Finite Group Databasebeta

← C2×#11736906 #14218845

Subgroups — C2×#11736906 #14218845

Order 1792.

2154 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1159C211yesmaximal, characteristic
2C2×C7×#435C211yesmaximal, characteristic, complemented
3C2×#89900C211yesmaximal, characteristic, complemented
4C2×#89890C211yesmaximal, characteristic, complemented
5C2×#89883C211yesmaximal, characteristic, complemented
6C22×Dic7⋊C8C211yesmaximal, characteristic, complemented
7C2×#89783C211yesmaximal, characteristic, complemented
8#11736906C2116yesmaximal, direct product factor
9C2×#89609C211yesmaximal, characteristic, complemented
10C2×#89600C211yesmaximal, characteristic, complemented
11C2×#89501C211yesmaximal, characteristic, complemented
12C2×#89502C211yesmaximal, characteristic, complemented
13C2×#89491C211yesmaximal, characteristic, complemented
14C2×#89490C211yesmaximal, characteristic, complemented
15C2×#89477C211yesmaximal, characteristic, complemented
16C2×#89473C211yesmaximal, characteristic, complemented
17C22×#1159C411yescharacteristic
18C22×C7×M16C2211yescharacteristic
19C23×C7×C8C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×D4×Dic7C411yescharacteristic
22C2×C4×C22⋊D7C2211yescharacteristic
23C2×C4×C22⋊D7C2211yescharacteristic
24C22×C4×Dic7C2211yescharacteristic
25C22×C4×Dic7C2211yescharacteristic
26C22×#1136C2211yescharacteristic
27C23×C7⋊C8C2211yescharacteristic
28C22×#1131C2211yescharacteristic
29C22×#1131C2211yescharacteristic
30C4×#1159C418yes—
31C4×#1159C2218yes—
32C2×#6455C411yescharacteristic
33C2×#6450C411yescharacteristic
34C2×(C22⋊D7)⋊C4C411yescharacteristic
35C2×(C22⋊D7)⋊C4C411yescharacteristic
36C2×#6440C411yescharacteristic
37C2×#6440C411yescharacteristic
38C2×C42×D7C2211yescharacteristic
39C2×C4×Dic14C2211yescharacteristic
40C7×#435C2218yescomplemented
41C2×C7×C4⋊C8C2211yescharacteristic
42C2×C7×C22⋊C8C2211yescharacteristic
43C2×C7×C22⋊C8C2211yescharacteristic
44C2×C7×#97C2211yescharacteristic
45C2×C22⋊(C7⋊C8)C2211yescharacteristic
46C2×C22⋊(C7⋊C8)C2211yescharacteristic
47#89900C2218yescomplemented
48#89890C2218yescomplemented
49#89883C2218yescomplemented
50C2×(C2×D7)⋊C8C2211yescharacteristic
51C2×(C2×D7)⋊C8C2211yescharacteristic
52C2×#6389C2211yescharacteristic
53C2×#6389C2211yescharacteristic
54C2×Dic7⋊C8C2211yescharacteristic
55C2×Dic7⋊C8C2211yescharacteristic
56C2×Dic7⋊C8C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×Dic7⋊C8C2211yescharacteristic
59C2×Dic7⋊C8C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×Dic7⋊C8C2211yescharacteristic
