×#89733C211yesmaximal, characteristic, complemented
15C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C24×C4×C7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C23×C22⋊D7C2211yescharacteristic
22C23×C4×D7C2211yescharacteristic
23C2×C4×C7×D4—28no—
24C2×C4×C7×D4C2218yescomplemented
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C42×C7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C2×C4×C22⋊D7—28no—
36C2×C4×C22⋊D7—28no—
37C2×C4×C22⋊D7C2218yescomplemented
38C2×C4×C22⋊D7C2218yescomplemented
39C22×(C2×D7)⋊C4C2211yescharacteristic
40C22×(C2×D7)⋊C4C2211yescharacteristic
41C22×(C2×D7)⋊C4C2211yescharacteristic
42C22×(C2×D7)⋊C4C2211yescharacteristic
43C2×#6489—28no—
44C2×#6489C2218yescomplemented
45C22×C4⋊Dic7C2211yescharacteristic
46C22×C4⋊Dic7C2211yescharacteristic
47C22×Dic7⋊C4C2211yescharacteristic
48C22×Dic7⋊C4C2211yescharacteristic
49C22×Dic7⋊C4C2211yescharacteristic
50C22×Dic7⋊C4C2211yescharacteristic
51C22×C4×Dic7C2211yescharacteristic
52C22×C4×Dic7C2211yescharacteristic
53C22×C4×Dic7C2211yescharacteristic
54#89995C2218yes—
55#89994C2218yescomplemented
56C4×C22⋊Dic7C2218yescomplemented
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61C2×C7⋊#95C2211yescharacteristic
62C2×C7⋊#95C2211yescharacteristic
63#89766C2218yescomplemented
64#89756C2218yescomplemented
65#89733C2218yescomplemented
66#89731C2218yescomplemented
67#89724C2218yescomplemented
68#89720C2218yescomplemented
69C4×(C2×D7)⋊C4C2218yescomplemented
70C4×Dic7⋊C4C2218yescomplemented
71C2×#2392—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C25×C7C2311yescharacteristic
74C24×D7C2311yescharacteristic
75C22×C7×D4—24no—
76C22×C7×D4—24no—
77C22×C7×D4—24no—
78C22×C7×D4C2314yes—
79C23×C4×C7—24no—
80C23×C4×C7—24no—
81C23×C4×C7—24no—
82C23×C4×C7—24no—
83C23×C4×C7—24no—
84C23×C4×C7D418yescomplemented
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2314yes—
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2314yes—
90C23×C4×C7C2311yescharacteristic
91C23×C4×C7C2311yescharacteristic
92C22×C22⋊D7—24no—
93C22×C22⋊D7—24no—
94C22×C22⋊D7—24no—
95C22×C22⋊D7—24no—
96C22×C22⋊D7—24no—
97C22×C22⋊D7—24no—
98C22×C22⋊D7C2314yes—
99C22×C22⋊D7C2314yes—
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2311yescharacteristic
105C23×Dic7C2311yescharacteristic
106C23×Dic7C2311yescharacteristic
107C22×C4×D7—24no—
108C22×C4×D7—24no—
109C22×C4×D7—24no—
110C22×C4×D7C2314yes—
111C4×C7×D4—232no—
112C2×C7×C4⋊C4—24no—
113C2×C7×C4⋊C4C2314yes—
114C2×C7×C22⋊C4—24no—
115C2×C7×C22⋊C4—24no—
116C2×C7×C22⋊C4C2314yes—
117C2×C7×C22⋊C4C2314yes—
118C2×C42×C7—24no—
119C2×C42×C7C2314yes—
120C2×C22⋊Dic7—24no—
121C2×C22⋊Dic7—24no—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7—24no—
124C2×C22⋊Dic7—24no—
125C2×C22⋊Dic7—24no—
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131C2×C22⋊Dic7C2314yes—