62C2×Dic7⋊C8C2218yescomplemented
63C2×C8×Dic7C2211yescharacteristic
64C2×C8×Dic7C2211yescharacteristic
65#89783C2218yescomplemented
66C2×C4⋊(C7⋊C8)C2211yescharacteristic
67C2×#6377C2211yescharacteristic
68#89609C2218yescomplemented
69#89600C2218yescomplemented
70#89502C2218yescomplemented
71#89501C2218yescomplemented
72#89491C2218yescomplemented
73#89490C2218yescomplemented
74#89477C2218yescomplemented
75#89473C2218yescomplemented
76C2×#2989—71nomaximal, Sylow
77C22×C7×D4C2×C411yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C22×C22⋊D7C2×C411yescharacteristic
81C22×C22⋊D7C2×C411yescharacteristic
82C23×Dic7C2×C411yescharacteristic
83C23×Dic7C2×C411yescharacteristic
84C23×Dic7C2×C411yescharacteristic
85C23×Dic7C2×C411yescharacteristic
86C2×#1159—28no—
87C2×#1159C2×C418yes—
88C22×C4×D7C2×C411yescharacteristic
89C22×C4×D7C2×C411yescharacteristic
90C22×C4×D7C2311yescharacteristic
91C22×Dic14C2×C411yescharacteristic
92C2×C7×M16—42no—
93C2×C7×M16C2314yes—
94C22×C7×C8—42no—
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C22×C7×C8C2311yescharacteristic
98C22×C7×C8C2311yescharacteristic
99C22×C7×C8C2314yes—
100C4×C7×D4C2×C414yes—
101C4×C7×D4C2314yes—
102C2×C7×C4⋊C4C2×C411yescharacteristic
103C2×C7×C22⋊C4C2×C411yescharacteristic
104C2×C7×C22⋊C4C2×C411yescharacteristic
105C2×C42×C7C2311yescharacteristic
106C2×C22⋊Dic7C2×C411yescharacteristic
107C2×C22⋊Dic7C2×C411yescharacteristic
108D4×Dic7C2×C418yes—
109C4×C22⋊D7C2×C414yes—
110C4×C22⋊D7C2×C414yes—
111C4×C22⋊D7C2314yes—
112C4×C22⋊D7C2314yes—
113C2×(C2×D7)⋊C4C2×C411yescharacteristic
114C2×(C2×D7)⋊C4C2×C411yescharacteristic
115C2×C4⋊Dic7C2×C411yescharacteristic
116C2×Dic7⋊C4C2×C411yescharacteristic
117C2×Dic7⋊C4C2×C411yescharacteristic
118C2×Dic7⋊C4C2×C411yescharacteristic
119C2×Dic7⋊C4C2×C411yescharacteristic
120C2×C4×Dic7C2×C411yescharacteristic
121C2×C4×Dic7C2×C411yescharacteristic
122C2×C4×Dic7C2×C411yescharacteristic
123C2×C4×Dic7C2×C411yescharacteristic
124C2×C4×Dic7C2×C411yescharacteristic
125C2×C4×Dic7C2×C411yescharacteristic
126C2×C4×Dic7C2×C414yes—
127C2×C4×Dic7C2×C414yes—
128C2×C4×Dic7C2311yescharacteristic
129C2×C4×Dic7C2311yescharacteristic
130C2×C4×Dic7C2311yescharacteristic
131C2×C4×Dic7C2314yes—
132C2×C4×Dic7C2314yes—
133C2×#1136—42no—
134C2×#1136C2314yes—
135C22×C7⋊C8—42no—
136C22×C7⋊C8C2311yescharacteristic
137C22×C7⋊C8C2311yescharacteristic
138C22×C7⋊C8C2311yescharacteristic
139C22×C7⋊C8C2311yescharacteristic
140C22×C7⋊C8C2314yes—
141C2×#1131—42no—
142C2×#1131—42no—
143C2×#1131C2314yes—
144C2×#1131C2314yes—
145#6455C2×C418yes—
146#6450C2×C418yes—
147(C22⋊D7)⋊C4C2×C418yes—
148(C22⋊D7)⋊C4C2×C418yes—
149#6440C2×C418yes—
150#6440C2×C418yes—
151C42×D7C2×C414yes—
152C42×D7C2314yes—
153C4×Dic14C2×C414yes—
154C4×Dic14C2314yes—
155C7×C4⋊C8C2314yes—
156C7×C22⋊C8C2314yes—
157C7×C22⋊C8C2314yes—
158C7×#97C2314yes—
159C22⋊(C7⋊C8)C2314yes—
160C22⋊(C7⋊C8)C2314yes—
161(C2×D7)⋊C8C2314yes—
162(C2×D7)⋊C8C2314yes—
163#6389C2314yes—
164#6389C2314yes—
165Dic7⋊C8C2314yes—
166Dic7⋊C8C2314yes—
167Dic7⋊C8C2314yes—
168Dic7⋊C8C2314yes—
169Dic7⋊C8C2314yes—
170Dic7⋊C8C2314yes—
171Dic7⋊C8C2314yes—
172Dic7⋊C8C2314yes—
173C8×Dic7C2314yes—
174C8×Dic7C2314yes—
175C4⋊(C7⋊C8)C2314yes—
176#6377C2314yes—
177C2×C4×#41—71no—
178#2989—716no—
179C2×#446—71no—
180C2×#446—71no—
181C2×#436—71no—
182C2×#436—71no—
183C2×#435—71no—
184C2×#435—71no—
185C2×#435—71no—
186C2×#435D711yescharacteristic, complemented
187C2×#432—71no—
188C2×#432—71no—
189C2×#431—71no—
190C2×#423—71no—
191C2×#423—71no—
192C22×C4⋊C8—71no—
193C24×C7C22×C411yescharacteristic
194C24×C7C22×C411yescharacteristic
195C23×D7C22×C411yescharacteristic
196C2×C7×D4—24no—
197C2×C7×D4C22×C414yes—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7C22×C411yescharacteristic
203C22×C4×C7C22×C411yescharacteristic
204C22×C4×C7C22×C412yes—
205C22×C4×C7C22×C412yes—
206C22×C4×C7C22×C411yescharacteristic
207C22×C4×C7C22×C411yescharacteristic
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C22×C4×C7C2411yescharacteristic
211C2×C22⋊D7—24no—
212C2×C22⋊D7—24no—
213C2×C22⋊D7C22×C414yes—
214C2×C22⋊D7C22×C414yes—
215C22×Dic7—24no—
216C22×Dic7—42no—
217C22×Dic7—42no—
218C22×Dic7M1618yescomplemented
219C22×Dic7C22×C414yes—
220C22×Dic7C22×C411yescharacteristic
221C22×Dic7C22×C411yescharacteristic
222C22×Dic7C22×C411yescharacteristic
223C22×Dic7C22×C411yescharacteristic
224C22×Dic7C22×C411yescharacteristic
225C22×Dic7C22×C414yes—
226C22×Dic7C22×C414yes—
227C22×Dic7C22×C411yescharacteristic
228C22×Dic7C22×C411yescharacteristic
229C22×Dic7C22×C414yes—
230#1159—232no—
231C2×C4×D7—22no—
232C2×C4×D7—22no—
233C2×C4×D7—24no—
234C2×C4×D7—42no—
235C2×C4×D7C22×C412yes—
236C2×C4×D7C22×C414yes—
237C2×C4×D7C22×C414yes—
238C2×C4×D7C2412yes—
239C2×Dic14—24no—
240C2×Dic14C22×C414yes—
241C7×M16—44no—
242C2×C7×C8—22no—
243C2×C7×C8—22no—
244C2×C7×C8—22no—
245C2×C7×C8—22no—
246C2×C7×C8—44no—
247C2×C7×C8C2412yes—
248C2×C7×C8C2412yes—
249C2×C7×C8C2412yes—
250C2×C7×C8C2412yes—
251C7×C4⋊C4C22×C414yes—
252C7×C22⋊C4C22×C414yes—
253C7×C22⋊C4C22×C414yes—
254C42×C7C22×C412yes—
255C42×C7C2412yes—
256C22⋊Dic7C22×C414yes—
257C22⋊Dic7C22×C414yes—
258(C2×D7)⋊C4C22×C414yes—