132C4×C22⋊D7—232no—
133C4×C22⋊D7—232no—
134C2×(C2×D7)⋊C4—24no—
135C2×(C2×D7)⋊C4—24no—
136C2×(C2×D7)⋊C4—24no—
137C2×(C2×D7)⋊C4—24no—
138C2×(C2×D7)⋊C4C2314yes—
139C2×(C2×D7)⋊C4C2314yes—
140C2×(C2×D7)⋊C4C2314yes—
141C2×(C2×D7)⋊C4C2314yes—
142#6489—232no—
143C2×C4⋊Dic7—24no—
144C2×C4⋊Dic7—24no—
145C2×C4⋊Dic7C2314yes—
146C2×C4⋊Dic7C2314yes—
147C2×Dic7⋊C4—24no—
148C2×Dic7⋊C4—24no—
149C2×Dic7⋊C4—24no—
150C2×Dic7⋊C4—24no—
151C2×Dic7⋊C4C2314yes—
152C2×Dic7⋊C4C2314yes—
153C2×Dic7⋊C4C2314yes—
154C2×Dic7⋊C4C2314yes—
155C2×C4×Dic7—24no—
156C2×C4×Dic7—24no—
157C2×C4×Dic7D418yescomplemented
158C2×C4×Dic7C2314yes—
159C2×C4×Dic7C2314yes—
160C2×C4×Dic7C2314yes—
161C7⋊#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C7⋊#95C2314yes—
166C7⋊#95C2314yes—
167C22×C4×D4—71no—
168C22×C4×D4—71no—
169C22×C4×D4D711yescharacteristic, complemented
170C22×#117—71no—
171#2392—716no—
172C2×#398—71no—
173C2×#397—71no—
174C2×#396—71no—
175C2×#396—71no—
176C2×#394—71no—
177C2×#394—71no—
178C2×#394—71no—
179C2×#392—71no—
180C2×C4×C4⋊C4—71no—
181C2×C4×C22⋊C4—71no—
182C2×C4×C22⋊C4—71no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7—22no—
189C24×C7—22no—
190C24×C7—22no—
191C24×C7—22no—
192C24×C7—22no—
193C24×C7—22no—
194C24×C7—22no—
195C24×C7C2×D414yes—
196C24×C7#4114yes—
197C24×C7C2412yes—
198C24×C7C2412yes—
199C24×C7C2411yescharacteristic
200C23×D7—22no—
201C23×D7—22no—
202C23×D7—22no—
203C23×D7—22no—
204C23×D7—22no—
205C23×D7—22no—
206C23×D7#4114yes—
207C23×D7C2412yes—
208C2×C7×D4—232no—
209C2×C7×D4—28no—
210C2×C7×D4—28no—
211C2×C7×D4—28no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—232no—
217C22×C4×C7—28no—
218C22×C4×C7—28no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—22no—
225C22×C4×C7—28no—
226C22×C4×C7—28no—
227C22×C4×C7—28no—
228C22×C4×C7—416no—
229C22×C4×C7C2×D414yes—
230C22×C4×C7C2×D414yes—
231C22×C4×C7C2×D414yes—
232C22×C4×C7C2×D4116yescomplemented
233C22×C4×C7#4114yes—
234C22×C4×C7#4114yes—
235C22×C4×C7C2412yes—
236C22×C4×C7C2412yes—
237C22×C4×C7C2412yes—
238C22×C4×C7C2412yes—
239C22×C4×C7C2412yes—
240C2×C22⋊D7—232no—
241C2×C22⋊D7—232no—
242C2×C22⋊D7—28no—
243C2×C22⋊D7—28no—
244C2×C22⋊D7—28no—
245C2×C22⋊D7—28no—
246C2×C22⋊D7—28no—
247C2×C22⋊D7—28no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—22no—
259C22×Dic7—22no—
260C22×Dic7—22no—
261C22×Dic7—22no—
262C22×Dic7—22no—
263C22×Dic7—22no—
264C22×Dic7—22no—
265C22×Dic7—22no—
266C22×Dic7C2×D414yes—
267C22×Dic7C2×D414yes—
268C22×Dic7#4114yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C22×Dic7C2412yes—
273C22×Dic7C2412yes—
274C22×Dic7C2412yes—
275C22×Dic7C2412yes—
276C2×C4×D7—28no—
277C2×C4×D7—28no—
278C2×C4×D7—28no—
279C2×C4×D7—416no—
280C7×C4⋊C4—28no—
281C7×C22⋊C4—28no—
282C7×C22⋊C4—28no—
283C42×C7—28no—
284C22⋊Dic7—28no—
285C22⋊Dic7—28no—
286C22⋊Dic7—28no—
287C22⋊Dic7—28no—
288C22⋊Dic7—28no—