259(C2×D7)⋊C4C22×C414yes—
260C4⋊Dic7C22×C414yes—
261Dic7⋊C4C22×C414yes—
262Dic7⋊C4C22×C414yes—
263Dic7⋊C4C22×C414yes—
264Dic7⋊C4C22×C414yes—
265C4×Dic7C22×C412yes—
266C4×Dic7C22×C412yes—
267C4×Dic7C22×C412yes—
268C4×Dic7C22×C414yes—
269C4×Dic7C22×C414yes—
270C4×Dic7C22×C414yes—
271C4×Dic7C22×C414yes—
272C4×Dic7C22×C414yes—
273C4×Dic7C22×C414yes—
274C4×Dic7C2412yes—
275C4×Dic7C2412yes—
276C4×Dic7C2412yes—
277#1136—44no—
278C2×C7⋊C8—22no—
279C2×C7⋊C8—22no—
280C2×C7⋊C8—22no—
281C2×C7⋊C8—22no—
282C2×C7⋊C8—44no—
283C2×C7⋊C8C2412yes—
284C2×C7⋊C8C2412yes—
285C2×C7⋊C8C2412yes—
286C2×C7⋊C8C2412yes—
287#1131—44no—
288#1131—44no—
289C22×#41—71no—
290C22×M16—71no—
291C22×M16—71no—
292C22×M16—71no—
293C22×M16C2×D711yescharacteristic
294C23×C8—71no—
295C23×C8C2×D711yescharacteristic
296C4×#41—78no—
297C4×#41—78no—
298C2×C4×Q8—71no—
299C2×C4×Q8—71no—
300C2×C4×D4—71no—
301C2×C4×D4—71no—
302C2×C4×D4—71no—
303C2×C4×D4—71no—
304C2×C4×D4—71no—
305C2×C4×D4C2×D711yescharacteristic
306C2×#117—71no—
307C2×#117—71no—
308C2×#117—71no—
309C22×C42—71no—
310C22×C42—71no—
311C22×C42—71no—
312#446—78no—
313#446—78no—
314#436—78no—
315#436—78no—
316#435—78no—
317#435—78no—
318#435—78no—
319#435C2×D718yescomplemented
320#432—78no—
321#432—78no—
322#431—78no—
323#423—78no—
324#423—78no—
325C2×C4⋊C8—71no—
326C2×C4⋊C8—71no—
327C2×C4⋊C8—71no—
328C2×C4⋊C8—71no—
329C2×C4⋊C8—71no—
330C2×C4⋊C8—71no—
331C2×C4⋊C8—71no—
332C2×C4⋊C8—71no—
333C2×C4⋊C8—78no—
334C2×C4⋊C8—71no—
335C2×C4⋊C8C2×D711yescharacteristic
336C2×C22⋊C8—71no—
337C2×C22⋊C8—71no—
338C2×C22⋊C8—71no—
339C2×C22⋊C8—71no—
340C2×C22⋊C8C2×D711yescharacteristic
341C2×C22⋊C8C2×D711yescharacteristic
342C2×#97—71no—
343C2×#97—71no—
344C2×#97—71no—
345C2×#97C2×D711yescharacteristic
346C2×C4×C8—71no—
347C2×C4×C8—71no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7C2×M1614yes—
354C23×C7C23×C412yes—
355C23×C7C23×C412yes—
356C23×C7C23×C411yescharacteristic
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7C23×C412yes—
361C7×D4—28no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—24no—
367C2×C4×C7—24no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7C23×C412yes—
373C2×C4×C7C23×C412yes—
374C2×C4×C7C23×C412yes—
375C2×C4×C7C23×C412yes—
376C2×C4×C7C23×C411yescharacteristic
377C2×C4×C7H(5,𝔽2)12yes—
378C2×C4×C72−1+412yes—
379C2×C4×C7C2511yescharacteristic
380C22⋊D7—28no—
381C22⋊D7—28no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—28no—
388C2×Dic7—44no—
389C2×Dic7—44no—
390C2×Dic7C2×M1614yes—
391C2×Dic7C2×M1614yes—
392C2×Dic7C2×M16116yescomplemented
393C2×Dic7C23×C412yes—
394C2×Dic7C23×C412yes—
395C2×Dic7C23×C412yes—
396C2×Dic7C23×C412yes—
397C2×Dic7C23×C412yes—
398C2×Dic7C23×C412yes—
399C2×Dic7C23×C412yes—
400C4×D7—24no—
401C4×D7—22no—
402C4×D7—22no—
403C4×D7—28no—
404C4×D7—44no—
405Dic14—28no—
406C7×C8—22no—
407C7×C8—22no—
408C7×C8—22no—
409C7×C8—22no—
410C7⋊C8—22no—
411C7⋊C8—22no—
412C7⋊C8—22no—
413C7⋊C8—22no—
414C2×#41—78no—
415C2×#41—148no—
416C22×Q8—71no—
417C22×D4—71no—
418C22×D4—71no—
419C22×D4C4×D711yescharacteristic
420C23×C4—71no—
421C23×C4—71no—
422C23×C4—71no—
423C23×C4—71no—
424C23×C4—71no—
425C23×C4—71no—
426C23×C4—71no—
427C23×C4C22×D711yescharacteristic
428C23×C4C22×D711yescharacteristic
429C2×M16—42no—
430C2×M16—74no—
431C2×M16—74no—
432C2×M16—74no—
433C2×M16—282no—
434C2×M16—282no—
435C2×M16—282no—
436C2×M16C22×D714yes—
437C22×C8—42no—
438C22×C8—71no—
439C22×C8—71no—
440C22×C8—71no—
441C22×C8—71no—
442C22×C8—74no—
443C22×C8—282no—
444C22×C8C22×D711yescharacteristic
445C22×C8C22×D711yescharacteristic
446C22×C8C22×D711yescharacteristic
447C22×C8C22×D711yescharacteristic
448C22×C8C22×D714yes—
449C4×Q8—78no—
450C4×Q8—74no—
451C4×Q8—74no—
452C4×D4—78no—
453C4×D4—74no—
454C4×D4—74no—
455C4×D4—74no—
456C4×D4—74no—
457C4×D4—78no—
458C4×D4—78no—
459C4×D4C4×D714yes—
460C4×D4C22×D714yes—
461#117—78no—
462#117—78no—
463#117—78no—
464C2×C4⋊C4—71no—
465C2×C4⋊C4—71no—
466C2×C4⋊C4—71no—
467C2×C4⋊C4—71no—
468C2×C4⋊C4—71no—
469C2×C4⋊C4C4×D711yescharacteristic
470C2×C22⋊C4—71no—
471C2×C22⋊C4—71no—
472C2×C22⋊C4—71no—
473C2×C22⋊C4—71no—
474C2×C22⋊C4C4×D711yescharacteristic
475C2×C22⋊C4C4×D711yescharacteristic
476C2×C42—71no—
477C2×C42—71no—
478C2×C42—71no—
479C2×C42—71no—
480C2×C42—71no—
481C2×C42—71no—
482C2×C42—74no—
483C2×C42—74no—
484C2×C42—74no—
485C2×C42—74no—
486C2×C42—71no—
487C2×C42—71no—
488C2×C42—71no—
489C2×C42—74no—
490C2×C42—74no—
491C2×C42C22×D711yescharacteristic
492C4⋊C8—74no—
493C4⋊C8—74no—
494C4⋊C8—74no—
495C4⋊C8—74no—
496C4⋊C8—74no—
497C4⋊C8—74no—
498C4⋊C8—74no—
499C4⋊C8—74no—
500C4⋊C8—74no—
501C4⋊C8C22×D714yes—
502C22⋊C8—74no—
503C22⋊C8—74no—
504C22⋊C8—74no—
505C22⋊C8—74no—
506C22⋊C8C22×D714yes—
507C22⋊C8C22×D714yes—
508#97—74no—
509#97—74no—
510#97—74no—
511#97C22×D714yes—
512C4×C8—74no—
513C4×C8—74no—
514C22×C7—22no—
515C22×C7—28no—
516C22×C7—22no—
517C22×C7—22no—
518C22×C7—22no—
519C22×C7—22no—
520C22×C7—44no—
521C22×C7#52012yes—
522C22×C7C22×M1614yes—
523C22×C7C22×M1612yes—
524C22×C7#56812yes—
525C22×C7C24×C411yescharacteristic
526C2×D7—22no—
527C2×D7—22no—
528C2×D7—22no—
529C2×D7—44no—
530C4×C7—22no—
531C4×C7—22no—
532C4×C7—22no—