289C22⋊Dic7—28no—
290(C2×D7)⋊C4—28no—
291(C2×D7)⋊C4—28no—
292(C2×D7)⋊C4—28no—
293(C2×D7)⋊C4—28no—
294C4⋊Dic7—28no—
295C4⋊Dic7—28no—
296Dic7⋊C4—28no—
297Dic7⋊C4—28no—
298Dic7⋊C4—28no—
299Dic7⋊C4—28no—
300C4×Dic7—28no—
301C4×Dic7—28no—
302C4×Dic7C2×D4116yescomplemented
303C23×D4—71no—
304C23×D4—71no—
305C23×D4C2×D711yescharacteristic
306C24×C4—71no—
307C24×C4C2×D711yescharacteristic
308C24×C4C2×D711yescharacteristic
309C2×C4×D4—28no—
310C2×C4×D4—78no—
311C2×C4×D4—78no—
312C2×C4×D4—148no—
313C2×C4×D4—148no—
314C2×C4×D4C2×D718yescomplemented
315C2×#117—78no—
316C2×#117—148no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4—71no—
323C22×C4⋊C4C2×D711yescharacteristic
324C22×C22⋊C4—71no—
325C22×C22⋊C4—71no—
326C22×C22⋊C4—71no—
327C22×C22⋊C4—71no—
328C22×C22⋊C4—71no—
329C22×C22⋊C4—71no—
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4—71no—
333C22×C22⋊C4—71no—
334C22×C22⋊C4C2×D711yescharacteristic
335C22×C22⋊C4C2×D711yescharacteristic
336C22×C42—71no—
337C22×C42—71no—
338C22×C42—71no—
339C22×C42C2×D711yescharacteristic
340#398—78no—
341#397—78no—
342#396—78no—
343#396—78no—
344#394—78no—
345#394—78no—
346#394—78no—
347#392—78no—
348C4×C4⋊C4—78no—
349C4×C22⋊C4—78no—
350C4×C22⋊C4—78no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—71no—
355C2×#95—71no—
356C2×#95—71no—
357C23×C7—28no—
358C23×C7—28no—
359C23×C7—28no—
360C23×C7—28no—
361C23×C7—28no—
362C23×C7—28no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—44no—
376C23×C7—44no—
377C23×C7—44no—
378C23×C7—44no—
379C23×C7—44no—
380C23×C7—44no—
381C23×C7—44no—
382C23×C7—44no—
383C23×C7C22×D412yes—
384C23×C7C22×D414yes—
385C23×C7C22×D412yes—
386C23×C7C2×#4114yes—
387C23×C7C2×#4112yes—
388C23×C7C2×#4112yes—
389C23×C7C2×#4112yes—
390C23×C7C2×#4112yes—
391C23×C7C2×#4112yes—
392C23×C7C2511yescharacteristic
393C22×D7—28no—
394C22×D7—28no—
395C22×D7—28no—
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—22no—
400C22×D7—22no—
401C22×D7—22no—
402C22×D7—44no—
403C22×D7—44no—
404C22×D7—44no—
405C22×D7—44no—
406C22×D7C2×#4114yes—
407C7×D4—232no—
408C2×C4×C7—28no—
409C2×C4×C7—28no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—232no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—44no—
422C2×C4×C7—44no—
423C2×C4×C7—416no—
424C2×C4×C7#121116yes—
425C2×C4×C7C22×D414yes—
426C2×C4×C7C22×D414yes—
427C2×C4×C7C22×D414yes—
428C2×C4×C7C2×#4114yes—
429C2×C4×C7C2×#4114yes—
430C22⋊D7—232no—
431C22⋊D7—232no—
432C2×Dic7—28no—
433C2×Dic7—28no—
434C2×Dic7—28no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—44no—
454C2×Dic7—44no—
455C2×Dic7—44no—
456C2×Dic7—44no—
457C2×Dic7C22×D414yes—
458C2×Dic7C22×D414yes—
459C2×Dic7C2×#4114yes—
460C4×D7—416no—
461C25—71no—
462C25C22×D711yescharacteristic
463C25C22×D711yescharacteristic
464C22×D4—24no—
465C22×D4—24no—
466C22×D4—24no—
467C22×D4—74no—
468C22×D4—74no—
469C22×D4—144no—
470C22×D4—144no—
471C22×D4—144no—
472C22×D4—144no—
473C22×D4—144no—
474C22×D4—144no—
475C22×D4C22×D714yes—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—71no—
487C23×C4—71no—
488C23×C4—74no—
489C23×C4—144no—
490C23×C4—144no—
491C23×C4—144no—
492C23×C4C22⋊D718yescomplemented
493C23×C4C22×D711yescharacteristic
494C23×C4C22×D711yescharacteristic
495C23×C4C22×D714yes—
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C23×C4C22×D714yes—
499C23×C4C22×D711yescharacteristic
500C4×D4—232no—
501C4×D4—1432no—
502C4×D4—1432no—
503#117—1432no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—74no—
506C2×C4⋊C4—74no—
507C2×C4⋊C4—74no—
508C2×C4⋊C4—74no—
509C2×C4⋊C4—74no—
510C2×C4⋊C4—74no—
511C2×C4⋊C4—144no—
512C2×C4⋊C4—144no—
513C2×C4⋊C4—144no—
514C2×C4⋊C4—144no—
515C2×C4⋊C4—144no—
516C2×C4⋊C4—144no—
517C2×C4⋊C4C22×D714yes—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—74no—
521C2×C22⋊C4—74no—
522C2×C22⋊C4—74no—
523C2×C22⋊C4—74no—
524C2×C22⋊C4—74no—
525C2×C22⋊C4—74no—
526C2×C22⋊C4—74no—
527C2×C22⋊C4—74no—
528C2×C22⋊C4—74no—
529C2×C22⋊C4—74no—
530C2×C22⋊C4—144no—
531C2×C22⋊C4—144no—
532C2×C22⋊C4—144no—
533C2×C22⋊C4—144no—
534C2×C22⋊C4—144no—
535C2×C22⋊C4—144no—
536C2×C22⋊C4—144no—
537C2×C22⋊C4—144no—
538C2×C22⋊C4—144no—
539C2×C22⋊C4—144no—
540C2×C22⋊C4C22×D714yes—
541C2×C22⋊C4C22×D714yes—
542C2×C42—24no—
543C2×C42—78no—
544C2×C42—74no—
545C2×C42—74no—
546C2×C42—74no—
547C2×C42—144no—
548C2×C42—144no—
549C2×C42C22×D714yes—
550#95—74no—
551#95—74no—
552#95—74no—
553#95—74no—
554#95—74no—
555#95—74no—
556C22×C7—24no—
557C22×C7—24no—
558C22×C7—24no—
559C22×C7—24no—
560C22×C7—24no—
561C22×C7—24no—
562C22×C7—416no—
563C22×C7—416no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—42no—
572C22×C7C2×#12114yes—
573C22×C7#52514yes—
574C22×C7#52514yes—
575C22×C7#52514yes—
576C22×C7#52914yes—
577C22×C7#52914yes—
578C22×C7#53214yes—
579C22×C7C23×D411yescharacteristic
580C22×C7C23×D411yescharacteristic
581C22×C7C22×#4111yescharacteristic
582C22×C7C22×#4111yescharacteristic
583C22×C7C22×#4111yescharacteristic
584C22×C7C22×#4111yescharacteristic
585C22×C7C22×#4111yescharacteristic
586C2×D7—24no—
587C2×D7—24no—
588C2×D7—24no—
589C2×D7—416no—
590C2×D7—42no—
591C2×D7—42no—
592C2×D7—42no—
593C2×D7—42no—
594C4×C7—24no—
595C4×C7—24no—
596C4×C7—42no—
597C4×C7—42no—
598C4×C7C2×#12118yes—
599Dic7—24no—
600Dic7—24no—
601Dic7—24no—
602Dic7—42no—
603Dic7—42no—
604Dic7—42no—
605Dic7—42no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—74no—
619C24—72no—
620C24—142no—
621C24—142no—
622C24—142no—
623C24—142no—
624C24—142no—
625C24—142no—
626C24#115714yes—
627C24C2×C22⋊D714yes—
628C24C23×D712yes—
629C24C23×D712yes—
630C24C23×D711yescharacteristic
631C2×D4—232no—
632C2×D4—28no—
633C2×D4—28no—
634C2×D4—28no—
635C2×D4—148no—
636C2×D4—148no—
637C2×D4—148no—