533C4×C7—22no—
534C4×C7#52012yes—
535C4×C7C2×H(5,𝔽2)11yescharacteristic
536C4×C7C2×2−1+411yescharacteristic
537Dic7—22no—
538Dic7—22no—
539Dic7—22no—
540Dic7—22no—
541Dic7—22no—
542Dic7C22×M1614yes—
543Dic7C22×M1614yes—
544C24—71no—
545C24C2×C4×D711yescharacteristic
546C24C2×C4×D711yescharacteristic
547#41—1432no—
548C2×Q8—74no—
549C2×Q8—144no—
550C2×D4—24no—
551C2×D4—74no—
552C2×D4—74no—
553C2×D4—144no—
554C2×D4—144no—
555C2×D4C2×C4×D714yes—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—78no—
561C22×C4—71no—
562C22×C4—71no—
563C22×C4—74no—
564C22×C4—71no—
565C22×C4—71no—
566C22×C4—71no—
567C22×C4—71no—
568C22×C4—71no—
569C22×C4—74no—
570C22×C4—74no—
571C22×C4—74no—
572C22×C4—74no—
573C22×C4—72no—
574C22×C4—72no—
575C22×C4—74no—
576C22×C4—144no—
577C22×C4—144no—
578C22×C4—142no—
579C22×C4—142no—
580C22×C4—282no—
581C22×C4—282no—
582C22×C4—282no—
583C22×C4C2×C4×D711yescharacteristic
584C22×C4C2×C4×D711yescharacteristic
585C22×C4C2×C4×D712yes—
586C22×C4C2×C4×D712yes—
587C22×C4C2×C4×D711yescharacteristic
588C22×C4C2×C4×D711yescharacteristic
589C22×C4C23×D712yes—
590C22×C4C23×D712yes—
591C22×C4C23×D711yescharacteristic
592M16—44no—
593M16—284no—
594M16—284no—
595M16—284no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—44no—
601C2×C8—72no—
602C2×C8—72no—
603C2×C8—72no—
604C2×C8—72no—
605C2×C8—142no—
606C2×C8—142no—
607C2×C8—142no—
608C2×C8—142no—
609C2×C8—284no—
610C2×C8C23×D712yes—
611C2×C8C23×D712yes—
612C2×C8C23×D712yes—
613C2×C8C23×D712yes—
614C4⋊C4—74no—
615C4⋊C4—74no—
616C4⋊C4—74no—
617C4⋊C4—74no—
618C4⋊C4—74no—
619C4⋊C4C2×C4×D714yes—
620C22⋊C4—74no—
621C22⋊C4—74no—
622C22⋊C4—74no—
623C22⋊C4—74no—
624C22⋊C4C2×C4×D714yes—
625C22⋊C4C2×C4×D714yes—
626C42—72no—
627C42—74no—
628C42—74no—
629C42—74no—
630C42—74no—
631C42—72no—
632C42—74no—
633C42—74no—
634C42—72no—
635C42—72no—
636C42—72no—
637C42—72no—
638C42C2×C4×D712yes—
639C42C23×D712yes—
640C2×C7—24no—
641C2×C7—42no—
642C2×C7#298914yescomplemented
643C2×C7C2×#52011yescharacteristic
644C2×C7C23×M1611yescharacteristic
645C2×C7C2×#56811yescharacteristic
646D7—42no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—72no—
653C23—142no—
654C23—142no—
655C23—142no—
656C23D7×M1614yes—
657C23C22×C4×D712yes—
658C23C22×C4×D712yes—
659C23C22×C4×D711yescharacteristic
660Q8—148no—
661D4—28no—
662D4—148no—
663D4—148no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—74no—
675C2×C4—74no—
676C2×C4—716no—
677C2×C4—72no—
678C2×C4—72no—
679C2×C4—72no—
680C2×C4—72no—
681C2×C4—72no—
682C2×C4—72no—
683C2×C4—72no—
684C2×C4—148no—