638C2×D4—148no—
639C2×D4—1432no—
640C2×D4—1432no—
641C2×D4—148no—
642C2×D4—148no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—232no—
648C22×C4—28no—
649C22×C4—28no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—28no—
657C22×C4—28no—
658C22×C4—28no—
659C22×C4—416no—
660C22×C4—74no—
661C22×C4—74no—
662C22×C4—74no—
663C22×C4—72no—
664C22×C4—72no—
665C22×C4—72no—
666C22×C4—72no—
667C22×C4—72no—
668C22×C4—72no—
669C22×C4—72no—
670C22×C4—142no—
671C22×C4—142no—
672C22×C4—142no—
673C22×C4—142no—
674C22×C4—142no—
675C22×C4—142no—
676C22×C4—142no—
677C22×C4—142no—
678C22×C4—142no—
679C22×C4—142no—
680C22×C4—142no—
681C22×C4—142no—
682C22×C4—142no—
683C22×C4—142no—
684C22×C4—142no—
685C22×C4—142no—
686C22×C4—142no—
687C22×C4—142no—
688C22×C4—148no—
689C22×C4—148no—
690C22×C4—148no—
691C22×C4—2816no—
692C22×C4#115714yes—
693C22×C4D4×D714yes—
694C22×C4#115914yes—
695C22×C4C2×C22⋊D714yes—
696C22×C4C2×C22⋊D714yes—
697C22×C4C2×C22⋊D7116yescomplemented
698C22×C4C23×D712yes—
699C22×C4C23×D712yes—
700C22×C4C23×D712yes—
701C22×C4C23×D712yes—
702C22×C4C23×D712yes—
703C4⋊C4—28no—
704C4⋊C4—148no—
705C4⋊C4—148no—
706C4⋊C4—148no—
707C4⋊C4—148no—
708C4⋊C4—148no—
709C4⋊C4—148no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—148no—
713C22⋊C4—148no—
714C22⋊C4—148no—
715C22⋊C4—148no—
716C22⋊C4—148no—
717C22⋊C4—148no—
718C22⋊C4—148no—
719C22⋊C4—148no—
720C22⋊C4—148no—
721C22⋊C4—148no—
722C42—28no—
723C42—716no—
724C42—148no—
725C42—148no—
726C2×C7—44no—
727C2×C7—44no—
728C2×C7#239218yescomplemented
729C2×C7C22×#12111yescharacteristic
730C2×C7C2×#52511yescharacteristic
731C2×C7C2×#52511yescharacteristic
732C2×C7C2×#52511yescharacteristic
733C2×C7C2×#52911yescharacteristic
734C2×C7C2×#52911yescharacteristic
735C2×C7C2×#53211yescharacteristic
736D7—44no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—74no—
764C23—148no—
765C23—148no—
766C23—148no—
767C23—142no—
768C23—142no—
769C23—142no—
770C23—142no—
771C23—142no—
772C23—142no—
773C23—284no—
774C23—284no—
775C23—284no—
776C23—284no—
777C23C2×#115714yes—
778C23C2×#115712yes—
779C23C2×#115712yes—
780C23C2×D4×D712yes—
781C23C2×#115912yes—
782C23D7×#4112yes—
783C23D7×#4112yes—
784C23C22×C22⋊D714yes—
785C23C22×C22⋊D712yes—
786C23C24×D711yescharacteristic
787D4—232no—
788D4—1432no—
789D4—1432no—
790C2×C4—28no—
791C2×C4—28no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—232no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—416no—
806C2×C4—74no—
807C2×C4—74no—
808C2×C4—74no—
809C2×C4—148no—
810C2×C4—148no—
811C2×C4—148no—
812C2×C4—142no—
813C2×C4—142no—
814C2×C4—142no—
815C2×C4—142no—
816C2×C4—142no—
817C2×C4—142no—
818C2×C4—142no—
819C2×C4—142no—
820C2×C4—142no—
821C2×C4—142no—
822C2×C4—142no—
823C2×C4—142no—
824C2×C4—142no—
825C2×C4—142no—
826C2×C4—142no—
827C2×C4—142no—
828C2×C4—142no—
829C2×C4—142no—
830C2×C4—284no—
831C2×C4—284no—
832C2×C4—284no—
833C2×C4—284no—
834C2×C4—2816no—
835C2×C4#6502116yes—
836C2×C4C2×#115714yes—
837C2×C4C2×D4×D714yes—
838C2×C4C2×#115914yes—
839C2×C4C22×C22⋊D714yes—
840C2×C4C22×C22⋊D714yes—
841C7C2×#239211yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—416no—
857C22—416no—
858C22—144no—
859C22—144no—
860C22—144no—
861C22—282no—
862C22—282no—
863C22—282no—
864C22—282no—
865C22—2816no—
866C22#9022914yes—
867C22#9023814yes—
868C22#9023914yes—
869C22#9024814yes—
870C22#9048214yes—
871C22C2×#650214yes—
872C22#9051914yes—
873C22C22×#115711yescharacteristic
874C22C22×#115711yescharacteristic
875C22C22×D4×D711yescharacteristic
876C22C22×#115911yescharacteristic
877C22C2×D7×#4111yescharacteristic
878C22C2×D7×#4111yescharacteristic
879C22C23×C22⋊D711yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—144no—
885C4—144no—
886C4—144no—
887C4—282no—
888C4—282no—
889C4—282no—
890C4—282no—
891C4C2×#650218yes—
892C2—44no—
893C2—44no—
894C2—284no—
895C2#1173979018yesdirect product factor
896C2C2×#9022911yescharacteristic
897C2C2×#9023811yescharacteristic
898C2C2×#9024811yescharacteristic
899C2C2×#9023911yescharacteristic
900C2C2×#9048211yescharacteristic
901C2C22×#650211yescharacteristic
902C2C2×#9051911yescharacteristic
subgroupG/H
centerC23×C4C22×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C4×C7×D4C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC22×C4×D4D7
hypocenterC7C2×#2392
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C7×D4C2semidirect
2. C22×C4×C22⋊D7C2semidirect
3. C22×C4×C22⋊D7C2semidirect
4. C22×#6489C2semidirect
6. C2×#89994C2semidirect
7. C2×C4×C22⋊Dic7C2semidirect
8. #11739790C2direct (N × H)
9. C2×#89766C2semidirect
10. C2×#89756C2semidirect
11. C2×#89731C2semidirect
12. C2×#89724C2semidirect
13. C2×#89720C2semidirect
14. C2×#89733C2semidirect
15. C2×C4×Dic7⋊C4C2semidirect
16. C2×C4×(C2×D7)⋊C4C2semidirect
24. C2×C4×C7×D4C22semidirect
37. C2×C4×C22⋊D7C22semidirect
38. C2×C4×C22⋊D7C22semidirect
44. C2×#6489C22semidirect
55. #89994C22semidirect
56. C4×C22⋊Dic7C22semidirect
63. #89766C22semidirect
64. #89756C22semidirect
65. #89733C22semidirect
66. #89731C22semidirect
67. #89724C22semidirect
68. #89720C22semidirect
69. C4×(C2×D7)⋊C4C22semidirect
70. C4×Dic7⋊C4C22semidirect
84. C23×C4×C7D4semidirect
157. C2×C4×Dic7D4semidirect
169. C22×C4×D4D7semidirect
232. C22×C4×C7C2×D4semidirect
302. C4×Dic7C2×D4semidirect
314. C2×C4×D4C2×D7semidirect
492. C23×C4C22⋊D7semidirect
697. C22×C4C2×C22⋊D7semidirect
728. C2×C7#2392semidirect
841. C7C2×#2392semidirect
895. C2#11739790direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
C22×C4×C22⋊D72
C22×#64892
C2×#899952
C2×#899942
C2×C4×C22⋊Dic72
#117397902
C2×#897662
C2×#897562
C2×#897312
C2×#897242
C2×#897202
C2×#897332
C2×C4×Dic7⋊C42
C2×C4×(C2×D7)⋊C42
C2×#23927