685C2×C4—148no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—144no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—284no—
695C2×C4—284no—
696C2×C4—284no—
697C2×C4C22×C4×D712yes—
698C2×C4C22×C4×D712yes—
699C2×C4C22×C4×D712yes—
700C2×C4C22×C4×D712yes—
701C2×C4C22×C4×D711yescharacteristic
702C2×C4#654812yes—
703C2×C4#655412yes—
704C2×C4C24×D711yescharacteristic
705C8—22no—
706C8—22no—
707C8—22no—
708C8—22no—
709C8—142no—
710C8—142no—
711C8—142no—
712C8—142no—
713C7C2×#298911yescharacteristic, complemented, Sylow
714C22—28no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—44no—
721C22—142no—
722C22—142no—
723C22—142no—
724C22—284no—
725C22#9023712yes—
726C22C2×D7×M1614yes—
727C22C2×D7×M1612yes—
728C22#9044112yes—
729C22C23×C4×D711yescharacteristic
730C4—22no—
731C4—22no—
732C4—22no—
733C4—22no—
734C4—74no—
735C4—74no—
736C4—142no—
737C4—142no—
738C4—142no—
739C4—142no—
740C4—142no—
741C4#9023712yes—
742C4C2×#654811yescharacteristic
743C4C2×#655411yescharacteristic
744C2—24no—
745C2—42no—
746C2—282no—
747C2#1173690614yesdirect product factor
748C2C2×#9023711yescharacteristic
749C2C22×D7×M1611yescharacteristic
750C2C2×#9044111yescharacteristic
subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC2×C4C24×D7
FittingC2×C7×#435C2
socleC23×C7C23×C4
prime radicalC22×#1159C4
cosocleC2×C4×C7C25
hypercenterC2×#435D7
hypocenterC7C2×#2989
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×C7×#435C2semidirect
3. C2×#89900C2semidirect
4. C2×#89890C2semidirect
5. C2×#89883C2semidirect
6. C22×Dic7⋊C8C2semidirect
7. C2×#89783C2semidirect
8. #11736906C2direct (N × H)
9. C2×#89609C2semidirect
10. C2×#89600C2semidirect
11. C2×#89501C2semidirect
12. C2×#89502C2semidirect
13. C2×#89491C2semidirect
14. C2×#89490C2semidirect
15. C2×#89477C2semidirect
16. C2×#89473C2semidirect
40. C7×#435C22semidirect
47. #89900C22semidirect
48. #89890C22semidirect
49. #89883C22semidirect
62. C2×Dic7⋊C8C22semidirect
65. #89783C22semidirect
68. #89609C22semidirect
69. #89600C22semidirect
70. #89502C22semidirect
71. #89501C22semidirect
72. #89491C22semidirect
73. #89490C22semidirect
74. #89477C22semidirect
75. #89473C22semidirect
186. C2×#435D7semidirect
218. C22×Dic7M16semidirect
319. #435C2×D7semidirect
392. C2×Dic7C2×M16semidirect
642. C2×C7#2989semidirect
713. C7C2×#2989semidirect
747. C2#11736906direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#11592
C2×C7×#4352
C2×#899002
C2×#898902
C2×#898832
C22×Dic7⋊C82
C2×#897832
#117369062
C2×#896092
C2×#896002
C2×#895012
C2×#895022
C2×#894912
C2×#894902
C2×#894772
C2×#894732
C2×#29897